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Risk-based warning system design methodology for multimode processes
9th International Symposium on Advanced Control of Chemical Processes 9th International Symposium on Advanced June 7-10, 2015. Whistler, British Columbia,Control Canadaof Chemical Processes 9th International Symposium on Advanced Control of Chemical Processes Available online at www.sciencedirect.com June 7-10, 2015. Whistler, British Columbia, Canada June 7-10, 2015. Whistler, British Columbia, Canada
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Risk-based warning system design methodology for multimode processes Risk-based Risk-based warning warning system system design design methodology methodology for for multimode multimode processes processes Hangzhou Wang, Faisal Khan*, Salim Ahmed, and Syed Imtiaz Hangzhou Wang, Faisal Khan*, Salim Ahmed, and Syed Imtiaz Salim Ahmed, and Syed Imtiaz Hangzhou Wang, Faisal Khan*, Safety and Risk Engineering Group, Safety and Risk Engineering Group, Faculty of Engineering and Applied Science, Safety and Risk Engineering Group, Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL A1B 3X5, Canada Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL A1B 3X5, Canada Memorial University, St. John’s, A1B 3X5, Canada (* correspondence author, phone: 709 84NL 8939 e-mail:[email protected]) (* correspondence author, phone: 709 84 8939 e-mail:[email protected]) (* correspondence author, phone: 709 84 8939 e-mail:[email protected]) Abstract: Complex chemical processes usually operate at multiple operating modes, resulting from Abstract: Complex processes operate at multiple operating modes, resulting various factors, suchchemical as changes in marketusually demand, set point modifications, and feedstock changes.from It is from Abstract: Complex chemical processes usually operate at multiple operating modes, resulting various factors, such as changes in market demand, set point modifications, and feedstock changes. Itthis is difficult to monitor a multimode process without generating significant number of false alarms. In various factors, such as changes in market demand, set point modifications, and feedstock changes. It is difficult to monitor a multimode process without generating significant number of false alarms. In this paper, system design is proposed to monitor multimode difficulta risk-based to monitor alarm a multimode processmethodology without generating significant number of false processes. alarms. In The this paper, a risk-based alarmofsystem design methodology proposed monitor processes. The methodology comprises three main steps: i) analysisis operatingto usingmultimode Gaussian mixture model, paper, a risk-based alarm system design methodology isofproposed todata monitor multimode processes. The methodology comprises of three main steps: i)modes analysis of operating datavirtual using Gaussian mixture model, ii) identification of independent operating (e.g. set points, state), and iii) methodology comprises of three main steps: i) analysis of operating data using transient Gaussian mixture model, ii) identification oftoindependent operating modes (e.g. set warning. points, virtual transient state), and iii) probabilistic model assess risk and activation of appropriate A continuous stirred tank reactor ii) identification of independent operating modes (e.g. set points, virtual transient state), and iii) probabilistic model to control assess risk and is activation of appropriate A continuous stirred tank reactor with model predictive system used to demonstrate thewarning. effectiveness of the proposed method. probabilistic model to assess risk and activation of appropriate warning. A continuous stirred tank reactor with model predictive control system is used to demonstrate the effectiveness of the proposed method. with model predictive control system is used to demonstrate the effectiveness of the proposed method. © 2015, IFAC (International Federation of Automatic Control)warning Hosting by Elsevier Ltd. All rightsmanagement; reserved. Keywords: multimode process; Gaussian mixture model; system design; alarm Keywords: multimodemodel process; Gaussian mixture model; warning system design; alarm management; probability graphical Keywords: multimode process; Gaussian mixture model; warning system design; alarm management; probability graphical model probability graphical model
1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION Over the past decades, more and more attentions have been Over the past decades, more and more have been paid to from attentions both academia and Over the the pastprocess decades,monitoring more and more attentions have been paid to the process monitoring from both academia and industry of its monitoring indispensable role both in guaranteeing paid to because the process from academia safe and industry because of its indispensable role in guaranteeing safe operation. Complex processes operatesafe at industry because of itschemical indispensable role inusually guaranteeing operation.operating Complex chemical processes operate at multiple resulting fromusually various factors, operation. Complex modes, chemical processes usually operate at multiple operating modes, resulting from various factors, such as changes in market pointvarious modifications, multiple operating modes, demand, resultingsetfrom factors, such as changeschanges in market demand, point modifications, and feedstock (Hwang and set Han, 1999). The realsuch as changes in market demand, set point modifications, and feedstock changes (Hwang and Han, 1999). The realtime monitoring and warning of danger in multimode and feedstock changes (Hwang and Han, 1999). The realtime monitoring and warning of danger in multimode processes is a challenging problem, whichin has drawn time monitoring and warning of danger multimode processes is a challenging problem, which has drawn increasing attention recently (Zhao et al., 2010). processes is a challenging problem, which has drawn increasing attention recently (Zhao et al., 2010). increasing attention recently (Zhao et al., 2010). To resolve the issues associated with monitoring multiple To resolvemodes the issues associated with monitoring operating processes, multivariate statistical multiple process To resolve the issues associated with monitoring multiple operating modes processes, multivariate statistical monitoring (MSPM) is becoming popular due process to the operating modes processes, multivariate statistical process monitoring of (MSPM) is of becoming popularbydue to the availability large sets data generated large-scale monitoring (MSPM) is becoming popular due to the availability of large sets of data generated by large-scale chemical processes et al., Qin, 2012). MSPM availability of large(Ning sets of data2014, generated by large-scale chemical processes (Ning et al., 2014, Qin, 2012). MSPM techniques, such as partial least-squares (PLS) and principal chemical processes (Ning et al., 2014, Qin, 2012). MSPM techniques, such as partial least-squares (PLS) and principal component analysis (PCA), have (PLS) been and intensively techniques, such as partial least-squares principal component (PCA), have been have intensively investigated analysis and fruitful of applications been component analysis (PCA), have been intensively investigated of applications beena demonstrated and (Wisefruitful and Gallagher, 1996). Zhao have proposed investigated and fruitful of applications have been demonstrated (Wise and Gallagher, 1996). Zhao proposed a method based on multiple partial least-squares models demonstrated (Wise and Gallagher, 1996). Zhao proposed toa method based on multiple partial least-squares models to monitor multimodal process (Zhao et al., 2006). Also, many method based on multiple partial least-squares models to monitor multimodal process al., 2006). Also, PCA-based techniques have (Zhao been et reported. Chen andmany Liu monitor multimodal process (Zhao et al., 2006). Also, many PCA-based techniques have been reported. Chen and Liu proposed a fault detection method using mixture of PCA PCA-based techniques have been reported. Chen and Liu proposed a fault detection method using mixture of PCA models, the number of clusters are determined proposed ina which fault detection method using mixture of PCA models, in which theand number of clusters are automatically (Chen Liu, 1999). Ng and determined Srinivasan models, in which the number of clusters are determined automatically (Chen and Liu, 1999). where Ng and Srinivasan proposed an Adjoined PCA approach, a mixture of automatically (Chen and Liu, 1999). Ng and Srinivasan proposed an Adjoined PCA approach, where a mixture of PCA models are adjoined and Srinivasan, Choi proposed an Adjoined PCA(Ng approach, where a 2009). mixture of PCA modelsthe aremaximum adjoined (Ng and Srinivasan, 2009). Choi formulated likelihood principal component PCA models are adjoined (Ng and Srinivasan, 2009). Choi formulated the maximum likelihood principal component analysis (MLPCA) mixture model to monitor process. Feital formulated the maximum likelihood principal component analysis (MLPCA) mixture model to monitor process. Feital proposed a multimodal modelling and monitoring approach analysis (MLPCA) mixture model to monitor process. Feital proposed a multimodal modelling and monitoring approach based on MLPCA analysis and presented an operating modes proposed a multimodal modelling and monitoring approach based on MLPCA analysis andetpresented an operating modes identification method (Feital al., 2013). All these PCAbased on MLPCA analysis and presented an operating modes identification method (Feital et al., 2013). All these PCAidentification method (Feital et al., 2013). All these PCA-
