T. Marwala

I. Boulkaibet, T. Marwala, M. I. Friswell et al.

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.

Collins Leke, Bhekisipho Twala, T. Marwala

This paper presents methods which are aimed at finding approximations to missing data in a dataset by using optimization algorithms to optimize the network parameters after which prediction and classification tasks can be performed. The optimization methods that are considered are genetic algorithm (GA), simulated annealing (SA), particle swarm optimization (PSO), random forest (RF) and negative selection (NS) and these methods are individually used in combination with auto-associative neural networks (AANN) for missing data estimation and the results obtained are compared. The methods suggested use the optimization algorithms to minimize an error function derived from training the auto-associative neural network during which the interrelationships between the inputs and the outputs are obtained and stored in the weights connecting the different layers of the network. The error function is expressed as the square of the difference between the actual observations and predicted values from an auto-associative neural network. In the event of missing data, all the values of the actual observations are not known hence, the error function is decomposed to depend on the known and unknown variable values. Multi-layer perceptron (MLP) neural network is employed to train the neural networks using the scaled conjugate gradient (SCG) method. Prediction accuracy is determined by mean squared error (MSE), root mean squared error (RMSE), mean absolute error (MAE), and correlation coefficient (r) computations. Accuracy in classification is obtained by plotting ROC curves and calculating the areas under these. Analysis of results depicts that the approach using RF with AANN produces the most accurate predictions and classifications while on the other end of the scale is the approach which entails using NS with AANN.

I. Boulkabeit, L. Mthembu, T. Marwala et al.

A recent nature inspired optimization algorithm, Fish School Search (FSS) is applied to the finite element model (FEM) updating problem. This method is tested on a GARTEUR SM-AG19 aeroplane structure. The results of this algorithm are compared with two other metaheuristic algorithms; Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). It is observed that on average, the FSS and PSO algorithms give more accurate results than the GA. A minor modification to the FSS is proposed. This modification improves the performance of FSS on the FEM updating problem which has a constrained search space.