基于t分布噪声的鲁棒PPLS回归模型

概率PLS(PPLS)模型中,数据源(主元)和噪声满足正态分布,容易受离群点的影响.鲁棒PPLS算法采用拖尾更长的t分布描述数据源和噪声,提高了模型的鲁棒性.但是,实际工业过程中,离群点由测量噪声导致,而不是由产生过程变量和质量变量的数据源产生.基于此,提出一种基于t分布噪声的鲁棒PPLS模型.该模型采用t分布拟合测量噪声的分布,而主元依然用标准正态分布描述,更符合实际测量状况.考虑到潜在变量的存在,采用极大似然方法结合EM算法对模型的参数进行了估计,并将该模型用于对过程变量和质量变量的回归估计.最后,通过仿真实例进行了验证.

Robust PPLS regression modeling subject to t-distributed noise

In the probabilistic partial least squares (PPLS) model, both the data source (scores) and noise satisfy Gaussian distribution, which makes it sensible to the outlier. In the existing robust PPLS model, to improve the model robustness, a t-distribution with a longer tail rather than a Gaussian distribution with a shorter tail is employed to describe the distribution of noise and scores. However, in the real industrial processes, it is the measurement noise rather than the data source which results in the outliers. To accurately extract the information hidden in the polluted data by noise, a robust PPLS model is proposed based on the t-distributed noise assumed, where similar to the PPLS model the latent variables are normally distributed to capture the character of measurements available. Due to latent variables involved in the model, the maximum likelihood method along with the EM algorithm are employed to estimate the model parameter. Furthermore, the proposed model is used for the estimation of process variables and quality variables. Finally, a simulation case is employed to verify the proposed model.