Fuzzy Finite Element Model Updating Using Metaheuristic Optimization Algorithms

Abstract

In this paper, a non-probabilistic method based on fuzzy logic is used to update finite element models (FEMs). Model updating techniques use the measured data to improve the accuracy of numerical models of structures. However, the measured data are contaminated with experimental noise and the models are inaccurate due to randomness in the parameters. This kind of aleatory uncertainty is irreducible, and may decrease the accuracy of the finite element model updating process. However, uncertainty quantification methods can be used to identify the uncertainty in the updating parameters. In this paper, the uncertainties associated with the modal parameters are defined as fuzzy membership functions, while the model updating procedure is defined as an optimization problem at each α-cut level. To determine the membership functions of the updated parameters, an objective function is defined and minimized using two metaheuristic optimization algorithms: ant colony optimization (ACO) and particle swarm optimization (PSO). A structural example is used to investigate the accuracy of the fuzzy model updating strategy using the PSO and ACO algorithms. Furthermore, the results obtained by the fuzzy finite element model updating are compared with the Bayesian model updating results.

Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty

“…This deterministic model updating step is then followed by the actual inverse identification of the interval (of fuzzy) description of the uncertain model parameters. The objective that is minimised in this context is expressed as the squared L 2 norm over the difference in interval radii between the intervals on the output parameters of the numerical model and intervals that are fitted around each measured response [38] Alternatively two separate squared L 2 norm formulations are constructed and summed, expressing respectively the difference between the upper and lower bounds of these intervals [173,66,63,17]:…”

Multivariate dependent interval finite element analysis via convex hull pair constructions and the Extended Transformation Method

“…Application of both types of optimizers has been documented in the context of the propagation of interval algorithms [1,36].…”

“…( 19), is constructed based on eqns. ( 34) - (36). The enriched transformation method is applied to discretise D into a set of vertices, which then are used to propagate the dependent intervals.…”

Fuzzy uncertainty analysis and reliability assessment of aeroelastic aircraft wings

“…Friswell and Mottershead (6) described various methods for parameter selection, error localisation, and sensitivity analysis and estimation, in mechanical structures. Also, many efforts were conducted on model updating in uncertain mechanical structures (33)(34)(35)(36) . The fuzzy approach has been used for uncertainty modeling and propagation, and this non-probabilistic method is computationally low-cost compared to probabilistic methods (37) .…”