Abstract
Inferential models are widely used in the chemical industry to infer key process variables, which are challenging or expensive to measure, from other more easily measured variables. The aim of this paper is three-fold: to present a theoretical review of some of the well known linear inferential modeling techniques, to enhance the predictive ability of the regularized canonical correlation analysis (RCCA) method, and finally to compare the performances of these techniques and highlight some of the practical issues that can affect their predictive abilities. The inferential modeling techniques considered in this study include full rank modeling techniques, such as ordinary least square (OLS) regression and ridge regression (RR), and latent variable regression (LVR) techniques, such as principal component regression (PCR), partial least squares (PLS) regression, and regularized canonical correlation analysis (RCCA). The theoretical analysis shows that the loading vectors used in LVR modeling can be computed by solving eigenvalue problems. Also, for the RCCA method, we show that by optimizing the regularization parameter, an improvement in prediction accuracy can be achieved over other modeling techniques. To illustrate the performances of all inferential modeling techniques, a comparative analysis was performed through two simulated examples, one using synthetic data and the other using simulated distillation column data. All techniques are optimized and compared by computing the cross validation mean square error using unseen testing data. The results of this comparative analysis show that scaling the data helps improve the performances of all modeling techniques, and that the LVR techniques outperform the full rank ones. One reason for this advantage is that the LVR techniques improve the conditioning of the model by discarding the latent variables (or principal components) with small eigenvalues, which also reduce the effect of the noise on the model prediction. The results also show that PCR and PLS have comparable performances, and that RCCA can provide an advantage by optimizing its regularization parameter.
Highlights
Models play an important role in various process operations, such as process control, monitoring, and optimization
To make statistically valid conclusions about the performances of the various modeling techniques, a Monte Carlo simulation of 1000 realizations is performed and the results are shown in Table 1 and Figure 2. These results show that the performance of RR is better than that of ordinary least square (OLS), and that the performances of the latent variable regression (LVR) modeling techniques (PCR, partial least squares (PLS), and regularized canonical correlation analysis (RCCA)) clearly outperform the performances of the full rank models (OLS and RR)
The optimum numbers of principal components used by the various LVR models for the case where signal-to-noise ratios (SNR)=20 are shown in Figures 3(a), (c) and (e), which show that the optimum number of principal components used in principal component regression (PCR) is usually more than what is used in PLS and RCCA to achieve a comparable prediction accuracy
Summary
Models play an important role in various process operations, such as process control, monitoring, and optimization. The control of distillation column compositions requires the availability of inferential models that can accurately predict the compositions from other variables, such as temperature and pressure at different trays of the column. These inferential models are expected to provide accurate predictions of the output variables over a wide range of operating conditions. Ential models is usually associated with many challenges, which include accounting for the presence of measurement noise in the data and dealing with collinearity or redundancy among the variables.
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