| Nonlinear factors are commonly present in structural dynamics,which brings difficulties to the analysis of structural characteristics and motion control.The traditional linear analysis theory has been unable to meet the increasingly complex engineering needs,and accurately obtaining the dynamic characteristics of nonlinear systems has gradually become the key to structural design.Considering the complexity of nonlinear sources and the lack of prior information such as unclear mechanism,it is necessary to carry out nonlinear modeling research based on data-driven system identification method.This paper is devoted to the parameter identification of nonlinear systems,and the main work is as follows:A variable selection based nonlinear parameter identification method is proposed by combining sparse Bayesian regression based on spike and slab priors with subspace theory to address the problem of unknown nonlinear positions and forms in local nonlinear structures.According to the nonlinear feedback idea and the linear superposition principle,the system response is divided into a combination of linear response under external excitation and nonlinear response under internal nonlinear feedback force.The nonlinear response is expressed as a set of convolution regression equations of nonlinear basis function and unit impulse response function,and the actual contribution terms in the candidate nonlinear terms are selected based on the spike and slab prior Bayesian inference method,and then the parameter estimation is performed based on the nonlinear subspace algorithm.Simulation studies were conducted on spring mass systems and cantilever beam structures,respectively.The research results showed that this method can accurately select nonlinear terms related to system dynamics,improve the confidence of parameter estimation,verify the effectiveness of the algorithm,and have good robustness.And experimental research was conducted to further verify the applicability of the method in practical engineering.Aiming at the problem that it is difficult to measure the excitation in engineering practice,a nonlinear parameter identification method based on pure output measurement is proposed based on the output only estimation theory of non linear subspace and mass disturbance method.Draw a phase diagram of normalized acceleration,displacement,and velocity without input to observe and distinguish various nonlinearities.The output and nonlinear Hankel matrices are constructed,and the nonlinear subspace output only estimation algorithm is applied to estimate the system matrix and nonlinear feedback matrix of the state space model.Change the Mass distribution of the structure by adding or reducing,estimate the frequency response function of the underlying linear system based on the change of the structural modal parameters,and identify the nonlinear parameters based on the least square method according to the relationship between linear and nonlinear frequency responses.The multi free discrete structures with different nonlinear types are taken as the research objects to carry out simulation research.The research results show that the proposed method can conduct effective nonlinear characterization and parameter estimation under the condition of unknown input,and has good applicability for different nonlinear types.Aiming at the problem of poor identification accuracy of nonlinear subspace method in noisy environment,a nonlinear parameter identification method based on automatic order determination and parameter optimization is proposed.First,the automatic and accurate order determination of the system model is realized.Input and output data are identified in different order nonlinear subspaces to obtain a large number of modal parameter identification results.A large number of errors and false modes are eliminated by applying data preprocessing and modal stability criteria.Then,the frequency and damping parameters of the stable modes are clustered by DBSCAN to achieve the system order determination.Then,based on the prediction error method,the state space model matrix identified by the nonlinear subspace identification algorithm is iteratively optimized to improve the identification accuracy of nonlinear parameters in the noise environment.The simulation and experimental studies are carried out respectively to discuss the effectiveness of the algorithm in different nonlinear structures.The research results show that the method has good applicability for nonlinear structures with different complexity.Compared with the traditional nonlinear subspace method,the method has higher accuracy and robustness. |
