Research On Statistical Process Monitoring Based On PCA

Process monitoring, which involves fault modeling, fault detection, fault isolation, fault diagnosis and process recovery, is used to monitor process operation. It enables detection and elimination of abnormal process behaviors and ensures the safety of planned operations and high quality of product. Because the monitoring method based on principal component analysis is only relying on process history data and general-purpose, it becomes one of the most active research areas in process control.In this thesis, some important problems of multivariate statistical process control (MSPC) based on PCA are studied systematically, focusing on process modeling, analysis of fault detection behaviors, and implementation of fault isolation by structured residuals.The main contributions are as follows:(1) An assessment approach for PCA statistical model is proposed. It can assess the influence of noise on PCA modeling and describe the approximate degree between models under and beyond noise. The assessment is implemented in residual subspace (RS) and principal component subspace (PCS) by parameter estimation and model similarity index (MSI) respectively. In addition, the effect of training data normalization on modeling is discussed. This assessment method is also developed to dynamic system. Simulations prove that PCA model is very close to true plant model under small magnitude noise.(2) An improved true value-based fault model is proposed and then the fault detection behaviors are studied deeply, which involve the effect on SPE and T~2's expectation of sensor fault, actuator fault, process fault and normal operation point change. These studies show the mathematic evidences for some qualitative conclusions and point out some exceptions with their physical and geometric meanings. To overcome the limitation of traditional detection statistic, we introduce a compound statistic of residual and score (CRS). The fault detection behaviors and sufficient conditions based on CRS are discussed. Simulations on CSTR prove these conclusions right.(3) Two graphical approaches to fault isolation in linear systems are developed. Traditional Q contribution plots can only determine a fault subset but not the faultoccurring. After the theory deficiency of Q contribution plots is analyzed by fault mapping vectors, a weighted Q contribution plots is proposed, which can isolate the faulty sensor accurately. Another graphical isolation approach based on structured residuals and fault mapping vectors is proposed to isolate all kinds of faults including process fault. The control limits, extraction algorithm of fault mapping vector's direction and effects of control loopsare studied. Simulations on CSTR show that weighted Q contribution plots can determinethe faulty sensor accurately and structured residuals based on mapping vectors can easily identify the occurring fault, including process fault.(4) Modeling and fault isolation theories are studied in dynamic system, especially under control loops. Moving windows dynamic PCA (DPCA) is proposed to obtain more concise PCA model with smaller computation scale. Partial DPCA combining moving windows DPCA and partial PCA is developed to implement sensor fault isolation in close-loop dynamic system. CRS statistic is introduced to resolve the problem leaded by independent variables. Multi-model DPCA (MmDPCA) is proposed to isolate all kinds of fault including process fault in close-loop dynamic system. Simulations on CSTR under dynamic scenario show the validity of these methods.(5) Nonlinear process monitoring based on kernel PCA (KPCA) is studied systematically. In the step of modeling, normalization in feature space is discussed. In the step of fault detection, SPE statistic is constructed more easily by virtue of the kernel matrix. Partial kernel PCA (PKPCA) is developed to extend the fault isolation based on structured residuals to nonlinear system. Simulations on CSTR under nonlinear scenario show the effectivity of PKPCA algorithm.Finally, some conclusions and further study areas are given.