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Journal of applied research and technology

versión On-line ISSN 2448-6736versión impresa ISSN 1665-6423

J. appl. res. technol vol.20 no.5 Ciudad de México oct. 2022  Epub 31-Jul-2023

https://doi.org/10.22201/icat.24486736e.2022.20.5.1606 

Articles

Health index for power transformer condition assessment: A comparison of three different techniques

D. A. Zaldivara  * 

A. A. Romeroa 

aInstituto de Energía Eléctrica, Universidad Nacional de San Juan - CONICET, Argentina


Abstract

In practice, the condition state of Power Transformers (PT) is quantified by using Health Index (HI). This paper analyzes and compares three different state-of-the-art algorithms to compute HI. The first one uses a Weighted Sum Model (WSM), the second is based on a Fuzzy Inference System (FIS), and the third combines both techniques, i.e., WSM and FIS. These three approaches are tested in a PT fleet composed of 30 units. Results show that each approach produces different HI values for the same PTs. Therefore, decision making regarding the PT fleet will depend on the selected approach for HI calculation. This work proposes merging the knowledge involved in each analyzed approach by using a K-means clustering technique to overcome this drawback. This solution could help the asset manager to make adequate decisions regarding the maintenance scheduling of PT when there is uncertainty about the appropriate approach to be selected.

Keywords: Health index; power transformers; fuzzy logic; condition assessment

1. Introduction

Power Transformers (PTs) constitute one of the most critical assets in power systems (Rønneberg, 2017). For this reason, special attention must be taken to reduce the PT failure rate to the minimum possible level.

Powe transformer condition assessment represents a key indicator to make adequate maintenance/replacing decisions, thus reducing the failure rates. Several techniques (Romero-Quete et al., 2017; Scatiggio et al., 2018; Vasquez & Jayaweera, 2020; Zeinoddini-Meymand & Vahidi, 2016) have been developed to assess the condition of PT. Health Index (HI) is one of these techniques, it uses as input parameters different criteria such as ageing of oil-impregnated paper (Liang et al., 2017), apparent age (Tamma et al., 2020), or the condition of other PT subsystems (e.g., load tap changer, bushings, cooling system) (Jian et al., 2020).

The development of a HI does not only include measurable parameters but, expert knowledge is also required to attain a more robust and reliable result (Bohatyrewicz et al., 2019). Even though HI tends to use almost the same input framework, employed algorithms take different approaches to process input data. For instance, main algorithms include systems based on Weighted Sum Models (WSM) (Jahromi et al., 2009; Jian et al., 2020; Naderian et al., 2008; Tamma et al., 2020), systems based on the Markov chain model (Yahaya et al., 2017), fuzzy logic systems (Cerón et al., 2015; Mharakurwa & Goboza, 2019; Rosero-Z et al., 2018), and systems based on artificial neural networks (Islam et al., 2017).

Despite the several and different techniques to compute a HI for PT, a simple question can arise for an asset manager in charge of a PT fleet: which one is the adequate tool to compute HI. Having in mind the above question, and after an in-depth review of the HI techniques listed in the previous paragraph, three of them were selected to be compared in this article, i.e., (Cerón et al., 2015; Li & Song, 2014; Mharakurwa & Goboza, 2019). The selection of the HI techniques was supported by the fact that these use clearly defined quantities, measures, and test regularly done by PT owners during routine inspections.

There are some differences between the three HI calculation techniques. Although (Li & Song, 2014) and (Cerón et al., 2015) use almost the same input parameters, (Li & Song, 2014) makes use of WSM to process data, while (Cerón et al., 2015) employs fuzzy logic. On the other hand, (Mharakurwa & Goboza, 2019) presents some differences in the set of input parameters regarding the other two techniques, and combines the weighting technique and the fuzzy logic methodology to reach the final HI score.

In this context, this work aims to analyze the three methods to determine the influence of the algorithm technique chosen and discern how the decisions made by the authors affect the evaluation of the condition of the PT. This will be particularly useful to attain a major understanding of the importance of the algorithm used for processing the input data and how this can influence the final HI value.

Section II presents a brief description of the weighting technique and the Fuzzy Inference System (FIS) technique. Section III introduces the three models studied in detail, meanwhile, Section IV explains the proposed comparison method, the results, and discussions.

