An Improved Diagnostic Tool for Control Valve Stiction based on

Subscriber access provided by University of Rochester | River Campus & Miner Libraries

Process Systems Engineering

An Improved Diagnostic Tool for Control Valve Stiction based on Nonlinear Principle Component Analysis Weng Kean Teh, Haslinda Zabiri, Yudi Samyudia, Suraj J. Sean, Bashariah Kamaruddin, Ahmad Azharuddin Azhari Mohd Amiruddin, and Nasser M. Ramli Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b01012 • Publication Date (Web): 22 Jul 2018 Downloaded from http://pubs.acs.org on July 29, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

An Improved Diagnostic Tool for Control Valve Stiction based on Nonlinear Principle Component Analysis Weng Kean Teh1, Haslinda Zabiri*1, Yudi Samyudia2, Sean S. Jeremiah1, Bashariah Kamaruddin1, Azhari A. A. Mohd Amiruddin1, Nasser M. Ramli1. 1

Department of Chemical Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610 Perak, Malaysia 2

School of Applied Science, Technology, Engineering and Mathematics, Universitas Prasetiya Mulya, BSD City, Tangerang 15339 Indonesia

Keywords-Stiction, NLPCA, Autocovariance, Detection.

ABSTRACT: Control valves suffer from wear and aging as the valves open and close. Such continuous movements result in many operational issues, and one of the widely known problems is stiction nonlinearity. Stiction results in inferior quality of the products, large rejection rates, increased energy consumption and reduced profitability. In this paper, a simple algorithm that combines preprocessing and post-processing as well as average crossing autocovariance (AC) together with the nonlinear principal component analysis (NLPCA) is investigated. The results obtained from the simulated and industrial case studies show that the proposed NLPCA-AC method has favorable proficiencies for control valve stiction detection.

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 51

I. INTRODUCTION There are typically hundreds of control loops consisting of a variety of control valves in a process plant 1. As the final control element in any control loops, control valve plays a vital role in ensuring the quality of the products and the well-being of the key assets of the plant 2. Even though it is timeconsuming 3, its operation must be maintained at the highest level due to the increase in environmental, societal and competitive requirements, exacerbated by the lack of adequate training and experience of staff in process control troubleshooting 4. In general, control valves are manipulated by the use of low energy input signals 5. Due to the continuous mechanical movements, the valve tends to deteriorate due to wear and aging. As a result, oscillatory problems like stiction, deadband, hysteresis, saturation, and backlash will ensue. Oscillatory problems will result in inferior quality of the products, substantial rejection rates, increased energy utilization and reduced profitability 6. Among all these problems, the most widespread and long-standing valve problem is stiction. It has been reported that 20% to 30% of oscillatory problems in process loops are attributable to stiction 7. However, stiction problems are trickier to detect as it can be misperceived with other sources of malfunctions such as erroneous controller tuning, the manifestation of external disturbances, multi-loop interactions, and other valve internal problems 8. The definite solution for a sticky valve is to execute maintenance work on the equipment 9. Nevertheless, this is seldom achievable in a running plant due to operational cost and safety considerations. An adequate mitigation of the stiction phenomenon will ensure a high-level operation of the control loops, an extended life expectancy of control valves and the diminution of maintenance cost 10

. Hence, the detection of control valve stiction is imperative for any such mitigation efforts to take

place.


Page 3 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Various methods for stiction detection have been reported in the literature. According to Jelali and Huang

11

, the stiction detection methods can be broadly categorized into four main categories: cross-

correlation function-based

12

, limit cycle patterns-based

13-15

, nonlinearity detection based

16-17

, and

waveform shape-based 18-20. Other forms of stiction detection methods are model-based method 10, 21 and other miscellaneous approaches

22-23

. However, as highlighted in Section II, different techniques show

various and even inconsistent results. Hence, the demand for an accurate stiction detection method is still an open research area. In this paper, a simple approach for stiction detection in control valves based on Nonlinear Principal Component Analysis (NLPCA)

22

is proposed. The efficiency of the proposed method is validated by

simulation case studies and benchmark industrial data sets from various industries in which loop conditions are known. Furthermore, a comparison of the proposed method with other published methods on well-known benchmark data obtained from various industrial control loops 11 is also presented. The rest of the paper is organized as follows: Section II presents the motivation of the current work, Section III provides the explanation on control valve stiction and the description of theories used in this paper. Section IV discusses on the proposed methodology adopted, and finally results and discussion are presented in Section V.

II. MOTIVATION OF RESEARCH Although various methods for stiction detection have been reported, a simple comparison of the methods mentioned in the previous section (as shown in Table 1) clearly indicated that different techniques show various and even inconsistent results 8. Hence, the demand for an accurate stiction detection method is highly relevant. NLPCA, in particular, is no stranger to stiction detection. NLPCA has been used by Zabiri and Ramasamy

22

to detect stiction through an index that they have developed. The unique shape of the



Page 4 of 51

signals caused by stiction and other sources of malfunctions are used. Along with the coefficient of resolution, the index simultaneously detects the presence of stiction and gauges the degree of nonlinearity. In spite of this, their method has certain limitations such as the need for many ensemble runs per data set to obtain an accurate reading of the unique shapes or curvatures and the requirement of a large quantity of raw data for it to operate accurately. The proposed method aims to improve the previous method by addressing these two flaws. In this paper, an alternative approach based on NLPCA is investigated, which combined preprocessing, post-processing and average crossing of the autocovariance by Thornhill 24. Processing of signal before and after testing detection methods was advocated by Zakharov, et al. 25 and Garcia, et al. 26

. The processing step is done to rectify noise, outliers, missing data, and magnitude problems. A close

observation on Figure 1 on the plot of NLPCA output versus time from a simple simulated data shows that the loop affected by stiction has a persistent oscillating behavior with constant amplitude. Thus, the average crossing of the autocovariance by Thornhill, et al. 24 is used in this paper to evaluate the NLPCA output and provides a decision on whether the loop has stiction or not. Please note that Figure 1 is generated from the simulation case study described in Section V in this paper, without any preprocessing or post-processing steps. Moreover, Zabiri and Ramasamy

22

reported that the resulting curvature from

the NLPCA output of 30 runs have to be scrutinized before it can be directly quantified via an INC index. On the other hand, the proposed method developed in this paper is able to evaluate the NLPCA output in a completely automated manner. Another main dissimilarity between the usage of NLPCA in this paper and that in Zabiri and Ramasamy’s paper

22

is in the utilization of the input and output variables. The

requirement of a curvature as an indication of stiction in the work of Zabiri and Ramasamy 22 is the main reason why such method necessitates a large quantity of data for it to operate accurately. While Zabiri


Page 5 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and Ramasamy 22 used both controller output, OP and process variable, PV, as inputs to the NLPCA, the work in this paper utilizes PV data only. Thus, this also contributes to the relatively smaller amount of data required for the proposed method to run. Furthermore, the five-layer feed-forward auto-associative neural network proposed in this paper follows a structure of 1-3-2-3-1 neurons per layer compared to the original 2-3-1-3-2 structure as done by Zabiri and Ramasamy 22.

Table 1. Comparison of selected stiction detection techniques on benchmark data of Jelali and Huang 11. LOOP NAME

STICTION?

