EffectivenessofHydraulicandHydrologicParametersin...

Research ArticleEffectiveness of Hydraulic and Hydrologic Parameters inAssessing Storm System Flooding

Basim K Nile

Kerbala University Engineering College Karbala 56100 Iraq

Correspondence should be addressed to Basim K Nile basimnileyahoocom

Received 7 January 2018 Accepted 6 March 2018 Published 2 May 2018

Academic Editor Venu G M Annamdas

Copyright copy 2018 Basim K Nile is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Storm sewer systems face many challenges in urban areas in particular those systems which are old and surpassing their designperiodis study has used data from an urbanized subcatchment covering 360 ha of dead run watershed in the Alkadeer districtKarbala Iraq Physically based models Autodesk Storm and Sanitary Analysis (ASSA) and multiple nonlinear regression(MNLR) were applied Hydrology data from 1980 to 2013 were inputted and examined over three scenariose results indicatedthat significant increase in peak flooding was produced by an increase in discharge values which may occur through a higherrainfall intensityemodel was examined and new equations were developed that may help us to better understand the hydraulicand hydrologic simulations that are identified as having the potential to better protect the environment against sudden rainfallintensitiese ratio of area of subcatchment to cross-sectional area of a pipe (AcAp) the ratio of slope of subcatchment to slope ofa pipe (ScSp) and the ratio of velocity in subcatchment to velocity in a pipe (VcVp) were the most sensitive parameters informingthe ratio of runoff discharge of a subcatchment pipe discharge (QcQp) is study suggests that a more effective management ofthe storm water system under critical circumstances could be achieved by limiting the above parameters and this increases theefficiency of storm water facilities

1 Introduction

Flooding in urban storm sewer systems could cause loss oflife and considerable damage [1 2] as well as posing a threatto property and the environment and public health Manyinner cities in Iraq have been exposed to flooding fora number of reasons including poor maintenance of stormsewer systems and outmoded and limited capacity of stormsystems with reference to instances of intense rain whichcause blockages in pipe electrical issues and numerousoperational problems [3] e daily use of storm sewersystems has rapidly resulted in outdated systems because oflarge variations in urban land use rising growth in pop-ulation and changing rainfall patterns [4]

City flooding during heavy precipitation is considereda natural phenomenon [5 6] e FACADE pattern is usedin an object-oriented design to integrate storm flow andoverland flow as well as implement an extensible integratedsystem for flood simulation in urban areas [6 7] Urbanflooding can be simulated by a two-dimensional flow model

depending on ground elevation land use and type of soil allthese parameters have a large impact on the degree of surfacerunoff [5 8]

Efficient drainage of the rain network has a strongconnection with the length of drain and time of concen-tration of subcatchment affecting velocity and peak runoffdischarges Urbanization also impacts hydrology which istypically characterized by raising the values of peak floodingand reducing the time lag thus causing an increase in runoffvolume [9 10]

Inundation and overland flow volume may increase upto ten times because of urbanization flooding which nor-mally would have occurred once every 100 years may bedoubled by more than 30 increase in urbanization [11ndash13]While it has been reported that regular flooding inmunicipalareas is probably the result of frequent high intensity andextreme rainfall events (Mailhot and Duchesne 2009) thechance of inner city flooding may increase because of theincrease in urban density especially in low-lying areas [15]Although many hydraulic and hydrology models have been

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 4639172 17 pageshttpsdoiorg10115520184639172

N

ndash125 to 1515ndash2323ndash3434ndash4949ndash68

68ndash9090ndash112112ndash133


Unit meter

133ndash157157ndash182

(a)

Alkadeer district(study area)

(b)

Figure 1 (a) Elevation map of Karbala city (b) Map of study area Alkadeer district in Karbala city centre Iraq generated by GIS based onavailable data adapted from [26 27]

Table 1 Data about the subcatchment area input to the model

Element ID Area (ha) Drainage node ID Average slope () Equivalent width (m)Sub-02 529 82 00100 11000Sub-03 545 81 00063 16500Sub-04 969 80 00096 19400Sub-05 926 45 00027 11000Sub-06 974 47 00043 14000Sub-07 580 83 00108 12000Sub-08 544 67 00001 12000Sub-09 637 82 00126 13100Sub-10 631 68 00000 14900Sub-13 1010 Out-01 00122 29600Sub-17 283 50 00130 11700Sub-18 520 41 00500 14000Sub-19 636 40 00008 15500Sub-20 557 43 00008 15000Sub-21 652 38 00234 19100Sub-22 650 27 00230 26300Sub-23 651 35 00210 14500Sub-24 529 34 00123 16100Sub-25 722 32 00113 19600Sub-26 807 22 00140 27200Sub-27 759 21 00130 26200Sub-28 743 20 00120 29300Sub-29 605 19 00110 27500Sub-30 822 53 00140 25000Sub-31 830 56 00100 19000Sub-33 489 16 00006 15000Sub-34 620 17 00120 28000Sub-35 1059 13 00130 30000Sub-36 2174 4 00040 35000Sub-37 764 60 00019 17000Sub-38 512 79 00085 17000Sub-39 872 3 00016 30000Sub-40 570 54 00050 15500Sub-41 629 51 00036 19000

2 Advances in Civil Engineering

Table 1 Continued

Element ID Area (ha) Drainage node ID Average slope () Equivalent width (m)Sub-42 615 52 00100 18000Sub-43 459 69 00280 20000Sub-44 378 70 00080 8000Sub-45 434 72 00090 20000Sub-46 321 73 00086 6000Sub-47 462 75 00130 28000Sub-48 345 59 00043 9500Sub-49 358 76 00130 11000Sub-50 544 10 00006 17500Sub-51 473 1 00200 13000Sub-52 878 77 00000 14000Sub-53 734 74 00001 11500Sub-54 626 71 00006 9500Sub-55 533 49 00166 16000Sub-56 493 48 00200 15000Sub-57 542 46 00130 12500Sub-58 502 45 00170 13000

Table 2 Data about the storm sewer manhole input into the model

ElementID

Xcoordinate

Ycoordinate

Invertelevation

(m)

Groundrim(maximum)elevation (m)

Groundrim(maximum)offset (m)

Initialwater

elevation(m)

Initialwaterdepth(m)

Surchargeelevation

(m)

Pondedarea(m2)

Minimumpipe cover

(m)

1 4054604 36092856 3197 3420 223 3245 048 3420 000 1633 4048259 36084766 3806 3948 142 3842 036 3948 000 0854 4046597 36083751 3844 3986 142 3880 036 3986 200 1027 4046559 36087445 3658 3895 237 3694 036 3895 200 1978 4048117 36088489 3609 3808 199 3645 036 3808 200 1599 4049383 36089419 3570 3770 200 3606 036 3770 200 16010 4050688 36090375 3529 3762 233 3565 036 3762 200 19311 4052346 36091513 3464 3702 238 3512 048 3702 200 17812 4046581 36081767 3927 4085 158 3963 036 4085 200 11813 4045964 36079134 4013 4198 185 4049 036 4198 200 14514 4047596 36080103 3853 4029 176 3889 036 4029 200 13615 4048783 36080792 3791 3975 184 3827 036 3975 200 14416 4050088 36081565 3724 3879 155 3760 036 3879 200 11517 4047844 36082531 3841 4025 184 3877 036 4025 200 14418 4049583 36083502 3705 3875 170 3741 036 3875 200 13019 4051011 36080048 3714 3872 158 3750 036 3872 200 11820 4049685 36079343 3763 3948 185 3800 037 3948 200 14521 4048323 36078584 3847 4080 233 3883 036 4080 200 19322 4046644 36077670 4072 4260 188 4108 036 4272 200 14823 4054939 36080018 3480 3723 243 3516 036 3723 200 15924 4053779 36079539 3624 3845 221 3660 036 3845 200 18125 4052544 36077384 3728 3908 180 3764 036 3908 200 14027 4050025 36075756 3998 4156 158 4032 034 4156 200 11828 4051861 36078388 3666 3881 215 3699 033 3881 200 17529 4049130 36076741 3937 4100 163 3973 036 4100 200 12332 4055974 36077793 3483 3669 186 3529 046 3669 200 14633 4054784 36077092 3518 3749 231 3554 036 3749 200 19134 4053752 36076454 3548 3762 214 3584 036 3762 200 17435 4052592 36075757 3677 3868 191 3713 036 3868 200 15136 4051301 36074946 3812 4034 222 3848 036 4034 200 18237 4050170 36074219 3920 4073 153 3956 036 4073 200 11338 4048865 36073390 3984 4146 162 4020 036 4146 200 12239 4047324 36072446 4029 4204 175 4075 046 4204 200 13540 4058854 36079613 3398 3587 189 3434 036 3587 200 14941 4060007 36080320 3291 3490 199 3327 036 3490 200 159

Advances in Civil Engineering 3

widely used to predict urban flooding there has beenlimited focus on different parameters particularly re-garding rapid and frequent hydrological phenomenaerefore an investigation involving simulation modellingand data analysis was conducted to explore the relationshipbetween the above factors to produce the best hydraulic andhydrologic model

In recent decades there has been much research intourban flooding with a focus on obtaining equations linkingcertain parameters involving topography slope of pipesvarying rainfall intensity size of watershed and runoffdischarges and major flooding parameters for developedareas Attention has also been paid to the effects of climatechange varying hydraulic data on storm sewer systemsand the increasing availability of knowledge aboutchanges in hydrological systems and insights Many urbandrainage systems can reach full capacity during heavyrainfall [16]

e issue of storm sewer modelling is currently one ofthe most dynamic areas in hydraulics and hydrology re-search Many software packages have been used to simulatepipe above ground hydraulics and hydrology models in therunoff of rainfall and pollutants from urban areas such asSWMM [17] XPSWAMM [18] ASSA [19] and MIKEMOUSE [20] One-dimensional sewer flow models (withinthe storm sewer-1D) and two-dimensional overland flow(within subcatchment-2D) models have been developed andused to examine urban flooding [21]

