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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。
The choice of regular parameters is the key to the Tikhonov regularization method of photon correlation spectroscopy (PCS) particle size inversion. In order to obtain the optimal regular parameter, a regular parameter selection strategy based on the Morozov deviation principle is proposed. The algorithm of the differential algorithm is used to optimize the regular parameters. Starting from a solution set of the canonical parameters, the three rules of differential mutation, crossover and selection are iterated continuously According to the objective function value of each solution, the survival of the fittest is eliminated, which leads the search process to approximate the optimal solution gradually. The simulation results of single peak, bimodal and broad distribution particles are respectively inversed. The inversion results show that the proposed method has good anti-noise performance. When the noise level is 0.000 0 ~ 0.001 0, The results are in good agreement with the theoretical distribution. The bimodal characteristics of bimodal distribution particles are obvious, and the maximum peak error of inversion is less than 5%. This shows that in the PCS granularity inversion, the difference algorithm is effective for optimizing regular parameters.