PCS粒度反演中基于差分算法的正则参数优化

Regularization parameter optimization based on differential algorithm in the particle size inversion of PCS

正则参数的选择是Tikhonov正则化法光子相关光谱（PCS）粒度反演的关键。为了获取最优正则参数,基于Morozov偏差原理正则参数选择策略,提出利用差分算法对正则参数进行优化,从正则参数的一个解集开始,按着差分变异、交叉和选择3种规则不断迭代,并根据每个解的目标函数值进行优胜劣汰,从而引导搜索过程逐渐逼近最优解。分别对单峰、双峰和宽分布颗粒的模拟数据进行了反演,反演结果表明,本文方法具有良好的抗噪性,在噪声水平为0.000 0-0.001 0时,单峰、宽分布颗粒的结果与理论分布吻合,双峰分布颗粒的双峰特征明显,反演的最大峰值误差不超过5%。由此说明,在PCS粒度反演中,差分算法用于优化正则参数是有效的。

Regularization parameter selection is the key of particle size inversion of photon correlation spectroscopy（PCS） by Tikhonov regularization method.In order to obtain the optimal regularization parameter,according to regularization parameter selection strategy of Morozov discrepancy principle and based on differential evolution algorithm,an optimization method of regularization parameter within the global range is proposed.This method begins from a solution set of regularization parameter,iteratively calculated by three kinds of operation rules.According to the objective function value of each solution,gradually the search process is guided to approach the optimal solution.Computer simulation data of unimodal,bimodal and wide distribution particles were inversed by this method respectively.The results show that this method has strong tolerance of noises,when the noise level is 0.000 0-0.001 0,results of unimodal and wide distribution particles agree with the theory distribution,the double-peak feature of bimodal distribution particles is clear,and the maximum error of the inversion peak is less than 5%.Therefore,it is an effective optimization method for regularization parameter in particle size inversion of PCS.