Research On Error Generation,transmission And Suppression Mechanism For Two-substructure Inverse Sub-structuring Method

The product transport packaging system can be regarded as an overall system formed by the product,packaging and carrier in the logistics transport process.The inverse sub-structuring method can predict the dynamic characteristics of the product in real time based on the dynamic characteristics of the "Product-Package-Carrier" coupled system.So,it is widely used in the dynamic optimization design and diagnosis of the logistics transport packaging system.However,the existing inverse sub-structuring methods are all based on the experimentally measured coupled system frequency response functions(FRFs)to predict the substructure frequency response function.In the engineering application of the actual transport packaging system,the measured frequency response function will inevitably be affected by the test operation or the noise interference,which will cause the measured frequency response function to carry measurement error,and the error will be transmitted and amplified with the matrix inversion operation of the theoretical calculation formula of the inverse sub-structuring method,resulting in unacceptable error in the predicted frequency response function of the product.This paper takes the theoretical analysis of two-substructure system as an example to explore the generation,transmission and suppression of error.The multi-threshold singular value decomposition(MTSVD)method is proposed to suppress the transmission and amplification of experimental error in the process of predicting the substructure frequency response function.The main contents are as follows:(1)Based on the least-squares(LS)method and matrix singular value decomposition method(SVD)method,the influence mechanism of the inverse sub-structure method measurement error on the predicted FRFs of substructure is theoretically analyzed,and the influence of the typical measurement error on the results of the predicted FRFs of substructure is analyzed.At the same time,a corresponding error analysis model is established and the main influencing factors of the error are clarified.(2)In order to prevent the error of measured FRFs being transmitted and amplified with the matrix inversion operation of the inverse sub-structuring method when predicting the FRFs of the substructure,a new error suppression method is proposed based on the Hankel matrix and the SVD method,namenly,the multiple threshold singular value decomposition(MTSVD)method.And the basic criteria for the selection of singular value threshold is put forward.The MTSVD method can effectively reduce the measurement error by modifying the singular value of the measured FRFs-matrix to different degrees to achieve the purpose of suppressing error amplification.(3)Taking the two-substructure single-coordinate,multi-coordinate flexiblely coupled system and the two-substructure single-coordinate,multi-coordinate rigidly coupled system as the research objects,the proposed MTSVD method is applied in the inverse sub-structuring method respectively to study the error suppression ability of the MTSVD method.At the same time,the lumped parameter model and experimental model are used to verify the feasibility and effectiveness of the MTSVD method.The results show that the proposed MTSVD method can effectively suppress the the amplification of the measurement error and reduce the impact of the measurement error on the results of the predicted FRFs of substructure.We conclude that the proposed MTSVD method may be used as a new error suppression tool for improving application precision of the inverse sub-structuring method.