A major obstacle for effective quality control for most chemical/biochemical processes is the lack of real-time information, since quality measurements are often sampled at a much lower frequency than other process variables. In addition, a lab analysis is often associated with a time delay that may vary from minutes up to several hours. Therefore, soft sensors that are able to provide a reliable real-time prediction are essential for effective product quality control. This paper investigates different approaches to design soft sensors using multi-rated sampled data. Recommendations and guidelines are provided based on cases studies of data-driven soft sensors for cement kiln processes.

A process model at the fast sampling rate cannot be directly derived using the original multi-rate data. Since inter-sample information is desirable for effective quality control, various approaches have been reported to estimate quality between samples. Numerical interpolation approach (Isaksson 1992) inserts predictions of the inter-sample outputs such that data has a uniformly fast sampling interval. On the other hand, data-lifting technique creates a uni-rate data set at the low sampling rate (Wang, Chen et al. 2004). A model in the lifted time domain is first identified, from which a model of fast sampling domain is extracted according to the relationship between the slow and the fast systems. Lu and Fisher (1989) proposed a polynomial transformation approach, where a predefined polynomial is multiplied on both sides of the original model such that the inter-sample outputs are no longer required for parameter estimation. Lin et al. (2005) applied a weighted partial least squares (WPLS) approach to develop quality estimators from multi-rate data. A soft sensor with fast sampling period is derived by applying the regression relationship to the regressor matrix.

The polynomial transformation, data lifting technique, and weighted partial least squares (WPLS) approaches are described and compared in this study. Their applicability, accuracy and robustness to process noise are evaluated with illustrative case studies, including single-input single output (SISO) and multiple inputs and multiple outputs (MIMO) systems, as well as with data collected from a cement kiln simulation system based on first principles models. Case studies reveal the superior performance of the WPLS approach, which provides one-step-ahead prediction reasonably well.

References:

1. Isaksson, A. J. (1992). On the use of linear interpolation in identification subject to missing data, Department of Electrical and Computer Engineering, University of New-castle, Australia.

2. Lin, B., B. Recke, et al. (2005). A Systematic Approach for Soft Sensor Development. European Symposium on Computer Aided Process Engineering -15, Barcelona.

3. Lu, W. and D. G. Fisher (1989). "Least-squares output estimation with multirate sampling." IEEE Trans. Automat. Control 34(6): 669–672.

4. Wang, J., T. Chen, et al. (2004). "Multirate sampled-data systems: computing fast-rate models." Journal of Process Control 14(1): 79-88.