based methods suffer drawbacks of dealing with nonbased methods suffer drawbacks dealing with nonGaussian distributed operating data in of process. based methods suffer drawbacks of dealing with nonGaussian distributed operating data in process. operating data in process. Gaussian distributed Compared to the PCA-based mixture models, advantages of Compared to mixture the PCA-based mixture includes: models, advantages of the Gaussian model (GMM) (1) the model Compared to the PCA-based mixture models, advantages of the Gaussian mixture model (GMM) includes: (1) the model structure is simple that it(GMM) is easyincludes: to understand to the Gaussian mixturesomodel (1) the and model structure is in simple so that it process, is easy to understand and to implement non-Gaussian (2) can be used structure is simple so that it is easy to understand and to to implement inmultimode non-Gaussian process,(3) (2) can handle be used to monitoring processes, implement in non-Gaussian process, (2) can can be used the to monitoring multimode processes, (3) GMM can handle the nonlinear process (Ge et al., 2013). The method can monitoring multimode processes, (3) can handle the nonlinear process industrial (Ge et al., 2013). dataset The GMM methodlocal can describe complex by several nonlinear process (Ge et al.,process 2013). The GMM method can describe complex industrial process dataset by several local linear models. To learn the Gaussian mixture model, the describe complex industrial process dataset by several local linear models. To learn the Gaussian mixture model, the Expectation-Maximization (EM) algorithm is employed to linear models. To learn the Gaussian mixture model, the Expectation-Maximization (EM) algorithm is employed to estimate the values of its parameters. GMM is promising Expectation-Maximization (EM) algorithm is employed to estimate the values of its parameters. GMM is promising method tothe monitor multimode (Ge et estimate valuesnon-Gaussian, of its parameters. GMMprocess is promising method to Choi monitor non-Gaussian, multimode process (Ge et al., 2013, et al., 2004, Yu, 2012, Yu and Qin, 2009, method to monitor non-Gaussian, multimode process (Ge et al., 2013, Choi et al., 2004, Yu, 2012, Yu and Qin, 2009, Chen2013, andChoi Zhang, Ververidis and al., et al., 2010). 2004, Yu, 2012, Yu(Ververidis and Qin, 2009, Chen and Zhang, 2010). (Ververidis Kotropoulos, 2008) and HennigVerveridis (Hennig, 2010) showed and the Chen and Zhang, 2010). Ververidis (Ververidis and Kotropoulos, 2008) and Hennig (Hennig, 2010) showed the strong ability of Gaussian mixture(Hennig, model to2010) separate different Kotropoulos, 2008) and Hennig showed the strong ability of Gaussian mixture model todeveloped separate different operating modes in process. Yu and Qin a finite strong ability of Gaussian mixture model to separate different operating process. Yu andand Qin developed a finite Gaussian modes mixturein (FGMM) the Bayesian operating modes inmodel process. Yu and Qin used developed a finite Gaussian mixture model (FGMM) and used the Bayesian inference-based (BIP)andindex for Bayesian process Gaussian mixture probability model (FGMM) used the inference-based probability index for process monitoring (Yu and Qin, 2008).(BIP) The number in a index offormodes process inference-based probability (BIP) (Yu and Qin, 2008). The number of modes in a monitoring GMM is automatically determined along with its other monitoring (Yu and Qin, 2008). The number of modes in a GMM is automatically determined along with its other parameters. GMM is automatically determined along with its other parameters. parameters. In this paper, a risk-based warning system design method In this the paper, a risk-based warning system design method using GMM is proposed to represent non-Gaussian, In this paper, a risk-based warning system design method using the GMM is proposed to represent non-Gaussian, multimode operating data and to separate different using the GMM is proposed to represent non-Gaussian, multimode operating to separate different operational modes. As adata result,and the process state (including multimode operating data and to separate different operational modes. As a result, the process state (including acceptable transient state) can be the identified operating data operational modes. As a result, processforstate (including acceptable transient state) can be identified forwhile operating data in real-time, give proper warning message minimize acceptable transient state) can be identified for operating data in give proper while minimize thereal-time, false alarms at the samewarning time. message in real-time, give proper warning message while minimize the false alarms at the same time. the false alarms at the same time. This paper proceeds as follows. First, the proposed This paper is proceeds follows. the by proposed methodology describedas Section 2First, followed a case This paper proceeds as infollows. First, the proposed methodology is described indiscussions Section 2 and followed by a case study in Section 3. Finally, conclusions are methodology is described in Section 2 followed by a case study in Section 3. Finally, discussions and conclusions are presented. study in Section 3. Finally, discussions and conclusions are presented. presented.
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2. METHODOLOGY
Max. Separated operate mode1 Separated operate mode2 Measured data Gaussian Mixed Model
Frequence
The proposed methodology of alarm management in multimode process is shown in Figure 1. The methodology is comprised of three important steps: i) analysis of operating data using Gaussian mixture model, ii) identification of independent operating modes (e.g. set points, virtual transient state), and iii) probabilistic model to assess risk and activation of appropriate warning. The details of the methodology is explained in following subsections.
0
sp1
Value
sp2
Chemical process
Figure 2. Measured values and separated operation modes Collect operational data
2.2 Identification of operating modes
Analysis data with Gaussian mixed model
In this example, there is a variable x, with two possible set point, sp1, and sp2. Also the system may be on the way from sp1 to sp2 or vice versa is considered, this is a transient mode. This situation is considered to be a normal situation, not to alarm as a false alarm. So a virtual operating mode is introduced, shown in Figure 3, to help identify the transient mode from operating point sp1 to sp2 , or vice versa. In this virtual mode, denoted as the OnTheWay mode, there is a special operating point. All transient operating trajectories frequently pass through it, and it can be a reference location to identify that the operating point is in its transient situation. Because it is a transient state, if all operating data are correctly recorded, this transient mode can be properly separated by the Gaussian mixture model.
Separate multiple operating modes
Construct OnTheWay node between every two operating modes
Analysis of operating data
Belongs to one operating mode
Update Gaussian Mixed model
Y
Add data to respond operating modes database
N Likely belongs to OnTheWay modes Y Start timer
Close timer
Add data to respond OnTheWay database
Y
Max.
