Deyun Xiao

Brief paper: Kalman filters in non-uniformly sampled multirate systems: For FDI and beyond

The first part of the paper is the development of a data-driven Kalman filter for a non-uniformly sampled multirate (NUSM) system. Algorithms for both one-step predictor and filtering are developed and analysis of stability and convergence is conducted in the NUSM framework. The second part of the paper investigates a Kalman filter-based methodology for unified detection and isolation of sensor, actuator, and process faults in the NUSM system with analysis on fault detectability and isolability. Case studies using data respectively collected from a pilot experimental plant and a simulated system are conducted to justify the practicality of the proposed theory.

Improved correlation analysis and visualization of industrial alarm data.

The problem of multivariate alarm analysis and rationalization is complex and important in the area of smart alarm management due to the interrelationships between variables. The technique of capturing and visualizing the correlation information, especially from historical alarm data directly, is beneficial for further analysis. In this paper, the Gaussian kernel method is applied to generate pseudo continuous time series from the original binary alarm data. This can reduce the influence of missed, false, and chattering alarms. By taking into account time lags between alarm variables, a correlation color map of the transformed or pseudo data is used to show clusters of correlated variables with the alarm tags reordered to better group the correlated alarms. Thereafter correlation and redundancy information can be easily found and used to improve the alarm settings; and statistical methods such as singular value decomposition techniques can be applied within each cluster to help design multivariate alarm strategies. Industrial case studies are given to illustrate the practicality and efficacy of the proposed method. This improved method is shown to be better than the alarm similarity color map when applied in the analysis of industrial alarm data.

Signed directed graph based modeling and its validation from process knowledge and process data

Signed directed graph based modeling and its validation from process knowledge and process data This paper is concerned with the fusion of information from process data and process connectivity and its subsequent use in fault diagnosis and process hazard assessment. The Signed Directed Graph (SDG), as a graphical model for capturing process topology and connectivity to show the causal relationships between process variables by material and information paths, has been widely used in root cause and hazard propagation analysis. An SDG is usually built based on process knowledge as described by piping and instrumentation diagrams. This is a complex and experience-dependent task, and therefore the resulting SDG should be validated by process data before being used for analysis. This paper introduces two validation methods. One is based on cross-correlation analysis of process data with assumed time delays, while the other is based on transfer entropy, where the correlation coefficient between two variables or the information transfer from one variable to another can be computed to validate the corresponding paths in SDGs. In addition to this, the relationship captured by data-based methods should also be validated by process knowledge to confirm its causality. This knowledge can be realized by checking the reachability or the influence of one variable on another based on the corresponding SDG which is the basis of causality. A case study of an industrial process is presented to illustrate the application of the proposed methods.

Progress in root cause and fault propagation analysis of large-scale industrial processes

In large-scale industrial processes, a fault can easily propagate between process units due to the interconnections of material and information flows. Thus the problem of fault detection and isolation for these processes is more concerned about the root cause and fault propagation before applying quantitative methods in local models. Process topology and causality, as the key features of the process description, need to be captured from process knowledge and process data. The modelling methods from these two aspects are overviewed in this paper. From process knowledge, structural equation modelling, various causal graphs, rule-based models, and ontological models are summarized. From process data, cross-correlation analysis, Granger causality and its extensions, frequency domain methods, information-theoretical methods, and Bayesian nets are introduced. Based on these models, inference methods are discussed to find root causes and fault propagation paths under abnormal situations. Some future work is proposed in the end.

Correlation analysis of alarm data and alarm limit design for industrial processes

The object of alarm rationalization is to check if alarms are set correctly with respect to high and low limits and also to ensure that critical alarms are not missed and that there are as few false alarms as possible. This paper outlines a procedure based on the similarity of correlation maps of physical process variables and their alarm history in combination with process connectivity information through causal maps to suggest optimal alarm settings. The process of correlation analysis clearly takes into account the multivariate nature of the process and thereby reduces the number of false and missed alarms.

Signed Directed Graph modeling of industrial processes and their validation by data-based methods

This paper is concerned with the fusion of information from process data and process connectivity and its subsequent use in fault detection and isolation and hazard assessment. The Signed Directed Graph (SDG), as a graphical model for capturing process topology and connectivity to show the causal relationships between process variables by flow and information paths, has been widely used in root cause and hazard propagation analysis. An SDG is usually built based on process knowledge as described by piping and instrumentation diagrams. This is a complex and experience-dependent task, and therefore the resulting SDG should be validated by process data before being used for analysis. This paper introduces two validation methods. The first method is based on cross-correlation analysis of process data with assumed time delays. The resulting correlation coefficients can then be validated by examining the paths in SDGs of all the variable pairs and also comparing the signs with the directions of causal relations. The second method is based on transfer entropy, where the information transfer from one variable to another can be computed to validate the corresponding arcs in SDGs. A case study of an industrial process is presented to illustrate the application of the proposed methods.

