Calibration, Prediction and Process Monitoring Model Based on Factor Analysis for Incomplete Process Data

Abstract

Unspecific missing of values in real chemical and biological industries have been found. Regardless of the incompleteness of the measured sample, a monitoring system should be designed to tackle the missing data problem and be applied to on-line systems immediately. A calibration method of a factor analysis (FA) model for incomplete data sets is proposed. And a prediction method based on the calibrated model is suggested in order to estimate missing values in incomplete calibration sets and incomplete test sets. An expectation and maximization (EM) algorithm is used to calibrate the model and expectation of conditional density is used to predict the model result. The proposed method is compared with the wellknown iterative singular values decomposition (iSVD) method, i.e. a principal component analysis (PCA) based method; and a simple data set is tested as an illustrative example. The proposed method gives better estimation results for the missing values than the well-known PCA based method. There are several advantages of the proposed method over the PCA based projection methods: (1) data pretreatment is not an essential step since the FA model is scale invariant whereas the PCA model is not, (2) since the proposed method utilizes probability information of all variables directly, to apply it as a statistical process monitoring technique is preferable to others, and (3) the single model can be extended to a mixture of such models by the virtue of the EM algorithm.

Data‐based linear Gaussian state‐space model for dynamic process monitoring

“…In fact, almost all process variables are contaminated by random noises. 13,14 In this monitoring method, different noise variances of process variables have been assigned, which is more practical in industry. Therefore, it is required that process monitoring should also be carried out through the statistical manner, and the monitoring decisions are made through a probabilistic way.…”

Noise-resistant joint diagonalization independent component analysis based process fault detection

“…(4) Based on the validating data, estimate the ICs using Eq. (17) and calculate the serial correlation information fr p ðtÞg N 2 t ¼ h of the dominant ICs using Eq. (25).…”

“…To ensure process safety and stability as well as to maintain high quality of final products, reliable and timely fault detection has emerged as an essential task. Due to the convenient availability of substantial measured data in industrial plants, multivariate statistical analysis methods, which can extract meaningful feature information from large amounts of the measured data for detecting various faults or abnormal situations of industrial processes, have attracted much attention from both process engineers and academic researchers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Principal component analysis (PCA), as one of the classical multivariate statistical analysis approaches, has found wideranging applications in the fault detection field [11][12][13][14][15][16][19][20][21][22].…”

“…To meet the critical demand of identifying fault variables that contribute to process faults, Chen and Sun [20] proposed a probabilistic contribution analysis method in conjunction with the PPCA model based on the concept of missing variable. Noting that the PPCA requires the same noise level in all the measured variables, Kim et al [17] utilized the factor analysis (FA), which can be regarded as an extension of PPCA and is capable of dealing with practical situations where the noise levels are different in different measured variables. Considering that fault information may not have a definite mapping relationship to a single factor and the useful information captured by some factors may be submerged in the insignificant information of the other factors, Jiang and Yan [18] further proposed the weighted FA (WFA) for process monitoring, which is capable of highlighting the useful information that is submerged in the insignificant information by suppressing the latter.…”

A Nonlinear Probabilistic Method for Process Monitoring

“…[1][2][3][4][5] To enhance the monitoring performance, some of these traditional methods have recently been extended to probabilistic counterparts such as probabilistic principal component analysis (PPCA) and factor analysis (FA). [6][7][8][9] However, those developed probabilistic MSPC methods are limited in monitoring linear processes. For nonlinear process monitoring, several kinds of methods have been developed in past decades, such as principal curve, neural network, kernel PCA, and others.…”