Signal Preprocessing for Stiction Detection Methods - ACS Publications

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Signal preprocessing for stiction detection methods Jônathan William Vergani Dambros, Marcelo Farenzena, and Jorge Otávio Trierweiler Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04441 • Publication Date (Web): 11 Dec 2017 Downloaded from http://pubs.acs.org on December 13, 2017

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Industrial & Engineering Chemistry Research

SIGNAL PREPROCESSING FOR STICTION DETECTION METHODS Jônathan W. V. Dambros,* Marcelo Farenzena, and Jorge O. Trierweiler Department of Chemical Engineering, Federal University of Rio Grande do Sul (UFRGS), Porto Alegre E-mail: [email protected] Keywords: Stiction, Stiction detection; Signal processing; Control valve; Process control

Abstract

Oscillation in control loops is a problem of high incidence, being stiction in control valves the most frequent cause. In the last two decades, many automatic stiction detection methods were proposed. These methods require certain signal preprocessing for proper use, where the choice of the appropriate preprocessing technique and parameters depends on the detection method and signal characteristics, and, due to the lack of information about its automatic application, are mostly led manually. The need for user interaction turns an automatic into a non-automatic detection method, which makes the application unfeasible to an entire plant with hundreds or even thousands of control loops. This work proposes techniques for automatic preprocessing according to the demands of each detection method. The techniques cover the main problems related to stiction identification: removal of noise excess, identification of peaks and valleys,

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removal of variable mean and zero-crossing identification. Satisfactory results are obtained for both simulated and industrial data.

1.

Introduction

Due to its impact on loop variability and its high incidence in process industries, studies on oscillation in control loops have been widely investigated. Oscillation can cause energy losses, reduction in product quality, increase in rejection rate and excessive valve wear.1 There are many reasons for the emergence of oscillation, among them, the most common is stiction, responsible from 20 to 30% of the cases.2 Basically, stiction is the mechanical resistance to the start motion caused by static friction in the valve stem. Once a valve with stiction stops, an extra force is required to overcome the static friction and put the valve in motion again. Overcoming the static friction, the additional force before stored as potential energy is relieved abruptly as kinetic energy, causing a jump in the valve position. If the relieved energy is higher than that required to put the valve in the desired position, the direction of movement changes and the valve stops and sticks again. The repetition of this phenomena causes the limit cycle when a controller with integral action is used, and the valve position fundamentally changes between two positions, above and below the desired point. Process industries have typically hundreds or even thousands of control valves, what makes manual stiction detection not feasible.3–5 Taking this into account, many methods for automatic stiction detection were proposed, which can be classified into four groups: limit cycle patternsbased,6,7 nonlinearity detection,8,9 waveform shape-based detection10–13 and methods based on other approaches14,15 Among these, three methods are highlighted due to the large number of citations in the literature, simplicity in implementation, and low computational cost requirement: cross-correlation,14 curve-fitting,12 and Yamashita.7


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Considering industrial data, where the presence of noise and external disturbances are common, most of the stiction detection methods require careful signal preprocessing for proper application.16 The choice of a suitable preprocessing technique and its parameters depend on the characteristics of the disturbance, noise, and signal itself. The decision may require tests and, consecutively, user interaction, what may turn an automatic into a non-automatic detection method. The use of signal preprocessing must be cautious, since the incorrect procedure can lead to signal degradation17,18 and, consequently, erroneous diagnosis of the oscillation cause. In the literature, little is discussed about the proper signal preprocessing for stiction detection. Moreover, according to Jelali and Huang19 the literature already presents a large number of methods for stiction detection, and the proposal of new ones may introduce confusion. Therefore, future research should be directed towards the improvement of existing techniques. Considering these two aspects, this work aims to present a methodology for automatic signal preprocessing for existing stiction detection methods in order to increase the accuracy of the detection and turn the methods automatic when applied to industrial data. Also, this work aims to present an overview of the importance of proper preprocessing in stiction detection, and open a discussion on this little-explored topic, intending to encourage and lead new research on the subject. In many points of the work, preprocessing techniques are presented and their role and effect in stiction detection are discussed. Besides making feasible the stiction detection to a complete plant, the automation of the signal preprocessing is essential so that the diagnosis is correctly managed. End-users often do not have sufficient knowledge in stiction detection and signal processing to avoid the degradation of the signal in manual preprocessing, which would lead to incorrect detection.


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The evaluation of the proposed techniques is focused on the three previously highlighted stiction detection methods, thus avoiding an excessively extensive analysis, which does not prevent the use to other detection methods. The paper is segmented as follows: in section 2 a brief description of the three highlighted methods is presented as well as the problems usually faced in industrial application. Section 3 presents the proposed techniques for noise excess removal, peaks and valleys identification, variable mean removal, and zeros identification. The proposed techniques are evaluated first to simulated data in section 4 and later to industrial data in section 5. Section 6 points the conclusions of this work.

