Experimental Study on Acceleration Measurement and Numerical Integral of Ships Wave Movement

Ai-Guo Chen 1, 2, Jia-Wei Ye 1 1. School of Civil Engineering and Transportation, South China University of Technology.

2. School of ship Engineering, Guangzhou Maritime College. Guangzhou, Guangdong China

ABSTRACT The experimental platform simulating ship wave movement for the measurement and integral of acceleration data, driven by hydraulic pressure, is designed and set up. By the spectral analysis and experimental research on integral of acceleration data, the solving measures to remove the direct-current component, low-frequency component, high-frequency component and integral constant item are put forth. The integral method of acceleration data in time domain and in frequency domain is also put forth. The key technical problems in measurement system of ships wave movement based on accelerometer array, the soft integral of the measured acceleration data, is successfully solved. KEY WORDS: ship; wave movement; accelerometer; sensor; inertial measurement system; numerical integral; acceleration. INTRODUCTION In accordance with the fore research on measurement principle of ship wave movement based on gyro-free accelerometers array (CHEN Ai-guoYE Jia-wei and CHEN Yuan-ming, 2010), the configuration of accelerometers array is shown in fig.1.

Fig.1 The configuration of accelerometers array

A tri-axial accelerometer is applied at point Q, respectively a Dual-Axis Accelerometer at point A, B and C. The measured acceleration data are used to calculate the angular velocity and angular acceleration of ship wave movement. With a tri-axial acceleration at any point D, the velocity and displacement at point D can be calculated by integral and coordinate conversion. It is the key in the measurement system of ship wave movement based on accelerometers array that the acceleration measurement and integral system can be established, which will be solved in this paper by experimental research (CHEN Ai-guoYE Jia-wei, 2009). ESTABLISHMENT OF THE ACCELERATION MEASUREMENT SYSTEM SIMULATING THE WAVE MOVEMENT OF SHIPS The acceleration measurement system simulating the wave movement of ships simply adopts three hydraulic cylinder, as shown in fig.2.It is composed of fixation frame , moving platform simulating the wave movement of ships, hydraulic cylinder , connecting rod , Thrusting spring , hinge , acceleration sensor , displacement sensor of hydraulic cylinder , displacement sensor of platform and relevant control unit. The high frequency action of three executive hydraulic cylinders is used to approximate the reciprocating movement of the moving platform simulating the wave movement of ships.

Fig.2 Schematic drawing of the system measuring acceleration

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Proceedings of the Twenty-first (2011) International Offshore and Polar Engineering ConferenceMaui, Hawaii, USA, June 19-24, 2011Copyright 2011 by the International Society of Offshore and Polar Engineers (ISOPE)ISBN 978-1-880653-96-8 (Set); ISSN 1098-6189 (Set); www.isope.org

As shown in fig.3, hydraulic circuit of the imitative system of ship wave movement is composed of hydraulic pump , relief valve , one-way valve , electro-hydraulic proportional directional control valve , hydraulic cylinder , displacement sensor and relevant control unit.

Fig.3 Hydraulic circuit of the system simulating ship wave movement

Flow chart of the control signals of the system measuring acceleration data is showed in fig.4.

Fig.4 Flow chart of the control signals of the system measuring

acceleration MEASUREMENT AND INTEGRAL ANALYSIS OF THE SYSTEM SIMULATING SHIP WAVE MOVEMENT The system simulating ship wave movement runs in the automatic mode 1, the period of the reciprocating movement of the moving platform set to 3 seconds. The displacement data of the platform and the acceleration data of three acceleration sensors are measured for analysis (ChEN Yuanming, 2007). Power Spectrum and Simple Integral of the Measured Acceleration Data Sampling time st=0.01 seconds, sampling frequency sf=1/st=100Hz2744 acceleration data are acquired by the accelerometer B, as shown in fig.5. Fast Fourier transform is adopted with the following formula:

( ) ( ) ( )( )=

=N

j

kjNjxkX

1

11 (1) Where, N is the number of the measured acceleration data,

( ) NiN e

= 2 (2)

Fig.5 Acceleration data acquired by the accelerometer B

Power Spectrum is calculated with the following formula: ( ) NFFTXconjXPXX /= (3) Power spectrum of the measured acceleration data is shown in fig.6

Fig.6 Power spectrum of the measured acceleration data

Fig.6 and further analysis show that main lobe is 6.6406Hz, major side lobe 0.3418Hz, and it has some smaller high-frequency side lobe.