BIC

CORR

HIST

RELAY

CURVE

AREA

HAMM 2

HAMM 3

SLOPE

ZONES

CHEM 1

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

CHEM 2

YES

YES

YES

YES

YES

YES

NIV

YES

YES

NO

NO

CHEM 3

NO

NO

YES

NO

YES

YES

NO

NO

NO

YES

YES

CHEM 4

NO

NA

NIV

NO

NO

NO

NIV

NO

YES

NO

UNC

CHEM 5

YES

NA

UNC

YES

YES

YES

NIV

YES

YES

UNC

UNC

CHEM 6

YES

YES

UNC

YES

UNC

YES

NO

YES

YES

YES

YES

CHEM 10

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

CHEM 11

YES

YES

UNC

NO

YES

NO

YES

YES

YES

YES

UNC

CHEM 12

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

CHEM 13

NO

NO

NO

NO

NO

NO

NO

NO

YES

NO

NO

CHEM 14

NO

YES

YES

YES

YES

YES

NIV

YES

YES

UNC

NO

CHEM 16

NO

YES

YES

YES

YES

YES

NIV

YES

NO

UNC

YES

CHEM 23

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

YES

CHEM 24

YES

YES

YES

YES

YES

YES

NO

YES

YES

YES

YES

CHEM 26

YES

YES

XX

YES

YES

YES

YES

YES

YES

YES

YES

CHEM 29

YES

YES

YES

UNC

YES

NO

NO

YES

YES

NO

NO

CHEM 32

YES

YES

UNC

NO

YES

NO

NO

YES

YES

YES

NO

CHEM 33

NO

YES

NO

YES

UNC

UNC

NIV

YES

YES

NO

NO

CHEM 58

NO

NO

NA

NA

YES

NA

NIV

YES

YES

NA

NA

MIN 1

YES

YES

UNC

YES

YES

YES

YES

YES

YES

YES

YES



Page 6 of 51

PAP 2

YES

YES

YES

NO

YES

UNC

YES

YES

YES

NO

NO

PAP 4

NO

YES

NO

NO

YES

UNC

YES

YES

YES

UNC

NO

PAP 5

YES

YES

YES

YES

YES

YES

NO

NO

NO

YES

YES

PAP 7

NO

NO

NO

YES

YES

UNC

YES

YES

NO

UNC

NO

PAP 9

NO

YES

NO

NO

NO

NO

NO

NO

YES

NO

NO

Symbols: YES: stiction, NO: no stiction, UNC: uncertain, NA: not applicable to data set, XX: not applicable to that kind of loop, NIV: verdict not issue, POW: power plants, CHEM: chemical plants, PAP: pulp and paper mills, BAS: commercial building, MIN: mining, MET: metal processing, BIC: Bicoherence and ellipse-fitting technique 6, 27, CORR: Cross-correlation-based method 12, HIST: Histogram-based method 28, RELAY: Relay technique 20, CURVE: Curve-fitting method 18, AREA: Area-peak-based method 29, HAMM2: Hammerstein-model-based technique 30, HAMM3: Hammerstein-model-based method 31, SLOPE: Slope method 32, ZONES: Zones method 32.

(A)

(B)

(C)

(D)


Page 7 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. Raw NLPCA analysis: (A) Graph of PV vs Samples in a Well-Tuned Controller, (B) Graph of PV vs Samples in a Controller with Excessive Integral, (C) Graph of PV vs Samples in a Controller with External Oscillatory Disturbance, and (D) Graph of PV vs Samples of a Controller with Stiction.

III. DEFINITION AND THEORIES A. STICTION Control valve stiction is a phenomena where the valve stem is unable to move when force is exerted on it due to static friction. According to Choudhury, et al.

33

, stiction is defined as a “property of an

element such that its smooth movement in response to a varying input is preceded by a sudden abrupt jump called the ‘slip-jump’. Slip-jump is expressed as a percentage of the output span. Its origin in a mechanical system is static friction which exceeds the friction during smooth movement”. As stated by ISA, stiction is gauged by computing the difference between the initial and final positions of the valve necessitated to overcome stiction. For example, 3% of stiction means that when the valve gets stuck, it will only start moving after the cumulative change of control exceed 3%34. Stiction can be illustrated in the phase plot of valve output (MV) vs valve input (OP) as shown in Figure 2 as follows: 1. 2. 3. 4.

(A-C) - The OP increases until it is able to overcome the deadband and stickband. (C-D) - Once it overcomes the deadband and stickband, the valve will have a sudden jump. (D-E) - The valve will continue moving until it stops and sticks again. (E-F-G-A) - The cycle is repeated when controller output changes direction.



Page 8 of 51

Figure 2. Phase Plot of Stiction (adapted from Zabiri and Ramasamy 22)

B. NLPCA NLPCA is a natural nonlinear generalization of principle component analysis (PCA) for feature extraction and was introduced in the early 1990s by Kramer 35. This neural-network based generalization of PCA permits nonlinear mapping between the original and the reduced dimensional spaces. NLPCA has been shown to operate satisfactorily in characterizing the lower-dimensional nonlinear structure of the data

35-37

. The applications of NLPCA can be found in chemical engineering, psychology, image

compression and climate data processing, oceanographic data, environmental systems, periodic and wave phenomena 37-40. NLPCA causes arbitrary nonlinear mapping from ℜm to ℜp. A more detailed account on NLPCA can be found in Zabiri and Ramasamy’s paper 22. Consider a mapping of the NLPCA in (1).

1

In this equation, f is a general nonlinear vector function that consists of p individual nonlinear functions; f = (f1, f2… fp) that is equivalent to the columns of P, such that, if Ti represents the ith element of T,


Page 9 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2

The second nonlinear vector function g = (g1, g2… gm) causes the reconstruction of the original data: ′

3

Subsequently, the missing information is calculated by e = X − X', and the functions f and g are selected to minimize e. For a more detailed explanation, please refer to Kramer’s paper 35. A five-layer auto-associative feed-forward neural network is used by Kramer 35 for this method. Each layer in the neural network is made of a dissimilar number of processing elements. The data is transmitted in a feed-forward direction layer-by-layer from the input to the output. If y(i)j is the output of the jth neuron of the ith layer, then

∑

+

is the output of the kth neuron of the (i +1) th layer. The elements of

vectors

4

are the weights, and the

are the biases.

The weights and biases are parameters that can be regulated. The transfer function for the (i +1) th layer is given by . Most layers use either a nonlinear or a linear transfer function

41

. Conversely,

the mapping and demapping layers must have nonlinear transfer functions for the network to have the capability of modeling arbitrary nonlinear functions in f and g. They may or may not have identical number of neurons 13.



Page 10 of 51

Figure 3. A general framework for a five-layer feed-forward auto-associative neural network used to perform NLPCA (adapted from Zabiri and Ramasamy 22) Figure 3 shows the general design of the five-layer neural network for the NLPCA method. The neural network is made of three hidden layers. The number of neurons in the bottleneck layer can be increased to obtain a better dimensional structure. The weights and biases are optimized using the Levenberg-Marquardt algorithm until the sum of squared differences, E of network input, X and output, X‘ is minimized as in (5), ( '

% ! ∑&'# ∑"

# $

5

where n is the number of observations, m is the number of input/output variables, p is the number of neurons in the bottleneck layer, j denotes the neuron in the hidden layer and i denotes which hidden layer the neuron is in. It is called auto-associative because the network is trained to be as close as possible with the input data itself 13, 41.

C. AUTOCOVARIANCE If stiction exists, the NLPCA output has a regular or persistent oscillatory time trend. This trend can be used to detect the presence of stiction through the help of autocovariance method. There are generally


Page 11 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


two average crossings for each oscillation, and the interval between the average crossings can be computed using (6),

*+,-./01 × 3' ± 5' 6 (

6

where ' is the mean period and 5' a random variation in the period. The standard deviation of the period is 8 ' 2 × &9:;? . An oscillation is deemed to be constant if the standard deviation of the period is less than one-third of the mean value, as shown in (7). If the value of R is above than 1, this means that the loop is constantly oscillating. The threshold value for R has a basis in statistics 42.

8C

@ × B F A D EC

7

D. PREPROCESSING AND POST-PROCESSING METHODS Industrial data tends to plagued with all kind of problems ranging from noises to external disturbances. Therefore, in order to obtain reliable data for stiction detection, the preprocessing and post-processing steps are required. As shown in Dambros, et al.

43

paper, the preprocessing and post-processing can

enhance the capabilities of the stiction detection techniques. However, the use of signal preprocessing must be well thought-out, since an incorrect procedure may lead to signal degradation

32, 44

and,

consequently, the erroneous diagnosis of the oscillation cause. The preprocessing and post-processing methods considered in this paper are as shown in Figure 4.