Belongs to one OnTheWay mode N Timer increase by an interval
N
Frequence
Exceed Max. allowed time
N
Analysis the new operating data
Separated operate mode1 Separated operate mode2 OnTheW ay virtual mode
Y Close timer
0 Activate early warning system
sp1
OnTheW ay Value
sp2
Figure 3. Operating modes and OnTheWay virtual mode stop
2.3 Risk estimation and activation of alarm
Figure 1. Methodology for alarm management in multimode process
With the OnTheWay virtual mode, process state can be monitored in real time. Fault probability for every operating point can be calculated over time. And then activate different level of early warnings according to the probability and severity. In this method, both severity and probability are represented in terms of distances from the centers. The severity classification schematic is shown in Figure 4. With the probability and severity values, the state of the current operating point can be identified, and give proper warning if it is necessary.
2.1 Gaussian mixture model to represent multimode Let us consider a simple situation. Suppose data from normal operating situations are represented in Figure 2. All records of operating point values can be represented by Gaussian mixture model, and also can be separated into different operating modes. In this example, there are two different operating modes with set point sp1 and sp2.
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on the probability of fault and the possible consequence loss. The state of current operating point can be correctly identified, and the risk is estimated. Finally, different warnings according the calculation result are activated.
Severity classification A
B Sp1
OnTheWay
3. CASE STUDY
Sp2
C
D
A continuous stirred tank reactor (CSTR) with model predictive control system is used to demonstrate the effectiveness of the proposed method. 3.1 CSTR process description
Figure 4. Severity classification schematic, the area A is the normal operation ranges, and area D is a possible fault requiring a warning message.
The schematic of the CSTR process (Seborg et al., 2010) is shown in Figure 6.
The severity corresponds to the potential consequence; the values are assigned in Table 1. Table 1. Severity classification Classification
Consequence
Meaning
Class A
1
Normal operation
Class B
10
Deviation acceptable
Class C
50
Deviation require attention
Class D
100
Fault require warning message
Main Main Reactor Reactor
Coolant Coolant
Figure 6. Schematic of CSTR with temperature controller A liquid phase, irreversible chemical reaction takes place in the reactor where chemical species A reacts to form species B. The rate of reaction is first order with respect to component A,
sp
1
Where r is the rate of reaction of A per unit volume, k is the reaction rate constant, and cA is the molar concentration of species A.
OTW: X ~ N μ OTW , Σ OTW
OTW
Fault
r kcA
n X R feasible
SP2
SP2 : X ~ N μ 2 , Σ2
k k0 e
sp
E RT
2
The inlet stream consists of pure component A with molar concentration, cAi. A cooling jacket is used to maintain the reaction mixture at the desired operating temperature.
Fault : X ~ 1 sp1 N sp1 μ1 , Σ1 sp2 N sp2 μ 2 , Σ2
OTW N OTW μOTW , ΣOTW N F μ F , Σ F
Early Warning Activation
Tc
Coolant Coolant
The probability graphical model is shown in Figure 5.
OnThe Way
q, cA , T
Product Product
Reactor Reactor Coolant Coolant Pump Pump
2.4 The probability graphical model for warning system
SP1 : X ~ N μ1 , Σ1 SP1
V , ,T
VT VT
The consequences in Table 1 denote the relative importance of operating points. These values will be used to calculate the potential risk at an operating point.
X
Temperature Temperature Controller Controller (TC) (TC)
q, cAi , Ti
From From Feed Feed Section Section
class A warning class B warning = Activation class C warning class D warning
EarlyWarning
A perfect mixing condition is assumed. The mass densities of reactant and product are assumed to be the same. The liquid volume of the reactor is kept constant. The dynamic model of the CSTR is as follow.
Figure 5. Probability graphical model for warning system. Here, the variable x is the value of operating point in feasible spaces, the node SP1 is a multivariate normal distribution to describe the probability of current operating point x belongs to the operating mode SP1, the mean is μ1 , which is an operating set point, and the variance is
dc A q(cAi cA ) VkcA dt dT V C wCp (Ti T ) ( H R )VkcA UA(Tc T ) p dt V
Σ1 . The same
The CSTR is under a model predictive controller (MPC). A Simulink model is developed to simulate the dynamic process.
situation can be found to node SP2. The node OnTheWay is a node for virtual operating mode, together with SP1 and SP2, the fault distribution can be calculated in Fault node, based 666
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3.2 Gaussian mixture model
Table 2. Set points for the CSTR process
Using the CSTR model, 1461 operating points are generated in simulation. Among all variables, the two key state variables, reactor temperature and concentration are shown in Figure 7.
set point 1, sp1
set point 2, sp2
units
Temperature, Tr
311.0
373.0
K
Concentration, Cr
8.5
2.0
kmol/m3
390
Reactor temperature Tr, K
380 370
These data can be well represented by three bivariate normal distributions, corresponding to two set points and an OnTheWay virtual state. The details of these three components of Gaussian mixture model are in Table 3.
360 350 340 330
Table 3. Components in the Gaussian mixture model
320 310
0
10
20
30 t
40
50
Component 1
Component 2
Component 3
Name
Set point 1
Set point 2
OnTheWay
Means
317.3 μ1 8.1
376.8 μ2 1.8
348.4 μ OTW 4.6
Variances
20.9 1.7 Σ1 1.7 0.1
12.5 0.9 Σ2 0.9 0.1
127.0 15.8 Σ OTW 15.8 2.0
Weights
0.30
0.40
0.30
60
(a) 9
Concentration Cr, kmol/m
3
8 7 6 5 4
The weights of these components are: 0.30, 0.40 and 0.30. The total 1461 operating points can be well represented by mixing these three bivariate normal distributions with the mentioned weights.
3 2 1
0
10
20
30 t
40
50
60
(b)
From Gaussian mixture model, these operating components are separated, including the mode around set points and the virtual OnTheWay mode. In practice even if the actual set points and the virtual modes are unknown, the GMM can separate them correctly with proper data. Next, a probability graphical model for warning system is developed.
Figure 7. Reactor temperature and concentration change with time, (a) temperature, (b) concentration The correlation between temperature and concentration are shown in 8.
3
Concentration Cr, kmol/m
3
Concentration Cr, kmol/m
7
9
8
Data Set point 1 Set point 2
8
6 5 4 3
8.5
7 Data 3 of SP1
6 5
3 of OTW 3 of SP2
3
330
340 350 360 Reactor temperature T , K
370
380
310
315
320
325
1.5
1 300
390
7
2
3
1 320
8 7.5
4 2.5
2
2 1 310
Gaussian mixture model
9
9
375 310
320
380
385
330 340 350 360 Reactor temperature T , K
370
380
390
r
r
Figure 9. Gaussian mixture model of operating data
Figure 8. Concentration and temperature There are two operating modes, and the set point values are listed in Table 2.
3.3 Warning (alarm) system model The probability graphical model of the CSTR for warning system is shown in Figure 10. According to this model, every operating point can be evaluated by all operating modes, that is, calculate probabilities of operating point that belongs to these operating modes (including virtual operating modes). With these probabilities, the probability of fault is calculated. Based on this probability and the consequence severity values,
From Figure 7 and Figure 8, it can be seen there is a transient between these two set points. With data in Figure 8, the Gaussian mixed model is established to represent the distribution of these operating data, details can be found in Figure 9. X 1N μ1 , Σ1 2N μ 2 , Σ 2 3N μ 3 , Σ 3 667
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the risk can be estimated and then different warning will be activated accordingly.
