On-line Prediction Of Non-stationary And Nonlinear Ship Motions At Sea

Ship motions will bring adverse effects on ship related maritime operations such as ship-borne helicopter recovery,float over and cargo transfer between ships etc.,especially in harsh sea conditions.Accurate and reliable on-line short-term prediction of ship motions with tens seconds ahead of time,provides compensation information for active control and safe time window for decision-making,are critical for both operational safety and efficiency.There are two kinds of problems involves in the on-line short-term predicitons of ship motions,they are the extreme short-term prediction and quiescent period prediction(QPP)problems.Short-term prediction of ship motions with a lead time of several seconds,usually used in accurate compensated control,is regared as the extreme short-term prediction problem.Otherwise,short-term prediction with a lead time of tens seconds,deployed in go/no-go decision making for maritime operations,is called as QPP problem.Generally,short-term prediction models for ship motion are developed base on time series analysis.Conventional approaches use the time series models such as auto-regressive(AR)model,auto-regressive moving average(ARMA)model and neural net-work models etc.to forecast the ship motions directly.In the present work,a wave effects based auto-regressive(WEAR)model derived from the ship motion equations with memory effect was proposed.Numerical results showed that the computational efficiency in model identification using time series was largely improved with equivalent prediction accuracy.The sensitive effects of the sampling frequency on efficiency and accuracy were also eliminated.To process the nonlinearity and non-stationarity,empirical mode decomposition(EMD)and Hilbert-Huang transform(HHT)were introduced to analyze the nonlinear and non-stationary ship motions.Comparisons between the conventional Fourier transform and HHT were discussed.Further more,EMD technique combining with linear AR and nonlinear support vector regression(SVR)models had been used to investigate the effects of nonlinearity and non-stationarity on prediction accuracy.Numerical results suggested spatial errors between the predicted and true values originate from nonlinearity while shifts between the predicted and true values result from non-stationarity.The effects of nonlinearity and non-stationarity on the prediction accuracy depend on the prediction lead times.When the lead time is smaller than a certain threshold,the forecasting errors are mainly contributed by the nonlinearity.However,the proportion of the errors resulted from non-stationarity increase as the lead time grows.The non-stationarity related errors was dominant part when the lead time exceeds the threshold.EMD technique is capable in processing nonlinear and non-stationary signals.Combination of prediction models with END technique is a important way to improving the prediction results of nonlinear and non-stationary ship motions.It was found that the on-line EMD processing produce an gain and an loss on forecasting accuracy instantaneously.The accuracy gain is contributed by the effective processing of nonlinearity and non-stationarity while the accuracy loss results from the on-line end effects of the EMD technique.The accuracy loss is able to be seen directly from the predicted time series where obvious "jumps"are widely spread.The EMD-based hybrid model performance worse than a single prediction when the accuracy loss is larger than the accuracy gain.To processing the accuracy loss,a midpoint and regression based empirical mode decomposition(MREMD)approach was proposed.Prediction results using ship motion time series obtained from numerical simulation,towing tests and sea trial consistently indicate that the on-line prediction accuracy of the hybrid MREMD-AR model was obvious better than the conventional EMD-AR model.In addition,the HHT can also be benefited by using the MREMD approach as the computational complexity was reduced and the end effects were better processed.In addition to extreme short-term prediction,the QPP was focused in the present work.Comparatively,QPP concerns about the ranges rather than accurate values of ship motions.However,it requires longer prediction lead time,usually more than 10～15 seconds.Direct prediction using time series has limited lead time where the prediction errors are unacceptable.As the limited lead time depends on the period of ship motion,their relationship was studied.An enhanced QPP approach,using indirect prediction of time series’ envelopes,was proposed base on the fact that the limited lead time is positive to the period of ship motion.Simulation results demonstrated that the enhanced QPP approach produces more reliable forecast and longer time window.