Data-Based Method To Diagnose Valve Stiction with Variable

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A data-based method to diagnose valve stiction with variable reference signal Jônathan William Vergani Dambros, Marcelo Farenzena, and Jorge Otávio Trierweiler Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b01234 • Publication Date (Web): 09 Sep 2016 Downloaded from http://pubs.acs.org on September 15, 2016

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Industrial & Engineering Chemistry Research

A data-based method to diagnose valve stiction with variable reference signal 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]

Abstract Stiction is a well-known villain in industry because of the limit-cycle imposed on the controller. Several methodologies are reported in the literature to automatically detect this problem using only normal operating data. However, this becomes more difficult when the loop with stiction is affected by disturbances or the sticky valve is inside a cascade loop. This study proposes two methods to automatically diagnose valve stiction when the reference signal is variable and centers primarily on recognizing triangular or sinusoidal patterns. The first method is based on the slope of the signal peaks and the second on data segmentation. These techniques were compared to a curve-fitting method, providing similar results when the reference is fixed. However, for processes significantly affected by disturbances or when the sticky valve was inside a cascade loop, stiction detection was better for both the methods proposed. These results are corroborated by simulation and industrial data.

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Introduction Oscillations in processes have recently garnered significant attention in the literature due to their impact on loop variability and high prevalence, affecting around 30% of control valves. 1 Oscillation can propagate through all the loops in a unit and the change in operating conditions causes energy losses, reduced product quality, increased rejection rates and excess valve wear. 2 The causes of oscillation include poor controller tuning, equipment failure due to malfunctioning sensors or actuators, poor process design, external disturbances and friction in actuators. The most common cause is stiction, responsible for 20-30% of oscillation cases. 3 Thus, methods aimed at the automatic detection of stiction are in high demand in industrial settings. The literature contains a significant number of methodologies to detect stiction, which can be classified into: 4 limit cycle patterns-based, 5,6 nonlinearity detection, 2,7 cross-correlation function-based, 8 and waveform shape-based detection. 9–12 With the exception of limit cycle patterns-based methods, the above mentioned techniques can detect a sticky valve using only the process variable (PV) and controller output (OP), meaning that no information on valve stem position (MV) is required. However, most of these methods consider that the process remains within a fixed reference value and is not affected by disturbances, which is not the case in most instances, Figure 1, for example, illustrates a sticky valve in a flow loop in a Brazilian refinery where the variable reference is evident. Moreover, a significant number of sticky valves is inside a cascade loop, which implies a variable operating point. In this scenario, the available methods will fail in a significant number of cases. This study aims to propose techniques to diagnose valve stiction for control loops subject to strong disturbances or cascade controllers, where there is no reference value or the mean value of process variables is time-varying. Both the methods proposed are based on waveform identification and require the location of signal peaks and valleys. To that end, a simple technique is proposed, based on segmentation of the signal into half-cycles. 2


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Stiction Models Among the different causes of variability in the system, stiction is the most difficult to model. 13 A stiction model may be needed for a number of reasons, including to simulate stiction behaviour and quantify or compensate for stiction problems. Stiction models are divided into two groups: first-principle models (describing friction phenomena through force balance and Newton’s second law of motion) and data-driven models (describing a heuristic relationship between valve input and output). First-principle models are not widely used due to the need for multiple physical parameters, such as diaphragm area, air pressure and spring constant, and because they are computationally expensive. Stenman et al. 14 introduced the first data-driven model in which the jump occurs when the force applied overcomes a stick parameter. Choudhury et al. 15 created a more precise model using two parameters, S and J (shown on Figure 2). Since Choudhury’s model cannot deal with stochastic signals, Kano et al. 6 proposed a model to correct this problem. With a view to simplifying it, He et al. 9 presented a new model with a reduced algorithm structure. Garcia 13 compared the aforementioned stiction models and proved that Kano’s model is the most efficient at characterizing stiction. In addition to dealing with both stochastic and deterministic signals, this method was the only one approved by all the ISA-recommended tests. 16,17 Thus, a stiction block based on Kano’s model was created and inserted between the controller and plant models to simulate stiction in a control loop during simulation studies.