Even though there are a number of studies conductedon flooding in storm sewer systems during heavy rainfallthese studies are still very limited in their infancy Some 2Dmodels with high-resolution grids have examined theconsequences of storm pipes [22] High-resolution digitalterrain data and instances of flooding in inner city areas wereused to simulate the multifaceted interaction between thestorm flow and surcharge-induced inundations in order to

Table 2 Continued

ElementID

Xcoordinate

Ycoordinate

Invertelevation

(m)



Initialwater

elevation(m)


Surchargeelevation

(m)

Pondedarea(m2)

Minimumpipe cover

(m)

42 4061483 36081232 3206 3397 191 3242 036 3397 200 13143 4057083 36078474 3450 3641 191 3496 046 3641 200 15145 4066400 36088035 2656 2898 242 2730 074 2898 200 16246 4065326 36087458 2664 2929 265 2728 064 2929 200 18547 4063994 36086589 2760 3031 271 2770 010 3031 200 19148 4062519 36085687 2856 3110 254 2889 033 3110 200 17449 4061248 36084928 2953 3213 260 3027 074 3213 200 18050 4059783 36084038 2967 3323 356 3031 064 3323 200 27651 4057198 36083251 3205 3331 126 3253 048 3331 200 05652 4055863 36082388 3238 3497 259 3286 048 3497 200 18653 4054213 36081337 3421 3621 200 3457 036 3621 200 14054 4059459 36084584 3015 3318 303 3063 048 3318 200 23855 4053706 36082188 3406 3636 230 3454 048 3636 200 15256 4053071 36083253 3425 3661 236 3473 048 3661 200 17357 4052482 36084240 3427 3662 235 3475 048 3662 200 17058 4051908 36085202 3425 3710 285 3473 048 3710 200 21259 4051377 36086092 3440 3668 228 3476 036 3668 200 16460 4050713 36087210 3448 3743 295 3484 036 3743 200 25563 4052434 36080754 3566 3824 258 3699 133 3824 200 21865 4051414 36082430 3635 3815 180 3671 036 3815 200 14066 4056206 36085106 3212 3462 250 3248 036 3462 200 21067 4058362 36086409 3094 3324 230 3130 036 3324 200 16668 4057678 36087588 3118 3341 223 3154 036 3341 200 15869 4056646 36086957 3236 3461 225 3272 036 3461 200 18570 4055571 36086229 3333 3533 200 3399 066 3533 200 16071 4057089 36088611 3113 3353 240 3149 036 3353 200 10072 4056179 36088121 3237 3499 262 3270 033 3499 200 22273 4055110 36087445 3414 3589 175 3440 026 3589 200 13574 4056495 36089665 3150 3397 247 3186 036 3397 200 18775 4055486 36089113 3297 3552 255 3333 036 3552 200 21576 4055909 36090654 3156 3433 277 3204 048 3433 200 21777 405530 36091668 3172 3431 259 3220 048 3431 200 19979 4050429 36084049 3677 3827 150 3713 036 3827 200 11080 4063346 36093570 2061 2495 434 2110 049 2495 200 00081 4064095 36092331 2100 2461 361 2140 040 2461 200 31182 4064859 36091069 2218 2700 482 2258 040 2700 200 43283 4065703 36089675 2430 2750 320 2470 040 2750 200 270


Table 3 Data about the storm sewer pipes input into the model

ElementID

From (inlet)node

To (outlet)node

Length(m)

Inlet invertelevation (m)

Outlet invertelevation (m)

Averageslope ()

Pipeshape

Pipediameter

(m)

Manningrsquosroughness

Link-01 39 38 18076 4029 3984 02500 Circular 0400 00130Link-03 38 37 15462 3984 3920 04100 Circular 0400 00130Link-04 37 36 13438 3920 3812 08000 Circular 0400 00130Link-05 36 35 15249 3812 3678 08800 Circular 0400 00130Link-06 35 34 13536 3677 3548 09500 Circular 0400 00130Link-07 34 33 12129 3548 3518 02500 Circular 0400 00130Link-08 33 32 13816 3518 3483 02500 Circular 0400 00130Link-10 32 43 13016 3483 3450 02500 Circular 0400 00130Link-11 43 40 21049 3450 3398 02500 Circular 0400 00130Link-12 40 41 13530 3398 3291 07900 Circular 0400 00130Link-13 41 42 17350 3291 3206 04900 Circular 0400 00130Link-14 42 50 32810 3206 2967 07300 Circular 0600 00130Link-15 50 49 17148 2967 2953 00800 Circular 0800 00130Link-16 49 48 14799 2953 2856 06600 Circular 0800 00130Link-17 48 47 17295 2856 2760 05600 Circular 0800 00130Link-18 47 46 15896 2760 2664 06000 Circular 0800 00130Link-19 46 45 12196 2664 2656 00700 Circular 0800 00130Link-21 81 80 14480 2100 2061 02700 Circular 0500 00130Link-22 82 81 14750 2218 2100 08000 Circular 0500 00130Link-23 83 82 16301 2430 2218 13000 Circular 0500 00130Link-24 45 83 17812 2667 2430 13300 Circular 0500 00130Link-25 27 25 29989 3998 3728 09000 Circular 0400 00130Link-26 25 28 12137 3728 3666 05100 Circular 0400 00130Link-27 28 24 22366 3666 3624 01900 Circular 0400 00130Link-28 29 23 12555 3624 3524 08000 Circular 0400 00130Link-29 23 53 15060 3484 3430 03600 Circular 0400 00130Link-30 53 52 19563 3425 3245 09200 Circular 0400 00130Link-31 52 51 15898 3251 3215 02300 Circular 0600 00130Link-32 51 54 26246 3215 3020 07400 Circular 0600 00130Link-33 54 50 6340 3020 2967 08400 Circular 0600 00130Link-34 29 28 31889 3937 3666 08500 Circular 0400 00130Link-35 22 21 19118 4072 3847 11800 Circular 0400 00130Link-36 21 20 15589 3847 3763 05400 Circular 0400 00130Link-37 20 19 15016 3763 3714 03300 Circular 0400 00130Link-38 19 63 15887 3714 3566 09300 Circular 0400 00130Link-39 63 53 18724 3566 3421 07700 Circular 0400 00130Link-40 13 14 18979 4013 3853 08400 Circular 0400 00130Link-41 14 15 13719 3853 3791 04500 Circular 0400 00130Link-42 15 16 15170 3791 3724 04400 Circular 0400 00130Link-43 16 65 15832 3724 3635 05600 Circular 0400 00130Link-44 65 63 19611 3635 3566 03500 Circular 0400 00130Link-45 12 17 14759 3927 3841 05800 Circular 0400 00130Link-46 17 18 19919 3841 3705 06800 Circular 0400 00130Link-47 18 79 10075 3705 3677 02800 Circular 0400 00130Link-48 79 65 18960 3677 3635 02200 Circular 0400 00130Link-49 4 3 19471 3844 3823 01100 Circular 0400 00130Link-52 7 8 18755 3658 3609 02600 Circular 0400 00130Link-53 8 9 15708 3609 3570 02500 Circular 0400 00130Link-54 9 10 16177 3570 3529 02500 Circular 0400 00130Link-55 10 11 20113 3529 3464 03200 Circular 0400 00130Link-56 11 1 26266 3464 3197 10200 Circular 0600 00130Link-57 1 77 13799 3197 3172 01800 Circular 0600 00130Link-58 77 76 11799 3172 3156 01400 Circular 0600 00130Link-59 76 74 11499 3156 3150 00500 Circular 0600 00130Link-60 74 71 12099 3150 3120 02500 Circular 0600 00130Link-61 68 71 11799 3118 3123 -00400 Circular 0600 00130Link-62 68 67 13629 3123 3098 01800 Circular 0600 00130Link-63 67 54 21299 3098 3020 03700 Circular 0600 00130


make reasonable predictions of likely ood damage in urbanzones [23] Hsu et al [24] coupled a 2D noninterior overowmodel with SWMM to estimate and simulate dynamic in-undation during heavy rainfall intensities in developedareas

e analysis of storm sewer systems in urban areas isconsidered as the most important measure taken to protectthe environment in the event of intense rainfall eanalysis of a storm sewer system postdesign and de-ployment is considered the best way to ensure reliable upto a certain frequency or level of service and the ability topredict potential of serious ooding Although manyphysically based and statistical models have been used forthese purposes the concept of having a model to simulateows in urban sewers and to predict risk of ooding inurban areas is still comparatively inaccessible in manycountries e present work aims to investigate a modelthat can provide a better understanding of the ability ofhydraulics and hydrology to predict and reduce risk ofooding in urban areas

2 Methods and Materials

21 Study Area Karbala is an ancient festival city situated100 km southwest of Baghdad Iraq (lat-N 32deg03prime51Primelong-E 44deg01prime29Prime) in a semiarid area [25] One of theKarbala cityrsquos districts has been chosen as the study areacomprising 360 ha (36 km2) as shown in Figure 1(a) epercentage of impervious area is 60ndash80 e topographymap of the Karbala city and the layout of the storm sewersystem which ows under gravity are shown in Figure 1(b)[26 27]

22 Data

221 Hydraulic Data e storm sewer system was built in2006 [25] with the design based on a spatially uniformrainfall intensity of 13mmh according to available datae parameters used as input data for the hydraulic andhydrology models are as follows subcatchment discharge(Qc) discharge of pipe (Qp) area of the subcatchment (Ac)

Table 3 Continued

ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)


Link-64 75 74 11500 3297 3150 12800 Circular 0400 00130Link-65 73 72 12650 3414 3237 14000 Circular 0400 00130Link-66 72 71 10337 3237 3213 02300 Circular 0400 00130Link-67 70 69 12981 3333 3236 07500 Circular 0400 00130Link-68 69 68 12096 3236 3118 09800 Circular 0400 00130Link-69 66 67 25186 3212 3094 04700 Circular 0400 00130Link-70 60 59 13010 3448 3444 00300 Circular 0400 00130Link-71 59 58 10360 3444 3438 00600 Circular 0600 00130Link-72 58 57 11200 3438 3432 00500 Circular 0600 00130Link-73 57 56 11500 3432 3428 00300 Circular 0600 00130Link-74 56 55 12400 3428 3424 00300 Circular 0600 00130Link-75 55 53 9899 3424 3421 00300 Circular 0600 00130Link-76 3 7 31733 3806 3658 04700 Circular 0400 00130

