邱逢琛Chiu, Forng-Chen工程科學及海洋工程學研究所刁文川Tiao, Wen-ChuanWen-ChuanTiao2010-07-142018-06-282010-07-142018-06-282007U0001-0312200713583600http://ntur.lib.ntu.edu.tw//handle/246246/188920船舶高速航行於波浪中，其運動及壓力反應皆呈現非線性的行為，同時線性統計理論亦不足以對不規則波中的統計特性一窺全貌；另一方面，Volterra模式已被應用於船舶非線性運動時的統計特性分析。因此本文重點在探討高速船在波中運動時水壓所呈現的非線性特性，特別是在乾濕變換的水線附近及承受衝擊壓的艏底位置。為確立Volterra模式對水壓分析的有效性，進而規劃一系列以RD200船型為對象之曳航試驗，量測包含起伏及俯仰二個運動、加速度及船殼25點的水壓等項目，同時本文亦提出該模式所需之頻率響應函數的計算方式，並以三階及五階Volterra模式進行討論分析，其結果確立三階Volterra模式可充份掌握水壓在規則波中變化的非線性特性。此外更進一步的藉由非線性截片法在規則波中所建構之理論基礎，經由非線性Volterra模式所架構之平台，來評估該理論來預測不規則波統計特性之可行性。透過時域及分散譜比較，累進分布機率及機率密度函數等統計分析，驗證了該模式可掌握非線性及非高斯水壓變化的特性。It is well known that the hydrodynamic responses of a high-speed vessel traveling in regular head waves even of moderate wave height can show significant nonlinear behavior, and so linear statistical techniques become insufficient for predicting the statistics of responses in irregular waves. On the other hand, it has been shown that an approximate third-order Volterra model is applicable to handling the statistics of some nonlinear seakeeping problems, such as motions and vertical hull girder loads. In the present study, the focus is on the nonlinear behavior of the pressure acting on the hull surface of a high-speed vessel in waves, especially on the pressure responses of alternately wet and dry areas near waterline and on the bow zone with high deadrise angles that may be subject to slight impact and water pile-up effects. To clarify the validity of applying Volterra modeling to this problem, a series of experiments in regular and irregular head waves are carried out, and approximate third-order and fifth-order Volterra models with proposed algorithm for finding frequency response functions (FRFs) were applied as a means of validation. It was confirmed that the approximate third-order Volterra model has adequate accuracy to simulate deterministically the variation of pressure responses in regular waves of different wave steepness up to a wave amplitude to wavelength ratio of 0.01 even for the highly nonlinear pressures acting on the above-mentioned areas of the hull surface. In additions, further validation was performed using experimental data and theoretical calculation in irregular waves. The frequency response functions (FRFs) obtained both from the experimental data or theoretical calculation in regular waves were applied to the approximate third-order Volterra model combining with the input of irregular waves to simulate deterministically the responses in irregular waves of sea state five, and then the spectra and statistics were analyzed. Through the comparisons of the simulated time histories, variance spectra, and statistics such as cumulative distributions of peak values, probability density functions with the experimental results of motions, accelerations and pressure responses in irregular waves, it was confirmed that the approximate third-order Volterra model has adequate accuracy to simulate deterministically and statistically the pressure responses in irregular head waves up to a sea state of five even for highly nonlinear and non-Gaussian pressures acting on the above-mentioned areas of the hull surface.Table of Contentsbstract iable of Contents ivist of Tables viiist of Figures ixist of Symbols xii. Introduction 1 1.1 Preface 1 1.2 Review and background 1 1.3 Framework of dissertation 5. Experiments 7 2.1 Experimental descriptions 7 2.2 Experimental conditions 9 2.3 Principle characteristics of incident wave 10 2.3.1 Regular wave characteristics 10 2.3.2 Irregular wave characteristics 11. Volterra modeling of a nonlinear system 13.1 Approximate Volterra model 13.2 Algorithm of finding Bj(�s) of FRFs.............................................................16. Simulation and comparison with experimental results in regular waves..................................................................................................................19.1 Comparisons of time histories by using third- or fifth-order Volterra modeling...................................................................................................19.2 Experimental results in regular waves.........................................................21.2.1 Mean values shift of responses...................................................................22.2.2 First harmonic components of responses...................................................23.2.3 Higher-order components of responses......................................................25.3 Harmonic components estimated by third- order Volterra modeling.......27. Simulation and comparison with experimental results in irregular waves.....................................................................................................................30.1 Comparisons of time histories......................................................................30.2 Simulation results in irregular waves..........................................................32.2.1 Response spectra........................................................................................32.2.2 Cumulative distributions of peak values of responses................................33.2.3 Probability density distribution of response...............................................35. Application of Volterra modeling to assess the nonlinear theory of ship responses..................................................................................................37.1 Formulation of a nonlinear strip synthesis.................................................37.1.1 Coordinate system.......................................................................................37.1.2 Sectional force components........................................................................38.1.3 Equations of motion....................................................................................40.1.4 Calculation of water