Experimental Testing of a Cross-Entropy Algorithm to Detect Damage

Abstract

Cross-entropy optimization has recently been applied to the damage detection in structures subject to static loading. The optimization procedure minimizes the error between the measured deflection data and theoretical deflection data obtained from artificially generated finite element models based on assumed statistical distributions of stiffness for each discretized element. Following a number of iterations, the finite element model with stiffness properties producing deflections closer to reality is established as the mathematical model closest to the true structure. However, while previous testing of the algorithm has been relatively successful, it has been limited to theoretical simulations. Therefore, this paper conducts lab experiments on a beam loaded statically to test the accuracy of the algorithm. Deflections are measured for beam scenarios under different loading levels. The accuracy of the results is discussed and recommendations are made to improve the performance of the algorithm when implemented in practice.

Regularization Methods Applied to Noisy Response from Beams under Static Loading

“…Tomas et al (2018) apply observability to this system for establishing the subset of structural parameters that can be identified with a given subset of measures. The problem of finding the stiffness for each element is addressed via an optimization cross-entropy algorithm in Walsh and González (2009) and González et al (2013) for a beam and in Walsh et al (2010) for a plate model. This algorithm involves an iterative approach that minimizes an objective function based on the difference between the simulated/measured displacements and those calculated from a discretized FE model of the structure.…”

Constrained observability method in static structural system identification

“…The parameters of physics‐based models represent the structural characteristics, for example, elastic modulus, inertias, and mass, whereas the parameters of the nonparametric models are weight factors of the adopted basis functions, which have no physical meaning and are determined by minimizing the discrepancy between the predicted and the measured response. From a statistical perspective, SSI methods can be categorized as probabilistic methods or deterministic methods . In the probabilistic methods, structural parameters are treated as random variables and their distributions are specified using prior knowledge.…”

“…From a statistical perspective, SSI methods can be categorized as probabilistic methods or deterministic methods . In the probabilistic methods, structural parameters are treated as random variables and their distributions are specified using prior knowledge. Structural parameter sets are generated by sampling each of these distributions.…”

Finite Element Updating using Cross-Entropy combined with Random Field Theory

“…It can be seen that the algorithm is successful in predicting the stiffness profile of the structure. Predictions for stiffness values at the supports are less accurate, particularly for one single application of the algorithm; this is reflected by the values of standard deviations associated to the final probability distributions, which are greater near the boundaries of the structure [8,9]. The average of five simulations is computed in order to smooth the final solution, especially near the supports.…”

“…In this context, Walsh and González [7] propose a method to predict the distribution of stiffness throughout the structure based on the finite element method (FEM), cross-entropy (CE) and static measurements. This technique has proven to be valid, under certain conditions, both in numerical simulations [7,8] and lab experiments [9]. One of the assumptions of this technique is that the stiffness of a specific finite element is independent from other elements.…”