2. Health index calculation

The Health Index is a magnitude that quantifies and easily provides an understanding of the general condition of a PT. HI is calculated by using most of the representative elements of PT diagnosis (Gorgan et al., 2010). Most of the methodologies to calculate HI employ WSMs. A WSM establishes linear relationships among a number of decision criteria (e.g., results of tests, diagnostics, visual inspections, etc.). Then, each criterion is assigned with a representative or performance value and a specific weight according to its importance. Finally, results of products between performance value and weight, for each criterion, are added into a summation which provides the resultant HI. Approaches based on WSM tend to use different relations to calculate the final value of the HI, but most of them are a variant of the formula used in (Naderian et al., 2008).

A Main drawback of WSM is that the definition of the criteria weights may differ from an expert to another since expert judgment is invariably required to construct the final HI formula. This variance of weights causes a different HI final score between the formulas proposed by different authors.

To overcome the above drawback, some authors (Idrees et al., 2019; Patil et al., 2019; Ranga et al., 2017) propose a different approach to the way the input data is processed. Based on the uncertainty generated by the different opinions of the experts when assigning weights to HI calculation criteria, they propose the use of the FIS to calculate the HI.

The implementation of a FIS-based methodology requires the fuzzification of input data for each criterion, which is often given in numerical values. The fuzzification process involves the definition of membership functions (i.e., related with linguistic variables as good, fair, bad, etc.) which represents states of condition for each criterion into its numerical range of variation.

To process the fuzzified data a FIS relies on inference rules based on non-numerical expressions. This characteristic allows to set aside the issue of assigning weights to the state elements, however, to design the inference rules is required to discern the level of criticality of each criterion and how they are related to the general PT condition, in (Ross, 2010; Singh, 2012; Trillas & Eciolaza, 2015) more detailed information about fuzzy systems can be found.

3. Techniques under analysis

3.1. Health index based on a weighted sum model

Developed by Li and Song (2014) and based on WSM, HIWSM is computed as the result of adding four health subindices, each one of the following criteria: 1) age of the PT, 2) the insulating paper, 3) Dissolved Gas Analysis (DGA) 4) Oil Quality Factor (OQF). The method involves a process where the input parameters are quantified and normalized employing linear functions. The tables concerned with the corresponding relationship to calculate the normalized parameters for each of the four parts and tables for the assigned weights can be consulted in (Li & Song, 2014).

The first health subindex HIage is concerned with the age and loading of the PT and is given by Equation (1).

HIage=HIOeBT2-T1 (1)

Where HIO, is the initial value, B is the aging coefficient calculated by the equations given in (Li & Song, 2014), T1 is the year corresponding to HIO, which is usually the year that the PT was put into operation, T2 is the year that the PT condition is analyzed, can be the current year or some year into the future.

The insulating paper subindex HIiso considerers the overall insulation aging characteristics and is constituted by two parts: subindex HICO formed by the contents of carbon and oxygen, and subindex HIfur formed by the Furfural Content (FC). DGA and FC analysis are the tests needed to obtain the input parameters to calculate the HIiso.

The subindex HICO consists of three parameters FCO(i), the three factors are considered to be equally important and all the weights are set as ω=0.333. The HICO is calculated using Equation (2).

HICO=i=13ωiFCOi (2)

HIfur reflects the FC results and it is given by (3).

HIfur=3.344Cfur0.413 (3)

The resultant HIiso can be obtained by adding HICO and HIfur together with their respective weights. In this paper, the weights are set to be 0.3 and 0.7, respectively. The index HIiso is shown in Equation (4).

Hiso=0.3HICO+0.7HIfur (4)

The subindex HICH based on DGA uses five gases, H2, CH4, C2H6, C2H2 and C2H4, to assess the health state of the PT. The subindex is calculated using Equation (5), which is a function of five hydrocarbon factors FCH(𝑖).

HICH=i=15ωiFCHi (5)

The subindex based on OQF HIoil analyses the proprieties of oil and how it is correlated with the overall state of the PT. Considered properties are moisture content, acid value, dielectric loss, and breakdown voltage (BV), each of them is represented by Foil(𝑖) and are linear functions.

The index HIoil is calculated using Equation (6) and the weights given (Li & Song, 2014).