Fig.7 Comparisons among kinds of velocity data

The methods of simple frequency-domain integral and time-domain Simpson integral are applied to gained the integral velocity and displacement of the acceleration data measured by the accelerometer B.

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The formula of three-point interpolation is adopted to gain the derivative velocity of the measured displacement (LI Qingyang, 2006). Their comparisons are shown in fig.7 and fig.8. They contain notable integral error and the accuracies are too low.

Fig.8 Comparisons among kinds of displacement data

Error Analysis of the Simple Time-Domain Integral Error analysis of the simple time-domain integral show that the main Factors Affecting time-domain integral as following Direct Current Component. Because of zero drift of acceleration sensor and measuring circuit, measured acceleration data inevitably contain direct current component, which causes monomial term error of integral velocity and quadratic term error of integral displacement. Especially, when the integral time is very long, the cumulative error will be very great. Direct current component can be removed by applying the reducing average value method or the least square method. Integral Constants. In the method of simple time-domain integral, initial velocity and initial displacement is set as zero when t=0, but they actually are not zero. That causes integral constants error. It can be removed by reducing average value of velocity data and reducing monomial term of displacement data. Low Frequency Component. The amplitude of the low frequency component in the measured acceleration data is only 12.35% of the frequency of the ship wave movement, but it becomes the main error of the simple time-domain integral. It can be removed by high-pass filtering, sector-by-sector polynomial fitting method and EMD method. High Frequency Component. High frequency component mainly caused the high-frequency fluctuate of the integral velocity which will caused the unnecessary frequent action of the velocity-control systems. It can be removed by the method of weighted average or low pass filtering. EFFECTIVE INTEGRAL METHODS OF THE MEASURED ACCELERATION DATA Further research shows that applying digital filtering can not gain the precise data at the end of sampling period, so it also can no be applied in real-time control system. Applying the two methods as following, satisfactory result can be gained. Time-Domain Integral Method after Frequency-Domain

Filtering Flow chart of time-domain integral method after frequency-domain filtering is shown in fig.9. After band-pass frequency-domain filtering at 0.2-0.5Hz, time-domain integral velocity and displacement of the measured acceleration are show in fig.10 and fig.11. The zero value of the displacement curve can be further corrected by adjusting the middle point to zero point.

Fig.9 Flow chart of acceleration-data integral in time domain with filter in

frequency domain

Fig.10Time-domain integral velocity with filter in frequency domain

Fig.11 Time-domain integral displacement with filter in frequency

domain Frequency -Domain Integral Method based on Frequency-Domain Filtering Flow chart of frequency-domain integral of the measured acceleration data is shown in fig.12. Frequency -domain integral velocity and displacement of the measured acceleration are show in fig.13 and fig.14.

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The figures show that integral velocity basically reflected the truth and can be applied in real-time control system, such as the compensative system of ships wave movement.

Fig.12 Flow chart of frequency-domain integral of the measured

acceleration data

Fig.13 Integral velocity in frequency domain

Fig.14 Integral displacement in frequency domain

CONCLUSIONS Due to not suitable frame of reference, measurement method of ship wave movement based on accelerometer array is very convenient and practical. Time-domain integral method after frequency-domain filtering and frequency-domain integral method based on frequency-domain filtering solve the difficult problem in the integral of the measured acceleration data. The establishment of the system measuring ship wave movement based on accelerometer array is promising and it would be able to be applied to measure ship wave movement. This research result also can be applied in the measurement of any other six degrees of freedom movement or the situation necessary soft integral, such as the measurement of the movement pose of airplane, spaceship and guided missile. REFERENCES : Chen, Ai-guo YE Jia-wei and CHEN Yuan-ming (2010).

Measurement Principle of Ship Wave Movement Based on Accelerometer Array, Journal of Shenzhen University Science and engineering, pp 374-378.

Chen, Ai-guoYE Jia-wei (2009). "Research on Four-Layer Back Propagation Neural Network for the Computation of Ship Resistance. 2009 IEEE International Conference on Mechatronics and Automation, pp 341-345.

Chen, Yuanming (2007). Experimental Study on a Heave Compensation System for Shipborne Helicopter Platform, South China University of Technology, pp 50-58.

Li, Qingyang (2006). Numerical Analysis. Tsinghua University Press, 240 pp.

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