Abstract
Data-driven damage identification based on measurements of the structural health monitoring (SHM) system is a hot issue. In this study, based on the intrinsic mode functions (IMFs) decomposed by the empirical mode decomposition (EMD) method and the trend term fitting residual of measured data, a structural damage identification method based on Mahalanobis distance cumulant (MDC) was proposed. The damage feature vector is composed of the squared MDC values and is calculated by the segmentation data set. It makes the changes of monitoring points caused by damage accumulate as “amplification effect,” so as to obtain more damage information. The calculation method of the damage feature vector and the damage identification procedure were given. A mass-spring system with four mass points and four springs was used to simulate the damage cases. The results showed that the damage feature vector MDC can effectively identify the occurrence and location of the damage. The dynamic measurements of a prestress concrete continuous box-girder bridge were used for decomposing into IMFs and the trend term by the EMD method and the recursive algorithm autoregressive-moving average with the exogenous inputs (RARMX) method, which were used for fitting the trend term and to obtain the fitting residual. By using the first n-order IMFs and the fitting residual as the clusters for damage identification, the effectiveness of the method is also shown.
Highlights
Luo et al [14] used the Mahalanobis distance corresponding to different crack degrees as the standard value and judged the damage degree by comparing the difference between the Mahalanobis distance and the standard value in the test group. e authors of [15] used the coefficient vectors of the autoregressive sliding average model to calculate Mahalanobis distance for damage localization of the shear frame structure
Liu et al [19, 20] used Mahalanobis distance as the damage characteristic value to evaluate the damage sensitivity vector of the autoregressive model, and the results showed that the method had good noise resistance
A structural damage identification method based on Mahalanobis distance cumulant with intrinsic mode functions (IMFs) and the fitting residual was proposed. e damage feature vector MDC calculation method and the damage identification procedure were given. rough the numerical simulation of the mass-spring system and the analysis of real bridge monitoring data, the sensitivity of the damage feature vector and the effectiveness of the method were verified
Summary
Huang et al [25, 26] proposed a time-domain analysis method for processing nonstationary and nonlinear signals, namely, empirical mode decomposition (EMD). E measured signal can be decomposed into intrinsic mode functions (IMFs) arranged from high frequency to low frequency. Yang et al proposed a damage detection method using the first IMF to find the spike at the moment of damage [27, 28]. From the EMD method, it can be seen that the signal can be decomposed into IMFs and a residual, which are arranged in the order of high frequency to low frequency. E NNRARMX model is fitted by the Levenberg–Marquardt method, which generally provides the minimization function of numerical solution in the parameter space of the nonlinear model. The unit sampling interval can be defined as t 1, 2, . . .. e input and output signals are u(t) and y (t), respectively. e relationship between input signals and output signals in the system can be expressed as
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