HIoil=i=14ωiFoili (6)

To compute the final HIWSM, Equation (7) is used.

HIWSM=0.569HIage+0.266HIiso+0.095HICH+0.07HIoil (7)

The overall condition of the PT based on the value of HI is presented in Table 1.

Table 1 PT condition based on HI. 

HIWSM Condition
0-3.5 Very good
3.5-5.5 Good
5.5-7 Bad
7-10 Very Bad

3.2. Health index based on fuzzy inference system

Proposed by Cerón et al. (2015) the second HI employs the FIS methodology to process the input data. It uses six parameters to calculate the final value, HIFIS, which are: BV, moisture content (humidity), acidity, power factor, FC and DGA. A membership function is designed for each input. The author employs (IEEE Std C57.152-2013, 2013) and (IEC 60422, 2013) to establish the limits to score the input data. The set of membership functions for the input parameters can be consulted in (Cerón et al., 2015).

The membership functions corresponding to the output HIFIS are presented in Figure 1.

Figure 1 Membership functions for the HIFIS. 

A Mamdani FIS composed by 80 rules is used to integrate the six linguistic inputs with the output. Once the output membership function is obtained, a defuzzification process takes place to convert the linguistic HI into a numerical value. The complete HI fuzzy model can be observed in Figure 2.

Figure 2 HI fuzzy model. 

3.3. Health index based on hybrid WSM-FIS

The third approach to compute a HI was proposed by Mharakurwa and Goboza (2019). It combines WSM with four FIS to assess the PT condition. The general approach is shown in Figure 3.

Figure 3 Health index calculation method based on WSM and FIS. 

The WSM component scores results of DGA, OQF and FC analysis, while the four FISs are implemented for different purposes. The first FIS evaluates the degree of polymerization (DP) based on the FC and the carbon dioxide (CO2) and carbon monoxide (CO) ratio. The second one assesses the operational stress of the PT, which depends on the load and the hotspot temperature. The third FIS combines the results of the previous two FISs, i.e., it combines the obtained scores for DP and operational stress. Afterwards, the four and last FIS uses the outputs of the WSM and the third FIS to obtain HIWSM-FIS finally.

To calculate the scores of DGAF, OQF and FC, tables given in (Mharakurwa & Goboza, 2019) are employed. After that, Equations (8) and (9) are applied in order to obtain the normalized score to be used in the fuzzy logic model.

Paremter Score=Ki+xi-aibi-ai2.5 (8)

Parameter Score=Ki+bi-xibi-ai2.5 (9)

Where Ki corresponds to the assigned minimum weight in the four conditions, xi is the current value of the parameter analyzed, ai and bi are the lower and upper limits of the conforming cluster of the parameter.

In order to compute the operational stress; hotspot temperature and load are taken into account. To calculate the DP value the furan content and CO2/CO will be considered. The membership functions for both parameters and the output can be consulted in (Mharakurwa & Goboza, 2019).

In Figures 4 to 6, the membership functions for the final HI value which combines the DGAF+OQF+FF and the DP- value+Operational stress are introduced.

Figure 4 Membership functions for DGAF+OQF+FF. 

Figure 5 Membership functions for DP value+Operational stress. 

Figure 6 Membership functions for the final HI. 

4. Case Study

4.1. Description of the performed comparison

Figure 7 presents a flowchart with the major key points of the methodology used to compare the different HI techniques.

Figure 7 Flowchart of the proposed comparison methodology. 

The three approaches presented in the previous section were tested in a PT fleet composed of thirty units. Table 2 summarizes the main results of the diagnostic tests for the complete fleet.

Table 2 Results of the diagnostic tests for the PT fleet. 

