Stepwise Response Surface Method and its Application in Reliability Analysis of Ship Hull Structure

Abstract

A stepwise response surface approach is proposed in this paper. The response surface is determined by modified stepwise regression, so that the square and cross terms can be absorbed into the model automatically according to their actual contribution, which is calculated by repeated variance analysis. Besides, by applying a weighting factor to the statistical value of contribution and changing the thresholds of introduction and rejection, the entry of each term can be controlled in a fairly flexible manner. None other criteria than those in the traditional statistics are needed to check the goodness of fit. Considering the relatively small sample set at the beginning, the algorithm starts with a linear response surface. As the adaptive iteration proceeds, the bar to quadratic terms is lifted gradually to allow ordered entry. Since the sampling points in one step of iteration are recycled in the succeeding ones, a simple experimental design is enough to fit a robust response surface. A double bottom hull system is analyzed with randomized Young’s modulus, load distribution, and geometric properties. The sensitivity analysis is also performed with respect to the random variables and the parameters in their distributions.