Stiction Diagnostics Stiction detection methods have been extensively studied in recent years, although initial research dates back to the 1950s. 18 These methods can be classified as manual or automatic. Although manual methods can easily identify stiction, they are neither feasible nor costeffective when applied across an entire plant site. 2 This makes automatic methods more attractive since they only needs normal operating data that is commonly available. The first automatic stiction method was proposed by Horch. 8 It is based on cross5



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correlation between PV and OP and is only applicable for self-regulating processes controlled by a proportional-integral controller. In order to address integrating processes, Horch and Isaksson 19 developed a method based on the probability density function of the second derivative of the process output where, for a Gaussian response, oscillation is due to stiction, and for a two maxima response stiction is not the cause. Based on the relationship between valve input (OP) and output (MV), a number of methods 5,6 were proposed aimed at identifying the parallelogram shape in an MV(OP) diagram. Since MV data are not often available, controlled variables (PV) are used as an approximation, which is reasonable in rapid dynamic processes (primarily flow control loops). The method proposed by Choudhury et al. 20 is based on high-order statistics and detects system nonlinearity. To that end, two indices based on the concepts of bispectrum and bicoherence are calculated and evaluated. Other methods detect stiction based on the signal waveform. In the method proposed by Singhal and Salsbury, 11 stiction is diagnosed based on the ratio of the areas before and after the peak in the process variable. If the areas are similar, no stiction is present; otherwise, it is the cause of oscillation. Rossi and Scali 10 proposed a fitting method to differentiate between triangular or relay signals (which characterize stiction) and sine waves (characterizes aggressive control or external disturbance). An improvement was proposed by He et al., 9 whereby only triangles and sine waves are interpolated. The signal is fit to each half-period in a piecewise manner using a simple least-squares method. This methodology is computationally more efficient than the original interpolation method and will therefore be our benchmark in this study. All the methods discussed are applicable for signals with a constant mean; however, when the sticky valve is inside a cascade loop or the loop is subject to disturbances, that is, the reference signal is not constant, their effectiveness declines (see case study 4.1).

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Proposed Techniques This section describes the two techniques proposed in this study to diagnose stiction in scenarios where the operating point is time-varying or the process is heavily influenced by disturbance. Both methods are based on waveform identification, whereby the signal is differentiated into triangular and sinusoidal waveforms. This method requires only controller output (OP) and process variable (PV) data. No information on the process or valve stem position (MV) is needed.

Technique 1: Peak Slope The first method proposed is based on the slope of signal peaks and valleys. Considering a triangular signal, the slope generated by a peak and the previous point is equal to the slope of the line generated by the peak and the previous valley. In the case of sinusoidal signals, the slope generated by a peak and the previous point is almost zero. Figure 3 shows the slope for a sine and triangular shaped signal. For this method, the slope of the signal is compared with the standard slope for triangular and sinusoidal signals. Stiction is diagnosed when the mean slope of the OP or PV signal is similar to a triangle shape. If the slope is closer to sinusoidal in shape, external disturbance or underdamped controller tuning is the source of the oscillation. The slope is evaluated using any point in the signal compared to the closer peak or valley, but, as per the Figure 3, the largest difference between the slopes of the triangular and sinusoidal signals occurs close to the peak and valley values, making a complete assessment of the signal unnecessary. The procedure for the first method is as follows: 1. OP data is collected for self-regulating processes or PV data in the case of integrating processes, and peaks and valleys are identified. 2. Signal slopes are computed for each half-cycle using peak or valley points and points belonging to the evaluation interval (as shown in Figure 3), the signal slope (Ssig ) is 7