25

20

15

10

5

0000

10

20

30

40

50

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Rain

fall

(mm

)

Tem

pera

ture

(degC)

Mean total rainfallMean maximum temperatureMean minimum temperature

Figure 2 Averagemonthly rainfall and temperature in the study area for the years 1980ndash2013 adapted fromWeather Forecast for Karbala [28]


cross-sectional area of pipe (Ap) slope of subcatchment (Sc)slope of pipe (Sp) velocity in subcatchment (Vc) velocity inpipe (Vp) time of concentration in subcatchment (Tcc) timeof concentration in pipe (Tcp) length of subcatchment (Lc)and length of pipe (Lp) Details of the storm sewer systemwere entered into the model manholes pipes pump stationtopography and land use quality ere are 51 subcatch-ments (Table 1) with 73 manholes (Table 2) and 72 pipeswith various diameters (315ndash800mm) as shown in Table 3[26 27]

222 Hydraulic Data e climate in Karbala is described ascold in winter (below minus41degF) and hot in summer (above 131degF)[26] Rainfall data recorded at a rain gauge station were usedas input data for the hydrology model as shown in Figure 2All of precipitation evaporation incurrenltration surface runoyenand currennal surface storage have been provided by the Di-rectorate of Karbala and Urban planning

3 Autodesk Storm and Sanitary Analysis andMultiple Nonlinear Regressions

31 Methods As illustrated in Figure 3 three scenarios ofrainfall intensities have been followed Climate changes inIraq and particularly in Karbala city are extreme and rapidtherefore this study has been examined using three scenariose currenrst scenario used normal rainfall intensities which were

recorded in Karbala city over the 33 last years [26 27]Moreover the second scenario used increased rainfall in-tensities (multiple values) while the currennal scenario usedrainfall intensities three times the normal rainfall intensities

32 Model Description e proposed methodology wascurrenrst applied to the urban storm sewer systems in diyenerentmunicipalities of Karbala city based on the hydrologysimulation and statistical data analysis In this studymodels based on actual hydraulic and hydrologic data weredeveloped using Autodesk Storm and Sanitary Analysis(ASSA) [29] and multiple nonlinear regressions (MNLR)in order to accurately examine all parameters involved inan urban ooding ASSA is considered an advancedpowerful and comprehensive model which is used toanalyse and design storm and sanitary sewer systems inurban areas [26] ASSA uses the rational equation to ex-amine the relationships between Qc Ac Sc Vc Tcc and Lcsubcatchment parameters Weather Forecast for Karbala[29] while the Manning equation was used to express therelationship between the storm network parameters QpAp Sp Vp Tcp and Lp [30] MNLR [31] is an importantmodel for estimating the frequencies of diyenerent variableswhich have nonuniform distribution [32 33]

e general method of approximation in nonlinear re-gression uses advanced multiple-linear regressions thathave been ayenected by logarithmic feature defects [34]Nonlinear methods for a choice of free parameters andnonnormally distribution for data allowed an interceptingnonlinear derivation e standard nonlinear regressionmodel is shown by the following equation

y f θ x1 x2 x3 + middot middot middot( ) + εrArr ε sim N 0 V2( ) (1)

Scenario 140

30

20

10

0

50

40

30

20

10

Rain

fall

dept

h (m

m)

0

Scenario 2

100

80

60

40

20

00 500 1000

Elapsed time (hour)1500

Scenario 3

Figure 3 Rainfall intensities for the three scenarios of the model [28]

LcLp

LcLp

QcQp1

TccTcp1 TccTcp2

TccTcp

H4

H3H1

ScSp

ScSp

VcVp

VcVp1 VcVp2 VcVp3

AcAp

AcAp

H2

H5

TccTcp3

QcQp2

QcQp

QcQp3

Figure 4 Model of the hypotheses model for the parameter ratios(3 scenarios)


7

6

5

4

3

2

1

00

Number of events 39Event frequency 0057Minimum value 0249Maximum value 15232Mean value 5444Standard deviation 3820Skewness coefficient 0751

Scenario 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Perc

ent o

f tot

al

0 05 1 15 2 25 3 35 4 45 5 55 6


Scenario 1

65

10

9

8

7

6

5

4

3

2

1

9

8

7

6

5

4

3

2

1

0

Number of events 53Event frequency 0077Minimum value 0267Maximum value 3076Mean value 8948Standard deviation 7938Skewness coefficient

Scenario 3

0978

2 4 6 8 10 12 14 16 18 20 22 24 26 28 300Daily peak flooding (cms)

(a)

Figure 5 Continued


where y is the dependent variable x1 x2 x3 are theindependent variables (possibly multivariate and oftencontrolled by experimenter) θ is the vector of the modelparameters characterizing the relationship between x and y

through the function f and ε is the residual error termthat is assumed to be normally distributed centred around0 and with unknown variance (V2) e residual errorterms have commonly been assumed independent as is

7222 7403 7584 7764 7944 8125 8305 8486 8667 8847

7222

Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

Scenario 1

0123456702468

1012141618

25201510

50

7403 7584 7764 7944 8125 8305 8486 8667 8847

7335 7523 7711 7899 8088 8275 8463 8651 8840 9028

7335

Scenario 2Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

0

05

10152025303540

5040302010

0

2468

10121416

7523 7711 7899 8088 8275 8463 8651 8840 9028

7315

Scenario 3Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

7503 7690 7878 8065 8253 8440 8628 8815 9003

731505

101520253035

0102030405060708090

10080604020

0

7503 7690 7878 8065Time (hour)

8253 8440 8628 8815 9003

(b)

Figure 5 (a) Daily peak ooding based on three scenarios for available rainfall data (1980ndash2013) (b) Relationships between rainfall runoyenand ooding over time for three scenarios of the model


0000 02 04

Observed cum prob

Normal P-P plot of QcQpEx

pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob

Normal P-P plot of AcAp

Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob

Normal P-P plot of ScSp

Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob

Normal P-P plot of VcVp

Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob

Normal P-P plot of TccTcpEx

pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob

Normal P-P plot of LcLp

Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob

Detrended normal P-P plot of VcVp

Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025

00 02 04Observed cum prob

Detrended normal P-P plot of TccTcp

Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob

Detrended normal P-P plot of LcLp

Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob

Detrended normal P-P plot of QcQp

Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob

Detrended normal P-P plot of AcAp

Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob

Detrended normal P-P plot of ScSpD

evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015

Figure 6 Normal and detrended P-P diagrams for all the parameters entered into the model


3

2

1

0

0Standardized observed value

Normal Q-Q plot of QcQpEx

pect

ed n

orm

al v

alue

2 4

ndash1

ndash2

ndash3ndash8 ndash6 ndash4 ndash2

3

2

1

0


Normal Q-Q plot of AcAp

Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2

ndash3ndash3 ndash2 ndash1 0

3

2

1

0


Normal Q-Q plot of ScSp

Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0


Normal Q-Q plot of LcLp

Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0


Normal Q-Q plot of TccTcpEx

pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0


Normal Q-Q plot of VcVp

Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1

Standardized observed value

Detrended normal Q-Q plot of QcQp

Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02


Detrended normal Q-Q plot of AcAp

Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02


Detrended normal Q-Q plot of ScSp

Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02


Detrended normal Q-Q plot of VcVp

Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01


Detrended normal Q-Q plot of TccTcp

Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01


Detrended normal Q-Q plot of LcLp

Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


Figure 7 Normal and detrended Q-Q plots for all the parameters entered into the model


normally assumed for standard nonlinear regressionanalysis [32 35 36] Goodness of current statistical analysis andthe NashndashSutcliyene model ecopyciency (NSE) was used toexamine the results for the calibration and validation ofthe model as shown by (2) and (3) respectively with therelative diyenerence error in QcQp [37ndash41]

NSE 1minussum Qo(t)minusQs(t)( )2

Qo(t)minusQs(t)( )2 (2)

where Qs(t) denotes simulated QcQp for time (t) Qo(t) isobserved QcQp for time (t) and Qo is the average dischargeof observed streamow

difference sumni0 Oi minus sum

ni1 Pi

∣∣∣∣∣∣∣∣

sumni1 Oitimes 100 (3)

whereOi is the observed data Pi is the modelled data and n isthe number of data In this study two theories have beenfollowed e currenrst calculates all the parameters of the sub-catchment (Qc Ac Sc Vc Tcc and Lc) without an urban stormwater system while the second includes a storm sewer systemand usesQp Ap Sp Vp Tcp and Lp erefore the hypothesesexamined based on the ratios of entered parameters includeratio of subcatchment discharge (Qc) to discharge of pipe(Qp) ratio of area of subcatchment (Ac) to cross-sectional areaof pipe (Ap) ratio of slope of subcatchment (Sc) to slope ofpipe (Sp) ratio of velocity in subcatchment (Vc) to velocity inpipe (Vp) ratio of time of concentration in subcatchment(Tcc) to time of concentration in pipe (Tcp) and ratio oflength of subcatchment (Lc) to length of pipe (Lp) as shownin Figure 4

4 Results and Discussion

41 Calibration and Validation of the Model For this studythe models were tested on three scenarios applied to the 121most intense rainy season ood events in 2013 and rainfalldata from 1980 to 2013 In the currenrst scenario there were 29ooding events with an event frequency less than 0042 andthese ranged between 0126 and 6587 cms In the secondscenario there were 39 ooding events with an event fre-quency less than 0057 and these ranged between 0429 and15232 cms In the third scenario there were 59 oodingevents with an event frequency greater than 0077 and therange was between 0267 and 3076 cms as shown in Figure 5