2.

Stiction detection methods and preprocessing

The number of proposed stiction detection methods is large, this section describes briefly the three methods highlighted previously and their problems when applied to industrial data. The Cross-correlation method14 is based on the cross-correlation evaluation between the control output (OP) and the process output (PV) signals. If the resulting cross-correlation function is odd, the oscillation is caused by stiction; if even, by external disturbances or unstable loop. As main drawbacks, this technique is applicable only to systems with self-regulating processes and PI controllers. Loops with sticky valves have well-defined patterns in the stem position (MV), PV, and OP signals, and, mainly, considering stiction as the cause of oscillation, for self-regulating processes, OP and PV signals exhibit triangular and square shapes respectively; for integrating processes, PV signal has a triangular shape. For processes where stiction is not the cause of oscillation, the shape of the signals is typically sinusoidal in all cases.20 The curve-fitting method12 uses this knowledge to distinguish loops with and without sticky valves. A triangular and a sinusoidal


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function are fitted to each half-cycle of the OP signal (for self-regulating processes) or PV signal (for integrating processes), better fit to the triangular function indicates the presence of stiction, otherwise, the cause of oscillation is other than stiction. Based on the identification of the MV(OP) pattern, the Yamashita method7 classifies the direction of movement in I (Increasing), D (Decreasing) or S (Steady). The sequence of directions is grouped in typical sequences for stiction case and general sequences. The number of sequences for each case is counted and used to assess the cause of oscillation. Usually, MV signal is not available, but satisfactory results are obtained by using PV signal for loops with fast dynamics (i.e. loops where the flow is the controlled variable.). Little is discussed about signal preprocessing for these methods, this information is presented in Table 1. Table 1. Problems and adopted solutions for signal preprocessing for the three previously selected stiction detection methods. Detection Method

Problems

Crosscorrelation14

Variable mean

Not discussed

Zeros identification

Low-pass filter (type and parameters not specified)

Variable mean

Detrend is applied automatically (technique not specified; if non-sinusoidal disturbance, method may fail)

Accurate zero values

Linear interpolation of two points on both sides of the axis

Curve-fitting12

Adopted solutions

Filter or neural network (type and parameters not specified) Yamashita

7

Noise

Sampling interval reduction to 16 data per cycle21 (choice for sampling interval not discussed)


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In the cross-correlation method, noise influence is minor, but external disturbance makes the mean of the cross-correlation function variable. Therefore trend removal is required for the accurate evaluation by the method. The curve-fitting methods divide the signal into half-cycles limited by the zeros of the signal. The zeros identification faces three problems in the industrial application: noise causes spurious zero-crossings, variable mean deflects zero positions, and the exact value of zeros does not exist for discrete data. For the third problem, the closest value may be chosen, but this approach fails for signals with a small number of data per cycle (i.e., small sampling). Figure 1 illustrates the three problems related to the zero detection.

Figure 1. Illustration of the problems associated with zero determination in signals with noise and disturbance. The Yamashita method obtains the direction of movement in OP and MV signals, and, from its combination, identifies stiction. Since the direction is obtained from the difference between the current and the previous values, the presence of noise influences the analysis.


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Among the few works that discuss preprocessing in well-established stiction detection techniques are: •

the noise-band based technique proposed by Salsbury and Singhal22, which intends to avoid the detection of spurious zero-crossings caused by noise in area-peak detection method;11

•

the sampling interval reduction to 16 data per cycle before the analysis by Yamashita method proposed by Kano et al.,21 and;

•

the, in most cases, manually selected preprocessing in the comparative work of Jelali and Scali.16

Zakharov et al.23 and Garcia et al.24 proposed a different approach to increasing the performance of the detection using well-established techniques. First, the data are characterized according to the level of oscillation, noise, disturbance, and non-linearity; after, suitable detection techniques are selected according to the characteristics of the data. The approaches intend to solve the problem of stiction detection by a different mean than creating a new detection technique, which is a remarkable contribution.

3.

Proposed techniques

Considering the significance of signal preprocessing for stiction detection and the lack of studies related to this topic, in this section, a new methodology is proposed for the solution of the problems usually faced, which are: noise excess removal, peaks and valleys identification, variable mean removal and zeros identification. 3.1. Noise excess removal The noise excess is usually removed by low-pass filters. The choice for the filter cutoff frequency must be careful when the objective is stiction identification. Low cutoff frequencies


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may efficiently eliminate the noise, but excessively smooth the signal, eliminating stiction features. High cutoff frequencies retain the shape of the signal, but the noise may be little removed. Thus, this section seeks to identify the ideal cutoff frequency of the low-pass filter, so that the filter maximally eliminates the effect of noise minimally changing the signal shape. Initially, Figure 2 shows the power spectrum for signals with 50 data per cycle for the four different shapes typically observed in stiction analysis: sinusoidal, triangular, sawtooth, and square.