Page 12 of 51

WAVELET TRANSFORM

NOISE

STANDARD DEVIATION OUTLIERS

Z-SCORE MADe

PRE/POST PROCESSING

ARITHMETIC IMPUTATION REGRESSION IMPUTATION LAST OBSERVATION CARRIED FORWARD MIN-MAX NORMALIZATION

MISSING DATA

MAGNITUDE Z-SCORE NORMALIZATION

Figure 4. Preprocessing and Post-Processing Methods

1) DENOISING Industrial data is afflicted by inconsistencies that are typically caused by noise. These problems can be caused by the electrical equipment, sensors or the process itself such as incomplete mixing, non-uniform multiphase flows, and turbulence 45-46. 47-50

Wavelet transform, which is frequently used for denoising

, is adopted in this paper. A

conventional wavelet transform method follows the equation shown in (8): , , + H,, , 1, … , +,

8

where ,L9L& is the observed values, H,L9L& is a centered Gaussian white noise of unknown variance ( and is an unknown function that is to be recovered through the observations.


Page 13 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For a wavelet transform model denoted by M3N ,O 6∈Q , R , L LS,∈Q Twhere N the associated scaling function, R is a wavelet, U is a suitably chosen decomposition level and where , V X

2WY 2W V $ Z, wavelet denoising proceeds in three steps: Step 1: Compute the wavelet decomposition of the observed signal up to level U Step 2: Threshold conveniently the wavelet detail coefficient Step 3: Reconstruct a denoised version of the original signal, from the threshold detail coefficients and the approximation coefficients, using the inverse wavelet transform For more information, please consult the paper by Aminghafari, et al. function from the MATLAB Toolbox is utilized to denoise the dataset

51

52

. In this paper, wmulden

. The wavelet sym4 is the

default wavelet family for wmulden. Wavelet transform with different level is tested against the noisy wavelet test data from Donoho and Johnstone’s paper 53-54 as shown in Table 2. The root mean squared error (RMSE) between the clean signal and the denoised signal is calculated. The decomposition level is chosen based on the level with the lowest RMSE for the majority of cases. Based on the results, the value of J is kept constant at 3.

Table 2. RMSE of the wavelet transfer function at different decomposition level, J against a set of noisy data from Donoho and Johnstone’s paper 53-54. Value of J

1

2

3

4

5

RMSE of Signal 1 0.774 0.646 0.619 0.647 0.708 RMSE of Signal 2 0.728 0.538 0.475 0.542 0.620 RMSE of Signal 3 0.729 0.533 0.378 0.278 0.257 RMSE of Signal 4 0.735 0.578 0.495 0.476 0.498



Page 14 of 51

RMSE of Signal 5 1.912 2.208 2.331 2.395 2.406 RMSE of Signal 6 2.162 2.379 2.661 2.865 2.897

2) DETECTION AND REMOVAL OF OUTLIER An outlier is a data point that diverges distinctly from other data points of the time series. Outliers have an undesirable bearing on the performance of any analysis

55

. Outliers are caused by imprecise

readings from instrumentation, hardware malfunction, transmission problems or bizarre process working conditions 56. Many techniques are available for removal of outliers, such as MADe, Standard Deviation Method (SD), Z-score etc. A comparison study reported by Seo

42

indicated that the MADe method is the most

flexible outlier detection method due to its ability to detect outliers regardless of the distribution of data. Therefore, the MADe method has been chosen in this paper to detect outliers for the NLPCA-AC algorithm. The detected outliers are subsequently removed by deletion. This technique uses an amalgamation of Median Absolute Deviation and median, and is not influenced by the presence of extreme data points as it uses two robust estimators that have a high breakdown point

57

. The MADe

method is represented by (9): [\]- [-,ℎ_`: [-`b0+ ± 3 [\]-

9

where MADe = 1.483×MAD. MAD can evaluate the spread of the data but has a 50% breakdown point 58. The MAD is calculated as shown in (10). [\] d-`b0+3eV – d-`b0+Veb 1, 2, . . . , +6 After the MAD is scaled by a factor of 1.483

58

10

, it has a result virtually similar to the standard

deviation in a normal distribution.

3) COMPUTING MISSING DATA


Page 15 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Missing data refers to the data points that do not represent correctly the real process state because the missing data points usually assume the values of ±∞ or 0. Data transfer, sensor removal, sensor maintenance or sensor failure are a few examples of the root cause of missing data 56. The Arithmetic mean imputation method can be used to overcome this problem. The method is described as in equation (11):

ijkl ijml (

11

where is the missing data, and and W are the next and previous data point respectively. Regression imputation is another method to compute the missing data. This approach replaces missing data with a probable value estimated by other available information 59. The existing variables are used to make a prediction though the piecewise cubic spline interpolation and then the predicted value is substituted as if an actual obtained value. Other than that, one of the most widely used imputation methods for missing data is the last observation carried forward (LOCF). This method replaces every missing value with the last observed value from the same subject. Whenever a value is missing, it is replaced with the last observed value 60. These three methods are tested on a sample data affected by missing data problems. The corrected data by the three methods are compared with the original sample data and the root mean squared error (RMSE) is calculated. The Arithmetic mean imputation method, which has the lowest RMSE is chosen for computing missing data for NLPCA-AC as shown in Table 3.

Table 3. Comparison of different computing missing data methods based on RMSE. METHOD ARITHMETIC MEAN IMPUTATION METHOD RMSE

0.0575

REGRESSION IMPUTATION METHOD

LOCF IMPUTATION METHOD

0.07618

0.0687



Page 16 of 51

4) NORMALIZATION Magnitude problems are commonly caused by variable units and the nature of the process. It is imperative to ensure each data set has consistent magnitude of scaling to prevent biasness in the subsequent analysis. The most common methods for data scaling are the min-max method and z-score method 61, as outlined in (12) and (13): Z-score normalization: V%

nWn̅ Dp

12

13

Min-max normalization: nWnqjr

V% n

qsp Wnqjr

× V % "=n $ V % " & + V % " &

where V and V′ are the unscaled and scaled variables, the min and max subscripts refer to the minimum and maximum of the variable, and V̅ and n are the mean and the standard deviation of the variable. According to Brasio 62, the Z-score normalization is mostly used for data scaling because this method is more robust even though there are outliers. Therefore, the Z-score normalization method is selected to scale the data sets in this paper.

IV. METHODOLOGY A. STICTION DETECTION USING COVARIANCE (NLPCA-AC)

NLPCA-AVERAGE

CROSSING

1) PREPROCESSING In this paper, several combinations of preprocessing are tested as shown in Figure 5.


AUTO-

Page 17 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


PREPROCESSING PATH

REMOVAL OF OUTLIERS

COMPUTING MISSING DATA

NORMALIZATION

DENOISING

DENOISING

NORMALIZATION

NO TREATMENT

NORMALIZATION

REMOVAL OF OUTLIERS


DENOISING

NORMALIZATION

DENOISING

REMOVAL OF OUTLIERS


Figure 5. Preprocessing Paths After a thorough trial-and-error analysis, the final path chosen for preprocessing is the normalization of the data followed by denoising the data. Please refer to Appendix B for more information on the extensive trial runs.

2) NLPCA In this paper, the NLPCA structure used is based on the general 5-layer auto-associative network shown in Figure 2. It has one input which is the PV data set. As noted by Monahan 36, if the dimensions of the mapping and demapping layers are large enough such that the functions f and g can be similar to arbitrary accuracy, this network should be able to recover optimally. The network is initialized with random weights and biases with fixed network architecture. The network contains three hidden layers. The bottleneck layer and the output layer use ‘purelin’ linear transfer functions. The input, mapping, and demapping layers use the ‘log sigmoid’ nonlinear transfer function. The weights and biases are optimized using a Levenberg-Marquardt algorithm. Utilizing PV data only as input, the structure of the five-layer feed-forward auto-associative neural network used in this work follows a structure of 1-3-2-31 neurons per layer.

3) POST-PROCESSING



Page 18 of 51

The NLPCA output is then passed through several post-processing methods. Different sequences of post-processing methods are tested as shown in Figure 6. NORMALIZATION POST-PROCESSING PATH

DENOISING

NORMALIZATION

NORMALIZATION

REMOVAL OF OUTLIERS


DENOISING

Figure 6. Post-processing Paths After extensive trial runs, it is found that the best post-processing path is the normalization of the data only. Please refer to Appendix B for more information on the extensive trial runs.

