Performance Assessment and Fault Dagnoss for Hydraulc Pump Based on WPT and SOM Be Jkun, Lu Chen and Wang Zl PERFORMANCE ASSESSMENT AND FAULT DIAGNOSIS FOR HYDRAULIC PUMP BASED ON WPT AND SOM. Be Jkun, Lu Chen and Wang Zl School of Relablty and Systems Engneerng, Behang Unversty, Chna Scence & Technology on Relablty & Envronmental Engneerng Laboratory, Bejng, Chna E-mal: luchen@buaa.edu.cn Abstract. Hydraulc pump s the heart of hydraulc system, therefore a real-tme condton montorng for hydraulc pump s crucal to the relablty of the entre system. In ths study, a method for performance assessment and fault dagnoss to hydraulc pump based on wavelet packet transform (WPT) and Self-organzng mappng (SOM) neural network s proposed. Frst, WPT s utlzed to decompose the vbraton sgnal nto components, energy of each component s extracted and normalzed to form the feature vector. Second, SOM neural network, traned only by normal data, s used to map feature vectors nto Mnmum Quantzaton Error (MQE), whch s then normalzed nto confdence values (CV). Performance assessment s accomplshed by trackng the trends of CVs. Fnally, when faults occur, SOM, traned by both normal and faulty samples, s employed to classfy the faults nto dfferent groups, whch delegates dfferent fault modes of the hydraulc pump. In addton, Taguch method s used to reduce the redundant features and extract the prncpal components to ensure the effectveness of the approach. A case study based on the vbraton dataset of test plunger pump rg s conducted to demonstrate that the proposed method s able to assess the performance of hydraulc pump and dagnose faults sutably.. Introducton Hydraulc pump s a crucal component n hydraulc system, ts performance drectly determnes the hydraulc pressure, whch reflect status of the entre system. Unexpected faults of pumps usually cause enormous losses, however, a condton montorng based process can gve a pre-warnng, then repars or replacements can be taken at the earlest or most convenent tme wth the mnmum loss of productvty. Faults of hydraulc pumps are generally accompaned wth changes n vbraton sgnal. Thus, vbraton dagnoss s mportant n ths feld and s also the foremost topc of nterest for researchers. Consderng the complexty of hydraulc pump and the workng condtons, data-drven methods are usually appled to onlne fault dagnoss. Nowadays, several data-drven methods exst for condton montorng, such as prncpal component analyss, dscrmnant analyss and cluster analyss, as well as artfcal neural networks. Self-organzng mappng (SOM) network, a data-drven neural network proposed by Kohonen, has been broadly used n dagnostc applcatons dealng wth data classfcaton, and the Mnmum Quantzaton Error (MQE) calculated by SOM offers a method for the assessment of performance. The advantage of SOM s that: () ts tranng process, wthout predetermned supervson, provdes favorable recognton rate to unknown sgnal; () the topology of ts network s self-adaptve, whch means self-stablzaton and mmunty from nterference. However, send the orgnal vbraton sgnal of hydraulc pump nto SOM seems complcated n computaton, and usually causes unsatsfactory results, therefore, a feature vector, carryng substantve characterstcs of the sgnal s needed n ths approach. Tradtonal sgnal processng technques, ncludng tme-doman and frequency-doman analyss, are based on the assumpton that the processng sgnals are statonary and lnear. Unfortunately, vbraton sgnals of abnormal hydraulc pump are both nonlnear and non-statonary. Here, wavelet packet transform (WPT), ntroduced by To whom any correspondence should be addressed. VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 3. VOLUME. ISSN 35-533 3
Cofman [], provdes an effectve way to process nonlnear and non-statonary sgnal. It decomposes a sgnal repeatedly nto successve low and hgh frequency components usng a recursve flterdecmaton operaton. After decomposton, the energy of each component s extracted and normalzed to form feature vector, whch represents the status of hydraulc pump. Addtonally, to ensure the effectveness of the approach and get rd of the well-known garbage n, garbage out problem, Taguch method s employed to determne the key features from the ntal feature set and screen out unsutable features. The man purpose of ths study s to propose a method for performance assessment and fault dagnoss to hydraulc pump based on WPT and SOM. In ths method, WPT and energy extracton s combned to extract feature; SOM based MQE, optmzng by Taguch method, s then employed to calculate confdence value (CV), whch represented performance of hydraulc pump; fnally, when faults occur, SOM, traned by both normal and faulty samples, s employed to classfy the faults nto dfferent fault modes. Ths