On the use of mode shape curvatures for damage localization under varying environmental conditions

Abstract

SummaryA novel damage localization method is introduced in this study, which exploits mode shape curvatures as damage features, while accounting for operational variability. The developed framework operates in an output-only regime,that is, it does not assume availability of records from the influencing environmental/operational quantities but rather from response quantities alone. The introduced tool comprises 3 stages pertaining to training, validation, and diagnostics. During the training stage, a representation of the healthy, or baseline, structural state is acquired over varying operational conditions. A data matrix is formulated, whose individual columns correspond to mode shape curvatures at distinct operational conditions, and principal component analysis (PCA) is applied for extraction of the imprints of separate operational sources on these curvatures. To this end, a residual matrix between the original and the PCA mapped data is formed serving for statistical characterization of each mode.Subsequently, during the validation and diagnostics stages, the mode shape curvature matrices for the currently inspected structural state are assembled and the same PCA mapping is enforced. A typical hypothesis test and a corresponding damage index are then adopted in order to firstly detect damage, and to secondly localize damage, should this exist. The implementation of the proposed method in 2 numerical case studies confirms its effectiveness and the encouraging results suggest further investigation on operating structural systems.

Recent progress and future trends on damage identification methods for bridge structures

“…A broadly exploited metric, relating to modal shapes, consists of using Mode Shape Curvatures (MSCs). Shokrani et al introduced a framework for detection and localization of damage under variability of environmental and operational parameters. Principal component analysis accounts for environmental variations, allowing their separation from structural damage; the method is verified on a simulated four‐span bridge model, where in a first phase, natural frequencies serve as features to detect potential damage, whereas in a second phase, MSCs serve for localization.…”

“…Beyond the previously mentioned principal component analysis‐based methods, Laory et al introduced a model‐free data‐interpretation method, which couples moving principal component analysis with four regression alternatives, namely, the robust regression analysis, the multiple linear analysis, the support vector regression, and the random forest method, for the purpose of damage identification under availability of continuous monitoring data. The method is implemented on a number of case studies including the Ricciolo viaduct, a bridge over the Swiss motorway A2, where data during construction serve as data of “anomalous behavior.” The results indicate superiority of combined methods in robustness and speed of identification.…”

Vibration‐based damage localization with load vectors under temperature changes

“…In data‐driven methods, the damage is located using only the recorded response of the structure. For example, damage localization can be performed on the basis of changes in natural frequency, mode shapes or modal curvature, or modal strain energy . Furthermore, artificial neural networks, genetic algorithms, wavelet‐based analysis, or other signal processing methods are applied among others.…”

“…On the other hand, statistical methods are often based on measurement data only without using any geometrical or material information, often without even using temperature measurements but a database under varying conditions instead. To eliminate the effect of perturbations in damage indicating features, the data are processed utilizing statistical models that describe empirically the temperature influence, for example, on modal parameters and eliminate their effect using, for example, regression analysis with autoregressive models, Gaussian mixture models, factor analysis, principal component analysis, and cointegration . Other statistical methods take into account physical properties of the temperature effect on the structure based on physical models .…”

Damage detection in bridges based on patterns of dynamic amplification

“…For a reinforced concrete beam and slab, Liu et al suggest that modal frequencies will decrease 0.12–0.33% per degree Celsius with respect to the modal frequencies at 0°C, being the variation of concrete elasticity modulus with temperature the main cause of these changes. There are two approaches towards separating effects due to operational conditions from effects due to damage: (a) input‐output methods, where operational variables such as temperature, humidity, and/or traffic loading are measured together with modal properties to establish their relationship, that is, via the polynomial chaos expansion method proposed by Spiridonakos et al and (b) output‐only methods, where operational variables are treated as embedded variables that do not need to be measured, as their influence will be discarded via methods such as neural networks, factor analysis, principal component analysis, or kernel principal component analysis …”