4) AVERAGE CROSSING AUTOCOVARIANCE After the NLPCA output has been post-processed, it is run through the average crossing of autocovariance method as previously elaborated in Section III part C. The flowchart of the proposed NLPCA-AC algorithm for stiction detection is presented in Figure 7.


Page 19 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Start

Import data (PV)

Preprocessing

Apply NLPCA

PostProcessing

Apply Average Crossing Autocovarianc e Check R-Value

No No Stiction

Is R > 1?

Yes Report Stiction

Figure 7. Flowchart of the proposed NLPCA-Average Crossing Auto-covariance (NLPCA-AC) Algorithm

V. RESULTS AND DISCUSSIONS The proficiency of the proposed NLPCA-AC algorithm is assessed through the use of simulated case study and data set from a number of benchmark industrial control loops. To highlight the capability of the proposed approach in filling some gaps in the knowledge in this field and in eliminating the



Page 20 of 51

disadvantages of earlier works as well as overcoming inadequacies of previous techniques, a comparison of the NLPCA-AC with other methods collected in the paper written by Jelali and Huang

11

is

performed.

A. SIMULATION CASE STUDY The performance of the proposed method is investigated using the case study used by Kano, et al. 13. In this paper, the stiction model developed by Choudhury, et al.

33

is used. A simple SISO feedback

control system 16 is used to generate the simulated data. The first order process with time delay is given by the following transfer function: tu W

v mw ×.xyvW vWz.{

14

The process is presumed to be linear and controlled by a Proportional-Integral (PI) controller. An integrated random noise is added to the process. The process output (PV) is used to detect nonlinearity present in the data for the four cases of (1) well-tuned controller, (2) controller with excessive control action, (3) well-tuned controller in the presence of external oscillatory disturbances, and (4) well-tuned controller in the presence of stiction. A total of 3000 samples is collected for each case at a sampling rate of 1s.

1) Well-tuned controller The PI controller parameters for this case are |} 0.15 and *

O~ j

0.15 W. The NLPCA

algorithm is applied to the data and the results are as shown in Table 4. The plot of PV before NLPCA vs samples can be seen in Figure 8A. The results after running through the NLPCA and average crossings of auto-covariance (AC) are shown in Figure 8B, where the blue line corresponds to the NLPCA output, and the red line represents average crossing line calculated by the AC method. Even though the NLPCA output is not consistent in nature, the R-value calculated by the AC method is well


Page 21 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


below 1. This indicates that the NLPCA output is not oscillating constantly, thus concluding that no stiction is detected.

(A)

(B)

Figure 8. Graph of PV vs Samples in a Well-Tuned Controller: (A) Using Raw Data, (B) After NLPCA.

2) Controller with excessive integral action For this case, the controller parameters were set to |} 0.15 and *

O~ j

0.27 W . It is

imperative to note here that the value of I as indicated by Choudhury, et al. 16 will result in an unstable feedback control loop. With I equal to 0.27, this controller has an excessive integral action in comparison to Case 1. Figure 9A shows the plot of PV before running through the NLPCA. After running the data through the NLPCA-AC algorithm, the value of 0.20713 is obtained for R as shown in Table 4, clearly indicating that the data is non-stiction. The corresponding plot can be seen in Figure 9B.

(A)

(B)



Page 22 of 51

Figure 9. Graph of PV vs Samples in a Controller with Excessive Integral: (A) Using Raw Data, (B) After NLPCA.

3) Well-tuned controller in the presence of external oscillatory disturbance For this case, a sinusoidal disturbance with an amplitude of 2 and a frequency of 0.01 is added to the process output in order to feed external oscillatory disturbances to the process. It can be observed from Figure 10B that the resulting NLPCA output has an inconsistent oscillatory behavior. This subsequently resulted in the R-value calculated to be below 1, clearly indicating that the oscillatory data is not caused by stiction.

(A)

(B)

Figure 10. Graph of PV vs Samples in a Controller with External Oscillatory Disturbance: (A) Using Raw Data, (V) After NLPCA.

4) Well-tuned controller in the presence of stiction In this case, J = 1 and S = 3 is used in the stiction model to represent the case of stiction in the control valve. Figure 11B clearly shows a constant oscillation in the NLPCA output, and this is confirmed by the R-value of 5.3929. The proposed NLPCA-AC method successfully detected the presence of stiction in the loop.


Page 23 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(A)

(B)

Figure 11. Graph of PV vs Samples of a Controller with Stiction Undershoot: (A) Using Raw Data, (B) After NLPCA. Table 4. NLPCA-AC results on the simulated case study. Simulation Case

T(s) Number of Time Series R-Value Decision

Well-Tuned

1

3000

0.40370

No Stiction

Excessive Integral

1

3000

0.18344

No Stiction

External Disturbance 1

3000

0.23958

No Stiction

1

3000

5.52730

Stiction

Stiction

B. INDUSTRIAL CASE STUDY 1) PERFORMANCE OF NLPCA-AC ON BENCHMARK INDUSTRIAL LOOPS

In any stiction detection algorithm, the key validation point is to evaluate the performance of the algorithm using real industrial data. In this paper, the benchmark industrial data widely used in literatures are utilized to test the proposed NLPCA-AC algorithm. The corresponding descriptions of these industrial loops are listed in Appendix A. This section aims to evaluate the performance of the proposed stiction detection method for different industrial control loops such as power plants (POW),



Page 24 of 51

chemical plants (CHEM), pulp and paper mills (PAP), commercial building (BAS), mining (MIN), and metal processing (MET) 11. In these industrial control loops, the actual root-causes for malfunctions are known. For each loop, the process output (PV) data is utilized. The comments from Jelali and Huang

11

are taken as the actual root-cause of malfunctions. The

proposed method is compared to the actual result based on the condition of the loop. It should be noted though that the individual descriptions of each loop are omitted here for the sake of brevity. However, interested readers may refer to Jelali and Huang 11 paper for further details.

a) Loops with Stiction There are 26 loops that have been documented as having stiction by Jelali and Huang

11

. As clearly

indicated in Table 5, the proposed NLPCA-AC method is able to correctly detect 14 out of these 26 loops. The raw PV plots before NLPCA for CHEM 1 and CHEM 7 loops are illustrated in Figures 12A and 12C, respectively. As a comparison analysis, Figures 12B and 12D show the corresponding NLPCA-AC output analysis for CHEM 1 and CHEM 7 loops. The persistent oscillation observed in the NLPCA output of CHEM 1 in Figure 12B is successfully detected via the auto-covariance test. The CHEM 7 loop obtained an uncertain (UNC) result due to the lack of oscillated data points as clearly depicted in Figure 12D, which is a necessary requirement when using the average crossing of autocovariance. It can be seen that for this case, the R-value obtained is -99. The proposed NLPCA-AC method is unable to give an accurate result if the data does not oscillate across the average crossing autocovariance line more than 2 times. Based on Table 5, it can be observed that the method has a 54% accuracy in correctly detecting stiction in these industrial loops.


Page 25 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(A)

(B)

(C)

(D)

Figure 12. Graph of PV vs Samples regarding: (A) Raw Data of CHEM 1 Flow Control Loop, (B) CHEM 1 Flow Control Loop After NLPCA, (C) Raw Data of CHEM 7 Pressure Control Loop, (D) CHEM 7 Pressure Control Loop After NLPCA. Table 5: Loops with stiction. LOOP NAME

