A Bayesian methodology for crack identification in structures using strain measurements

Abstract

A Bayesian system identification methodology is presented for estimating the crack location, size and orientation in a structure using strain measurements. The Bayesian statistical approach combines information from measured data and analytical or computational models of structural behaviour to predict estimates of the crack characteristics along with the associated uncertainties, taking into account modelling and measurement errors. An optimal sensor location methodology is also proposed to maximise the information that is contained in the measured data for crack identification problems. For this, the most informative, about the condition of the structure, data are obtained by minimising the information entropy measure of the uncertainty in the crack parameter estimates. Both crack identification and optimal sensor location formulations lead to highly non-convex optimisation problems in which multiple local and global optima may exist. A hybrid optimisation method, based on evolutionary strategies and gradient-based techniques, is used to determine the global minima. The effectiveness of the proposed methodologies is illustrated using simulated data from a single crack in a thin plate subjected to static loading.

Bayesian optimal sensor placement for crack identification in structures using strain measurements

“…Next, it is assumed that the prediction error standard deviation for each model prediction component is expressed as a percentage σ of the absolute value of the corresponding component, and the covariance matrix becomes Σ e ( σ )= σ 2 d i a g ( g 1 ( d , θ ) 2 ,…, g N ( d , θ ) 2 ). A more sophisticated study of the prediction error for crack identification problems can be found in Gaitanaros et al() Herein, the prediction error parameter σ is considered to be unknown and is included in the parameters to be inferred by the Bayesian formulation by augmenting the parameter set θ ={ X c , Y c , L , ϕ , σ } with one additional parameter.…”

“…This paper investigates the problem of finding the optimal location, number, and density of strain sensors in a loaded plate for the goal of accurate and reliable identification of a crack using strain measurements. The proposed study is an extension of the work in Gaitanaros et al,() using different theoretical foundations and computational tools. A Bayesian formulation for the optimal design of strain sensor locations for crack identification is presented based on the expected Kullback–Liebler (KL) divergence measure.…”

A Bayesian approach for impact load identification of stiffened composite panel

“…Similar likelihood functions can be found in reference. [14][15][16][17][19][20][21] The likelihood function pðwjh; r 2 e Þ is a probabilistic statement about the distribution of the measured data w ¼ ½wð1Þ; . .…”

“…The computational code is programmed by MATLAB script. [31] By using MATLAB function 'c2d', the continuous state-space model in Equations (19) and (20) is easily transformed to a discrete form which can be iteratively solved step by step. After the generalised force, mass and stiffness matrices in Equations (17) and (18) are calculated beforehand, it takes less than 0.05 s for the forward state-space model to calculate the impact responses for 10 ms with a time step of 0.1 ms on a PC with Intel P4 3.0 GHz CPU and 1 GB memory.…”

“…Rather than pinpointing a single solution using deterministic approaches, the Bayesian approach can provide the probability density function (PDF) of the system parameters, giving both point and interval estimates. [17,[19][20][21][22] The aim of this work is to provide a statistical Bayesian approach to identify the impact location and approximately reconstruct the impact force history simultaneously while considering uncertainties from modelling error and measurement noise. In particular, a case of impact load identification for stiffened composite panel is presented.…”