In this chapter, we discuss the description of two related yet different notions-connectivity and causality. Connectivity shows a physical or information linkage between process units; this linkage illustrates qualitative process knowledge without using first-principle models. The main resources for establishing connectivity are process flow diagrams (PFDs) and piping and instrumentation diagrams (P & IDs); thus we need to convert them into standard formats, such as adjacency matrices, digraphs, and semantic web models, which are easily accessible and computer-friendly. Causality between process variables can be built through process data as well as process knowledge; thus it can be described qualitatively, yet sometimes with certain quantitative information, by structural equation models, matrices and digraphs, and matrix layout plots.

Plant-wide oscillations are common in many industrial processes. They may impact the overall process performance and reduce profitability. It is important to detect and diagnose such oscillations. This paper reviews advances in diagnosis of plant-wide oscillations. The main focus of this study is on identifying possible root causes of oscillations using two techniques, one based on data analysis in the temporal and spectral domains and the other based on process connectivity analysis. The process data-based analysis provides an effective way to capture the difference between the root cause variable and the secondary propagated oscillating variables. It is shown that process topology-based methods are capable of finding oscillation propagation pathways and, thus, help in determining the root cause. This paper discusses and compares five such methods—spectral envelope, adjacency matrix, Granger causality, transfer entropy, and Bayesian network inference methods— by application to an industrial benchmark dataset. © 2014 American Institute of Chemical Engineers AIChE J , 60: 2019–2034, 2014

In large-scale industrial processes and other complex systems, elements are not independent. To describe the relationship between process variables, different concepts, such as connectivity and causality, are often used. The background and motivation of investigatingconnectivity and causality in complex systems are discussed; these two concepts are clarified with examples. Causality describes the cause-effect relationship between changes of process variables; while connectivity is generally concerned with physical and information paths in a process. The causality relationships can be described by process topology. A brief chapter preview is then included to give a big picture of this brief, and to provide guidance for interested readers to different topics covered in the brief.

Detection of causality is an important and challenging problem in root cause and hazard propagation analysis. A new information theory-based measure, transfer 0-entropy, is proposed for causality analysis on the basis of the definitions of 0-entropy and 0-information without assuming a probability space. For the cases of more than two variables, a direct transfer 0-entropy concept is presented to detect whether there is a direct information and/or material flow pathway from one variable to another. Estimation methods for the transfer 0-entropy and the direct transfer 0-entropy are addressed. The effectiveness of the proposed method is illustrated by two numerical examples and one experimental case study.

Detection of causality is an important and challenging problem in root cause and hazard propagation analysis. It has been shown that the transfer entropy approach is a very useful tool in quantifying directional causal influence for both linear and nonlinear relationships. A key assumption for this method is that the sampled data should follow a well-defined probability distribution; yet this assumption may not hold for some industrial process data. In this paper, a new information theory-based measure, transfer 0-entropy (T0E), is proposed for causality analysis on the basis of the definitions of 0-entropy and 0-information without assuming a probability space. For the cases of more than two variables, a direct T0E (DT0E) concept is presented to detect whether there is a direct information and/or material flow pathway from one variable to another. Estimation methods for the T0E and the DT0E are addressed. The effectiveness of the proposed method is illustrated by two data sets, one based on data from a pilot scale process and a second evaluation based on data from a benchmark industrial case study.

Data is a valuable resource for modeling and analysis. Process data is a set of timeseries of process variables. In this chapter, we focus on the relationship between different time series to capture causality in the process. For a pair of process variables, various data-based methods can be applied to detect causality. These methods can be categorized into three classes: lag-basedmethods, such as the Granger causality and transfer entropy; conditional independence methods, such as the Bayesian network; and higher order statistics, such as the Patel's pairwise conditional probability approach. In this work, we focus on the first group of methods, which are the most commonly used, and then briefly discuss some remaining methods. Based on the results of pairwise causality analysis, one can construct a causal network that is composed of the links between every two nodes. For multivariate systems, network topology can be determined by using statistical confounding analysis.

Connectivity and causality have a lot of potential applications, among which we focus on analysis and design of large-scale complex industrial processes. A direct application by establishing connectivity and causality is to build a topological model before parameter identification for complex industrial processes that areusually multi-input, multi-output systems with many internal closed loops. In abnormal situation management, process topology can be employed for root cause analysis, risk analysis, and consequential alarm identification using the information of fault propagation. These potential applications include both off-line analysis andon-line diagnosis. In addition, process topology can eventually be used in design of control structures because process topology determinesthe natural structure of the distributed plant-wide control.

Process knowledge is the most reliable resource for qualitative modeling of complex industrial processes, which is typically expressed in natural language and stored in human brains. We thus need to capture useful connectivity and causality from such resources and convert the information into computer accessible formats. From first-principle structural models, causality can be captured and expressed as structural equations. From unstructured process knowledge and dynamic and algebraic equations, graphical models, in particular signed directed graphs and variants, can be obtained. Graphic models are widely used due to their computer tractability and human readability. Rule-based models are another alternative, which is used in expert systems. When the process information is accessible in web language, connectivity can be retrieved by query.

The detection of direct causality, as opposed to indirect causality, is an important and challenging problem in root cause and hazard propagation analysis. Several methods provide effective solutions to this problem when linear relationships between variables are involved. For nonlinear relationships, currently only overall causality analysis can be conducted, but direct causality cannot be identified for such processes. In this paper, we describe a direct causality detection approach suitable for both linear and nonlinear connections. Based on an extension of the transfer entropy approach, a direct transfer entropy (DTE) concept is proposed to detect whether there is a direct information flow pathway from one variable to another. Especially, a differential direct transfer entropy concept is defined for continuous random variables, and a normalization method for the differential direct transfer entropy is presented to determine the connectivity strength of direct causality. The effectiveness of the proposed method is illustrated by several examples, including one experimental case study and one industrial case study.

Direct causality detection is an important and challenging problem in root cause and hazard propagation analysis. Several methods provide effective solutions to this problem for linear relationships. For nonlinear situations, currently only causality analysis can be conducted, but the direct causality cannot be identified based on process data. In this paper, we describe a direct causality detection approach suitable for both linear and nonlinear connections. Based on an extension of the transfer entropy approach, a direct transfer entropy (DTE) concept is proposed to detect whether there is a direct information and/or material flow pathway from one variable to another. A discrete DTE and a differential DTE are defined for discrete and continuous random variables, respectively; and the relationship between them is discussed. The effectiveness of the proposed method is illustrated by two examples and an experimental case study.

Ni reaction with amorphous SiGe (a-SiGe) thin film on SiO2 substrate through rapid thermal annealing (RTA) was investigated. The amorphous SiGe thin film was deposited by ion beam sputtering. X-ray diffraction (XRD), Auger electron spectroscopy (AES) depth profiling, and four point probe (FPP) were used to check the phase formation, atom distribution, and sheet resistance during the reaction. It was found that the Ni reaction with a-SiGe was different from the Ni reaction with poly-SiGe. Besides an orthorhombic NiSi phase, a tetragonal η-NiSi phase was formed during Ni reaction with an a-SiGe layer and remained stable after 800°C annealing. A NiSi2 phase was formed at temperature as low as 550°C along with the crystallization of SiGe.When annealed at a higher temperature, Ge outdiffused to the surface and Ni diffused to the interface of SiGe∕SiO2 where it formed a thin layer of Ni silicide. The cause of the reduced temperature for formation of NiSi2 from Ni reaction with amorphous SiGe is discussed.