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Classification of radial compressor faults using pattern-recognition techniques N. Aretakis*, K. Mathioudakis Laboratory of Thermal Turbomachines, National Technical University of Athens, Department of Mechanical Engineering, P.O. Box 64069, 15710 Athens, Greece Received 29 July 1997

Abstract An application of pattern-recognition techniques for the classification of faults in a radial compressor is presented. A number of mechanical alterations, simulating faults, are introduced in a test compressor. They include the insertion of an inlet obstruction, an obstruction in a diffuser passage, variation of impeller tip clearance and impeller fouling. Two kinds of measurements, namely sound emission and casing vibration, are examined. Three kinds of pattern-recognition techniques with increasing complexity are used in order to classify the examined faults correctly according to engine condition. The possibility of using each one of these techniques for diagnosing faults in a radial compressor is also examined. It is demonstrated that minor faults, which do not affect performance, can be identified using the proposed techniques. 1998 Published by Elsevier Science ¸td. All rights reserved. Keywords: Pattern recognition, radial compressor, diagnostics, gas turbines

1. Introduction Although diagnostic techniques for turbomachines have advanced significantly in recent years, they have been dealing mainly with axial flow machines. Radial compressors have not received attention to the same extent, mainly because they do not usually form part of the large energy-producing machines or jet engines. Aretakis and Mathioudakis (1996), have commented on this situation, introducing an experimental investigation related to fault diagnostics in radial compressors. They have used fast response measurements for creating signatures of different artificially introduced faults in a test radial compressor. In that investigation it was found that signatures from faults in a radial compressor may be of an ill-defined nature, while they exhibit a dependence on operating conditions. It was therefore decided to apply techniques of pattern recognition to these data, in order to examine the possibility of classifying signatures from the different faults implanted during the experimental study.

*Corresponding author. E-mail: [email protected]

The merit of employing such techniques is expected to be twofold. First, they may reveal the existence of common features between different data sets, not apparent to visual inspection. Second, once the applicability of the techniques is demonstrated, a tool for automated fault diagnosis becomes available for this type of applications. In this way, the decision about the existence of a fault is extracted by a digital computer, eliminating the need for interpretation of the results by specialised personnel. Although such methods have been applied in various other cases, to the authors’ knowledge it is the first time that these techniques are being applied for the identification of radial compressor faults, and especially with the present dynamic measurement setup. It must be commented here that the possibilities for diagnosing faults in radial compressors are becoming increasingly interesting, as this type of turbomachinery component becomes more widely used. A field of application which presents increasing interest is the field of small gas turbines, which have become more and more popular in recent years. Application may extend to other fields as well, such as, for example, process compressors or turbochargers.

0967-0661/98/$ — see front matter 1998 Published by Elsevier Science Ltd. All rights reserved PII: S 0 9 6 7 - 0 6 6 1 ( 9 8 ) 0 0 0 8 5 - 9

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2. Experimental data – background of the present study The data on which the present study is based come from an experimental investigation, described by Aretakis and Mathioudakis (1996). Mechanical alterations were induced on a radial compressor, in order to simulate faults that may occur during operation. The compressor was equipped with a set of instruments to measure different dynamic quantities, namely unsteady pressure, vibration and sound. The fault situations considered were a diffuser passage obstruction, an inlet obstruction, impeller fouling and two sizes of tip clearance increase. A description of the faults is provided by (Mathioudakis and Tsalavoutas, 1995). The compressor layout and a representation of the faults are shown in Fig. 1. A first report on the results of an analysis of fast response data has provided their features, and demonstrated possible ways of identifying the faults (Aretakis and Mathioudakis, 1996). Time signals were Fourier analysed, and fault signatures were derived as differences of spectra for faulty conditions from the corresponding ones for the healthy condition. The analysis was carried

Table 1 Data sets for microphone. The corresponding operating points on the compressor map are shown in Fig. 2 Test case

Operating point

1 2 3 4 5 6 7 8

A F H J A F H J

9 10 11 12 13 14 15 16

A F H J A F H J

17 18 19 20 21 22 23 24

A F H J A F H J

Fault

Date

3/6 Diffuser Fault "M1 7/6

6/6 3/6 Fouling"M2 6/6 7/6

3/6 Inlet Distortion "M3 7/6

out for different operating points on the compressor map, and for the different measuring instruments. In the present work, the data are further analysed by employing pattern-recognition techniques. The purpose of the investigation is to examine whether common features exist in the fault signatures, leading to a classification which cannot be revealed by simple visual inspections. Two representative instruments are being considered: a microphone and an accelerometer placed on the diffuser plate. These instruments are denoted as M and V respectively, and their locations are shown in Fig. 1. Data covering the entire operating range of the compressor are used. Sets from independent experiments, carried out on different dates, are employed, in order to provide a broader statistical basis for the observations. The different data sets employed are tabulated in Tables 1 and 2. The operating points on the compressor map are shown in Fig. 2.

