Prediction Of Vibration Responses Of Linear System Under Uncorrelated Multi-source Unknown Loads

The prediction of structural vibration response in frequency domain under the excitation of multi-source random loads has always been a hot and difficult issue.However,the current research is based on the known multi-source loads,which cannot be applied to the prediction of vibration response under the unknown multi-source loads.In order to solve the problem of predicting vibration response of linear structures in frequency domain under multi-source unknown loads,a series of methods of predicting the vibration frequency response under uncorrelated multi-source unknown loads are proposed.(1)The problem of predicting the vibration frequency response of unmeasured points under multi-source unknown loads is proposed.The physical explanation and formal description of the problem are given.The problem is transformed into a mathematical model and the conditions for the existence of the solution are given theoretically.Vibration response experiments of suspended cylindrical shells under combined excitation of exciter and spherical noise sources were carried out to collect the measured frequency-domain data of vibration response at different magnitudes.The prediction data set of frequency-domain vibration response of linear systems under uncorrelated multi-source unknown loads was constructed,and the evaluation criteria for error comparison between predicted vibration response data and real vibration response data were given.(2)A method of vibration response prediction based on transfer function is proposed.Based on loads identification and vibration response prediction method of transfer functions,it is proposed that when the multi-source loads are unknown,the uncorrelated multi-source loads can be identified by using the vibration response of known points and the transfer function from known response points to load points,and then the vibration responses can be predicted based on the transfer functions from load points to unmeasured response points,and the experimental verification is completed and the error is analyzed.(3)A frequency domain vibration response prediction method based on multiple linear regression is proposed.Through theoretical deduction,it is found that for linear time-invariant systems,there is a linear relationship between the vibration response of known points and that of unmeasured vibration points.On this basis,the multi-linear regression model between the vibration response of known points and the vibration response of unmeasured points is trained,the known measuring points as input and the vibration response of unmeasured points as output.Under the actual working condition,the vibration response of the known measured points is put into the multivariate linear regression model,and the output of the model can be used as the predicted value of the vibration response of the unmeasured points.The experimental results of cylindrical shells show that the accuracy of the method basically meets the engineering application requirements,but the error is large around the resonance frequency domain.(4)A series of linear regression models are used to improve the accuracy of multiple linear regression based method.Firstly,the prediction great error reasons of multiple linear regression based is large in resonance frequency domain is analyzed:the strong correlation of known measurement points does not accord with the linear independence between input variables of multiple linear regression model,and the condition number at resonance frequency is large.In order to solve these problems,partial least squares model and multiple input multiple output LS-SVM model are tried respectively.The validation results on the experimental data of cylindrical shells show that the accuracy of these methods is higher than that of frequency domain vibration response prediction methods based on multiple linear regression.Finally,the advantages and disadvantages of the above methods in are compared in terms of theory,applicable conditions,scope and prediction error,and looks forward to the possibility of applying them to non-linear systems.