- Email: [email protected]
Using Cognitive Computing for the Control Room of the Future
Mario R. Eden, Marianthi Ierapetritou and Gavin P. Towler (Editors) Proceedings of the 13th International Symposium on Process Systems Engineering – PSE 2018 July 1-5, 2018, San Diego, California, USA © 2018 Elsevier B.V. All rights reserved. https://doi.org/10.1016/B978-0-444-64241-7.50103-8
Using Cognitive Computing for the Control Room of the Future Sambit Ghosha, B. Wayne Bequettea* a
Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180, USA [email protected]
Abstract Chemical manufacturing processes are often complex and large-scale, with many variables to monitor and control. The startup and shutdown of process units can be particularly challenging, with specific and coordinated sequences of events to assure safety while completing operation goals in a reasonable amount of time. Recent advances in cognitive computing, “big data” and process data analytics have great potential to improving the transient operation of chemical processes. A framework to study process startups, shutdowns and abnormal events using graph theory, cognitive computing and machine learning is presented. Preliminary results based on a simple two-tank problem show the usefulness of graph-based analyses. The procedure detects a sensor fault and startup protocol deviations. Ongoing research tests the proposed strategy on more realistic larger scale chemical processes. Keywords: Startup/shutdown, manufacturing
cognitive
computing,
process
operators,
smart
1. Introduction Startups and shutdowns (SU/SD) are the most hazardous times during process operations, yet most process systems engineering research has been focused on continuous, steadystate operation. Startups and shutdowns have an incident rate 10 times that of steady-state operation (CSB, 2007). While chemical processes are highly automated, it is during these times that the human-in-the-loop plays a critical role, and several disasters have occurred because proper protocols were not followed. SU/SD involves a combination of manual and automatic operations. Sometimes loops are put into manual because the response is faster than a closed-loop controller Li et al. (2016) use a fuzzy logic based approach to analyze the interactions between operators in a nuclear power plant. Sand and Terwiesch (2013) note that process plant operators have the tasks of SU/SD, supervising the automated operation, and diagnosing and managing disturbances. They stress the need to increase the performance of human-machine interfaces. Our research effort uses several mathematical and computational tools to analyse the complex non-linearities during SU/SD and provides a framework for the “control room of the future,”. This paper focuses on the use of graph theory to detect process deviations or faults. Network and Graph theory has been applied to a range of problems, with important results by Fiedler (1973). Spectral graph theory, especially using the normalized Kirchoff (or Laplacian matrix in graph theory) matrix was discussed in Chung (1994). In process dynamics and control, Jogwar and Daoutidis (2017) use the concept of
650
S. Ghosh and B.W. Bequette
communities to design controllers, while Heo and Daoutidis (2015) use graph representations to simplify the analysis of a complex plant. Much of the focus on fault detection has been steady-state or small dynamic perturbations from steady-state. Isermann (2005) provide reviews of fault detection, with selected applications, of quantitative model-based fault detection and diagnosis techniques. Datadriven approaches for detecting multiple faults are detailed by He et al. (2014). Severson et al. (2016) provide an overview of recent work in process monitoring. Most notable for our application, Wang et al. (2012) develop a hybrid fault diagnosis strategy for chemical process start-up. In the following sections, a novel method is proposed that involves human-machine interactions during a dynamic process
2. Methodology The goal of this paper is to define a framework to analyse complex dynamic processes and include the human elements in the analysis to understand the temporal patterns over which such a process operates. Fig 1 outlines our complete research goal and vision. The work highlighted in blue in Fig 1 is presented by using a simple proof-of-concept example. Consider a system of two tanks in series along with the individuals responsible for managing the process (Fig 2) Process model equations are shown in Table 1. The inlet flow to T1 is controlled by control valve 1 (CV1). CV2 controls the flow between T1 and T2, and CV3 controls the flow out of T2. There are two shifts of operators with their respective supervisors. Shift 1 has Supervisor 1 (S1) with Operators 1 and 2 (O1 and O2). Shift 2 has Supervisor 2 (S2) with Operators 3 and 4 (O3 and O4). Here we assume only shift 1 is active. O1 controls CV1 and O2 controls CV2 and CV3. Finally, Sensor 1 and 2 (Sen1 and Sen2) give the tank height readings to the shift operators.