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the mean of the absolute value of all slope values found for all half-cycles; 3. The standard slope mean for triangular (Stri ) and sine (Ssin ) signals with the same frequency and amplitude are calculated; 4. The Stiction Index (SIsl ) is computed based simply on Stri , Ssin and Ssig :

SIsl =

Ssig − Ssin Stri − Ssin

(1)

5. The following rules are used to diagnose stiction, based on our experience: • SIsl ≥ 0.5 ⇒ stiction; • SIsl ≤ 0.3 ⇒ external disturbance or tight controller tuning; • 0.3 < SIsl < 0.5 ⇒ undetermined; Note that the index does not necessarily belong to the range between 0 and 1, if the mean slope for the original signal is greater than the slope for the triangular signal, the index is greater than 1, if it is less than the slope for the sine signal, the index is less than 0. The evaluation interval corresponds to the points located 20% to the right and left of a peak or valley in each half-cycle, this ensures that only the region with the largest difference between the slope of the triangular and sine signal is used. For better understanding, consider the signal (CHEM1) borrowed from Jelali and Scali 21 and shown in Figure 4(A). The data is derived from a chemical plant, where the flow is the controlled variable, so the process is self-regulating and the analyzed signal is the controller output (OP), furthermore, according to the authors, the presence of stiction is certain. To simplify the analysis, a segment was isolated and nine general points were selected for further analysis. Figure 4(B) shows the slope to the original signal, as noted, the slope must always be calculated from the peak or valley belonging to the same evaluation interval, the width of this region is variable according to the period of each half cycle, that different

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from He et al. 9 and Rossi and Scali 10 methods, are limited by peaks and valleys and not by zero-crossing values. The sinusoidal signal in Figure 4(C) is built for each half cycle by Equation 2. pi+1 + pi pi+1 − pi fi (t) = + ∗ sin 2 2

π t − Ti ∗π+3∗ 2 ∗ (Ti+1 − Ti ) 2

(2)

where p and T are vectors of size N corresponding respectively to OP or PV, and time values for the peaks and valleys and i = 1, 2, ..., N − 1 corresponds to each half-cycle. Similarly, triangular signal is created for each half-cycle by interpolation between peaks and valleys, and then the slopes are calculated. As shown by Figure 4(D), it is not required to calculate the slope for all points, since the slope is the same for points belonging to the same evaluation interval (demonstrated by points P7, P8 and P9). In order to demonstrate the slope behavior to a point outside the evaluation interval, a point located in the middle of the half-cycle was chosen. As show in Figure 4, the slope is identical to triangular and sinusoidal signal, so that, the differentiation between them cannot be made. Table 1 shows the results to the selected points. Table 1: Slope for original, triangular and sine signal for selected points; average of the absolute values of the slopes for the selected points and for all points within the evaluation interval (10−3 ). Points P1 t (s) 600 Original -8,49 Sine -3,21 Triang. -12,58

P2 P3 P4 P5 628 701 705 727 9,90 2,64 5,45 -9,62 2,76 2,20 1,62 -4,64 6,46 6,46 6,46 -13,31

P6 P7 P8 P9 772 790 792 794 -11,63 5,71 7,05 8,39 -4,61 1,35 1,72 2,09 -13,31 7,75 7,75 7,75

Selec. All 7,65 8,23 2,69 2,45 9,09 10,46

Due to the presence of noise, there are points with slope values closer to triangular signal and others closer to the sine signal (P3 for this analysis), but on average, the slope resembles the slope of a triangular signal and the SIsl value calculated by equation 1 is equal to 0.775. The complete evaluation for all points belonging to the evaluation interval resulted in SIsl equal to 0.722.

