Research On Adaptive Multivariable Statistical Process Monitoring

Multivariate Statistical Process Control(MSPC) can monitor the relationship among the performance indicators and process variables to find the incipent problems in the industry process, as a result, MSPC method is paid great attentions. Based on the statistic analysis of data, the inherent characteristics and change rules are recognized, and the reasons of abnormal conditions in the industrial process are obtained. The dependence on the data makes MSPC have the strong commonality.However, the process data should meet the requirements of Gaussian, linear, time-invatiance and independent distribution in the traditional MSPC method, which is strict to the complex industrial process. For the time-varying system with the properties, such as nonlinear and dynamics etc, the existing algorithms are improved and various adaptive MSPC methods are proposed in this paper, including,(1) Due to the high computational complexity of EVD/SVD decomposition, the core technique of the traditional Principal Component Analysis (PCA), Kernel Principal Component Analysis (KPCA) and Subspace Identification (SID), a fast Adaptive Non-linear Iterative Partial Least Squares (ANIPALS) algorithm is proposed for the rank-k modification of EVD on the basis of the standard Non-linear Iterative Partial Least Squares (NIPALS). The multiplication calculation between large-scale matrix and large-dimension vector is avoided in the adaptive NIPALS algorithm, which converts the updation of large-dimension eigenvector into the updation of three small dimensionauxiliary vectors and describes the deflation operation of NIPALS algorithm as a rank-1 modification formulation. This algorithm not only ensures the accuracy, but also reduces the computational complexity to order 1.(2) For the high computational complexity and low update efficiency of the traditional KPCA algorithm under the nonlinear time-varying conditions, an adaptive KPCA (AKPCA) algorithm based on moving window method is generated. This algorithm cannot only update Gram matrix accurately, but adaptto the change of the mean data. Through rearrangingthe Gram matrix elements, the updating and downdatingoperations of Gram matrix are combined and formulated as a series of rank-1 modification. The eigenvalue and eigenvectorof the new Gram matrix are modified by using the adaptive NIPALS algorithm in (1). The effectiveness of the AKPCA algorithm is verified by the analysis of the computational complexity and precision.(3) Because of the inefficient calculation when KPCA algorithm selects model parameters by Leave Out One Cross Validation (LOOCV) method, based on the AKPCA algorithm discussed in (2), a fast LOOCV algorithm suitable for KPCA algorithm is proposed. Each modeling of LOOCV algorithm could be regarded as a moving window update on the basis of initial KPCA model, so the efficiency of modelling is improved to update the model by AKPCA algorithm employed in (2). The fast LOOCV algorithm is applied in the industrial distillation process monitoring to verify the effectiveness by computational complexity and simulation results.(4) According to the requirements of removing the dynamics of process data online under the dynamic time-varying conditions, a series of adaptive subspace identification algorithms are proposed and integrated into PCA monitoring. The algorithms use adaptive QR decomposition or adaptive oblique projection method to update projection and apply ANIPALS algorithm proposed in (1) to update the eigenvalue and eigenvector. By analyzing computational complexity and comparing the results of running time, it indicates the more the output variables and rows of Hankelmatrixare, the higher the computational efficiency of the algorithms is. Theeffectiveness of the algorithms is validated by the numerical simulation and the application in the industrial process monitoring.(5) Given that it cannot be described that only part of input variables are related with output variables by the standard PLS algorithm, MRPLS algorithmis proposed, which divideslatent variables into two parts, correlated and uncorrelated components. Meanwhile, the adaptive MRPLS algorithm is also proposed to be used for the updating the model online. Besides, Error-In-Variable (EIV) formulation of the objective function is presented to deal with the measurement noise in the collected input and output data. It indicates that the computational efficiency of MRPLS algorithm is 20% higher than other algorithmby analyzing the complexity and results of running time. The application in the industrial process monitoring validates the effectiveness of the MRPLS algorithm.Finally, conclusion and futher research are discussed.