Table 4 e results of QcQp by the model equations

Case TccTcp LcLp AcAp ScSp VcVp QcQp

Minimum 139 079 11062123 0004 001 minus574Average 5335 075 14170579 025 020 098Maximum 127600 536 80235145 300 398 703

Table 5 Partial correlations for QcQp AcAp ScSp VcVp TccTcp and LcLp

QcQp AcAp ScSp VcVp TccTcp LcLpQcQp 1000 minus0992 00128 0287 0136 0182AcAp minus0992 1000 0041 minus0227 minus0162 minus0235ScSp 00128 0041 1000 0448 0576 minus0062VcVp 02870 minus0227 0448 1000 0493 0073TccTcp 01360 minus0162 0576 0493 1000 minus0118LcLp 01820 minus0235 minus0062 0073 minus0118 1000

VcVp

ScSp

AcAp

LcLp

TccTcp

Figure 8 Correlations for all the parameters related to QcQp

Mean = 1139045Standard deviation = 0930661

00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal

95 lower confidence band95 upper confidence band

F(x)

Figure 9 Empirical cumulative distribution function (CDF)


e eyenect of rainfall intensity and surface runoyen dischargeon the magnitude of ooding in the storm sewer system asexamined by the three model scenarios are illustrated inFigure 6

e relationships among the parameters (QcQp AcApScSp VcVp TccTcp and LcLp) were tested using linear andnonlinear equations e best relationships were loga-rithmic normal and detrended P-P diagrams (Figure 6)e MNLR works on the assumption that both depen-dent and independent variables should be nonnormallydistributed e plots showed that all points were more or

less situated along a line particularly for QcQp indicatingthe data were not normally distributed Normal anddetrended Q-Q plot data were tested revealing the nonlinearrelationships between the parameters (Figure 7)

Equations (4)ndash(6) represents nonlinear (logarithmic)relationships between parameters QcQp AcAp ScSpVcVp TccTcp and LcLp e currenrst equation represents theminimum ratio of discharge in subcatchment (Ac) to pipedischarge (Qp) the second equation denotes the averagedischarge ratios while the currennal equation denotes maximumdischarge ratios as per the model

15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3

Subcatchments of study area

Scenario 3Scenario 2Scenario 1

(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)

Figure 10 (a) ree model scenarios for QcQp (a) and VcVp (b) based on diyenerent rainfall intensities


Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055

minus 074 times lnTcc

Tcp1113888 1113889

05

minus 3230 times lnLc

Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)

With the input of three values (minimum average andmaximum) for each parameter (AcAp ScSpVcVpTccTcp andLcLp) into the above (4)ndash(6) the results ofQcQp (min)QcQp(ave) and QcQp (max) are extracted as shown in Table 4

e optimal case of QcQp 1 was based on the rec-ommended runoff surface needed to prevent flooding Stormsewers in urban areas are only partially designed mostconcentrated downstream of streets and subareas unlikesanitary sewers which are designed to be downstream of eachhouse e model examined the percentage completely filledby storm network e results indicated that the average ofQcQp was 098 which supports the idea that the flood eventsare correctly defined However the maximum value ofQcQp was 703 meaning that the subcatchment runoffdischarge was larger than the discharge in the pipes leadingto flooding in the storm sewer network as defined in thisstudy Dependant on the minimum average and maximumparameters entered into the equation model the weight ofAcAp gave equations of 735 and therefore is consideredthe most effective parameter in the equation for QcQp enext dimensionless parameters in the model are the ratiosVcVp and ScSpeweight of these parameters in themodelwas 78 e ratio of TccTcp was 72 influence the lowestimpact on QcQp 37 with the ratio LcLp e computedwater stage is overestimated if the dynamic interactionbetween surcharge and discharge of themanhole is neglectedin the simulation [5] However these equations could still beused to estimate the volume of flooding

Using logarithmic regressions the correlations betweenparameters are reported in Table 5 and shown in Figure 8e results showed that there are significant correlationsfound between dimensionless parameters listed in Table 5As shown in Table 5 the ratios were 1 minus0992 00128 02870136 and 0182 for Q A S V T and L respectively It wasalso found that QcQp and ScSp had low correlations at00128 erefore a regression analysis was conducted toestimate the effects of all the parameter ratios on stormwaterflooding

e normality of the data was checked using theKolmogorovndashSmirnov test and the empirical cumulativedistribution function (CDF) for observation data is exam-ined as shown in Figure 9 is figure shows a lack ofmapping of the CDF line to the line representing normality(blue) providing evidence for a nonlinear distributionBased on the model findings and its scenarios both QcQpand VcVp increase with increasing rainfall intensity asshown in Figure 10

Regarding the calibration of the model Figure 11 showsthe observed QcQp versus modelled QcQp based on theparameters with a confidence interval of 95e data showa trend towards the observedQcQp data which could be dueto the nonlinear relationships for QcQp with the otherparameters

All parameters determined during the process of cali-bration were used to validate the model and the percent ofdifference is 2 (significant if less than 10) between observedand predicted data for QcQp based on the ratios of enteredparameters e efficiency of NSE was 033gt 0 indicatingthat the model predictions were as accurate as the mean ofobserved data Figure 12 presents images for the parametersAcAp ScSp and VcVp predicting QcQp an importantmeans to understand the relationships among the param-eters and particularly the dependence of QcQp on the otherparameters One of the most significant current discussions

00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp

95 confidence interval

Figure 11 Model calibration of QcQp based on the parameterswith a confidence interval of 95


regarding this model is the possibility of using the extractedmodel equations to predict ooding in any storm sewer andits subareas under extremely intense rainfall

5 Summary and Conclusions

One of the major challenges when designing a storm sewersystem is identifying the likely impact of identicurrened pa-rameters at the planning stage in order to eliminate ormitigate frequency of ooding Many storm sewer simula-tionmodels exist but this study has attempted to currennd amoreaccurate way to examine the relationships between runoyendischarge and storm pipe discharge topography of sub-catchment and network slope velocity in subareas andvelocity in storm pipe size of urban areas and cross-sectional

area of storm pipe is numerical study was carried out todetermine which factor was more important based on theequations developed in the model Conclusions drawn fromthis model include the following

(1) e computed water stage (703 QcQp) is over-estimated when the dynamic interaction betweensurcharge and discharge in manholes is neglected inthe simulation [6] ese equations (3)ndash(5) can alsobe used to estimate the volume of ooding a newapproach in this area of research

(2) is model can be used to predict ooding inurban areas and to estimate the percentage of stormnetworks needed in subcatchments to limit cityooding

gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5

3D surface QcQp versus ScSp versus AcApAcAp = distance-weighted least squares

01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5

3D surface QcQp versus VcVp versus AcApAcAp = distance-weighted least squares

01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20

3D surface QcQp versus VcVp versus TccTcpTccTcp = distance-weighted least squares

ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02

ltndash04ltndash06ltndash08

3D surface QcQp versus VcVp versus ScSpScSp = distance-weighted least squares

ndash12ndash10ndash08ndash06ndash04ndash02000204060810

ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05

3D surface QcQp versus ScSp versus LcLpLcLp = distance-weighted least squares

0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40

3D surface QcQp versus LcLp versus TccTcpTccTcp = distance-weighted least squares

ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)

Figure 12 ree-dimensional surfaces of the model parameters


(3) e calculations suggest that the use of irregularclassifications of rainfall data could increase thecomputational complexity essential to rebuild themodel and significantly increase the time requiredfor simulation runs In compensation the relation-ship between parameters entered into the model waslogarithmic and the distribution of data is nonlinear

(4) is study recommends that the design and analysisprocedure for a storm sewer systemmust include themitigation of the risk flooding in urban areas

ese results may simplify developments in the pre-diction of urban flooding and thus protect resources as wellas reduce flood risk Given that storm sewer systems havehistorically been designed to consider limited rainfall in-tensity this model can allow for varying rainfall intensities inunusual situations e model has also established a clearerrelationship between relevant parameters It may thereforebe useful worldwide in a range of different scenarios

Conflicts of Interest

e author declares that there are no conflicts of interestregarding the publication of this paper

References

[1] S T Ashley and W S Ashley ldquoFlood fatalities in the UnitedStatesrdquo Journal of Applied Meteorology and Climatologyvol 47 no 3 pp 805ndash818 2008

[2] B E Montz and E Gruntfest ldquoFlash flood mitigation recom-mendations for research and applicationsrdquo Global EnvironmentalChange Part B EnvironmentalHazards vol 4 no1 pp15ndash22 2002

[3] H A Obaid S Shahid K N Basim and C ShreeshivadasanldquoModeling sewerage overflow in an urban residential areausing storm water management modelrdquoMalaysian Journal ofCivil Engineering vol 26 pp 163ndash171 2014

[4] H T Huong and A Pathirana ldquoUrbanization and climatechange impacts on future urban flooding in Can o cityVietnamrdquoHydrology and Earth System Sciences vol 17 no 1pp 379ndash394 2013

[5] T V Hromadka II and C Lai ldquoSolving the two-dimensional diffusion flow modelrdquo in Proceedings of theSpecialty Conference on Hydraulics and Hydrology in theSmall Computer Age pp 555ndash562 Lake Buena Vista FLUSA August 1985

[6] S Lee H Nakagawa K Kawaike and H Zhang ldquoUrbaninundation simulation considering road network and build-ing configurationsrdquo Journal of Flood Risk Management vol 9no 3 pp 224ndash233 2016

[7] E Gamma Design Patterns Elements of Reusable Object-Oriented Software Pearson Education Delhi India 1995

[8] S S Lin H K Chang S H Hsieh J T Kuo and J S Lai AnIntegrated Approach for Inundation Simulation in an UrbanArea IAHS Publication Wallingford UK 2004

[9] L B Leopold Hydrology for Urban Land Planning AGuidebook on the Hydrologic Effects of Urban Land Use 1968

[10] F L Ogden N Raj Pradhan C W Downer and J A ZahnerldquoRelative importance of impervious area drainage densitywidth function and subsurface storm drainage on floodrunoff from an urbanized catchmentrdquo Water Resources Re-search vol 47 no 12 2011

