Examination of Statistics and Modulation of Underwater ...

Defence Research and Development Canada Scientific Report

DRDC-RDDC-2021-R027

March 2021

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Examination of Statistics and Modulation of Underwater Acoustic Ship Signatures

Mark Trevorrow DRDC – Atlantic Research Centre Terms of Release: This document is approved for public release.

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Template in use: EO Publishing App for SR-RD-EC Eng 2021-02-11.dotm © Her Majesty the Queen in Right of Canada (Department of National Defence), 2021

© Sa Majesté la Reine en droit du Canada (Ministère de la Défense nationale), 2021

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IMPORTANT INFORMATIVE STATEMENTS

This document was reviewed for Controlled Goods by Defence Research and Development Canada (DRDC) using the Schedule to the Defence Production Act.

Disclaimer: This publication was prepared by Defence Research and Development Canada an agency of the Department of National Defence. The information contained in this publication has been derived and determined through best practice and adherence to the highest standards of responsible conduct of scientific research. This information is intended for the use of the Department of National Defence, the Canadian Armed Forces (“Canada”) and Public Safety partners and, as permitted, may be shared with academia, industry, Canada’s allies, and the public (“Third Parties”). Any use by, or any reliance on or decisions made based on this publication by Third Parties, are done at their own risk and responsibility. Canada does not assume any liability for any damages or losses which may arise from any use of, or reliance on, the publication.

Endorsement statement: This publication has been peer-reviewed and published by the Editorial Office of Defence Research and Development Canada, an agency of the Department of National Defence of Canada. Inquiries can be sent to: [email protected].

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Abstract

This Scientific Report examines ship underwater acoustic signature amplitude statistics and statistical distributions. This explores the hypothesis that ship signatures exhibit amplitude fluctuations that are different from Rayleigh-distributed ambient ocean noise. Signature measurements from two different ships conducting a variety of manoeuvres are examined, focusing on those conditions where propeller cavitation and broadband signal modulation occur, specifically during maximum speed runs, accelerations, and turning manoeuvres. A key difference for a ship signature is the amplitude modulation generated by propeller cavitation, and this is found to be associated with super-Rayleigh signal characteristics. The use of new cyclostationary processing techniques is used to estimate propeller shaft and blade rate modulation. Under conditions of stronger propeller modulation, time-series statistics scintillation index and skewness show values significantly in excess of Rayleigh-distributed values. Ship signature amplitude probability density functions were found to be better matched by a K-distribution model with small shape factor, indicating increased presence of higher-amplitude signal components.

Significance to Defence and Security

The ship signature statistics examined in this study quantify the acoustic texture of the signal, describing features that might be used intuitively by experienced acoustic operators to identify a ship signature and determine its operating state (e.g., steady cruising vs. manoeuvring). It is believed that this result may be useful in advanced sonar detectors and classifiers, including use in modern artificial intelligence algorithms, against surface ships and other vehicles employing propellers.

Conventional active and passive sonar processors generally use detection thresholds based on the assumption of Rayleigh statistics for the background noise. When ship noise contributes to the background noise for active and passive sonars, this super-Rayleigh behaviour may generate increased false alarms, or require an increase in sonar detection thresholds thus reducing potential target detection ranges.

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Résumé

Le présent rapport scientifique porte sur les distributions statistiques et les statistiques d’amplitude de la signature acoustique sous-marine des navires. On examine l’hypothèse selon laquelle la signature des navires présente des fluctuations d’amplitude différentes du bruit océanique ambiant réparti selon la loi de Rayleigh. On étudie les mesures de la signature de deux navires distincts exécutant diverses manœuvres en s’attardant surtout aux conditions dans lesquelles on observe une cavitation des hélices et une modulation des signaux à large bande, en particulier lors de déplacements à vitesse maximale, d’accélérations et de virages. L’une des principales différences dans la signature des navires est la modulation d’amplitude produite par la cavitation des hélices, modulation qui s’avère être associée aux caractéristiques des signaux en régime super-Rayleigh. On utilise de nouvelles techniques de traitement cyclostationnaire pour déterminer la modulation de l’arbre porte-hélice et de la fréquence des pales. En cas de forte modulation de l’hélice, l’indice de scintillation et l’asymétrie de statistiques provenant de séries chronologiques affichent des valeurs nettement supérieures à celles obtenues selon la distribution de Rayleigh. Ainsi, on a constaté que les fonctions de densité de probabilités de l’amplitude de la signature des navires correspondaient davantage à un modèle de distribution K avec un faible coefficient de forme, ce qui indique la présence accrue de composantes de signaux de plus grande amplitude.

Importance pour la défense et la sécurité

Les statistiques sur la signature des navires examinées dans la présente étude permettent de quantifier la texture acoustique des signaux en décrivant des caractéristiques que des opérateurs acoustiques chevronnés pourraient utiliser de manière intuitive pour identifier la signature d’un navire et déterminer son état de marche (p. ex., régime de croisière stable par rapport aux manœuvres). On croit que ces résultats pourraient être utiles pour les récepteurs sonar et les classificateurs plus perfectionnés. On pourrait les utiliser notamment dans les algorithmes d’intelligence artificielle modernes, pour les navires de surface et autres véhicules à hélice.

Les processeurs de sonars actifs et passifs classiques utilisent généralement des seuils de détection fondés sur l’hypothèse des statistiques de Rayleigh sur le bruit de fond. Si le bruit des navires contribue au bruit de fond des sonars actifs et passifs, ce régime super-Rayleigh peut entraîner une augmentation des fausses alarmes ou bien nécessiter un seuil accru de détection sonar, réduisant ainsi la portée de détection de cibles potentielles.

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Table of Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Significance to Defence and Security . . . . . . . . . . . . . . . . . . . . . . . . . i

Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Importance pour la défense et la sécurité . . . . . . . . . . . . . . . . . . . . . . . ii

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Review of Ship Signature Characteristics . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Ship Signature Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Propeller Modulation Effects . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 DEMON Processing . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.2 Cyclic Modulation Coherence (CMC) . . . . . . . . . . . . . . . . . . 6

2.3 Ship Signature Statistical Models . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 Time-series Statistics . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.2 Probability Density Function (PDF) Models . . . . . . . . . . . . . . . 7

2.3.3 PDF Generation and Fitting . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4.1 Spectral Shaping and PDF . . . . . . . . . . . . . . . . . . . . . . 9

2.4.2 Time-series Statistics . . . . . . . . . . . . . . . . . . . . . . . 12

2.4.3 Ship Signature Modulation . . . . . . . . . . . . . . . . . . . . . 13

3 Instrumentation and Sea-Trials . . . . . . . . . . . . . . . . . . . . . . . . 16

3.1 Broadband Underwater Recording Buoys . . . . . . . . . . . . . . . . . . 16

3.2 Spectral Processing . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 Lloyd’s Mirror Effects . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4 Test Ships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.5 Ship Manoeuvre Types . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.6 Sea-trial Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 CCGS VECTOR Sea-Trials, April 2005 . . . . . . . . . . . . . . . . . . . . . 22

4.1 Straight-Line Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1.1 Example Run 1302 Straight Pass at 11 Knots . . . . . . . . . . . . . . 22

4.1.1.1 Spectral Levels and Lloyd’s Mirror . . . . . . . . . . . . . . 23

4.1.1.2 Signature PDF and Statistics . . . . . . . . . . . . . . . . . 24

4.1.1.3 Propeller Modulation . . . . . . . . . . . . . . . . . . . 27

4.1.2 SSL and Propeller Rate Variation with Speed . . . . . . . . . . . . . . 29

4.1.3 Variability in PDF and Statistics . . . . . . . . . . . . . . . . . . . 30

4.2 Turning Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

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4.2.1 Example Run 1404: 180 Starboard Turn at 11.3 Knot In-run . . . . . . . . 31

4.2.1.1 Spectral Levels through Turns . . . . . . . . . . . . . . . . 33

4.2.1.2 Signature PDF and Statistics . . . . . . . . . . . . . . . . . 34

4.2.1.3 Propeller Modulation . . . . . . . . . . . . . . . . . . . 37

4.2.2 Example Run 1308: 110 Port Turn at 11.3 Knot In-run . . . . . . . . . . 38

5 CFAV QUEST Sea-Trials, Sept. 2005 . . . . . . . . . . . . . . . . . . . . . . 42

5.1 Straight-Line Constant-Speed Runs . . . . . . . . . . . . . . . . . . . . 42

5.1.1 Spectral Source Levels . . . . . . . . . . . . . . . . . . . . . . 42

5.1.2 Signature PDF and Statistics . . . . . . . . . . . . . . . . . . . . 43

5.1.3 Propeller Modulation . . . . . . . . . . . . . . . . . . . . . . . 44

5.2 Straight-Line Accelerating Runs . . . . . . . . . . . . . . . . . . . . . . 45




5.3 Turning Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48




6 Summary Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.1 Recommendations for Further Work . . . . . . . . . . . . . . . . . . . . 58

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

List of Symbols/Abbreviations/Acronyms/Initialisms . . . . . . . . . . . . . . . . . . 61

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List of Figures

Figure 1: Comparison of empirical ship signature models, compared to example ship SSL for CCGS VECTOR at speed of 11 knots. . . . . . . . . . . . . . . . . . . . . . . . 4

Figure 2: Comparison of signal power spectra vs. bandwidth and with ship signature shaping. . . 9

Figure 3: Comparison of simulated BB noise signal PDF vs. LP bandwidth, with best-fit Rayleigh and K-distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Figure 4: Comparison of simulated ship signature PDF between broadband, ship spectral shaping, and single-propeller shaft and blade rate modulation. Rayleigh model is fit to ship signature with no modulation. K-distribution model is fit to ship signature with modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Figure 5: Comparison of simulated ship signature PDF including dual-propeller shaft and blade rate modulation. Rayleigh model is fit to ship signature with no modulation. K-distribution model is fit to ship signature with modulation. . . . . . . . . . . . . . . . . 12

Figure 6: Ship signature cyclic modulation coherence (CMC) based on 3 s simulated time-series with 10 kHz LP filtering and inverse-frequency squared spectral shaping. Simulation uses 4 Hz shaft and 12 Hz blade rates, with added 1500 Hz NB tonal. . . . . . . . . . 14

Figure 7: Ship signature ICMC, based on simulated data in Figure 6 integrated over 1–8 kHz bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Figure 8: Comparison of simulated ship signature DEMON spectra at 3 s (1024-pt FFT) and 10 s (4096-pt FFT) data record length. . . . . . . . . . . . . . . . . . . . . . 15

Figure 9: (left) Photograph of a Broadband Underwater Recording Buoy (BURB), with (right) detail on the hydrophone and attachment of lead weight. . . . . . . . . . . . . . . 16

Figure 10: Photograph of CCGS VECTOR conducting a run past two BURBS, April 13, 2005. . 22

Figure 11: Plot of ship speed (from GPS) and horizontal range to BURBs for VECTOR Run 1302. 23

Figure 12: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at CPA for all BURBs in VECTOR Run 1302, compared to empirical relation due to Ross (Equation (2)) at ship speed of 11.0 knots. Hydrophone depths (upper) 5 m and (lower) 15 m. . . . . . . . . . . 24

Figure 13: Comparison of data and best-fit model PDF for VECTOR Run 1302 BURB2 for an 8 s period at CPA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 14: Data PDF vs. time for VECTOR Run 1302, BURB2, channel 2. Top plot shows best fit K-distribution shape parameter. Vertical dashed line is CPA. . . . . . . . . . . 26

Figure 15: Skewness vs. scintillation index (1-s blocks) for VECTOR Run 1302, BURB 2 for the period ±30 s from CPA. Dashed lines show Rayleigh values. . . . . . . . . . . 27

Figure 16: Scintillation index vs. K-distribution shape factor for VECTOR Run 1302, BURB 2 for the period ±30 s from CPA. Linear fit shown. . . . . . . . . . . . . . . . . . . 27

Figure 17: Contour plot of CMC frequency vs. modulation for VECTOR Run 1302, BURB4 channel 2 (15 m depth) calculated over 3 s at CPA (17:35:55 UT). . . . . . . . . 28

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Figure 18: ICMC vs. modulation frequency for VECTOR Run 1302, BURB4 at CPA. . . . . 29

Figure 19: DEMON spectrum from VECTOR Run 1302 BURB4, computed over 3 s at CPA. . 29

Figure 20: Propeller shaft rate (inferred from ICMC analysis) vs. speed for CCGS VECTOR from multiple straight runs. . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Figure 21: Plan view of VECTOR Run 1404. Events A–D described in text. . . . . . . . . 32

Figure 22: Plot of ship speed and turn-rate (relative to ground) and horizontal range to BURBs vs. time for VECTOR Run 1404. Events A–D described in text. . . . . . . . . . . 32

Figure 23: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at CPA for all four BURBs in VECTOR Run 1404, compared to empirical relation due to Ross (Equation (2)) for ship speed of 11.3 knots. Hydrophone depths (upper) 5 m and (lower) 15 m. . . . . . . 33

Figure 24: Data PDF vs. time for VECTOR Run 1404, BURB2, channel 2. Top plot shows best fit K-distribution shape parameter. Vertical dashed line is CPA and arrows denote events A to C discussed in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Figure 25: Comparison of data and best-fit model PDF for VECTOR Run 1404 for an 8 s period at CPA. (left) BURB2 at event A + 5 s, (right) BURB1 at event B + 5 s. . . . . . . . 35

Figure 26: Time variation of scintillation index and skewness for VECTOR Run 1404, BURB2. CPA at 51 s. Arrows denote events A to C discussed in text. . . . . . . . . . . . . 36

Figure 27: Skewness vs. scintillation index (1-s blocks) for VECTOR Run 1404, BURB 2 for the period 120 s period covering start of turn. Dashed lines show Rayleigh values. Red lines show hypothesized bi-linear relationship. . . . . . . . . . . . . . . . . . . 37

Figure 28: ICMC modulation frequency vs. time for VECTOR Run 1404 BURB3 channel 2. . . 37

Figure 29: Plot of ship speed and turn-rate (from GPS) and horizontal range to BURB 1 vs. time for VECTOR Run 1308, a 110 turning run at 11.3 knots in-run. Events A–D described in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Figure 30: Data PDF vs. time for VECTOR Run 1308, BURB1, channel 2. Top plot shows best fit K-distribution shape parameter. Vertical dashed line is CPA and arrows denote events A to C discussed in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Figure 31: Comparison of data and best-fit model PDF for VECTOR Run 1308, BURB 1, for an 8 s period near the point of maximum turn rate. . . . . . . . . . . . . . . . . . 40

Figure 32: Time variation of scintillation index and skewness for VECTOR Run 1308, BURB1. Vertical dashed line shows CPA at 180 s. Arrows denote events A to C discussed in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Figure 33: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at CPA for B3 and B4 for QUEST Run 09, compared to empirical relation due to Ross (Equation (2)) at ship speed of 12.0 knots. Hydrophone depth was 20 m. . . . . . . . . . . . . . . . . . . 43

Figure 34: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at CPA for B3 and B4 for QUEST Run 12, compared to empirical relation due to Ross (Equation (2)) at maximum ship speed of 13.7 knots. Hydrophone depth was 20 m. . . . . . . . . . . . . . . . . . 43

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Figure 35: Comparison of data and best-fit model PDF for QUEST Run 12 (straight pass at 13.7 knots) for an 8 s period at CPA. (left) B3, (right) B4. . . . . . . . . . . . 44

Figure 36: ICMC vs. modulation frequency for QUEST Run 12, B3 and B4 at CPA. . . . . . 45

Figure 37: Plot of run parameters for QUEST Run 15, a straight acceleration from 6 to 13 knots. (upper) ship speed and horizontal range to B3 and B4 vs. time; (lower) propeller shaft rate and advance ratio. Events A–C described in text. . . . . . . . . . . . . . . . 46

Figure 38: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at 3 times for B3 and B4 during QUEST Run 15, a straight acceleration pass. Spectra are compared to empirical relation due to Ross (Equation (2)) at ship speed of 14.0 knots. Hydrophone depth was 20 m. 47

Figure 39: Data PDF for QUEST Run 15, straight accelerating run, compared to best-fit K-distributions for events A, B, C (as discussed in text). Rayleigh curve best-fit to event A data.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Figure 40: ICMC vs. modulation frequency for QUEST rn 15, at events A, B, C. Arrows denote identified blade rate modulation. . . . . . . . . . . . . . . . . . . . . . . 48

Figure 41: Plan view of QUEST Run 21, a 180 port turn at maximum in-run speed. Events A–D described in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Figure 42: Time-series of run parameters for QUEST Run 21, a 180 port turn at maximum in-run speed. (upper) ship speed and horizontal range to B4 vs. time; (lower) propeller shaft rate and advance ratio. Events A–D described in text. . . . . . . . . . . . . . . . 50

Figure 43: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at 5 times through QUEST Run 21, a 180 turning manoeuvre. Spectra are compared to empirical relation due to Ross (Equation (2)) at ship speed of 13.6 knots. Hydrophone depth was 20 m. Events A–D described in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Figure 44: Data PDF vs. time for QUEST Run 21, B4, channel 2. Top plot shows best fit K-distribution shape parameter. Arrows denote events A to D discussed in text. . . . 52

Figure 45: Time variation of scintillation index and skewness for QUEST Run 21, B4. Events A to D discussed in text. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Figure 46: ICMC modulation frequency vs. time (6 s averages) for QUEST Run 21, B4 channel 2. Events A to D discussed in text. . . . . . . . . . . . . . . . . . . . . . . 53

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List of Tables

Table 1: Comparison of scintillation index and skewness statistics between different simulated noise and ship signature time-series, based on 10-s time-series. . . . . . . . . . 13

Table 2: Ship physical characteristics. . . . . . . . . . . . . . . . . . . . . . . . 20

Table 3: Summary of time-series statistics and K-distribution shape parameter averaged over 8 s at CPA for each BURB for Run 1302 (straight-line at 11 knots). Rayleigh values included in last row for reference. . . . . . . . . . . . . . . . . . . . . . . . . . . 26

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1 Introduction

Moving ships are an important source of underwater noise. Ship noise is a prominent contributor to the background noise in the ocean at very low frequencies [1–3]. This noise, herein denoted the ship’s acoustic signature, can also be used to detect and classify the ship type, and in some cases identify an individual ship. Ship signatures can also impose significant constraints on the operation of low and medium frequency sonars operated from the ship, or by nearby consort ships, particularly when these ships are operated at higher speeds.