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processes, peaks and valleys are identified. 2. The signal is segmented into zones and signal frequency (Fsig ) is calculated been the number of points inside the top and bottom zones divided by the total number of points; 3. Standard distribution is computed for sine (Fsin ) and triangular (Ftri ) shaped signals in each zone and the mean between top and bottom zones is calculated; 4. The Stiction Index (SIzn ) is computed based on Fsin , Ftri , and Fsig :

SIzn = 1 −

Fsig − Ftri Fsin − Ftri

(3)

5. The following heuristic is used to diagnose stiction, based on our experience: • SIzn ≥ 0.4 ⇒ stiction; • SIzn ≤ 0.2 ⇒ external disturbance or tight controller tuning; • 0.2 < SIzn < 0.4 ⇒ undetermined; Again, the index range is not limited to the interval between 0 and 1, by the same reason already mentioned. However, it is very improbable this occurrence. As an example, consider again the signal from Figure 4, after the peaks and valleys identification, each half-cycle (limited by a peak and a valley or vice versa) is divided into 6 equally spaced zones. The signal frequency (Fsig ) is calculated for each zone as the percentage of points in the present half-cycle that belongs to a particular zone. The zone segmentation of a fragment from this signal is presented in Figure 6. Knowing that the valve has stiction, the signal must exhibit triangular shape and each segment must provide the distribution of about 16.6% (following Figure 5). The presence of noise deviates the found values from the ideal values, but the average distribution of the zones decreases the deviation. For the complete signal, the value found for SIzn was 0.89 indicating evident presence of stiction. 13




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proposed by He et al.. 9 The feedback loop used in all the simulations has a PI controller and a first order plant. In the first and second analyses, stiction detection capacity of the proposed techniques was compared to the original curve-fitting technique, 9 with a fixed reference value. In the third analysis disturbances the output of the feedback loop, while setpoint is kept constant and for the fourth analysis a cascade loop is used, thus highlighting the advantages of the techniques proposed here. In the first analysis, a standard SISO loop is studied with a stiction model inserted between the plant and the controller. The stiction model used was proposed by Kano et al.. 6 In this case, no disturbance or noise was added and the reference value was kept constant. A total of 27,720 scenarios were analyzed, with different stiction, controller and plant parameters, whose intervals are shown in Table 2. The process gain remains constant at a unitary value. Table 2: Parameters for the first analysis: no disturbance or noise added. Variable S J τ KP τI

Description Staticband (stickband + deadband) Slipjump Process time constant PI controller gain Integral action of controller

Value [3, 4, ..., 8] [0.5, 0.7, ..., 1.5] * S [10,20, ..., 100] [1, 1.4, ..., 3] [1, 1.3, ..., 2.8] * τ

The aim here is to evaluate type 2 error (i. e. the valve is sticky, but the method does not diagnose the problem) for all the methods. Based on Table 3, we can conclude that the detection capacity of both the proposed techniques and traditional curve-fitting method is almost the same. However, the zone method exhibited slightly poorer performance than the other techniques. Table 3: Percentage correct detection for the first analysis. Method InterpStic SlopeStic ZonesStic Results 99.9% 99.4% 98.4%

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A complementary analysis was also carried out in the form of type 1 error assessment, that is, when stiction is not present in the loop, but the algorithm incorrectly diagnoses it. Once again, a feedback loop with a first order plant and PI controller were used. In this case, no stiction was added and a periodic disturbance with variable frequency was inserted in the process variable output. Table 4 shows the parameter values for each scenario in the second analysis. Table 4: Parameters for the second analysis: periodic disturbance added and stiction block removed. Variable τ DP er KP τI

Description Process time constant Disturbance period PI controller gain Integral action of controller

Value [10,20, ..., 100] [16, 32, 64, 128, 512] [1, 1.4, ..., 3] [1, 1.3, ..., 2.8] * τ

As shown in Table 5, all the methods detected external disturbances in almost all cases. This corroborates the previous results, where both the proposed methods and the original interpolation technique provide similar results for stiction or external disturbance detection when the reference value is fixed. Table 5: Percentage correct detection for the second analysis. Method InterpStic SlopeStic ZonesStic Results 98.3% 100.0% 100.0%