Figure 2. Time and frequency response for sinusoidal, triangular, sawtooth and square signals with 50 data per cycle. Figure 2 shows the fundamental frequency, which for all cases are 0.04 (normalized frequency between 0 and 1) and the harmonics corresponding to each signal. Triangular and square signals have only odd harmonics while sawtooth signal has even and odd harmonics. Similar observations and harmonic analysis on stiction typically found signals have already been made by Dambros et al.18 and Ahammad and Choudhury.25 The fundamental frequency represents a purely sinusoidal function in the signal oscillation frequency, while the harmonics are sinusoidal functions that modify the waveform, turning the


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sinusoidal signal into, in these cases, triangular, sawtooth and square signals. The use of lowpass filters, in addition to eliminate noise, also removes some higher frequency harmonics, so, the signal tends to become smoother (or closer to a sinusoidal function) by reducing the number of harmonics (or decreasing the cutoff frequency). Thus, before searching for the ideal cutoff frequency, it is sought to identify the minimum number of harmonic required to maintain the shape of the signal. For this, we consider first the Fourier series for triangular, sawtooth and square waveform, represented respectively by Equations 1, 2 and 3: =

∗

()**+ = −

(./ =

01

∑ ,,,…

-

∗ sin #2%/'

∗ ∑ ∗ sin #2%/'-

∗ ∑ ,,,… ∗ sin #2%/'

(1)

(2)

(3)

where Ci and Li for i = 1, 2 and 3 are respectively the amplitude and the period of oscillation of the signals. Through the Fourier series, it is again noted that the triangular and square functions have only odd harmonics (n is only odd), while the sawtooth function has also even harmonics. Through the truncation of the Fourier series, it is possible to observe the effect of the number of harmonics in the shape of the signal. For this, the number of terms is limited from 1 to M, for M = 1, 2, 3, …, 20, and the Mean Squared Error (MSE) of the truncated series is calculated in relation to the series without truncation. The result for the 3 waveforms is shown in Figure 3.


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Figure 3. Normalized Mean Squared Error (MSE) between the truncated and nontruncated series as a function of the number of terms. As seen, the error of the triangular wave decays more rapidly with increasing number of terms (or harmonics), whereas for the square wave the decay is slower. Empirically, the minimum value of 5 harmonics is established for the filtering for any of the three signals. Although square wave is overly smoothed, the practical application has shown good results for this choice. With the minimum number of harmonics set and equal to 5, the cutoff frequency of the lowpass filter must be established between the frequency of the fifth and sixth harmonics. The intermediate value equal to 5.5 is used in this work. This value corresponds to a frequency equal to 5.5 times the fundamental frequency of the signal (or oscillation frequency), in this way, the cutoff frequency can be calculated from the oscillation frequency of the signal, which in turn can be obtained both in the time domain (inverse of the period between peaks, for example) or in the frequency domain (spectral peak identification, for example).


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The performance of the noise removal is influenced by signal sampling. For signals with a low number of data per cycle the cutoff frequency will be high, resulting in a large low-frequency band without noise removal. This problem does not influence the significance of the proposed technique since low sampling signals are not recommended for stiction detection regardless of the presence or absence of noise.26 3.2. Peaks and valleys identification, trend removal and zeros identification In addition to noise, another major problem encountered in industrial data is the presence of variable mean. Mainly found in processes with cascade controller or with external disturbances, the variable mean deflects zeros position and autocorrelation function. A third problem is the signal small sampling, which can affect zeros position. 3.2.1. Peaks and Valleys identification Peaks and valleys in smooth signals are easily identified by the zero-crossing of the first derivative, which is not valid for noisy signals. Noise removal by low-pass filter is an alternative, but, for the removal of all the peaks and valleys caused by noise, it would be necessary to use a filter with low cutoff frequency, which would exceedingly smooth the signal and affects stiction detection. Recently, a new method for peak and valley identification was proposed by Zakharov et al..23 The technique divides the signal into windows of length equal to the length of the half-cycle, then, the maximum (peaks) and minimums (valleys) values are found intercalated. Although simple, the application of the method requires guesses for the half-cycle length, also, because the length value is kept constant, the windows tend to be divided incorrectly over time. For this work, the technique proposed by Dambros et al.18 is slightly modified and used for peaks and valleys identification. The algorithm is described below:


