概率PLS保证了过程变量和质量变量的主元相关性最大，但是无法约束过程变量和质量变量的残差，导致残差中可能包含了大量的信息。提出一种基于残差再提取的概率PLS模型，在概率PLS的基础上，从残差中进一步提取出主要成分，从而将过程变量和质量变量划分为相关主元空间、与质量变量无关的过程变量的主元空间、无法预测的质量变量主元空间、过程变量残差空间和质量变量残差空间。采用极大似然算法，结合EM算法估计了模型参数，并构建了基于该模型的过程监控指标。在数字仿真例子中的应用验证了该算法的有效性。

The objective of the probabilistic partial least square (PPLS) algorithm is to maximize the correlation of scores of process variables and quality variables, and imposes no restriction on residuals, which will result in large information containing in the residuals. The paper proposes a PPLS algorithm based on re-extraction of residuals. After the development of the PPLS model, this algorithm performs further decomposition on residuals to obtain another set of scores and residuals. As a result, process variables and quality variables can be projected into the correlation score subspace, the score subspace for the quality-irrelevant process variables, the residual subspace for process variables, the score subspace for un-predicted quality variables, and the residual subspace for quality variables. To identify the parameters, the maximum-likelihood method along with the expectation-maximization (EM) algorithm is employed. Moreover, by constructing the monitoring statistics, this model is introduced into process monitoring, and its application in the numerical simulation case illustrates its validity.