Figure 1. Flowchart of proposed fault detection methodology using process dynamics, graph theory, machine learning and CISL facilities. Color code – Green (available information for any process), Red (external disturbances affecting the startup sequence), Blue (Ongoing work in the lab), Yellow (Future work)
2.1 Spectral analysis Using the above description, the following steps are executed: 1. The total number of physical units = 13 (6 personnel, 3 CVs, 2 tanks, 2 sensors). 2. Define a symmetric matrix called the adjacency matrix Ad of size 13X13 where each node is a physical unit. This is described in Table 2. 3. Define the links (connection between each node) as follows:
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651
S1 with O1, O2 (and S2 with O3, O4) – weights vary from 0 to 1 depending on the level of interaction between the supervisor and the operators. A higher weight indicates more interaction during a process. In the present example, the weights are assigned based on assumptions. In future studies these will be determined from humaninteraction based models (Riley et al, 2016) and cognitive computing. O1 with CV1 - fraction of the valve opened (K1, ranges from 0-1). O2 with CV2 and CV3 - fraction of the valve opened (K2, K3 ranges from 0-1). CV1 with T1 – Flow in (F1). Figure 2. Two tank interacting system hierarchy CV2 with T1, T2 – Flow out of T1 or flow in to T2 (F2). CV3 with T2 – Flow out of T3 (F3). Sen1 with T1 and Sen2 with T2 – 1 in case of no fault and 1.3 (i.e a sensor bias) in the faulty scenario. Sen1 with O1 and Sen2 with O2 – Tank height readings. 4. From these definitions, at each time step, the matrix Ad can be created using data from the plant. Ad thus forms a connectivity matrix (or adjacency matrix) for the entire plant. The connectivity changes with respect to the SU sequences with time. As a result, analysing changes in the matrix Ad connectivity gives us consolidated information about the entire plant. Table 1: Two-tank interacting system model Equations dh1/dt = (F1 – F2)/A1 dh2/dt = (F2 – F3)/A2 F1 = K1*Fin F2 = K2*β1√(h1-h2) F3 = K3* β2√h2
Definitions h1, h2 fluid heights of T1 and T2 (m). A1, A2 are cross-sectional area Fin is 1m3 F1 is flow in to tank 1 in m3/min , F2 is flow in to tank 2 in m3/min, F3 is flow out of tank 2 in m3/min β1 (=1) and β2 (=1) are flow coefficients in m3/min/m0.5 K1-K3 are fraction open of CV1-CV3
An example of the Ad matrix is given below ª0 «0 « «[0,1] « «[0,1] «0 « «0 Ad « 0 « «0 «0 « «0 « «0 «0 « ¬0
0 0 0 0 [0,1] [0,1] 0 0 0 0 0 h1 0
[0,1] 0 0 0 0 0 K1 0 0 0 0 0 h2
[0,1] 0 0 0 0 0 0 K3 K3 0 0 0 0
0 [0,1] 0 0 0 0 0 0 0 0 0 0 0
0 [0,1] 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 h1 K1 0 0 0 0 0 0 K3 K3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 F1 0 0 0 0 0 F2 F2 0 0 0 0 0 F3 0 F1 F 2 0 0 0 1 0 F 2 F3 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
0º 0 »» h2 » » 0» 0» » 0» 0» » 0» 0» » 0» » 1» 0» » 0¼
Table 2: Defined nodes for the process Nodes 1 2 3 4 5 6 7 8 9 10 11 12 13
Description Supervisor 1 (S1) Supervisor 2 (S2) Operator 1 (O1) Operator 2 (O2) Operator 3 (O3) Operator 4 (O4) Control valve 1 (CV1) Control valve 2 (CV2) Control valve 3 (CV3) Tank 1 (T1) Tank 2 (T2) Sensor 1 (Sen1) Sensor 2 (Sen2)
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S. Ghosh and B.W. Bequette
5. We now borrow concepts from network/graph theory to analyse Ad. Let L = D-Ad where Ad is the adjacency matrix, D is the degree matrix and L is the Kirchoff (also called Laplacian in graph theory) matrix. The degree matrix is defined as a diagonal matrix whose elements are the sum of all edges for a particular node in Ad. 6. Define L* = D-1/2LD-1/2 where L* gives us the normalized Kirchoff matrix and the eigen-decomposition of L* = ΘΛΘT where Θ are the eigenvectors and Λ the eigenvalues. For a nXn matrix, there will be n eigenvalues and n eigenvectors (Chung, 1994). Some key features from this decomposition are as follows: • The set of eigenvectors Θ form an orthonormal basis of the network and eigenvalues of L* are scaled from 0-2 for any symmetric matrix • The multiplicity of zero eigenvalues give the number of connected components in the graph/network and number of eigenvalues equal to 1 gives information about similar nodes (especially isolated nodes) • The eigenvector corresponding to the first non-zero (and thus second smallest) eigenvalue is called the Fiedler vector - gives information about the clustering or grouping of nodes in a network and is often used to compare networks. In this example, the Fiedler vector will be used to show the differences in the SU sequences. 2.2 Shortest paths Shortest path analyses are very useful to understand the information flow in a complex network. In this work, we use MATLAB’s shortest path module on the Ad matrices and Dijktra’s algorithm (Dijktra, 1959) to find the information flow between the components. An analysis of three different SU procedures is presented below.
