The operation and control of chemical processes needs to account for the inherent complexity of the process operation (nonlinear behavior, uncertainty, constraints) as well as to guard against faults in the process equipments (such as sensor or actuator malfunctions). The highly nonlinear behavior of many chemical processes has motivated extensive research on nonlinear process control subject to uncertainty and constraints (see [1] for a recent review). Fault-tolerant control has been studied in the context of chemical processes mostly using a linear process description (e.g., [2]), while more recently, results that explicitly account for the presence of process nonlinearity and constraints have become available [3,4]. The prerequisite to implementing fault-tolerant control is the knowledge of the occurrence of a fault. In [3], a hybrid systems approach to fault-tolerant control was employed where, under the assumption of full state measurements and knowledge of the fault, stability region-based reconfiguration is implemented to achieve fault-tolerant control. In [4] a fault-detection filter is designed and integrated within a fault-tolerant controller. The fault-detection filter in [4] uses the measurements, together with a process model, to identify the deviation of the process operation from normal plant operation to detect the occurrence of a fault. This approach, the model based approach, is one of the two approaches used in the design of fault-detection filters, and allows for a nice characterization of the fault-detection capabilities of the filter.

The availability of large amounts of process data (and the difficulty in building a first-principles based process model) has motivated the design of fault-detection filters that use historical plant-data for the purpose of fault-detection filters. Statistical and pattern recognition techniques for data analysis and interpretation (e.g., [5,6,7]) use the plant-data to essentially build a `data-based' model that identifies the important variables that have an impact on the process outputs and subsequently quantifies their effect on the process variables. Such a model describes the normal operation of the plant together with confidence limits that can be used to detect `faulty' plant operation. Data-based approaches alleviate the task of building a first-principles based-model, however, the success of these approaches relies on the information content of the data-set used for building the model.

While the strengths (and shortcomings) of model-based and data-based fault-detection filter designs are evident, there is a lack of results that unite model-based and data-based approaches for the design of integrated fault-detection and fault-tolerant control structures. Motivated by these considerations, we consider in this work the problem of using the causal information available through the model structure (not necessarily dependent on the specific values of the process model parameters) to aid the task of building data-based fault-detection filters. In using data-based approaches, some variable can be incorrectly deemed important (in terms of the effect that they have on the output variables) due to the presence of measurement noise and uncertainty in the data. In the proposed method geometric concepts such as relative degree will be used to pre-select the variables that can have an impact on the process outputs (and exclude those that cannot have an impact on a certain process variable) to eliminate such inaccuracies and to obtain a more meaningful model using the data-based approaches. The fault-detection filter is subsequently integrated within a fault-detection and fault-tolerant control structure in a way that accounts for the presence of nonlinearity and constraints. The application of the proposed methods will be demonstrated using a chemical process example.

References

[1] P. D. Christofides and N. H. El-Farra, Control of Nonlinear and Hybrid Process Systems: Designs for Uncertainty, Constraints and Time-Delays. New York: Springer, 2005.

[2] J. Bao, W. Z. Zhang, and P. L. Lee, ``Decentralized fault-tolerant control system design for unstable processes,'' Chem. Eng. Sci., vol. 58, pp. 5045-5054, 2003.

[3] N. H. El-Farra, A. Gani, and P. D. Christofides, ``Fault-tolerant control of process systems using communication networks,'' AIChE J., vol. 51, pp. 1665-1682, 2005.

[4] P. Mhaskar, A. Gani, N. H. E.-F. C. McFall, P. D. Christofides, and J. F. Davis, ``Integrated fault-detection and fault-tolerant control for process systems,'' AIChE J., vol. 52, pp. 2129-2148, 2006.

[5] J. V. Kresta, J. F. Macgregor, and T. E. Marlin, ``Multivariate statistical monitoring of process operating performance,'' Can. J. Chem. Eng., vol. 69, pp. 35-47, 1991.

[6] J. F. Davis, M. L. Piovoso, K. Kosanovich, and B. Bakshi, ``Process data analysis and interpretation,'' Advances in Chemical Engineering, vol. 25, pp. 1-103, 1999.

[7] H. B. Aradhye, B. R. Bakshi, J. F. Davis, and S. C. Ahalt, ``Clustering in wavelet domain: A multiresolution art network for anomaly detection,'' AIChE J., vol. 50, pp. 2455-2466, 2004.