A ship acoustic signature is generally the sum of propeller generated sound, sound generated by breaking waves around the ship hull, and machinery sounds, the latter being transmitted through the ship’s hull. Thus, a ship signature contains both narrowband (NB) tonals and broadband (BB) components, generally extending from of order 1 Hz up to 100 kHz. Broadband ship signature spectra are generally dominated by low-frequency components, exhibiting an inverse-frequency-squared dependence above approximately 100 Hz. The strength of a ship’s acoustic signature increases strongly with ship speed [2, 4–10], particularly when the ship is operated at speeds above a propeller cavitation inception speed (CIS). The CIS is typically near one-half the maximum ship speed, depending on propeller and hull design. Another subtle feature of ship acoustic signatures is that the broadband propeller sound in the 1–10 kHz band can be modulated at the propeller shaft rate and blade passage rate [11]. These features of the ship signature are all known to change with ship speed and manoeuvring state.

The ship signature characteristics examined in this study are both the signal amplitude time-series statistics and probability density functions (PDF). These statistics quantify the acoustic texture of the ship signature, describing features that might be described qualitatively as “spikiness” or “choppiness.” Such qualitative information is often used intuitively by experienced acoustic operators to identify a ship signature and determine is operating state (e.g., steady cruising vs. manoeuvring). As a first approximation, underwater noise signals usually exhibit amplitude PDF that are Rayleigh distributed [12]. However, several previous studies have produced evidence for non-Rayleigh and non-linear characteristics of ambient noise containing ship signatures [12–14]. Where the background noise is non-Rayleigh, increases must be made in sonar detection thresholds. As will be examined below, broadband ship signatures can often exhibit signals that are super-Rayleigh, with an increased proportion of high-amplitude signal components. This will affect the performance of conventional automated detectors that assume Rayleigh signal statistics, but may also provide features for ship signature detection and classification.

The overall goal of this study is to examine ship signature statistics and modulation under a controlled set of ship operating conditions, including aggressive manoeuvres.1 Short-range, broadband acoustic recordings from two different ships are examined. The data were recorded during separate sea-trials in April and Sept. 2005 against the CCGS VECTOR and CFAV QUEST, respectively. The VECTOR was a small (40 m length, 520 t) oceanographic ship with a single, three-bladed propeller. The QUEST was a medium-size (76 m, 2130 t) naval auxiliary with twin, five-bladed propellers. In addition to the propulsion differences, the QUEST was acoustically quieted by design, through vibration-isolation of key machinery and use of highly-skewed-blade propellers. These ship signatures are examined here with

1 This work was conducted under Defence Research and Development Canada (DRDC) Project ATRIUM.

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particular emphasis on conditions that exhibit super-Rayleigh characteristics, such as maximum speed and manoeuvring.

The following frequency band definitions will be utilized in this work: very low frequency (VLF) 10–100 Hz, low frequency (LF) 100–2000 Hz, medium frequency (MF) 2.0–10 kHz, and high frequency (HF) 10–100 kHz.

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2 Review of Ship Signature Characteristics

This section describes relevant ship signature characteristics, including propeller modulation and the statistical models used to examine the sea-trial data.

In all of the following, the ship signature data is assumed to be recorded in data blocks that are long compared to the variability of interest. The data used herein were recorded in 1-second blocks at 40,000 samples per second with 16-bit resolution. Signals are continuous across successive blocks. The raw data acquisition utilized an anti-aliasing filter at 18 kHz. From this base time-series, various types of filtering and other signal processing can then be applied. This analysis utilizes the instantaneous amplitude, A(t), of the signature time-series, X(t), which is computed as the absolute amplitude of the so-called analytic function, i.e.,

�(�) = �� (�)��

+ ��(�)��

� (1)

where H( ) is the Hilbert transform. It is insufficient to simply take the absolute value of X(t) without additional signal processing (e.g., root-mean-square averaging).

2.1 Ship Signature Spectra

A ship signature is generally the sum of propeller-generated sound, sound generated by breaking waves around the ship hull, and internal machinery sounds transmitted through the ship’s hull. Broadband propeller sound is created by turbulence and cavitation bubbles [2–3]. The propeller cavitation and wave-breaking wave sounds are mediated by small (< 1 mm radius) bubbles in the water, which produce BB sound in the 100 Hz–100 kHz bands. The strength of the signature spectrum for various ships has been extensively studied [4–10]. Earlier work by the author also examined the effects of directionality and turning manoeuvres on a ship source spectra [4]. While the models proposed in these studies have generally been empirical, a common feature is an inverse-frequency-squared dependence of signature power spectrum, dominated by low-frequency machinery sounds below approximately 200–500 Hz, with BB propeller sound dominating in the MF and HF bands. The strength of a ship signature generally increases strongly with ship speed, particularly if it is operated at speeds above the propeller CIS (i.e., above approximately one-half the maximum ship speed).

The fundamental parameter of a ship signature measurement is the spectral source level (SSL in dB re 1 Pa2/Hz at 1 m), which has been corrected for propagation effects between the ship and receiver. This is sometimes known as the monopole source spectrum, and does not include any correction for surface reflections such as Lloyd’s Mirror effects (these will be discussed in Section 3). There are well-known empirical relations for ship SSL, such as the reference spectrum due to Ross [2],

)(log20)15.5/(log53190)( 1010 fUfSSL , (2)

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where U is the ship speed (m/s). Note the strong dependence (power of 5.3) on ship speed. Ross also proposed an alternate reference curve based on propeller characteristics,

)(log20)4/(log10)25/(log60195)( 101010 fBUfSSL t , (3)

where Ut is the propeller tip speed (m/s) and B is the number of blades. For example with one of the ships in this study (CCGS VECTOR) the 3-bladed propeller was operated near 300 revolutions per minute (RPM) at a ship speed of 11 knots, equivalent to Ut = 28.3 m/s. A more recent study by Wales & Heitmeyer [7] generated a different relation, without a speed dependence, fit to an ensemble of measurements on roughly 50 merchant ships over a 30 to 1200 Hz band, i.e.,

21010 )340/(1log17.9)(log9.35230)( fffSSL . (4)

The typical ship speeds in the Wales & Heitmeyer study were between 10 and 15 knots. All of these empirical references represent averages among an ensemble of different merchant and naval ships, with typical variability of 6 dB about the mean, thus the signature of any particular ship may not be an exact match.

Figure 1: Comparison of empirical ship signature models, compared to example ship SSL for CCGS VECTOR at speed of 11 knots.

Figure 1 compares the different empirical relations with an example ship SSL at a speed of 11 knots. The ship signature data has a 5 kHz low-pass (LP) filter applied. Overall there is a reasonable agreement in level and frequency dependence between the measured and empirical spectra at frequencies above 150 Hz. In addition to the general inverse-frequency-squared BB components, the VECTOR signature contains a number of narrowband machinery tonals approximately 2 to 5 dB higher than the references. There were particularly prominent lines at 400, 500, 550–870, 1060–1570, and 2320 Hz.

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Another useful parameter for understanding ship signatures is the propeller advance ratio, J, defined

� = � ��⁄ , (5)

where n is the propeller rotational speed (revolutions per second) and Dp is the propeller diameter. This non-dimensional parameter is the distance advanced by the propeller in one revolution normalized by the propeller diameter. For a given ship and propeller combination, there is a design value of J for cruising at an efficient speed, typically in the range 0.6 to 1.0. For example with the CCGS VECTOR in the above example, at a speed of 11 knots (5.7 m/s) the 1.8 m diameter propeller was operated near 300 RPM, thus implying J = 0.629. For CFAV QUEST in straight, cruising mode J was near 1.0. In general, as J decreases the propeller thrust and torque increase and propulsive efficiency decreases (see Ross [2], Section 8.3). Increasing propeller thrust and torque was found to increase ship signature levels [4]. The same study also found that strong application of the rudder during manoeuvres could enhance signature levels relative to straight-line runs.

2.2 Propeller Modulation Effects

At higher ship speeds the primary source of acoustic energy in the propeller signal is provided by cavitation [2, 3, 10, 11]. Cavitation is a process whereby bubbles are drawn out of the water by pressure gradients on the propeller blade surfaces and edges. These bubbles are unstable, and their collapse produces BB noise with spectral content out to at least 100 kHz. The degree of cavitation is related to the local water pressure, which varies with depth and non-uniformity in the flow field around the propeller due to the hull, rudder, and shaft support brackets. Thus the propeller signal has characteristics of an amplitude-modulated, BB cavitation carrier, with a modulation frequency at the propeller shaft and blade rates [11]. Furthermore, it can be shown that the generation of ordinary acoustic signals at the shaft and blade rates (generally below 20 Hz) has generally low signal-to-noise properties compared to the amplitude modulation of the broadband MF and HF components of the signal [11].

This modulation can be analyzed in two ways: (i) detection of envelope modulation on noise (DEMON) processing; and (ii) use of cyclostationary processing, as explained in [11]. The former technique is common in naval sonar applications, but is essentially an empirical technique requiring tuning of the processing parameters. The term cyclostationary refers to a special class of non-stationary signals which are random in nature, but exhibit periodicity in their statistics. The application of cyclostationary processing to ship noise provides a more rigorous signal processing approach.

2.2.1 DEMON Processing

The intent of DEMON processing is to estimate the VLF spectral content of the signal amplitude time-series. The estimation of signal amplitude can be done in several ways, either through root-mean-square averaging or via a Hilbert transform as in Equation (1). In the case of root-mean-square averaging this naturally imposes a LP filtering effect. For more analytic amplitude calculations, a specific LP filter must be applied. Then standard fast Fourier transform (FFT) processing is applied to the resulting amplitude time-series. In order to achieve the desired VLF spectral resolution it is necessary to sub-sample the original waveform. Record lengths of several seconds duration are required to achieve sub-1 Hz frequency resolution.

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For the specific data format examined in this work, the ship signature signal is sampled at 40,000 samples per second. The amplitude function is then calculated using Equation (1). After demeaning and LP-filtering with 100 Hz corner frequency, the signal amplitude time-series is then sub-sampled by a factor of 40, resulting in a subsidiary time-series sampled at 1000 Hz. Three 1-second blocks of data are used in the FFT calculation, producing a frequency resolution ∆� = (� ∙ ∆�)��, where M = 3 x 1000 is the number of samples and t = 0.001 s is the sample rate. This evaluates to f = 0.333 Hz, which is sufficient to resolve propeller shaft and blade rates in the 1 to 20 Hz band. The absolute spectral intensities are no longer meaningful.

2.2.2 Cyclic Modulation Coherence (CMC)

The approach here follows theory outlined in [11] for detecting a cyclostationary ship propeller signal nature in the presence of noise. This involves calculating the cyclic modulation spectrum of the ship signature. The basic idea is to examine the VLF spectral dependence of short-time windowed spectral components of the amplitude signal; there is no need to explicitly calculate the waveform amplitude. This approach uses two frequency dimensions: (i) the conventional signal frequency denoted f, and (ii) the modulation frequency denoted α. The original time-series is parsed using a 75% overlapped sliding window, within which the conventional power spectra are computed. Then, for each real frequency component, the power spectrum over incremental time is computed, resulting in a cyclic modulation spectral matrix in f and α coordinates. This is normalized to form cyclic modulation coherence (CMC) by dividing by the frequency spectrum at α = 0. Examination of the frequency vs. modulation coherence matrix can then identify a broadband frequency range (typically MF and/or HF bands) within which there is strong modulation. A simplified detection vector can then be generated by integrating over this strong modulation band, producing integrated CMC (ICMC) which is only a function of α. This processing will be illuminated through a numerical example in Section 2.4.

Specific to the data formats in this work, to achieve the desired frequency resolution it is once again necessary to use 3 x 1-second data records, or a total of NT = 120,000 data samples. The signature is band-pass filtered with corner frequencies of 100 Hz and 10 kHz. Then, a sequence of 512-point FFTs with 75% overlap are computed. A standard Hanning window is applied to each 512-point block. The power spectrum is computed for each block. The total number of overlapped FFT’s is then � = (�� − ��)/� + 1, where NN = FFT size, and R is the amount of shift (NN/4 = 128 points). Thus there are a total of M = 934 spectral samples over the 3-s data block. The frequency resolution of the normal spectral processing is simply (NNt)-1, where t = 40,000-1, equal to 78.1 Hz. Then, for each of the NN/2 real frequencies, a FFT is computed over the 934 output spectra. This produces a modulation frequency resolution ∆� = (� ∙ ∆� ∙ �)��, or 0.334 Hz. The resulting CMC matrix is normalized by dividing by the frequency spectrum at α = 0. Finally, the ICMC is computed by integrating (summing) over the 1 to 8 kHz band.

2.3 Ship Signature Statistical Models

This sub-section will outline the statistical models used to examine the ship signatures.

2.3.1 Time-series Statistics

In addition to the standard mean (�̅) and variance (��) parameters, there were two other non-dimensional parameters that are useful in describing signal fluctuations [15], namely the scintillation index (SI) and skewness (S), defined by,

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2

22 )(1

V

VA

NSI (6)

and

2/3

3)(1

V

AA

NS (7)

where N is the number of points in the data block (in this case 40,000). For Rayleigh distributed signals, SI and S take values of 1.0 and 0.631, respectively [16]. For signals with a super-Rayleigh distributions, SI and S values are slightly larger. It was found that kurtosis (K) and other higher-order moments of the time-series were too unstable to be useful.

2.3.2 Probability Density Function (PDF) Models

Target detectability in the presence of noise depends on the statistical properties of the signal and background. These statistics can be related to the combination of receiver characteristics (e.g., bandwidth) and signal properties. These statistical properties are captured by the PDF of signal amplitude. Because a small detection probability of false alarm is desired, typically less than 0.1%, details of the PDF at higher relative amplitudes are important in setting a detector threshold.

Two reference distributions were fit to the experimental PDF: Rayleigh and K. These are defined by [following 17],

22 exp2 xxPRayleigh ; (8)

and

x

Kx

PK

2

)(

41

(9)

where x is the normalized echo amplitude (�/�̅), is the Rayleigh variance parameter, () is the gamma function, Kn() is the modified Bessel function of the 3rd kind, and and are the K-distribution scale and shape parameters. For the K distribution, the variance is 2.

The Rayleigh distribution, which is the simplest and most widely used, describes signals whose amplitudes are normally distributed arising from a sufficiently large number of signals or sources for the central limit theorem to hold [12, 17].

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The K-distribution describes the product of a rapidly fluctuating, Rayleigh-distributed random variable and a slowly varying, Chi-distributed variable [17]. In the limit of large shape parameter, , the K-distribution is equivalent to the Rayleigh distribution. Thus the shape parameter can be interpreted as the degree of Rayleighness in the signal distribution, with smaller values ( < 20) denoting super-Rayleigh distributions. The K-distribution is a standard model for radar clutter, and has been used successfully to describe seabed reverberation [17–19]. Studies by Abraham [18, 19] have related the K-distribution shape parameter to increases in signal detection thresholds relative to active sonar reverberation.

