Comparison of stochastic fault detection and classification algorithms for nonlinear chemical processes

Abstract This paper presents a comparative study of two methods to identify and classify intermittent stochastic faults occurring in a dynamic nonlinear chemical process. The methods are based on two popular stochastic modelling techniques, i.e., generalized polynomial chaos expansion (gPC) and Gaussian Process (GP). The goal is to assess which method is more efficient for fault detection and diagnosis (FDD) when using models with parametric uncertainty, and to show the capabilities and drawbacks of each method. The first method is based on a first-principle model combined with a gPC expansion to represent the uncertainty. Resulting statistics such as probability density functions (PDFs) of the measured variables is further used to infer the intermittent faults. For the second method, a GP model is used to project multiple inputs into a univariate model response from which the fault can be identified based on a minimum distance criterion. The performance of the proposed FDD algorithms is illustrated through two examples: (i) a chemical process involving two continuous, stirred tank reactors (CSTRs) and a flash tank separator, and (ii) the Tennessee Eastman benchmark problem.

[1]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[2]  Richard D. Braatz,et al.  Fault Detection and Diagnosis in Industrial Systems , 2001 .

[3]  Yuncheng Du,et al.  Fault detection and diagnosis with parametric uncertainty using generalized polynomial chaos , 2015, Comput. Chem. Eng..

[5]  Paul M. Frank,et al.  Issues of Fault Diagnosis for Dynamic Systems , 2010, Springer London.

[6]  R. B. Gopaluni,et al.  Fault detection and isolation in stochastic non-linear state-space models using particle filters , 2012 .

[7]  Rolf Isermann,et al.  Fault-diagnosis systems : an introduction from fault detection to fault tolerance , 2006 .

[8]  Erik Frisk,et al.  A method for quantitative fault diagnosability analysis of stochastic linear descriptor models , 2013, Autom..

[9]  Yuncheng Du,et al.  Parameter Estimation for an Inverse Nonlinear Stochastic Problem: Reactivity Ratio Studies in Copolymerization , 2017 .

[10]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[11]  Jie Chen,et al.  Observer-based fault detection and isolation: robustness and applications , 1997 .

[12]  Ahmet Palazoglu,et al.  An adaptive multimode process monitoring strategy based on mode clustering and mode unfolding , 2013 .

[13]  Yuncheng Du,et al.  Generalized Polynomial Chaos-Based Fault Detection and Classification for Nonlinear Dynamic Processes , 2016 .

[14]  Rolf Isermann,et al.  Model-based fault-detection and diagnosis - status and applications , 2004, Annu. Rev. Control..

[15]  Janos Gertler,et al.  Fault detection and diagnosis in engineering systems , 1998 .

[16]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[17]  Raghunathan Rengaswamy,et al.  A review of process fault detection and diagnosis: Part I: Quantitative model-based methods , 2003, Comput. Chem. Eng..

[18]  Robert V. Brill,et al.  Applied Statistics and Probability for Engineers , 2004, Technometrics.

[19]  Hector Budman,et al.  Integration of fault diagnosis and control based on a trade-off between fault detectability and closed loop performance , 2016 .

[20]  Arthur K. Kordon,et al.  Fault diagnosis based on Fisher discriminant analysis and support vector machines , 2004, Comput. Chem. Eng..

[21]  Thomas F. Edgar,et al.  Process Dynamics and Control , 1989 .

[22]  T. Choi,et al.  Gaussian Process Regression Analysis for Functional Data , 2011 .

[23]  Stephen J. Wright,et al.  Cooperative distributed model predictive control , 2010, Syst. Control. Lett..

[24]  Hui Yang,et al.  Statistical Metamodeling and Sequential Design of Computer Experiments to Model Glyco-Altered Gating of Sodium Channels in Cardiac Myocytes , 2016, IEEE Journal of Biomedical and Health Informatics.

[25]  Robert L Harrison,et al.  Introduction To Monte Carlo Simulation. , 2010, AIP conference proceedings.

[26]  Mohieddine Jelali,et al.  Revision of the Tennessee Eastman Process Model , 2015 .

[27]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[28]  Yuncheng Du,et al.  Stochastic Fault Diagnosis using a Generalized Polynomial Chaos Model and Maximum Likelihood , 2015 .

[29]  E. F. Vogel,et al.  A plant-wide industrial process control problem , 1993 .

[30]  Rajagopalan Srinivasan,et al.  STATE-SPECIFIC KEY VARIABLES FOR MONITORING MULTI-STATE PROCESSES , 2007 .

[31]  D. Xiu.  Numerical Methods for Stochastic Computations: A Spectral Method Approach , 2010 .