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1. OP or PV signal is collected and subtracted by its mean value; 2. The signal is smoothed by using a forward-backward low-pass filter, the second derivative is calculated, and the second derivative zero-crossing points are located; 3. The original signal (before smoothing) is divided into windows limited by previously identified zero-crossing values; 4. Finally, the extreme value is defined in each window (maximum and minimums values intercalated), corresponding to peaks and valleys. For signal smoothing (step 2), the use of the forward-backward filter is required to avoid delay in the smoothed signal. The cutoff frequency of the filter is defined as equal to the oscillation frequency of the signal, which is represented by a peak in the frequency domain. Consequently, the resulting smoothed signal is approximately a sinusoidal function of the same frequency as the original signal with the presence of variable mean. In this study fifth-order Butterworth filter is used, but the use of other IRR or even FIR filters could be considerated. The use of a filter for smoothing the signal (instead of spline function) is the only difference when compared to the original algorithm proposed by Dambros et al.,18 since the selection of parameters for automating the method is easier (just the cutoff frequency is required). For general cases, the highest peak in the time domain corresponds to the oscillation frequency, but for the presence of disturbance, there may be a higher peak at frequencies close to zero. In order to eliminate the influence of the disturbance, the spectral density is divided into segments where only values above two standard deviations are considered (eliminating the influence of noise and harmonics). Finally, the maximum value of the segment of highest frequency is considered the oscillation frequency and, therefore, the cutoff frequency.


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As an example, Figure 4 illustrates the spectral density for a strongly disturbed signal. The spectrum is divided into two segments, and the oscillation frequency is the frequency of the second segment peak, which is approximately equal to 0.018.

Figure 4. Identification of the oscillation/cutoff frequency by spectral density for a signal strongly disturbed. Figure 5 presents the step-by-step procedure for the identification of peaks and valleys, where a noisy square-shaped signal is used.


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Figure 5. Identification of peaks and valleys for a noisy square-shaped signal: (A) PV data is collected; (B) Signal smoothed by filter and inflection points located (second derivative zerocrossing); (C) Splitting the original signal into windows bounded by the inflection points of the filtered signal; (D) location of the extreme point for each window. (Loop CHEM1 borrowed from Jelali and Huang19) The technique depends on the signal oscillation frequency value for the appropriate cutoff frequency choice, which creates problems for signals with multiple oscillations and oscillation with variable frequency, restricting the application of the method to signals with single and regular oscillation. Both restrictions can be evaluated using the oscillation detection method proposed by Thornhill et al..27 Despite the restrictions, the methodology continues to be applicable for most cases where stiction is present. 3.2.2. Trend Removal The trend (variable mean) can be easily removed by the application of high-pass filters. For this, it would be enough to use a cutoff frequency below the fundamental frequency (or


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oscillation frequency), but its use causes distortion in the original signal, especially for signals with a low number of oscillation periods (fundamental frequency close to zero). Another alternative to removing the variable mean is through the use of curve fitting, mainly linear, which is not valid for most industrial signals, where the trend has behavior hardly represented by a mathematical function. From the peaks and valleys previously located, the trend can be easily found. For this, two lines are fitted using third order spline interpolation: one for the peaks and another for the valleys. The average value between the lines is the trend of the signal. Then, for trend removal, the obtained average signal is subtracted from the original signal. This process is similar to that proposed by Srinivasan et al.28 with the difference that only the values of the peaks and valleys of the main oscillation are employed in the interpolation. The use of third-order interpolation causes a problem for extrapolation. Thus it is advisable to keep the extreme values constant. Figure 6 shows the interpolated lines and the trend signal.

Figure 6. Evaluation of the variable mean for a signal affected by disturbance. (Loop CHEM1 borrowed from Jelali and Huang19)


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3.2.3. Zeros identification The removal of the variable mean is only the first step on zeros identification. In addition to the disturbance, the noise and the small sampling of the signal negatively influence the identification. Spurious zeros may be detected due to noise and therefore must be disregarded for the stiction analysis. Again, knowing the location of the peaks and valleys, zeros can be easily identified. A zero must always be followed by a peak or valley, which, in turn, must be followed by another zero, if there is more than one consecutive zero, then there is zero caused by noise. The number of zeros between a peak and a valley is always odd, regardless the presence or absence of noise, so for this method, only the median value is considered. The third and final problem related to the zero identification is caused by the sampling rate, which if overly small in relation to the oscillation frequency, may not find values close to zero. This problem is easily corrected by the use of linear interpolation between the point before and after zero-crossing, as proposed by He et al..12 The signal after the complete preprocessing is illustrated in Figure 7.


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Figure 7. Zeros detection after variable mean removal. (Loop CHEM1 borrowed from Jelali and Huang19)

4.

Case study 1 – simulated data

In this work, the model proposed by Kano et al.6 is used to simulate the stiction behavior, since this model was approved by all ISA tests, according to Garcia.29 The process and controller transfer functions used also come from the work of Kano et al..6 For self-regulating processes, the transfer function is represented by Equation 4,

23 = 4.-(6

(4)

and the controller transfer function by Equation 5.

