Three-Parameter P-S-N Curve Fitting Based on Improved Maximum Likelihood Estimation Method

The P-S-N curve is a vital tool for dealing with fatigue life analysis, and its fitting under the condition of small samples is always concerned. In the view that the three parameters of the P-S-N curve equation can better describe the relationship between stress and fatigue life in the middle- and long-life range, this paper proposes an improved maximum likelihood method (IMLM). The backward statistical inference method (BSIM) recently proposed has been proven to be a good solution to the two-parameter P-S-N curve fitting problem under the condition of small samples. Because of the addition of an unknown parameter, the problem exists in the search for the optimal solution to the three-parameter P-S-N curve fitting. Considering that the maximum likelihood estimation is a commonly used P-S-N curve fitting method, and the rationality of its search for the optimal solution is better than that of BSIM, a new method combining BSIM and the maximum likelihood estimation is proposed. In addition to the BSIM advantage of expanding the sample information, the IMLM also has the advantage of more reasonable optimal solution search criteria, which improves the disadvantage of BSIM in parameter search. Finally, through the simulation tests and the fatigue test, the P-S-N curve fitting was carried out by using the traditional group method (GM), BSIM, and IMLM, respectively. The results show that the IMLM has the highest fitting accuracy. A test arrangement method is proposed accordingly.