In this paper, a novel baseline free approach for continuous online damage detection of multi degree of freedom vibrating structures using Recursive Principle Component Analysis (RPCA) in conjunction with Time Varying Auto-Regressive Modeling (TVAR) is proposed. In this method, the acceleration data is used to obtain recursive proper orthogonal components online using rank-one perturbation method, followed by TVAR modeling of the first transformed response, to detect the change in the dynamic behavior of the vibrating system from its pristine state to contiguous linear /non-linear-states that indicate damage. Most of the works available in the literature deal with algorithms that require windowing of the gathered data owing to their data-driven nature which renders them ineffective for online implementation. Algorithms focussed on mathematically consistent recursive techniques in a rigorous theoretical framework of structural damage detection is missing, which motivates the $ Fully documented templates are available in the elsarticle package on CTAN.

In this paper, a novel baseline free approach for continuous online damage detection of multi degree of freedom vibrating structures using recursive principal component analysis (RPCA) in conjunction with online damage indicators is proposed. In this method, the acceleration data is used 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 vibrating system 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 on five-degree of freedom nonlinear system under white noise and El Centro 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.

A novel baseline free approach for continuous online damage detection of multi degree of freedom vibrating structures using Recursive Singular Spectral Analysis (RSSA) in conjunction with Time Varying Auto-Regressive Modeling (TVAR) is proposed in this paper. The acceleration data is used to obtain recursive proper orthogonal components online using rank-one perturbation method, followed by TVAR 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 /non-linear-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 focussed on mathematically consistent recursive techniques in a rigorous theoretical framework of structural damage detection is 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 RSSA 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 TVAR models are applied on the transformed responses to improve detectability. Numerical simulations performed on a 5-dof nonlinear system and on an SDOF 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.

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Dynamic mode decomposition (DMD) has emerged as a leading data‐driven technique to identify the spatio‐temporal coherent structure in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems with external forcing, the identified model should not only be suitable for a specific forcing function but should generally approximate the input‐output behavior of the data source. In this work, we propose a novel methodology, called the wavelet‐based DMD (WDMD), that integrates wavelet decompositions with ioDMD to approximate dynamical systems from partial measurement data. The method is validated using a numerical and experimental case study involving modal analysis on a simple finite element model and free‐free beam respectively.