TYPE OF LOOP

NLPCA-AC ACTUAL MALFUNCTION

BAS 6

TEMPERATURE CONTROL LOOP

YES

STICTION

BAS 7


YES

STICTION

CHEM 1

FLOW CONTROL LOOP

YES

STICTION

CHEM 2

FLOW CONTROL

NO

STICTION



Page 26 of 51

LOOP CHEM 5

FLOW CONTROL LOOP

YES

STICTION

CHEM 6

FLOW CONTROL LOOP

NO

STICTION

CHEM 7

PRESSURE CONTROL LOOP

UNC

STICTION

CHEM 8


YES

STICTION

CHEM 9


YES

STICTION

CHEM 0


YES

STICTION

CHEM 11

FLOW CONTROL LOOP

YES

STICTION

CHEM 12

FLOW CONTROL LOOP

NO

STICTION

CHEM 25


YES

STICTION

CHEM 29

FLOW CONTROL LOOP

NO

STICTION

CHEM 30

FLOW CONTROL LOOP

NO

STICTION

MIN 1


NO

STICTION

POW 1

LEVEL CONTROL LOOP

NO

STICTION

POW 2

LEVEL CONTROL LOOP

YES

STICTION

POW 4

LEVEL CONTROL LOOP

NO

STICTION

PAP 1

FLOW CONTROL LOOP

YES

STICTION


Page 27 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


PAP 2

FLOW CONTROL LOOP

YES

STICTION

PAP 3

LEVEL CONTROL LOOP

YES

STICTION

PAP 5

CONCENTRATION CONTROL LOOP

NO

STICTION

PAP 11

LEVEL CONTROL LOOP

NO

STICTION

PAP 12

LEVEL CONTROL LOOP

NO

STICTION

PAP 13

LEVEL CONTROL LOOP

YES

STICTION

b) Loops with Fair Presence of Stiction Based on the paper by Jelali and Huang 11, there are 10 loops that have been classified as loops with fair presence of stiction. The proposed NLPCA-AC method is able to detect accurately 6 out of the 10 loops as shown in Table 6. Therefore, the proposed method is able to accurately detect 60% of loops with fair presence of stiction.

Table 6. Loops with fair presence of stiction. LOOP NAME

TYPE OF LOOP

NLPCA-AC

ACTUAL MALFUNCTION

CHEM 18

FLOW CONTROL LOOP

NO

FAIR PRESENCE OF STICTION

CHEM 19

FLOW CONTROL LOOP

YES


CHEM 20

FLOW CONTROL LOOP

NO


CHEM 22

FLOW CONTROL LOOP

YES


CHEM 23

FLOW CONTROL

YES

FAIR PRESENCE OF



Page 28 of 51

LOOP

STICTION

CHEM 24

FLOW CONTROL LOOP

NO


CHEM 26

LEVEL CONTROL LOOP

YES


CHEM 28


YES


CHEM 32

FLOW CONTROL LOOP

YES


CHEM 35

FLOW CONTROL LOOP

NO


c) Loops without Stiction According to Jelali and Huang

11

, 23 of the 78 loops reported have been diagnosed as having no

stiction and does not suffer from any valve problems. When these loops are tested against the proposed method, 18 of the 23 loops have been detected accurately as shown in Table 7, resulting in an accuracy of 78%. The BAS 1, BAS 2 as well as CHEM 48 loop caused the proposed NLPCA-AC method to show an UNC result as these loops do not have enough oscillating data to give an accurate result. Figure 13 illustrates the graphical analysis of industrial level control loop (PAP 8) and temperature control loop (BAS 1), respectively. Figures 13A and 13C reveal the raw PV data for PAP 8 and BAS 1 before the loops are tested against the proposed method. For PAP 8, the R-value calculated by the proposed method is well below 1, clearly indicating that no stiction is present in the loop. As mentioned previously, the lack of oscillating data in BAS 1 as shown in Figure 13D causes the proposed method to show an UNC result. However, it should be noted that most other established methods also failed to detect properly for loop BAS 1 (as well as BAS 2 and CHEM 48) due to the nature of the data 11.


Page 29 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(A)

(B)

(C)

(D)

Figure 13. Graph of PV vs Samples regarding: (A) Raw Data of PAP 8 Level Control Loop, (B) PAP 8 Level Control Loop After NLPCA, (C) Raw Data of BAS 1 Temperature Control Loop, (D) BAS 1 Temperature Control Loop After NLPCA. Table 7. Loops without stiction. LOOP NAME

TYPE OF LOOP

NLPCA ACTUAL MALFUNCTION

BAS 1


UNC

NO STICTION/VALVE PROBLEM

BAS 2


UNC


BAS 8


NO


CHEM 40

TEMPERATURE

NO

NO STICTION/VALVE



CONTROL LOOP

PROBLEM

CHEM 44


YES


CHEM 45


NO


CHEM 46


NO


CHEM 47


NO


CHEM 48


NO


CHEM 52

LEVEL CONTROL LOOP

NO


CHEM 53

LEVEL CONTROL LOOP

NO


CHEM 54

LEVEL CONTROL LOOP

NO


CHEM 56

FLOW CONTROL LOOP

NO


CHEM 58

FLOW CONTROL LOOP

NO


CHEM 59

FLOW CONTROL LOOP

NO


CHEM 61

FLOW CONTROL LOOP

NO


CHEM 62

FLOW CONTROL LOOP

NO


MET 3

GAUGE CONTROL

NO


POW 3

LEVEL CONTROL LOOP

NO


POW 5

LEVEL CONTROL LOOP

NO



Page 30 of 51

Page 31 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


PAP 6

LEVEL CONTROL LOOP

YES


PAP 8

LEVEL CONTROL LOOP

NO


PAP 9


YES


d) Loops with problems other than stiction In this section, the proposed NLPCA-AC performance is applied to 19 oscillating loops that suffer from various problems other than stiction problem. For example, CHEM 3 loop suffers from quantization issue. Other than that, CHEM 15 and 16 are suffering from interaction problems. External disturbance issues can be seen in CHEM 21, 27, 33-34, 36-39, MET 1-2, PAP 4, and 7. Besides that, CHEM 13, 14, and 17 have faulty sensor problems. CHEM 4 and PAP 4 have problems due to controller tuning. Figure 14 and Figure 15 illustrates the behavior of these loops before and after running through NLPCA as well as the corresponding R-value calculated by the NLPCA-AC method. After running through the loops data via the NLPCA-AC method, Table 8 shows that 16 loops are accurately diagnosed, giving it an 84% accuracy for diagnosing oscillating loops with problems other than stiction.

(A)

(B)



Page 32 of 51

(C)

(D)

(E)

(F)

Figure 14. Graph of PV vs Samples regarding: (A) Raw Data of CHEM 3 Temperature Control Loop (Quantization Issue) After NLPCA, (B) CHEM 3 Temperature Control Loop (Quantization Issue), (C) Raw Data of CHEM 4 Level Control Loop (Tuning Problem), (D) CHEM 4 Level Control Loop (Tuning Problem) After NLPCA, (E) Raw Data of CHEM 13 Analyzer Control Loop (Faulty Sensor), (F) CHEM 13 Analyzer Control Loop (Faulty Sensor) After NLPCA.


Page 33 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(A)

(B)

(C)

(D)

Figure 15. Graph of PV vs Samples regarding: (A) Raw Data of CHEM 15 Pressure Control Loop (Interaction Problem), (B) CHEM 15 Pressure Control Loop (Interaction Problem) After NLPCA, (C) Raw Data of CHEM 21 Flow Control Loop (External Disturbance), (D) CHEM 21 Flow Control Loop (External Disturbance) After NLPCA. Table 8. Loops with problems other than stiction. LOOP NAME

TYPE OF LOOP

NLPCA

ACTUAL MALFUNCTION

CHEM 3


NO

QUANTISATION

CHEM 4

LEVEL CONTROL LOOP

YES

TUNING PROBLEM

CHEM 13

ANALYSER CONTROL LOOP

NO

FAULTY SENSOR

CHEM 14

FLOW CONTROL LOOP

NO

FAULTY SENSOR

CHEM 15


NO

INTERACTION

CHEM 16


NO

INTERACTION

CHEM 17

TEMPERATURE

NO

FAULTY SENSOR



Page 34 of 51

CONTROL LOOP CHEM 21

FLOW CONTROL LOOP

NO

LIKELY DISTURBANCE

CHEM 27

LEVEL CONTROL LOOP

NO

LIKELY DISTURBANCE

CHEM 33

FLOW CONTROL LOOP

NO

LIKELY DISTURBANCE

CHEM 34

FLOW CONTROL LOOP

NO

LIKELY DISTURBANCE

CHEM 36

LEVEL CONTROL LOOP

NO

LIKELY DISTURBANCE

CHEM 37

LEVEL CONTROL LOOP

NO

LIKELY DISTURBANCE

CHEM 38


YES

LIKELY DISTURBANCE

CHEM 39


NO

LIKELY DISTURBANCE

MET 1

GAUGE CONTROL

NO

LIKELY DISTURBANCE

MET 2

GAUGE CONTROL

NO

LIKELY DISTURBANCE

PAP 4

CONCENTRATION CONTROL LOOP

YES

DEADZONE AND TIGHT TUNING

PAP 7

FLOW CONTROL LOOP

NO

EXTERNAL DISTURBANCE

2) COMPARISON ANALYSIS WITH ESTABLISHED DETECTION METHODS

In this section, a comparison analysis is performed between the proposed NLPCA-AC method and established stiction detection methods in literatures such as BIC by Choudhury, et al.