27 = 0.5 :1 < = 4.(

(5)

For integrating processes, the process transfer function is the represented by Equation 6,

2 = > ( (

(6)

and the controller transfer function by Equation 7.

27 = 3 :1 < = 4(

(7)


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For the cases without stiction, sinusoidal signals with oscillation period and amplitude similar to those generated for the case with stiction are created. The noise signal is generated as a random signal of normal distribution. The disturbance signal is generated from a second random signal modified by the transfer function presented by Equation 8. The degree of the noise and disturbance is measured by the variance of each signal.

2@ = 444(6

(8)

During the tests, 10 standard disturbances (D1, D2, ..., D10) generated from different random signals are used. The standard signals are shown in Figure 8.

Figure 8. Standard disturbance signals employed in the simulations for the analysis of the proposed techniques. Finally, the loop used for the simulation is presented in Figure 9, where C, S and G are respectively the controller, stiction and process block.


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Figure 9. Representation of the loop used in simulated case study. During the analysis, the S (deadband + stickband) and J (slip jump) parameters for Kano stiction model remain constant and respectively equal to 5 and 1. All signals, except when specified, are simulated for 2000 seconds with sampling rate equal to 1 second. The analyzes are performed in different ways for each of the previously selected detection methods, aiming to evaluate the influence of only the problems that can lead to incorrect stiction detection. Thus, the analyses are divided into sections, one for each method. Each section discusses: • Signal problems that affect the identification and the conventional preprocessing applied; • How data are generated for preprocessing analysis; • How preprocessing analysis is performed; • Results and ideal preprocessing definition. 4.1. Evaluation of the cross-correlation detection method For cross-correlation method, the presence of disturbance causes variation in the mean of the cross-correlation function (presence of trend), which compromises the stiction analysis. The conventional preprocessing for this technique is the trend removal by the use of a high-pass filter or by some curve-fitting. The presence of noise does not affect the cross-correlation method since its effect is damped by the correlation calculation, so only the influence of the variable mean will be analyzed.


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For the analysis, the 10 standard disturbance signals with variance equal to [0, 0.025, 0.05, ..., 1.000] are used. Self-regulating processes with and without the presence of stiction are considered, and thus, 820 pairs of signals are generated. The evaluation is not done to integrating processes since the detection method is not applicable to this type of process. Figure 10 illustrates a signal generated for the analysis, as seen, the variable mean is evident for the OP signal.

Figure 10. OP and PV signals generated for cross-correlation method analysis, where the D5 standard disturbance signal with variance equal to 1 is used. The preprocessing tests are conducted in three ways: without the use of any signal preprocessing technique, use of the proposed methodology for trend removal only in the OP signal and use of the methodology in both signals. The use of the methodology only to the OP signal is valid for cases where the setpoint is kept constant, and the variable mean in the PV signal is not observed. The result for the two stiction indices for the cross-correlation method (∆δ and ∆τ) is presented in Table 2. Table 2. Variation of the stiction index for the cross-correlation method using the proposed methodology for the removal of the variable mean.


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∆δ

Without Stiction

Preprocessing

With Stiction

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


Min.

Max. Mean

∆τ Var.

Min.

Max.

Mean

Var.

Without

0.001 0.004 0.002 0.001

0.021

0.080 0.054 0.016

Only on OP signal

0.000 0.005 0.002 0.001

0.000

0.080 0.040 0.019

On both signals

0.000 0.004 0.001 0.001

0.000

0.091 0.042 0.021

Without

0.552 0.999 0.888 0.090

0.818

1.000 0.980 0.039

Only on OP signal

0.899 0.927 0.917 0.005

1.000

1.000 1.000 0.000

On both signals

0.918 0.929 0.922 0.002

1.000

1.000 1.000 0.000

The analysis proves the greater variability in both the stiction indexes where the preprocessing is not used, mainly to the signals with the presence of stiction. Even so, all indexes evaluated are within the correct identification range. Figure 11 shows an example of the signals analyzed, where Figure 11(A) presents, respectively, the OP and PV signals not affected by any disturbance, affected by the disturbance and, finally, the signals after the removal of the variable mean. In Figure 11(B), the crosscorrelation for the three OP-PV pairs are presented. As seen, the line for the cross-correlation for the cases without the presence of disturbance (black line) and with the presence of disturbance and use of preprocessing (green line) are overlapped. For the case without preprocessing (blue line), the line has an explicit variable mean, but it is closer to the other in the central region, which is the region used by the method to evaluate the stiction presence. As seen in Figure 11(B), all cross-correlation functions are clearly even.