paper s organzed as follows: Secton ntroduces WPT, SOM, Taguch method and the proposed method for fault dagnoss and performance assessment; Secton 3 descrbes the case studes performed to valdate the method; and Secton gves conclusons and some deas for future work.. Methodology.. Sgnal processng by wavelet packet transform WPT s consdered as a generalzaton of the wavelet transform, the decomposton s performed on both low and hgh frequency components of any waveform []. After the decomposton of the jth level, the orgnal sgnal f ( t ) can be constructed by the sum of j components as: j = j () = f ( t) f ( t) where f ( t ) s the wavelet packet component sgnal that can be expressed by a lnear combnaton of j wavelet packet functons as: f ( t) = c ( t) () j j, kψ j, k k = where, j and k are ntegers and defned as the modulaton, scale and translaton parameter, respectvely; c j, k s the wavelet packet coeffcents, ψ, ( t) s wavelet packet functon. j k.. Feature extracton by energy extracton Here, feature extracton s performed by energy extracton, each component ( ) where E s the energy of each component, normalzed t as below: c t s processed wth: E= c ( t) dt (3) + n n n '' T = E E, E E,..., En E = = = () '' where T s the normalzed feature vector, whch carres the nformaton of sgnal. It can be used to classfy sgnals, so as to assess the performance status. VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 3. VOLUME. ISSN 35-533
.3. Fault dagnoss and MQE calculaton by SOM network In SOM, each neuron s represented by a dmensonal weght vector and connected to adjacent neurons by a neghborhood relaton, whch ndcates the topology of the map [3]. Durng tranng procedure, take vector X for example, the dstance between t and all the weght vectors of SOM s computed by usng dstance measure. The neuron whose weght vector s closest to X s called Best Matchng Unt (BMU) []. The weght vector of BMU s enhanced by the learnng rule. After tranng, the neurons are grouped n clusters by ther dstance n the structure, whch form a new knd of topology. When test vectors nput, the vector s compared wth the weght vectors of all map unts n SOM. Fault mode can be judged by the topologcal structure of SOM. And, dependng on how faraway the current data s devatng from the tran data, a quanttatve assessment ndex can be obtaned by calculaton of the Mnmum Quantzaton Error (MQE) [5]. MQE value s fgure out by: where, X nput s the nput data vector, and MQE = X w (5) nput bmu w bmu s the weght vector of BMU... Feature optmzaton by Taguch method The optmzaton starts wth the normal and faulty feature vector, then the MQE s fgure out as precedng part of ths text. After that, Taguch method creates a standard orthogonal array (OA), whch depends on the number of factors and levels needed. The optmum expermental condtons can be easly determned wth the OA. In the OA, features have two levels. Level- represents the presence of a feature, whle level- represents the absence of a feature. Here, nne MQEs are calculated wth the combnaton of the features dctated by the OA and the larger-the-better sgnal-to-nose rato (SNR) s calculated as follows: n m = log n j= MQE j () where m s the SNR for the th run of the OA, and n s the sample sze of each abnormalty. Then, an average SNR at level- and level- of each feature s obtaned and the gan s calculated as below []. Gan = Mean Mean (7) level level Accordng to prncple, features wth postve gan are selected for the performance assessment and the rest are dscarded..5. Performance assessment by CV In ths approach, CV, proposed by Qu et al. [7], s ntroduced as an ndex to evaluate the performance status. The CV can be formulated as below: MQE CV = exp c where MQE s just the MQE under the montorng data offered by SOM runnng. c s scale parameter determned by the MQE under the normal state and the predetermned CV. Accordng to the prncples of SOM and MQE, normal sgnals wth the smlar features to the traned dataset, wll gather around the normal cluster, whch should have a mnmum MQE value relatve to that of other faulty status. Along wth the operaton of pump, features of the sgnal turn to be dfferent from the traned data, therefore MQEs of them wll become hgher. CV s nverse proportonal to the MQE, so normal pump get hgher CV, and faulty ones trend to be lower as well. () VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 3. VOLUME. ISSN 35-533 5
