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.

为了提高三参数威布尔分布的参数估计精度，提出了一种采用混沌模拟退火粒子群算法（CSAPSO）的参数估计新方法。根据大都市的接受标准，使用模拟退火（SA）算法更新粒子群优化（PSO）算法的惯性权重。根据混沌的性质将Chebyshev映射引入到PSO中，以自适应地使早熟粒子发生突变。此外，为了减小PSO的搜索范围，提高参数估计的速度，将通过图形参数估计方法获得的初始估计作为PSO的初始解。将提出的CSAPSO算法与遗传算法（GA），PSO和SAPSO进行了比较。这四种算法用于估计三组符合Weibull分布的样本数据的参数。平均绝对百分比误差（MAPE），相关系数\（\ rho \），Anderson Darling（AD）测试值和收敛步数用作评估指标。实验结果表明，与其他三种算法相比，所提出的CSAPSO算法对于不同数量的样本和不同的三参数Weibull分布设置参数具有最佳的参数估计精度。