Analysis Of Reconstruction Method Of Dynamics System Under Measurement Noise

With the development of measurement technology,big data has been acquired.Inferring the system dynamics from the measurable data is named dynamics reconstruction.At present,some reconstruction methods have been proposed from different perspectives,however,most of them cannot be applied in strong measurement noises.Yang Chen et al.proposed a reconstruction method called as a high-order correlation computation(HOCC)method,which can effectively detect nonlinear dynamics systems subject to fast-varying noises.But HOCC will bring great reconstruction error when the measurable data contain strong measurement noise.In this thesis,we further investigate HOCC under the conditions of strong measurement noises and hidden variables,and make the following progress:(?)We study how to reduce the influence of measurement noise on HOCC method.We improve HOCC method by using three data processing methods:smoothing method,difference method and average method.The influences of these three processing methods on the reconstructed results of HOCC are theoretically analyzed.The analysis shows that smoothing method,difference method and average method can effectively reduce the reconstruction error,and the average method is more remarkable than the others when the system noises are great.Therefore,when system noises and measurement noises cannot be ignored,the average method is better.We discuss the influence of time step,noise intensity,smoothing window size,and sampling size on the reconstruction effect of these methods.The analysis is confirmed by numerical r-esults.(?)We study how to reduce the reconstruction errors of HOCC under the conditions of measurement noise and hidden variables.Generally we are not able to obtain the time series of all variables,thus it is significant to infer system dynamics when some variables are hidden.Yang Chen et al.proposed a method via calculating high-order differentials to solve the hidden variable problem.But when measurement noise is strong,calculating high-order differentials will produce great errors.In this thesis,we improve HOCC with high-order differentials by using one-time smoothing,two-time smoothing and the average smoothing.The numerical results show that the two-time smoothing and average smoothing methods can effectively reduce reconstruction errors of HOCC.