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Figure 11. Application of the cross-correlation method to signal without disturbance, with disturbance not using preprocessing and with disturbance using preprocessing for the fourth disturbance standard (D4) with variance equal to 1. Thus, removal of the variable mean is not entirely necessary for cross-correlation method. Most of the incorrect identification may be caused due to another source of shift in the process. Although, the use of trend removal is advisable to reduce the misclassification. 4.2. Evaluation of the curve-fitting detection methods The curve-fitting methods depend on the correct half-cycle segmentation. In this way, the preprocessing aims to remove noise and variable mean in order to identify correctly the zeros. The conventional procedure is the removal of noise through the use of low-pass filters and trend removal by linear fitting. The use of the filter, as stated before, may depend on user interaction, and the removal of the variable mean by linear fitting does not always completely solve the problem. To corroborate with this statement, Figure 12 presents the OP signal with the presence of stiction, using disturbance (D9 standard disturbance) of variance equal to 1 and noise of variance equal to 0.1. As observed, the trend removal by linear fitting slightly corrected the


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signal. For better results, the trend could be removed by a different fitting function (second order or sinusoidal function, for example) or by using only part of the signal for the analysis, but both alternatives may require user interaction.

Figure 12. Comparison between the proposed technique and the commonly used linear fitting for trend removal in a signal strongly affected by disturbance. For the preprocessing analysis of the curve-fitting method, the proposed techniques are applied to self-regulating and integrating processes with stiction presence and sinusoidal signals (without stiction). The 10 disturbance patterns with variance equal to [0, 0.1, 0.2, ..., 1.0] and noise signal with variance equal to [0, 0.01, 0.02, ..., 0.10] are used. The preprocessing tests are performed in four different ways: without the use of preprocessing, using only the techniques for noise excess removal, using only the techniques for trend removal and zeros identification, and, finally, using the all proposed techniques. Table 3 presents the result after the use of the four different forms of preprocessing. The signal is considered not suitable to be analyzed due to the presence of noise when there is more than one zero between a peak and a valley or vice versa and considered not suitable to be analyzed


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due to the presence of variable mean when the signal is moved up or down the zero line in such a way that some half-cycle presents less than 10 points. Table 3. Comparison of the result for different types of preprocessing for the curve-fitting method.

Preprocessing

Applicable

Zeros caused by noise

Variable mean

Both problems

Without

404

821

554

1851

Filter (noise excess rem.)

1232

0

2083

315

Trend rem. and zero iden.

3599

0

31

0

Complete technique

3630

0

0

0

As seen, the proposed techniques can remove noise excess, and variable mean for all the signals. It is worth mentioning that the generated signals present oscillation frequency virtually constant (regular and single oscillation), a requirement for the application of the techniques. Otherwise, the efficiency would be reduced. Another remark in Table 3 is that filtering is not ultimately required to make the signals suitable for the application of the curve-fitting method, but noise may interfere on stiction index. For this reason, a second test is carried out using all the signals where the trend is removed without and with the removal of noise excess (column 3 and 4, respectively). Figure 13 presents the results for self-regulating and integrating processes with stiction and processes without stiction where the given value is the mean of the stiction indexes for all the 10 disturbance patterns.


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Figure 13. Detection index for curve-fitting method as a function of the disturbance and noise variance using the proposed techniques for: (A) Self-regulating process without prefiltering; (B) With prefiltering; (C) Integrating process without prefiltering; (D) With prefiltering; (E) Sinusoidal signal without prefiltering; (F) With prefiltering. Knowing that the index for the curve-fitting method should be greater than 0.6 to indicate the presence of stiction and lower than 0.4 to indicate another cause of oscillation, through Figure 13, it is possible to conclude that excessive noise interferes in the curve-fitting method, causing the stiction index to tend to 0.5 with the increase of the noise magnitude. The filter incorporation demonstrated an improvement in the results, where the variation of the stiction index is smoother with the growth of the magnitude of the noise and the disturbance. Still, it is important to realize that for the region where there is no noise and disturbance (lower left area for all graphs), the stiction index for the analysis with and without the filter resulted in almost the same result, indicating that there is no excessive smoothing of the signal by the use of the filter.


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The applied methodology presented similar results for both self-regulating and integrating processes, which is valid since the signal analyzed for both processes has the same shape (triangular form). Finally, for the curve-fitting method, the use of all the proposed techniques is advisable to correct zero identification and reduce the variability of the stiction index caused by noise. 4.3. Evaluation of the Yamashita detection method The preprocessing for the Yamashita method aims to remove the noise effect that is amplified by signal differentiation since the direction of movement in the MV(OP) plot is obtained by the difference between the current and previous points. The conventional procedure is to use of low-pass filter for noise removal and, for cases where the oscillation frequency is known, the downsampling, which, according to Kano et al.,16 should be lead in such a way that the final sampling would be equal to 16 data per cycle (states without proof). For the analysis, self-regulating processes with stiction and sinusoidal signals are used, the signals are generated with sampling rate of approximately 1000 data per cycle and noise with variance equal to [0, 0.005, 0.010, ..., 0.100] is used. The preprocessing analysis is conducted in two ways: using only downsampling and using downsampling and noise excess removal. Figure 14 shows the results in the form of a contour plot.


