Using neural network function approximation for optimal design of continuous-state parallel–series systems

Abstract

This paper presents a novel continuous-state system model for optimal design of parallel–series systems when both cost and reliability are considered. The advantage of a continuous-state system model is that it represents realities more accurately than discrete-state system models. However, using conventional optimization algorithms to solve the optimal design problem for continuous-state systems becomes very complex. Under general cases, it is impossible to obtain an explicit expression of the objective function to be optimized. In this paper, we propose a neural network (NN) approach to approximate the objective function. Once the approximate optimization model is obtained with the NN approach, the subsequent optimization methods and procedures are the same and straightforward. A 2-stage example is given to compare the analytical approach with the proposed NN approach. A complicated 4-stage example is given to illustrate that it is easy to use the NN approach while it is too difficult to solve the problem analytically. Scope and purpose The classical reliability theory assumes that the system and each component may only be in one of two possible states: working or failed. Thus, it is also referred to as binary reliability theory. A well-known reliability design problem under the binary reliability theory involves the determination of the number of redundancies in a parallel–series system which consists of N subsystems connected in series whereas each subsystem consists of a few components connected in parallel. In this paper, we consider the optimal design problem of a multi-state parallel–series system wherein both the system and its components may assume more than two levels of performance. Specifically, we assume that the state of each component and the system may be represented by a continuous random variable that may take values in the closed interval [0,1]. An optimization model is formulated for the determination of the number of redundancies in order to maximize the system's expected utility function. Because of the complexity of the optimization problem, we propose a neural network (NN) approach to approximate the objective function. The resulting optimization model is much easier to solve. Examples are given to illustrate the proposed approach.