Reconstructing Plant Connectivity using Directed Spectral Decomposition
TL;DR: In this article, the authors developed a methodology for reconstruction of plant connectivity from dynamic data using directional spectral analysis, a novel adaptation of ideas from neurosciences and econometrics.
About: This article is published in IFAC Proceedings Volumes.The article was published on 2012-01-01. It has received 9 citations till now.
Citations
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Journal Article•
TL;DR: A new frequency-domain approach to describe the relationships (direction of information flow) between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models is introduced.
Abstract: Abstract. This paper introduces a new frequency-domain approach to describe the relationships (direction of information flow) between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models. We discuss its application and compare its performance to other approaches to the problem of determining neural structure relations from the simultaneous measurement of neural electrophysiological signals. The new concept is shown to reflect a frequency-domain representation of the concept of Granger causality.
176 citations
TL;DR: The proposed method is developed in the framework of sparse optimization while adopting a parametric approach using vector auto-regressive (VAR) models, where both the temporal and spatial correlations can be exploited for efficient data recovery.
Abstract: Recovery of missing observations in time-series has been a century-long subject of study, giving rise to two broad classes of methods, namely, one that reconstructs data and the other that directly estimate the statistical properties of the data, largely for univariate processes. In this work, we present a data reconstruction technique for multivariate processes. The proposed method is developed in the framework of sparse optimization while adopting a parametric approach using vector auto-regressive (VAR) models, where both the temporal and spatial correlations can be exploited for efficient data recovery. The primary purpose of recovering the missing data in this work is to develop a directed graphical or a network representation of the multivariate process under study. Existing methods for data-driven network reconstruction are built on the assumption of data being available at regular intervals. In this respect, the proposed method offers an effective methodology for reconstructing weighted causal networks from missing data. The scope of this work is restricted to linear, jointly stationary multivariate processes that can be suitably represented by VAR models of finite order and missing data of the random type. Simulation studies on different data generating processes with varying proportions of missing observations illustrate the efficacy of the proposed method in recovering the multivariate signals and thereby reconstructing weighted causal networks.
8 citations
Posted Content•
TL;DR: It is shown that identification is equivalent to learning a model which captures the approximate linear relationships between the different variables comprising $\mathbf{X}$ such that A_n is full rank (highest possible) and consistent with a network node-edge incidence structure.
Abstract: We solve the problem of identifying (reconstructing) network topology from steady state network measurements. Concretely, given only a data matrix $\mathbf{X}$ where the $X_{ij}$ entry corresponds to flow in edge $i$ in configuration (steady-state) $j$, we wish to find a network structure for which flow conservation is obeyed at all the nodes. This models many network problems involving conserved quantities like water, power, and metabolic networks. We show that identification is equivalent to learning a model $\mathbf{A_n}$ which captures the approximate linear relationships between the different variables comprising $\mathbf{X}$ (i.e. of the form $\mathbf{A_n X \approx 0}$) such that $\mathbf{A_n}$ is full rank (highest possible) and consistent with a network node-edge incidence structure. The problem is solved through a sequence of steps like estimating approximate linear relationships using Principal Component Analysis, obtaining f-cut-sets from these approximate relationships, and graph realization from f-cut-sets (or equivalently f-circuits). Each step and the overall process is polynomial time. The method is illustrated by identifying topology of a water distribution network. We also study the extent of identifiability from steady-state data.
7 citations
17 Jun 2013
TL;DR: The EAUDI method is further extended to detect causality from process data, and it can also provide models of all connecting paths simultaneously and hypothesis testing is proposed to verify the results of this approach (by testing cross-regressive coefficients).
Abstract: To the best of our knowledge, there are few methods which can determine both causality and models from process data, although both of them are crucial in practical applications The extended augmented UD identification (EAUDI) is an identification approach which does not need a priori causal relationship between variables in advance In this method, however, the information contained in the augmented information matrix (AIM) is still not fully utilized and yet helpful for causality analysis, namely, whether the values of cross-regressive coefficients are sufficiently weak to be considered as insignificant Based on this, the EAUDI method is further extended to detect causality from process data, and it can also provide models of all connecting paths simultaneously Moreover, hypothesis testing (F-distribution) is proposed to verify the results of this approach (by testing cross-regressive coefficients) The effectiveness of the proposed method is demonstrated by numerical examples
3 citations
01 Apr 2017
TL;DR: This paper presents a method to reconstruct the causal graph from data with missing observations using sparse optimization (SPOPT) techniques, particularly devised for jointly stationary multivariate processes that have vector autoregressive (VAR) structure representations.
