Cause and Effect Dynamic Modeling of Real Processes Under Freely Existing Data Collection

Due to continual advancements of sensor technology, computer technology and electronic data storage, the number of variables and their frequency of sampling and storage are growing at tremendous rates. While the plant data bases utilizing this growing technology have proven invaluable for diagnostic and health monitoring, there are two critical reasons that they have not been widely exploited in the development of cause and effect modeling which would allow direct implementation into manual or automatic model-based control strategies. The first reason is the low signal-to-noise ratio since the data are collected under operating conditions where the objective is to minimize process variability. The second reason is the highly correlated natural behavior of the variables that is called multicollinearity that impedes the ability to associate a specific change in one variable with a specific amount of change in the response of interest. To overcome these critical challenges, modelers rely on the use of experimental design where an intelligent sequence of changes are made to the inputs to maximize information content both by the size of the changes and type of changes. However, there are two major drawbacks of this approach. The first one is the cost to run the experiments due to production interruption; which often leads to unusable products since the changes have to be outside of normal operating regions. The second one is the limited duration of the plant test because cost increases with duration. Limited duration impacts the ability to fully include the cyclical nature of unmeasured disturbances in model development. This limitation results in poor model performance as these disturbances move away from the conditions when the model was developed.

To overcome these challenges, the continuous-time Wiener block-oriented modeling approach developed by Bhandari and Rollins (2003) is extended to discrete-time modeling and input correlation is minimized by passing each input through a separate dynamic block and using a static linear function on the outputs from these blocks to maintain accuracy for mild extrapolation. By modeling over a sufficiently long period which is possible from archived data, information content is strengthened and the impact of unmeasured disturbances on measurement bias is minimized.

            This talk will present results of this approach for a model of top tray temperature of a pilot distillation column on at least 10 independent runs over a three year period. The model was built from nine inputs, that were highly correlated in some cases, under open loop conditions. The fitted correlation coefficient (r_fit) for training and validation were 0.96 and 0.97, respectively. For the test data sets, which were run under closed-loop control, r_fit ranged from 0.61 to 0.93, with an average greater than 0.8, supporting the ability of this approach to develop accurate models with long term stability from data under a different correlation structure. In addition, a method based on principal component analysis (PCA) is presented for elimination of cases representing extreme extrapolation.

Bhandari, N. and D. K. Rollins, “A Continuous-Time MIMO Wiener Modeling Method,”Industrial and Engineering Chemistry Research, 42(22), pp. 5583-5595 (2003).