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calculate the dynamic risk of the process, the result is shown in Figure 12.
X {(Tr , Cr ) | Tr [300, 400], Cr [0,10]}
100
X
90 80
OTW: X ~ N μ OTW , Σ OTW
317.3 μ1 SP1 8.1 20.9 1.7 Σ1 1.7 0.1
OnThe Way
1
1
SP2 : X ~ N μ 2 , Σ2
348.4 μ OTW 4.6 127.0 15.8 Σ OTW 15.8 2.0
SP2
70
376.8 μ2 1.8 12.5 0.9 Σ2 0.9 0.1
60 Risk
SP1 : X ~ N μ1 , Σ1
40
1
Fault
30 20
Fault : X ~ 1 N sp1 μ1 , Σ1 N sp2 μ2 , Σ2
10
N OTW μOTW , ΣOTW
Early Warning Activation
EarlyWarning Activation
50
0 PFault 0.900, 0.900 P 0.990, Fault 0.990 PFault 0.999, 0.999 PFault 1.0,
0
class A warning
0
10
20
class B warning
3.4 Risk-based warning (alarm) system
Here 800 operating point data are generated for testing, some of them with very large deviation from neither the set points operating modes nor the OnTheWay mode. These operating points are shown in Figure 13.
410 10
390
9
380
8 3
400
Concentration Cr, kmol/m
Reactor temperature Tr, K
60
3.5 Identify run away operating points
With probability graphical model, the operating data sequences can be analyzed and identified dynamically over time. Figure 11 shows the recorded data in CSTR with a runaway situation.
370 360 350 340 330
Generated test data
7 6 5 4 3 2
320 0
10
20
30 t
40
50
1
60
0 300
310
320
330 340 350 360 Reactor temperature T , K
370
380
390
r
(a)
Figure 13. Generated data for testing
9
With the established probability graphical model, the state of every operating point can be identified, and the proper early warning of different classes is issued.
8
3
7
Concentration Cr, kmol/m
50
From Figure 12 the different level of risk can be identified and the corresponding early warning is given accordingly. When the calculated risk value is greater than 50, it indicates that there is an unacceptable deviation from any operating mode (including the transient mode).
Parameter values in this probability model will be continuously updated with increasing dataset and feedbacks.
6
With the same threshold, these testing operating point data can be classified into different classes with/without virtual mode, details as follow in Table 4:
5 4 3 2
Table 4. Comparison between with/without OnTheWay mode in testing data classification
1 0
40
Figure 12. Dynamic risk in CSTR process
class D warning
Figure 10. Probability graphical model of CSTR for warning system.
310
30 t
class C warning
0
10
20
30 t
40
50
60
(b) Figure 11. Simulation with temperature and concentration run away There are totally 122 operational data here to simulate with temperature and concentration run away, and these data in sequence can be classified into different severity classes. The consequence value to every probability are considered to 668
Type
With OnTheWay mode
Without OnTheWay mode
Class A
479
350
Class B
115
52
Class C
20
12
Class D
186
386
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It can be seen from Table 4, with the OnTheWay virtual mode which determined by the proposed methodology, the transient states can be identified, and the false alarm of the fault (e.g. the class D) is reduced significantly; 200 false alarms are avoided (from 386 to 186 in Class D). The virtual mode is separated by GMM-based methodology, in this way, the number of false alarm is reduced greatly.
Industrial & Engineering Chemistry Research, 53, 11084-11095. Qin, S. J. (2012). Survey on data-driven industrial process monitoring and diagnosis. Annual Reviews in Control, 36, 220-234. Seborg, D. E., Mellichamp, D. A., Edgar, T. F. and Doyle Iii, F. J. (2010). Process dynamics and control, John Wiley & Sons. Ververidis, D. and Kotropoulos, C. (2008). Gaussian Mixture Modeling by Exploiting the Mahalanobis Distance. Signal Processing, IEEE Transactions on, 56, 27972811. Wise, B. M. and Gallagher, N. B. (1996). The process chemometrics approach to process monitoring and fault detection. Journal of Process Control, 6, 329-348. Yu, J. (2012). A nonlinear kernel Gaussian mixture model based inferential monitoring approach for fault detection and diagnosis of chemical processes. Chemical Engineering Science, 68, 506-519. Yu, J. and Qin, S. J. (2008). Multimode process monitoring with Bayesian inference-based finite Gaussian mixture models. AIChE Journal, 54, 1811-1829. Yu, J. and Qin, S. J. (2009). Multiway Gaussian Mixture Model Based Multiphase Batch Process Monitoring. Industrial & Engineering Chemistry Research, 48, 8585-8594. Zhao, C., Yao, Y., Gao, F. and Wang, F. (2010). Statistical analysis and online monitoring for multimode processes with between-mode transitions. Chemical Engineering Science, 65, 5961-5975. Zhao, S. J., Zhang, J. and Xu, Y. M. (2006). Performance monitoring of processes with multiple operating modes through multiple PLS models. Journal of Process Control, 16, 763-772.
4. CONCLUSION Multiple operating modes should be considered carefully in daily operation. The Gaussian mixture model can represent data set of operating points involving different operating modes, Furthermore, it can separate the operating modes, together with on the way virtual mode, as independent components. With these multiple components, the probability graphical model for warning system can be established to analyze the operating data and give proper warning at different safety levels. Furthermore, with the increasing number of operating data, the parameters of Gaussian mixture model and the probability graphical model can be updated, and the performance of the methodology can be improved continuously. As a result, the false alarms can be reduced greatly and the different early warning messages can be properly passed to operators based on the dynamic risk in multimode process.