Optimal Sensor Location Design for Reliable Fault Detection in Presence of False Alarms

To improve fault detection reliability, sensor location should be designed according to an optimization criterion with constraints imposed by issues of detectability and identifiability. Reliability requires the minimization of undetectability and false alarm probability due to random factors on sensor readings, which is not only related with sensor readings but also affected by fault propagation. This paper introduces the reliability criteria expression based on the missed/false alarm probability of each sensor and system topology or connectivity derived from the directed graph. The algorithm for the optimization problem is presented as a heuristic procedure. Finally, a boiler system is illustrated using the proposed method.

Qualitative Fault Detection and Hazard Analysis Based on Signed Directed Graphs for Large-Scale Complex Systems

Nowadays in modern industries, the scale and complexity of process systems are increased continuously. These systems are subject to low productivity, system faults or even hazards because of various conditions such as mis-operation, equipment quality change, external disturbance, and control system failure. In these systems, many elements are interacted, so a local fault can be propagated and probably spread to a wide range. Thus it is of great importance to find the possible root causes and consequences according to the current symptom promptly. Compared with the classic fault detection for local systems, the fault detection for large-scale complex systems concerns more about the fault propagation in the overall systems. And this demand is much close to hazard analysis for the system risks, which is a kind of qualitative analysis in most cases prior to quantitative analysis. The signed directed graph (SDG) model is a kind of qualitative graphical models to describe the process variables and their cause-effect relations in continuous systems, denoting the process variables as nodes while causal relations as directed arcs. The signs of nodes and arc correspond to variable deviations and causal directions individually. The SDG obtained by flowsheets, empirical knowledge and mathematical models is an expression of deep knowledge. Based on the graph search, fault propagation paths can be obtained and thus certainly be helpful for the analysis of root causes and sequences (Yang & Xiao, 2005a). And with development of the computer-aided technology, graph theory has been implemented successfully by some graph editors, some of which, like Graphviz (2009), can transform text description into graphs easily. Hence the SDG technology can be easily combined with the other design, analysis and management tools. The SDG definition and its application in fault diagnosis were firstly presented by Iri et al. (1979). Ever since then, many scholars have contributed to this area, including modeling, inference, software development and applications. Many efforts have been particularly made to implement the methods and to overcome the disadvantages, such as spurious solutions. Here we recognize some representatives among them. Kramer & Palowitch (1987) 3

Worst-Case Identification of Errors-in-Variables Models in Closed Loop

A worst-case identification method in frequency domain is proposed to cope with the identification of errors-in-variables models (EIVMs) in closed loop. With a priori bound for the disturbing noises of an EIVM in closed loop, a frequency-domain normalized coprime factor model (NCFM) with perturbation is derived and thus the identification of the EIVM becomes that of the NCFM. By employing the v-gap metric as an optimization criterion, the worst-case error for an identified nominal NCFM is easily quantified and the parameter optimization can be effectively solved by linear matrix inequalities (LMIs). During the parameter optimization, the derivative of the nominal NCFM is constrained to some degree to reduce the effect of overfitting phenomenon. Different from other EIVM identification methods, we use v-gap metric to characterize the disturbing noises and quantify the worst-case error for the nominal NCFM. As a result, the identification result is not a deterministic model but a model set. Moreover, this model set can be perfectly combined with the robust controller design. Finally, a numerical simulation is presented to verify the proposed method.

SDG (Signed Directed Graph) Based Process Description and Fault Propagation Analysis for a Tailings Pumping Process

Abstract Variables in a process are interacting, thus they can be described as an SDG in which arcs show causal relations between variables. Based on the SDG, the fault propagation can be tracked along consistent paths. Hence the SDG modeling can form the basis of fault propagation analysis. Regarding the modeling issue, this paper suggests a knowledge-based method to capture connectivity information between and within units from piping and instrumentation diagrams and other process knowledge. On the other hand, process data can be employed to construct SDGs by correlation analysis. An SDG generation procedure is proposed in this paper. The individual disadvantages of these two methods are summarized. However it is shown that they complement each other when combined. The SDG modeling and fault propagation analysis are applied to a tailings pumping process to illustrate and validate the methods proposed in this paper.