Gaussian mixture models have been widely applied to predict those significant but hard-to-measure quality variables in industrial processes. However, outliers that result from disturbances of noise, and incorrect instrument readings, will deteriorate the prediction accuracy of Gaussian mixture models. Student’s-t mixture regression and its variants have been proposed for robust inferential sensor development. Nevertheless, for those Student’s-t mixture regression-based inferential sensors, the functional dependency between the quality and process variables in each component is assumed to be linear. Such configuration in practice might be incapable of adequately modeling the complicated nonlinearity between the quality and process variables. In addition, large amounts of unlabeled samples are easily to be obtained and informative for model performance improvement, however, the computations are significantly increased as well. To get over these issues, this paper proposes a novel semisupervised nonlinear variational Bayesian Student’s-t mixture regression model, in which the nonlinear component model can effectively capture the non-linearity between the quality and process variables. For tackling the low training efficiency issue caused by large number of training samples, the parallel computing strategy is introduced to complete model training. A numerical example and two real industrial processes are supplied to validate the effectiveness of the proposed method.

高斯混合模型已被广泛应用于预测工业过程中那些重要但难以测量的质量变量。然而，由噪声干扰和不正确的仪器读数引起的异常值会降低高斯混合模型的预测精度。Student's- t混合回归及其变体已被提议用于稳健的推理传感器开发。然而，对于那些Student's- ŧ基于混合回归的推理传感器，假设每个组件中的质量和过程变量之间的函数依赖性是线性的。在实践中，这种配置可能无法充分模拟质量和过程变量之间的复杂非线性。此外，大量未标记的样本很容易获得并为模型性能改进提供信息，但是，计算量也显着增加。为了克服这些问题，本文提出了一种新颖的半监督非线性变分贝叶斯Student's- ŧ混合回归模型，其中非线性分量模型可以有效捕捉质量和过程变量之间的非线性。针对训练样本量大导致训练效率低的问题，引入并行计算策略完成模型训练。提供了一个数值例子和两个真实的工业过程来验证所提出方法的有效性。