2.3.3 PDF Generation and Fitting

This sub-section presents details on the calculation of signal amplitude PDF and data fitting. The ship signature amplitude (calculated as in Equation (1)) was normalized by dividing by the ensemble (1-s data block) mean amplitude. Then a normalized amplitude histogram was computed using a normalized amplitude bin size of 0.1. It was found that the first 80 amplitude bins were sufficient to span the data distribution; only the first 40 bins were used for fitting and calculation of goodness of fit statistics. The resulting histogram was converted to a data PDF by normalizing so that the integral over all amplitudes was unity.

The above mentioned model functions were fit to the data PDF using an iterative non-linear curve fitting routine, minimizing the mean-squared-error residual. For the K-distribution calculations the shape parameter, , was limited to the interval 1 to 25 due to numerical constraints on the calculation of the gamma and Bessel functions. To determine the goodness of fit two statistical tests were used, namely the Chi-squared test and the Kolmogorov-Smirnov (KS) test. The reduced Chi-squared statistic was calculated using [following 17],

M

m m

mm

xP

xPxPDF

DF 1 0

2

02

)(

)()(1 , (10)

where DF is the number of degrees of freedom, M is the number of bins used in fitting the data PDF, and

P0 is value of the reference distribution (either Rayleigh, K, or mixture). Larger values of 2 indicate

that it is unlikely that the data is consistent with the reference distribution. Generally it can be assumed

that 2 < 10-3 produces an acceptable fit. The degrees of freedom for the Rayleigh distribution

(one free-parameter) were DF = M – 1 = 39 and DF = 38 for the K-distribution (2 free parameters). This calculation was dominated by data vs. model mismatch for the larger values of P0 found at lower relative amplitudes. The KS test (calculation details described in [17]) produces a p-value (0 to 1) quantifying the probability that the observed data follow the reference distribution. The KS p-value is determined by the maximum data vs. model mismatch in the cumulative density function.

2.4 Numerical Simulations

A series of simple numerical simulations can be performed to illuminate the concepts and algorithms discussed above. The first step was to generate a zero-mean, broadband, random noise time-series of total length 10 s. Numerically the amplitude was scaled so that the time-series maximum values were near 30,000 so that 16-bit integers could be used to export in WAV-file format. The signal processing was

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done using float-point. In order to properly resolve the MF and HF bands, this random noise was generated at twice the normal sample rate, or 80,000 samples per second, then LP filtered at either 2, 5, or 10 kHz. Then a ship signature spectral shape was applied at frequencies above 100 Hz by dividing the amplitude spectrum by the frequency (this is equivalent to an inverse frequency-squared power-spectral dependence). Finally a propeller shaft and blade-rate amplitude modulation was applied to the time-series using the function,

�(�) = 0.7 + 0.1 ∗ cos�(2��) + 0.3 ∗ cos� (2��) (11)

where fs is the shaft rate and fb is the blade rate. For example with a 3-bladed propeller operating at 180 RPM, the shaft rate was 3.0 Hz and the blade rate was 9.0 Hz. In Equation (11) these propeller rates must be divided by two because of the cosine-squared frequency doubling. This modulation can be expanded to include dual propellers by adding similar modulation components with slightly different frequencies.

2.4.1 Spectral Shaping and PDF

As a first step, the generation of BB noise and application of various LP filtering functions can be verified, including the application of ship signature spectral shaping. BB noise time-series 10 s in length were created, then LP filtered at 2, 5, and 10 kHz corner frequencies. Power spectra were created using a 4096-pt FFT, 50% overlapped, using a Hanning taper window. A similar time-series with 10 kHz LP filtering and ship signature shaping (but no modulation) was also generated. Figure 2 shows a comparison. The application of LP filtering reduces the flat portion of the BB noise spectra, and shows the filtering sidelobes at least 50 dB below the main level. The ship signature shaping shows the distinctive inverse-frequency-squared dependence above 100 Hz. Clearly the ship signature spectrum has a greatly reduced effective bandwidth compared to simple filtering of BB noise.

Figure 2: Comparison of signal power spectra vs. bandwidth and with ship signature shaping.

It is expected that the amplitude of the simple BB noise signals would exhibit Rayleigh statistics, independent of bandwidth. This was tested as follows. For each of the above time-series, the signal amplitude time-series (Equation (1)) was calculated. The mean value and other statistics of the amplitude

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time-series were then calculated. Then the normalized amplitude PDF was calculated over each 10 s time-series, as explained in Section 2.3.3.

Figure 3 shows the simulated PDF comparison for varying bandwidths of BB noise, along with best-fit Rayleigh and K-distribution models. Over the high-probability region (PDF > 0.1, normalized amplitude < 2.0) there are negligible differences between the data-PDF with varying bandwidth. The best-fit Rayleigh and

K-distribution models are also a good fit (very small 2 values), with the relatively large K-distribution

shape parameter ( = 24.9) indicating Rayleigh behaviour. The KS goodness of fit p-values are both 0.999.

Based on the 2 values, the Rayleigh distribution is a better fit, particularly at amplitudes > 2. At higher

amplitudes (> 2) the data PDF are slightly sub-Rayleigh, approaching the Rayleigh model as the LP filter corner frequency is reduced. This is attributed to a subtle numerical simulation effect where the digital sampling frequency was too low to accurately resolve the highest-frequency signal components.

Figure 3: Comparison of simulated BB noise signal PDF vs. LP bandwidth, with best-fit Rayleigh and K-distributions.

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Figure 4: Comparison of simulated ship signature PDF between broadband, ship spectral shaping, and single-propeller shaft and blade rate modulation. Rayleigh model is fit to ship signature with no

modulation. K-distribution model is fit to ship signature with modulation.

The addition of propeller shaft and blade-rate modulation changes the statistics to a super-Rayleigh condition. Figure 4 shows the transition from sub- to super-Rayleigh behaviour as the ship signature includes amplitude modulation (following Equation (11)). This case assumes a 3-bladed propeller operating at 180 RPM. The propeller-modulated data-PDF no longer follows the best-fit Rayleigh distribution of the unmodulated signal. The best-fit K-distribution to the modulated signature shows a shape parameter of 5.1, definitely super-Rayleigh. Also, the propeller modulated signature-PDF (and best-fit K-distribution) exhibits a shift in peak PDF values towards lower amplitudes (relative to the un-modulated signal). This latter effect is due to the mean amplitude being increased by the infrequent high-amplitude values.

This tendency for super-Rayleigh statistics is similar but slightly stronger for dual-propellers, as shown in Figure 5. This case assumes dual 5-bladed propellers, with one shaft at 120 RPM and the other at 121 RPM. As for the single-propeller case, the propeller modulated data PDF is best fit with a K-distribution, with the shape parameter (4.0) indicating super-Rayleigh statistics.

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Figure 5: Comparison of simulated ship signature PDF including dual-propeller shaft and blade rate modulation. Rayleigh model is fit to ship signature with no modulation.

K-distribution model is fit to ship signature with modulation.

A key conclusion from the simulations shown in Figures 3–5 is that simple spectral shaping, either through LP filtering or using an inverse-frequency-squared weighting, has only minor effect on the signal amplitude statistics. They remain essentially Rayleigh distributed independent of bandwidth or spectral slope. Only the addition of propeller modulation forces the PDF to super-Rayleigh characteristics.

2.4.2 Time-series Statistics

The SI and S statistics are also sensitive quantifiers of the amplitude PDF. Table 1 summarizes SI and S computed from a variety of noise and ship signature simulations. For reference, the theoretical values for a Rayleigh distribution are shown in the first row. For the BB noise time-series, the values approach the Rayleigh limit as the LP filter corner frequency is reduced, in accordance with the PDF result shown in Figure 3. When the ship signature spectral shaping is applied (without modulation) the statistics remain near the Rayleigh expectation. For the ship signature shaping the sensitivity of the statistics to LP filtering is drastically reduced, with the 2 kHz LP showing the closest to Rayleigh values. In contrast, when blade-rate modulation is applied (using the 10 kHz LP filtering) the statistics jump to super-Rayleigh values. The SI and S statistics are even larger for the dual-propeller case.

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Table 1: Comparison of scintillation index and skewness statistics between different simulated noise and ship signature time-series, based on 10-s time-series.

Case SI S

Rayleigh theoretical 1.0 0.631

BB noise, 10 kHz LP filter 0.883 0.493



ship spectral shaping, no modulation, 10 kHz LP filter 0.990 0.621



ship signature, 3-Hz blade-rate modulation, 10 kHz LP filter 1.370 0.954

dual propeller, 10-Hz blade-rate modulation, 10 kHz LP filter 1.413 0.970

2.4.3 Ship Signature Modulation

The CMC processing outlined in Section 2.2.2 can be readily applied to the modulated ship signature time-series. In anticipation of the data processing needs, a 3-s data record was generated. This simulation also included an added 1500 Hz NB tonal to assess the effects of this in the CMC calculation. The full CMC for this simulation is shown in Figure 6. The figure shows clear shaft and blade rate lines extending from 0 to 10.5 kHz at the correct modulation frequencies. The upper limit is presumably due to the 10 kHz LP filtering. The blade rate line is stronger because its original modulation was stronger in Equation (11). The signal to noise (power) ratio of the blade rate line is near 25 (14 dB). This simple cosine-squared amplitude modulation (Equation (11)) applied does not create any 2nd or 3rd harmonics; real data often shows higher harmonics. The 1500 Hz tonal manifests itself in the CMC output as a drop-out across all modulation frequencies. This drop-out is a result of the normalization by the spectrum at α = 0.

From Figure 6 it is clear that the propeller modulation extends across the 0–10 kHz frequency band, so integration within this band can distill the signature information into a single vector. Note that real ship signature data may only have observable modulation over a reduced bandwidth, so that examination of the CMC is still advisable. Figure 7 shows the ICMC result integrated over 1 to 8 kHz bandwidth. This result clearly shows the original shaft and blade-rate modulation with 0.33 Hz resolution. This incoherent summation has not improved the signal-to-noise ratio; it remains 13 dB for the blade-rate tonal and 7 dB for the shaft-rate, however the noise floor appears to be relatively flat and featureless.

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Figure 6: Ship signature cyclic modulation coherence (CMC) based on 3 s simulated time-series with 10 kHz LP filtering and inverse-frequency squared spectral shaping. Simulation uses

4 Hz shaft and 12 Hz blade rates, with added 1500 Hz NB tonal.

Figure 7: Ship signature ICMC, based on simulated data in Figure 6 integrated over 1–8 kHz bandwidth.

An alternate way to expose the propeller modulation is through DEMON processing, as outlined in Section 2.2.1. This appears to be a more direct and quicker calculation, but the overall signal-to-noise properties and frequency resolution depend on the data integration period (record length). Figure 8 compares DEMON spectra for a 3 s and 10 s record length, using a 1024-pt and 4096-pt FFT length, respectively. Clearly, the longer record length has the dual benefit of better frequency resolution (0.24 Hz vs. 0.98 Hz) and improved signal-to-noise properties. The SNR of the blade rate tonal is approximately 14 dB for the 3 s record, increasing to 21 dB for the 10 s record. Using the 3-s record length it is difficult to clearly identify the 4 Hz shaft rate. Compared to the ICMC output (Figure 7) the

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background noise in the DEMON case is more spikey (larger variance), hence the ICMC appears to be better at isolating the shaft and blade rate tonals. This comparison (ICMC vs. DEMON) will be re-examined with real ship data later in this report.

Figure 8: Comparison of simulated ship signature DEMON spectra at 3 s (1024-pt FFT) and 10 s (4096-pt FFT) data record length.

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3 Instrumentation and Sea-Trials

This section provides detail on the acoustic recording systems, the ships, and sea-trials.

3.1 Broadband Underwater Recording Buoys

The Broadband Underwater Recording Buoys (BURBs—see photo in Figure 9) were developed to provide broadband, short time-scale measurement of vessel underwater radiated signatures. A detailed description of the BURB electronics is given in [20]. The BURB system was intended to remedy problems of positioning, calibration, signal dynamic range, lifetime, and background noise encountered with the use of conventional sonobuoys. There were four identical BURBs, each completely self-contained with an operational duration in excess of 24 hours.

Figure 9: (left) Photograph of a Broadband Underwater Recording Buoy (BURB), with (right) detail on the hydrophone and attachment of lead weight.

Each BURB continuously records two hydrophone channels onto an internal hard-drive. Each hydrophone channel is sampled at 40,000 samples per second with 16-bit (92 dB) dynamic range. Additionally, an automatic gain control (AGC) adjusts the recording levels by up to 58 dB in order to avoid clipping or under-resolving low amplitude signals. The buoys record their own position at 1 s intervals through an onboard differential global positioning system (DGPS) receiver. Each buoy is approximately 110 cm high by 60 cm maximum diameter, with weight of 45 kg. In these trials the two hydrophones on each BURB were suspended at depths of 5 and 15 m (April 2005) and 5 and 20 m (Sept 2005) below the surface. The hydrophones are inexpensive commercial units approximately 10 cm in length by 2 cm diameter with integral pre-amplifier. Note that the use of two different hydrophone depths allows a consistency check on the propagation loss corrections [4]. For simplicity the hydrophones were deployed without special

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suspension gear (e.g., damping plates and elastic sections); this was expected to have only minor impact on the acoustic recordings under the relatively calm conditions encountered in these sea-trials. The hydrophones and cables were attached to a 1-cm diameter braided rope with a 2.5 kg weight at the bottom (Figure 9 right). The hydrophones were held away from the rope and cables with a U-shaped wire stiffener.

Detailed acoustic calibrations of the eight BURB hydrophones were conducted between the April and Sept. 2005 sea-trials (reported in [20]). The calibration technique involved broadcasting a series of continuous wave tones at known source level at frequencies from 500 to 20,000 Hz in steps of 100 Hz, and comparing results to a reference hydrophone. The measured VLF and LF hydrophone responses were approximately -185 dB re 1 V/Pa. The function of the AGC was also verified using different source levels. Detailed spectral response compensation curves were generated for each hydrophone. This spectral response processing and AGC correction were applied as a first step in all subsequent signal processing. Unfortunately most of the BURB hydrophones exhibited a complicated response (due to a mechanical resonance) in the 6 to 10 kHz region, with multiple smaller resonances above 10 kHz (see [20]). Under some conditions the spectral response compensation amplified background noise in the low-sensitivity portion of the resonance effect, slightly contaminating the signal above 5 kHz. Fortunately the dominant energy in the ship signatures was below 5 kHz. Thus, in all the ship signature power spectral processing that follows a 5 kHz LP filter was applied. However, for calculations of signal amplitude PDF and CMC a 10 kHz LP filter was applied. Recall the conclusion from Section 2.4.1 that spectral shaping has only minor effect on signal amplitude statistics. Therefore the 10 kHz bandwidth data was considered suitable for exploring the ship signature statistics and modulation under consideration here.

Instrumental and background noise levels imposed some constraints on the ship signature measurements. Internal electronic noise levels had an equivalent sound pressure level (SPL) near 50 dB (re 1 Pa2/Hz), which was more than 40 dB below the typical ship signatures encountered during the trials. In actual sea-trials the measured background acoustic noise SPL were between 60 and 70 dB, decreasing with frequency. An approximate fit to the background noise during the sea-trials was found to be SPLnoise = 118 - 16*log10(f) (dB re 1 Pa2/Hz), or approximately equivalent to open-ocean wind-wave noise at Sea-State five (wind speeds 20 to 25 knots, as cited in Wenz [1]). Even taking into consideration the shallow water conditions, which are known to exhibit higher ambient noise at a given sea-state, this noise level was in excess of that expected from the local winds (10–12 knots). The excess was attributed to the combination of a few small motor boats operating in the vicinity and buoy external self-noise, such as waves slapping against the buoy floatation and/or cable motion. Overall, this posed some limitations for MF and HF (> 2 kHz) measurements at ship-buoy ranges greater than a few hundred meters. Because of this background noise the acoustic ship-signature data were only used for ship-buoy ranges < 300 m and where the measured SPL exceeded the background noise curve by at least 6 dB.

