A Novel Three-parameter Weibull Distribution Parameter Estimation Using Chaos Simulated Annealing Particle Swarm Optimization in Civil Aircraft Risk Assessment

In order to improve the parameter estimation accuracy of three-parameter Weibull distribution, a novel parameter estimation method using chaos simulated annealing particle swarm optimization (CSAPSO) algorithm is proposed. The simulated annealing (SA) algorithm is used to update the inertia weight of particle swarm optimization (PSO) algorithm according to the Metropolis acceptance criteria. The Chebyshev mapping is introduced into PSO according to the properties of chaos to make adaptively chaos mutate for premature particle. Moreover, in order to reduce the search range of PSO and improve the speed of parameter estimation, the initial estimation obtained by graphical parameter estimation method is taken as the initial solution of PSO. The proposed CSAPSO algorithm is compared with genetic algorithm (GA), PSO and SAPSO. These four algorithms are used to estimate the parameters of three sets of sample data which are conform to the Weibull distribution. The mean absolute percentage error (MAPE), correlation coefficient $$\rho $$ , Anderson Darling (AD) test value and the number of convergence step are used as evaluation indexes. The experimental results show that compared with the other three algorithms, the proposed CSAPSO algorithm has best parameter estimation accuracy for different number of samples and different setting parameters of three-parameter Weibull distribution.