Reconstruction Of Dynamic Atructures Of Experimental Setups Based On Measurable Experimental Data Only

Nonlinear dynamic system structure reconstruction is a very challenging inverse problem.In general,the system structure and node dynamics are unknown,and only the time series data output by nodes can be measured.And sometimes only limited data can be obtained from the dynamic changes of each unit in a nonlinear system,it is impossible to directly measure the interaction between nodes,resulting in that the topology in the system can not be directly obtained.Therefore,in this era of data explosion,how to mine more and more meaningful information through available information,such as the dynamic mechanism behind the data becomes especially important.In this context,this paper is innovative in two aspects:(Ⅰ)For noise-driven systems,we propose a new method(HOCC)to reconstruct the system structure and the noise statistics of the affected systems.The proposed method can derive the network structure,node nonlinear dynamics and noise statistics using the high-order correlation matrix when using only the measured data of the system,using the difference method.This method does not require any other information to understand the system structure,dynamics,noise statistics.The characteristics of HOCC method are as follows:Firstly,when the difference is correlated,the kinematics and noise statistics of the coupled system are separated and calculated separately;secondly,the high-order correlation matrix is used to process the nonlinearity of the system and finally the reconstruction of the complex network The problem is decomposed into a simple problem of linear matrix equation calculation.(Ⅱ)In the past,most works in this respect were based on theoretical analyses and numerical verifications.Direct analyses of experimental data have been very seldom.Especially,in physical science disciplines,most of the analyses of experimental setups were based on the first principles of physics laws,i.e.,so-called botton-up analyses.In this paper,we conduct an experiment of "Boer resonant instrument for forced vibration"(BRIFV)and infer the dynamic structure of the experimental set purely from the analysis of the measurable experimental data,i.e.,applying,up-down strategy.Dynamics of the experimental set is strongly nonlinear and its subjects to inevitable noises.We propose to use high-order correlation computations to treat nonlinear dynamics;use two-time correlations to decorrelate effects of noise effects.By applying these approaches,we have successfully reconstructed the structure of experimental setup,and dynamic system reconstructed with the measured data reproduces well experimental results in wide range of parameters.