[11] F L Ogden H O Sharif S U Senarath J A SmithM L Baeck and J R Richardson ldquoHydrologic analysis ofthe Fort Collins Colorado flash flood of 1997rdquo Journal ofHydrology vol 228 no 1 pp 82ndash100 2000

[12] G E Hollis ldquoe effect of urbanization on floods of differentrecurrence intervalrdquo Water Resources Research vol 11 no 3pp 431ndash435 1975

[13] N A Campana and C E Tucci ldquoPredicting floods from urbandevelopment scenarios case study of the Diluvio Basin PortoAlegre Brazilrdquo Urban Water vol 3 no 1 pp 113ndash124 2001

[14] A Mailhot and S Duchesne ldquoDesign criteria of urbandrainage infrastructures under climate changerdquo Journal ofWater Resources Planning and Management vol 136 no 2pp 201ndash208 2010

[15] J Blanc J W Hall N Roche et al ldquoEnhanced efficiency ofpluvial flood risk estimation in urban areas using spatialndashtemporal rainfall simulationsrdquo Journal of Flood Risk Man-agement vol 5 no 2 pp 143ndash152 2012

[16] R Gaudio N Penna and V Viteritti ldquoA combined method-ology for the hydraulic rehabilitation of urban drainage net-worksrdquo Urban Water Journal vol 13 no 6 pp 644ndash656 2016

[17] L A Rossman Storm Water Management Model UserrsquosManual Version 50 National Risk Management ResearchLaboratory Office of Research and Development US Envi-ronmental Protection Agency Cincinnati OH USA 2010

[18] B C Phillips S Yu G Rompson and N De Silva ldquo1D and2Dmodelling of urban drainage systems using XP-SWMMandTUFLOrdquo in Proceedings of the 10th International Conference onUrban Drainage pp 21ndash26 Copenhagen Denmark August2005

[19] S V Kanitkar A D ube and R N Sankhua ldquoOptimaldesign model for a fixed layout storm water networkrdquo In-ternational Journal of Water vol 10 no 4 p 375 2016

[20] DHI and Hydraulics DHMIKE 21 ampMIKE 3 FLOWMODELHydrodynamic Module Scientific Documentation DHI Wateramp Environment Hoslashrsholm Denmark 2005

[21] C P Burgess M A Taylor T Stephenson and A MandalldquoFrequency analysis infilling and trends for extreme pre-cipitation for Jamaica (1895ndash2100)rdquo Journal of HydrologyRegional Studies vol 3 pp 424ndash443 2015

[22] A Chen S Djordjevic J Leandro B Evans and D SavicldquoSimulation of the building blockage effect in urban floodmodellingrdquo in Proceedings of the 11th International Confer-ence on Urban Drainage pp 1ndash10 Edinburgh UK August-September 2008

[23] S D Seyoum Z Vojinovic R K Price and S WeesakulldquoCoupled 1D and noninertia 2D flood inundation model forsimulation of urban floodingrdquo Journal of Hydraulic Engi-neering vol 138 no 1 p 23 2011

[24] M H Hsu S H Chen and T J Chang ldquoInundation sim-ulation for urban drainage basin with storm sewer systemrdquoJournal of Hydrology vol 234 no 1-2 pp 21ndash37 2000

[25] Karbala-Iraq Governorates (KIG) Regions and Major CitiesmdashStatistics and Maps on City Population KIG Karbala Iraq 2013

[26] Directorate of Sewerage of Karbala ldquoReport of operationdepartment 2016rdquo Rep DSK-214 Governorate of KarbalaKarbala Iraq 2016

[27] Directorate of Karbala Urban Planning ldquoPlanning and designdepartment 2016rdquo Rep JIK-202 Governorate of KarbalaKarbala Iraq 2016

[28] World Weather Information Service ldquoWeather forecast for Kar-balardquo 2016 httpworldweatherwmointencityhtmlcityId1465

[29] Autodesk Autodesk Storm and Sanitary Analysis ManualAutodesk San Rafael CA USA 2016


[30] C Maksimovic D Prodanovic S Boonya-AroonnetJ P Leitatildeo S Djordjevic and R Allitt ldquoOverland flow andpathway analysis for modelling of urban pluvial floodingrdquoJournal of Hydraulic Research vol 47 no 4 pp 512ndash5232009

[31] P Gauckler EtudesEeoriques et Pratiques sur lrsquoEcoulement etle Mouvement des Eaux Gauthier-Villars Paris France 1867

[32] G Terdik and W A Woyczynski ldquoRosinski measures fortempered stable and related OrnsteinndashUhlenbeck processesrdquoProbability and Mathematical Statistics vol 26 no 2 p 2132006

[33] D M Bates and D G Watts Nonlinear Regression Analysisand Its Applications Wiley New York NY USA 1988

[34] C M Crainiceanu and D Ruppert ldquoLikelihood ratio tests inlinear mixed models with one variance componentrdquo Journalof the Royal Statistical Society Series B vol 66 no 1pp 165ndash185 2004

[35] S Huet A Bouvier M A Poursat and E Jolivet StatisticalTools for Nonlinear Regression A Practical Guide with S-Plusand R Examples Springer Science amp Business Media BerlinGermany 2006

[36] F Baty C Ritz S Charles M Brutsche J P Flandrois andM L Delignette-Muller ldquoA toolbox for nonlinear regressionin R the package nlstoolsrdquo Journal of Statistical Softwarevol 66 no 5 p 1 2015

[37] R H Shumway and D S Stoffer ARIMA Models In TimeSeries Analysis and Its Applications Springer New York NYUSA 2011

[38] W An and J M Gianvito ldquoKiski Valley WPCA CombinedSewer System Long Term Model Studyrdquo Journal of WaterManagement Modeling 2011

[39] P M Bentler and D G Bonett ldquoSignificance tests andgoodness of fit in the analysis of covariance structuresrdquoPsychological Bulletin vol 88 no 3 pp 588ndash606 1980

[40] H W Marsh J R Balla and R P McDonald ldquoGoodness-of-fit indexes in confirmatory factor analysis the effect of samplesizerdquo Psychological Bulletin vol 103 no 3 pp 391ndash490 1988

[41] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part Imdasha discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[42] Directorate of Karbala Weather Forecast ldquoReport of Accu-Weather forecast for Karbala Iraqrdquo Rep DWK-88 Gover-norate of Karbala Karbala Iraq 2016

[43] E Tsykin ldquoMultiple nonlinear regressions derived with choiceof free parametersrdquo Applied Mathematical Modelling vol 8no 4 pp 288ndash292 1984


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Submit your manuscripts atwwwhindawicom

N

ndash125 to 1515ndash2323ndash3434ndash4949ndash68



Unit meter

133ndash157157ndash182

(a)

Alkadeer district(study area)

(b)

Figure 1 (a) Elevation map of Karbala city (b) Map of study area Alkadeer district in Karbala city centre Iraq generated by GIS based onavailable data adapted from [26 27]

Table 1 Data about the subcatchment area input to the model

Element ID Area (ha) Drainage node ID Average slope () Equivalent width (m)Sub-02 529 82 00100 11000Sub-03 545 81 00063 16500Sub-04 969 80 00096 19400Sub-05 926 45 00027 11000Sub-06 974 47 00043 14000Sub-07 580 83 00108 12000Sub-08 544 67 00001 12000Sub-09 637 82 00126 13100Sub-10 631 68 00000 14900Sub-13 1010 Out-01 00122 29600Sub-17 283 50 00130 11700Sub-18 520 41 00500 14000Sub-19 636 40 00008 15500Sub-20 557 43 00008 15000Sub-21 652 38 00234 19100Sub-22 650 27 00230 26300Sub-23 651 35 00210 14500Sub-24 529 34 00123 16100Sub-25 722 32 00113 19600Sub-26 807 22 00140 27200Sub-27 759 21 00130 26200Sub-28 743 20 00120 29300Sub-29 605 19 00110 27500Sub-30 822 53 00140 25000Sub-31 830 56 00100 19000Sub-33 489 16 00006 15000Sub-34 620 17 00120 28000Sub-35 1059 13 00130 30000Sub-36 2174 4 00040 35000Sub-37 764 60 00019 17000Sub-38 512 79 00085 17000Sub-39 872 3 00016 30000Sub-40 570 54 00050 15500Sub-41 629 51 00036 19000


Table 1 Continued



ElementID

Xcoordinate

Ycoordinate

Invertelevation

(m)



Initialwater

elevation(m)


Surchargeelevation

(m)

Pondedarea(m2)

Minimumpipe cover

(m)

1 4054604 36092856 3197 3420 223 3245 048 3420 000 1633 4048259 36084766 3806 3948 142 3842 036 3948 000 0854 4046597 36083751 3844 3986 142 3880 036 3986 200 1027 4046559 36087445 3658 3895 237 3694 036 3895 200 1978 4048117 36088489 3609 3808 199 3645 036 3808 200 1599 4049383 36089419 3570 3770 200 3606 036 3770 200 16010 4050688 36090375 3529 3762 233 3565 036 3762 200 19311 4052346 36091513 3464 3702 238 3512 048 3702 200 17812 4046581 36081767 3927 4085 158 3963 036 4085 200 11813 4045964 36079134 4013 4198 185 4049 036 4198 200 14514 4047596 36080103 3853 4029 176 3889 036 4029 200 13615 4048783 36080792 3791 3975 184 3827 036 3975 200 14416 4050088 36081565 3724 3879 155 3760 036 3879 200 11517 4047844 36082531 3841 4025 184 3877 036 4025 200 14418 4049583 36083502 3705 3875 170 3741 036 3875 200 13019 4051011 36080048 3714 3872 158 3750 036 3872 200 11820 4049685 36079343 3763 3948 185 3800 037 3948 200 14521 4048323 36078584 3847 4080 233 3883 036 4080 200 19322 4046644 36077670 4072 4260 188 4108 036 4272 200 14823 4054939 36080018 3480 3723 243 3516 036 3723 200 15924 4053779 36079539 3624 3845 221 3660 036 3845 200 18125 4052544 36077384 3728 3908 180 3764 036 3908 200 14027 4050025 36075756 3998 4156 158 4032 034 4156 200 11828 4051861 36078388 3666 3881 215 3699 033 3881 200 17529 4049130 36076741 3937 4100 163 3973 036 4100 200 12332 4055974 36077793 3483 3669 186 3529 046 3669 200 14633 4054784 36077092 3518 3749 231 3554 036 3749 200 19134 4053752 36076454 3548 3762 214 3584 036 3762 200 17435 4052592 36075757 3677 3868 191 3713 036 3868 200 15136 4051301 36074946 3812 4034 222 3848 036 4034 200 18237 4050170 36074219 3920 4073 153 3956 036 4073 200 11338 4048865 36073390 3984 4146 162 4020 036 4146 200 12239 4047324 36072446 4029 4204 175 4075 046 4204 200 13540 4058854 36079613 3398 3587 189 3434 036 3587 200 14941 4060007 36080320 3291 3490 199 3327 036 3490 200 159






