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469677 Comparison of Stochastic Fault Detection and Diagnosis Algorithms for Nonlinear Chemical Processes

In terms of applications, many industrial processes are intrinsically nonlinear systems and they are operated at different operating conditions according to economic considerations [5]. Due to nonlinearity, the performance of linear FDD algorithms reported in literature [6] may be inaccurate and lead to missed detection of faults, since the process model will change from one operating conditions to another. It is critical to develop new methodologies for the detection of faults in the context of nonlinear chemical processes with multiple operating conditions [5].

Since most of the FDD schemes are invariably based on either first principle models or empirical models [3], a main restrictive factor of an efficient FDD system is the model uncertainty. Such uncertainty may originate from either intrinsic time varying phenomena of model parameters or may result from inaccurate measurements due to noise. Models with large uncertainties make the detection and isolation of small faults very difficult. However, the step of quantifying and propagating the uncertainties onto the measured quantities that can be used for fault detection is typically omitted in reported FDD studies, leading to a loss of useful information arising from these uncertainties [7]. Moreover, the quantitative analysis of the detectability of faults in the presence of uncertainty can provide more information to improve the development of FDD algorithm. For example, engineering effort can be saved, if it is impossible to detect a fault in reality due to uncertainties such as large measurement noise [8].

To evaluate the effect of uncertainty on FDD, one possibility is to propagate stochastic variations with Monte Carlo (MC) simulations [9], which involve drawing a large number of samples and running the models with each of these samples. However, approaches such as MC simulations are computationally prohibitive especially for complex processes as shown later in the manuscript. To improve the computational efficiency, this paper presents and compares two FDD algorithms in the presence of uncertainties. The uncertainty includes the parametric uncertainty of a process and measurement noise. In addition, the faults in this current work are stochastic perturbations superimposed on intermittent step changes in specific input variables for a nonlinear chemical plant. For the first FDD method, generalized polynomial chaos (gPC) [10, 11] in combination with first principlesâ€™ process models are used to quantify and propagate the uncertainty onto the measured quantities, which can be used for the detection of faults. For the second method, a surrogate metamodel is developed with Gaussian Process (GP) [12], which is calibrated with a minimal model adjustment algorithm and can be used estimate the value of fault.

The objective in this work is to address the capabilities of these methods and propose a possible strategy to overcome their limitation by combing their outcomes. For this purpose, the performance of each method is evaluated in terms of fault detection rate in the context of stochastic parametric input faults. These faults occur intermittently with stochastic perturbations, i.e., the mean value of faults switch between the non-faulty and faulty operating conditions in a random fashion. For simplicity, the stochastic perturbations are assumed to be time-invariant uncertainties. Thus, the key point is to identify and diagnose these step changes in the presence of the random perturbations in the parametric input faults, using available measurements corrupted with measurement noise. The performance of the above mentioned methods is evaluated in terms of fault detection rate by applying them to a chemical plant of two continuously stirred tank reactors (CSTRs) and a flash tank separator. The proposed methods are successful in detecting and diagnosing intermittent faults in the presence of uncertainty.

References

[1] J. Gerlter, Fault detection and diagnosis in engineering systems, NJ, USA: Taylor & Francis, 1998.

[2] R. Isermann, "Model based fault detection and diagnosis - status and applications," Annual reviews in control, vol. 29, pp. 71-85, 2005.

[3] V. Venkatasubramanian, R. Rengaswamy, K. Yin and S. Kavuri, "A review of process fault detecion and diagnosis Part I: Quantitative model-based methods," Computers and Chemical Engineering, vol. 27, pp. 293-311, 2003.

[4] R. Isermann, Fault diagnosis systems: An introduction from fault detection to fault tolerance, Berlin, Germany: Springer, 2006.

[5] A. Haghani, T. Jeinsch and S. X. Ding, "Quality related fault detection in industrial multimode dynamic processes," IEEE Transactions on Industrial Electronics, vol. 61, no. 11, pp. 6446 - 6453, 2014.

[6] X. Li and G. Yang, "Fault detection for linear stochastic systems with sensor stuck faults," Optimal control applications and methods, vol. 33, no. 1, pp. 61-80, 2012.

[7] R. J. Patton, P. M. Frank and R. N. Clark, Issues of fault diagnosis for dynamic systems, Springer, 2010.

[8] D. Eriksson, E. Frisk and M. Krysander, "A method for quantitative fault diagnosability analysis of stochastic linear descriptor models," Automatica, vol. 49, pp. 1591-1600, 2013.

[9] R. L. Harrison, "Introduction to Monte Carlo simulation," in AIP conference proceedings, Bratos;ava, 2010.

[10] R. Ghanem and P. Spanos, Stochastic finite elements: a spectral approach, 2nd ed., Berlin: Springer-Verlag, 1991.

[11] D. Xiu, Numerical Methods for Stochastic Computation: A Spectral Method Approach, Princeton University Press, 2010.

[12] C. E. Rasmussen and C. K. L. Williams, Gaussian processes for machine learning, Cambridge, MA: The MIT Press, 2006.

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