3. Results The SU/SD of a plant is defined by a Standard Operating Procedure (SOP) containing a series of sequential steps. As a result, SU/SDs are temporal in nature and any deviations in it should be studied in a simple manner to detect process deviations. Since SU/SD disasters occur due to deviations from the SOPs, it is pertinent to have a method to detect these deviations. In this study, the use of network parameters like Fiedler vectors (FVs) and shortest paths are used to show how different kinds of information can be extracted from a dynamic process as defined before. For the process in Fig 2, an SOP is defined as given in Table 3. Table 3: SOP of the two-tank system Startup sequence Correct
Deviated (to fill the tank faster compared to the Correct startup sequences) Deviated+Faulty (Starts with the same protocol as Deviated but changes to a more ad-hoc scenario due to the faulty sensor reading)
Fraction of valve opened in the startup protocol 0-50mins – K1=0.5, K2=1, K3=0 51-100mins – K1 = 0.1, K2=0, K3=0 101-150mins – K1=1, K2=1, K3=1 0-30mins – K1=1, K2=1, K3=0 31-150mins – K1=1, K2=1, K3=1 0-30mins – K1=1, K2=1, K3=0 31-60mins – K1=1, K2=1, K3=1 61-90mins – K1=0.8, K2=1, K3=1 91-120mins – K1=0.92, K2=1, K3=1 121-150mins – K1=0.92, K2=0.9, K3=1
Simulating the process for the three different SU sequences, the Ad matrices for the three SU: Correct, Deviated and Deviated+Faulty are found at each time step using steps 3-4
Using Cognitive Computing for the Control Room of the Future
653
in Methodology. Using the three sets of Ad matrices, the spectral decomposition is computed and the FV are obtained using steps 5-6 in Methodology. Fig 3 plots the FV for the three SU at 3 different time steps. At t=15 and 60 mins, both the Deviated and Deviated+Faulty SU show differences with the Correct SU as this is the transient region. However, at t=135 mins, the Correct and Deviated cases have the exact same plant state (all weights are same) as they reach steady state. As a result, their FV match exactly, indicating that the two processes are the same at all hierarchy. In Fig 4, it is shown that when we change S1-O1 and S1-O2 to 0.5 (indicating occasional interaction of operators with supervisors) only for the Deviated scenario, even at t=135 when all the process variables are having the same values (steady state), due to a change in S1-O1 and S1-O2 weights from the Correct scenario (=0.1), the FV do not match. The shortest path can provide insights about the flow of information in the network. Using the graphshortestpath() command in MATLAB the following paths were found: 1. 2. 3.
S1-O2-Sen2-T2, S1-O2-CV2-T2, S1-O2-CV2-T1, S1-O2-CV3-T2 S1-O1-Sen1-T1, S1-O1-CV1-T1 S2-O3, S2-O4
It is easy to see that if Shift 2 was in charge, then the paths would have been different and hence we end up with a technique to see changes in shift with time. Interestingly, this change is also captured in the eigenvalues reported in Table 4. The multiplicities of eigenvalues (=1) equals the number of human personnel not connected to the process due to a different shift. This can be generalized to any process equipment as well.
Figure 3. Fiedler vector comparison of the three SU sequences at three time snapshots.