Table 2 Continued

ElementID

Xcoordinate

Ycoordinate

Invertelevation

(m)



Initialwater

elevation(m)


Surchargeelevation

(m)

Pondedarea(m2)

Minimumpipe cover

(m)

42 4061483 36081232 3206 3397 191 3242 036 3397 200 13143 4057083 36078474 3450 3641 191 3496 046 3641 200 15145 4066400 36088035 2656 2898 242 2730 074 2898 200 16246 4065326 36087458 2664 2929 265 2728 064 2929 200 18547 4063994 36086589 2760 3031 271 2770 010 3031 200 19148 4062519 36085687 2856 3110 254 2889 033 3110 200 17449 4061248 36084928 2953 3213 260 3027 074 3213 200 18050 4059783 36084038 2967 3323 356 3031 064 3323 200 27651 4057198 36083251 3205 3331 126 3253 048 3331 200 05652 4055863 36082388 3238 3497 259 3286 048 3497 200 18653 4054213 36081337 3421 3621 200 3457 036 3621 200 14054 4059459 36084584 3015 3318 303 3063 048 3318 200 23855 4053706 36082188 3406 3636 230 3454 048 3636 200 15256 4053071 36083253 3425 3661 236 3473 048 3661 200 17357 4052482 36084240 3427 3662 235 3475 048 3662 200 17058 4051908 36085202 3425 3710 285 3473 048 3710 200 21259 4051377 36086092 3440 3668 228 3476 036 3668 200 16460 4050713 36087210 3448 3743 295 3484 036 3743 200 25563 4052434 36080754 3566 3824 258 3699 133 3824 200 21865 4051414 36082430 3635 3815 180 3671 036 3815 200 14066 4056206 36085106 3212 3462 250 3248 036 3462 200 21067 4058362 36086409 3094 3324 230 3130 036 3324 200 16668 4057678 36087588 3118 3341 223 3154 036 3341 200 15869 4056646 36086957 3236 3461 225 3272 036 3461 200 18570 4055571 36086229 3333 3533 200 3399 066 3533 200 16071 4057089 36088611 3113 3353 240 3149 036 3353 200 10072 4056179 36088121 3237 3499 262 3270 033 3499 200 22273 4055110 36087445 3414 3589 175 3440 026 3589 200 13574 4056495 36089665 3150 3397 247 3186 036 3397 200 18775 4055486 36089113 3297 3552 255 3333 036 3552 200 21576 4055909 36090654 3156 3433 277 3204 048 3433 200 21777 405530 36091668 3172 3431 259 3220 048 3431 200 19979 4050429 36084049 3677 3827 150 3713 036 3827 200 11080 4063346 36093570 2061 2495 434 2110 049 2495 200 00081 4064095 36092331 2100 2461 361 2140 040 2461 200 31182 4064859 36091069 2218 2700 482 2258 040 2700 200 43283 4065703 36089675 2430 2750 320 2470 040 2750 200 270



ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)








22 Data


Table 3 Continued

ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)



25

20

15

10

5

0000

10

20

30

40

50


Rain

fall

(mm

)

Tem

pera

ture

(degC)












Scenario 140

30

20

10

0

50

40

30

20

10

Rain

fall

dept

h (m

m)

0

Scenario 2

100

80

60

40

20

00 500 1000


Scenario 3


LcLp

LcLp

QcQp1

TccTcp1 TccTcp2

TccTcp

H4

H3H1

ScSp

ScSp

VcVp

VcVp1 VcVp2 VcVp3

AcAp

AcAp

H2

H5

TccTcp3

QcQp2

QcQp

QcQp3



7

6

5

4

3

2

1

00


Scenario 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Perc

ent o

f tot

al

0 05 1 15 2 25 3 35 4 45 5 55 6


Scenario 1

65

10

9

8

7

6

5

4

3

2

1

9

8

7

6

5

4

3

2

1

0


Scenario 3

0978


(a)

Figure 5 Continued




7222 7403 7584 7764 7944 8125 8305 8486 8667 8847

7222

Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

Scenario 1

0123456702468

1012141618

25201510

50

7403 7584 7764 7944 8125 8305 8486 8667 8847

7335 7523 7711 7899 8088 8275 8463 8651 8840 9028

7335

Scenario 2Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

0

05

10152025303540

5040302010

0

2468

10121416

7523 7711 7899 8088 8275 8463 8651 8840 9028

7315

Scenario 3Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

7503 7690 7878 8065 8253 8440 8628 8815 9003

731505

101520253035

0102030405060708090

10080604020

0

7503 7690 7878 8065Time (hour)

8253 8440 8628 8815 9003

(b)



0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025



Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob


evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015



3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Table 1 Continued



ElementID

Xcoordinate

Ycoordinate

Invertelevation

(m)



Initialwater

elevation(m)


Surchargeelevation

(m)

Pondedarea(m2)

Minimumpipe cover

(m)

1 4054604 36092856 3197 3420 223 3245 048 3420 000 1633 4048259 36084766 3806 3948 142 3842 036 3948 000 0854 4046597 36083751 3844 3986 142 3880 036 3986 200 1027 4046559 36087445 3658 3895 237 3694 036 3895 200 1978 4048117 36088489 3609 3808 199 3645 036 3808 200 1599 4049383 36089419 3570 3770 200 3606 036 3770 200 16010 4050688 36090375 3529 3762 233 3565 036 3762 200 19311 4052346 36091513 3464 3702 238 3512 048 3702 200 17812 4046581 36081767 3927 4085 158 3963 036 4085 200 11813 4045964 36079134 4013 4198 185 4049 036 4198 200 14514 4047596 36080103 3853 4029 176 3889 036 4029 200 13615 4048783 36080792 3791 3975 184 3827 036 3975 200 14416 4050088 36081565 3724 3879 155 3760 036 3879 200 11517 4047844 36082531 3841 4025 184 3877 036 4025 200 14418 4049583 36083502 3705 3875 170 3741 036 3875 200 13019 4051011 36080048 3714 3872 158 3750 036 3872 200 11820 4049685 36079343 3763 3948 185 3800 037 3948 200 14521 4048323 36078584 3847 4080 233 3883 036 4080 200 19322 4046644 36077670 4072 4260 188 4108 036 4272 200 14823 4054939 36080018 3480 3723 243 3516 036 3723 200 15924 4053779 36079539 3624 3845 221 3660 036 3845 200 18125 4052544 36077384 3728 3908 180 3764 036 3908 200 14027 4050025 36075756 3998 4156 158 4032 034 4156 200 11828 4051861 36078388 3666 3881 215 3699 033 3881 200 17529 4049130 36076741 3937 4100 163 3973 036 4100 200 12332 4055974 36077793 3483 3669 186 3529 046 3669 200 14633 4054784 36077092 3518 3749 231 3554 036 3749 200 19134 4053752 36076454 3548 3762 214 3584 036 3762 200 17435 4052592 36075757 3677 3868 191 3713 036 3868 200 15136 4051301 36074946 3812 4034 222 3848 036 4034 200 18237 4050170 36074219 3920 4073 153 3956 036 4073 200 11338 4048865 36073390 3984 4146 162 4020 036 4146 200 12239 4047324 36072446 4029 4204 175 4075 046 4204 200 13540 4058854 36079613 3398 3587 189 3434 036 3587 200 14941 4060007 36080320 3291 3490 199 3327 036 3490 200 159






Table 2 Continued

ElementID

Xcoordinate

Ycoordinate

Invertelevation

(m)



Initialwater

elevation(m)


Surchargeelevation

(m)

Pondedarea(m2)

Minimumpipe cover

(m)

42 4061483 36081232 3206 3397 191 3242 036 3397 200 13143 4057083 36078474 3450 3641 191 3496 046 3641 200 15145 4066400 36088035 2656 2898 242 2730 074 2898 200 16246 4065326 36087458 2664 2929 265 2728 064 2929 200 18547 4063994 36086589 2760 3031 271 2770 010 3031 200 19148 4062519 36085687 2856 3110 254 2889 033 3110 200 17449 4061248 36084928 2953 3213 260 3027 074 3213 200 18050 4059783 36084038 2967 3323 356 3031 064 3323 200 27651 4057198 36083251 3205 3331 126 3253 048 3331 200 05652 4055863 36082388 3238 3497 259 3286 048 3497 200 18653 4054213 36081337 3421 3621 200 3457 036 3621 200 14054 4059459 36084584 3015 3318 303 3063 048 3318 200 23855 4053706 36082188 3406 3636 230 3454 048 3636 200 15256 4053071 36083253 3425 3661 236 3473 048 3661 200 17357 4052482 36084240 3427 3662 235 3475 048 3662 200 17058 4051908 36085202 3425 3710 285 3473 048 3710 200 21259 4051377 36086092 3440 3668 228 3476 036 3668 200 16460 4050713 36087210 3448 3743 295 3484 036 3743 200 25563 4052434 36080754 3566 3824 258 3699 133 3824 200 21865 4051414 36082430 3635 3815 180 3671 036 3815 200 14066 4056206 36085106 3212 3462 250 3248 036 3462 200 21067 4058362 36086409 3094 3324 230 3130 036 3324 200 16668 4057678 36087588 3118 3341 223 3154 036 3341 200 15869 4056646 36086957 3236 3461 225 3272 036 3461 200 18570 4055571 36086229 3333 3533 200 3399 066 3533 200 16071 4057089 36088611 3113 3353 240 3149 036 3353 200 10072 4056179 36088121 3237 3499 262 3270 033 3499 200 22273 4055110 36087445 3414 3589 175 3440 026 3589 200 13574 4056495 36089665 3150 3397 247 3186 036 3397 200 18775 4055486 36089113 3297 3552 255 3333 036 3552 200 21576 4055909 36090654 3156 3433 277 3204 048 3433 200 21777 405530 36091668 3172 3431 259 3220 048 3431 200 19979 4050429 36084049 3677 3827 150 3713 036 3827 200 11080 4063346 36093570 2061 2495 434 2110 049 2495 200 00081 4064095 36092331 2100 2461 361 2140 040 2461 200 31182 4064859 36091069 2218 2700 482 2258 040 2700 200 43283 4065703 36089675 2430 2750 320 2470 040 2750 200 270



ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)








22 Data


Table 3 Continued

ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)



25

20

15

10

5

0000

10

20

30

40

50


Rain

fall

(mm

)

Tem

pera

ture

(degC)












Scenario 140

30

20

10

0

50

40

30

20

10

Rain

fall

dept

h (m

m)

0

Scenario 2

100

80

60

40

20

00 500 1000


Scenario 3


LcLp

LcLp

QcQp1

TccTcp1 TccTcp2

TccTcp

H4

H3H1

ScSp

ScSp

VcVp

VcVp1 VcVp2 VcVp3

AcAp

AcAp

H2

H5

TccTcp3

QcQp2

QcQp

QcQp3



7

6

5

4

3

2

1

00


Scenario 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Perc

ent o

f tot

al

0 05 1 15 2 25 3 35 4 45 5 55 6


Scenario 1

65

10

9

8

7

6

5

4

3

2

1

9

8

7

6

5

4

3

2

1

0


Scenario 3

0978


(a)

Figure 5 Continued




7222 7403 7584 7764 7944 8125 8305 8486 8667 8847

7222

Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

Scenario 1

0123456702468

1012141618

25201510

50

7403 7584 7764 7944 8125 8305 8486 8667 8847

7335 7523 7711 7899 8088 8275 8463 8651 8840 9028

7335

Scenario 2Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

0

05

10152025303540

5040302010

0

2468

10121416

7523 7711 7899 8088 8275 8463 8651 8840 9028

7315

Scenario 3Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

7503 7690 7878 8065 8253 8440 8628 8815 9003

731505

101520253035

0102030405060708090

10080604020

0

7503 7690 7878 8065Time (hour)

8253 8440 8628 8815 9003

(b)



0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025



Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob


evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015



3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Table 2 Continued

ElementID

Xcoordinate

Ycoordinate

Invertelevation

(m)



Initialwater

elevation(m)


Surchargeelevation

(m)

Pondedarea(m2)

Minimumpipe cover

(m)

42 4061483 36081232 3206 3397 191 3242 036 3397 200 13143 4057083 36078474 3450 3641 191 3496 046 3641 200 15145 4066400 36088035 2656 2898 242 2730 074 2898 200 16246 4065326 36087458 2664 2929 265 2728 064 2929 200 18547 4063994 36086589 2760 3031 271 2770 010 3031 200 19148 4062519 36085687 2856 3110 254 2889 033 3110 200 17449 4061248 36084928 2953 3213 260 3027 074 3213 200 18050 4059783 36084038 2967 3323 356 3031 064 3323 200 27651 4057198 36083251 3205 3331 126 3253 048 3331 200 05652 4055863 36082388 3238 3497 259 3286 048 3497 200 18653 4054213 36081337 3421 3621 200 3457 036 3621 200 14054 4059459 36084584 3015 3318 303 3063 048 3318 200 23855 4053706 36082188 3406 3636 230 3454 048 3636 200 15256 4053071 36083253 3425 3661 236 3473 048 3661 200 17357 4052482 36084240 3427 3662 235 3475 048 3662 200 17058 4051908 36085202 3425 3710 285 3473 048 3710 200 21259 4051377 36086092 3440 3668 228 3476 036 3668 200 16460 4050713 36087210 3448 3743 295 3484 036 3743 200 25563 4052434 36080754 3566 3824 258 3699 133 3824 200 21865 4051414 36082430 3635 3815 180 3671 036 3815 200 14066 4056206 36085106 3212 3462 250 3248 036 3462 200 21067 4058362 36086409 3094 3324 230 3130 036 3324 200 16668 4057678 36087588 3118 3341 223 3154 036 3341 200 15869 4056646 36086957 3236 3461 225 3272 036 3461 200 18570 4055571 36086229 3333 3533 200 3399 066 3533 200 16071 4057089 36088611 3113 3353 240 3149 036 3353 200 10072 4056179 36088121 3237 3499 262 3270 033 3499 200 22273 4055110 36087445 3414 3589 175 3440 026 3589 200 13574 4056495 36089665 3150 3397 247 3186 036 3397 200 18775 4055486 36089113 3297 3552 255 3333 036 3552 200 21576 4055909 36090654 3156 3433 277 3204 048 3433 200 21777 405530 36091668 3172 3431 259 3220 048 3431 200 19979 4050429 36084049 3677 3827 150 3713 036 3827 200 11080 4063346 36093570 2061 2495 434 2110 049 2495 200 00081 4064095 36092331 2100 2461 361 2140 040 2461 200 31182 4064859 36091069 2218 2700 482 2258 040 2700 200 43283 4065703 36089675 2430 2750 320 2470 040 2750 200 270



ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)








22 Data


Table 3 Continued

ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)



25

20

15

10

5

0000

10

20

30

40

50


Rain

fall

(mm

)

Tem

pera

ture

(degC)












Scenario 140

30

20

10

0

50

40

30

20

10

Rain

fall

dept

h (m

m)

0

Scenario 2

100

80

60

40

20

00 500 1000


Scenario 3


LcLp

LcLp

QcQp1

TccTcp1 TccTcp2

TccTcp

H4

H3H1

ScSp

ScSp

VcVp

VcVp1 VcVp2 VcVp3

AcAp

AcAp

H2

H5

TccTcp3

QcQp2

QcQp

QcQp3



7

6

5

4

3

2

1

00


Scenario 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Perc

ent o

f tot

al

0 05 1 15 2 25 3 35 4 45 5 55 6


Scenario 1

65

10

9

8

7

6

5

4

3

2

1

9

8

7

6

5

4

3

2

1

0


Scenario 3

0978


(a)

Figure 5 Continued




7222 7403 7584 7764 7944 8125 8305 8486 8667 8847

7222

Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

Scenario 1

0123456702468

1012141618

25201510

50

7403 7584 7764 7944 8125 8305 8486 8667 8847

7335 7523 7711 7899 8088 8275 8463 8651 8840 9028

7335

Scenario 2Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

0

05

10152025303540

5040302010

0

2468

10121416

7523 7711 7899 8088 8275 8463 8651 8840 9028

7315

Scenario 3Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

7503 7690 7878 8065 8253 8440 8628 8815 9003

731505

101520253035

0102030405060708090

10080604020

0

7503 7690 7878 8065Time (hour)

8253 8440 8628 8815 9003

(b)



0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025



Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob


evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015



3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)








22 Data


Table 3 Continued

ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)



25

20

15

10

5

0000

10

20

30

40

50


Rain

fall

(mm

)

Tem

pera

ture

(degC)












Scenario 140

30

20

10

0

50

40

30

20

10

Rain

fall

dept

h (m

m)

0

Scenario 2

100

80

60

40

20

00 500 1000


Scenario 3


LcLp

LcLp

QcQp1

TccTcp1 TccTcp2

TccTcp

H4

H3H1

ScSp

ScSp

VcVp

VcVp1 VcVp2 VcVp3

AcAp

AcAp

H2

H5

TccTcp3

QcQp2

QcQp

QcQp3



7

6

5

4

3

2

1

00


Scenario 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Perc

ent o

f tot

al

0 05 1 15 2 25 3 35 4 45 5 55 6


Scenario 1

65

10

9

8

7

6

5

4

3

2

1

9

8

7

6

5

4

3

2

1

0


Scenario 3

0978


(a)

Figure 5 Continued




7222 7403 7584 7764 7944 8125 8305 8486 8667 8847

7222

Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

Scenario 1

0123456702468

1012141618

25201510

50

7403 7584 7764 7944 8125 8305 8486 8667 8847

7335 7523 7711 7899 8088 8275 8463 8651 8840 9028

7335

Scenario 2Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

0

05

10152025303540

5040302010

0

2468

10121416

7523 7711 7899 8088 8275 8463 8651 8840 9028

7315

Scenario 3Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

7503 7690 7878 8065 8253 8440 8628 8815 9003

731505

101520253035

0102030405060708090

10080604020

0

7503 7690 7878 8065Time (hour)

8253 8440 8628 8815 9003

(b)



0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025



Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob


evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015



3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






22 Data


Table 3 Continued

ElementID

From (inlet)node

To (outlet)node

Length(m)



Averageslope ()

Pipeshape

Pipediameter

(m)



25

20

15

10

5

0000

10

20

30

40

50


Rain

fall

(mm

)

Tem

pera

ture

(degC)












Scenario 140

30

20

10

0

50

40

30

20

10

Rain

fall

dept

h (m

m)

0

Scenario 2

100

80

60

40

20

00 500 1000


Scenario 3


LcLp

LcLp

QcQp1

TccTcp1 TccTcp2

TccTcp

H4

H3H1

ScSp

ScSp

VcVp

VcVp1 VcVp2 VcVp3

AcAp

AcAp

H2

H5

TccTcp3

QcQp2

QcQp

QcQp3



7

6

5

4

3

2

1

00


Scenario 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Perc

ent o

f tot

al

0 05 1 15 2 25 3 35 4 45 5 55 6


Scenario 1

65

10

9

8

7

6

5

4

3

2

1

9

8

7

6

5

4

3

2

1

0


Scenario 3

0978


(a)