In the third analysis, a feedback loop with stiction is affected by two ramp disturbances and one colored noise. The block diagram for the system is shown in Figure 8. Where C is the PI controller, G is the first order plant, S is the stiction model, SP is the setpoint, OP the controller output, and PV the process variable. The disturbance through a combination of three contributions: • Ramp 1: ramp with positive slope slp1 and initial time 0; • Ramp 2: ramp with negative slope slp2 and initial time 1500; 17




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Table 7: Variable parameters and their intervals for the third analysis where the process was affected by two ramp disturbances and one colored disturbance. Variable S J slp1 slp2 cnp

Description Value Staticband (stickband + deadband) [3, 4, ..., 8] Slipjump [0.5 0.7, ..., 1.5] * S Disturbance ramp positive slope [0, 0.001, 0.005, 0.01, 0.05] Disturbance ramp negative slope [0, 0.001, 0.005, 0.01, 0.05] White noise power [0, 10, 50, 100, 500, 1000]

different from peaks and valleys values used by the proposed techniques. Thus, the results for peak slope and zone segmentation methods were respectively 0.785 and 0.826, indicating evident presence of stiction, curve fitting method result was equal to 0.572 representing the uncertainty region. Table 8 highlights the advantage of the proposed algorithms over the original interpolation procedure: the technique based on peak slopes detected almost all cases, while the method that applies zone segmentation exhibited better stiction detection capacity than the benchmark used here. Table 8: Percentage correct detection for the third analysis. Method InterpStic SlopeStic ZonesStic Results 72.0% 98.0% 87.0%

The fourth analysis examined a cascade loop what means that, different from third analysis, setpoint is variable. Two PI controllers were used, but only the inner loop exhibited stiction. Disturbances were added to the outer loop. Figure 10 depicts the block diagram for the fourth analysis. The same disturbance patterns used in the third analysis (see Table 7) were applied here. Parameters for the controllers and plants studied are shown in Table 9. In this analysis, the output reference value was fixed. Table 10 summarizes the results, indicating the detection percentage for each algorithm. Figure 11 shows an example of signal from the fourth simulation. In this case, the reference presents more pronounced variation what makes part of the signal to be positioned 19




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Table 10: Percentage correct detection for the fourth analysis. Method InterpStic SlopeStic ZonesStic Results 77.0% 100% 89.0% Analyses 1 and 2 demonstrated that the results for the proposed methods are similar to the curve fitting method in the case where the signal has constant reference. However, analyses 3 and 4 demonstrated the benefits of the proposed techniques over the traditional interpolation procedure in valve stiction diagnosis. While the original method failed in around 25% of the valves studied, the zone segmentation technique failed in 12%, and the method based on peak slopes in only 1% of all cases. Specific cases analysis In order to evaluate the efficiency of the proposed techniques to different scenarios, the third simulation was reevaluated for noise sensitivity, dead time and integration processes analysis. Noise sensitivity analysis For the analysis of sensitivity to noise, a signal from the third simulation was used and white noise with variance ranging from 0 to 0.1 was added to the normalized signal as demonstrated in Figure 12 . Tests were made to the curve fitting and the proposed techniques, where the results are shown in Figure 13(A). As noted, stiction index for the proposed methods is affected by high variance noise, what makes data pre-processing necessary for these cases. Since the value of the peaks and valleys are known, the oscillation frequency of the signal is easily calculated, and from this, cutoff frequency can be chosen in order to eliminate the noise without loss of key features that characterize the stiction. To identify the optimal cutoff frequency, a triangular signal with oscillation period equal to 100 data per cycle was considered. Figure 14 presents the power spectrum of this signal demonstrating the fundamental frequency and the harmonics that for the triangular signal are just odd. The triangular signal was filtered using a Butterworth low pass filter with cutoff frequen-

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controller tuning. For the evaluation of the proposed techniques for integrating processes, the third simulation was reevaluated using the transfer function indicated by Equation 4 and the parameters from 6.