3. Application of classification methods

Fig. 1. Compressor layout and representation of the faults. (a) Inlet obstruction, (b) obstruction in diffuser passage, (c) tip clearance increase and (d) impeller fouling.

The aim of the investigation is to study whether by defining appropriate reference fault signatures, the data sets can be correctly classified according to the condition of the machine to which they correspond. Several methods will be employed, in order to assess their effectiveness for this type of application.

N. Aretakis, K. Mathioudakis/Control Engineering Practice 6 (1998) 1217–1223 Table 2 Data sets for diffuser accelerometer. The corresponding operating points on the compressor map are shown in Fig. 2 Test case

Operating point

Fault

1 2 3 4 5 6

A F A F A F

7 8 9 10 11

H J H J J

Diffuser Fault (H-J) "V12

12 13 14

M N M

Diffuser Fault (M-N)"V13

15 16 17 18 19 20 21 22 23 24

A F H J M A F H J M

25 26 27 28

A F H J

Small Tip Clearance Increase "V3

29 30 31 32

A F H J

Large Tip Clearance Increase "V4

Date 3/6

Diffuser Fault (A-F) "V11

7/6 30/5 1/6 3/6 7/6 30/5

Fouling "V2

3/6 6/6 7/6

3/6 6/6

6/6 7/6

Fig. 2. Operating points for the experiments on the compressor map.

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3.1. Reference signature derivation For one fault a number of signatures are available (see Tables 1 and 2). The reference signature for this fault is defined as the ensemble average of all the available signatures: 1 + S (i) " S (i), i"1, . . , N (1) P H M H where M is the number of available signatures and S (i), H i"1, . . . , N is the set of values constituting one signature. Fig. 3 depicts a set of signatures and the corresponding average derived by Eq. (1) above. 3.2. Geometric pattern recognition Using now the reference signatures derived in this way, a geometrical pattern classification is applied by employing the Euclidean distance Eud and the correlation coefficient Ccd as similarity parameters (see the Appendix for their definition). An example showing how the classification of a fault signature corresponding to the first fault and for a microphone based on this method is achieved, is shown in Fig. 4. The fault signature is most similar to the reference signature giving the smallest distance from the origin. The overall results of the classification process based on geometric pattern recognition are shown in Fig. 5 for microphone data sets. In this figure the test cases which belong to the three faults M1 to M3 are separated with two vertical lines. The fault for each category is presented at the top of each column region, while the detected fault for each test case is denoted with a black dot above each test case number. It is observed that, with the exception of five data sets, one from the first fault, three from the second and one from the third, the remaining ones are correctly classified. Similar comments apply to Fig. 6, where the same type of results for vibration measurement data are presented.

Fig. 3. Spectral differences (signatures) from diffuser obstruction (V13) on diffuser accelerometer (—) and the corresponding reference signature ( ).

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3.3. Statistical pattern recognition

Fig. 4. Geometric classification of a microphone data set corresponding to diffuser obstruction (M1).

Using the same parameters as above, a statistical pattern recognition procedure is applied (see Appendix). The results for microphone data are shown in Fig. 7. The probability of the presence of each fault, assigned to each one of the data sets, is shown in this figure, while the right fault for each data set is shown at the bottom of the figure. In this case, it is clear that the right fault is always assigned the maximum probability, significantly more often than probabilities of other faults (larger than 75%), in all cases. For example, the worst case is the test case 7. For that case the method gives 75% as belonging to fault M1 (which is the right fault), 20% belonging to fault M2 and the remaining 5% belonging to fault M3. This result is interpreted as a 100% successful classification of all data sets. Examining the results of the application of this method to vibration data as illustrated in Fig. 8, in this case there is an incorrect classification for some data sets, leading to a success rate of 87.5%. 3.4. Statistical pattern recognition with optimal directions As a final step, the technique of optimised identification technique is applied (Loukis et al., 1994). Fig. 9 shows the result of application to microphone data. This technique fails at one point, point 2. It is interesting to notice that it gives the same answer as the geometric approach (see Fig. 5). Application to the vibration data, however, turns the success rate to 100%, as can be seen from Fig. 10.

Fig. 5. Total results of geometric classification for microphone data sets.

Fig. 6. Total results of geometric classification for diffuser accelerometer data sets.

Fig. 7. Total results of statistical pattern recognition for microphone data sets.

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Fig. 8. Total results of statistical pattern recognition for diffuser accelerometer data sets.

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Fig. 10. Total results of statistical pattern recognition with optimal directions for diffuser accelerometer data sets.

Fig. 11. A typical screen from the interactive environment implementing the techniques presented here.

Fig. 9. Total results of statistical pattern recognition with optimal directions for microphone data sets.

4. Discussion Application of the three classification techniques has shown that their effectiveness is different for each measuring instrument. What is of interest, however, is that although there is not one single method that gives a fully successful classification for one data set, a combination of them always gives the correct fault. If the six result charts are inspected, it can be observed that for any fault there are always many more positive than negative indications. If, therefore, the number of right answers from the application of three techniques is used as a criterion, a correct classification is always achieved.

