Indirect Reconstruction of Structural Responses Based on Transmissibility Concept and Matrix Regularization

Chudong Pan,Zhuo Sun,Liwen Zhang,Yaobing Zhao

doi:10.1155/2021/5176613

Abstract

A novel method is proposed based on the transmissibility concept and matrix regularization for indirectly measuring the structural responses. The inputs are some measured responses that are obtained via physical sensors. The outputs are the structural responses corresponding to some critical locations where no physical sensors are installed. Firstly, the transmissibility concept is introduced for expressing the relationship between the measured responses and the indirectly measured ones. Herein, a transmissibility matrix is formulated according to the theory of force identification under unknown initial conditions. Then, in order to reduce the size of the transmissibility matrix, structural responses are reshaped in a form of a matrix by using the concept of moving time windows. According to the matrix form of input-output relationship, indirect reconstruction of responses is boiled down to an optimization equation. Since inverse problem may be ill-conditioned, matrix regularization such as F-norm regularization is then recommended for improving the optimization problem. Herein, the penalty function is defined by using a weighted sum of two F-norm values, which correspond to the estimated responses of physical sensors and the ones of the concerned critical locations, respectively. Numerical simulations and experimental studies are finally carried out for verifying the effectiveness and feasibility of the proposed method. Some results show that the proposed method can be applied for indirectly measuring the responses with good robustness.

Highlights

Measurement of structural responses is a fundamental task in structural health monitoring (SHM). e common measuring methods can be divided into two categories: contact and noncontact methods
Structural responses can be usually measured by using the laser measuring technology, image/video-based measuring method, or even global positioning systems (GPS) [1,2,3]
Empirical mode decomposition (EMD) and Kalman filter are two classical technologies. He et al [23] proposed an empirical mode decomposition-based method for response reconstruction in time domain, wherein EMD is applied for estimating the model responses. is idea can be seen in other research works [24, 25]

Summary

Introduction

Measurement of structural responses is a fundamental task in structural health monitoring (SHM). e common measuring methods can be divided into two categories: contact and noncontact methods. E transmissibility concept can be developed based on the basic theory of force identification [16,17,18] In these methods, the dynamic forces acting on the structure are firstly identified by using the measured responses. Empirical mode decomposition (EMD) and Kalman filter are two classical technologies He et al [23] proposed an empirical mode decomposition-based method for response reconstruction in time domain, wherein EMD is applied for estimating the model responses. One advantage of the Kalman filter-based strategy is that it can be used for dealing with different types of structural responses [31] These methods solved the problem step by step in the time domain.

Theoretical Background

Numerical Simulations

Findings

Experimental Verifications