Mixtures of Probabilistic Principal Component Regression: Application in Optimality Assessment

• Author / Creator

  Sedghi, Shabnam

• Performance of the operating processes may change by time due to uncertainties and process condition changes. Hence, online operating performance assessment has attracted attentions from academia and industry. One of the main ingredients of performance assessment is optimality assessment. On one hand, the optimal condition for an operating process can be estimated by known process optimization methods as an initial design. On the other hand, performance may alter from the optimal design due to disturbances, process condition changes or product driven operating mode changes. As a result, optimality assessment, i.e., monitoring the operating process performance in terms of optimality is of great importance. The main objective of this thesis is to develop a general framework for optimality assessment in multi-mode systems with non-Gaussian behavior by employing probabilistic principal component regression (PPCR) method. High dimensionality of the process datasets, multiple operating regions caused by uncertainties and simultaneous missing inputs and outputs due to the device failure or delays in measuring certain variables are some of the challenges in optimality assessment. Mixture semi-supervised probabilistic principal component regression (MSPPCR) model is employed that inherently addresses high dimensionality, multimodal behavior and missing outputs. In addition, it is developed under expectation maximization (EM) framework in order to deal with simultaneous missing inputs and outputs. The proposed model is capable of making the most use of all available information for predictive model building. In many processes, steady state operating modes do not follow Gaussian distribution since they have different operating regions that are caused by uncertainties. Due to the lack of information regarding operating regions, a hierarchical mixture PPCR method is proposed in order to automatically estimate the number of operating regions, and the parameters are estimated through maximum a posteriori (MAP) principle under EM framework that incorporates prior distributions. This method is based on a divisive hierarchical algorithm; however, a merging step is proposed in order to control splitting steps and avoid overestimation of the number of mixture components. Due to its hierarchical nature, a prior knowledge of the possible range of the number of components is not required compared to the traditional methods. Moreover, it is capable of detecting overlapped components because of utilizing minimum message length criterion (MML) as the selection criterion. A probabilistic framework for optimality assessment and non-optimum cause diagnosis for multi-mode processes with non-Gaussian behavior is proposed. In this framework, operating regions are compared with operating modes that are caused by uncertainties and known governing factors, respectively. Density based clustering (DENCLUE) method is modified and improved for offline operating mode detection. In addition, a predictive operating modes classifier is built based on modified mixture discriminant analysis (MclustDA) method, and it is incorporated with process knowledge in order to improve estimation. For optimality analysis and prediction, MSPPCR model is employed for steady state modes, and dynamic principal component regression (DPCR) is employed for transitions. A probabilistic framework through sequential forward floating search (SFFS) method is adopted for non-optimum cause diagnosis. The proposed method is capable of optimality assessment for general high dimensional multi-modal systems with non-Gaussian behavior. Finally, the performance and validity of the proposed methods are verified through various numerical, simulation and industrial examples.

• Subjects / Keywords

  • Optimality Assessment
  • Multi-mode Processes
  • Probabilistic PCA

• Graduation date

  Spring 2017

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3RX93R7W

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.