A Comparative Study On The Probability Distributions Of Fatigue Life

The reliability problem caused by structural fatigue has received much attention and they are commonly suggested to be considered in reliability analysis.Generally speaking,there is largescatter on fatigue life due to the inherent non-uniformity of materials and the difference of processing technic and boundary conditions.Probabilistic and statistics methodsareused to describe the scatter of fatigue life,standard probability distribution models,such as logarithmic normal distribution and Weibull distribution,areoften good choices.In addition,Birnbaum–Saunders(BS)distribution family deduced from the fatigue crack propagation mechanism and Extreme value distribution,which have good flexibility,are also used to describe the scatter of fatigue life.Considering that the accuracy of fatigue life prediction and analysis depend on whether these distribution models can truly reflect the scatter of fatigue life,it is necessary to carry out a comparative study on these probabilisticdistribution models and further obtain better knowledge of the flexibility and fitting precision of them.Logarithmic normal distribution,Weibull distribution,Generalized Extreme Value distribution and BS distribution familyare studied and compared for identifying the probability distribution of fatigue life in this thesis.Parameter estimation methods are also proposed to estimate the distributional parameters of the above distributions.Combining two groups of fatigue data sets available in the literature,two fit indexes are used to measure the goodness-of-total-fit and the goodness-of-tail-fit of the above distributionsIt is well-known that the above distribution models are generally based on engineering experience.In order to reduce the introduction of subjective uncertainties and obtain rational probability distributions,a computational method based on the maximum entropy principle is proposed for identifying the probability distribution of fatigue life in this thesis.The first four statistical moments of fatigue life are involved to formulate constraints in the maximum entropy principle optimization problem.An accurate algorithm named Nelder-Mead algorithm is also presented to find the Lagrange multipliers in the maximum entropy distribution,which can avoid the numerical singularity when solving a system of equations.The computational results show that the extended BS distribution and the maximum entropy distribution have better flexibility and precision in identifying probability distribution of the fatigue life when compared with other probabilistic distributions.