Neural network initialization with prototypes function approximation in engineering mechanics applications

A prototype-based initialization methodology is proposed to approximate functions that are used to characterize nonlinear stress-strain, moment-curvature, and load-displacement relationships, as well as restoring forces and time histories in engineering mechanics applications. Three prototypes are defined by exploiting the capabilities of linear sums of sigmoidal functions. By using the proposed prototypes either individually or combinatorially, successful training can take place for ten specific types of nonlinear functions and far beyond when the required number of hidden nodes and initial values of weights and biases can always be derived before the training starts. Some mathematical insights to this initialization methodology and a few prototypes are offered, while training examples are provided to demonstrate a clear procedure that is used to implement this methodology. With the derived numbers of hidden nodes in each approximation, applying the Nguyen-Widrow algorithm is enabled and the training performance is compared between the existing and the proposed initialization options.