Figure 5 Continued




7222 7403 7584 7764 7944 8125 8305 8486 8667 8847

7222

Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

Scenario 1

0123456702468

1012141618

25201510

50

7403 7584 7764 7944 8125 8305 8486 8667 8847

7335 7523 7711 7899 8088 8275 8463 8651 8840 9028

7335

Scenario 2Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

0

05

10152025303540

5040302010

0

2468

10121416

7523 7711 7899 8088 8275 8463 8651 8840 9028

7315

Scenario 3Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

7503 7690 7878 8065 8253 8440 8628 8815 9003

731505

101520253035

0102030405060708090

10080604020

0

7503 7690 7878 8065Time (hour)

8253 8440 8628 8815 9003

(b)



0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025



Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob


evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015



3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Scenario 140

30

20

10

0

50

40

30

20

10

Rain

fall

dept

h (m

m)

0

Scenario 2

100

80

60

40

20

00 500 1000


Scenario 3


LcLp

LcLp

QcQp1

TccTcp1 TccTcp2

TccTcp

H4

H3H1

ScSp

ScSp

VcVp

VcVp1 VcVp2 VcVp3

AcAp

AcAp

H2

H5

TccTcp3

QcQp2

QcQp

QcQp3



7

6

5

4

3

2

1

00


Scenario 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Perc

ent o

f tot

al

0 05 1 15 2 25 3 35 4 45 5 55 6


Scenario 1

65

10

9

8

7

6

5

4

3

2

1

9

8

7

6

5

4

3

2

1

0


Scenario 3

0978


(a)

Figure 5 Continued




7222 7403 7584 7764 7944 8125 8305 8486 8667 8847

7222

Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

Scenario 1

0123456702468

1012141618

25201510

50

7403 7584 7764 7944 8125 8305 8486 8667 8847

7335 7523 7711 7899 8088 8275 8463 8651 8840 9028

7335

Scenario 2Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

0

05

10152025303540

5040302010

0

2468

10121416

7523 7711 7899 8088 8275 8463 8651 8840 9028

7315

Scenario 3Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

7503 7690 7878 8065 8253 8440 8628 8815 9003

731505

101520253035

0102030405060708090

10080604020

0

7503 7690 7878 8065Time (hour)

8253 8440 8628 8815 9003

(b)



0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025



Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob


evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015



3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


7

6

5

4

3

2

1

00


Scenario 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Perc

ent o

f tot

al

0 05 1 15 2 25 3 35 4 45 5 55 6


Scenario 1

65

10

9

8

7

6

5

4

3

2

1

9

8

7

6

5

4

3

2

1

0


Scenario 3

0978


(a)

Figure 5 Continued




7222 7403 7584 7764 7944 8125 8305 8486 8667 8847

7222

Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

Scenario 1

0123456702468

1012141618

25201510

50

7403 7584 7764 7944 8125 8305 8486 8667 8847

7335 7523 7711 7899 8088 8275 8463 8651 8840 9028

7335

Scenario 2Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

0

05

10152025303540

5040302010

0

2468

10121416

7523 7711 7899 8088 8275 8463 8651 8840 9028

7315

Scenario 3Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

7503 7690 7878 8065 8253 8440 8628 8815 9003

731505

101520253035

0102030405060708090

10080604020

0

7503 7690 7878 8065Time (hour)

8253 8440 8628 8815 9003

(b)



0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025



Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob


evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015



3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




7222 7403 7584 7764 7944 8125 8305 8486 8667 8847

7222

Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

Scenario 1

0123456702468

1012141618

25201510

50

7403 7584 7764 7944 8125 8305 8486 8667 8847

7335 7523 7711 7899 8088 8275 8463 8651 8840 9028

7335

Scenario 2Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

0

05

10152025303540

5040302010

0

2468

10121416

7523 7711 7899 8088 8275 8463 8651 8840 9028

7315

Scenario 3Rain

fall

(mm

hr)

Runo

ff (c

ms)

Floo

ding

(cm

s)

7503 7690 7878 8065 8253 8440 8628 8815 9003

731505

101520253035

0102030405060708090

10080604020

0

7503 7690 7878 8065Time (hour)

8253 8440 8628 8815 9003

(b)



0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025



Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob


evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015



3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


pect

ed cu

m p

rob

06 08 10

02

04

06

08

10

0000 02 04

Observed cum prob


Expe

cted

cum

pro

b

06 08 10

02

04

06

08

10

ndash00400 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash002

000

002

004

006

ndash0025



Dev

iatio

n fro

m n

orm

al

06 08 10

0000

0025

0050

0075

0100

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash0300 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash02

ndash01

00000

01

02

03

ndash01000 02 04

Observed cum prob


Dev

iatio

n fro

m n

orm

al

06 08 10

ndash005

000

005

010

ndash01500 02 04

Observed cum prob


evia

tion

from

nor

mal

06 08 10

ndash010

ndash005

00000

005

010

015



3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


3

2

1

0



pect

ed n

orm

al v

alue

2 4

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


3

2

1

0



pect

ed n

orm

al v

alue

2 3

ndash1

ndash2


3

2

1

0



Expe

cted

nor

mal

val

ue

2 3

ndash1

ndash2


1

0

ndash1



Dev

iatio

n fro

m n

orm

al

0 2

ndash2

ndash3


06

04

00000

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02

ndash04


04

00

02



Dev

iatio

n fro

m n

orm

al

1 32

ndash02


05

00

04

03

02



Dev

iatio

n fro

m n

orm

al

1 32

01

ndash01


04

ndash01

03

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02


03

ndash01

02

01



Dev

iatio

n fro

m n

orm

al

1 32

00000

ndash02









ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







ni1 Pi

∣∣∣∣∣∣∣∣










VcVp

ScSp

AcAp

LcLp

TccTcp



00 05 10 15 20 25 30 35 40 45QcQp

0102030405060708090

100

Empirical CDFNormal


F(x)







15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






15

0

05

1

2

25

3

35

4

45Su

b-02

Sub-

03Su

b-04

Sub-

05Su

b-06

Sub-

07Su

b-08

Sub-

09Su

b-10

Sub-

13Su

b-17

Sub-

18Su

b-19

Sub-

20Su

b-21

Sub-

22Su

b-23

Sub-

24Su

b-25

Sub-

26Su

b-27

Sub-

28Su

b-29

Sub-

30Su

b-31

Sub-

33Su

b-34

Sub-

35Su

b-36

Sub-

37Su

b-38

Sub-

39Su

b-40

Sub-

41Su

b-42

Sub-

43Su

b-44

Sub-

45Su

b-46

Sub-

47Su

b-48

Sub-

49Su

b-50

Sub-

51Su

b-52

Sub-

53Su

b-54

Sub-

55Su

b-56

Sub-

57

QcQp-1QcQp-2QcQp-3



(a)

0

05

1

15

2

25

3

35

4

45

Sub-

02Su

b-03

Sub-

04Su

b-05

Sub-

06Su

b-07

Sub-

08Su

b-09

Sub-

10Su

b-13

Sub-

17Su

b-18

Sub-

19Su

b-20

Sub-

21Su

b-22

Sub-

23Su

b-24

Sub-

25Su

b-26

Sub-

27Su

b-28

Sub-

29Su

b-30

Sub-

31Su

b-33

Sub-

34Su

b-35

Sub-

36Su

b-37

Sub-

38Su

b-39

Sub-

40Su

b-41

Sub-

42Su

b-43

Sub-

44Su

b-45

Sub-

46Su

b-47

Sub-

48Su

b-49

Sub-

50Su

b-51

Sub-

52Su

b-53

Sub-

54Su

b-55

Sub-

56Su

b-57

VcVp-1VcVp-2VcVp-3



(b)



Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Qc

Qp1113888 1113889min 3147 times ln

Ac

Ap1113888 1113889

04

+ 399 times lnSc

Sp1113888 1113889

005

+ 825 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 1110

(4)

Qc

Qp1113888 1113889ave 4650 times ln

Ac

Ap1113888 1113889

04

+ 930 times lnSc

Sp1113888 1113889

005

+ 1360 times lnVc

Vp1113888 1113889

0055


Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 775

(5)

Qc

Qp1113888 1113889max 6165 times ln

Ac

Ap1113888 1113889

04

+ 1460 times lnSc

Sp1113888 1113889

005

+ 1897 times lnVc

Vp1113888 1113889

0055

+ 042 times lnTcc

Tcp1113888 1113889

05


Lp1113888 1113889

05

minus 440

(6)







00 05 10 15 20 25 30 35 40 45Predicted QcQp

00

05

10

15

20

25

30

35

40

45

Obs

erve

d Q

cQp










gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








gt8E5lt8E5lt7E5

lt6E5lt5E5lt4E5

lt3E5lt2E5lt1E5


01E52E53E54E55E56E57E58E59E5

ndash010001020304

0908070605

45403530252015100500

A cA

p

Sc Sp Q cQ p

(a)

gt6E5lt55E5lt45E5

lt35E5lt25E5lt15E5


01E52E53E54E55E56E57E58E59E5

ndash0200

0204

0608

10121416

00051015202530354045

A cA

p

Vc V

pQ cQ p

(b)

gt100lt80ltndash20


ndash10016

141210080604

0200

ndash02

45403530252015100500

0100200300400500600700

Vc V

pQ cQ p

T ccT

cp

(c)

gt06lt06lt04

lt02lt0ltndash02




ndash0200

0204

0608

1012

1416

00051015202530354045

Vc V

p Q cQ p

S cS

p

(d)

gt2lt15lt05


0123456

ndash0100

0102

0304050607

0809

00051015202530354045

Sc S

p Q cQ p

L cL

p

(e)

gt100lt60ltndash40


ndash1000

100200300400500600700

01

23

45

6

00051015202530354045

Lc L

pQ cQ p

T ccT

cp

(f)








References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







References
















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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