No. Age Color Moisture (ppm) BV (KV) IFT (dynes/cm) Acidity (mgKOH/g) PF (%) H2 (ppm) CH4 (ppm) CO (ppm) C2H4 (ppm) C2H6 (ppm) C2H2 (ppm) CO2 (ppm) HST (°C) Furans (ppm) DCG (ppm)
1 23 1.5 22 52 30 0.07 0.14 234 300 700 29 56 52 5495 60 0.25 671
2 24 2 23 44 24 0.13 0-264 607 119 189 67 257 3 2011 61 1.37 1053
3 23 2 16.5 61 27 0.058 0.174 32.5 45.8 697 21.31 25.54 17 3685 49 0.49 142.15
4 33 2.5 28 40 20 0.18 0.266 74 347 8197 172 194 35 22789 78 4.5 822
5 24 2.5 19 38 23 0.15 0.185 71 65 582 79 127 18 4567 58 1.1 360
6 19 1.5 26 48 25 0.09 0.249 107 129 892 68 55 0 7038 66 0.1 359
7 38 3 23.2 51.7 26 0.251 0.458 979 236 1843 180 183 112 2492 75 5.76 1690
8 43 4 33 35 25 0.19 0.593 1498 395 1582 395 323 26 12371 66 3.9 2637
9 23 2.5 9 49 35 0.08 0.1 294 748 669 1348 212 6 6764 77 0.83 2608
10 22 3.5 42 46 21 0.22 0.221 163 106 299 1517 298 9 2348 64 4.48 2093
11 21 2 6 64 27 0.13 0.566 151 8 297 10 151 8 2323 68 0.22 328
12 19 1 11 70 38 0.05 0.113 678 368 162 108 92 163 1139 81 0.16 1409
13 4 0 9 71 45 0.04 0.068 893 724 242 18 6 1 1883 56 0.03 1642
14 24 1 6 66 41 0.03 0.207 195 660 356 79 127 22 3347 53 0.09 1083
15 29 2 12 65 28 0.05 0.319 440 522 685 62 31 183 5382 50 0.31 1238
16 9 1 10 55 42 0.03 0.15 15 8 902 5 9 0 7135 61 0.1 37
17 14 1.5 10 62 29 0.09 0.733 1176 4 637 10 4 1 4991 53 0.83 1195
18 18 3 32 55 26 0.25 0.328 441 678 1695 62 73 55 13345 77 5.1 1309
19 19 3 40 31 22 0.092 0.416 75 44 261 13 106 0 7846 61 2.4 238
20 17 3 21.2 33.5 20 0.349 0.257 181 79 192.6 29 56 21.1 713 50 8.91 366.1
21 13 1.5 13.9 48 39.25 0.025 0.003 1638 1242 139 17755 8647 5 1296 54 0.01 40287
22 15 6 19.46 33 21.47 0.139 0.9 5 35 964 41 21 1 4002 60 0.033 103
23 11 1.5 12.4 44.4 31.27 0.025 0 4 13 102 22 10 0 1274 35 0.036 49
24 15 5.5 13.6 30 29.8 0.085 0.2 10 8 542 46 2 0 2346 61 0.066 66
25 15 2.5 12.5 56.2 26.2 0.065 0.101 4 13 101 22 10 0 1274 56 0.017 49
26 13 2 10.9 56.2 39.5 0.02 0 160 176 156 7 58 0 2763 60 0.01 401
27 16 1.5 11.9 58.1 38.95 0.009 0.1 225 116 401 146 29 28 2757 58 0.01 544
28 18 0.5 7.1 50.4 47 0.008 0 14 12 271 27 6 0 7454 40 0.01 59
29 16 2 12.1 54.8 38.96 0.042 0.04 3 16 136 1 6 0 2669 53 0.01 26
30 13 1.5 9 58 35.94 0.015 0.038 6 1 240 25 0 3 2059 56 0.01 35

According to Hughes (2003) and Jürgensen et al. (2017), HI is an indicator that enables an effective prioritization/ranking of the assets, in order to support maintenance and replacement decisions.

Therefore, by using the computed HIs, the transformer fleet will be categorized into groups based on level of priority following the guidelines presented in Table 3.

Table 3 Decision-making categorization groups. 

Index value Condition Recommended action
0-3.5 Good Continue the maintenance scheme.
3.5-6.5 Normal Increment the number of inspections, a transition to condition-based maintenance (CBM) is suggested.
6.5-10 Bad Implement CBM, degradation indicates approaching end of life.

Then, the results of the three methods are combined using the well-known K-means clustering technique to obtain a final categorization ranking and performing a comparison with the rest of the rankings previously obtained.

