Estimating S–N curves and their scatter using a differential ant-stigmergy algorithm

Abstract We present an alternative approach to the rapid estimation of S–N curves and their scatter. A simultaneous estimation of the S–N curve and its scatter is achieved by applying a two-parametric Weibull distribution to describe the scatter of a number of load cycles to failure at an arbitrary amplitude stress level. The shape of the S–N curve is generally modelled as a linear dependence between the logarithmic value of the number of load cycles to failure and the logarithmic value of the amplitude stress level. This dependence is described by two parameters: a constant term and a scale coefficient of the S–N curve in a log-log scale. Therefore, the same formulation was applied to model the dependence between a scale parameter of the Weibull distribution and the logarithmic value of the amplitude stress level. In this manner the S–N curve and its scatter are described by three parameters: the constant term, the scale coefficient and the shape parameter of the Weibull distribution. The three parameters are estimated with a differential ant-stigmergy algorithm from the experimental data. In the article a mathematical background of the approach is presented and applied to three cases of experimentally obtained durability data. The results are analysed and discussed.