A question that would require further research before being answered is what the level of generality of the present approach is. While the applicability of the techniques would be expected to be successful, the main question is whether the baseline information and the signatures obtained on the present compressor would be similar for another radial compressor. To answer this question, investigations should be performed on different machines, in order to examine to what extent similarities can be found. The methods presented in the sections above process features, which make them useful for implementation in practical industrial situations of fault diagnosis. Their most useful feature is that they incorporate data processing and decision making, while they can be implemented by a computer system.

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The authors have actually implemented the classification methods described above on a PC in a user-friendly environment. An example of one screen display is given in Fig. 11. On this figure can be seen the results from statistical pattern recognition using optimal directions on a specific data set presented in this paper.

5. Conclusions An application of pattern — recognition techniques for the classification of radial compressor faults has been presented. Three classification methods were used, with increasing complexity, in order to correctly classify the examined fault signatures according to machine condition. They were geometric, statistical and statistical pattern recognition using optimal directions. The fault signatures examined were derived from data acquired during the performance of two types of dynamic measurements, namely sound emission and vibration. It was demonstrated that these data sets can be correctly classified using only the geometric approach, except for a few data sets. Application of the two other techniques, however, turns the success rate to 100% for both measurements.

It takes values between 0 and 1 and increases for increasing similarity between the two signatures (the better the similarity the closer to 1 the value). A.2. A geometric procedure for fault signature classification The first step in geometric pattern recognition is to calculate the characteristic vector X for all available fault signatures, which has as components a number of discriminants with respect to the reference signatures of the faults being examined. X"[Eud , Ccd , . . . , Eud , Ccd , . . . , Eud , Ccd ] (4) H H ,D ,D where Eud , Ccd are the two calculated discriminants H H with respect to j-fault, Nf is the number of faults. In order to classify an examined signature to a particular fault, based on the corresponding characteristic vector, one can calculate the classification index CQ of this signature for all the examined faults according to the following relation: CQ "((Eud#(1!Ccd )), j"1, . . . , Nf. H H H

(5)

The decision is made classifying the signature to the fault that corresponds to the minimum classification index.

Appendix A.1. Definition of fault signature discriminants In order to classify the fault signatures correctly according to the corresponding machine condition two discriminant functions were selected (see Loukis et al., 1992). One of them is expressing the quantitative similarity, the other expressing the shape similarity. The first function is the usual Euclidean distance between the signatures, when they are viewed as points in a N-dimensional space. The following relation defines the Euclidean distance between a signature S and the reference signature Sr of the k-fault: I 1 , Eud " E (S(i)!Sr (i)) . (2) I I N G Small values of this quantity indicate that S and Sr are I similar. It increases for decreasing quantitative similarity between S and Sr . I The second discriminant is the normalised cross-correlation coefficient, and does not depend on the range of values of the signatures. For the signatures S and Sr , it is I defined by the following equation:

, (S(i)!S) E (Sr (i)!Sr ) I I G Ccd " . I , , (S(i)!S) E (Sr (i)!Sr ) I I G G

(3)

A.3. A statistical procedure for fault signature classification The main feature of this procedure is that it is based, not on a single parameter (CQ) derived from a characteristic vector, but on entire characteristic vector X. In this procedure the decision is made to classify this vector to the fault that corresponds to the maximum probability, while the rest of the faults are ranked according to their relative probabilities: X3Fault!i IF: ,D Pr(X/Fault!i)"max [Pr(X/Fault!j)]. H

(6)

The probability of having a given vector X when fault-i is present, is expressed by an equation of the form: 1 z G 6\6G 2 (7) Pr(X/Fault!i)" e\6\6 G z !\ (2n)L E "C " G where X and C , i"1, . . , Nf are the average characterG G istic vector and the covariance matrix for each of the faults, and n is characteristic vector’s dimension, n"2Nf.

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References Aretakis, N., & Mathioudakis, K. (1996). ‘‘Radial Compressor Fault Identification using Dynamic Measurement Data’’. ASME paper 96-GT-102, 41th ASME International Gas Turbine and Aeroengine Congress and Exposition, June 1996, Birmingham, UK. Loukis, E., Mathioudakis, K., & Papailiou, K.D. (1992). ‘‘A procedure for Automated Gas Turbine Blade Fault Identification Based on Spectral Pattern Analysis’’. Journal of Engineering for Gas ¹urbine and Power, ASME, 114(2), 201—208.

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Loukis, E., Mathioudakis, K., & Papailiou, K.D. (1994).‘‘Optimising Automated Gas Turbine Fault Detection Using Statistical Pattern Recognition’’. Journal of Engineering for Gas ¹urbine and Power, ASME, 116(1), 165—171. Mathioudakis, K., & Tsalavoutas, A. (1995). ‘‘Identification of Mechanical Alterations from their Effect on Performance of a Radial Compressor’’, paper ASME 95-GT-62, 40th ASME International Gas Turbine and Aeroengine Congress and Exposition, June 1995, Houston, Texas, USA.