Gaussian Process Time-Series Models for Structures under Operational Variability

Abstract

A wide range of vibrating structures are characterized by variable structural dynamics resulting from changes in environmental and operational conditions, posing challenges in their identification and associated condition assessment. To tackle this issue, the present contribution introduces a stochastic modeling methodology via Gaussian Process (GP) time-series models. In the presently introduced approach, the vibration response is represented by means of a random coefficient time-series model, whose coefficients comply with a GP regression on the environmental and operational parameters. The approach may be implemented in conjunction to any type of linear-in-the-parameters time-series model, ranging from simple AR models to more complex non-linear or nonstationary time-series models. The obtained GP time-series modeling approach provides an effective and compact global representation of the vibrational response of a structure under a wide span of environmental and operational conditions. The effectiveness of the postulated GP time-series models is demonstrated through two case studies: the first involves the identification of the vertical vibration response of the Humber bridge, evaluated over a period of three years; the second considers the long-term simulated vibration response of a wind turbine featuring non-stationary dynamics stemming from the rotor speed. In both cases, the variation of the average wind speed is the main driver of uncertainty, while, through application of the proposed GP time-series models, it is possible to track the resulting variation in modal quantities.

Damage detection under temperature variability using closed-loop mode shapes

“…Obviously, one does not know the damaged state, so a maximum allowable damage extent is defined and the design model is perturbed accordingly to ascertain the compliance with the constraints. The first constraint in (22) ensures system stability, while the second and third constraints are defined such that the particular CL eigenvalue of interest is identifiable through system identification and in the vicinity of the corresponding OL eigenvalue. In particular,ζ U is an upper bound on the CL damping ratio andω L i andω U i bound the associated CL damped eigenfrequency.…”

“…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.…”

“…Damage is then detected if the current observation differs significantly from what the regression model predicts. Some documented application studies on the use of regression for damage detection under temperature variability can be seen in [22,24,9].…”

Output-Only Vibration-Based Monitoring of Civil Infrastructure via Sub-Nyquist/Compressive Measurements Supporting Reduced Wireless Data Transmission

“…Since no explicit loading information is assumed available, output-only techniques commonly assume ambient conditions corresponding to a flat spectrum over a wide range of frequencies (i.e., a white noise excitation assumption). Such techniques are shown to perform well, even under the challenge of varying environmental and operational conditions (Reynders et al, 2013;Shi et al, 2016;Avendaño-Valencia et al, 2017) while the extracted modal structural properties may be then exploited for a variety of tasks including condition assessment, design verification, structural health monitoring (SHM) and, ultimately, residual life prediction of civil structures (Straub et al, 2017). Still, OMA has been mostly demonstrated for use with tethered sensing configurations.…”

Features of Cross-Correlation Analysis in a Data-Driven Approach for Structural Damage Assessment

“…Additionally, the authors of [ 13 ] propose the use of statistical and modal damage detection methods for the damage detection problem in a small-scale wind turbine. Other authors, such as those of [ 14 ], have presented the use of a time-series as a modeling approach to provide an effective and compact global representation of the vibrational response of a structure under a wide span of environmental and operational conditions. As a result, the state of the art indicates that statistically based methods using data-driven approaches have been reported to be successful for structural condition assessment.…”