GP-ARX-Based Structural Damage Detection and Localization under Varying Environmental Conditions

Abstract

The representation of structural dynamics in the absence of physics-based models, is often accomplished through the identification of parametric models, such as the autoregressive with exogenous inputs, e.g. ARX models. When the structure is amenable to environmental variations, parameter-varying extensions of the original ARX model can be implemented, allowing for tracking of the operational variability. Yet, the latter occurs in sufficiently longer time-scales (days, weeks, months), as compared to system dynamics. For inferring a “global”, long time-scale varying ARX model, data from a full operational cycle has to typically become available. In addition, when the sensor network comprises multiple nodes, the identification of long time-scale varying, vector ARX models grow in complexity. We address these issues by proposing a distributed framework for structural identification, damage detection and localization. Its main features are: (i) the individual estimation of local, single-input-single-output ARX models at every operational point; (ii) the long time-scale representation of each individual ARX coefficient via a Gaussian process regression, which captures dependency on varying Environmental and Operational Conditions (EOCs); (iii) the establishment of a distributed residual generation algorithm for damage detection, which produces time-series of well-defined stationary statistics, with detected discrepancies used for damage diagnosis; and, (iv) exploitation of ARX-inferred mode shape curvatures, obtained via ARX-inferred global state-space models, of the healthy and damaged states, for damage localization. The method is assessed via application on two numerical case studies of different complexity, with the results confirming its efficacy for diagnostics under varying EOCs.

System Identification at the Extreme Edge for Network Load Reduction in Vibration-Based Monitoring

“…A plurality of methods has been proposed to tackle this challenge, which are usually based on statistical metrics, such as the Bayesian information criterion (BIC) adopted in this work [41]. Once estimated on a meaningful batch of data, the model order is assumed constant; noteworthy, this is a reasonable choice considering the slow-varying structural properties characterizing the majority of civil and industrial structures [42].…”

Damage detection under temperature variability using closed-loop mode shapes

“…which constitutes the feature vector used in the proposed damage detection scheme. A series of N tr ≥ mq realizations of (23) are extracted in the undamaged structural state and gathered in the matrix Σ = Ξ tr 1 Ξ tr…”

“…Regression-based methods have also been suggested to mitigate the effect of temperature variability by explicitly taking into account both the vibration features and covariate information from temperature measurements. Such methods operate by capturing the influence of measured temperature variability on the features by a functional dependence model attained via, for instance, polynomial chaos expansions [21], Gaussian process regression [22,23], or Bayesian learning [9]. Damage is then detected if the current observation differs significantly from what the regression model predicts.…”

Spectral Dependence

“…Multivariate time series data, sets of a discretely sampled sequence of observations, are the natural approach for analyzing phenomena that display simultaneous, interacting, and time-dependent stochastic processes. As a consequence, they are actively studied in a wide variety of fields: environmental and climate science [1,2,3,4,5,6], finance [7,8,9,10,11,12], computer science and engineering [13,14,15,16,17,18], public health [19,20,21,22,23], and neuroscience [24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39]. Considering the inherent complexity of those studied phenomena, one of the most common challenges and tasks is identifying and explaining the interrelationship between the various components of the multivariate data.…”