自适应SA-PSO优化的威布尔混合分布参数估计方法及应用

针对采用传统参数估计方法得到的模型拟合误差较大的问题，建立多重威布尔混合分布参数估计的非线性最小二乘模型，并提出基于模拟退火（SA）思想的自适应粒子群（PSO）算法进行求解。在PSO算法优化过程中，采用自适应方法调整惯性权重和加速因子，加快其收敛速度；引入模拟退火机制，根据Metropolis准则确定最优粒子的取舍，改善其全局搜索能力。将该方法应用到某型柴油机喷油器失效分布的参数估计中，并与图解法、基于Levenberg-Marquardt的非线性最小二乘法、标准PSO算法、自适应PSO算法求解的结果进行比较，分析所提方法的优化性能及精度。结果表明，该方法能够有效提高多重威布尔混合分布模型参数估计的精度和效率。

Research on Parameter Estimation Method with Application of Mixed Weibull Distribution Based on Adaptive SA-PSO

Aiming at the problem of large fitting error of the model obtained by using the traditional parameter estimation method, a nonlinear least squares (NLS) model for parameter estimation of the mixed Weibull distribution is established. Furthermore, an adaptive particle swarm optimization (PSO) based on the idea of simulated annealing (SA) is proposed to solve the optimization problem. In the process of PSO algorithm optimization, the adaptive method is used to adjust the inertia weight and acceleration factor to speed up its convergence speed.The simulated annealing mechanism is introduced to determine the optimal particle selection according to the Metropolis criterion and improve its global searching ability.This method is applied to the parameter estimation of the failure distribution of a diesel fuel injector, and compared with the results obtained by the graphic method, the nonlinear least square method based on Levenberg-Marquardt, the standard PSO algorithm and the adaptive PSO algorithm, the optimization performance and accuracy of the proposed method are analyzed.The results show that this method can effectively improve the accuracy and efficiency of parameter estimation in the multi-Weibull mixed distribution model.