REFERENCES Chen, J. and Liu, J. (1999). Mixture Principal Component Analysis Models for Process Monitoring. Industrial & Engineering Chemistry Research, 38, 1478-1488. Chen, T. and Zhang, J. (2010). On-line multivariate statistical monitoring of batch processes using Gaussian mixture model. Computers & Chemical Engineering, 34, 500507. Choi, S. W., Park, J. H. and Lee, I.-B. (2004). Process monitoring using a Gaussian mixture model via principal component analysis and discriminant analysis. Computers & Chemical Engineering, 28, 1377-1387. Feital, T., Kruger, U., Dutra, J., Pinto, J. C. and Lima, E. L. (2013). Modeling and performance monitoring of multivariate multimodal processes. AIChE Journal, 59, 1557-1569. Ge, Z., Song, Z. and Gao, F. (2013). Review of Recent Research on Data-Based Process Monitoring. Industrial & Engineering Chemistry Research, 52, 3543-3562. Hennig, C. (2010). Methods for merging Gaussian mixture components. Advances in Data Analysis and Classification, 4, 3-34. Hwang, D.-H. and Han, C. (1999). Real-time monitoring for a process with multiple operating modes. Control Engineering Practice, 7, 891-902. Ng, Y. S. and Srinivasan, R. (2009). An adjoined multimodel approach for monitoring batch and transient operations. Computers & Chemical Engineering, 33, 887-902. Ning, C., Chen, M. and Zhou, D. (2014). Hidden Markov Model-Based Statistics Pattern Analysis for Multimode Process Monitoring: An Index-Switching Scheme. 669
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Risk-based warning system design methodology for multimode processes Risk-based Risk-based warning warning system system design design methodology methodology for for multimode multimode processes processes Hangzhou Wang, Faisal Khan*, Salim Ahmed, and Syed Imtiaz Hangzhou Wang, Faisal Khan*, Salim Ahmed, and Syed Imtiaz Salim Ahmed, and Syed Imtiaz Hangzhou Wang, Faisal Khan*, Safety and Risk Engineering Group, Safety and Risk Engineering Group, Faculty of Engineering and Applied Science, Safety and Risk Engineering Group, Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL A1B 3X5, Canada Faculty of Engineering and Applied Science, Memorial University, St. John’s, NL A1B 3X5, Canada Memorial University, St. John’s, A1B 3X5, Canada (* correspondence author, phone: 709 84NL 8939 e-mail:[email protected]) (* correspondence author, phone: 709 84 8939 e-mail:[email protected]) (* correspondence author, phone: 709 84 8939 e-mail:[email protected]) Abstract: Complex chemical processes usually operate at multiple operating modes, resulting from Abstract: Complex processes operate at multiple operating modes, resulting various factors, suchchemical as changes in marketusually demand, set point modifications, and feedstock changes.from It is from Abstract: Complex chemical processes usually operate at multiple operating modes, resulting various factors, such as changes in market demand, set point modifications, and feedstock changes. Itthis is difficult to monitor a multimode process without generating significant number of false alarms. In various factors, such as changes in market demand, set point modifications, and feedstock changes. It is difficult to monitor a multimode process without generating significant number of false alarms. In this paper, system design is proposed to monitor multimode difficulta risk-based to monitor alarm a multimode processmethodology without generating significant number of false processes. alarms. In The this paper, a risk-based alarmofsystem design methodology proposed monitor processes. The methodology comprises three main steps: i) analysisis operatingto usingmultimode Gaussian mixture model, paper, a risk-based alarm system design methodology isofproposed todata monitor multimode processes. The methodology comprises of three main steps: i)modes analysis of operating datavirtual using Gaussian mixture model, ii) identification of independent operating (e.g. set points, state), and iii) methodology comprises of three main steps: i) analysis of operating data using transient Gaussian mixture model, ii) identification oftoindependent operating modes (e.g. set warning. points, virtual transient state), and iii) probabilistic model assess risk and activation of appropriate A continuous stirred tank reactor ii) identification of independent operating modes (e.g. set points, virtual transient state), and iii) probabilistic model to control assess risk and is activation of appropriate A continuous stirred tank reactor with model predictive system used to demonstrate thewarning. effectiveness of the proposed method. probabilistic model to assess risk and activation of appropriate warning. A continuous stirred tank reactor with model predictive control system is used to demonstrate the effectiveness of the proposed method. with model predictive control system is used to demonstrate the effectiveness of the proposed method. © 2015, IFAC (International Federation of Automatic Control)warning Hosting by Elsevier Ltd. All rightsmanagement; reserved. Keywords: multimode process; Gaussian mixture model; system design; alarm Keywords: multimodemodel process; Gaussian mixture model; warning system design; alarm management; probability graphical Keywords: multimode process; Gaussian mixture model; warning system design; alarm management; probability graphical model probability graphical model
1. INTRODUCTION 1. INTRODUCTION 1. INTRODUCTION Over the past decades, more and more attentions have been Over the past decades, more and more have been paid to from attentions both academia and Over the the pastprocess decades,monitoring more and more attentions have been paid to the process monitoring from both academia and industry of its monitoring indispensable role both in guaranteeing paid to because the process from academia safe and industry because of its indispensable role in guaranteeing safe operation. Complex processes operatesafe at industry because of itschemical indispensable role inusually guaranteeing operation.operating Complex chemical processes operate at multiple resulting fromusually various factors, operation. Complex modes, chemical processes usually operate at multiple operating modes, resulting from various factors, such as changes in market pointvarious modifications, multiple operating modes, demand, resultingsetfrom factors, such as changeschanges in market demand, point modifications, and feedstock (Hwang and set Han, 1999). The realsuch as changes in market demand, set point modifications, and feedstock changes (Hwang and Han, 1999). The realtime monitoring and warning of danger in multimode and feedstock changes (Hwang and Han, 1999). The realtime monitoring and warning of danger in multimode processes is a challenging problem, whichin has drawn time monitoring and warning of danger multimode processes is a challenging problem, which has drawn increasing attention recently (Zhao et al., 2010). processes is a challenging problem, which has drawn increasing attention recently (Zhao et al., 2010). increasing attention recently (Zhao et al., 2010). To resolve the issues associated with monitoring multiple To resolvemodes the issues associated with monitoring operating processes, multivariate statistical multiple process To resolve the issues associated with monitoring multiple operating modes processes, multivariate statistical monitoring (MSPM) is becoming popular due process to the operating modes processes, multivariate statistical process monitoring of (MSPM) is of becoming popularbydue to the availability large sets data generated large-scale monitoring (MSPM) is becoming popular due to the availability of large sets of data generated by large-scale chemical processes et al., Qin, 2012). MSPM availability of large(Ning sets of data2014, generated by large-scale chemical processes (Ning et al., 2014, Qin, 2012). MSPM techniques, such as partial least-squares (PLS) and principal chemical processes (Ning et al., 2014, Qin, 2012). MSPM techniques, such as partial least-squares (PLS) and principal component analysis (PCA), have (PLS) been and intensively techniques, such as partial least-squares principal component (PCA), have been have intensively investigated analysis and fruitful of applications been component analysis (PCA), have been intensively investigated of applications beena demonstrated and (Wisefruitful and Gallagher, 1996). Zhao have proposed investigated and fruitful of applications have been demonstrated (Wise and Gallagher, 1996). Zhao proposed a method based on multiple partial least-squares models demonstrated (Wise and Gallagher, 1996). Zhao proposed toa method based on multiple partial least-squares models to monitor multimodal process (Zhao et al., 2006). Also, many method based on multiple partial least-squares models to monitor multimodal process al., 2006). Also, PCA-based techniques have (Zhao been et reported. Chen andmany Liu monitor multimodal process (Zhao et al., 2006). Also, many PCA-based techniques have been