Detection and quantification of valve stiction based on normality test and Hammerstein system identification Yonatan C. A. Hutabarat, Awang N. I. Wardana, and Widya Rosita
Citation: AIP Conference Proceedings 1755, 170002 (2016); View online: https://doi.org/10.1063/1.4958604 View Table of Contents: http://aip.scitation.org/toc/apc/1755/1 Published by the American Institute of Physics
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Detection and Quantification of Valve Stiction Based on Normality Test and Hammerstein System Identification Yonatan C.A. Hutabarat a), Awang N.I. Wardanab), Widya Rosita Department of Nuclear Engineering and Engineering Physics, Universitas Gadjah Mada, Yogyakarta, Indonesia Corresponding author: a)
[email protected] b)
[email protected] Abstract. The presence of static friction or stiction in a valve can lead to poor performance in industrial automation and control system. This paper presents a method to detect and quantify stiction based on normality test and Hammerstein system identification. Detection and quantification are showed by the ݂௦ and ݂ௗ parameters, where the value of ݂௦ and ݂ௗ greater than 0 indicate the valve suffer from stiction. The proposed method is implemented to a confirmed sets of industrial data as a validation. The result show that the proposed method can accurately detect the presence of stiction and distinguish it to other problem in control loops.
INTRODUCTION Automation and control system is one of the major aspects in the process industry. A control system in process industry has a function to maintain process parameters at a certain desired value in order to maintain the output of the process at the desired specification. Poor performance in the control system may lead to a certain loss in output quality and lower the efficiency of energy and resources. Nonlinearity is one cause of the poor performance of the control system. Nonlinearity in the control system can be caused by actuator nonlinearity, valve nonlinearity, and nonlinearities in the process. One form of valve nonlinearity is the existence of stiction. Stiction is a condition where the valve stem resists movement or not giving a response to the output signal from the controller. Stiction is a general problem in spring-diaphragm actuated control valve [1]. This type of control valve is widely found in the process industry. Stiction can be detected using several methods. This method is divided into two major groups, first is a shape based method such as curve fitting method and relay [2], and second is a correlation based method such as model-based method and decomposition method [3]. Method presented in this paper is a correlation based method, i.e. Hammerstein model. Hammerstein model consists of a nonlinear static block, i.e. stiction, followed by a linear dynamic block, i.e. the process. The input to this system is controller output signal (OP), and the output will be the process variable (PV). This model will provide the static friction coefficient (݂௦ ) and dynamic friction coefficient (݂ௗ ) as stiction parameters. Normality test is added before Hammerstein model analysis as a filter to distinguish between the presence of nonlinearity and linear problem in control loops such as external oscillatory disturbances and tightly tuned controller. The proposed method is validated using a various set (PV and OP) of industrial valve data that have been confirmed the existing problem present on each set of data.
HAMMERSTEIN MODEL IN CONTROL LOOP Hammerstein system identification is one of the nonlinear system identification which model the system into two blocks, a nonlinear static block and followed by a dynamic linear time invariant (LTI) block. Figure 1 explains the simplified control system diagram with stiction problem.
Advances of Science and Technology for Society AIP Conf. Proc. 1755, 170002-1–170002-6; doi: 10.1063/1.4958604 Published by AIP Publishing. 978-0-7354-1413-6/$30.00
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ε
Hammerstein system
Linear element
Disturbances
Nonlinear element SV Controller
OP
Stiction
MV
PV Process
Valve dynamics
Measurement element
FIGURE 1. Hammerstein system in control loop
Stiction Model There are two major classifications of stiction modelling, i.e. physical modelling and data-driven modelling. Physical modelling is based on the physical phenomenon that derived into mathematical equations with a number of parameters. The physical model is the closest to true model as the system is directly derived into mathematical equations. The disadvantage of using physical model is that the requisite of finding parameters from the equations, such as the mass of the system and friction force. That makes physical model infeasible to practical industrial cases. Data-driven modelling is a practical model that only use routine data in the industry such as OP and PV. There are several data-driven models available, such as He’s stiction model, Kano’s stiction model, and Choudhury’s stiction model [2]. The data-driven model that is used in this research is He’s 3 parameters stiction model as this stiction model is the closest to the physical model [4]. This model algorithm is presented in Fig 2. Normalised OP ݑሺݐሻ
݁ሺݐሻ ൌ ݑሺݐሻ െ ݑ௩ ሺ ݐെ ͳሻ
Yes
ȁ݁ሺݐሻȁ ݂௦
ݑ௩ ሺݐሻ ൌ ݑ௩ ሺ ݐെ ͳሻ ܭሺ݁ሺݐሻ െ ݊݃݅ݏ൫݁ሺݐሻ൯݂ௗ ሻ
No
ݑ௩ ሺݐሻ ൌ ݑ௩ ሺ ݐെ ͳሻ
FIGURE 2. Flow diagram of He’s 3 parameter model [4]
Figure 2 shows all variables are dimensionless. Therefore only ordinary algebra is done. ݑሺݐሻ is OP, ݁ሺݐሻ is the difference between OP at time t and manipulated variable (MV) or often called valve position (VP) at time t-1. Valve position will change if the value of ݁ሺݐሻ is greater than the static friction band fs, otherwise valve will stay at the last position. There is a certain amount of overshoot when the valve travel, and it accounted by ܭwhich is a constant approximately equal to 1.99 [4].