pressure.....................................................................40.2 Comparisons of time histories in regular waves by using nonlinear strip synthesis...........................................................................................................42.3 Frequency response functions.......................................................................43.4 Simulated results of nonlinear strip synthesis in irregular waves...........45.5 Statistical characteristics in irregular waves.............................................46. Conclusions........................................................................................................49eferences................................................................................................................52ppendix A. Digital filter algorithms...............................................................87ppendix B. Definitions of mathematical expression in motions..............90ppendix C. Frequency response functions of measured responses.........91ppendix D. Statistics of responses in irregular waves..............................118able 2.1 Principle particulars of the 1:36 model of a patrol ship...............................57able 2.2 Locations of pressure sensors. C.L., center line; W.L., calm water line......60able 2.3 Calibration record of pressure sensor..........................................................62able 6.1 Statistical analysis of the heave/pitch motions in irregular waves..............83able 6.2 Statistical analysis of the accelerations in irregular waves..........................84able 6.3 Statistical analysis of the pressures in irregular waves................................85able C.1 Frequency response functions of heave motion..........................................91able C.2 Frequency response functions of pitch motion...........................................92able C.3 Frequency response functions of acceleration, A1......................................93able C.4 Frequency response functions of acceleration, A2......................................94able C.5 Frequency response functions of acceleration, A3......................................95able C.6 Frequency response functions of acceleration, A4......................................96able C.7 Frequency response functions of pressure, P10, in the Z1 zone.................97able C.8 Frequency response functions of pressure, P11, in the Z1 zone.................98able C.9 Frequency response functions of pressure, P14, in the Z1 zone.................99able C.10 Frequency response functions of pressure, P18, in the Z2 zone..............100able C.11 Frequency response functions of pressure, P19, in the Z2 zone..............101able C.12 Frequency response functions of pressure, P20, in the Z2 zone..............102able C.13 Frequency response functions of pressure, P21, in the Z2 zone..............103able C.14 Frequency response functions of pressure, P22, in the Z3 zone..............104able C.15 Frequency response functions of pressure, P23, in the Z3 zone..............105able C.16 Frequency response functions of pressure, P24, in the Z3 zone..............106able C.17 Frequency response functions of pressure, P25, in the Z3 zone..............107able C.18 Frequency response functions of pressure, P12, in the Z4 zone..............108able C.19 Frequency response functions of pressure, P15, in the Z4 zone..............109able C.20 Frequency response functions of pressure, P2, in the Z4 zone................110able C.21 Frequency response functions of pressure, P13, in the Z5 zone..............111able C.22 Frequency response functions of pressure, P16, in the Z5 zone..............112able C.23 Frequency response functions of pressure, P3, in the Z5 zone................113able C.24 Frequency response functions of pressure, P5, in the Z6 zone................114able C.25 Frequency response functions of pressure, P6, in the Z6 zone................115able C.26 Frequency response functions of pressure, P8, in the Z6 zone................116able C.27 Frequency response functions of pressure, P9, in the Z6 zone................117able D.1 Statistical analysis of the stern accelerations, A4......................................118able D.2 Statistical analysis of the pressure responses, P11, in the Z1 zones..........118able D.3 Statistical analysis of the pressure responses, P14, in the Z1 zones..........119able D.4 Statistical analysis of the pressure responses, P18, in the Z2 zones..........119able D.5 Statistical analysis of the pressure responses, P19, in the Z2 zones..........119able D.6 Statistical analysis of the pressure responses, P21, in the Z2 zones..........120able D.7 Statistical analysis of the pressure responses, P22, in the Z3 zones..........120able D.8 Statistical analysis of the pressure responses, P24, in the Z3 zones..........120able D.9 Statistical analysis of the pressure responses, P25, in the Z3 zones..........121able D.10 Statistical analysis of the pressure responses, P12, in the Z4 zones........121able D.11 Statistical analysis of the pressure responses, P2, in the Z4 zones..........121able D.12 Statistical analysis of the pressure responses, P13, in the Z5 zones........122able D.13 Statistical analysis of the pressure responses, P3, in the Z5 zones..........122able D.14 Statistical analysis of the pressure responses, P6, in the Z6 zones..........122able D.15 Statistical analysis of the pressure responses, P8, in the Z6 zones..........123able D.16 Statistical analysis of the pressure responses, P9, in the Z6 zones..........123igure 1.1 Analysis flowchart of nonlinear ship responses in waves..........................56igure 2.1 Brief type of RD-200 model......................................................................57igure 2.2 Layout of experiment equipments at towing tank......................................58igure 2.3 Experimental setup. P1-P25, pressure sensors; A1-A4, accelerations.......59igure 2.4 Locations of pressure sensors. W.L., waterline; S.S., sectional station.....59igure 2.5 Flowchart of analysis process in experimental data...................................61igure 2.6 2nd and 3rd harmonic components of incident regular waves.....................63igure 2.7 Variance spectra of incident irregular waves. (left: Fn = 0.31; right: Fn = 0.42)................................................................................................................ 