Over-fitting of noisy teacher data is a serious problem for artificial neural networks (NNs). Their learning method based on Bayesian inference was proposed by MacKay in order to prevent over-fitting and generate a smooth response surface (RS). Using this method, the response surface of neural networks can be used to predict optimal input conditions, because it has good generalization (interpolation) ability. We specified and verified the learning algorithm and the modification method of hyper parameters, which are coefficients that appear in an objective function with penalty terms. After three different modification methods were applied to interpolation examples, we chose the superior modification method. Finally, the response surface of neural networks using the superior method was applied to an optimization problem in which the fiber orientations of a laminated composite structure were determined so as to minimize the difference in two displacements. We concluded that the learning algorithm and the modification method are effective to optimization problem.

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A lamination parameter approach, recently proposed by the authors, is extended in this work to solve a minimum weight design problem for optimizing buckling behavior of laminated composite plates. The present approach basically consists of two parts: the first part is to optimize the lamination parameters by a gradient method, and the second part is to obtain the optimum lay-up (i.e., the fiber orientation angles) by minimizing the errors between the optimum parameters and the parameters for all possible discrete lay-up designs. In the extension of approach, the minimum number of layers with equal thickness is determined so that the plate has higher buckling loads than the specified values. Numerical examples demonstrate that the proposed approach is quite effective in determining the optimum lay-ups for the minimum weight design.

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