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Figure 14. Detection index for the Yamashita method as a function of the sampling rate and noise variance for the cases: (A) with presence of stiction and without noise removal; (B) with stiction and with noise removal; (C) without stiction and without noise removal; And (D) without stiction and noise removal. Knowing that for the Yamashita method, the index must be greater than 0.25 to indicate stiction presence and less than this value to indicate another cause of oscillation, Figure 14 shows that: •

For the case with stiction and sampling rate of approximately 25 data per cycle, the stiction index remains high even without the use of filters. For the case without stiction, the value of the index is adequate for the whole analyzed range.

•

Removing noise excess eliminates the problem for high sampled signals.

•

The use of filter results in a small decrease in the stiction index for sampling rate equal to 25 data per cycle (Figure 14(B)), indicating excessive signal smoothing, even though the index still indicates strong evidence of stiction.


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Thus, it is concluded that both sampling reduction to values close to 25 data per cycle and noise excess removal is efficient as preprocessing techniques for the Yamashita method.

5.

Case study 2 – industrial data

In the extensive work of Jelali and Scali,16 eleven stiction detection methods were tested on 93 control loops from real plants. Depending on the method and the characteristic of the signals, preprocessing was used or not. The choice of the preprocessing technique was individual for each loop for many cases (for details, see original work). Some of the preprocessing techniques were: low-pass and Savitzky-Golay filters for noise removal, high-pass filter and linear fitting for trend removal. In this section, the proposed techniques for signal preprocessing are tested to selected loops and compared to the results obtained by Jelali and Scali, considered here as a benchmark. The result for all 93 loops is presented in the Supporting Information. Among the 93 loops provided by the benchmark, 18 are pre-classified as non-oscillatory. Among the remaining, 6 loops are diagnosed in this work with non-regular oscillation (changes in oscillation frequency over time), 4 loops with multiple oscillations (several peaks in the power spectrum) and 3 loops without oscillation (diagnosed by visual inspection). These loops are not appropriated to be analyzed by the proposed technique, although it is analyzed for the cases with multiple and irregular oscillation for comparison purposes. Since few loops provided by the benchmark have known cause of oscillation (20 loops), the comparison is made between the benchmark results and the results obtained by the application of the proposed techniques, then, an example of contrasting result is analyzed in more details. Figure 15 shows a preview application of the proposed techniques for three different loops. As seen, the resulting PV(OP) diagram does not exhibit center displacement which is characteristic


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for cases with variable mean (before preprocessing) as well as the noise excess is efficiently removed.

Figure 15. Application of the proposed techniques to loops CHEM1, CHEM15, and CHEM25 4.1. Evaluation of the cross-correlation detection method As discussed in the previous section, the use of preprocessing for the stiction identification by the cross-correlation method is not entirely required, althought is advised in order to reduce misclassification. The benchmark uses high-pass filters to eliminate the variable mean where the cutoff frequency is based on the oscillation frequency, but detailed specifications are not provided. For the comparison, the technique proposed for the variable mean removal is used for all loops. Discarding previously the loops without oscillation presence and loops from integrating processes, where the cross-correlation method is not applied, 57 loops are analyzed and compared with the benchmark results. Among these, 48 present the same result and 9 present different results. Similar results prove that data preprocessing is not very relevant to this method or that the preprocessing used by the benchmark is also efficient in the variable mean removal.


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Figure 16 shows one of the examples that obtained different results (CHEM49) for the comparison. The cross-correlation function between OP and PV signals (before and after preprocessing) shows that there is little displacement between the cases with and without preprocessing, both indicating clear odd cross-correlation function (stiction presence). Again, preprocessing is not completely required for the correct identification. For the benchmark, the result is the uncertain cause of the oscillation. As the specifications for the preprocessing by the benchmark were not provided, a deeper analysis cannot be lead, one of the reasons for this difference may be the excessive signals smoothing caused by incorrect cutoff frequency selection.

Figure 16. Cross-correlation for the signal without and with preprocessing for loop CHEM49. 4.2. Evaluation of the curve-fitting detection method For the curve-fitting method, the preprocessing adopted is the noise excess removal, trend removal, and zeros identification. The benchmark uses several strategies for preprocessing for this method, among them: trend removal (not detailed), use of only part of the signal and Savitzky-Golay filter. The approach seems to be chosen manually for each signal.


