This manuscript provides a detailed synopsis of the contemporary advancements in the nascent area of real-time structural damage detection for vibrating systems. The paper mainly focuses on the theoretical development and engineering applications of algorithms that are based on first-order perturbation (FOP) techniques applied to vibration responses. The importance of this work stems from the fact that recent developments in the field of online structural health monitoring (SHM) have given rise to algorithms that are computationally complex and, consequently, are not amenable to real-time implementation. In this paper, we discuss and demonstrate the FOP-based algorithms in the light of all the contemporary nonadaptive/nonrecursive techniques to establish their relevance. We review 216 papers in this regard. The efficacy, efficiency, robustness, and the applicability of the FOP family of algorithms are highlighted in light of several experimental, theoretical, and field studies.

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In this article, a robust output-only real-time damage detection technique for multi-degree-of-freedom degrading systems using recursive canonical correlation analysis is presented. It has been observed that the impact of damage to a vibrating system gradually advances with time that sustains until the system degrades up to a considerable extent. Of significant interest is the effect of sudden damage in presence of continuous degradation in real-time, which is studied in the form of a sudden stiffness reduction in a separate floor. The proposed recursive canonical correlation analysis algorithm estimates the iterative update of eigenspace at each instant from the response data, thereby capturing the features of a time varying degrading structure in an online framework. Furthermore, recursive canonical correlation analysis algorithm is shown to reduce the computational cost by updating the eigenspace at each instant of time. This article explores newly developed recursive condition indicators: recursive Mahalanobis distance and recursive Itakura distance that elicit damage information from the eigenspace. In order to model degradation, simulations aimed at successfully capturing the behavior of the process in real-time becomes imperative. A general stochastic formulation of the coupled response-degradation problem accounting for the evolution of degradation is presented in the light of stiffness degradation problems. The evolution of time varying system responses is generated using a newly proposed Ito–Taylor expansion-based stochastic numerical integration formulation. Numerically simulated structural vibrating systems, namely, 2-degree-of-freedom base-isolated and 4-degree-of-freedom linear systems, have been used to check the performance of the recursive canonical correlation analysis method. The spatial damage detectability of the algorithm in real-time is explored through identifying crack location on a beam traversed by a vehicle. Finally, an experimental case study has been carried out to verify the robustness of the proposed algorithm. The identification results for both numerical and experimental cases demonstrate the efficacy of the proposed algorithm in identification of nonlinear and time varying behavior associated with degrading structural systems.

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