3.2 Spectral Processing

In addition to the amplitude statistics and modulation processing described in Section 2, the raw acoustic time-series were also processed for the sound pressure level (SPL) spectra (dB re Pa2/Hz) using the individual hydrophone calibrations and AGC. The goal of this analysis was to determine the vessel spectral source level (SSL) corrected to a standard distance of 1 m, hence in units of dB re Pa2/Hz at 1 m. Variations in the SSL with aspect angle, ship speed, and turning rate at relatively short time intervals were examined in a previous study [4]. Generally, the measured SPL was strongly dependent on frequency and

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the distance between the source vessel and the buoy. At these short distances the transmission loss can be approximated by a spherical spreading law and a frequency-dependent absorption term, i.e.,

��(�) = ��(�) − 20 ∙ ��[�] − �(�) ∙ �(dB re 1 Pa2/Hz) (12)

where r is the slant range (m) between vessel and hydrophone and f is frequency (Hz). The absorption term, (f), is dependent on water properties (e.g., temperature and salinity) [21], and is generally small (< 3 x 10-4 dBm-1) at frequencies below 5 kHz. It should be noted that reflections from the ocean surface have the potential to complicate the transmission loss calculation (to be discussed in the next subsection).

The SPL analysis started with the calculation of frequency spectra at 1 s intervals. A decision was made to sacrifice frequency-resolution in favour of stable, short-duration spectral estimates. The precise measurement of narrowband machinery signals was not a goal in this work. Each BURB channel was processed using 4096-pt fast Fourier transforms, demeaned and tapered using a Hanning window, yielding a 9.8 Hz frequency resolution. For each 1-s block of data (40,000 samples), a total of seventeen 50%-overlapped raw spectra were averaged. Spectral averaging was always done using the linear (not decibel) values.

The experimental geometry was well-resolved, with estimates of ship-to-buoy horizontal range and ship speed, heading, and turn rate produced at 1 s intervals. The slant range to each hydrophone depth was then used to convert each 1-s-averaged SPL to an equivalent SSL using Equation (12). Measurements were only used at horizontal ranges between 20 m and 300 m. A detailed investigation of the SPL time series for straight-ahead runs found that the maximum acoustic output was coincident with the closest point of approach (CPA) of the propeller. The ship turn-rate was calculated by differentiation (with smoothing) of the ship heading vs. time. An additional calculation was the ship azimuthal aspect angle to each buoy.

3.3 Lloyd’s Mirror Effects

It is well known that acoustic interference effects can be created by the combination of direct and surface-reflected acoustic paths. A similar, weaker effect can be generated in shallow waters by acoustic reflections from the seabed. This interference pattern, seen as a range-dependent pattern of alternating peaks and nulls in frequency-time spectrograms, is known as the Lloyd’s Mirror effect. Important physics of this effect are that reflections from the ocean surface incur only small losses and that the reflection incurs a 180 phase shift. Owing to this reflection phase shift destructive interference occurs at longer ranges and low frequencies, where the difference between direct and surface-reflected path lengths becomes small relative to a wavelength. At low-frequency and/or long range, the source with its surface reflection behaves as a vertically-oriented dipole (see Ross [2] Chapter 4).

A relatively simple theory can be used to quantify the Lloyd’s Mirror effect [22]. The basic theory assumes a point source and receiver, at depths d0 and d1 respectively, and specular reflection from a nominally flat ocean surface. The surface-reflected path can be assumed to emanate from a virtual source located a distance d0 above the boundary. The theory also allows use of a reflection coefficient, R, which is less than 1.0 if the boundary reflection is imperfect. Using these parameters a Lloyd’s Mirror Interference Pattern (LMIP) relative to spherical spreading can be given by,

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�� = 10 ∙ ��[1 + �� − 2 ∙ � ∙ ��(4��/(��))], (in dB) (13)

where c is the (average) sound speed (m/s) and r is slant range (m). This relation will exhibit a series of peaks and nulls in frequency and/or range, with amplitude controlled by R. Note that this reflection coefficient can differ from unity due to rough surface scattering and bubble scattering and absorption losses, and thus should generally be regarded as frequency, sea-state, and grazing-angle dependent. This theory [22] can also account for refraction effects due to a sound speed gradient, which are ignored in this work. This theory predicts frequencies of the first two LMIP peaks at approximately,

�� = �� (4��)⁄ and �� = 3 ∙ �� (14)

At frequencies below the first peak, the LMIP drops strongly. For example, at a slant range of 30 m with d0 = 2 m and d1 = 15 m, the first two peaks are 375 Hz and 1175 Hz. Thus for the deeper hydrophone the signals are attenuated below 375 Hz. For a shallower hydrophone (d1 = 5 m) the peak frequencies are higher, i.e., fp1 = 1125 Hz, so that the VLF/LF response is more strongly attenuated relative to the deeper hydrophone.

Note that the determination of the effective source depth for a ship is not straight-forward, as in reality a ship is a complicated, distributed acoustic source. It is generally accepted that the propeller is the dominant acoustic source in the VLF and LF bands [2, 3, 10]. However, it is likely that the propeller is a distributed (vice point) acoustic source in depth, obscuring the peaks and nulls predicted in the simple theory (see [4]). Furthermore, surface-reflected paths from the propeller may be partially blocked by the ship’s hull. Additionally, unless special mountings are used, machinery noise can be coupled into the hull and radiate from regions not co-located with the propeller. There are additional broadband acoustic contributions from breaking bow, quarter, and stern-waves and turbulent hull flow that will be distributed over the length and depth of the ship hull. Gray & Greeley [10] suggested that an effective source depth for a propeller could be taken as the ship draft minus 85% of the propeller diameter.

While the LMIP effects will be discussed in the context of ship SSL measurements, the LMIP corrections will not be applied in calculations of signal statistics, PDF, and CMC. This simplification is based on the result from Section 2.4.1 that signal spectral shaping has only a minor effect on amplitude statistics and PDF.

3.4 Test Ships

These field measurements utilized two ships: (i) a small coastal oceanographic vessel, the CCGS VECTOR; and (ii) a medium-sized Naval auxiliary CFAV QUEST. Dimensions and propeller details of the two ships are presented in Table 2. The two ships are significantly different in size, machinery, and propeller types. VECTOR has a single, three-bladed, variable pitch, 1.8 m diameter propeller driven by a 600 kW diesel engine. At speeds above a few knots the propeller pitch is set to maximum. The propulsion throttle control appears to maintain a set shaft rate, thus the propeller advance ratio will vary with ship speed through manoeuvres. The propeller is located 3 m forward of the transom with its axis at 2.3 m depth. A single 1.2 m wide by 2.5 m tall rudder is mounted immediately astern of the propeller. VECTOR does not utilize special acoustic quieting techniques, such as vibration isolation mounts and skewed-blade propellers.

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The CFAV QUEST utilizes twin, 3.1 m diameter, 5-bladed propellers driven by diesel-electric engines. The control system for the drive motors appears to maintain set power (or torque), allowing the propeller shaft rate to vary through manoeuvres. QUEST utilizes one or two diesel engines generating electrical power to drive motors for each propeller. At speeds up to 10 knots one engine is sufficient; above 10 knots two engines are required. QUEST has two rudders, located behind each propeller. Furthermore, QUEST was designed to be acoustically quiet, utilizing special vibration-isolation mounts for engines and generators and highly-skewed propeller blades designed to minimize cavitation-mediated noise. Thus its SSL was observed to be considerably lower than VECTOR at the same speed, creating measurement signal-to-noise problems at lower ship speeds.

Table 2: Ship physical characteristics.

CCGS VECTOR CFAV QUEST

Length 39.7 m 76 m

Beam 9.5 m 12.6 m

Draft 3.5 m 4.8 m

Displacement 516 t 2130 t

Max Speed 11.5 knots 14.5 knots

Propeller(s) single, 3 blades, 1.8 m dia. twin, 5 blades, 3.1 m dia.

During the April 2005 sea-trials the VECTOR was outfitted with two DGPS recorders, one at the bow and one on the aft deck. The aft DGPS was located 4.5 m ahead of the propeller location. The ship’s position, speed, and heading over ground were recorded on each system at 1 s intervals. The use of two separate DGPS receivers allowed estimation of the instantaneous ship heading through incoherent differencing of the antenna positions. This technique was used to avoid the complication of tapping into the ship’s gyrocompass. VECTOR did not have systems for recording machinery parameters such as propeller RPM and rudder angle; occasional notes were taken of bridge read-outs.

During the September 25th sea-trials the QUEST utilized its own non-acoustic data recording system, which included DGPS position, speed, and heading relative to the ground, speed relative to water, ship gyro heading, rudder angle, and propeller RPM. This was recorded at 5 to 10-s intervals throughout the tests.

3.5 Ship Manoeuvre Types

For both ships the sea-trial plan included a similar set of measurement runs. Through combining data from all four buoys at different locations, these runs were intended to assess the directionality of ship signature and examine the increased signature generated by aggressive ship manoeuvres. These runs can be grouped into three types:

1. Straight-line, constant speed runs at speeds from 6 to 12 knots, with specific runs at maximum ship speed.

2. Straight-line, accelerating runs, inbound at 6 knots then accelerating to maximum speed near CPA to the buoys, continuing for no less than 5 minutes (only for QUEST).

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3. Turning runs, either 90 or 180, inbound at the maximum ship speed with propulsion control maintained at maximum throughout the turn. Standard or one-half standard helm was applied resulting in varying turn diameters.

Multiple runs of each type were performed. The use of multiple buoys during manoeuvring runs allows assessment of earlier and later parts of the manoeuvre, which were observed to exhibit different characteristics.

3.6 Sea-trial Locations

Measurements on the VECTOR were conducted in the middle of Saanich Inlet, near Victoria, B.C. (Canada). This inlet is approximately 30 km long by 5 to 8 km at its widest, with depths in the central inlet reaching up to 220 m, overlying a soft sandy mud bottom. The inlet is completely sheltered against ocean swell and has only modest tidal currents. This location is only a few kilometers from the Institute of Ocean Sciences, which provided shore facilities and access to small boats. In April 2005 the surface waters of the inlet were relatively unstratified, with only a mild upward-refracting sound speed gradient in the upper 90 m. Acoustic propagation modelling suggested that the dominant propagation effects were spherical spreading and sea-surface reflection, and that internal refraction effects would only be relevant at ranges beyond 1 km. During the trials the local winds (monitored via a nearby meteorological buoy) were typically 10–12 knots or less, with local wind-wave heights < 0.3 m (estimated visually), corresponding to Sea-State 2. This sea-state created some acoustic interference in the BURB recordings, decreasing measurement signal-to-noise at lower ship speeds (< 8 knots).

The measurements on the QUEST were conducted on September 25th, 2005 in Emerald Basin, approximately 100 km SSE of Halifax on the Scotian Shelf. The water depth in this area was approximately 220–260 m. The area is completely open to ocean waves and swell, however the weather conditions on this day were relatively calm (estimated Sea-State 3, winds 10–12 knots). Similar to the VECTOR measurements, this sea-state generated a background of acoustic interference which limited the signal-to-noise of the ship acoustic measurements. The sound speed profiles on this day showed a well-mixed surface layer up to 25 m deep, with a strong thermocline to a sound speed minimum at 50 m, with upward-refracting conditions below.

Both environments had similar water depth and seabed sediments. For these short-range (< 300 m) ship signature measurements seabed reflections were near normal incidence, thus suffering an estimated seabed reflection greater than 10 dB at frequencies under consideration here (100 Hz to 5 kHz). This reflection loss, in combination with the greater acoustic path length (400 to 500 m), suggests that seabed reflections would be roughly 15–30 dB lower than the direct paths, depending on ship to buoy range. Thus seabed reflections can be ignored.

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4 CCGS VECTOR Sea-Trials, April 2005

This section summarizes analysis results from sea-trials with the CCGS VECTOR during 12–14 April 2005 in Saanich Inlet, B.C. A total of 32 separate runs were made over the three days, as shown for example in Figure 10. Multiple straight-line runs at 6, 8, 10, and 11.5 knots were made. A total of 17 maximum speed turning runs through either 90 or 180 were conducted. The run naming convention utilized the day of April plus run number on that day, i.e., run 1304 is the 4th run on April 13th. Runs were conducted at intervals of at least 15 minutes to allow wake bubbles to dissipate.

Figure 10: Photograph of CCGS VECTOR conducting a run past two BURBS, April 13, 2005.

The ship SSL, including directionality and manoeuvring effects, from this sea-trial were summarized in a 2008 scientific paper [4], and will only be briefly mentioned here. The focus here will be on the modulation and statistics of the ship signatures under a variety of conditions, particularly at maximum speed (approx. 11.4 knots) and through turning manoeuvres. The ship SSL and CMC in the lower speed runs (6, 8, 10 knots) were found to be relatively weak, with the time-series and PDF exhibiting close to Rayleigh behaviour; discussion of these does not uncover novel results.

4.1 Straight-Line Runs

This section will highlight the behaviour from the straight-line runs, starting with an example of a maximum speed (near 11 knots) run.

4.1.1 Example Run 1302 Straight Pass at 11 Knots

The straight line runs exhibited a simple hyperbolic trajectory in ship to buoy range vs. time, as shown in Figure 11. In this example, the ship was southbound (heading 188 true) at a nominal speed of 11 knots, slightly accelerating from 10.8 to 11.1 knots over this run. Since the maximum speed of VECTOR was observed (in other runs) to be near 11.4 knots, it is presumed that the in-run was not quite long enough to reach maximum speed. The CPA to each buoy is easy to identify in time and range, with distances between 19 m and 33 m. The ship was within 300 m of each buoy for approximately 100 s.

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Figure 11: Plot of ship speed (from GPS) and horizontal range to BURBs for VECTOR Run 1302.

4.1.1.1 Spectral Levels and Lloyd’s Mirror

The received SSL at CPA observed at each buoy were all very similar (see Figure 12). There was also good agreement with the reference relation due to Ross (Equation (2)), indicating that the VECTOR can be considered a typical ship from an acoustic signature perspective. The spectra showed strong peaks in the 100–150 Hz region with a general broadband, inverse-frequency-squared dependence out to 5 kHz. The VECTOR signature also exhibited a broad SSL excess in the 500–2000 Hz region, more prominent in the deeper hydrophone, attributed generally to machinery noise. There were only a few prominent NB machinery lines (e.g., 400 Hz, 500 Hz, 700 Hz, and 2340 Hz). The spectra were all at least 20 dB above the self-noise level.

The Lloyd’s Mirror effects in these uncorrected SSL spectra in Figure 12 were subtle. The primary effect was that the peaks at 100–150 Hz were approximately 4–5 dB higher in the deeper (15 m) hydrophone. Note that the first LMIP peaks are predicted (Equation (14)) to be 350 Hz and 930 Hz for the 15 m and 5 m depth hydrophones, respectively. Thus, the shallower hydrophone should see a greater attenuation (relative to the deep hydrophone) below 900 Hz. From Equation (13) the difference in LMIP between the two hydrophones is predicted to be approximately 5–7 dB at frequencies below 300 Hz.

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Figure 12: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at CPA for all BURBs in VECTOR Run 1302, compared to empirical relation due to Ross (Equation (2))

at ship speed of 11.0 knots. Hydrophone depths (upper) 5 m and (lower) 15 m.

4.1.1.2 Signature PDF and Statistics

For these straight-line, maximum speed runs the signature amplitude PDF were close to Rayleigh-distributed, with some subtle variations exposed by the sensitivity of the K-distribution shape factor to higher amplitude signature components. Figure 13 shows a data PDF at CPA for a straight-line, maximum speed run at 11.0 knots (1302). The data PDF (both channels) were better matched by the K-distribution rather than Rayleigh model, following the heavier-tailed data PDF observed at normalized amplitudes > 2. The best-fit K-distribution shape parameter = 13.6 suggests mildly non-Rayleigh characteristics. The signature at CPA to BURBs 1, 3, and 4 also showed similar K-distributed behaviour.

In all cases here (and for all straight-line runs with VECTOR) the best-fit 2 values were sufficiently

small (< 10-3), with the KS significance p-values > 0.999, so that these fits could be concluded as statistically significant.

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Figure 13: Comparison of data and best-fit model PDF for VECTOR Run 1302 BURB2 for an 8 s period at CPA.

Taking a more detailed look at the data PDF variation with time suggests an interesting behaviour as the ship travelled through CPA. In this analysis the data PDF was calculated over a 3-s running window over a period ±40 s relative to CPA time. Then the K-distribution was fit to the data PDF at each time, with the shape parameter () indicating the degree of Rayleighness. Results are shown in Figure 14.

During the in-run portion, up to about 10 s prior to CPA, the data PDF showed a consistent Rayleigh distribution with 25. Starting at 10 s before CPA the data PDF showed increased presence of higher-amplitude (> 3) signals and a corresponding downward shift in the peak amplitude. This causes the best-fit shape parameter to drop down to values near 5. The 8 s averaged PDF shown in Figure 13 spans this transition. Examination of (and listening to) the raw hydrophone time-series found that good signal resolution with clear propeller modulation occurred from approximately 200 s to 240 s (on this time scale), but with two distinct impulsive transients at 234 s and 239 s (as indicated by arrows in Figure 14 top). These impulses are also clear in the data PDF. These transients are attributed to the ship bow and stern waves impacting the buoy hull. Ignoring these transients, there remains a clear drop in K-distribution shape parameters indicating a shift to non-Rayleigh statistics for a period of roughly 30 s. Beyond 250 s the data PDF returned to Rayleigh behaviour.

