Real-time unified single- and multi-channel structural damage detection using recursive singular spectrum analysis

A novel baseline-free approach for continuous online damage detection of multidegree of freedom vibrating structures using recursive singular spectral analysis in conjunction with time-varying autoregressive modeling is proposed in this article. The acceleration data are used to obtain recursive proper orthogonal components online using rank-one perturbation method, followed by time-varying autoregressive modeling of the first transformed response, to detect the change in the dynamic behavior of the vibrating system from its original state to contiguous linear/nonlinear states indicating damage. Most work to date deal with algorithms that require windowing of the gathered data that render them ineffective for online implementation. Algorithms focused on mathematically consistent recursive techniques in a rigorous theoretical framework of structural damage detection are missing that motivates the development of the present framework. The response from a single channel is provided as input to the algorithm in real time. The recursive singular spectral analysis algorithm iterates the eigenvector and eigenvalue estimates for sample covariance matrices and new data point at each successive time instants. This eliminates the need for offline post processing and facilitates online damage detection especially when applied to streaming data without requiring any baseline data. Lower order time-varying autoregressive models are applied on the transformed responses to improve detectability. Numerical simulations performed on a five-degree of freedom nonlinear system and on a single degree of freedom system modeled using a Duffing oscillator under white noise excitation data, with different levels of nonlinearity simulating the damage scenarios, demonstrate the robustness of the proposed algorithm. The method further validated on results obtained from experiments performed on a cantilever beam subjected to earthquake excitation; a toy cart experiment model with springs attached to either side; demonstrate the efficacy of the proposed methodology as an appropriate candidate for real-time, reference-free structural health monitoring.