Mixture Semi-supervised Robust L1 Probabilistic Principal Component Regression And Soft Sensor Modeling

With the advent of the industry 4.0 era,modern industrial systems are developing toward automation,intelligence,and informationization.Data obtained from systems contains a large amount of process information,which is of great significance for system monitor and control.However,the temperature,pressure,material flow and level measured by conventional sensors cannot meet the increasingly complicated industry’s requirements.In addition to static one,dynamic information is needed.On the other hand,the accuracy and stability requirements are also increasing.In some practical applications,it is also necessary to integrate measurement information of multiple instruments to achieve efficient,stable and reliable process control,system states monitoring and fault detection.Soft sensor is an effective way to solve these problems.Data-driven based,soft sensor has been extensively researched and developed in recent years.What’s more,probabilistic principal component regression has received extensive attention in this research field and has been successfully applied in lots of industrial production processes.However,it is worth noting that the traditional probabilistic principal component regression method has many limitations.For example,it can only construct the model of one system under a single stable operation point and can only be applied to labeled data set.Due to the assumption that all model variables are all following Gaussian distributions,the conventional method suffer from widely existing outliers.Based on the research of predecessors at home and abroad,we propose a mixture robust probabilistic principal method that can tolerant outliers in many complex industrial processes along with multiple operating points.Besides,this method can make use of the unlabeled data samples to help construct a better soft sensor model.The specific research contents are as follows:(1)For complex industrial processes with multiple operating points,compared with the classic probabilistic principal component regression method,a traditional mixture PPCR model is introduced which can estimate sub-model parameters respectively.And the soft sensor model for this method is presented.(2)In traditional researches,the variables are assumed following Gaussian distribution.In industrial process data,outliers widely exist due to recording mistake,process noise and interference,which can lead to model distortion.Therefore,this paper introduces the multivariate Laplace distribution with thick tail instead of Gaussian distribution,which improves the anti-outliers performance of the algorithm and enhances the robustness.(3)Traditional methods generally use supervised learning theory,which means only labeled data can be used.Considering that there is a large amount of unlabeled data in industrial practice,and these data samples still contains a lot of important process and system parameters information,this paper introduces semi-supervised learning theory,which makes unlabeled data can help build a better soft sensor model.(4)The soft sensor model is constructed by Expectation Maximum algorithm.The effectiveness of the proposed method is verified through a numerical example and the Tennessee Eastman benchmark process.And the comparisons with the existing methods.The simulation results conclude that the proposed method gives better modeling results.In the conclusion part,the research contents of this topic are summarized,and the future research work is envisioned and prospected.