Fatigue property assessment of parallel wire stay cable I: fatigue life model for wire

As the first part with respect to the fatigue property assessment of the parallel wire stay cable, a fatigue life model of the steel wire is established. The three-parameter power function is employed to describe the fatigue stress-life model, and the two-parameter Weibull distribution is used to represent the fatigue life of steel wire under the specified stress range. Supposed that the fatigue life of individual wire calculated by the two models are equivalent under the specified stress range with the identical survival probability, a novel multi-parameter Weibull model for the fatigue life assessment of steel wire is deduced, in which fatigue life and stress range are compatible. On the basis of conditional probability distribution of the censored data, an improved expectation maximization (EM) algorithm is employed to estimate the parameters of the proposed model. The fatigue data of the strands from the literature are analyzed to illustrate the fitness and characteristics of the proposed model. Finally, the fatigue life model for the steel wire is established based on the fatigue data obtained by fatigue experiment. The results indicate that the proposed fatigue life model can fit the fatigue data of strands and steel wires better. For the specified stress range, the probability distribution of the fatigue life is simplified as a two-parameter Weibull model. For the specified fatigue life, the probability distribution of the corresponding stress range is simplified as a three-parameter Weibull model. It is convenient to deal with the censored data with the proposed EM algorithm. The whole fatigue data are pooled together to estimate the parameters of the proposed fatigue life model, thus the accuracy of the parameter estimation can be improved.