G(s) =

k τ ∗s

(4)

The results obtained are shown in Table 12, as seen, there is not significant variation to the proposed methods, but there is an improvement in the performance of the curve fitting method. As the analyzed signal (PV) is corrected by the controller and the set-point is kept constant in this case, there is no variable reference, thus any method can be used with equal efficiency. Table 12: Percentage correct detection for integrating process analysis. Method InterpStic SlopeStic ZonesStic Results 97.0% 99.0% 91.5%

Industrial Studies In this section, the industrial applicability of the proposed techniques is validated using two industrial valves provided by a Brazilian refinery, and data kindly provided by Jelali and Scali. 21 The first valve was a flow loop, with PV and OP data shown in Figure 16. Stiction behaviour is clearly evident in the phase plot. Moreover, the signal can be considered easy to analyze since the reference value is kept constant. All three algorithms applied correctly diagnosed stiction. The second industrial valve, whose PV and OP data are shown in Figure 17, is the secondary valve in a cascade loop. This valve also suffers from stiction, which is confirmed on visual inspection. The main difference in relation to the other case studies is the variable reference for PV and OP signals. When the three techniques were applied, a triangular signal was correctly identified in OP analysis by both the proposed methods. The curve-fitting method resulted in uncertain 27




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behaviour. As a second comparison of industrial data, 20 loops with known problems studied by Jelali and Scali 21 were analyzed. All the loops are self-regulating processes and the stiction results for some methods were assessed in the aforementioned study. The proposed techniques were evaluated and the results are shown in Table 13. The results for all the 93 loops provided by Jelali and Scali 21 are presented in Appendix A. Table 13: Analysis of the efficiency of the proposed methods applied to industrial data borrowed from Jelali and Scali 21 Method Correctly Identified Wrongly Identified Uncertain InterpStic 55.0% 30.0% 15.0% . SlopeStic 60.0% 20.0% 20.0% ZonesStic 65.0% 25.0% 10.0% Based on Table 13, both the proposed techniques produced better results for the analysis when compared to the benchmark method. However, the method based on the peak slope achieved less incorrect results, while the zone segmentation method achieved more correct results. These results demonstrate the advantage of the proposed techniques for industrial data, where the presence of variable reference is often found. As an example, loop CHEM14 (Figure 18) presents a clear evidence of variable reference, it is known that stiction is not the cause of oscillation. Applying the three techniques the result was: presence of stiction for curve fitting method, uncertain cause of oscillation for peak slope method and no evidence of stiction for point distribution method. Another example, loop CHEM13 (Figure 19) has evident variable reference. As noted, the zero-cross values cannot be directly identified as part of the signal is completely above or below the zero-line. Two alternatives are feasible: evaluation only for the part of the signal where the reference is constant or the alternative adopted by Jelali and Scali 21 which is the trend removal. A linear fit for the trend removal reduces, but does not completely eliminate the problem. Overall, the stiction index found by curve fitting method was 0.33, near the uncertain region (between 0.4 and 0.6) for the proposed method, the value for SIsl and SIzn 29




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at the same rate. For the analysis of integrating processes, the proposed methods showed similar results to the self-regulating process while the benchmark showed improvement in performance. The industrial applicability of the proposed techniques was corroborated by their application in two valves from a refinery as well as data taken from Jelali and Scali, 21 and the results demonstrate their advantages.

Associated content Appendix A are found in a separated document. This information is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The authors are very grateful for the grants from CAPES as well as Jelali and Scali and PETROBRAS for the industrial data provided.

References (1) Bialkowski, W. L. Dreams vs. reality: A view from both sides of the gap. Control Systems. 1993; pp 283–294. (2) 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, 1395–1412. (3) 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.

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Data-Based Method To Diagnose Valve Stiction with Variable

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