Figure 4. Fiedler Vector of Correct and Deviated. S1-O1 and S1-O2 are 0.1 and 0.5 for Correct and Deviated respectively.
Table 4: Eigenvalues of the normalized Laplacian at t=135 minutes. Correct
0
0
0.009
0.813
0.921
1
1
1
1.078
1.186
1.99
2
2
Deviated
0
0
0.009
0.812
0.921
1
1
1
1.078
1.186
1.99
2
2
Deviated+Faulty
0
0
0.068
0.617
0.991
1
1
1
1.080
1.382
1.931
2
2
654
S. Ghosh and B.W. Bequette
4. Conclusion and Future work Graph theory was used to analyse SU of a simple process. The results from the FV show that sets of sequential processes will show differences if the links in the individual networks change. It is also useful to analyse the sequences with time; a user-defined time window can be defined to get average Ad matrices and FV. Similarly, deviations in shortest paths of SU sequences and eigenvalues of a process indicate a change in information flow paths between the physical units and the connectivity of a node in a network. It is evident from these results that for a complex process, such an information transformation helps to identify the changes that are taking place dynamically. These are preliminary results and that we have a vision of the control room of the future that includes the use of IBM Watson based facilities at RPI and machine learning approaches to improve operations.
References CSB report on Texas City explosion. U.S. Chemical Safety and Hazard Investigation Board. Investigation report: refinery explosion and fire, BP Texas City, Texas. Report no. 2005-04-ITX. March 2007. Available at: http://www.csb.gov/ assets/1/19/csbfinalreportbp.pdf. Chung, F. R. K. (1994) ‘Spectral Graph Theory’, Conference Board of the Mathematical Sciences, (92), p. 214. Dijkstra, E.W., 1959. A note on two problems in connexion with graphs. Numerische mathematik, 1(1), pp.269-271. Fiedler, M., 1973. Algebraic connectivity of graphs. Czechoslovak mathematical journal, 23(2), pp.298-305. He Y-L, Wang R, Kwong S, Wang X-Z. Bayesian classifiers based on probability density estimation and their applications to simultaneous fault diagnosis. Information Sciences 2014;259:252-268. Heo, S. and Daoutidis, P. (2015) ‘Graph-Theoretic Analysis of Multitime Scale Dynamics in Complex Material Integrated Plants’, Ind. Eng. Chem. Res., 54(42), pp. 10322–10333. Isermann R. Model-based fault-detection and diagnosis—status and applications. Annu Rev Control. 2005;29:71-85. Jogwar, S. S. and Daoutidis, P. (2017) ‘Community-based synthesis of distributed control architectures for integrated process networks’, Chem. Eng Sci., 172, pp. 434–443. Li, P.C., Chen, G.H., Dai, L.C., Zhang, L., Zhao, M. and Chen, W., 2016. Methodology for analyzing the dependencies between human operators in digital control systems. Fuzzy Sets and Systems, 293, pp.127-143. Riley, W.T., Martin, C.A., Rivera, D.E., Hekler, E.B., Adams, M.A., Buman, M.P., Pavel, M. and King, A.C., 2016. Development of a dynamic computational model of social cognitive theory. Translational behavioral medicine, 6(4), pp.483-495. Sand G, Terwiesch P. Closing the loops: An industrial perspective on the present and future impact of control. European J. Control. 2013;19:341-350. Severson K, Chaiwatanodom P, Braatz RD, Perspectives on process monitoring of industrial systems, In Annual Reviews in Control, 2016; 42:190-200. Wang Z, Zhao J, Shang H. A hybrid fault diagnosis strategy for chemical process startups. J. Proc. Cont. 2012;22:1287-1297.