A similar analysis to that described above found that the data PDF for BURBs 1, 3, and 4 of this same run (1302) behaved similarly, with a drop in K-distribution shape parameter just at CPA lasting for approximately 30 s. The reason for this change in data PDF shape to super-Rayleigh conditions at CPA is hypothesized as due to ship signature directionality. Prior to CPA the receiver buoy was in the forward aspect angle to the ship, such that some of the ship signature was blocked by the ship’s hull. In particular the strong cavitation signal at the top of propeller sweep may have been blocked. After CPA the buoy was in the aft aspect, presumably exposing the full propeller signal including a surface reflection. At 30 s after CPA the horizontal range reached 200 m, such that LF signals were increasingly attenuated by the Lloyd’s Mirror effect.

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Figure 14: Data PDF vs. time for VECTOR Run 1302, BURB2, channel 2. Top plot shows best fit K-distribution shape parameter. Vertical dashed line is CPA.

The time-series statistics (scintillation index, SI, and skewness, S) provided additional evidence for non-Rayleigh behaviour, as shown in Table 3. In all cases the SI and S values exceeded the Rayleigh values, although the difference was relatively small (10%). Throughout this run the propeller was operated at its maximum (308 RPM), corresponding to a propeller advance ratio averaging 0.615.

Table 3: Summary of time-series statistics and K-distribution shape parameter averaged over 8 s at CPA for each BURB for Run 1302 (straight-line at 11 knots).

Rayleigh values included in last row for reference.

BURB Speed (knots) Shape Factor SI S

1 11.1 16.74 1.05 0.682

2 11.0 13.6 1.11 0.718

3 11.0 13.3 1.12 0.732

4 11.1 12.9 1.07 0.670

Rayleigh > 25 1.00 0.631

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A definite relationship was observed between the SI and S values, as shown in Figure 15. This shows a clear linear relation between SI and S for values of SI < 1.5 and S < 1.0. This linear portion spanned both sub- and super-Rayleigh conditions. Data with SI > 1.5 corresponded to impulsive transients which were observed in the data PDF (and the raw time-series). These can be ignored as they are assumed not part of the ship signature.

Figure 15: Skewness vs. scintillation index (1-s blocks) for VECTOR Run 1302, BURB 2 for the period ±30 s from CPA. Dashed lines show Rayleigh values.

It is tempting to conclude that there was also a strong relation between data PDF shape parameter and time-series statistics. This turns out to not be the case, as shown in Figure 16. The data show that within the range 0.8 < SI < 1.6 the shape parameter can take on almost any value between 3 and 25, with the slope of the best-fit line close to zero. The small linear regression coefficient also suggests low confidence that there is a linear relation. As in the previous figure, values with SI > 1.6 correspond to data contaminated with impulsive transients.

Figure 16: Scintillation index vs. K-distribution shape factor for VECTOR Run 1302, BURB 2 for the period ±30 s from CPA. Linear fit shown.

4.1.1.3 Propeller Modulation

At speeds near its maximum, the VECTOR signature exhibited clear propeller modulation. Figure 17 shows the full CMC spectrum computed over a 3 s period at CPA (using methods described in

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Section 2.2.2). This spectrogram shows clear blade-rate modulation, with fundamental at 15.4 Hz and two harmonics (31 Hz and 46 Hz). The blade-rate modulation appears strongest from 3–12 kHz, however above roughly 8 kHz there is increasing background interference. There is also a weak shaft-rate modulation, mostly seen in the 5 Hz spacing of higher harmonics. For a 3-bladed propeller 15.4 Hz blade-rate corresponds to shaft rate of 308 RPM, in agreement with the noted engine rate during these straight-line runs. For the VECTOR at 11.0 knots this implies operating at J = 0.612.

Figure 17: Contour plot of CMC frequency vs. modulation for VECTOR Run 1302, BURB4 channel 2 (15 m depth) calculated over 3 s at CPA (17:35:55 UT).

The propeller modulation can be clearly isolated by integrating the CMC over a 2–8 kHz frequency band, with result shown in Figure 18. This clearly shows the 15.4 Hz blade-rate and its first 4 harmonics (31, 46, 62, and 77 Hz). There are also harmonics of the 5 Hz shaft rate, e.g., lines at 21, 26, 36, 41, and 51 Hz. The signal-to-background ratio of the blade-rate fundamental is near 18 (12.5 dB), but decreases for higher modulation harmonics. The ICMC spectra are very similar comparing the two hydrophone depths.

Figure 19 shows the same data examined using the DEMON processing algorithm (as described in Section 2.2.1). Compared to the ICMC the blade-rate modulation is not quite as prominent and the shaft-rate lines are stronger, so that the NB structure looks like a simple 5 Hz fundamental with multiple higher harmonics. The background interference also appears to have greater variance, with a few peaks not present in the ICMC spectrogram (e.g., 8, 29, 39 Hz), resulting in a more cluttered overall display.

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Figure 18: ICMC vs. modulation frequency for VECTOR Run 1302, BURB4 at CPA.

Figure 19: DEMON spectrum from VECTOR Run 1302 BURB4, computed over 3 s at CPA.

4.1.2 SSL and Propeller Rate Variation with Speed

The SSL variation with speed for the VECTOR was previously examined [4], and will only be summarized here. A total of 12 straight run at speeds from 5.5–11.4 knots were conducted during the first two days of operations. In this analysis the SSL(f) was integrated over 120 Hz to 5 kHz to produce a broadband source level (BSL, dB re Pa). This was computed from 5-s averaged SSL at CPA for each buoy. The results across multiple runs and buoys yielded a clear trend of increasing BSL with speed. A linear regression to these data yielded the relation,

�� = 142 + 37.4 ∙ ��[�] . (15)

This regression generated a correlation coefficient of 0.97. This is a slightly weaker speed dependence than specified by Ross (in Equation (2)), likely due to the data spanning a lower range of speeds where the contribution of non-propulsion-related machinery sound was greater. The previous analysis also

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showed that restricting BSL data to speeds of 8 knots and greater, which can be taken as an estimate of the CIS, the best-fit slope was 54.9, which is much closer to the reference.

The CMC analysis described above was used to assess the so-called turns per knot relationship for this ship. For each straight-line pass, observed at multiple buoys, the primary blade rate was extracted, although at the lowest speeds the propeller modulation was weak. The shaft rate is simply the blade rate divided by three. In all the maximum speed runs (11.1–11.5 knots) the blade rate was at a maximum of 15.4 Hz (308 RPM). The overall relation for the VECTOR is shown in Figure 20. The data are well-fit by a simple linear regression, with slope 0.5 turn/s per knot.

Figure 20: Propeller shaft rate (inferred from ICMC analysis) vs. speed for CCGS VECTOR from multiple straight runs.

4.1.3 Variability in PDF and Statistics

While the general characteristics of the data PDF and time-series behaviour were similar to those discussed above (Section 4.1.1.2), there were a few exceptions which must be discussed. Primarily the variations in signal statistics were created by the ship either accelerating or decelerating during the CPA to a given buoy. This was common in the slower speed runs, where the helmsman was constantly adjusting the throttle control to reach a particular speed. The general result of acceleration was to create non-Rayleigh behaviour. For the case of the ship decelerating, the data PDF and statistics exhibited Rayleigh characteristics.

An interesting example occurred during three maximum speed runs on April 13th (Runs 1301, 1302, and 1303). The CPA distances were similar for all three runs. The propeller shaft rate, as determined by ICMC analysis, was the same for all three runs (308 RPM). Runs 1301 and 1303 were northbound with speed (over ground) of 11.4 knots, while Run 1302 was southbound at 11.0 knots. This difference was believed to be due to a small northerly tidal current (0.2 knots); an actual water speed of 11.2 knots can be inferred. Clearly a speed-through-water measurement using an acoustic Doppler speed log should have been recorded to enable a better estimate of advance ratio. However, this tidal current alone should not have pushed the two northbound runs towards more Rayleigh behaviour. Specifically, for Run 1301 the average K-distribution shape factor was 24.9, SI = 0.936, and S = 0.566. For Run 1303 the shape factor was 25.0, SI = 0.948, and S = 0.562. These values are all very close to, but slightly less than, the Rayleigh

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expectations. Run 1302 parameters are given in Table 3, and were concluded to be slightly non-Rayleigh. A very mild acceleration was observed during Run 1302.

4.2 Turning Runs

This section will highlight key results from the turning runs, starting with an example of a maximum in-run speed (near 11.3 knots) 180 turning run. The key differences in these turning runs are that (i) the ship speed drops significantly through the turn, and (ii) the application of the rudder significantly increases the ship signature (see [4]). Because the VECTOR propulsion control maintained propeller shaft rate through the turns, the propeller advance ratio dramatically dropped with ship speed, generating more thrust and hence greater acoustic signature.

4.2.1 Example Run 1404: 180 Starboard Turn at 11.3 Knot In-run

A plan-position plot of the turning manoeuvre is shown in Figure 21. The turning manoeuvres can be described by four primary events, denoted A–D in the plot:

A = start of turn, application of rudder (here 19:39:38UT).

B = minimum speed (here 8.1 knots at 19:40:18UT), rudder returned to amidships.

C = straighten up on final course (here heading 070 True at 19:40:35UT, speed 9.5 knots).

D = return to initial speed (here reached 11.3 knots at 19:41:05UT).

Figure 22 shows the ship speed, turn-rate, and range to each of the four BURBs. The manoeuvre started with the ship heading 255True at 11.3 knots. The final state was ship heading 070 at 11.4 knots. Note that after the initial application of the rudder at event A the ship required some time, approximately 15 s, to reach maximum turn rate. During this time the ship slowed, heeled towards the outside of the turn, and started to slew partially sideways (ship heading leads course over ground by a few degrees). A similar time delay (17 s) was required for the ship to straighten up onto its final course after the rudder was returned amidships. The turn radius was approximately 70 m, with a relatively constant turn rate near 4 deg/s between event A + 20 s and event B + 5 s. The total manoeuvre time (events A to D) was 87 s. The CPA distances from each of the four buoys were 43 m, 21 m, 51 m, and 30 m for BURBs 1–4, respectively. The ship was within 300 m of each buoy for approximately 100 s.

As will be shown below in more detail, the ship propeller shaft rate remained approximately constant during the entire manoeuvre; it was set to the maximum 5.13 revolutions per second or 308 RPM. Thus the propeller advance rate varied with speed from 0.629 at the in-run speed (event A) to a minimum of 0.451 at event B.

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Figure 21: Plan view of VECTOR Run 1404. Events A–D described in text.

Figure 22: Plot of ship speed and turn-rate (relative to ground) and horizontal range to BURBs vs. time for VECTOR Run 1404. Events A–D described in text.

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4.2.1.1 Spectral Levels through Turns

Turning manoeuvres generated increased ship acoustic signature relative to straight-line, constant-speed runs, because of both the changes in in-flow conditions to the propeller and the application of the rudder. As the ship slowed while the engine control maintained a constant shaft rate, the propeller advance ratio (J) dropped, indicating that the propeller was increasingly driven out of equilibrium with its inflow conditions. Propeller thrust and torque generally increase with decreasing J (see Ross [2], Section 8.3). The increased thrust is hypothesized to cause increased cavitation and propeller cyclic modulation. Additionally, cavitation can occur around the rudder. The acoustic signature increases as a function of turn-rate were investigated in an earlier study [4] and will be only summarized here. Generally, after correcting for ship speed and aspect angle dependencies, SSL anomalies up to 15 dB were observed near the minimum speed point (event B). The SSL anomalies were stronger at frequencies of 500 Hz and above, and were concluded to have a linear dependence on turn-rate with slopes from 1.6 to 3.1.

Figure 23: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at CPA for all four BURBs in VECTOR Run 1404, compared to empirical relation due to Ross (Equation (2))

for ship speed of 11.3 knots. Hydrophone depths (upper) 5 m and (lower) 15 m.

The received SSL at CPA observed at each buoy showed significant differences (see Figure 23), due to the CPA times being in different regions of the turning manoeuvre. For example, the B2 signature was taken just after the turn start (event A + 4 s), while the B1 and B3 (at event B + 8 s and event C, respectively) signatures were taken after the minimum speed point. All of the SSL taken after the turn start were approximately 6–10 dB above the reference. In contrast the spectra for B4 (event A - 9 s) were similar to the reference, as this CPA was during the straight in-run prior to the start of the turn. The spectra for B1 and B3 were later in the turn, where the effects of reduced speed (decreases SSL) and increased turn-rate (increases SSL) partially cancelled out. All of the SSL showed strong machinery tonals

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below 1 kHz, and the deeper hydrophone showed larger SSL below 400 Hz due to the Lloyd’s Mirror effect. The SSL for channel 2 showed less spread between minimum and maximum through the turn.

4.2.1.2 Signature PDF and Statistics

For these turning runs the ship signature PDF varied with time depending on the state of the turning manoeuvre, becoming more non-Rayleigh through the highest turn-rate portion. Figure 24 shows the time-variation of the data PDF and best-fit K-distribution shape parameter for the buoy closest to the start of the turn.

Figure 24: Data PDF vs. time for VECTOR Run 1404, BURB2, channel 2. Top plot shows best fit K-distribution shape parameter. Vertical dashed line is CPA and

arrows denote events A to C discussed in text.

During the in-run portion the acoustic signature was Rayleigh distributed ( 25). After event A (start of turn) the data PDF showed a gradual increase in occurrence of higher-amplitude (> 3) signals and a decrease in peak amplitude, creating a decrease in the best-fit K-distribution shape parameter indicating non-Rayleigh behaviour. At 63 s (event A + 16 s) there was a strong increase in the higher amplitude (> 4) portion of the signal which lasted until event B (minimum speed, rudder returning to amidship). This corresponded to the highest turn-rate portion of the manoeuvre (see Figure 22). During this period signals with normalized amplitude > 6 occurred at the 0.1% level. This is distinctly different from the straight-line runs (see Figure 14) where signals were confined to normalized amplitudes < 4. The data

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PDF showed non-Rayleigh behaviour ( = 5–10) over the period 53–79 s, however the fits had relatively

high 2 values (> 0.01) from 63–87 s, suggesting that the K-distribution was not a good match to the data

PDF. After the rudder was returned amidships (at event B) the strong, high-amplitude tail of the data PDF

disappeared, with the PDF returning to Rayleigh distributed. After event B the best-fit 2 values returned

to acceptable levels (< 10-3). There was no change in behaviour at event C (straight course, accelerating). The other BURBs showed similar behaviour.

The increased presence of high amplitude signature components during the high turn-rate portion of the manoeuvre suggests the presence of a second, supplemental sound generation mechanism. These higher amplitude signature components could not be fit with a single K-distribution, thereby creating the larger

2 goodness of fit values. Figure 25 shows more detailed data vs. model comparisons at two points in the

turning manoeuvre. Just at the start of the turn (Figure 25 left) the signature was definitely non-Rayleigh ( = 10.2), with a good match to the data up to amplitudes of 3.2. In contrast the data PDF just after event B (minimum speed, see Figure 25 right) showed significant excess at normalized amplitudes from 3 to > 8. This is on top of strongly non-Rayleigh behaviour ( = 3.9) exhibited at lower amplitudes (< 3), suggesting the presence of a secondary process. Note that in Figure 25 (right) there is an inflexion point in the data PDF near amplitude of 3, which cannot be matched by the K-distribution. This high-amplitude signature excess was consistent in both hydrophone channels.

Figure 25: Comparison of data and best-fit model PDF for VECTOR Run 1404 for an 8 s period at CPA. (left) BURB2 at event A + 5 s, (right) BURB1 at event B + 5 s.

In Figure 25 the presence of this secondary process can be modelled using a mixture model combining the log-normal and K-distributed model, i.e.,

�� = � ∙ �� + (1 − �) ∙ �� , (16)

where is the mixing ratio (in this example 10%) and

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�� = �√2� ∙ � ∙ ��

�� (� ��⁄ )�

�� , (17)

with xc and w the log-normal centre and width parameters, respectively. The log-normal distribution is a reasonable match to the data PDF at normalized amplitudes from 3 to 8. The physical explanation for this hypothesized secondary generation mechanism is not known at this time. It is speculated to be due to some stronger type of propeller or rudder cavitation that only occurs during the application of maximum rudder.