reported. Chen and Liu proposed a fault detection method using mixture of PCA PCA-based techniques have been reported. Chen and Liu proposed a fault detection method using mixture of PCA models, the number of clusters are determined proposed ina which fault detection method using mixture of PCA models, in which theand number of clusters are automatically (Chen Liu, 1999). Ng and determined Srinivasan models, in which the number of clusters are determined automatically (Chen and Liu, 1999). where Ng and Srinivasan proposed an Adjoined PCA approach, a mixture of automatically (Chen and Liu, 1999). Ng and Srinivasan proposed an Adjoined PCA approach, where a mixture of PCA models are adjoined and Srinivasan, Choi proposed an Adjoined PCA(Ng approach, where a 2009). mixture of PCA modelsthe aremaximum adjoined (Ng and Srinivasan, 2009). Choi formulated likelihood principal component PCA models are adjoined (Ng and Srinivasan, 2009). Choi formulated the maximum likelihood principal component analysis (MLPCA) mixture model to monitor process. Feital formulated the maximum likelihood principal component analysis (MLPCA) mixture model to monitor process. Feital proposed a multimodal modelling and monitoring approach analysis (MLPCA) mixture model to monitor process. Feital proposed a multimodal modelling and monitoring approach based on MLPCA analysis and presented an operating modes proposed a multimodal modelling and monitoring approach based on MLPCA analysis andetpresented an operating modes identification method (Feital al., 2013). All these PCAbased on MLPCA analysis and presented an operating modes identification method (Feital et al., 2013). All these PCAidentification method (Feital et al., 2013). All these PCA-
based methods suffer drawbacks of dealing with nonbased methods suffer drawbacks dealing with nonGaussian distributed operating data in of process. based methods suffer drawbacks of dealing with nonGaussian distributed operating data in process. operating data in process. Gaussian distributed Compared to the PCA-based mixture models, advantages of Compared to mixture the PCA-based mixture includes: models, advantages of the Gaussian model (GMM) (1) the model Compared to the PCA-based mixture models, advantages of the Gaussian mixture model (GMM) includes: (1) the model structure is simple that it(GMM) is easyincludes: to understand to the Gaussian mixturesomodel (1) the and model structure is in simple so that it process, is easy to understand and to implement non-Gaussian (2) can be used structure is simple so that it is easy to understand and to to implement inmultimode non-Gaussian process,(3) (2) can handle be used to monitoring processes, implement in non-Gaussian process, (2) can can be used the to monitoring multimode processes, (3) GMM can handle the nonlinear process (Ge et al., 2013). The method can monitoring multimode processes, (3) can handle the nonlinear process industrial (Ge et al., 2013). dataset The GMM methodlocal can describe complex by several nonlinear process (Ge et al.,process 2013). The GMM method can describe complex industrial process dataset by several local linear models. To learn the Gaussian mixture model, the describe complex industrial process dataset by several local linear models. To learn the Gaussian mixture model, the Expectation-Maximization (EM) algorithm is employed to linear models. To learn the Gaussian mixture model, the Expectation-Maximization (EM) algorithm is employed to estimate the values of its parameters. GMM is promising Expectation-Maximization (EM) algorithm is employed to estimate the values of its parameters. GMM is promising method tothe monitor multimode (Ge et estimate valuesnon-Gaussian, of its parameters. GMMprocess is promising method to Choi monitor non-Gaussian, multimode process (Ge et al., 2013, et al., 2004, Yu, 2012, Yu and Qin, 2009, method to monitor non-Gaussian, multimode process (Ge et al., 2013, Choi et al., 2004, Yu, 2012, Yu and Qin, 2009, Chen2013, andChoi Zhang, Ververidis and al., et al., 2010). 2004, Yu, 2012, Yu(Ververidis and Qin, 2009, Chen and Zhang, 2010). (Ververidis Kotropoulos, 2008) and HennigVerveridis (Hennig, 2010) showed and the Chen and Zhang, 2010). Ververidis (Ververidis and Kotropoulos, 2008) and Hennig (Hennig, 2010) showed the strong ability of Gaussian mixture(Hennig, model to2010) separate different Kotropoulos, 2008) and Hennig showed the strong ability of Gaussian mixture model todeveloped separate different operating modes in process. Yu and Qin a finite strong ability of Gaussian mixture model to separate different operating process. Yu andand Qin developed a finite Gaussian modes mixturein (FGMM) the Bayesian operating modes inmodel process. Yu and Qin used developed a finite Gaussian mixture model (FGMM) and used the Bayesian inference-based (BIP)andindex for Bayesian process Gaussian mixture probability model (FGMM) used the inference-based probability index for process monitoring (Yu and Qin, 2008).(BIP) The number in a index offormodes process inference-based probability (BIP) (Yu and Qin, 2008). The number of modes in a monitoring GMM is automatically determined along with its other monitoring (Yu and Qin, 2008). The number of modes in a GMM is automatically determined along with its other parameters. GMM is automatically determined along with its other parameters. parameters. In this paper, a risk-based warning system design method In this the paper, a risk-based warning system design method using GMM is proposed to represent non-Gaussian, In this paper, a risk-based warning system design method using the GMM is proposed to represent non-Gaussian, multimode operating data and to separate different using the GMM is proposed to represent non-Gaussian, multimode operating to separate different operational modes. As adata result,and the process state (including multimode operating data and to separate different operational modes. As a result, the process state (including acceptable transient state) can be the identified operating data operational modes. As a result, processforstate (including acceptable transient state) can be identified forwhile operating data in real-time, give proper warning message minimize acceptable transient state) can be identified for operating data in give proper while minimize thereal-time, false alarms at the samewarning time. message in real-time, give proper warning message while minimize the false alarms at the same time. the false alarms at the same time. This paper proceeds as follows. First, the proposed This paper is proceeds follows. the by proposed methodology describedas Section 2First, followed a case This paper proceeds as infollows. First, the proposed methodology is described indiscussions Section 2 and followed by a case study in Section 3. Finally, conclusions are methodology is described in Section 2 followed by a case study in Section 3. Finally, discussions and conclusions are presented. study in Section 3. Finally, discussions and conclusions are presented. presented.
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2. METHODOLOGY
Max. Separated operate mode1 Separated operate mode2 Measured data Gaussian Mixed Model
Frequence
The proposed methodology of alarm management in multimode process is shown in Figure 1. The methodology is comprised of three important steps: i) analysis of operating data using Gaussian mixture model, ii) identification of independent operating modes (e.g. set points, virtual transient state), and iii) probabilistic model to assess risk and activation of appropriate warning. The details of the methodology is explained in following subsections.
0
sp1
Value
sp2
Chemical process
Figure 2. Measured values and separated operation modes Collect operational data
2.2 Identification of operating modes
Analysis data with Gaussian mixed model
In this example, there is a variable x, with two possible set point, sp1, and sp2. Also the system may be on the way from sp1 to sp2 or vice versa is considered, this is a transient mode. This situation is considered to be a normal situation, not to alarm as a false alarm. So a virtual operating mode is introduced, shown in Figure 3, to help identify the transient mode from operating point sp1 to sp2 , or vice versa. In this virtual mode, denoted as the OnTheWay mode, there is a special operating point. All transient operating trajectories frequently pass through it, and it can be a reference location to identify that the operating point is in its transient situation. Because it is a transient state, if all operating data are correctly recorded, this transient mode can be properly separated by the Gaussian mixture model.
Separate multiple operating modes
Construct OnTheWay node between every two operating modes
Analysis of operating data
Belongs to one operating mode
Update Gaussian Mixed model
Y
Add data to respond operating modes database
N Likely belongs to OnTheWay modes Y Start timer
Close timer
Add data to respond OnTheWay database
Y
Max.