Using Cognitive Computing for the Control Room of the Future Sambit Ghosha, B. Wayne Bequettea* a
Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, NY 12180, USA [email protected]
Abstract Chemical manufacturing processes are often complex and large-scale, with many variables to monitor and control. The startup and shutdown of process units can be particularly challenging, with specific and coordinated sequences of events to assure safety while completing operation goals in a reasonable amount of time. Recent advances in cognitive computing, “big data” and process data analytics have great potential to improving the transient operation of chemical processes. A framework to study process startups, shutdowns and abnormal events using graph theory, cognitive computing and machine learning is presented. Preliminary results based on a simple two-tank problem show the usefulness of graph-based analyses. The procedure detects a sensor fault and startup protocol deviations. Ongoing research tests the proposed strategy on more realistic larger scale chemical processes. Keywords: Startup/shutdown, manufacturing
cognitive
computing,
process
operators,
smart
1. Introduction Startups and shutdowns (SU/SD) are the most hazardous times during process operations, yet most process systems engineering research has been focused on continuous, steadystate operation. Startups and shutdowns have an incident rate 10 times that of steady-state operation (CSB, 2007). While chemical processes are highly automated, it is during these times that the human-in-the-loop plays a critical role, and several disasters have occurred because proper protocols were not followed. SU/SD involves a combination of manual and automatic operations. Sometimes loops are put into manual because the response is faster than a closed-loop controller Li et al. (2016) use a fuzzy logic based approach to analyze the interactions between operators in a nuclear power plant. Sand and Terwiesch (2013) note that process plant operators have the tasks of SU/SD, supervising the automated operation, and diagnosing and managing disturbances. They stress the need to increase the performance of human-machine interfaces. Our research effort uses several mathematical and computational tools to analyse the complex non-linearities during SU/SD and provides a framework for the “control room of the future,”. This paper focuses on the use of graph theory to detect process deviations or faults. Network and Graph theory has been applied to a range of problems, with important results by Fiedler (1973). Spectral graph theory, especially using the normalized Kirchoff (or Laplacian matrix in graph theory) matrix was discussed in Chung (1994). In process dynamics and control, Jogwar and Daoutidis (2017) use the concept of
650
S. Ghosh and B.W. Bequette
communities to design controllers, while Heo and Daoutidis (2015) use graph representations to simplify the analysis of a complex plant. Much of the focus on fault detection has been steady-state or small dynamic perturbations from steady-state. Isermann (2005) provide reviews of fault detection, with selected applications, of quantitative model-based fault detection and diagnosis techniques. Datadriven approaches for detecting multiple faults are detailed by He et al. (2014). Severson et al. (2016) provide an overview of recent work in process monitoring. Most notable for our application, Wang et al. (2012) develop a hybrid fault diagnosis strategy for chemical process start-up. In the following sections, a novel method is proposed that involves human-machine interactions during a dynamic process
2. Methodology The goal of this paper is to define a framework to analyse complex dynamic processes and include the human elements in the analysis to understand the temporal patterns over which such a process operates. Fig 1 outlines our complete research goal and vision. The work highlighted in blue in Fig 1 is presented by using a simple proof-of-concept example. Consider a system of two tanks in series along with the individuals responsible for managing the process (Fig 2) Process model equations are shown in Table 1. The inlet flow to T1 is controlled by control valve 1 (CV1). CV2 controls the flow between T1 and T2, and CV3 controls the flow out of T2. There are two shifts of operators with their respective supervisors. Shift 1 has Supervisor 1 (S1) with Operators 1 and 2 (O1 and O2). Shift 2 has Supervisor 2 (S2) with Operators 3 and 4 (O3 and O4). Here we assume only shift 1 is active. O1 controls CV1 and O2 controls CV2 and CV3. Finally, Sensor 1 and 2 (Sen1 and Sen2) give the tank height readings to the shift operators.
