Joint estimation of E–N curves and their scatter using evolutionary algorithms

• E–N curves and their scatter were estimated by a two-parametric Weibul PDF.
• Conditional PDF of load cycles to failure depends on strain amplitude.
• Parameters of PDF were estimated by evolutionary algorithms (GA and DASA).
• The estimated PDF models well the E–N curves and their scatter.

We present an approach for estimating E–N curves and their scatter. The scatter of a number of load cycles to failure at an arbitrary amplitude-strain level is modelled using a two-parametric Weibull distribution with the constant shape parameter β and the scale parameter η dependent on the strain amplitude by the Coffin–Manson equation. In this way the E–N curve and its scatter can be described using five parameters: the four parameters of the Coffin–Manson equation for the scale parameter of the Weibull distribution and the shape parameter of the Weibull distribution. The objective was to estimate these five parameters, which are generally unknown (since the data from the literature are manly known only for the median E–N curves), on the basis of the known fatigue-life data to obtain not only the trend of the E–N curve, but also its scatter. In order to estimate these parameters on the basis of the fatigue-life data, two evolutionary algorithms were applied: a real-valued genetic algorithm (GA) and the differential ant-stigmergy algorithm (DASA). In the article a mathematical background of the approach is presented and applied to 27 test cases of simulated fatigue-life data and one real case of experimentally obtained fatigue-life data. The results are analysed and discussed.