Local Sparse Screening Identification Algorithm Of Nonlinear Systems And Its Applications

In recent years,data-driven modeling methods have become an important topic in the field of nonlinear system identification.As compared with traditional theoretical modeling methods,data-driven modeling doesn't rely on prior knowledge,and can directly recover governing equations from experimental or simulation data sets.It is especially suitable for analyzing strong nonlinear system data sets affected by noise factors.Based on the sparse identification nonlinear dynamic algorithm(SINDy)recently proposed by the researchers,this paper proposes two data-driven modeling methods.One is local sparse screening identification algorithm for ODE systems,which combines local linear embedding,SINDy algorithm and mean error screening algorithm,and effectively improves the applicability and identification precision of the original SINDy algorithm.Another one is alternating Ridge-regression identification algorithm(ARRI)for PDE systems,which combines the alternating vector multiplier method,Pareto front analysis and Ridge-regression algorithm.It effectively solves complicated problems,such as multiple solutions of sparse coefficients and selection of basic functions in calculation process.The main research contents and achievements of this paper are embodied in the following aspects:Firstly,the LSSI algorithm is proposed for analyzing ODEs.The LLE algorithm is applied to complete the data filtering process.Based on the noise-free time series,the SINDy algorithm is applied to calculate sparse vectors in the coordinate space,and then the nonlinear term coefficients are determined.Subsequently,the multi-solution problem of calculation process is optimized using the MES algorithm to obtain the optimal sparse coefficient,which completes the reconstruction of governing equations.As compared with the traditional methods,the advantages are described in several parts:on the one hand,it can get rid of the dependence of empirical parameters.Meanwhile,the algorithm can effectively solve the multi-solution problems of sparse coefficient vectors.In addition,the scope of application of the SIDNy algorithm is expanded.The computational efficiency and precision of solving problems is enhanced.Secondly,the LSSI algorithm is used to identify different kinds typical nonlinear system equations.As compared with SINDy algorithm,the new algorithm is verified with the calculation precision and robustness.As a practical application,a class of membrane structure electromagnetic vibration energy harvester is taken as the research object.The LSSI algorithm is used to identify the hidden nonlinear components in the system,and complete the theoretical modeling,making it close to the system in the real world.Finally,the ARRI algorithm is proposed for discussing PDEs.It combines the ADMM algorithm with Pareto front analysis to automatically obtain the optimal combination from the basis function groups,and solves the key problem of basic function selection.The efficiency of the analysis problem is enhanced.As an application,a class of typical PDE models are analyzed to quickly recover the governing equations from noisy simulation data.