A Novel Causality Method for Reconstruction of Process Topology in Multivariable LTI Dynamical Systems
01 Sep 2019-pp 199-204
TL;DR: A new definition of direct causality for deterministic linear time-invariant (LTI) dynamical systems is presented and a novel causality detection method based on delay estimation from noisy multivariable measurements is presented, well-suited to handle low excitation signals and does not require the specification of any model structure.
Abstract: Reconstruction of process topology from cause-effect analysis of measurements finds applications in root-cause analysis, identification of disturbance propagation pathways, estimation of fault propagation times, and interaction assessment. A widely used technique based on the notion of Granger causality (GC), but is well-suited only for stationary stochastic processes. The GC-based measures and methods, while being useful in certain cases, can be highly restrictive and produce misleading results in engineering applications since changes in process variables are frequently deterministic. The lack of sufficient excitation and presence of measurement errors further restricts their applicability. In this respect, we present (i) a new definition of direct causality for deterministic linear time-invariant (LTI) dynamical systems, and (ii) a novel causality detection method based on delay estimation from noisy multivariable measurements. Efficient estimates of time delays are obtained from recently developed non-parametric frequency domain method based on partial coherence and Hilbert transform relations. In addition to the ability of handling deterministic variations, the proposed causality detection method is well-suited to handle low excitation signals and does not require the specification of any model structure. Case studies involving data from synthetic and benchmark processes are presented to illustrate the utility and efficacy of the proposed method.
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References
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01 Jan 2012
139,059 citations
"A Novel Causality Method for Recons..." refers background in this paper
...Works in [9, 10] deal with networks between state variables and present the formal theory of such network representations through what are termed as dynamical structure functions....
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TL;DR: In this article, the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation, and measures of causal lag and causal strength can then be constructed.
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.
16,349 citations
01 Jan 2001
TL;DR: In this article, it is shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation, and measures of causal lag and causal strength can then be constructed.
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recordhag information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalization of this result with the partial cross spectrum is suggested.The object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the two-variable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those aspects of spectral methods, model building, and causality which are required later. Section IV presents the results for the two-variable case and Section V generalizes these results for three variables.
11,896 citations
"A Novel Causality Method for Recons..." refers background or methods in this paper
...A variable zj does not Granger-cause zi if and only if |ψij(ω)|2 = 0, ∀ω....
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...With respect to the data, measurement errors (D1) result in spurious Granger-causality [6] except under some very special conditions....
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...Among many definitions of causality, Granger causality (GC) is the most widely used and has received much attention in econometrics and systems biology....
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...An abstraction of related ideas was initially proposed by [1], which was subsequently formalized and shaped by [2] in the framework of multivariate stationary stochastic processes (see Section 2....
[...]
...An abstraction of related ideas was initially proposed by [1], which was subsequently formalized and shaped by [2] in the framework of multivariate stationary stochastic processes (see Section 2.1 for technical details of Granger causality)....
[...]
TL;DR: In this paper, a frequency-domain approach to describe the relationships between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models is introduced.
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.
1,584 citations
TL;DR: In this article, it was shown that even when a transfer function can be identified perfectly from input-output data, not even Boolean reconstruction is possible, in general, without more information about the system.
Abstract: This paper formulates and solves the network reconstruction problem for linear time-invariant systems. The problem is motivated from a variety of disciplines, but it has recently received considerable attention from the systems biology community in the study of chemical reaction networks. Here, we demonstrate that even when a transfer function can be identified perfectly from input-output data, not even Boolean reconstruction is possible, in general, without more information about the system. We then completely characterize this additional information that is essential for dynamical reconstruction without appeal to ad-hoc assumptions about the network, such as sparsity or minimality.
216 citations