基于PCA-BP神经网络的光谱消光法颗粒粒径反演算法研究

光谱消光法广泛应用于颗粒粒径测量领域，在利用光谱消光法对颗粒粒径进行反演的过程中，由于颗粒的消光系数存在理论复杂、计算繁琐、收敛速度慢以及求解不稳定等问题，很大程度上影响了整个反演过程的快速性和准确性。且在众多波长的消光数据中，存在较多重复冗余的信息，也很大程度上增加了反演算法的时间。针对光谱消光法粒径反演算法计算繁琐、反演效率低的问题，提出了基于主成分分析（PCA）和BP神经网络的光谱消光颗粒粒径分析方法。基于Mie散射理论对不同粒径、不同波长下的光谱消光值进行了仿真计算，通过对光谱消光数据集的主成分分析及各个波长综合载荷系数的计算，实现了最优特征波长的选取，利用降维后的光谱消光数据训练了PCA-BP神经网络模型，并利用该网络模型计算了粒径颗粒分布。通过仿真计算，比较了PCA-BP神经网络模型与传统的BP神经网络模型的预测精度，并分析了波长数目对两种神经网络模型预测结果的影响。针对训练得到的PCA-BP神经网络模型开展光谱消光法粒径参数反演算法的验证实验，搭建了光谱消光法颗粒粒径参数测量实验系统，测量了粒径范围在0.5～9.7 μm内的6种不同粒径参数的聚苯乙烯标准颗粒。仿真和实验结果表明：基于主成分分析方法可确定各个波长向量之间的相关性，利用综合载荷系数选取最优特征波长对应的消光值对整体的光谱数据具有较好的代表性，可实现光谱数据的降维。相比传统的BP神经网络模型，基于PCA-BP神经网络模型的颗粒粒径分布的分析方法预测精度更高，对于较分散颗粒系的分布参数的预测有更加明显的优势。而且，被选取的波长数较少时，PCA-BP神经网络模型依然有较高的预测精度。利用训练好的PCA-BP神经网络模型对颗粒粒径参数进行实验验证，预测结果可瞬时输出，颗粒粒径分布误差在5%以内，验证了该算法的可行性。

Inversion of Particle Size Distribution in Spectral Extinction Measurements Using PCA and BP Neural Network Algorithm

Spectral extinction method is widely used in the field of Particle Size Distribution (PSD) measurement. During the inversion process of particle size by spectral extinction method, the speed and accuracy of the whole inversion process are greatly affected due to the problems of complex theory, complicated calculation, slow convergence speed and unstable solution of particle extinction coefficient. Moreover, in the extinction data of many wavelengths, there is more repeated redundant information, which also greatly increases the time of the inversion algorithm. Aiming at the problems of complicated calculation and low inversion efficiency of spectral extinction PSD inversion algorithm, a spectral PSD analysis method based on Principal Component Analysis (PCA) and Back Propagation (BP) neural network was proposed. Based on Mie scattering theory, the spectral extinction values under different particle sizes and wavelengths were simulated and calculated. Through the PCA of the spectral extinction data set and the calculation of the comprehensive load coefficient of each wavelength, the optimal characteristic wavelength was selected. The PCA-BP neural network model was trained by using the reduced spectral extinction data, and the PSD was calculated by using the network model. Through simulation calculation, the prediction accuracy of PCA-BP neural network model was compared with the traditional BP neural network model, and the influence of wavelengths number on the prediction results of the two neural network models was analyzed. Based on the trained PCA-BP neural network model, the verification experiment of spectral extinction inversion algorithm of PSD was carried out, and an experimental system for PSD measurement by spectral extinction method is established. Six types of standard polystyrene particles with different particle size parameters ranging from 0.5 to 9.7 μm were measured. Simulation and experimental results show that the correlation between each wavelength vector can be determined based on the PCA method, and the extinction value corresponding to the optimal characteristic wavelength can be selected by using the comprehensive load coefficient, which has good representativeness of the overall spectral data and can realize the dimensionality reduction of spectral data. Compared with the traditional BP neural network model, the analysis method of PSD based on the PCA-BP neural network model has higher prediction accuracy and has more obvious advantages for predicting distribution parameters of more dispersed particle systems. Moreover, when the number of selected wavelengths is small, the PCA-BP neural network model still has high prediction accuracy. The trained PCA-BP neural network model is used to verify the particle size parameters experimentally. The PSD prediction results can be output instantaneously, and the error is within 5%, which verifies the algorithm’s feasibility.