Figure 1. Flowchart of proposed fault detection methodology using process dynamics, graph theory, machine learning and CISL facilities. Color code – Green (available information for any process), Red (external disturbances affecting the startup sequence), Blue (Ongoing work in the lab), Yellow (Future work)
2.1 Spectral analysis Using the above description, the following steps are executed: 1. The total number of physical units = 13 (6 personnel, 3 CVs, 2 tanks, 2 sensors). 2. Define a symmetric matrix called the adjacency matrix Ad of size 13X13 where each node is a physical unit. This is described in Table 2. 3. Define the links (connection between each node) as follows:
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651
S1 with O1, O2 (and S2 with O3, O4) – weights vary from 0 to 1 depending on the level of interaction between the supervisor and the operators. A higher weight indicates more interaction during a process. In the present example, the weights are assigned based on assumptions. In future studies these will be determined from humaninteraction based models (Riley et al, 2016) and cognitive computing. O1 with CV1 - fraction of the valve opened (K1, ranges from 0-1). O2 with CV2 and CV3 - fraction of the valve opened (K2, K3 ranges from 0-1). CV1 with T1 – Flow in (F1). Figure 2. Two tank interacting system hierarchy CV2 with T1, T2 – Flow out of T1 or flow in to T2 (F2). CV3 with T2 – Flow out of T3 (F3). Sen1 with T1 and Sen2 with T2 – 1 in case of no fault and 1.3 (i.e a sensor bias) in the faulty scenario. Sen1 with O1 and Sen2 with O2 – Tank height readings. 4. From these definitions, at each time step, the matrix Ad can be created using data from the plant. Ad thus forms a connectivity matrix (or adjacency matrix) for the entire plant. The connectivity changes with respect to the SU sequences with time. As a result, analysing changes in the matrix Ad connectivity gives us consolidated information about the entire plant. Table 1: Two-tank interacting system model Equations dh1/dt = (F1 – F2)/A1 dh2/dt = (F2 – F3)/A2 F1 = K1*Fin F2 = K2*β1√(h1-h2) F3 = K3* β2√h2
Definitions h1, h2 fluid heights of T1 and T2 (m). A1, A2 are cross-sectional area Fin is 1m3 F1 is flow in to tank 1 in m3/min , F2 is flow in to tank 2 in m3/min, F3 is flow out of tank 2 in m3/min β1 (=1) and β2 (=1) are flow coefficients in m3/min/m0.5 K1-K3 are fraction open of CV1-CV3
An example of the Ad matrix is given below ª0 «0 « «[0,1] « «[0,1] «0 « «0 Ad « 0 « «0 «0 « «0 « «0 «0 « ¬0
0 0 0 0 [0,1] [0,1] 0 0 0 0 0 h1 0
[0,1] 0 0 0 0 0 K1 0 0 0 0 0 h2
[0,1] 0 0 0 0 0 0 K3 K3 0 0 0 0
0 [0,1] 0 0 0 0 0 0 0 0 0 0 0
0 [0,1] 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 h1 K1 0 0 0 0 0 0 K3 K3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 F1 0 0 0 0 0 F2 F2 0 0 0 0 0 F3 0 F1 F 2 0 0 0 1 0 F 2 F3 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
0º 0 »» h2 » » 0» 0» » 0» 0» » 0» 0» » 0» » 1» 0» » 0¼
Table 2: Defined nodes for the process Nodes 1 2 3 4 5 6 7 8 9 10 11 12 13
Description Supervisor 1 (S1) Supervisor 2 (S2) Operator 1 (O1) Operator 2 (O2) Operator 3 (O3) Operator 4 (O4) Control valve 1 (CV1) Control valve 2 (CV2) Control valve 3 (CV3) Tank 1 (T1) Tank 2 (T2) Sensor 1 (Sen1) Sensor 2 (Sen2)
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S. Ghosh and B.W. Bequette
5. We now borrow concepts from network/graph theory to analyse Ad. Let L = D-Ad where Ad is the adjacency matrix, D is the degree matrix and L is the Kirchoff (also called Laplacian in graph theory) matrix. The degree matrix is defined as a diagonal matrix whose elements are the sum of all edges for a particular node in Ad. 6. Define L* = D-1/2LD-1/2 where L* gives us the normalized Kirchoff matrix and the eigen-decomposition of L* = ΘΛΘT where Θ are the eigenvectors and Λ the eigenvalues. For a nXn matrix, there will be n eigenvalues and n eigenvectors (Chung, 1994). Some key features from this decomposition are as follows: • The set of eigenvectors Θ form an orthonormal basis of the network and eigenvalues of L* are scaled from 0-2 for any symmetric matrix • The multiplicity of zero eigenvalues give the number of connected components in the graph/network and number of eigenvalues equal to 1 gives information about similar nodes (especially isolated nodes) • The eigenvector corresponding to the first non-zero (and thus second smallest) eigenvalue is called the Fiedler vector - gives information about the clustering or grouping of nodes in a network and is often used to compare networks. In this example, the Fiedler vector will be used to show the differences in the SU sequences. 2.2 Shortest paths Shortest path analyses are very useful to understand the information flow in a complex network. In this work, we use MATLAB’s shortest path module on the Ad matrices and Dijktra’s algorithm (Dijktra, 1959) to find the information flow between the components. An analysis of three different SU procedures is presented below.