6, 27

, CORR by

Horch 12, HIST by Horch 28, RELAY by Rossi and Scali 20, CURVE by He, et al. 18, AREA by Salsbury


Page 35 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and Singhal

29

, HAMM2 by Lee, et al.

ZONES by Dambros, et al.

32

30

, HAMM3 by Karra and Karim

31

and SLOPE as well as

, for a total of 78 industrial loops reported by Jelali and Huang

11

. The

summary of the comparison analysis is presented in Table 9. The accuracy of all the existing stiction detection method can be calculated based on the most correct readings compared to the actual malfunctions that have been published by Jelali and Huang 11. The most accurate existing stiction detection technique is the BIC technique with the result of 46 correct readings. On the other hand, the proposed NLPCA-AC method is able to correctly diagnose 54 out of the 78 loops tested, indicating that the proposed method is more reliable in detecting stiction compared to the other existing methods.

Table 9. Comparison analysis between NLPCA-AC and other published stiction detection methods. Stiction Detection Method Number of Correct Diagnosis BIC

46/78

CORR

19/78

HIST

30/78

RELAY

34/78

CURVE

27/78

AREA

27/78

HAMM2

39/78

HAMM3

43/78

SLOPE

28/78

ZONES

26/78

Proposed NLPCA-AC

54/78



Page 36 of 51

VI. CONCLUSION An improved method for the detection of stiction in control valves based on NLPCA and autocovariance has been proposed in this paper. To demonstrate the performance of the proposed NLPCA-AC method, a comparison of the proposed approach with other published techniques on data sets obtained from various benchmark industrial control loops has been performed. The proposed NLPCA-AC technique, which overcomes some limitations of an earlier approach, has the important features of not requiring a large amount of data and does not require many ensemble runs per data set. Although the proposed method is unable to work properly in the presence of inadequate oscillating average crossing data, the capability of the proposed algorithm to diagnose stiction from different type of industrial loops makes the proposed approach a very promising technique, as an approximately 10% improvement can be observed over the BIC method.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

ACKNOWLEDGMENT The authors would like to thank MOSTI grant e-ScienceFund 03-02-02-SF0236 for the funding provided for this work. The authors also would like to thank Universiti Teknologi PETRONAS (UTP) for the support provided for this research.

REFERENCES (1) Choudhury, M. A. A. S.; Shah, S. L.; Thornhil, N. F. In Detection and Quantification of Control Valve Stiction, The Proceedings of DYCOPS, 2004.


Page 37 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(2) Mohammad, M. A. Detection and Compensation for Stiction in Multi-Loop Control Systems. University of Alberta, Edmonton, Alberta, Canada, 2011. (3) Yamashita, Y., Qualitative Analysis for Detection of Stiction in Control Valves. In KnowledgeBased and Intelligent Information and Engineering Systems, Springer: Berlin, Heidelberg, 2004; Vol. 3214, pp 391-397. (4) Desborough, L.; Miller, R., Increasing Customer Value of Industrial Control Performance Monitoring - Honeywell’s Experience. In AIChE Symposium Series 2001, 2002; Vol. 326, pp 172-192. (5) Zabiri, H.; Samyudia, Y.; Zainudin, W. N. W. M., Neural Network Modeling of Valve Stiction Dynamics. In World Congress on Engineering and Computer Science, San Francisco, USA, 2007. (6) Choudhury, M. A. A. S.; Shah, S. L.; Thornhill, N. F.; Shook, D. S., Stiction-Definition, Modelling, Detection and Quantification. Journal of Process Control 2008, 18, 232-243. (7) Paulonis, M. A.; Cox, J. W., A Practical Approach for Large-Scale Controller Performance Assessment, Diagnosis, and Improvement. Journal of Process Control 2003, 13, 155-168. (8) Capaci, R. B. d.; Scali, C., Review and Comparison of Techniques of Analysis of Valve Stiction: From Modeling to Smart Diagnosis. Chemical Engineering Research and Design 2018, 130, 230-265. (9) Gerry, J.; Ruel, M. In How to Measure and Combat Valve Stiction Online, ISA, Houston, Texas, USA, Instrumentation, Systems and Automation Society: Houston, Texas, USA, 2001. (10) Brásio, A. S. R.; Romanenko, A.; Fernandes, N. C. P., Modeling, Detection and Quantification, and Compensation of Stiction in Control Loops: The State of the Art. Industrial & Engineering Chemistry Research 2014, 53 (39), 15020-15040. (11) Jelali, M.; Huang, B., Detection and Diagnosis of Stiction in Control Loops. Springer-Verlag: London, U.K, 2010; p 391.



Page 38 of 51

(12) Horch, A., A Simple Method for Detection of Stiction in Control Valves. Control Engineering Practice 1999, 7, 1221-1231. (13) Kano, M.; Hiroshi, M.; Kugemoto, H.; Shimizu, K., Practical Model and Detection Algorithm for Valve Stiction. In IFAC DYCOPS, Boston, MA, USA, 2004. (14) Yamashita, Y., An Automatic Method for Detection of Valve Stiction in Process Control Loops. Control Engineering Practice 2006, 14, 503-510. (15) Scali, C.; Ghelardoni, C., An Improved Qualitative Shape Analysis Technique for Automatic Detection of Valve Stiction in Flow Control Loops. Control Engineering Practice 2008, 16, 1501-1508. (16) Choudhury, M. A. A. S.; Shah, S. L.; Thornhill, N. F., Diagnosis of Poor Control Loop Performance using Higher Order Statistics. Automatica 2004, 40, 1719-1728. (17) Thornhill, N. F., Finding the Source of Nonlinearity in a Process with Plant-Wide Oscillation. IEEE Transactions on Control Systems Technology 2005, 13, 434-443. (18) He, Q. P.; Wang, J.; Pottmann, M.; Qin, S. J., A Curve Fitting Method for Detecting Valve Stiction in Oscillating Control Loops. Industrial & Engineering Chemistry Research 2007, 46, 4549-4560. (19) Srinivasan, R.; Rengaswamy, R.; Miller, R., Control Loop Performance Assessment. 1. A Qualitative Approach for Stiction Diagnosis. Industrial & Engineering Chemistry Research 2005, 44, 6708-6718. (20) Rossi, M.; Scali, C., A Comparison of Techniques for Automatic Detection of Stiction: Simulation and Application to Industrial Data. Journal of Process Control 2005, 15 (5), 505-514. (21) Daneshwar, M. A.; Noh, N. M., Valve Stiction in Control Loops - A Survey on Effective Methods of Detection and Compensation. In International Conference on Control System, Computing and Engineering, Penang, Malaysia, 2012.


