Structures and mechanisms in the engineering field possess characteristics such as high dimen-sions,nonlinearity,and strong coupling,leading to complex dynamic behaviors.In the related research field,the dimensionality reduction method is of great significance for the study of high-dimensional com-plex nonlinear dynamical systems.These methods can reduce the complexity of data,overcome the"curse of dimensionality"in dynamical systems,and improve computational efficiency.They can also compress and reconstruct the characteristics of high-dimensional data,extracting core characteristics to better reveal its inherent laws and features.Furthermore,they can simplify models,reduce model com-plexity,and improve model stability and interpretability.In recent years,the dimension reduction meth-od system has gradually developed and improved,and many scholars have utilized them to achieve theo-retical research on high-dimensional complex systems.Based on this,this paper summarizes the dimen-sion reduction theory for nonlinear high-dimensional systems.It focuses on introducing the basic ideas,application status,and advantages and disadvantages of dimension reduction methods such as Central Manifold Theorem dimension reduction method,Lyapunov-Schmidt method,Proper Orthogonal Decom-position method(POD),and nonlinear Galerkin method.Additionally,it briefly introduces the applica-tion of other dimension reduction methods in practical problems.Finally,aiming at the problems exist-ing in current dimension reduction methods,it proposes possible improvement plans and prospects for future research directions.
维普
万方数据