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Among the 93 loops provided by the benchmark, 28 are not analyzed because of the nonoscillatory pattern, among the others, 52 presented the same result, and 13 presented different results for stiction detection. Again, the comparison is little divergent, even considering that many loops show variable mean, which should compromise the use of the method. In this way, the preprocessing utilized by the benchmark gave virtually the same results. Since the benchmark choice for preprocessing is individual for each loop, the proposed technique proves to be advantageous, since its preprocessing and, consequently, stiction identification is automatic. In Figure 17, two selected loops where the results are different (CHEM 13 and CHEM 49) are shown and, as seen, the two loops present evident variable mean. For the benchmark, the first loop is corrected by trend removing; the second is analyzed without the use of preprocessing, the result is the stiction index respectively equal to 0.12 and 0.14 (no stiction in both cases). For the proposed techniques, the trend is efficiently removed, and the result is respectively equal to 0.46 and 0.49 (uncertain presence of stiction in both cases). Figure 17 shows the loops before and after the preprocessing.

Figure 17. Loop CHEM13 and CHEM 49 before and after preprocessing. 4.3. Evaluation of the Yamashita detection method


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The preprocessing technique for Yamashita method is the noise excess removal by a low-pass filter and/or the downsampling to values close to 25 data per cycle. The benchmark only uses noise removal by filter usage, but the criteria used is not specified. Since MV data are not available, the analysis should be lead only for fast dynamics processes using PV signal. Thus, the benchmark evaluates 44 loops but includes in the analysis loops without the presence of oscillation. For the comparison, only the 35 loops with the presence of oscillation are tested. Among these, 22 loops presented the same result, and 13 presented different results. The divergence may be mainly due to the different choice for preprocessing. For loop CHEM23 (Figure 18) different results were obtained, where, by visual inspection, the presence of stiction is clear. For the benchmark, the stiction index was 0.167, not indicating stiction presence, while the index after the application of the proposed preprocessing is 0.45, indicating a strong presence of stiction. As the preprocessing technique used by the benchmark was not detailed, it is not possible to do a deeper analysis. The probable cause of misclassification for the benchmark is the use of high cutoff frequency, which was not sufficient for the noise excess removal.

Figure 18. Application of the downsampling to loop CHEM23 for later application to the Yamashita method.


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Overall, the results obtained by the application of the proposed techniques are similar to those reported by the benchmark. The results are summarized in Table 4. Table 4. Summary of the results for the comparison with the benchmark. Detection method

Number of evaluated Loops

Same diagnostic as benchmark

Percentage

Cross-correlation14

57

48

84,2

Curve-fitting12

65

52

80,0

Yamashita7

35

22

62,9

5. Conclusions In the present study, signal preprocessing techniques for stiction detection methods are proposed. The techniques aim to automate the preprocessing and, therefore, the detection methods. The techniques are created with the care of preserving signal form, necessary to allow the correct stiction evaluation. The article presents a technique for noise excess removal, peaks and valleys identification, trend removal and zero identification. The noise excess is removed by the use of low-pass filter with cutoff frequency equal to 5.5 times the fundamental frequency (oscillation frequency). Peaks and valleys are identified by dividing the signal into windows bounded by inflection points of the smoothed signal. The variable mean is the mean of the third-order spline functions fitted to the peaks and valleys. Finally, the zeros are identified as the median value of all zeros found between a peak and a valley, and vice versa. The choice of the preprocessing technique depends on the stiction detection method. In this work, the proposed techniques are evaluated to three stiction detection methods. For the cross-


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correlation method, the technique for trend removal is used. Preprocessing for the curve-fitting is the complete proposed methodology. For the Yamashita method, either downsampling at values close to 25 data per cycle or noise excess removal can be used as a preprocessing method. The proposed preprocessing techniques are compared with data borrowed from of Jelali and Huang19. The results of the proposed techniques and the benchmark presented similar results for a large number of analyzes, indicating a satisfactory result, considering that the benchmark uses individual preprocessing according to the need for most cases. Some loops that obtained different results by the comparison clearly demonstrate problems due to the poor use of preprocessing by the benchmark. Despite the good results, the proposed technique is limited because the peak identification technique required the identification of a peak in the power spectrum of the signal, which makes the techniques restricted to signals with regular and single oscillation. Besides presenting techniques for signal preprocessing on stiction detection, this work introduces the importance of the topic. Over the last 20 years, efforts have been put in order to create an efficient stiction detection method, resulting in a large number of methods (over 30) and a persistent problem. This work seeks the solution from a different perspective: preprocess the signal to facilitate the subsequent diagnosis. The work present import insights in the topic with the intention of facilitating and encouraging further research on the subject. Supporting Information The results for the application of the proposed techniques for all 93 loops borrowed from Jelali and Huang19 are found in a separated document. This information is available free of charge via the Internet at http://pubs.acs.org/. Acknowledgement


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The authors are very grateful for the grants from CAPES and Petrobras. References (1)

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Table of Contents (TOC)


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Signal Preprocessing for Stiction Detection Methods - ACS Publications

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