Page 39 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(22) Zabiri, H.; Ramasamy, M., NLPCA as a Diagnostic Tool for Control Valve Stiction. Journal of Process Control 2009, 19 (8), 1368-1376. (23) Ahammad, M.; Choudhury, M. A. A. S., A Simple Harmonics Based Stiction Detection Method. In 9th IFAC DYCOPS, Leuven, Belgium, 2010; pp 671–676. (24) Thornhill, N. F.; Huang, B.; Zhang, H., Detection of Multiple Oscillations in Control Loops. Journal of Process Control 2003, 13, 91-100. (25) Zakharov, A.; Zattoni, E.; Xie, L.; Garcia, O. P.; Jämsä-Jounela, S.-L., An Autonomous Valve Stiction Detection System Based on Data Characterization. Control Engineering Practice 2013, 21, 1507-1518. (26) Garcia, O. P.; Zakharov, A.; Jämsä-Jounela, S.-L., Data and Reliability Characterization Strategy for Automatic Detection of Valve Stiction in Control Loops. IEEE Transactions on Control Systems Technology 2016, 99, 1-12. (27) Choudhury, M. A. A. S.; Shah, S. L.; Thornhill, N. F.; Shook, D. S., Automatic Detection and Quantification of Stiction in Control Valves. Control Engineering Practice 2006, 14 (12), 1395-1412. (28) Horch, A. Method and a System for Evaluation of Static Friction. 2006. (29) Salsbury, T. I.; Singhal, A., Shape-Based Stiction Detection using Area Calculations, Detection and Diagnosis of Stiction in Control Loops. Advances in Industrial Control 2010, 183-204. (30) Lee, K. H.; Ren, Z.; Huang, B., Stiction Estimation using Constrained Optimization and Contour Map. Detection and Diagnosis of Stiction in Control Loops 2010, 229-266. (31) Karra, S.; Karim, M. N., Comprehensive Methodology for Detection and Diagnosis of Oscillatory Control Loops. Control Engineering Practice 2009, 17, 939-956.



Page 40 of 51

(32) Dambros, J. W. V.; Farenzena, M.; Trierweiler, J. O., Data-Based Method to Diagnose Valve Stiction with Variable Reference Signal. Industrial & Engineering Chemistry Research 2016, 55 (39), 10316-10327. (33) Choudhury, M. A. A. S.; Shah, S. L.; Thornhill, N. F., Modelling Valve Stiction. Control Engineering Practice 2005, 13, 641-658. (34) ISA, Process Instrumentation Terminology. 1979. (35) Kramer, M. A., Nonlinear Principal Component Analysis using Autoassociative Neural Networks. AIChE Journal 1991, 31, 233-243. (36) Monahan, A., Nonlinear Principal Component Analysis by Neural Networks: Theory and Application to the Lorenz System. Journal of Climate 2000, 13, 821-835. (37) Monahan, A., Nonlinear Principal Component Analysis: Tropical Indo-Pacific Sea Surface Temperature and Sea Level Pressure. Journal of Climate 2001, 14, 219-233. (38) Botelho, S. S. C.; Bern, R. A.; Almeida, I. L.; Mata, M. M. In C-NLPCA: Extracting Nonlinear Principal Components of Image Datasets, Anais XII Simposio Brasileiro de Sensoriamento Remoto, Goiania, Brazil, 16-21 April; INPE: Goiania, Brazil, 2005; pp 3495-3502. (39) Bernhardt, K.; Wirtz, K. W., Reduction of Complex Models using Data-Mining and Nonlinear Projection Techniques. 2004. (40) Hiesh, W., Nonlinear Principal Component Analysis by Neural Networks. Tellus A: 2001; p 559615. (41) Singhal, A.; Salsbury, T. I., A Simple Method for Detecting Valve Stiction in Oscillating Control Loops. Journal of Process Control 2005, 15, 371-382. (42) Seo, S. A review and comparison of methods for detecting outliers in univariate data sets. University of Pittsburgh, 2006.


Page 41 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(43) Dambros, J. W.; Farenzena, M.; Trierweiler, J. O., Signal Preprocessing for Stiction Detection Methods. Industrial & Engineering Chemistry Research 2017, 57 (1), 302-315. (44) Salsbury, T. I.; Singhal, A. In A New Approach for ARMA Pole Estimation using Higher-Order Crossings, American Control Conference, Portland, OR, USA, IEEE, Ed. Portland, OR, USA, 2005; pp 4458-4463. (45) Seborg, D.; Edgar, T.; Mellichamp, D.; Francis J. Doyle, I., Process Dynamics and Control. John Wiley & Sons: 2010. (46) Verhaegen, M.; Verdult, V., Filtering and System Identification: A Least Squares Approach. Cambridge University Press 2012. (47) Akyilmaz, O.; Kutterer, H.; Shum, C. K.; Ayan, T., Fuzzy-Wavelet Based Prediction of Earth Rotation Parameters. Applied Soft Computing 2011, 11, 837-841. (48) Srivastava, S.; Singh, M.; Hanmandlu, M.; Jha, A. N., New Fuzzy Wavelet Neural Networks for System Identification and Control. Applied Soft Computing 2005, 6, 1-17. (49) Zainuddin, Z.; Pauline, O., Modified Wavelet Neural Network in Function Approximation and Its Application in Prediction of Time-Series Pollution Data. Applied Soft Computing 2011, 11, 4866-4874. (50) Zanchettin, C.; Ludermir, T. B., Wavelet Filter for Noise Reduction and Signal Compression in an Artificial Nose. Applied Soft Computing 2007, 7, 246-256. (51) Aminghafari, M.; Cheze, N.; Poggi, J. M., Multivariate denoising using wavelets and principal component analysis. Computational Statistics & Data Analysis 2006, 50 (9), 2381-2398. (52) Matlab. (53) Donoho, D. L.; Johnstone, I. M., Adapting to Unknown Smoothness via Wavelet Shrinkage. Journal of the American Statistical Association 1995, 90 (432), 1200-1224.



Page 42 of 51

(54) Donoho, D. L.; Johnstone, J. M., Ideal Spatial Adaptation by Wavelet Shrinkage. Biometrika 1994, 81 (3), 425-455. (55) Di-Bella, A.; Fortuna, L.; Graziani, S.; Napoli, G.; Xibilia, M., A Comparative Analysis of the Influence of Methods for Outliers Detection on the Performance of Data Driven Models. In IEEE Conference on Instrumentation and Measurement Technology, 2007; pp 1-5. (56) Kadlec, P.; Gabrys, B., Architecture for Development of Adaptive Online Prediction Models. Memetic Computing 2009, 1 (4), 241-269. (57) Burke, S. Missing Values, Outliers, Robust Statistics and Non-Parametric Methods Computational Statistics & Data Analysis [Online], 2001, p. 19-24. (58) Iglewicz, B.; Hoaglin, D., How to Detect and Handle Outliers. ASQC Quality Press: 1993. (59) Kang, H., The Prevention and Handling of the Missing Data. Korean Journal of Anesthesiology 2013, 64 (5), 402-406. (60) Hamer, R. M.; Simpson, P. M., Last Observation Carried Forward Versus Mixed Models in the Analysis of Psychiatric Clinical Trials. American Psychiatric Associsation: 2009. (61) Fortuna, L.; Graziani, S.; Rizzo, A.; Xibilia, M., Soft Sensors for Monitoring and Control of Industrial Processes. Springer: 2007. (62) Brasio, A. S. R. Industrial Processes Monitoring Methodologies. University of Coimbra, 2015. (63) Jelali, M.; Scali, C., Comparative Study of Valve Stiction Detection Methods. In Detection and Diagnosis of Stiction in Control Loops, 1st ed.; Springer: London, UK, 2010.


Page 43 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


APPENDIX A STICTION IDENTIFICATION ANALYSIS BY NLPCA-AC FOR ALL 78 INDUSTRIAL LOOPS 63 BORROWED FROM JELALI AND SCALI Ts [s]