Finally, in a second stage, to assess how the HIs evolve with time, an extrapolation for five years is performed for the PT diagnosis test. For this purpose, the normal limits for oil condition given by IEEE Std C57.106TM-2002, (2003) are employed and normalized for a yearly increase according to the equations suggested by Irungu et al. (2017). The change rate per year for the oil condition is calculated based on a normally expected life span for a PT, which is 40 years. To extrapolate FC, acidity, moisture, and power factor equation (10) is used. The normal rate of change for BV and interfacial tension is calculated based on (11).

xyearly=xextreme-xnormal40 (10)

xyearly=xnormal-xextreme40 (11)

The normal rate of increment for the dissolved gases in parts per million per year and per day can be found in IEC 60599, (2015) and Gray (2009) respectively. The consequent values for normal increment for both oil condition and DGA are presented in Table 4.

Table 4 Rate of increment limits. 

Yearly rate of change for oil condition parameters
Ageing indicator Normal limits (per yr.)
Furans (ppm) <0.0225
Acidity (mg KOH/g) <0.00125
Moisture (ppm) <0.25
IFT (dynes/cm) <0.2
BV (kV) <0.5
PF (%) <0.0225
Yearly rate of change for dissolved gases
Gas type Normal limits (per yr.)
H2 (ppm) 35-132
CH4 (ppm) 10-120
CO (ppm) 260-1060
C2H4 (ppm) 32-146
C2H6 (ppm) 5-90
C2H2 (ppm) 0-37
CO2 (ppm) 1700-10000

4.2. Results and discussions

Table 5 shows the HI ranking obtained from each approach for the assessed fleet. From HI results, it is noted that the three methods produce different rankings. Moreover, from Table 5, it can be inferred that also different decisions will be made depending on the approach selected by the asset manager.

Table 5 Comparison of the HI ranking for the assessed fleet for years 1 and 5. 

Order HIWSM HIFIS HIWSM-FIS
1 T23 0.10357 T28 0.1104 T27 0.1104
2 T30 0.11042 T30 0.1104 T30 0.1104
3 T16 0.11072 T26 0.1719 T16 0.1104
4 T13 0.11135 T23 0.1739 T13 0.1104
5 T25 0.12812 T3 0.3 T14 0.129
6 T29 0.13396 T27 0.3 T23 0.275
7 T26 0.14722 T16 0.3 T26 0.275
8 T24 0.1487 T24 0.3 T24 0.275
9 T28 0.16993 T25 0.3 T25 0.275
10 T22 0.17511 T22 0.3 T22 0.275
11 T21 0.18422 T29 0.3 T29 0.275
12 T17 0.18449 T11 0.3464 T11 0.275
13 T11 0.1993 T6 0.3862 T6 0.275
14 T27 0.20965 T1 0.4297 T1 0.275
15 T6 0.22354 T5 0.4442 T28 0.275
16 T12 0.22528 T14 0.4816 T12 0.275
17 T3 0.23301 T15 0.5222 T3 0.275
18 T14 0.25386 T12 0.525 T17 0.375
19 T1 0.26838 T13 0.525 T5 0.5
20 T19 0.28424 T19 0.525 T15 0.5
21 T9 0.29509 T21 0.525 T21 0.5
22 T5 0.29801 T17 0.5672 T9 0.556
23 T2 0.30052 T2 0.5996 T2 0.634
24 T20 0.32773 T9 0.6033 T19 0.992
25 T15 0.33322 T8 0.7879 T8 0.992
26 T10 0.36696 T4 0.7945 T4 0.992
27 T18 0.39995 T10 0.9334 T10 0.992
28 T4 0.53692 T7 0.9364 T7 0.992
29 T7 0.61924 T18 0.9392 T18 0.992
30 T8 0.74717 T20 0.9392 T20 0.992

General Coincidence ●Coincidence for Methods 1 and 2 ●Coincidence for Methods 1 and 3 ●Coincidence for Methods 2 and 3

There is a level of coincidence between methods 2 and 3, but there are cases where important differences between them can be found. Method 1 returned the lowest HI values for all PTs and always maintained a margin of difference in relation to methods 2 and 3. For the fleet of thirty PTs, the three methods only agreed in the ranking in four cases, i.e., PTs: T2, T22, T24, and T30.

As mentioned above, a clustering technique was applied to combine HI results. Figure 8 shows the clusters representing the three methods and the centroids of the k-means technique.

Figure 8 Cluster for the categorization groups of PT conditions. 

