Probabilistic Data-driven Modeling And Monitoring For Industrial Processes

The national strategies,such as German Industry 4.0 and the China Manufacturing 2025 Plan,have been gradually implemented,which has brought about tremendous changes in the industrial production process.Data and data processing technologies have received unprecedented attention.In the modern process monitoring,the focus of attention gradually shifts from how to obtain the status of process operation by the multi-dimensional and high-precision sensors to how to achieve the evaluation of process operation by infusing all available information.The latent variable model can extract the feature information from multi-dimensional data,and it can be employed for the monitoring of complex multivariate processes based on the statistical process monitoring idea.The latent variable model has been widely used in industrial processes.The probabilistic latent variable model shares the same advantages with the latent variable model.At the same time,it is highly scalable and provides a probabilistic statistical framework.As a result,it is easy to introduce statistical analysis,Bayesian principles,and statistical reasoning methods to deal with complex problems in industrial processes.This paper investigates the probabilistic latent variable modeling and the design of monitoring indices in the presence of missing data,outliers in the industrial process.The research content is as follows:(1)For the problem of missing quality variables and process variables,by estimating the probability distributions of missing data,latent variables,and residuals,and constructing monitoring indices using the estimated probability distributions,a process monitoring method for incomplete data is proposed based on the concurrent partial least squares(CPLS)model.Different from the traditional methods,this proposed method introduces the idea of statistical monitoring into the estimation of missing data,latent variables,and residuals,so that the missing data,latent variables and residuals conform to statistical laws,but are no longer deterministic items.Random monitoring indices are constructed based on the random latent variables and residuals,and the uncertainty of monitoring indices caused by missing data is computed.(2)Probabilistic expansion of the CPLS model.Factor analysis is used instead of principal component analysis to extract the uncorrelated information between process variables and quality variables,and a semi-probabilistic extension model of CPLS is obtained.Further,assuming that all latent variables and residuals satisfy the normal distribution,a probabilistic CPLS algorithm is proposed to implement the full-probability extension of the CPLS model.The PCPLS model overcomes the disadvantage that the measurement of optimization goals for CPLS modeling is inconsistent with that of the statistical monitoring indices for latent variables.(3)In response to the problem of outliers and missing data in actual industrial processes,the t-distribution is used instead of the normal distribution to describe variables,latent variables and residuals.By using the Bayesian rule and statistical inference methods,the missing data and latent variables are estimated.The distributions of variables and residuals enable robust probability PLS(PPLS)modeling and monitoring under missing data.The robust PPLS model can reduce the influence of outliers and increase the model robustness.(4)For the large conservativeness of the robust probabilistic latent variable model casued by the assumption that both latent variables and residuals satisfy the t-distribution,the reasons for the outliers are analyzed.A robust probabilistic latent variable modeling and monitoring method based on the t-distribution noise is proposed by considering that the outliers are mostly caused by random disturbances in the actual industrial process.According to the proposed model,the conservativeness of distributions of latent variables can be reduced on the basis of ensuring the model robustness.(5)The monitoring indices based on the probabilistic latent variables model only use the expectations of latent variables and residuals,resulting in the problem of large false negative rate.The covariances of latent variables and residuals are introduced into the monitoring indices,and the reason for bad performance of commonly used monitoring indices is analyzed.The uncertainty region of commonly used monitoring indices is calculated,and then it is integrated into the construction of monitoring indices according to the statistical monitoring idea.The proposed monitoring indices can reduce the false negative rate by fully considering the uncertainty of latent variables and residuals.