Process Model The process is the linear part of Hammerstein model as seen in Fig 1. The structure of the model is in the form of Auto-Regressive Moving Average eXogeneous input (ARMAX) model. The discrete equation of ARMAX model is given by Eq. (1) to Eq. (4) [5]. ܣሺି ݍଵ ሻݕሺݐሻ ൌ ି ݍఛ ܤሺି ݍଵ ሻݑሺݐሻ ܥሺି ݍଵ ሻߝሺݐሻ (1) (2) ܣሺି ݍଵ ሻ ൌ ͳ ܽଵ ି ݍଵ ܽଶ ି ݍଶ ڮ ܽ ି ݍ ܤሺି ݍଵ ሻ ൌ ܾ ܾଵ ି ݍଵ ܾଶ ି ݍଶ ڮ ܾ ି ݍ (3)
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ܥሺି ݍଵ ሻ ൌ ͳ ܿଵ ି ݍଵ ܿଶ ି ݍଶ ڮ ܿ ି ݍ (4) Equation 1 denotes that ߬is input-output time delay, and ߝሺݐሻ is noise model. Equation 2 denotes that ܽ and ݊ are the constant and order for ܣrespectively. Equation 3 denotes that ܾ and ݉ are the constant and order for ܤrespectively. Equation 4 denotes that ܿ and are the constant and order for ܥrespectively, while ି ݍ ݕሺݐሻ is backwards operation, i.e. ି ݍ ݕሺݐሻ ൌ ݕሺ ݐെ ݅ሻ.
STICTION DETECTION AND QUANTIFICATION METHOD The method of stiction detection and quantification presented in this paper is a combination of PV normality test and Hammerstein system identification. Flowchart of the proposed method is presented in Fig 3. Data : PV, OP
PV Normality Test
No
Yes
ଶ ܤܬ ߯ఈǡଶ
(Gaussian)
(Non-Gaussian) Hammerstein modelling
Possible cause(s) : - External disturbance(s) - Tightly tuned controller - Other linear problem Yes
݂௦ Ͳ and ݂ௗ Ͳ
Check heck for Saturation
Yes
No
No Stiction
VP >100 or VP < 0
Saturation / Deadzone
No
Stiction
FIGURE 3. Decision making of the proposed method
Figure 3 conclude that there are 4 possible conclusions from the proposed method, i.e. stiction, saturation / dead zone, no stiction, and linear problem.
PV Normality Test PV normality test is needed to determine whether the process is normally distributed. A normally distributed process indicate that the process is natural and stiction detection technique is not needed as the problem itself come from the linear problem, i.e., external disturbance, tuning problem. Normality test presented in this paper is based on the measurement of skewness and kurtosis of series of PV. The test itself is known as Jarque-Bera (JB) test [6]. JB test is defined in Eq (5) while skewness and kurtosis are defined in Eq. (6) and Eq. (7) respectively.
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ଵ
ଵ
ܤܬൌ ݊ ቀܵ ଶ ሺܭ െ ͵ሻଶ ቁ
ܵ ൌ
ସ
భ σ ሺ௫ ି௫ҧ ሻయ సభ యൗ భ మ ሺ௫ ି௫ҧ ሻయ ቁ ቀ σ సభ భ σ ሺ௫ ି௫ҧ ሻర సభ మ భ ቀ σసభሺ௫ ି௫ҧ ሻమ ቁ
ܭ ൌ
(5) (6) (7)
Eq. (5) to Eq. (7) denotes that ݔ is the series of PV, ݔҧ denotes the mean of PV, ݊ denotes the total data, ܵ denotes the skewness, ܭ denotes the kurtosis, ܤܬis the value of JB test. The conclusion of this test is based on chi-square distribution with two degrees of freedom at certain significance level α. Null hypotesis (H0) will be PV is normally distributed. H0 is fullfilled if ܤܬis less or equal to the chi-square distribution at certain significance level α ( ܤܬ ଶ ଶ ߯ఈǡଶ ). Significance level used in this research is 1% (α=0.01), thus the value of ߯Ǥଵǡଶ will be 9.21.
