(202j) Adaptive Soft Sensor Model Using Online Support Vector Regression and the Time Variable

Soft sensors are widely used to predict process variables that are difficult to measure online. An inferential model is constructed between the variables that are easy to measure online and those that are not, and an objective variable, y, is then predicted using that model. Through the use of soft sensors, the values of ycan be predicted with a high degree of accuracy. One of the crucial difficulties of soft sensors is that predictive accuracy drops due to changes in state of chemical plants. This is called as the degradation of soft sensor models. If the degradation is not solved, it is difficult to identify reasons of abnormal situations.

To reduce the degradation, the model is reconstructed with newest data. A moving window (MW) model is constructed with data that are measured most recently and a just-in-time (JIT) model is constructed with data that are more similar to prediction data than other data. Meanwhile, a model based on the time difference of y and that of explanatory variables, X, was proposed. This model is referred to as a time difference (TD) model. The models such as MW, JIT, and TD models that can predict y-values while adapting to states of a plant are called adaptive models. In addition, when data distributions are multimodal, multiple modeling approaches can be combined with adaptive models.

There are no adaptive models having high predictive ability in all process states and the prediction accuracy of each adaptive model depends on a process state. Previously the degradation of a soft sensor model was categorized and characteristics of adaptive models such as MW, JIT and TD models were discussed, based on the classification results. The predictive ability of current MW, JIT and TD models is not entirely sufficient when rapid changes of the slope, i.e. time-varying changes in a process, occur, and thus, novel techniques are required to solve this problem. Additionally, to the best of our knowledge, there is no description of the degradation in the presence of nonlinearity between X and yin any references.

The objectives in this study are therefore as follows:
(1) The improvement of predictive ability of soft sensor models in the degradation that the changes in processes, or the slope changes, are rapid and time-dependent
(2) The handling of any nonlinear relationships between X and y
When both (1) and (2) are achieved, we can cope with abrupt changes in process characteristics.

We adopt a sequentially updating approach since not TD and JIT models but a traditional MW model, which is a linear model, can adapt to gradual changes of the slope. By updating a nonlinear regression model, both (1) and (2) will be able to be solved because the change of the slope is equivarent to the nonlinear change of the slope. However sequential updates of a nonlinear regression model take a lot of time. We therefore apply the online support vector regression (OSVR) method that efficiently update a support vector regression model, which is a nonlinear regression model, to soft sensor modeling. Nevertheless, it will be difficult for a nonlinear regression model to adapt to time-varying processes even when the model is updated, and thus, we propose to add a variable representing time in X-variables.

Through the analyses of the various simulation data, it was confirmed that the OSVR models with the time variable had the good performance of prediction when the relationship between X and y changed from moment to moment and had the strong nonlinearity. In addition, the proposed model could deal with the new nonlinear relationships between X and y that did not exist in the database. Additionaly, the superiority of the proposed method was confirmed through the real industrial data analyses. The proposed model can acculately adapt to the nonlinear relationships between X and yand the time-varying changes in the relationships, i.e. the changes in process characteristics.

We believe that by applying our proposed method to process control and achieving the adaptation to process characteristics and the highly accurate prediction, chemical plants will be operated effectively and stably.