Table 6 presents the categorization groups for the three methods and the inclusion of the k-means merged results. Clear differences can be observed in how the methods categorized the PT fleet.

Table 6 Categorization groups in agreement with Table 3

Condition Method 1 Method 2 Method 3 Merged Method
Good 25 12 17 16
Normal 4 12 6 7
Bad 1 6 7 7
% of coincidence 60.00% 83.30% 96.67%

The first method ranks almost all units in good condition and only one of them receives a bad score, method 2 and 3 showed different results as well. The degree of coincidence between method 1 and 2 is around forty percent as for method 3 the value increases to sixty percent; for method 2 the level of agreement with method 3 is eighty percent. Thus, the overall coincidence of the three methods was around forty percent. The k-means method presented a ranking similar to the one proposed in method 3, the degree of coincidence with method 2 and 3 is greater than eighty percent and for method 1 is placed around sixty percent.

On the other hand, in Figure 9, an individual analysis for each method is developed to simulate how each type of HI varies with time, by using the extrapolated values for the diagnosis tests.

Figure 9 a) to c). Individual comparison for the three methods for the five-year period. a) Health index based on a weighted sum model. b) Health index based on fuzzy inference system. c) Health index based on hybrid WSM-FIS. 

For method 1, the HI rose every year, the increment rate shaped a quasi-linear function as the sample ages. The growth can be explained due to the weight assigned to the age of the PT (56%), in contrast, DGA and oil condition were given much lower weights (26% and 9%). Method 2 presented a different perspective during the five-year period, only fifty percent of the samples presented changes, the rest remained at the same value, this can be attributable to the nature of the trapezoidal fuzzy membership functions (TFMF), where they maintain the same value unless the input value moves to an interception zone between membership functions or another function at all.

It is important to note that this method does not consider, age, load or CO2/CO relation but shows good performance Method 3 was a particular case, it showed similar results with method 2, but during the five years, there were some samples whose HI experimented a decrease in value (samples 2,9 and 19). The reason for that decrement was the change in the CO2/CO relation, which has an essential role in the final value in the degradation level of the insulating paper. Also, it can be observed a stiffer rate of change than in method 2, this behavior responds to the nature of the TFMF that is amplified by the multi-FIS scheme employed in the method.

5. Conclusions

The three methods yielded to different HI results and individual analysis was necessary to understand these differences.

The method based on WSM showed the least promising results. In this approach, the weighting distribution is dominated by the PT age criterion. Then for those cases of PTs with average calendar ages, the resulting HI will show good condition health despite the poor performance of other criteria such as OQF and DGA.

The method based on FIS presented more consistent results and the increment of the HI during the five years was normal. A certain grade of inelasticity was found, but this can be attributed to the nature of the membership functions on a FIS. As an improvement recommendation, the method should consider the age and the load of the unit.

The hybrid method WSM-FIS, even though it encloses the highest number of diagnosis criteria, showed an irregular behavior specifically during the five-year analysis. The CO2/CO relation played a major role in its performance. A grade of inelasticity, higher than method 2, was also noted, the multi-FIS employed in the model was responsible for that level of stiffness.

In summary, FIS-based approaches showed the most promising results. Although both methods exhibited a certain degree of inelasticity, this can be reduced by using a higher number of membership functions by criterion or by replacing the trapezoidal with triangular or Gaussian distribution functions.

The health index is mainly a tool for decision-making support into an asset management framework. In this context, this paper demonstrated that decision-making depends on the adopted approach for HI calculation. To overcome this problem, a good compromise solution is to combine the results of different techniques by using clustering techniques, such as the K-means technique.

Several experts advise electrical utilities in developing their own HI approach for PT, in agreement with their needs and available data. However, a good understanding of the different techniques proposed in the literature could help these utilities to choose the most suitable alternative, or even more to select a set of approaches and combine their HI outputs, as it is proposed in this work.

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Acknowledgments. Diego. A. Zaldivar acknowledges the German Academic Exchange Service (DAAD) for the master’s scholarship granted, and to Universidad Nacional de San Juan, Argentina.

Financing. The authors received no specific funding for this work.

Received: May 13, 2021; Accepted: March 29, 2022

*Corresponding author. E-mail address: dzaldivar@iee.unsj.edu.com (D. A. Zaldivar).

Conflict of interest. The authors have no conflict of interest to declare.

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