Small Sample Data-Driven Method for Interval Prediction on Structural Responses

Abstract

This paper proposes an approach of intervals prediction on the structural responses under the limited samples by using Grey-BP neural networks (GBP) and genetic algorithm (GA). For the response prediction of complex structures, the presented method can ensure the necessary accuracy and can greatly reduce the cost of computation. Meanwhile, the method is different from the other traditional neural networks, which represents the superiority of dealing with the interval prediction under limited samples with help of the grey theory. In this paper, the Grey-BP neural networks are established by introducing the grey theory, which is used to achieve the mapping relationship between input and output of the system and accomplish the approximation of real mapping. The accuracy of built the mapping model can be tested by error analysis. Subsequently, the issue of interval prediction can be translated to optimal problem for extremum value. Although the explicit expression of the established mapping relationship is unknown, the fitness of every value includes the information of extremum. So, the best fitness and worst fitness can be searched in the given bound of uncertain variables based on genetic algorithm, and then achieve the upper bound and lower bound of the system response depending on the capability of global search. After proposed technologies are given in detail, one numerical example and one engineering example are presented and the results are discussed with common methods based on traditional BP neural network and Monte Carlo, which demonstrates the validity and reasonability of the developed methodology.