Online damage detection via a synergy of proper orthogonal decomposition and recursive Bayesian filters

Abstract

In this paper, an approach based on the synergistic use of proper orthogonal decomposition (POD) and Kalman filtering is proposed for the online health monitoring of damaged structures. The reduced-order model of a structure is obtained during an (offline) initial training stage of monitoring; afterward, effective estimations of a possible structural damage are provided online by tracking the evolution in time of stiffness parameters and projection bases handled in the model order reduction procedure. Such tracking is accomplished via two Kalman filters: a first (extended) one to deal with the time evolution of a joint state vector, gathering the reduced-order state and the stiffness terms degraded by damage; a second one to deal with the update of the reduced-order model in case of damage evolution. Both filters exploit the information conveyed by measurements of the structural response to the external excitations.Results are reported for a (pseudo-experimental) benchmark test on an eight-story shear building.Capability and performance of the proposed approach are assessed in terms of tracked variation of the stiffness terms of the reduced-order model, identified damage location and speed-up of the whole health monitoring procedure.Keywords structural health monitoring (SHM); reduced-order modeling; damage detection; model updating; Kalman filtering; proper orthogonal decomposition (POD).

Structural Health Monitoring for Condition Assessment Using Efficient Supervised Learning Techniques

“…Several methods have been developed in the past decades for the relevant structural health monitoring (SHM), which aims to detect any possible damage and classify the conditions of structures. Methods can be distinguished into model-driven [1][2][3][4], see also Farrar and Worden [5], or data-driven ones. The model-driven SHM approach is based on an analytical or finite element model of the structure [6].…”

Damage detection in structural systems utilizing artificial neural networks and proper orthogonal decomposition

“…Astroza et al proposed a joint input parameter estimation for nonlinear, distributed plasticity systems . Performance of the aforementioned methods relies profoundly on the number of unknown parameters in the system, model class selection, and user expertise.…”

“…More recently, Shane et al employed POD to detect damage severity and location in a composite beam numerical model . Eftekhar Azam et al studied damage detection in a building subjected to base shear excitations using variations in an SVD subspace . Bellino et al proposed a PCA‐based method for detecting damage in linear time‐varying systems .…”

Coupled Systems in Mechanics: Fluid Structure Interactions

“…Energy partition with the Smooth Orthogonal Decomposition 106 KΨ = MΨΩ. (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26) Then the two expressions represent two equivalent eigenvalue problems (7-25) and (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26). As they represent they same mechanical system they have to be equivalent, this leads to equivalences between the modal quantities, in terms of natural frequencies and mode shapes:…”

“…This turns the method the ideal way to deal with the identification of systems under ambient excitations (considering Operational Modal Analysis as in [22], [58] or [59]), as wind or waves for instance, which can be hard to compute or to describe. Also, this family of methods can be used for damage detection such as in [23].…”