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We frequently develop mathematical models of system behavior and sometimes use test data to help identify the parameters of the mathematical model. However, no general purpose technique exists for formally, statistically judging the quality of a model. The paper suggests a formal statistical procedure for the validation of mathematical models of systems when data taken during operation of the system are available. The statistical validation procedure is based on the bootstrap, and it seeks to build a framework where a statistical test of hypothesis can be run to determine whether or not a mathematical model is an acceptable model of a system with regard to user specified measures of system behavior. A numerical example is presented to demonstrate the application of the technique.

Mathematical models of physical systems are used, among other purposes, to improve our understanding of the behavior of physical systems, predict physical system responses, and control the responses of systems. Phenomenological models are frequently used to simulate system behavior, but an alternative is available-the artificial neural network (ANN). We demonstrate that a particular ANN, the connectionist normalized linear spline (CNLS) network, can be used to simulate mechanical system behavior accurately and efficiently. The system simulations are performed in the non recurrent and recurrent frameworks. The paper provides brief discussions on the operation of ANNs in general and the CNLS net in particular, the operation of two different types of mechanical systems, and approaches to the solution of some special problems that occur in connection with ANN simulation of physical system response. Numerical examples are presented.