Reconstructing Plant Connectivity using Directed Spectral Decomposition

Abstract Process connectivity is a key information that is sought in a diverse set of applications ranging from design to fault diagnosis of engineering and biological processes. The present work develops a methodology for reconstruction of plant connectivity from dynamic data using directional spectral analysis, a novel adaptation of ideas from neurosciences and econometrics. The method is based on the concept of Granger causality while the procedure rests on the directional decomposition of power spectrum into direct and indirect energy transfers. The quantification of effective connectivity is obtained using a structural vector auto-regressive (SVAR) representation of the process. Results from simulation studies demonstrate the potential of the proposed method.

[1]  C. Granger.  Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[2]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[3]  M. Gevers,et al.  Representations of jointly stationary stochastic feedback processes , 1981 .

[4]  J. Geweke,et al.  Measurement of Linear Dependence and Feedback between Multiple Time Series , 1982 .

[5]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[6]  J. Geweke,et al.  Measures of Conditional Linear Dependence and Feedback between Time Series , 1984 .

[7]  Steven W. Smith,et al.  The Scientist and Engineer's Guide to Digital Signal Processing , 1997 .

[8]  David S. Stoffer,et al.  Time series analysis and its applications , 2000 .

[9]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[10]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.

[11]  Raghunathan Rengaswamy,et al.  A systematic framework for the development and analysis of signed digraphs for chemical processes. 2. Control loops and flowsheet analysis , 2003 .

[12]  R. Rengaswamy,et al.  A Systematic Framework for the Development and Analysis of Signed Digraphs for Chemical Processes. 1. Algorithms and Analysis , 2003 .

[13]  Katarzyna J. Blinowska,et al.  A new method of the description of the information flow in the brain structures , 1991, Biological Cybernetics.

[14]  Michael Eichler,et al.  On the Evaluation of Information Flow in Multivariate Systems by the Directed Transfer Function , 2006, Biological Cybernetics.

[15]  Laura Astolfi,et al.  Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data , 2006, IEEE Transactions on Biomedical Engineering.

[16]  Nina F. Thornhill,et al.  Using process topology in plant-wide control loop performance assessment , 2006, Comput. Chem. Eng..

[17]  K. Hlavácková-Schindler,et al.  Causality detection based on information-theoretic approaches in time series analysis , 2007 .

[18]  L.A. Baccald,et al.  Generalized Partial Directed Coherence , 2007, 2007 15th International Conference on Digital Signal Processing.

[19]  Nina F. Thornhill,et al.  Finding the Direction of Disturbance Propagation in a Chemical Process Using Transfer Entropy , 2007, IEEE Transactions on Control Systems Technology.

[20]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[21]  Bernhard Pfaff,et al.  VAR, SVAR and SVEC Models: Implementation Within R Package vars , 2008 .

[22]  M. Eichler,et al.  Assessing the strength of directed influences among neural signals using renormalized partial directed coherence , 2009, Journal of Neuroscience Methods.

[23]  Sirish L. Shah,et al.  Root cause diagnosis of plant-wide oscillations using the concept of adjacency matrix , 2009 .

[24]  Andreas Daffertshofer,et al.  Functional similarities and distance properties , 2009, Journal of Neuroscience Methods.

[25]  Arun K. Tangirala,et al.  Quantitative analysis of directional strengths in jointly stationary linear multivariate processes , 2010, Biological Cybernetics.

[26]  Mark W. Woolrich,et al.  Network modelling methods for FMRI , 2011, NeuroImage.

[27]  Katarzyna J. Blinowska,et al.  Review of the methods of determination of directed connectivity from multichannel data , 2011, Medical & Biological Engineering & Computing.