63igure 2.8 Cumulative distributions of peaks (Left) and Probability density distribution (Right) of incident irregular waves. (Fn = 0.42, sea state 5).....................63igure 4.1 Raw data of wave, motions and accelerations. (�f/L = 1.30, Hw/�f = 1/51, Fn = 0.42)...........................................................................................................64igure 4.2 Raw data of pressure responses. (�f/L = 1.30, Hw/�f = 1/51, Fn = 0.42).....64igure 4.3 Time histories of pressure responses. (�f/L = 1.10, Fn = 0.42)...................65igure 4.4 Time histories of pressure responses. (�f/L = 1.50, Fn = 0.42)...................65igure 4.5 Steady-run responses as function of the Froude number...........................66igure 4.6(a) 1st harmonic components of motion responses. (Fn = 0.42)..................66igure 4.6(b) 1st harmonic components of pressure responses. (Fn = 0.42)...............67igure 4.7 Amplitudes of 2nd harmonic components of measured responses. (Fn = 0.42)..................................................................................................................68igure 4.8 Amplitudes of 3rd harmonic components of measured responses. (Fn = 0.42)..................................................................................................................68igure 5.1(a) Time histories of motions and accelerations. (Fn = 0.42, Sea state 5) 69igure 5.1(b) Time histories of pressure responses. (Fn = 0.42, Sea state 5)..............69igure 5.1(c) Time histories of pressure at P10. (Fn = 0.42, Sea state 5)...................70igure 5.1(d) Time histories of pressure at P16. (Fn = 0.42, Sea state 5)...................70igure 5.2(a) Variance spectra of vertical motions and accelerations. (Fn = 0.42, Sea state 5).........................................................................................................71igure 5.2(b) Variance spectra of pressure responses. (Fn = 0.42, Sea state 5)..........71igure 5.3(a) Cumulative distributions of vertical motions and accelerations peaks.Fn = 0.42, Sea state 5)..........................................................................72igure 5.3(b) Cumulative distributions of pressures peaks. (Fn = 0.42, Sea state 5) 72igure 5.4 Probability density functions of pressure responses. (Fn = 0.42, Sea state 5).....................................................................................................................73igure 6.1 Coordinate systems....................................................................................74igure 6.2 Time histories of responses at �f/L = 0.95 and Fn = 0.42. (From left to right: Hw/�f = 1/97, 1/77, 1/50)...........................................................................74igure 6.3 Time histories of responses at �f/L = 1.30 and Fn = 0.42. (From left to right: Hw/�f = 1/90, 1/75, 1/50)...........................................................................75igure 6.4 Mechanism of pressure response near waterline. (�f/L = 1.30, Hw/�f = 1/90, Fn = 0.42)..................................................................................................76igure 6.5 Variation of FRFs in motion and acceleration responses...........................76igure 6.6 Variation of FRFs in pressure responses....................................................77igure 6.7(a) Comparisons of time histories in motions and accelerations. (Fn=0.42, Sea state 5).......................................................................................................78igure 6.7(b) Comparisons of time histories in pressure responses. (Fn=0.42, Sea state 5)..................................................................................................................79igure 6.8(a) Comparisons of variance spectra in vertical motions and accelerations. (Fn = 0.42, Sea state 5)..............................................................................80igure 6.8(b) Comparisons of variance spectra in pressure responses. (Fn = 0.42, Sea state 5).......................................................................................................80igure 6.9(a) Comparisons of cumulative distributions in vertical motions and accelerations peaks. (Fn = 0.42, Sea state 5).............................................81igure 6.9(b) Comparisons of cumulative distributions in pressure peaks. (Fn = 0.42, Sea state 5).................................................................................................81igure 6.10 Comparisons of probability density functions in pressure responses. (Fn = 0.42, Sea state 5)........................................................................................82igure A.1 Low-pass FIR filter designed via the Blackman window. .......................87igure A.2 Comparison of P16��s time histories between raw data and filtered data in regular wave..............................................................................................87igure A.3 Magnitude response of adaptive filter. ....................................................88igure A.4 Comparison of P10��s time histories between raw data and filtered data in irregular wave............................................................................................897137828 bytesapplication/pdfen-US�D�u��#�O���t���T��Volterra�Ҧ��W�v�T3���Nonlinear pressureHigh-speed vesselThird-order Volterra modelFrequency response functionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/188920/1/ntu-96-D90525001-1.pdf