Hammerstein Modelling Hammerstein modelling is the key step of the stiction detection and quantification method used in this research. The output of the modelling will be ݂௦ and ݂ௗ parameters that will be used to determine whether the valve suffer from stiction. The first step in modelling is to detrend the PV and OP. Detrend is needed to obtain a stationer PV and OP data. Next step is to normalize the PV and OP into a range of 0 to 1. Normalizing data is needed to rank the stiction level on each valve easily. The third step is the time delay estimation between the PV and OP and ARMAX order estimation. Both of this process is done by using Akaike’s Information Criterion (AIC) [7]. To estimate the time delay, a fixed ARMAX model of ݊ ൌ ͵ and ݉ ൌ ൌ ʹ, ARMAX(3,2,2,τ) is used [8]. After that, the ARMAX order ݊ǡ ݉ǡ is searched using AIC and will be used as the process model. The ARMAX order approximation will be constrained only until third order for computational efficiency. AIC is defined in Eq. (8), where n is the total data used, y is the true output, yp is the prediction of output, and K is the total parameters used in the model. ܥܫܣൌ ݊ ൬
σ సబ൫௬ି௬ ൯
మ
൰ ʹܭ
(8)
Next step is to generate a grid and grid boundary for ݂௦ and ݂ௗ . Grid and the boundary are defined in Eq. (9) to Eq. (12) [9], where ܵ௫ denote the OP span, ܵ is the sum of ݂௦ and ݂ௗ or known as deadband and stickband parameter, ܬis the difference between ݂௦ and ݂ௗ or known as slip jump parameter. ݂ ݏ ݂݀ ܵ௫ ݂݀ െ ݂ ݏ Ͳ ଵ ݂݀ ܵ௫ ଶ ܵǡ ܬǡ ݂ݏǡ ݂݀ Ͳ
(9) (10) (11) (12)
Grid is created in 2.5% resolution [10]. Each grid is evaluated to obtain a VP data. The VP and PV will be the input and output respectively to process model to determine the ARMAX model of the process. After the process model is found, VP will be inputted to the process model to obtain the Process Variable prediction (PV prediction) data. The conclusion of Hammerstein modelling is given by Mean Squared Error (MSE) from PV and PVprediction in Eq. (13), where ݊ is the total data. The smallest value of MSE means that the model prediction is the closest to the true model, thus the݂௦ and ݂ௗ parameters contained in the model prediction are the stiction parameters. ଵ
ܧܵܯൌ σୀሺܸܲ െ ܸܲௗ௧ ሻଶ
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(13)
If the stiction is detected using the Hammerstein model, the final step is to check if saturation exists on the valve to distinguish nonlinearity caused by stiction and nonlinearity caused by valve saturation or dead zone. VP data along with ݂௦ and ݂ௗ parameters are used to predict whether the saturation exist.
IMPLEMENTATION TO INDUSTRIAL CASE DATA The proposed method is needed to be validated by implementing it to the confirmed sets of industrial data. There are 6 sets of industrial case data that will be presented in this paper. All of these data are obtained in [2], consists of pulp and paper (PAP) industry data and chemical (CHEM) industry data. Computation is done using Intel® Core™ i3 1.9 GHz Processor with 6 GB RAM. The result of implementing the proposed method to the industrial case data is presented in Table 1.
PAP2
Controlled variable Flow
PAP4
Concentration
Loop
TABLE 1. Result of the proposed method with validation Data CPU ࡶ ࢌ࢙ ࢌࢊ Conclusion size time (s) 1196 46.35 0.15 0.15 36.02 Stiction 1196
122.09
0
0
31.72
No Stiction
PAP9 Temperature 1800 CHEM4 Level 200 CHEM6 Flow 650 CHEM21 Flow 721 Note : NC = Not Calculated
134.23 5.75 40.39 7.39
0 NC 0.1 NC
0 NC 0.1 NC
47.23 0.07 17.52 0.09
No Stiction Gaussian Stiction Gaussian
Validation Stiction Deadzone, No Stiction No Stiction Tuning Problem Stiction Disturbance (likely)
Discussion Table 1 shows that the proposed method can accurately give the right conclusion to every set of the industrial data. Stiction is confirmed in PAP2 and CHEM6 with only dead band exist (ܵ ൌ ͲǤ͵ for PAP2 and ܵ ൌ ͲǤʹ for CHEM6), ܬൌ Ͳ in both loops. A contour map of 1/MSE, valve signature curve, and OP-VP comparison are presented in Fig 4 to easily differentiate what types of stiction exist in valve and understand how valve travel under stiction problem.
