Toward constructive methods for sigmoidal neural networks - function approximation in engineering mechanics applications

This paper reports a continuous development of the work by the authors presented at IJCNN 2005 & 2007 [1, 2]. A series of parsimonious universal approximator architectures with pre-defined values for weights and biases called “neural network prototypes” are proposed and used in a repetitive and systematic manner for the initialization of sigmoidal neural networks in function approximation. This paper provides a more in-depth literature review, presents one training example using laboratory data indicating quick convergence and trained sigmoidal neural networks with stable generalization capability, and discusses the complexity measure in [3, 4]. This study centers on approximating a subset of static nonlinear target functions - mechanical restoring force considered as a function of system states (displacement and velocity) for single-degree-of-freedom systems. We strive for efficient and rigorous constructive methods for sigmoidal neural networks to solve function approximation problems in this engineering mechanics application and beyond. Future work is identified.