3. Results The SU/SD of a plant is defined by a Standard Operating Procedure (SOP) containing a series of sequential steps. As a result, SU/SDs are temporal in nature and any deviations in it should be studied in a simple manner to detect process deviations. Since SU/SD disasters occur due to deviations from the SOPs, it is pertinent to have a method to detect these deviations. In this study, the use of network parameters like Fiedler vectors (FVs) and shortest paths are used to show how different kinds of information can be extracted from a dynamic process as defined before. For the process in Fig 2, an SOP is defined as given in Table 3. Table 3: SOP of the two-tank system Startup sequence Correct
Deviated (to fill the tank faster compared to the Correct startup sequences) Deviated+Faulty (Starts with the same protocol as Deviated but changes to a more ad-hoc scenario due to the faulty sensor reading)
Fraction of valve opened in the startup protocol 0-50mins – K1=0.5, K2=1, K3=0 51-100mins – K1 = 0.1, K2=0, K3=0 101-150mins – K1=1, K2=1, K3=1 0-30mins – K1=1, K2=1, K3=0 31-150mins – K1=1, K2=1, K3=1 0-30mins – K1=1, K2=1, K3=0 31-60mins – K1=1, K2=1, K3=1 61-90mins – K1=0.8, K2=1, K3=1 91-120mins – K1=0.92, K2=1, K3=1 121-150mins – K1=0.92, K2=0.9, K3=1
Simulating the process for the three different SU sequences, the Ad matrices for the three SU: Correct, Deviated and Deviated+Faulty are found at each time step using steps 3-4
Using Cognitive Computing for the Control Room of the Future
653
in Methodology. Using the three sets of Ad matrices, the spectral decomposition is computed and the FV are obtained using steps 5-6 in Methodology. Fig 3 plots the FV for the three SU at 3 different time steps. At t=15 and 60 mins, both the Deviated and Deviated+Faulty SU show differences with the Correct SU as this is the transient region. However, at t=135 mins, the Correct and Deviated cases have the exact same plant state (all weights are same) as they reach steady state. As a result, their FV match exactly, indicating that the two processes are the same at all hierarchy. In Fig 4, it is shown that when we change S1-O1 and S1-O2 to 0.5 (indicating occasional interaction of operators with supervisors) only for the Deviated scenario, even at t=135 when all the process variables are having the same values (steady state), due to a change in S1-O1 and S1-O2 weights from the Correct scenario (=0.1), the FV do not match. The shortest path can provide insights about the flow of information in the network. Using the graphshortestpath() command in MATLAB the following paths were found: 1. 2. 3.
S1-O2-Sen2-T2, S1-O2-CV2-T2, S1-O2-CV2-T1, S1-O2-CV3-T2 S1-O1-Sen1-T1, S1-O1-CV1-T1 S2-O3, S2-O4
It is easy to see that if Shift 2 was in charge, then the paths would have been different and hence we end up with a technique to see changes in shift with time. Interestingly, this change is also captured in the eigenvalues reported in Table 4. The multiplicities of eigenvalues (=1) equals the number of human personnel not connected to the process due to a different shift. This can be generalized to any process equipment as well.
Figure 3. Fiedler vector comparison of the three SU sequences at three time snapshots.
Figure 4. Fiedler Vector of Correct and Deviated. S1-O1 and S1-O2 are 0.1 and 0.5 for Correct and Deviated respectively.
Table 4: Eigenvalues of the normalized Laplacian at t=135 minutes. Correct
0
0
0.009
0.813
0.921
1
1
1
1.078
1.186
1.99
2
2
Deviated
0
0
0.009
0.812
0.921
1
1
1
1.078
1.186
1.99
2
2
Deviated+Faulty
0
0
0.068
0.617
0.991
1
1
1
1.080
1.382
1.931
2
2
654
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4. Conclusion and Future work Graph theory was used to analyse SU of a simple process. The results from the FV show that sets of sequential processes will show differences if the links in the individual networks change. It is also useful to analyse the sequences with time; a user-defined time window can be defined to get average Ad matrices and FV. Similarly, deviations in shortest paths of SU sequences and eigenvalues of a process indicate a change in information flow paths between the physical units and the connectivity of a node in a network. It is evident from these results that for a complex process, such an information transformation helps to identify the changes that are taking place dynamically. These are preliminary results and that we have a vision of the control room of the future that includes the use of IBM Watson based facilities at RPI and machine learning approaches to improve operations.
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