NUMBER OF DATA POINTS

ACTUAL MALFUNCTION

NLPCAAC

SELF REGULATING PROCESS

1

65536

NO STICTION

UNC



1

65536

NO STICTION

UNC

BAS 6



1

501

STICTION

YES

BAS 7



1

560

STICTION

YES

BAS 8



60

42512

NO STICTION

NO

CHEM 1

FLOW CONTROL LOOP


1

1625

STICTION

YES

CHEM 2

FLOW CONTROL LOOP


1

1000

STICTION

NO

CHEM 3



30

1945

QUANTISATION

NO

CHEM 4

LEVEL CONTROL LOOP

INTEGRATING PROCESS

1

200

TUNING PROBLEM

YES

CHEM 5

FLOW CONTROL LOOP


1

201

STICTION

YES

CHEM 6

FLOW CONTROL LOOP


1

1000

STICTION

NO

CHEM 7

PRESSURE CONTROL

SELF REGULATING

1

4685

STICTION

UNC

LOOP NAME

TYPE OF LOOP

PROCESS TYPE

BAS 1


BAS 2



Page 44 of 51

LOOP

PROCESS

CHEM 8



1

900

STICTION

YES

CHEM 9



1

2732

STICTION

YES

CHEM 10



1

1000

STICTION

YES

CHEM 11

FLOW CONTROL LOOP


1

1000

STICTION

YES

CHEM 12

FLOW CONTROL LOOP


1

2000

STICTION

NO

CHEM 13

ANALYSER CONTROL LOOP


20

1500

FAULTY SENSOR

NO

CHEM 14

FLOW CONTROL LOOP


20

1500

FAULTY SENSOR

NO

CHEM 15



20

1500

INTERACTION

NO

CHEM 16



20

1500

INTERACTION

NO

CHEM 17



20

1500

FAULTY SENSOR

NO

CHEM 18

FLOW CONTROL LOOP


12

1040

LIKELY STICTION

NO

CHEM 19

FLOW CONTROL LOOP


12

721

LIKELY STICTION

YES

CHEM 20

FLOW CONTROL LOOP


12

721

LIKELY STICTION

NO

CHEM 21

FLOW CONTROL LOOP


12

721

LIKELY DISTURBANCE

NO

44 Environment ACS Paragon Plus

Page 45 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CHEM 22

FLOW CONTROL LOOP


12

721

LIKELY STICTION

YES

CHEM 23

FLOW CONTROL LOOP


12

1500

LIKELY STICTION

YES

CHEM 24

FLOW CONTROL LOOP


12

1500

LIKELY STICTION

NO

CHEM 25



12

721

STICTION

YES

CHEM 26

LEVEL CONTROL LOOP

INTEGRATING PROCESS

12

1094

LIKELY STICTION

YES

CHEM 27

LEVEL CONTROL LOOP

INTEGRATING PROCESS

12

1333

LIKELY DISTURBANCE

NO

CHEM 28



12

721

LIKELY STICTION

YES

CHEM 29

FLOW CONTROL LOOP


60

7201

STICTION

NO

CHEM 30

FLOW CONTROL LOOP


15

17281

STICTION

NO

CHEM 32

FLOW CONTROL LOOP


10

1998

LIKELY STICTION

YES

CHEM 33

FLOW CONTROL LOOP


12

721

LIKELY DISTURBANCE

NO

CHEM 34

FLOW CONTROL LOOP


10

719

LIKELY DISTURBANCE

NO

CHEM 35

FLOW CONTROL LOOP


10

2000

LIKELY STICTION

NO

CHEM 36

LEVEL CONTROL LOOP

INTEGRATING PROCESS

12

804

LIKELY DISTURBANCE

NO

CHEM

LEVEL CONTROL

INTEGRATING

12

1711

LIKELY

NO



Page 46 of 51

37

LOOP

PROCESS

DISTURBANCE

CHEM 38



10

933

LIKELY DISTURBANCE

YES

CHEM 39



60

719

LIKELY DISTURBANCE

NO

CHEM 40



60

1441

NO OSCILLATION

NO

CHEM 44



60

1441

NO OSCILLATION

YES

CHEM 45



60

1441

NO OSCILLATION

NO

CHEM 46



60

1441

NO OSCILLATION

NO

CHEM 47



60

1441

NO OSCILLATION

NO

CHEM 48



60

1441

NO OSCILLATION

NO

CHEM 52

LEVEL CONTROL LOOP

INTEGRATING PROCESS

60

1441

NO OSCILLATION

NO

CHEM 53

LEVEL CONTROL LOOP

INTEGRATING PROCESS

60

1441

NO OSCILLATION

NO

CHEM 54

LEVEL CONTROL LOOP

INTEGRATING PROCESS

60

1441

NO OSCILLATION

NO

CHEM 56

FLOW CONTROL LOOP


60

1441

NO OSCILLATION

NO

CHEM 58

FLOW CONTROL LOOP


60

1441

NO OSCILLATION

NO

CHEM 59

FLOW CONTROL LOOP


60

1441

NO OSCILLATION

NO


Page 47 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CHEM 61

FLOW CONTROL LOOP


60

1441

NO OSCILLATION

NO

CHEM 62

FLOW CONTROL LOOP


60

1441

NO OSCILLATION

NO

MET 1

GAUGE CONTROL LOOP


0.05

1716

LIKELY DISTURBANCE

NO

MET 2

GAUGE CONTROL LOOP


0.05

4411

LIKELY DISTURBANCE

NO

MET 3

GAUGE CONTROL LOOP


0.05

5642

NO OSCILLATION

NO

MIN 1



60

2641

STICTION

NO

POW 1

LEVEL CONTROL LOOP

INTEGRATING PROCESS

5

8641

STICTION

NO

POW 2

LEVEL CONTROL LOOP

INTEGRATING PROCESS

5

8641

STICTION

YES

POW 3

LEVEL CONTROL LOOP

INTEGRATING PROCESS

5

8641

NO STICTION

NO

POW 4

LEVEL CONTROL LOOP

INTEGRATING PROCESS

5

8641

STICTION

NO

POW 5

LEVEL CONTROL LOOP


5

8641

NO STICTION

NO

PAP 1

FLOW CONTROL LOOP


1

849

STICTION

YES

PAP 2

FLOW CONTROL LOOP


1

1196

STICTION

YES

PAP 3

LEVEL CONTROL LOOP

INTEGRATING PROCESS

1

1147

STICTION

YES

PAP 4

CONCENTRATI ON CONTROL

SELF REGULATING

1

1196

DEADZONE AND

YES



Page 48 of 51

LOOP

PROCESS

TIGHT TUNING

PAP 5

CONCENTRATI ON CONTROL LOOP


0.2

18000

STICTION

NO

PAP 6

LEVEL CONTROL LOOP

INTEGRATING PROCESS

1

846

NO STICTION

YES

PAP 7

FLOW CONTROL LOOP


0.2

14101

EXTERNAL DISTURBANCE

NO

PAP 8

LEVEL CONTROL LOOP

INTEGRATING PROCESS

5

1800

NO STICTION

NO

PAP 9



5

1800

NO STICTION

YES

PAP 11

LEVEL CONTROL LOOP


15

4179

STICTION

NO

PAP 12

LEVEL CONTROL LOOP


15

4462

STICTION

NO

PAP 13

LEVEL CONTROL LOOP

INTEGRATING PROCESS

15

4237

STICTION

YES


Page 49 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


APPENDIX B TRIAL AND ERROR TESTING FOR PREPROCESSING AND POSTPROCESSING SELECTION Different combination of preprocessing (START) and post-processing (END) is used for NLPCA-AC. The combinations are tested out on the industrial loops shown in APPENDIX A. The combination that gives the highest correct identification is chosen to be used for the NLPCA-AC •

START 1 : No Treatment

•

START 2 : Detection and removal of outliers + Computing Missing Data + Denoising + Normalization

•

START 3 : Normalization + Detection and removal of outliers + Computing Missing Data + Denoising

•

START 4 : Normalization + Denoising

•

START 5 : Normalization + Denoising + Detection and removal of outliers + Computing Missing Data

•

END 1 : Normalization + Denoising

•

END 2 : Normalization

•

END 3 : Normalization + Detection and removal of outliers + Computing Missing Data + Denoising



Page 50 of 51

PREPROCESSING

POST-PROCESSING

RESULT

START 1

END 1

48/78

START 2

END 1

52/78

START 3

END 1

52/78

START 4

END 1

54/78

START 5

END 1

54/78

START 1

END 2

44/78

START 2

END 2

52/78

START 3

END 2

52/78

START 4

END 2

54/78

START 5

END 2

54/78

START 1

END 3

45/78

START 2

END 3

48/78

START 3

END 3

52/78

START 4

END 3

54/78

START 5

END 3

48/78

However, the results show that there are multiple combinations that gives the best result. Therefore, the combination with the least amount of processing steps and is the simplest is chosen to be used for the NLPCA-AC, which is START 4 with END 2.


Page 51 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic

Start

Import data (PV)

Preprocessing

Apply NLPCA

Post-Processing

Apply Average Crossing Autocovariance

Check R-Value

No No Stiction

Is R > 1?

Yes

Report Stiction


An Improved Diagnostic Tool for Control Valve Stiction based on

Recommend Documents