This excess high-amplitude signature also had a strong effect on the time-series statistics SI and S (see Figure 26). Similar to the signal amplitude PDF, the statistics showed a strong increase between 63–79 s, coincident with the high turn-rate portion of the turn. The SI statistic showed values up to 11, much larger than exhibited in earlier/later parts of the turn and significantly larger than values up to 1.5 observed in straight-line runs (see Figure 15).

Figure 26: Time variation of scintillation index and skewness for VECTOR Run 1404, BURB2. CPA at 51 s. Arrows denote events A to C discussed in text.

Figure 27 shows the relationship between SI and S for this example. Outside of the high turn-rate region, at SI < 2.5 and S < 2.0, the relationship was approximately linear and similar to behaviour previously observed in straight-line runs (see Figure 15). Within the high-turn region, for SI > 2.5 and S > 2.0, the relationship was again linear but with a much smaller slope. This change in behaviour provides further support for the hypothesis that a secondary sound generation mechanism was present.

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Figure 27: Skewness vs. scintillation index (1-s blocks) for VECTOR Run 1404, BURB 2 for the period 120 s period covering start of turn. Dashed lines show

Rayleigh values. Red lines show hypothesized bi-linear relationship.

4.2.1.3 Propeller Modulation

The VECTOR signature during this turning run exhibited clear propeller modulation, the strength of which depended on the manoeuvring state. Figure 28 shows the time variation of the ICMC spectrum computed (using methods described in Section 2.2.2) over the entire manoeuvre (events A–D) for BURB3. This figure shows clear blade-rate modulation, with fundamental at 15.4 Hz and two harmonics (31 Hz and 46.5 Hz). For a 3-bladed propeller a 15.4 Hz blade-rate corresponds to 308 RPM, which was the usual maximum observed for this ship. There was also a weak shaft-rate modulation, seen at 5 Hz with multiple higher harmonics. The modulation frequencies were constant in time over the entire manoeuvre, in spite of the strong changes in ship speed and turn rate. It is presumed that the propulsion control system adjusted the throttle to maintain constant shaft rate.

Figure 28: ICMC modulation frequency vs. time for VECTOR Run 1404 BURB3 channel 2.

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Note that the strength of the modulation increased within two periods. The first (26–36 s) started with the initiation of the turn (event A). The second period (45–70 s) spanned the minimum speed, high turn-rate portion of the turn (up to event B). The CPA to BURB3 at 84 s was coincident with event C (straighten up). The blade rate modulation continued through the straight out-run acceleration to event D, at 114 s, and beyond.

4.2.2 Example Run 1308: 110 Port Turn at 11.3 Knot In-run

The statistical behaviour described above was not limited to 180 turning runs. Figure 29 shows the ship speed and range for an example 110 turning manoeuvre. Events A–D (as defined previously) are shown. The manoeuvre started with the ship heading 143 True at 11.3 knots. The final state was ship heading 252 at 11.0 knots, after which the ship slowed. The CPA to BURB 1 occurred after the turn, as the ship was returning to full speed on the new heading. Similar to the 180 turn described in the previous section, after the initial application of the rudder at event A the ship required approximately 20 s to reach maximum turn rate and minimum speed. The turn rate (not shown) increased to a maximum near 4.8/s just prior to event B, then dropped away to less than 0.5/s by event C. The total manoeuvre time (events A to D) was 76 s. Similar to the previous 180 turn, the ship propeller shaft rate (from CMC analysis) remained constant during the entire manoeuvre; it was set to the maximum 5.13 Hz or 308 RPM. Thus the propeller advance ratio varied from 0.629 at the in-run speed (event A) to a minimum of 0.474 at event B. There were strong modulation bursts at event A + 6 s and event B - 6 s.

Figure 29: Plot of ship speed and turn-rate (from GPS) and horizontal range to BURB 1 vs. time for VECTOR Run 1308, a 110 turning run at 11.3 knots in-run. Events A–D described in text.

Similar to the previous example the ship signature PDF varied with time depending through this turning manoeuvre, becoming more non-Rayleigh through the highest turn-rate portion. Figure 30 shows the time-variation of the data PDF and best-fit K-distribution shape parameter.

During the in-run portion of the manoeuvre (up to 128 s) the signature was Rayleigh distributed ( 25). After event A the data PDF showed a strong increase in higher-amplitude (> 3) signals and a slight decrease in peak amplitude, generating a decrease in the best-fit K-distribution shape parameter indicating non-Rayleigh behaviour. At 144 s (event A + 17 s) there was a strong increase in the higher amplitude portion of the signal. This lasted until 154 s (event B + 4 s) when the rudder was returned to amidship. The data PDF showed non-Rayleigh behaviour ( = 3–14) over the period 130–155 s, with two distinct

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minima. The fits had relatively low 2 values (< 2 x 10-3) in the first minimum from 132–140 s, but were

higher (> 0.01, indicating behaviour not following K-distribution) in the second minimum from 144–154 s. This latter period corresponded to the highest turn-rate portion of the manoeuvre, with turn-rates near 4.8/s. During this period signals with normalized amplitude > 6 occurred at the 0.1% level. These two periods of K-distribution shape minima also corresponded in time to strong modulation bursts observed in the ICMC vs. time analysis. After the rudder was returned amidships (at event B + 4 s) the strong, high-amplitude tail of the data PDF disappeared, with the statistical behaviour returning to Rayleigh distributed. There was no change in behaviour at event C (straight course, accelerating). The drop in near 185 s was due to ship wave transients interacting with the buoy.

Figure 30: Data PDF vs. time for VECTOR Run 1308, BURB1, channel 2. Top plot shows best fit K-distribution shape parameter. Vertical dashed

line is CPA and arrows denote events A to C discussed in text.

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Figure 31: Comparison of data and best-fit model PDF for VECTOR Run 1308, BURB 1, for an 8 s period near the point of maximum turn rate.

Figure 31 shows the data PDF and model fits for the high-turn-rate portion (144–152 s) of this manoeuvre. This shows a strong occurrence of high-amplitude (> 3) signals, in this case exceeding normalized amplitudes of 8 with PDF level > 1 x 10-4. The data PDF is reasonably well fit by the K-distribution up to normalized amplitudes of 3, showing strongly non-Rayleigh behaviour ( = 4.1). However, the data PDF at amplitudes > 3 greatly exceed the K-distribution model in both hydrophone channels, with an inflexion point at amplitude near 3, suggesting a second sound generation mechanism best modelled using a log-normal distribution. This strongly non-Rayleigh behaviour was consistent in both hydrophone channels. All of these characteristics are the same as in the 180 turning manoeuvre examined previously (see Figure 25 right).

This excess high-amplitude signature also had a strong effect on the time-series statistics SI and S. This is shown in Figure 32. The statistics revealed two peaks, with the second peak (between 144–154 s) exhibiting a strong increase coincident with the high turn-rate portion of the turn. The SI statistic shows values up to 8.5, similar to the large values seen in the 180 turning run (see Figure 26) but distinctly different from the straight-line runs. The relationship between SI and S was similar to that shown for the 180 turning manoeuvre (see Figure 27).

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Figure 32: Time variation of scintillation index and skewness for VECTOR Run 1308, BURB1. Vertical dashed line shows CPA at 180 s. Arrows denote events A to C discussed in text.

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5 CFAV QUEST Sea-Trials, Sept. 2005

This section summarizes analysis results from sea-trials with the CFAV QUEST on 25 Sept. 2005 in Emerald Basin (Scotian Shelf). A total of 21 separate runs were conducted, including multiple straight-line runs at 6, 8, 10, 12, and 13.5 knots, two accelerating runs, and five turning runs. For runs at 10 knots and below the QUEST was operated on one main engine; runs at higher speed and in manoeuvres used two main engines. Due to the open ocean environment in which the data was collected, the background noise levels were slightly higher (relative to VECTOR measurements), especially for the shallower (5 m depth) hydrophone. Due to generally larger CPA distances (100 m) the shallow hydrophone also suffered from strong Lloyd’s Mirror attenuation at frequencies below approximately 2 kHz. The higher background noise coupled with the significantly lower acoustic signature of the QUEST (especially on one engine) and generally larger CPA distances created poor signal-to-noise conditions for the lower-speed runs (10 knots and below). Thus, this section will focus only on higher speed and manoeuvring runs for BURB channel 2 hydrophone (at 20 m depth).

5.1 Straight-Line Constant-Speed Runs

5.1.1 Spectral Source Levels

The observed acoustic signature of the QUEST was significantly lower than that of the VECTOR, as shown for example in Figure 33 with a straight-line run at 12 knots. Overall the observed SSL was 10–14 dB less than the reference curve due to Ross (Equation (2)), and only about 10 dB above the self-noise floor at higher frequencies. Recall that the VECTOR signature was in close agreement with the Ross reference (see Figure 12). Furthermore, the QUEST signature lacked the prominent NB tonals of the VECTOR signature, due to special vibration isolation of QUEST machinery. The QUEST signature had a consistent LF peak near 400 Hz, with a weak secondary peak near 800 Hz and a weak drop-out at 850 Hz. The SSL from both BURBs were in close agreement over the entire frequency span.

In Run09 the CPA distances to B3 and B4 were near 90 m, so that the first two predicted Lloyds Mirror peaks for this hydrophone geometry were 470 Hz and 1.4 kHz, with a null near 900 Hz. The uncorrected SSL data exhibited a clear peak at 400 Hz with nulls at 200 Hz and 900 Hz.

The SSL behaviour was similar at the maximum ship speed (see Figure 34). Overall the observed SSL was 7–12 dB less than the reference curve due to Ross (Equation (2)), with a similar absence of clear NB machinery tonals. The measurement signal-to-noise levels were in excess of 16 dB. The SSL curves for the two buoys were generally in close agreement, except for differences in the 100–400 Hz range due to Lloyd’s Mirror effects with differing CPA distances (B3 122 m; B4 57 m).

Acoustic signature power spectral measurements were difficult to make at speeds of 10 knots and lower due to the low SSL of the QUEST and the relatively large CPA distances (100 m). The measurement signal-to-noise levels were roughly 6 dB or less.

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Figure 33: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at CPA for B3 and B4 for QUEST Run 09, compared to empirical relation due to Ross (Equation (2))

at ship speed of 12.0 knots. Hydrophone depth was 20 m.

Figure 34: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at CPA for B3 and B4 for QUEST Run 12, compared to empirical relation due to Ross (Equation (2))

at maximum ship speed of 13.7 knots. Hydrophone depth was 20 m.

5.1.2 Signature PDF and Statistics

For these straight-line, maximum speed runs the QUEST signature amplitude PDF exhibited clearly non-Rayleigh behaviour, with in some cases substantial levels of higher amplitude (4–8) signature components. Figure 35 shows two data PDF at CPA for a straight-line, maximum speed run at 13.7 knots (Run 12). In both cases the data PDF are better matched by the K-distribution rather than Rayleigh model, at least up to normalized amplitudes of approximately 4.0. These best-fit K-distribution shape parameters ( = 4.0, 2.75) indicate non-Rayleigh behaviour. These values are also slightly lower than those extracted from the VECTOR data (see Figures 13 and 14). In the B3 data PDF there is suggestion of a secondary,

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log-normal distributed process appearing at normalized amplitudes > 4. It is unclear whether this is a characteristics of the ship signature or an artifact of the background noise. The fact that this higher amplitude component does not appear in the B4 data supports the latter explanation. For the B4 data the

best-fit 2 value was sufficiently small (< 10-3) that this could be concluded as statistically significant.

For the B3 data (Figure 35 left) the2 value was slightly higher (2.3 x 10-3), but the KS significance p-

value for this was 0.999, so it can also be considered a valid fit.

Figure 35: Comparison of data and best-fit model PDF for QUEST Run 12 (straight pass at 13.7 knots) for an 8 s period at CPA. (left) B3, (right) B4.

The time-series statistics (SI, S) also showed non-Rayleigh values. For the same CPA data period as shown in Figure 35, for channel 2 (20 m hydrophone), the SI values were 1.68 ±0.3 and 1.86 ±0.4 for B3 and B4 respectively. The corresponding S values were 1.19 ±0.2 and 1.20 ±0.3. These are all clearly larger than the Rayleigh values (SI = 1.0, S = 0.631).

Lower speed (10, 12 knots) straight runs were also examined, but the PDF data were found to be contaminated by acoustic transients believed to due to wave impacts on the buoy hulls. The reduced SSL of the QUEST at these lower speeds, combined with the relatively large CPA distances (> 100 m), produced unreliable PDF and time-series statistics results.

5.1.3 Propeller Modulation

The measurement of propeller shaft rates on the QUEST during this sea-trial allowed validation of the CMC analysis. During the straight-line runs the propeller shaft rate was constant, with little port-starboard difference, and the average was found to be in close agreement with the CMC analysis. Figure 36 shows an example from Run 12 (at 13.7 knots). During this run the average (in time and port-starboard) shaft rate was 136 ±1 RPM, corresponding to an Advance Ratio of 1.0 ±0.008. The figure shows a first blade rate line (both BURBs) at 11.3 Hz, with weaker 2nd and 3rd harmonics at 22.6 Hz and 33.9 Hz. For a 5-bladed propeller this blade rate corresponds to a shaft rate of 136 RPM. There was no clear evidence for a shaft rate modulation, which would appear near 2.3 Hz.

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Figure 36: ICMC vs. modulation frequency for QUEST Run 12, B3 and B4 at CPA.

A similar ICMC analysis found for Run 09, a 12 knot straight pass, a clear blade rate peak at 10.0 Hz, with a weaker 2nd harmonic at 20.0 Hz. During this pass the average propeller shaft rate was 118 ±1 RPM, equivalent to 9.8 Hz blade rate. Since the modulation frequency resolution of the ICMC analysis is 0.33 Hz, these are also in agreement. No blade-rate peaks were found in QUEST runs at speeds of 10 knots and below. This was likely due to the combination of weak propeller cavitation and low measurement signal-to-noise at the lower ship speeds.

5.2 Straight-Line Accelerating Runs

Accelerating manoeuvres were found to generate significant excess acoustic signature levels. In these manoeuvres the QUEST approached the line of buoys at 6 knots. At CPA to the first buoy the ship began maximal acceleration to speed in excess of 13 knots, continuing on a straight heading past the last buoy. Two of these manoeuvres were performed, with similar results.

Figure 37 shows the ship speed, range to buoys, and propeller parameters for one of the acceleration runs. The in-run was at 6.3 knots, with the acceleration up to 13 knots requiring 105 s. The acceleration was clearly not linear, with stronger acceleration in the early part of the manoeuvre. For this accelerating manoeuvre three key events can be identified:

A: start of acceleration and CPA to B3, at 16:45:11 (UT).

B: minimum propeller advance ratio, at 16:45:28 (+17 s after A).

C: ship reached advance ratio J = 0.90, at 16:46:30 (+79 s after A).

Two buoys (B3 and B4) were selected for analysis because their CPA were located close to events A and C. The CPA were both near 135 m, with the CPA to B4 occurring 72 s later than at B3. Over this period the ship increased speed from 6.3 knots to 12.7 knots.

The propeller shaft rate during the in-run (averaged over 1 minute prior to A) was 63 ±2 RPM, corresponding to J = 1.03 ±0.02. At event A the propeller shaft rate rapidly increased, inducing a dramatic drop in J and generating increased propeller thrust. The minimum advance ratio (event B) was near 0.585

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at a shaft rate of 125 RPM. After event B the propeller shaft rate increased asymptotically to the maximum of 138 RPM by event C, with the advance ratio returning to 1.0.

Figure 37: Plot of run parameters for QUEST Run 15, a straight acceleration from 6 to 13 knots. (upper) ship speed and horizontal range to B3 and B4 vs. time;

(lower) propeller shaft rate and advance ratio. Events A–C described in text.


This acceleration by the QUEST greatly increased the SSL, as shown in Figure 38 with a comparison of the SSL at the three manoeuvre events. Prior to event A the QUEST signature was undetectable; the B3 signal was dominated by background noise at this slow ship speed. In this example the SSL at events A + 8 s and B + 10 s were very similar, and exceeded the Ross reference curve by 4–6 dB at frequencies above 1.5 kHz. This was a big increase in SSL relative to straight, constant speed at 13.7 knots (see Figure 34). Specifically, the accelerating SSL exceeded the constant speed case by 15 dB and 16 dB at 2 kHz and 4 kHz, respectively. There was also much stronger SSL at the lowest frequencies (< 400 Hz), in spite of the Lloyds Mirror attenuation. By event C, 75 s after the acceleration start, the SSL had dropped by approximately 10 dB relative to event A, but was still roughly 6 dB above the constant speed case. Similar to the straight, constant speed runs the QUEST signature still lacked any prominent NB tonals.