Abstract: 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.
3 citations
Cites background from "Reconstructing Plant Connectivity u..."
...For a link connecting source xj to sink xi, the normalized connectivity strength is defined as [3]...
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...gene regulatory networks), neurosciences (for understanding neural connections of the brain), econometrics, climatology [1],[2],[3] etc....
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References
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TL;DR: In this paper, the authors focus on the systematic development of graph models and the conceptual relationship between the analysis of graph model and the underlying mathematical description and the analysis procedures for the graph model.
Abstract: In the recent past, graph-based approaches have been proposed by various researchers for safety analysis and fault diagnosis of chemical process systems. Though these approaches have shown promise, there are a number of important issues that have not been adequately addressed in the literature. The issue of systematic development of graph representations for chemical processes has not been addressed in the literature. This is an important issue because the development of digraphs is error-prone and time-consuming. Further, little attention has been paid toward understanding the conceptual relationship between the underlying mathematical description and the analysis procedures for the graph model. Also, the utility of these graph-based approaches at a flowsheet level has not been studied. With these issues in perspective, in this first part of the two-part paper, we focus on the systematic development of graph models and the conceptual relationship between the analysis of graph models and the underlying ma...
124 citations
TL;DR: A new method to diagnose the root cause of plant-wide oscillations using the adjacency matrix is proposed using the information in the process flowsheet and it complements the data based methods very well and it is best used in combination with other data-based methods to provide powerful diagnosis.
91 citations
"Reconstructing Plant Connectivity u..." refers background or methods in this paper
...Construction of signed digraph (SDG) [Maurya et al., 2003a,b], computer aided engineering exchange (CAEX) software [Sim et al., 2006] and adjacency matrix [Jiang et al., 2009] are a few of them....
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..., 2006] and adjacency matrix [Jiang et al., 2009] are a few of them....
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TL;DR: In this paper, the authors present a signed digraph (SDG) model for control loops and discuss a framework for application of graph-based approaches at a flowsheet level.
Abstract: The objectives of this part of the two part paper are (i) development of signed digraph (SDG) models for control loops and (ii) discussion of a framework for application of graph-based approaches at a flowsheet level. Further, two case studies are used to explain the methods developed in part 11 (Ind. Eng. Chem. Res. 2003, 42, in press) and this paper. The first case study (continuous stirred tank reactor case study) explains the basic concepts of the generate and test method for SDG analysis, generation of redundant equations using algebraic manipulation, and analysis of systems with a single control loop. Case study 2 (flash vaporizer case study) deals with different methods of generating redundant equations and the analysis of systems with multiple interacting control loops.
78 citations
TL;DR: In this article, the closed-loop representation of a jointly stationary vector (y, u)-proccss was studied and conditions were derived on the closed loop models for the joint process model to be stable and minimum phase.
Abstract: Stable constant linear closed-loop systems relating an input vector u to an output vector u and vice versa produce a jointly stationary (y, u)-procoss. On the other hand it is often natural to split up a stationary vector random process z into component vectors yand u, and to examine the closed-loop relations between y and u. This paper presents a number of new results on the spectral factorization and the closed-loop representation of a jointly stationary vector (y, u)-proccss. Conditions are derived on the closed-loop models for the joint process model to bo oE minimal degree, stable and minimum-phase. Relations between different joint process models producing the same spectrum φyu(z)are established.
76 citations
"Reconstructing Plant Connectivity u..." refers methods in this paper
...The basis for the proposed method of analysis for plant topology is the well-known spectral factorization theorem [Gevers and Anderson, 1981]....
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TL;DR: A prototype software has been designed and implemented which, when given an electronic process schematic of a plant and results from a data-driven analysis, allows the user to pose queries about the plant and to find root causes of plant-wide disturbances.
70 citations