Random Dynamic Load Identification Based On Spectrum Decomposition

Dynamic load identification technology is widely used in manufacturing,construction and aerospace engineering.In these engineering practices,external incentives are difficult to measure.The emergence of load identification provides an indirect way to obtain the external dynamic load of the system.By means of easily measured system response and known system structure characteristics,the external load can be inversely solved by a specific algorithm,which can be used in reliability analysis,structural optimization and other design.Traditional load identification methods mainly focus on deterministic load identification methods.Random loads exist widely in various scientific fields.Compared with deterministic load,random load is more difficult to study.It can not be expressed as a deterministic function of time.In practical applications,engineers often simplify it to a deterministic load for calculation.However,such recognition results only correspond to one sample in the original random process,which is not universal and can not predict the real excitation of the system in each time period very well.Only by solving a large number of sample data can all stochastic processes be obtained.Therefore,how to reverse the random excitation of the system and improve the accuracy of load identification has gradually become an important field of inverse problem research.In view of this phenomenon,a method of identifying stationary random dynamic loads based on spectral decomposition is proposed,which can effectively identify stationary random loads The main contents of this paper are as follows:(1)On the basis of probabilistic and statistical characteristics of stationary random loads and structural dynamic response,a forward problem model for stationary random loads identification in time domain is established.Although stationary stochastic processes can not be represented by deterministic time functions,their properties can be generalized by introducing their numerical characteristics such as mean function and correlation function or covariance function.The response of stationary random excitation through linear system also satisfies the condition of stationary random excitation.The structural dynamic convolution relation of stationary random response is substituted into its correlation function,and the relation between stationary random excitation and response with respect to covariance is deduced.A positive problem model for stationary random load identification is constructed by using covariance matrix and kernel function matrix of the system.(2)A method for identifying stationary random loads based on spectral decomposition is proposed.The covariance matrix of stationary random excitation and response is decomposed by matrix spectral decomposition.The superposition form of eigenvalues and eigenvectors of covariance matrix is obtained.The inverse process of global covariance matrix under stationary random excitation is decomposed into eigenvalue matrices ofeach order and then superposed.The identification model of each order characteristic matrix of stationary random excitation is very similar to the traditional deterministic load identification model.In the process of recognition,the existence of measurement noise leads to large error of recognition results.The ill-posedness of random load identification model is discussed with reference to deterministic load identification.A regularization method to improve the kernel function matrix is proposed.Based on RAAE model,the relativeerror criterion of covariance matrix is proposed to solve the optimal regularization parameters,and the optimal inverse solution is obtained.The accuracy of the single-point stationary random dynamic load identification algorithm based on spectral decomposition is verified by two-degree-of-freedom and door structure examples.(3)Based on the single-point stationary random load identification model,a multi-point stationary random load identification model is constructed.By introducing the correlation analysis of stochastic processes,a multi-point stationary random load identification method based on spectral decomposition is proposed.The stationary random excitation in three cases of complete correlation,partial correlation and complete irrelevance is analyzed.The validity of this method for identifying two-point random loads is verified by 25-bar truss structure.The method of identifying stable load based on spectral decomposition is applied to the engineering example of identifying road roughness.A seven-degree-of-freedom vehicle model is established to identify the road smooth excitation of four wheels and their correlation,and good results are obtained.It is shown that the identification method of stationary random dynamic loads based on spectral decomposition is of great significance in practical engineering.