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Figure 38: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at 3 times for B3 and B4 during QUEST Run 15, a straight acceleration pass. Spectra are compared to empirical relation

due to Ross (Equation (2)) at ship speed of 14.0 knots. Hydrophone depth was 20 m.


The signature amplitude PDF for this acceleration manoeuvre were similar to those exhibited during straight, constant speed manoeuvres. Figure 39 shows a comparison of the data PDF with their best-fit K-distributions for the three events identified in Run15. All three are very similar, with clearly non-Rayleigh behaviour. The best-fit K-distribution shape parameters were in the range 7.4 to 11.1, with statistically valid fits. Events B and C showed greater occurrence of signals with amplitude > 4.0, yet event A had the smallest K-distribution shape factor.

Figure 39: Data PDF for QUEST Run 15, straight accelerating run, compared to best-fit K-distributions for events A, B, C (as discussed in text). Rayleigh curve best-fit to event A data.

The time-series statistics SI and S were both greater than the expected Rayleigh values. Specifically the SI at events A, B, and C were 1.21, 1.56, and 1.43, respectively (all ±0.2). The corresponding S values were

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0.81, 1.06, and 1.03 (all ±0.1). These suggest that the signature at event B showed the greatest deviation from Rayleigh behaviour. These were all clearly larger than the Rayleigh values (SI = 1.0, S = 0.631).


During the accelerating runs the ICMC short-period (3 s) analysis tracked the time-variation in propeller shaft rate, as shown in Figure 40. During the in-run the propeller shaft rate was 63 RPM, corresponding to a blade rate of 5.3 Hz. However, the ICMC analysis showed no modulation peaks until after the shaft rate started rapidly increasing. At the in-run speed (6.3 knots) it can be assumed that the QUEST propellers did not cavitate. The first clear modulation appeared at event A + 8 s, which showed a blade rate peak at 7.6 Hz, corresponding to shaft rate of 91 RPM. Somewhere in this 8 s period the propellers started to cavitate. At this specific time (event A + 8 s) the measured shaft rate was 89 RPM, but was rapidly increasing. The propeller advance ratio at this time was near 0.7. By event B + 10 s (in Figure 40) the ICMC blade rate had increased to 10.7 Hz (shaft rate 128 RPM). This agrees with the measured shaft rate (130 RPM) at this time. By event C - 6 s the ICMC blade rate had increased to 11.7 Hz (140 RPM), compared to the measured shaft rate of 138 RPM.

Figure 40: ICMC vs. modulation frequency for QUEST rn 15, at events A, B, C. Arrows denote identified blade rate modulation.

5.3 Turning Runs

Aggressive turning manoeuvres with QUEST were also found to generate high acoustic signature levels with associated propeller blade rate modulation and non-Rayleigh characteristics. A total of five turning runs, either through 90 or 180, were conducted. Run 21 (plan view shown in Figure 41) presents a good example for analysis. In this Run the ship passed the line of buoys in a straight, constant speed near 13.6 knots, then turned to port with maximum helm (32 rudder angle) when abeam of last buoy (B4). This placed B4 near the centre of the manoeuvre, so that only data from a single buoy need to be examined. The QUEST engine control remained at maximum power throughout the turn. The following events can be defined.

A: start of turn, ship at 13.6 knots, range to B4 = 200 m, 18:16:35.

B: minimum speed, ship at 9.1 knots, range to B4 = 200 m, 18:17:15 (A + 40 s).

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C: rudder amidships, ship at 11.5 knots, range to B4 = 98 m, 18:18:00 (A + 85 s).

D: reach original speed, range to B4 = 347 m, 18:18:55 (A + 140 s).

Figure 41: Plan view of QUEST Run 21, a 180 port turn at maximum in-run speed. Events A–D described in text.

The ship speed, range to B4, and propeller parameters are shown in Figure 42. At the turn start the ship was at maximum speed of 13.6 knots with propeller shaft rate of 136 ±1 RPM and J = 1.00 ±0.01. The QUEST required roughly 20–30 s to transition into a turn, during which time the ship slowed, heeled towards the outside of the turn, and started to slew partly sideways, resulting in the ship gyro heading leading the course over ground by a few degrees. Moving the rudder from amidships to maximum port turn required approximately 15 s. As the helm was applied the ship lost speed and the port and starboard propeller shaft rates also decreased and diverged, with the starboard (outer) propeller shaft rate dropping more than the port (inner) propeller. The point of minimum shaft rate was not coincident with the minimum advance ratio, but both were within a few seconds of event B (minimum speed point). The minimum shaft rates were port 123 RPM and starboard 103 RPM at event B - 4 s. The minimum advance ratios were port 0.636 and starboard 0.745 at event B + 7 s. After event B the rudder was slowly eased over the next 45 s, allowing the ship to begin straightening out and accelerate. By event C the ship had accelerated to 11.5 knots, with the propeller shaft rates returning to near pre-turn levels (port 135 RPM, starboard 130 RPM). However, at event C the propeller advance ratios (near 0.8) were still below normal cruising levels, generating the excess thrust needed to get the ship up to full speed. By event D the ship was following a straight course with the averaged propeller shaft rate 138 RPM, slightly higher than during the in-run.

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Figure 42: Time-series of run parameters for QUEST Run 21, a 180 port turn at maximum in-run speed. (upper) ship speed and horizontal range to B4 vs. time; (lower)

propeller shaft rate and advance ratio. Events A–D described in text.


This aggressive turning manoeuvre by the QUEST greatly increased the SSL, as shown in Figure 43 with a comparison of the SSL at 5 points during the manoeuvre. Prior to event A the QUEST signature was relatively low, and similar to the SSL measured during other straight, constant speed runs near 13.7 knots (see Figure 33). By 20 s after event A the SSL had jumped by 16–18 dB relative to the in-run condition across the entire frequency band. The SSL was reduced slightly by event B, when the ship was turning but at a reduced speed (9.1 knots). The SSL continued to decrease as the ship transitioned back to a straight heading at event C, but was still above the in-run condition at 20 s prior to event D. In all of these spectra there was a consistent peak and null feature at 800–1000 Hz, which was also seen weakly in the straight, constant speed runs.

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Figure 43: SSL (dB re Pa2/Hz at 1 m) spectra averaged over 8 s at 5 times through QUEST Run 21, a 180 turning manoeuvre. Spectra are compared to empirical relation due to Ross (Equation (2))

at ship speed of 13.6 knots. Hydrophone depth was 20 m. Events A–D described in text.


Similar to turning manoeuvres with the VECTOR, the PDF characteristics for the QUEST depended on the ship manoeuvring state during the turn. Figure 44 shows a time-series of the PDF and best-fit K-distribution shape factor during this turning manoeuvre. In this plot the data PDF were calculated over 1-s blocks of acoustic data. However, the hydrophone data suffered from increased interference from impulsive transients, likely due to surface wave impacts on the buoy or hydrophone cable tugging, but it is also plausible that some of these transients were part of the ship signature. When computed on short time-scales (1 s) the presence of these transients became more prominent, biasing the PDF towards more non-Rayleigh characteristics. Thus, in the calculation of the best-fit K-distribution shape parameter, the data PDF were first averaged over a 5-s running window. While there remains some interference from transients, a few relatively unaffected (clean) periods, 5–10 s in duration, with approximately constant PDF characteristics can be seen.

During the in-run (focusing on the relatively constant PDF from -26 s to -20 s) the best-fit K-distribution

showed close to Rayleigh characteristics ( averaging 19.8) with 2 less than 1 x 10-4 (i.e., a statistically

valid fit). This K-distribution shape parameter was larger than previous straight-ahead results (e.g., Figure 35, 2–5), probably as a result of this present measurement being taken 20 s before CPA, at bow aspect angles where the propeller signals might have been partially blocked by the ship’s hull.

During the actual start of the turn near event A (±10 s) the data PDF became highly variable and strongly non-Rayleigh, with best-fit near 2. This was similar to previous maximum-speed, straight-ahead runs at CPA (see Figure 35). During this period the ship also passed through a first CPA, thereby transitioning to a near-broadside aspect and exposing the propellers more directly to the hydrophone. There was a strong increase in high amplitude (> 4) portions of the signature from event A + 10 s up to event B, coincident with maximum helm being applied. Between event A + 10 s and event B - 3 s the PDF showed moderately non-Rayleigh characteristics, with averaging 7.6 ±2. This is similar to values observed during straight, accelerating runs (see Section 5.2.2). Between Events B and C there were several clean

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periods of data PDF with similar shape factors (10 < < 15). The clean patch between 96 s and 107 s showed slightly non-Rayleigh characteristics, with averaging 17 ±5. Finally, a short clean patch near 120 s (event C + 35 s) showed Rayleigh distributed behaviour ( 25). This is surprising since the ship was still accelerating at this time, with J 0.9, and the buoy was located on the stern quarter of the ship (i.e., no hull blockage).

Figure 44: Data PDF vs. time for QUEST Run 21, B4, channel 2. Top plot shows best fit K-distribution shape parameter. Arrows denote events A to D discussed in text.

The ship manoeuvring state also had a strong effect on the time-series statistics SI and S, as shown in Figure 45. Overall, the SI statistic showed values typically from 1 up to 5, with two stronger transients at 26 s and 31 s. The S statistic was typically in the range 0.5 to 4. Both of these showed maxima that were much larger than the corresponding Rayleigh distribution values (SI = 1.0, S = 0.631).

Since the hydrophone data were known to be contaminated by transients believed due to wave impacts on the buoy, a focus on a few relatively clean periods is appropriate. During the in-run (clean period from -26 s to -20 s relative to event A) the SI and S values were close the Rayleigh expectation, in agreement with the PDF-based results discussed above. Between event A + 10 s and event B - 3 s the PDF data (Figure 44) were relatively clean with moderately non-Rayleigh characteristics. However, the SI and S statistics through this period exhibited large variability. Between events B and C there were several clean periods of data PDF, for example between 96 s and 107 s the statistics showed slightly

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non-Rayleigh characteristics. The average values of SI and S in the period 94–102 s were 1.37 ±0.2 and 1.00 ±0.2, respectively. Finally, a short clean patch near 120 s showed Rayleigh distributed behaviour with SI and S values of 1.08 ±0.2 and 0.69 ±0.2, respectively.

Figure 45: Time variation of scintillation index and skewness for QUEST Run 21, B4. Events A to D discussed in text.


During this turning manoeuvre there was a significant difference in shaft rate between the port and starboard propellers (see Figure 42); it was not immediately clear which would dominate the propeller modulation effects. The starboard propeller shaft rate dropped more strongly during the turn (see Figure 42, lower). A detailed ICMC analysis was conducted for Buoy 4, as it was located near the centre of the turn. Short time-averages of ICMC are presented in Figure 46.

Figure 46: ICMC modulation frequency vs. time (6 s averages) for QUEST Run 21, B4 channel 2. Events A to D discussed in text.

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During the straight in-run period (before start of turn at event A) the ICMC result showed a clear blade rate modulation at 11.3 Hz (136 RPM), with 2nd and 3rd harmonics at 22.6 Hz and 34.1 Hz. This is in close agreement with the measured shaft rate before the turn. During the initial parts of the turn, from event A + 5 s to event B (minimum speed), there was no clear ICMC blade rate signal. This is hypothesized to be due to the significant difference between the port and starboard shaft rates during this period and the rapid time rate-of-change of both. Recall that the ICMC was calculated over a sliding 3 s window, so that if the modulation rates changed significantly over a 3 s period the energy would have been smeared over adjacent frequency bins. At the minimum speed point (curve B + 5 s in Figure 46) the blade rate peak reappeared at 9.3 Hz (112 RPM), which is close to the measured shaft rate for the starboard propeller. The ICMC estimated blade rate continued to increase as the ship accelerated out of the turn: at event B + 35 s the blade rate was 10.7 Hz (128 RPM) and at event C + 20 s the blade rate was 11.1 Hz (133 RPM). These are similarly in agreement with the shaft rate for the starboard propeller. Finally, by event D the estimated blade rate returned to the nominal maximum straight-line value of 11.4 Hz (137 RPM) with weak 2nd and 3rd harmonics. In the event D result a weak shaft rate (one-fifth of blade rate) can also be seen at 2.3 Hz.

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6 Summary Discussions

This report has examined ship acoustic signature amplitude statistics and statistical distributions. The objective was to explore the hypothesis that ship signatures exhibit amplitude fluctuations that are different from Rayleigh-distributed ambient ocean noise. Signature measurements from two different ships, one with a single, 3-bladed propeller and the other with twin 5-bladed propellers, conducting a variety of manoeuvres were examined. A key feature of a ship acoustic signature at higher speeds was found to be the broadband amplitude modulation generated by propeller cavitation, and this was generally found to be associated with non-Rayleigh acoustic signature characteristics. This report was focused on those conditions where strong propeller cavitation and signal modulation occurred, specifically during maximum speed runs, accelerations, and turning manoeuvres. Clear non-Rayleigh amplitude time-series statistics and PDF were observed associated with propeller modulation.

The practical significance of this result is twofold. Since ship signatures (including nearby consort ships in a task group) can be an important contributor to background noise, a consequence of this result is that sonar detection thresholds may need to be increased relative to values calculated assuming Rayleigh distributed noise. If the actual background noise contains more frequent, high-amplitude components, the assumption of Rayleigh statistics may lead to excess false alarms. This is primarily important for VLF passive sonars such as towed arrays and sonobuoys. On the threat detection side, there is potential application of these findings in automated sonar detectors and classifiers. Simple time-series statistics, such as SI and S, can be included as features in automated threat classifiers, including use in modern artificial intelligence algorithms. For example, propeller cavitation statistics greatly exceeding Rayleigh may be associated with a shallow-running torpedo, as opposed to signals with lower SI and S associated with nearby consort ships.

Three advanced processing concepts were newly applied to ship signature analysis. The first was Cyclic Modulation Coherence, based on theoretical work by Antoni and Hansen [11]. This was found to produce better estimates of propeller shaft and blade rate modulation than the well-known DEMON technique. Secondly, the calculation of signature amplitude PDF and fitting of the K-distribution model were successful in identifying ship signatures exhibiting non-Rayleigh characteristics. Finally, higher-order time-series statistics SI and S were also found to be sensitive indicators of non-Rayleigh signature characteristics.

Simple numerical experiments were used to establish a link between propeller modulation of the broadband ship signature and non-Rayleigh characteristics. Synthetic broadband ship noise signals based on white random-noise, with varying degrees of LP filtering and spectral shaping, always showed close to Rayleigh-distributed behaviour. Non-Rayleigh behaviour only appeared when propeller shaft- and blade-rate modulation was applied.

In both the VECTOR and QUEST measurements, accelerating and turning manoeuvres were found to generate a significant increase in ship SSL relative to straight-line transits at the same speed. Typically up to approximately 15 dB broadband SSL excess was observed associated with maximal acceleration or turning manoeuvres. This suggests that strong propeller cavitation occurred during these manoeuvres, which was verified by the simultaneous presence of strong broadband propeller blade-rate modulation extracted from the CMC analysis. For both ships the blade-rate modulation was stronger than the shaft-rate modulation, the latter being frequently absent. It was common for 2nd and 3rd harmonics of the

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blade-rate to be observed. Also, during turns evidence likely due to rudder cavitation was also seen. These results are not new or surprising, but the measurements shown herein provide additional validation of this mechanism. What is new here is the association of this SSL excess during manoeuvres with non-Rayleigh signal amplitude characteristics.

While both ships exhibited qualitatively similar acoustic signature statistical behaviour, the differences between the ship size, propellers, rudder, and propulsion control need to be emphasized. The QUEST was specifically designed to reduce acoustic signature whereas the VECTOR was not, resulting in the QUEST being roughly 12–15 dB quieter (reduced BB SSL) at speeds near 12 knots. In addition to the propeller differences, the QUEST was roughly twice as long with four times the displacement, hence having a much larger turning radius. The QUEST maximum speed was near 13.5 knots while the VECTOR maximum speed was near 11.5 knots. The steady state propeller advance ratios were also significantly different: VECTOR near 0.61 and QUEST near 1.0. QUEST had two rudders while VECTOR had one. The propulsion control was also different, exhibiting different behaviour during turns: VECTOR varied engine power to maintain constant shaft rate while QUEST applied constant power letting the propeller shaft rate vary differently for the two shafts. It is likely that the VECTOR propeller was more strongly cavitating during the turning manoeuvres. QUEST also showed only minimal presence of the log-normally distributed secondary process observed with VECTOR, hypothesized to be generated by rudder cavitation.

