Multi-modal modeling of stress spectrum using genetic algorithm and finite mixture distributions

In this study, a genetic algorithm-based (GA-based) method for the estimation of the parameters in the finite mixture distributions is proposed and applied to the multi-modal modeling of the stress spectrum of a typical welded joint of Tsing Ma Bridge. Firstly, the temperature effect on the original strain monitoring data is eliminated by wavelet transform. The rainflow counting algorithm is employed to transfer the strain stress histories into daily stress spectra. A standard daily stress spectrum accounting for highway traffic, railway traffic, and typhoon effects is derived. Then, the multi-modal modeling of the stress range is conducted by use of three types of finite mixture distributions (normal, lognormal, and Weibull) in conjunction with the GA-based mixture parameter estimation method. The optimal finite mixed model is determined by the Akaike's information criterion (AIC). Finally, the joint probability density function (PDF) of the stress range and the mean stress is obtained using the bivariate finite mixture distributions and the GA-based mixture parameter estimation method. The results show that the proposed GA-based mixture parameter estimation method is adequate in the probabilistic modeling of two random variables.