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  • Basuraj Bhowmik

Online damage detection using recursive principal component analysis and condition indicators

Updated: May 22, 2021

In this paper, a novel baseline free approach for continuous online damage detection of multidegree of freedom vibrating structures using recursive principal component analysis(RPCA) in conjunction with online damage indicators is proposed. In this method, the acceleration data isused to obtain recursive proper orthogonal modes in online using the rank-one perturbation method, and subsequently utilized to detect the change in the dynamic behavior of the vibratingsystem from its pristine state to contiguous linear/nonlinear-states that indicate damage. The RPCA algorithm iterates the eigenvector and eigenvalue estimates for sample covariance matrices and new data point at each successive time instants, using the rank-one perturbation method. An online condition indicator(CI)based on the L2 norm of the error between actual response and the response projected using recursive eigenvector matrix updates over successive iterations is proposed. This eliminates the need for offline post processing and facilitates online damage detection especially when applied to streaming data. The proposed CI, named recursive residual error, is also adopted for simultaneous spatio–temporal damage detection. Numerical simulations performed onfive-degree of freedom nonlinear system under white noise and ElCentro excitations, with different levels of nonlinearity simulating the damage scenarios,demonstrate the robustness of the proposed algorithm. Successful results obtained from practical case studies involving experiments performed on a cantilever beam subjected to earthquake excitation, for full sensors and underdetermined cases; and data from recorded responses of the UCLA Factor building(full data and its subset)demonstrate the efficacy of the proposed methodology as an ideal candidate for real-time, reference free structural health monitoring

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