Research On Parameter Identification Of Chaotic Systems Based On Sparse Identification Algorithm

Nonlinear dynamics is the science that studies the quantitative and qualitative laws of various states of motion in nonlinear dynamical systems,especially the evolutionary behavior of motion patterns,and chaos is an important branch of nonlinear dynamics.In nonlinear dynamical systems,chaotic systems are highly sensitive to parameters and initial conditions,and the slightest perturbation may lead to completely different results,so it is especially important to identify the parameters of chaotic systems accurately.In general,the control equations of most chaotic systems are only determined by a few variables.At this time,the control equations are sparse in the possible function space,which makes it possible to apply the sparse recognition algorithm in machine learning to the parameter identification of chaotic system control equations.In recent years,the research based on SINDy algorithm is relatively hot,while the traditional Lasso and its optimization algorithm have been less studied.Recent studies have pointed out that the Lasso algorithm is not effective for the identification of control equations with strong nonlinear terms.Based on this,this paper compares the parameter recognition effects of Lasso,SCAD,Adaptive Lasso,Elastic Net and SINDy sparse recognition algorithms,and proposes a sparse recognition algorithm based on Bagging ensemble idea to further improve the parameter recognition accuracy and application scope.The specific research is as follows :(1)Five sparse identification algorithms are applied to the parameter identification of chaotic Lorenz system and new three-dimensional chaotic system,and the results are compared in the algorithm,the order of the base function library and the noise level,then a series of relevant conclusions are obtained.The results show that the recognition effect of SCAD algorithm and Adaptive Lasso algorithm is better than Lasso algorithm,and the recognition effect of Elastic Net algorithm is the worst.SINDy algorithm is limited by threshold and base function library order,and the recognition effect is unstable.Considering the accuracy and scope of application,the SCAD algorithm is considered to have the best recognition effect.(2)It is found that the five algorithms such as Lasso cannot accurately identify some parameters in the two chaotic systems.In order to solve this problem,inspired by the above conclusions and Bagging integration ideas,the SCAD algorithm is combined with the autonomous sampling method and voting decision method in the Bagging integration algorithm to obtain the ensemble library SCAD algorithm(EL-SCAD).The EL-SCAD algorithm is applied to the parameter identification of two chaotic systems.The results show that the EL-SCAD algorithm can accurately identify the equation parameters that cannot be identified by a single algorithm,and the recognition accuracy is high and the error is small.It shows that the EL-SCAD algorithm successfully screens the variables of the base function library under the integration idea,improves the accuracy of recognition by reducing the interference variables,and highlights the superiority of the SCAD algorithm when the coefficients in the control equation are greatly different.The combination of the two method makes the EL-SCAD algorithm improve the accuracy and scope of application of variable recognition,and has certain application prospects.