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To properly depict the heteroscedasticity when analyzing strain-based fatigue reliability, this paper proposes a novel P-ε-N model from both viewpoints of geometric properties and statistical characteristics. The constructed approach deals with the elastic strain and plastic strain separately, where the logarithmic fatigue life is considered as normally distributed with linear mean and standard deviation (std) functions of logarithmic elastic strain or plastic strain, respectively. P-ε-N curve with any percentile can be derived to facilitate the reliability analysis. An improved parameter estimation method based on maximum likelihood estimation (MLE) via genetic algorithm (GA) is further established. The presented method is illustrated and verified via a comprehensive simulation study and two real applications by comparing with the conventional homoscedasticity model. Corresponding results indicate that our proposed method can enhance the modeling accuracy and provide an extensive adaptation.

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Simultaneous CO2 removal with renewable biofuel production can be achieved by methanogens through conversion of CO2 and H2 into CH4. However, the low gas–liquid mass transfer (kLa) of H2 limits the commercial application of this bioconversion.

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