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. © 2012 IFAC.

Arun K. Tangirala

Department Of Chemical Engineering

S. Gigi

decomposition

Economics

Energy transfer

Fault detection

Frequency domain analysis

Spectrum Analysis

Statistics

Causality

Connectivity

DIRECTED ENERGY

Frequency domains

VECTOR AUTOREGRESSIVE MODEL

Process control

Fulltext

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Reconstructing Plant Connectivity using Directed Spectral Decomposition

IFAC Proceedings Volumes (IFAC-PapersOnline)

Learning temporal causal relationships between time series is an important tool for the identification of causal network structures in linear dynamic systems from measurements. The main objective in network reconstruction is to identify the causal interactions between the variables and determine the connectivity strengths from time-series data. Among several recently introduced data-driven causality measures, partial directed coherence (PDC), directed partial correlation (DPC) and direct power transfer (DPT) have been shown to be effective in both identifying the causal interactions as well as quantifying the strength of connectivity. However, all the existing approaches assume that the observations are available at all time instants and fail to cater to the case of missing observations. This paper presents a method to reconstruct the causal graph from data with missing observations using sparse optimization (SPOPT) techniques. The method is particularly devised for jointly stationary multivariate processes that have vector autoregressive (VAR) structure representations. Demonstrations on different linear causal dynamic systems illustrate the efficacy of the proposed method with respect to the reconstruction of causal networks. © 2017 IEEE.

2017 4th International Conference on Control, Decision and Information Technologies, CoDIT 2017

Reconstruction of causal graphs for multivariate processes in the presence of missing data

Identification of network structure and quantifying the connectivity strengths in multivariate systems is an important problem in many scientific areas. Data-driven approach to network reconstruction based on causality measures is an emerging field of research in this respect. Among several recently introduced data-driven causality measures, the partial directed coherence (PDC) and direct power transfer (DPT) have been shown to be very effective for linear systems. While the PDC is useful in reconstructing the network, DPT has been proved to be effective in both identifying the network structure as well as quantifying the strength of connectivity. In this work, we study the problem of obtaining efficient estimates of network connectivity strengths, which has hitherto not been addressed in the literature. To this end, we study two different estimation methods for network connectivity strengths and demonstrate that the goodness of estimates depends on nature of the data generating process (DGP). In order to characterize the multivariate DGP, we introduce two statistics, namely, the vector-valued autocorrelation function (VACF) and the vector-valued partial autocorrelation function (VPACF), and estimators of the same. Our studies show that the parametric models used in estimating connectivity strengths should be commensurate with the dynamics of the process as characterized by the newly introduced VACF and VPACF. Simulation studies are presented under different scenarios to support our findings and the newly introduced measures. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

IFAC-PapersOnLine

Estimation of network connectivity strengths in linear causal dynamic systems

Identification and analysis of directed influences in multivariate systems is an important problem in many scientific areas. Recent studies in neuroscience have provided measures to determine the network structure of the process and to quantify the total effect in terms of energy transfer. These measures are based on joint stationary representations of a multivariate process using vector auto-regressive (VAR) models. A few important issues remain unaddressed though. The primary outcomes of this study are (i) a theoretical proof that the total coupling strength consists of three components, namely, the direct, indirect, and the interference produced by the direct and indirect effects, (ii) expressions to estimate/calculate these effects, and (iii) a result which shows that the well-known directed measure for linear systems, partial directed coherence (PDC) only aids in structure determination but does not provide a normalized measure of the direct energy transfer. Simulation case studies are shown to illustrate the theoretical results. © 2010 Springer-Verlag.

Biological Cybernetics

Quantitative analysis of directional strengths in jointly stationary linear multivariate processes

Brain Signals

Interpreting MEG and EEG Data

Medical & Biological Engineering & Computing

Review of the methods of determination of directed connectivity from multichannel data

Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Publisher	IFAC Secretariat
ISSN	14746670
Open Access	Yes