Belongs to one OnTheWay mode N Timer increase by an interval
N
Frequence
Exceed Max. allowed time
N
Analysis the new operating data
Separated operate mode1 Separated operate mode2 OnTheW ay virtual mode
Y Close timer
0 Activate early warning system
sp1
OnTheW ay Value
sp2
Figure 3. Operating modes and OnTheWay virtual mode stop
2.3 Risk estimation and activation of alarm
Figure 1. Methodology for alarm management in multimode process
With the OnTheWay virtual mode, process state can be monitored in real time. Fault probability for every operating point can be calculated over time. And then activate different level of early warnings according to the probability and severity. In this method, both severity and probability are represented in terms of distances from the centers. The severity classification schematic is shown in Figure 4. With the probability and severity values, the state of the current operating point can be identified, and give proper warning if it is necessary.
2.1 Gaussian mixture model to represent multimode Let us consider a simple situation. Suppose data from normal operating situations are represented in Figure 2. All records of operating point values can be represented by Gaussian mixture model, and also can be separated into different operating modes. In this example, there are two different operating modes with set point sp1 and sp2.
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on the probability of fault and the possible consequence loss. The state of current operating point can be correctly identified, and the risk is estimated. Finally, different warnings according the calculation result are activated.
Severity classification A
B Sp1
OnTheWay
3. CASE STUDY
Sp2
C
D
A continuous stirred tank reactor (CSTR) with model predictive control system is used to demonstrate the effectiveness of the proposed method. 3.1 CSTR process description
Figure 4. Severity classification schematic, the area A is the normal operation ranges, and area D is a possible fault requiring a warning message.
The schematic of the CSTR process (Seborg et al., 2010) is shown in Figure 6.
The severity corresponds to the potential consequence; the values are assigned in Table 1. Table 1. Severity classification Classification
Consequence
Meaning
Class A
1
Normal operation
Class B
10
Deviation acceptable
Class C
50
Deviation require attention
Class D
100
Fault require warning message
Main Main Reactor Reactor
Coolant Coolant
Figure 6. Schematic of CSTR with temperature controller A liquid phase, irreversible chemical reaction takes place in the reactor where chemical species A reacts to form species B. The rate of reaction is first order with respect to component A,
sp
1
Where r is the rate of reaction of A per unit volume, k is the reaction rate constant, and cA is the molar concentration of species A.
OTW: X ~ N μ OTW , Σ OTW
OTW
Fault
r kcA
n X R feasible
SP2
SP2 : X ~ N μ 2 , Σ2
k k0 e
sp
E RT
2
The inlet stream consists of pure component A with molar concentration, cAi. A cooling jacket is used to maintain the reaction mixture at the desired operating temperature.
Fault : X ~ 1 sp1 N sp1 μ1 , Σ1 sp2 N sp2 μ 2 , Σ2
OTW N OTW μOTW , ΣOTW N F μ F , Σ F
Early Warning Activation
Tc
Coolant Coolant
The probability graphical model is shown in Figure 5.
OnThe Way
q, cA , T
Product Product
Reactor Reactor Coolant Coolant Pump Pump
2.4 The probability graphical model for warning system
SP1 : X ~ N μ1 , Σ1 SP1
V , ,T
VT VT
The consequences in Table 1 denote the relative importance of operating points. These values will be used to calculate the potential risk at an operating point.
X
Temperature Temperature Controller Controller (TC) (TC)
q, cAi , Ti
From From Feed Feed Section Section
class A warning class B warning = Activation class C warning class D warning
EarlyWarning
A perfect mixing condition is assumed. The mass densities of reactant and product are assumed to be the same. The liquid volume of the reactor is kept constant. The dynamic model of the CSTR is as follow.
Figure 5. Probability graphical model for warning system. Here, the variable x is the value of operating point in feasible spaces, the node SP1 is a multivariate normal distribution to describe the probability of current operating point x belongs to the operating mode SP1, the mean is μ1 , which is an operating set point, and the variance is
dc A q(cAi cA ) VkcA dt dT V C wCp (Ti T ) ( H R )VkcA UA(Tc T ) p dt V
Σ1 . The same
The CSTR is under a model predictive controller (MPC). A Simulink model is developed to simulate the dynamic process.
situation can be found to node SP2. The node OnTheWay is a node for virtual operating mode, together with SP1 and SP2, the fault distribution can be calculated in Fault node, based 666
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3.2 Gaussian mixture model
Table 2. Set points for the CSTR process
Using the CSTR model, 1461 operating points are generated in simulation. Among all variables, the two key state variables, reactor temperature and concentration are shown in Figure 7.
set point 1, sp1
set point 2, sp2
units
Temperature, Tr
311.0
373.0
K
Concentration, Cr
8.5
2.0
kmol/m3
390
Reactor temperature Tr, K
380 370
These data can be well represented by three bivariate normal distributions, corresponding to two set points and an OnTheWay virtual state. The details of these three components of Gaussian mixture model are in Table 3.
360 350 340 330
Table 3. Components in the Gaussian mixture model
320 310
0
10
20
30 t
40
50
Component 1
Component 2
Component 3
Name
Set point 1
Set point 2
OnTheWay
Means
317.3 μ1 8.1
376.8 μ2 1.8
348.4 μ OTW 4.6
Variances
20.9 1.7 Σ1 1.7 0.1
12.5 0.9 Σ2 0.9 0.1
127.0 15.8 Σ OTW 15.8 2.0
Weights
0.30
0.40
0.30
60
(a) 9
Concentration Cr, kmol/m
3
8 7 6 5 4
The weights of these components are: 0.30, 0.40 and 0.30. The total 1461 operating points can be well represented by mixing these three bivariate normal distributions with the mentioned weights.
3 2 1
0
10
20
30 t
40
50
60
(b)
From Gaussian mixture model, these operating components are separated, including the mode around set points and the virtual OnTheWay mode. In practice even if the actual set points and the virtual modes are unknown, the GMM can separate them correctly with proper data. Next, a probability graphical model for warning system is developed.
Figure 7. Reactor temperature and concentration change with time, (a) temperature, (b) concentration The correlation between temperature and concentration are shown in 8.
3
Concentration Cr, kmol/m
3
Concentration Cr, kmol/m
7
9
8
Data Set point 1 Set point 2
8
6 5 4 3
8.5
7 Data 3 of SP1
6 5
3 of OTW 3 of SP2
3
330
340 350 360 Reactor temperature T , K
370
380
310
315
320
325
1.5
1 300
390
7
2
3
1 320
8 7.5
4 2.5
2
2 1 310
Gaussian mixture model
9
9
375 310
320
380
385
330 340 350 360 Reactor temperature T , K
370
380
390
r
r
Figure 9. Gaussian mixture model of operating data
Figure 8. Concentration and temperature There are two operating modes, and the set point values are listed in Table 2.
3.3 Warning (alarm) system model The probability graphical model of the CSTR for warning system is shown in Figure 10. According to this model, every operating point can be evaluated by all operating modes, that is, calculate probabilities of operating point that belongs to these operating modes (including virtual operating modes). With these probabilities, the probability of fault is calculated. Based on this probability and the consequence severity values,
From Figure 7 and Figure 8, it can be seen there is a transient between these two set points. With data in Figure 8, the Gaussian mixed model is established to represent the distribution of these operating data, details can be found in Figure 9. X 1N μ1 , Σ1 2N μ 2 , Σ 2 3N μ 3 , Σ 3 667
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the risk can be estimated and then different warning will be activated accordingly.