(a)
(b)
(c)
FIGURE 4. PAP2 under stiction condition (ܵ ൌ ͲǤ͵ǡ ܬൌ Ͳ), (a) Contour map of 1/MSE (b) Valve signature curve (c) Comparison between actual OP and VP prediction
Figure 4 (a) gives the information about what types of stiction [9] exist in the valve. Area i is where only the dead band exist (݂௦ ൌ ݂ௗ ሻ. Solution to PAP2 is given by the box dotted line under area i. Area ii is where only stick and slip jump exist (݂ௗ ൌ Ͳ ) Area iii is where deadband with stick and slip jump exist (݂௦ ݂ௗ ). Figure 4 (b) visualize the ideal valve signature for ܵ ൌ ͲǤ͵ǡ ܬൌ Ͳ. Point A describe the initial position of valve. The valve will start to move at point B, i.e. after OP has changed about 30% of the total span. If the difference between current OP and previous OP under 30%, valve will stay at the previous position. Figure 4 (c) visualize the OP and the VP prediction under the stated stiction condition. It can be seen that even though the OP send a signal to open valve at 21.5 %, the predicted actual valve position can only reach 20.5 % opening. The same approach can be done to interpret other loop under stiction condition.
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Both of CHEM4 and CHEM12 have a Gaussian PV distribution shown by the value of ܤܬ, which less than 9.21. The validation data show that CHEM4 has a tuning problem, while CHEM12 is likely to have a disturbance. It can be concluded that the proposed method give the same conclusion with the validation even though still can not differentiate between tuning and disturbance causes. No stiction is confirmed in PAP4 and PAP9 while the validation result shows that PAP4 is also suffering from dead zone. Using the VP data of PAP4 presented in Fig 5 conclude that the PAP4 also may reach and crossed the saturation line of the valve, i.e. fully closed (red line), at a certain point.
FIGURE 5. Indication of valve saturation in PAP4
CONCLUSION The proposed method consists of PV normality test and Hammerstein system identification, with ܤܬtest as the method to test the normality of PV, He’s 3 parameter model is used as stiction model, and ARMAX structure is used as process model. Time delay between PV and OP and ARMAX order estimation is done by using AIC, while stiction parameters are search by grid search technique using 2.5% grid resolution. The result of implementing the proposed method to six sets of confirmed industrial data shows that the proposed method can accurately detect and quantify stiction and also distinguish it with other nonlinear problem, i.e. saturation, as well as the linear problem, i.e. tuning and disturbance. The future work of this research is to find the suitable optimization technique such as simulated annealing in searching stiction parameter and ARMAX order estimation to achieve more efficiency in computation.
REFERENCES 1.
M. A. A .S. Choudhury, S. L. Shah and N. F. Thornhill, Diagnosis of Process Nonlinearities and Valve Stiction (Springer, London, 2008). 2. M. Jelali and B. Huang, Detection and Diagnosis of Stiction in Control Loops (Springer, London, 2010). 3. A. N. I. Wardana, “A Method for Detecting the Oscillation in Control Loops Based on Variational Mode Decomposition”, in Proceeding of 2015 International Conference on Computer, Control, Informatics and it’s Application, (IEEE, Piscataway, NJ, 2015), pp 181-186. 4. Q. P., He and J. Wang, Industrial & Engineering Chemistry Research 53, 12010-12022 (2014). 5. F. Ding, and T. Chen, Automatica 41,1479-1489 (2005). 6. T. Thadewald, and H. Büning, Journal of Applied Statistics 34, 87-105 (2007). 7. S. Hu, Akaike Information Criterion. (Center for Research in Scientific Computation, North Carolina, 2007). 8. M. Jelali, Journal of Process Control 18, 632-642 (2008). 9. K. H. Lee, Z. Ren, and B. Huang, Novel Closed-Loop Stiction Detection and Quantification Method via System Identification. in Proceeding of 2008 ADCONIP Conference, pp. 4-7. 10. Y. C. A. Hutabarat, “Application of Hammerstein System Identification for Control Valve Stiction Detection”, B.Eng Thesis,Universitas Gadjah Mada, 2015.
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