The following specific results can be derived from the detailed sea-trial analyses:

From the CCGS VECTOR sea-trials:

Both the ambient noise and low-speed (< 10 knots) ship runs showed Rayleigh signal characteristics and only minimal propeller modulation (as determined from the CMC analysis). This suggests that at lower speeds the ship’s propeller was only weakly cavitating. However at maximum speed and during turning manoeuvres, the ship SSL greatly increased, propeller shaft- and blade-rate modulation appeared, and non-Rayleigh signal amplitude characteristics were observed. The latter aspect was seen by both the signal amplitude PDF showing smaller K-distribution shape factors ( 5–10) and the SI and S statistics exceeding their Rayleigh values (SI > 1.0 and S > 0.631).

During straight line passes at maximum speed, slightly increased non-Rayleigh behaviour was observed after CPA, when the full acoustic signal arrived directly from the propeller and was not partially blocked by the ship’s hull.

At maximum turn rates, starting approximately 15 s after the start of the turn, PDF analyses showed the presence of secondary process at higher relative amplitudes. This secondary process showed PDF values roughly 10% of the main signal process, and was consistent in shape with a log-normal distribution. A combination signal model, being a weighted sum of a K-distribution and a log-normal distribution, was proposed to account for this behaviour. The occurrence of this secondary process was associated with greatly increased time-series statistics (SI and S), typically 10 times greater than Rayleigh expectations. It was observed that this higher-amplitude secondary process disappeared when the rudder was returned to amidships to bring the ship out of the turn. All this supports a hypothesis of rudder cavitation being the source of this secondary process.

For straight, constant speed runs a clear linear relationship was observed between the SI and S, spanning both sub- and super-Rayleigh conditions for values of SI ≤ 1.5 and S ≤ 1.0. In turning manoeuvres a bi-linear relation between SI and S was observed (see Figure 15). Outside of the high

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turn-rate region, for SI ≤ 2.5 and S ≤ 2.0, the relationship was approximately linear with similar slope to that observed in straight-line runs. For the higher turn-rate portion (for SI > 2.5 and S > 2.0), the relationship was again linear but with a much smaller slope. This change in behaviour provides further support for the hypothesis that a second sound generation mechanism was present.

From the CFAV QUEST sea-trials:

The measured blade-rates extracted from the CMC analysis were generally in close agreement with the measured shaft-rates of the QUEST propellers.

During straight-line, maximum speed (13.5 knot) runs the signal amplitude statistics and PDF exhibited clearly non-Rayleigh characteristics. Best-fit K-distribution shape parameters at CPA were in the range 2–5, clearly indicating non-Rayleigh behaviour. These shape parameters were also slightly lower than those extracted from the VECTOR data under the same conditions, in agreement with predictions from the numerical simulations (Section 2.4) for a twin-propeller ship. Averaged SI and S values were near 1.7 and 1.2, respectively, significantly greater than Rayleigh expectations (SI = 1.0, S = 0.631). Data from straight-line passes at speeds of 12 knots and lower had insufficient data quality to assess signal statistics and PDF.

CMC analysis for straight-line runs was successful in isolating blade rate modulation at speeds of 12 and 13.5 knots. This is in spite of the fact that propeller advance ratios were near 1.0 at these speeds. At speeds of 10 knots and below propeller modulation was not observed, due to two interrelated factors. Firstly the QUEST SSL was very low at those speeds, producing low measurement signal-to-noise ratios. Secondly, the low SSL was almost certainly due to weak (or nil) propeller cavitation, thus it can be speculated that even with higher signal-to-noise measurements only a weak propeller blade rate modulation would be observable, with the ship signature exhibiting near-Rayleigh characteristics. This is reasonable given that QUEST propellers were specifically designed for low acoustic signature through minimizing cavitation.

For maximum-power acceleration, CMC analysis only showed blade-rate modulation after the propeller shaft rates had increased from 63 RPM (at 6.3 knots in-run speed) to 90 RPM, corresponding to a drop in propeller advance ratio from 1.0 to 0.7. Blade-rate modulation was clearly observed through an advance ratio minimum of 0.585 (at a shaft rate of 125 RPM) and into the maximum speed cruising condition at 13.5 knots. This modulation was associated with clearly non-Rayleigh PDF through the main part of the acceleration, i.e., with best-fit K-distribution shape parameters in the range 7.4 to 11.1. During the acceleration, time-series statistics SI and S showed averaged values near 1.4 and 0.97, respectively.

During early parts of maximum speed, maximum rudder turns the CMC analysis was unable to identify propeller shaft- or blade-rate modulation, in spite of that fact that propeller cavitation must have occurred (i.e., associated with >15 dB increase in broadband SSL). This was believed to be due to the strong time-variation in propeller shaft rate and a significant difference in the shaft rates for the port and starboard propellers. The propeller modulation reappeared after the minimum speed point (9.1 knots), showing blade-rate modulation in agreement with the shaft-rate of the outboard (starboard) propeller. From this result it can be inferred that the outboard (starboard) propeller was more heavily loaded, and thus cavitating more strongly, during this manoeuvre.

The experimental techniques used in this work posed some limits on the statistical analysis, particularly for the ships at lower speeds where the BB SSL was reduced. The analysis of signal statistics was found to be more sensitive to acoustic background interference than ordinary power spectral measurements.

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Hydrophone signals must be better isolated against surface-wave induced transients through the use of better hydrophone suspension and re-designing the surface float to have a smaller surface footprint. The earlier work by Trevorrow et al. [4] presented a discussion on suggested improvements. Also, greater hydrophone depths (suggest 30–50 m) would have reduced the Lloyd’s Mirror effects, thereby allowing more consistent VLF signal measurements. Alternately, the use of bottom-mounted or bottom-moored hydrophones would solve this problem. In the case of measurements with VECTOR, the relatively sheltered conditions of Saanich Inlet reduced the level of buoy noise to acceptable levels. However, buoy noise was a problem for QUEST measurements due to the combination of much lower ship SSL, generally larger CPA distances to the buoys, and open ocean conditions with greater surface wave activity. In the QUEST data analysis this prevented good quality measurements at ship speeds of 10 knots and below. At 12 knots, measurements of SSL were adequate but the PDF and associated time-series statistics were still contaminated by sea-surface wave effects on the buoys.

6.1 Recommendations for Further Work

This present work has examined unclassified data on two non-naval ships. It is an obvious next step to assess the statistics of naval ship acoustic signatures. Specific recordings with the BURBs were acquired in 2005 and 2006 with two different HALIFAX-class frigates. These sea-trials included a variety of high-speed straight and turning manoeuvres, similar to those examined in this work. This work will be classified.

Additionally, this type of analysis should be performed on acoustic recordings from variety of propeller-driven vehicles of naval interest, such as torpedoes and Rigid-Hull Inflatable Boats (using both inboard and outboard engines). The venting of engine exhaust gases underwater is speculated to enhance the non-Rayleigh acoustic signal characteristics. The CF Acoustic Data Analysis Centre should be able to provide these additional recordings.

Application of these techniques to naval submarines presents significant challenges. Under normal circumstances submarines are operated in a manner that specifically avoids any form of propeller cavitation. Submarine signature levels are also generally very low compared to surface ships, presenting significant measurement challenges in typical coastal ambient noise environments. Recordings using bottom-mounted hydrophones in low-background noise locations may be necessary. Submarine propellers may cavitate during aggressive underwater manoeuvres and during surfaced operations, and these situations may be of interest.

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References

[1] Wenz, G., 1962. Acoustic ambient noise in the ocean: spectra and sources. J. Acoust. Soc. Am. 34(12): 1936–1956.

[2] Ross, D., Mechanics of Underwater Noise (Peninsula, Los Altos, CA), 1987.

[3] Ross, D., 2005. Ship sources of ambient noise, IEEE J. Oceanic Eng. 30(2), 257–261.

[4] Trevorrow, M., Vasiliev, B., and Vagle, S., 2008. Directionality and maneuvering effects on a surface ship underwater acoustic signature, J. Acoustical Soc. Am. 124(2), 767–778.

[5] Scrimger, P., and Heitmeyer, R., 1991. Acoustic source level measurements for a variety of merchant ships, J. Acoust. Soc. Am. 89(2): 691–699.

[6] Arveson, P., and Vendittis, D., 2000. Radiated noise characteristics of a modern cargo ship, J. Acoust. Soc. Am. 107(1): 118–129.

[7] Wales, S., and Heitmeyer, R., 2002. An ensemble source spectra merchant ship-radiated noise, J. Acoust. Soc. Am. 111(3): 1211–1231.

[8] McKenna, M., Ross, D., Wiggins, S., and Hildebrand, J., 2012. Underwater radiated noise from modern commercial ships, J. Acoust. Soc. Am. 131(1): 92–103.

[9] Gassmann, M., Wiggins, S., and Hildebrand, J., 2017. Deep-water measurement of container ship radiated noise signatures and directionality, J. Acoust. Soc. Am. 142(3): 1563–1574.

[10] Gray, L., and Greeley, D., 1980. Source level model for propeller blade rate radiation for the world’s merchant fleet, J. Acoust. Soc. Am. 67(2): 516–522.

[11] Antoni, J., and Hansen, D., 2012. Detection of surface ships from interception of cyclostationary signature with the Cyclic Modulation Coherence, IEEE J. Oceanic Eng. 37(3), 478–493.

[12] Urick, R., 1977. Models for the amplitude fluctuations of narrow-band signals and noise in the sea, J. Acoust. Soc. Am. 62(4): 878–887.

[13] Brockett, P., Hinich, M., and Wilson, G., 1987. Nonlinear and non-Gaussian ocean noise, J. Acoust. Soc. Am. 82(4): 1386–1394.

[14] Hinich, M., Marandino, D., and Sullivan, E., 1989. Bispectrum of ship-radiated noise, J. Acoust. Soc. Am. 85(4): 1512–1517.

[15] Trevorrow, M., 2004. Statistics of fluctuations in high-frequency low grazing-angle backscatter from a rocky seabed, IEEE J. Oceanic Eng. 29(2), 236–245.

[16] Siddiqui, M., 1964. Statistical inference for Rayleigh distributions, J. Res. National Bureau Standards: Sec D Radio Science, 68D(9), 1007—(cited in Wikipedia: Rayleigh Distribution).

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[17] Lyons, A., and Abraham, D., 1999. Statistical characterization of high-frequency shallow-water seafloor backscatter, J. Acoust. Soc. Am. 106(3), 1307–1315.

[18] Abraham, D., and Lyons, A., 2002. Novel physical interpretations of K-distributed reverberation, IEEE J. Oceanic Eng. 27(4), 800–813.

[19] Abraham, D., and Lyons, A., 2004. Reverberation envelope statistics and their dependence on sonar bandwidth and scattering patch size, IEEE J. Oceanic Eng. 29(1), 126–137.

[20] Trevorrow, M., Vagle, S., and Hall-Patch, N., 2005. Description and field evaluation of the Broad-Band Underwater Recording Buoy system, Defence R&D Canada – Atlantic, Technical Memorandum, DRDC Atlantic TM 2005-231, 40 pages.

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List of Symbols/Abbreviations/Acronyms/Initialisms

AGC automated gain control

BB broadband

BSL broadband source level

BURB Broadband Underwater Recording Buoy

CCGS Canadian Coast Guard Ship

CFAV Canadian Forces auxiliary vessel

CIS cavitation inception speed

CMC cyclic modulation coherence

CPA closest point of approach

DEMON detection of envelope modulation on noise

DGPS differential global positioning system

DRDC Defence Research and Development Canada

FFT fast Fourier transform

HF high frequency (10–100 kHz)

ICMC integrated cyclic modulation coherence

K kurtosis

KS Kolmogorov-Smirnov (statistical test)

LF low frequency (100–2000 Hz)

LMIP Lloyd’s Mirror Interference Pattern

LP low-pass (filtering)

MF medium frequency (2–10 kHz)

NB narrowband

PDF probability density function

RPM revolutions per minute

S skewness

SI scintillation index

SPL sound pressure level (dB re Pa2/Hz)

SSL spectral source level (dB re Pa2/Hz at 1 m)

VLF very low frequency (10–100 Hz)

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DOCUMENT CONTROL DATA *Security markings for the title, authors, abstract and keywords must be entered when the document is sensitive

1. ORIGINATOR (Name and address of the organization preparing the document. A DRDC Centre sponsoring a contractor's report, or tasking agency, is entered in Section 8.)

DRDC – Atlantic Research Centre Defence Research and Development Canada 9 Grove Street P.O. Box 1012 Dartmouth, Nova Scotia B2Y 3Z7 Canada

2a. SECURITY MARKING (Overall security marking of the document including special supplemental markings if applicable.)

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2b. CONTROLLED GOODS

NON-CONTROLLED GOODS DMC A

3. TITLE (The document title and sub-title as indicated on the title page.)

Examination of Statistics and Modulation of Underwater Acoustic Ship Signatures

4. AUTHORS (Last name, followed by initials – ranks, titles, etc., not to be used)

Trevorrow, M.

5. DATE OF PUBLICATION (Month and year of publication of document.)

March 2021

6a. NO. OF PAGES (Total pages, including Annexes, excluding DCD, covering and verso pages.)

69

6b. NO. OF REFS (Total references cited.)

22

7. DOCUMENT CATEGORY (e.g., Scientific Report, Contract Report, Scientific Letter.)

Scientific Report

8. SPONSORING CENTRE (The name and address of the department project office or laboratory sponsoring the research and development.)

DRDC – Atlantic Research Centre Defence Research and Development Canada 9 Grove Street P.O. Box 1012 Dartmouth, Nova Scotia B2Y 3Z7 Canada

9a. PROJECT OR GRANT NO. (If appropriate, the applicable research and development project or grant number under which the document was written. Please specify whether project or grant.)

01cc

9b. CONTRACT NO. (If appropriate, the applicable number under which the document was written.)

10a. DRDC PUBLICATION NUMBER (The official document number by which the document is identified by the originating activity. This number must be unique to this document.)

DRDC-RDDC-2021-R027

10b. OTHER DOCUMENT NO(s). (Any other numbers which may be assigned this document either by the originator or by the sponsor.)

11a. FUTURE DISTRIBUTION WITHIN CANADA (Approval for further dissemination of the document. Security classification must also be considered.)

Public release

11b. FUTURE DISTRIBUTION OUTSIDE CANADA (Approval for further dissemination of the document. Security classification must also be considered.)

12. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Use semi-colon as a delimiter.)

ship acoustic signature; signal statistics; cyclic modulation

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13. ABSTRACT (When available in the document, the French version of the abstract must be included here.)

This Scientific Report examines ship underwater acoustic signature amplitude statistics and statistical distributions. This explores the hypothesis that ship signatures exhibit amplitude fluctuations that are different from Rayleigh-distributed ambient ocean noise. Signature measurements from two different ships conducting a variety of manoeuvres are examined, focusing on those conditions where propeller cavitation and broadband signal modulation occur, specifically during maximum speed runs, accelerations, and turning manoeuvres. A key difference for a ship signature is the amplitude modulation generated by propeller cavitation, and this is found to be associated with super-Rayleigh signal characteristics. The use of new cyclostationary processing techniques is used to estimate propeller shaft and blade rate modulation. Under conditions of stronger propeller modulation, time-series statistics scintillation index and skewness show values significantly in excess of Rayleigh-distributed values. Ship signature amplitude probability density functions were found to be better matched by a K-distribution model with small shape factor, indicating increased presence of higher-amplitude signal components.

Le présent rapport scientifique porte sur les distributions statistiques et les statistiques d’amplitude de la signature acoustique sous-marine des navires. On examine l’hypothèse selon laquelle la signature des navires présente des fluctuations d’amplitude différentes du bruit océanique ambiant réparti selon la loi de Rayleigh. On étudie les mesures de la signature de deux navires distincts exécutant diverses manœuvres en s’attardant surtout aux conditions dans lesquelles on observe une cavitation des hélices et une modulation des signaux à large bande, en particulier lors de déplacements à vitesse maximale, d’accélérations et de virages. L’une des principales différences dans la signature des navires est la modulation d’amplitude produite par la cavitation des hélices, modulation qui s’avère être associée aux caractéristiques des signaux en régime super-Rayleigh. On utilise de nouvelles techniques de traitement cyclostationnaire pour déterminer la modulation de l’arbre porte-hélice et de la fréquence des pales. En cas de forte modulation de l’hélice, l’indice de scintillation et l’asymétrie de statistiques provenant de séries chronologiques affichent des valeurs nettement supérieures à celles obtenues selon la distribution de Rayleigh. Ainsi, on a constaté que les fonctions de densité de probabilités de l’amplitude de la signature des navires correspondaient davantage à un modèle de distribution K avec un faible coefficient de forme, ce qui indique la présence accrue de composantes de signaux de plus grande amplitude.

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