667
calculate the dynamic risk of the process, the result is shown in Figure 12.
X {(Tr , Cr ) | Tr [300, 400], Cr [0,10]}
100
X
90 80
OTW: X ~ N μ OTW , Σ OTW
317.3 μ1 SP1 8.1 20.9 1.7 Σ1 1.7 0.1
OnThe Way
1
1
SP2 : X ~ N μ 2 , Σ2
348.4 μ OTW 4.6 127.0 15.8 Σ OTW 15.8 2.0
SP2
70
376.8 μ2 1.8 12.5 0.9 Σ2 0.9 0.1
60 Risk
SP1 : X ~ N μ1 , Σ1
40
1
Fault
30 20
Fault : X ~ 1 N sp1 μ1 , Σ1 N sp2 μ2 , Σ2
10
N OTW μOTW , ΣOTW
Early Warning Activation
EarlyWarning Activation
50
0 PFault 0.900, 0.900 P 0.990, Fault 0.990 PFault 0.999, 0.999 PFault 1.0,
0
class A warning
0
10
20
class B warning
3.4 Risk-based warning (alarm) system
Here 800 operating point data are generated for testing, some of them with very large deviation from neither the set points operating modes nor the OnTheWay mode. These operating points are shown in Figure 13.
410 10
390
9
380
8 3
400
Concentration Cr, kmol/m
Reactor temperature Tr, K
60
3.5 Identify run away operating points
With probability graphical model, the operating data sequences can be analyzed and identified dynamically over time. Figure 11 shows the recorded data in CSTR with a runaway situation.
370 360 350 340 330
Generated test data
7 6 5 4 3 2
320 0
10
20
30 t
40
50
1
60
0 300
310
320
330 340 350 360 Reactor temperature T , K
370
380
390
r
(a)
Figure 13. Generated data for testing
9
With the established probability graphical model, the state of every operating point can be identified, and the proper early warning of different classes is issued.
8
3
7
Concentration Cr, kmol/m
50
From Figure 12 the different level of risk can be identified and the corresponding early warning is given accordingly. When the calculated risk value is greater than 50, it indicates that there is an unacceptable deviation from any operating mode (including the transient mode).
Parameter values in this probability model will be continuously updated with increasing dataset and feedbacks.
6
With the same threshold, these testing operating point data can be classified into different classes with/without virtual mode, details as follow in Table 4:
5 4 3 2
Table 4. Comparison between with/without OnTheWay mode in testing data classification
1 0
40
Figure 12. Dynamic risk in CSTR process
class D warning
Figure 10. Probability graphical model of CSTR for warning system.
310
30 t
class C warning
0
10
20
30 t
40
50
60
(b) Figure 11. Simulation with temperature and concentration run away There are totally 122 operational data here to simulate with temperature and concentration run away, and these data in sequence can be classified into different severity classes. The consequence value to every probability are considered to 668
Type
With OnTheWay mode
Without OnTheWay mode
Class A
479
350
Class B
115
52
Class C
20
12
Class D
186
386
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It can be seen from Table 4, with the OnTheWay virtual mode which determined by the proposed methodology, the transient states can be identified, and the false alarm of the fault (e.g. the class D) is reduced significantly; 200 false alarms are avoided (from 386 to 186 in Class D). The virtual mode is separated by GMM-based methodology, in this way, the number of false alarm is reduced greatly.
Industrial & Engineering Chemistry Research, 53, 11084-11095. Qin, S. J. (2012). Survey on data-driven industrial process monitoring and diagnosis. Annual Reviews in Control, 36, 220-234. Seborg, D. E., Mellichamp, D. A., Edgar, T. F. and Doyle Iii, F. J. (2010). Process dynamics and control, John Wiley & Sons. Ververidis, D. and Kotropoulos, C. (2008). Gaussian Mixture Modeling by Exploiting the Mahalanobis Distance. Signal Processing, IEEE Transactions on, 56, 27972811. Wise, B. M. and Gallagher, N. B. (1996). The process chemometrics approach to process monitoring and fault detection. Journal of Process Control, 6, 329-348. Yu, J. (2012). A nonlinear kernel Gaussian mixture model based inferential monitoring approach for fault detection and diagnosis of chemical processes. Chemical Engineering Science, 68, 506-519. Yu, J. and Qin, S. J. (2008). Multimode process monitoring with Bayesian inference-based finite Gaussian mixture models. AIChE Journal, 54, 1811-1829. Yu, J. and Qin, S. J. (2009). Multiway Gaussian Mixture Model Based Multiphase Batch Process Monitoring. Industrial & Engineering Chemistry Research, 48, 8585-8594. Zhao, C., Yao, Y., Gao, F. and Wang, F. (2010). Statistical analysis and online monitoring for multimode processes with between-mode transitions. Chemical Engineering Science, 65, 5961-5975. Zhao, S. J., Zhang, J. and Xu, Y. M. (2006). Performance monitoring of processes with multiple operating modes through multiple PLS models. Journal of Process Control, 16, 763-772.
4. CONCLUSION Multiple operating modes should be considered carefully in daily operation. The Gaussian mixture model can represent data set of operating points involving different operating modes, Furthermore, it can separate the operating modes, together with on the way virtual mode, as independent components. With these multiple components, the probability graphical model for warning system can be established to analyze the operating data and give proper warning at different safety levels. Furthermore, with the increasing number of operating data, the parameters of Gaussian mixture model and the probability graphical model can be updated, and the performance of the methodology can be improved continuously. As a result, the false alarms can be reduced greatly and the different early warning messages can be properly passed to operators based on the dynamic risk in multimode process.
REFERENCES Chen, J. and Liu, J. (1999). Mixture Principal Component Analysis Models for Process Monitoring. Industrial & Engineering Chemistry Research, 38, 1478-1488. Chen, T. and Zhang, J. (2010). On-line multivariate statistical monitoring of batch processes using Gaussian mixture model. Computers & Chemical Engineering, 34, 500507. Choi, S. W., Park, J. H. and Lee, I.-B. (2004). Process monitoring using a Gaussian mixture model via principal component analysis and discriminant analysis. Computers & Chemical Engineering, 28, 1377-1387. Feital, T., Kruger, U., Dutra, J., Pinto, J. C. and Lima, E. L. (2013). Modeling and performance monitoring of multivariate multimodal processes. AIChE Journal, 59, 1557-1569. Ge, Z., Song, Z. and Gao, F. (2013). Review of Recent Research on Data-Based Process Monitoring. Industrial & Engineering Chemistry Research, 52, 3543-3562. Hennig, C. (2010). Methods for merging Gaussian mixture components. Advances in Data Analysis and Classification, 4, 3-34. Hwang, D.-H. and Han, C. (1999). Real-time monitoring for a process with multiple operating modes. Control Engineering Practice, 7, 891-902. Ng, Y. S. and Srinivasan, R. (2009). An adjoined multimodel approach for monitoring batch and transient operations. Computers & Chemical Engineering, 33, 887-902. Ning, C., Chen, M. and Zhou, D. (2014). Hidden Markov Model-Based Statistics Pattern Analysis for Multimode Process Monitoring: An Index-Switching Scheme. 669