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Since small sample data are obtained in the material fatigue life test, the result of S-N curve can deviate greatly from the real results. In order to address this kind of problem and improve the credibility of S-N curve, we introduce the error circle in the Bootstrap method, which makes the results of the sample more reasonable. Bootstrap error circle method is proposed in this paper, and the parameter characteristics of samples in the error range such as mean and confidence interval by processing the original samples are acquired, which improves the reasonable of the samples. The Bootstrap error circle method is used to modify the limitations of the Bootstrap method so as to reduce the sample error and obtain a more reasonable estimate. In this paper, a more reasonable S-N curve is obtained, and it can predict the life of product.

To improve the shortcomings of peak over threshold (POT) extrapolation method and reflect the diversity and dynamics of road conditions, an improved POT extrapolation method to reconstruct the load sequence in the middle of threshold is proposed. Based on the improved extrapolated load, the distribution characteristics of mean and amplitude are analyzed and the two-dimensional joint probability distribution is established. To discuss the influence of low load strengthening characteristics on fatigue life under random load, based on the two-dimensional joint probability distribution, the theory of low load strengthening is introduced in compiling load spectrum. The fatigue life predicted by 8-level load spectrum and 10-level strengthened load spectrum are compared with the test results, respectively. Which verifies the effectiveness and accuracy of life prediction based on improved POT extrapolation and low load strengthening under random load.