Neural networks with modified backpropagation learning - Applied to structural optimization

Abstract

A multilayer feedforward neural network with a modification to the standard backpropagation training of neural nets is considered. Information on the gradients of target outputs with respect to network inputs is used in this modification. This modified neural network is then applied for approximating design requirements of aerospace composite components, such as an aircraft engine guide vane and a satellite reflector assembly. This neural network functional approximator is then used with an optimization algorithm for determining the optimal parameters for component design requirements. The modified neural network provides for faster convergence of learning process and requires a smaller number of hidden layer nodes for convergence to similar training error levels. HE application of neural networks as universal approximators has been the focus of tremendous amount of activity in the past few years.16 Neural networks have been used for approximating and modeling both memoryless systems and dynamical systems with memory. This paper does not go into the various neural net architectures and training schemes, and the interested reader could refer to standard texts on this subject matter.1'2 This paper considers static neural networks (systems without memory) formed by interconnections without loops, called feedforward networks.2 In addition, this work considers a backpropagation learning scheme with adaptation of learning rate. There have been many additions to, or adaptations of, the basic backpropagation scheme, such as adaptive learning rate, learning with momentum, and the like,1'2 for improving convergence of the learning scheme, and these are not addressed in this paper. This paper explores a modification of the backpropagation learning scheme using information on the gradient of the target outputs with respect to the inputs of the network. The performance of the modified learning scheme is compared with that of the standard backpropagation learning scheme.2 A feedforward network with a single hidden layer trained with this modified learning scheme is applied in structural optimization problems. Figure 1 shows a feedforward net with a single hidden layer. The restriction to a single hidden layer is not a limitation of the modified learning scheme, and the new training scheme can be used on networks with multiple hidden layers also. The use of neural networks for structural response approximation has been reported by several authors.46 The primary reason for investigating such properties is to assess the applicability of trained neural networks for quick and accurate approximation of response functions during structural design optimization. Structural optimization, utilizing either gradient-based numerical search or genetic search algorithms, requires repeated function (response) evaluations during the search process. A single finite element analysis of large-scale structures requires a significant amount of computational time and resource and hence the need for robust approxima