Online damage detection using recursive principal component analysis and recursive condition indicators

Krishnan, Manu; Bhowmik, Basuraj; Tiwari, Anuj; Hazra, Budhaditya

doi:10.1088/1361-665x/aa7220

Cited by 21 publications

(50 citation statements)

References 47 publications

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“…The updates W k = W k − 1 Q k and Ω k = Λ k / k can be estimated through an iterative calculation of Q k and Λ k as discussed in an associated study. 29 In this regard, the authors have resorted to the use of matrix inversion lemma 50 that can provide the inverse of any full-rank positive definite matrix. The inverse EVD at the ( k + 1 ) th step, therefore, becomes…”

Section: Recursive Ccamentioning

confidence: 99%

“…Krishnan et al 29 proposed a recursive principal component analysis (RPCA)-based online damage detection algorithm employing FOEP techniques to obtain updates for eigenspace at each time instant when a new data sample is received. The method inherently embodies a model order reduction scheme that makes it computationally efficient.…”

Section: Introductionmentioning

confidence: 99%

“…To the authors’ knowledge, the concept of employing RCCA as an extension of traditional CCA 26–28 toward damage detection of degrading systems has not yet been reported in the literature. As the family of BSS methods falls within the ambit of CCA-based schemes, a direct implementation of RCCA as a real-time damage detection approach promises to be more efficient when formulated in the backdrop of FOEP techniques 29–31 , applied to generalized eigenvalue problems.…”

Section: Introductionmentioning

confidence: 99%

“…34 Thus, certain condition indicators (CIs) need to be developed that is sensitive in accommodating differences not only in the perturbation matrices and small-magnitude structural damages, but can also simultaneously operate in an online framework in conjunction with the proposed algorithm. In recent years, the use of time varying auto-regressive (TVAR) coefficients 30 and recursive residual error (RRE) 29 as a criterion for structural damage detection has been extensively studied. The present work focuses on the development of CIs sensitive to damages, namely, recursive Mahalanobis distance (RMD) and recursive Itakura distance (RID).…”

Section: Introductionmentioning

confidence: 99%

“…It is worth noting that a slightly different structure of the covariance matrix will give back the traditional PCA -based approach, a concept that has consistently exhibited its potential in identifying spatial and temporal patterns of structural damage, over the recent years. 29,30,45 PCA, a special instance of CCA, can be formulated on substituting the matrices E and F as E = C xx and F = I . PCA is a dimensionality reduction approach that projects the data onto principal subspace, such that the variance of the projected data is maximized.…”

Section: Introductionmentioning

confidence: 99%

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Real-time damage detection of degrading systems

Tripura

Bhowmik

Pakrashi

et al. 2019

Structural Health Monitoring

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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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Section: Recursive Ccamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Real-time damage detection of degrading systems

Tripura

Bhowmik

Pakrashi

et al. 2019

Structural Health Monitoring

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Learning methods for structural damage detection via entropy‐based sensors selection

Smarra

Tjen

D’Innocenzo

2022

Intl J Robust & Nonlinear

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In this article the problem of data‐driven structural damage detection is considered exploiting historical data collected from a structure. First, a novel technique based on Kalman filtering and on a combination of regression trees theory from machine learning and auto‐regressive system identification from control theory is derived to build switching models that can be used to detect structural damages. A technique is also proposed leveraging principal component analysis together with the poly‐exponential approach to create nonlinear models to be used for structural damage detection. Finally, a novel sensors selection algorithm based on the notions of entropy and information gain from information theory is developed to reduce the number of sensors without affecting or even improving, as it happens in our experimental setup, the model accuracy. The presented techniques are validated on three independent experimental datasets, showing that the proposed algorithms outperform previous and classical approaches, improving the prediction accuracy and the damage detection sensitivity while reducing the number of sensors.

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