.. Flow of the proposed method The aforementoned consttutes performance assessment and fault dagnoss. The process can be summarzed as Fgure. 3. Expermental Verfcaton Fgure. Flow of the proposed method. 3.. Experment setup In ths study, a test plunger pump rg was tested and analyzed to verfy the presented method. The vbraton sgnal was acqured from the end face of the plunger pump wth a stablzed motor speed of 5r/mn, and samplng rate of Hz, as shown n Fgure. Two commonly occurrng faults n the plunger pump were set, namely, swash plate wear and rotor wear. Fgure. Test plunger pump rg. X - 3 5 7 9. C -. 3 5 7 9.5 C -.5 3 5 7 9. C3 -. 3 5 7 9.5 C -.5 3 5 7 9. C5 -. 3 5 7 9. C -. 3 5 7 9. C7 C -. 3 5 7 9. -. 3 5 7 9 Sample Fgure 3. A sample of WPT results of hydraulc pump sgnal. VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 3. VOLUME. ISSN 35-533
3.. Experment results and dscusson 3... Feature extracton. Orgnal vbraton sgnal of hydraulc pump s shown n Fgure 3. Here, WPT s employed to decompose t nto components. Energy of components s extracted to form feature vector. Table shows groups of normalzed feature vectors from the normal samples. Table. Feature vector. NO. E E E3 E E5 E E7 E.3393.539.79.7..393.3.73.37.5.3..3.33.5.39 3.3.55.57.3.7.9..399.99.575.5.95.77.9.373.3 5.7.53.7.99.97.3.93.999.3.59..59.59.999.7.357 7.37.53.5.55.9.9.39.7.3.55.77.5553.93.93.793.79 Table. Result of Taguch method. Factor E 3 5 7 m.5-3.3 3. -.5 5 -.7-3.9 7 -.5 -.39 9-3.39 Meanlevel -. -.5 -. -.37 -.5 -.3 -.7 -. Meanlevel -.97 -.9 -. -.7 -. -.5 -.7 -.3 Gan.. -.7.9.55.5.97. 3... SOM-based MQE calculaton wth Taguch method. SOM s traned by the vector from normal samples. Wth the traned SOM, MQE of each vector can be calculated. Then, Taguch method s ntroduced n optmzaton, two samples from normal and faulty pumps, respectvely, are sent to Taguch experment. The result s shown as Table. Accordng to the rules of Taguch method, factor-3 wth negatve gan should be dscarded. The rest are selected to consttute fnal vectors. 3..3. Performance assessment. In ths experment, thrty samples from normal and two modes of faulty pump, respectvely, are chosen to assess, the MQE and CV curves are shown n Fgure. 5.95.9.5 MQE 3 CV..75.7.5. 5 5 5 3 Sample.55 5 5 5 3 Sample Fgure. MQE and CV of the hydraulc pump. VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 3. VOLUME. ISSN 35-533 7
3 3 7 Hts 5 5 PERFORMANCE ASSESSMENT AND FAULT DIAGNOSIS FOR HYDRAULIC PUMP BASED ON WPT AND SOM. The blue curve n the fgure shows trend of CV, the frst ten samples from normal pump show hgh CVs above 9., whch ndcates hydraulc pumps are n good state; whle, CVs of the last twenty ones from faulty pumps fall down obvously. Thus, t s clear that CV concdently represents the performance of hydraulc pumps, and t s also dstnctly proved that ths approach to performance assessment s feasble. 3... Fault dagnoss. Here, three hundred from normal and two modes of faulty pump, respectvely, are chosen to tran SOM. Wth the traned SOM, datasets from three modes of pumps s employed to fault dagnoss, the topologcal structure and the result s shown n Fgure 5. As s shown n Fgure, Samples from three modes severally maps n the topologcal structure whch represents normal, rotor wear, swash plate wear. Fault mode of hydraulc pump can be judged drectly by the topologcal fgure, whch shows the effectveness of the approach. Hts 9 3 3 5 3 5 3 5 7 9 Normal Rotor Wear Swashplate Wear 7 3 3 3 3 3 3 3 7 5 7 3 3 Hts 5 5 Hts 3 5 9 9 5 5 5 5 5 5 Fgure 5. Topologcal structure of traned SOM and results of fault dagnoss (from left to rght, normal, rotor wear, swash plate wear).. Conclusons In ths paper, a method for performance assessment and fault dagnoss to hydraulc pump s proposed. WPT s utlzed as a powerful sgnal processng method for nonlnear and non-statonary vbraton sgnal. A SOM based MQE chart s employed to assess performance of hydraulc pump by trackng the trends of CVs. Meanwhle, topologcal fgure of the SOM, traned by both normal and faulty samples, classfy the faults nto dfferent fault modes. Addtonally, the employment of Taguch method makes the result more accurate, and the optmzaton of the feature vector reduce computatons as well, whch s meanngful for real-tme assessment. Acknowledgements Ths research was supported by the Natonal Natural Scence Foundaton of Chna (Grant Nos. 73, 5755 and 559), as well as the Technology Foundaton Program of Natonal Defense (Grant No. Z3B). References [] Peng X L, Hao H and L Z X Engneerng Structures 39 5 5 [] Jafar Z and Javad P 7 Trbology Internatonal 73 9 [3] A C S, Sun Y J, He G W and Ze X B The Internatonal Journal of Advanced Manufacturng Technology 57 3 [] Pham D T, Dmov S S, Bgot S, Ivanov A and Popov K Journal of Materals Processng Technology 9 5 7 [5] Yu J B and Wang S J 9 Computers & Industral Engneerng 57 3 [] Taguch G and Jugulum R The Mahalanobs Taguch Strategy: A Pattern Technology System [7] Qu H, Lee J, Ln J and Yu G 3 Advanced Engneerng Informatcs 7 7 VIBROENGINEERING. VIBROENGINEERING PROCEDIA. NOVEMBER 3. VOLUME. ISSN 35-533