Proceedings of the 3rd Internationa Conference on Automation & Computing, University of Huddersfied, Huddersfied, UK, 7-8 September 017 Waveet Packet Anaysis and Empirica Mode Decomposition for the Faut Diagnosis of Reciprocating Compressors Ugonnaya E.Muo, Misan Madamedon, Fengshou Gu, Andrew.D. Ba Centre for Efficiency and Performance Engineering University of Huddersfied Huddersfied, UK Ugonnaya.Ogbuafor@hud.ac.uk Abstract this paper investigates the use of advance signa processing techniques for the cassification of four common reciprocating compressor conditions. Non-stationary vibration signas from the compressor are decomposed based on two emerging techniques: WPT (Waveet Packet Transform) and EMD (Empirica Mode Decomposition) and harmonic changes of the optima components of each technique are used for condition monitoring and diagnostics of the machine. Performance comparison of WPT and EMD is done for the enveope anaysis of the optima waveet packet and the IMF (Intrinsic Mode Function) component that can extract saient features of the four compressor conditions incuding one norma and three faut conditions (intercooer eakage, discharge vave eakage and the combination of intercooer and discharge vave eakage). Harmonic changes produced after enveope anaysis of the best packet and IMF component are used for cassification and resuts show that WPT technique is more robust and effective in faut cassification compared to EMD. Keywords-; Condition monitoring; Waveet packet transform;vibration anaysis; Empirica mode decomposition; Faut diagnosis I. INTRODUCTION Reciprocating compressors are machines widey used in manufacturing industries such as oi and gas refineries, petrochemica industria pants for production purposes. Therefore, eary detection of fauts occurring in these machines is important to avoid serious breakdown that may ead to disruption of production process and human casuaties. In condition monitoring of reciprocating compressors, one of severa ways to diagnose faut is by monitoring/characterizing the magnitude of frequency components to determine when the norma frequency characteristic trend deviates indicating that there is a probem. Vibration measurement is a usefu too for detecting fauts in reciprocating compressors and advances in signa processing techniques have aowed the anaysis of vibration signa to pay an important roe in faut diagnosis of machines in genera. Vibration signas from a reciprocating compressor are often non-inear and non-stationary making it difficut to use traditiona signa processing methods to estabish the characteristics of the vibration signa. Signa anaysis is a significant too for extracting faut features and faut patterns in mechanica faut diagnosis appications. Unti now, many conventiona vibration based signa anaysis methods, such as time-domain anaysis, Fourier anaysis, etc., are unabe to effectivey characterize noninear and non-stationary vibration signas for faut detection and condition monitoring of machines. In this paper, findings from two widey used signa processing techniques: WPT (Waveet Packet Transform) and EMD (Empirica Mode Decomposition) are compared to determine their effectiveness in faut diagnosis of a twostage reciprocating compressor for condition monitoring. In recent years, time-frequency anaysis such as waveet anaysis has attracted much attention in non-stationary signa processing because of successfu appications in transient signa anaysis, imagine anaysis and communications systems to name a few [1]. Moreover, it is very usefu in anayzing data with gradua frequency change and presents the time-frequency distribution properties of a vibration signa []. A comparative assessment of WPT and other time-frequency anaysis for bearing heath monitoring was investigated by [3] and their findings proved that WPT coud identify defects-induced transient components buried within the vibration signa. The WPT was aso used as a pre-processor to decompose vibration signa into narrow band signas to improve the performance of Hibert-Huang transform [4]. However, the resuts of waveet transform depend on the choice of the waveet basis function and ony signa characters that correate we with the shape of the waveet basis function have a chance to ead to coefficients of high vaue, whie a other features wi be masked or even competey ignored [5]. Recenty, a new time-frequency anaysis method empirica mode decomposition was proposed by Huang and his coeagues []. This method can decompose a signa into a set of intrinsic mode functions (IMF), which are amost orthogona [6]. EMD has gained steady increasing popuarity over the past decade because of its sef-adaptive property suitabe for noninear and non-stationary signa processing. Moreover, it has been widey adopted in various appications such as, process contro [7], modeing [8], medicine and bioogy [9], and many more. The foowing two sections (II and III) gives a brief expanation of how the two techniques: WPT and EMD respectivey functions and their appication process in this paper. Furthermore, section (IV) iustrates the
experimenta test rig setup for the two-stage reciprocating compressor whie section (V) presents resuts and discussions of findings from both WPT and EMD techniques for comparison purpose and section (VI) ays out the concusive remarks. II. WAVELET PACKET TRANSFORM The waveet packet transform (WPT) is a muti-stage fitering process most suitabe for obtaining noninear properties of a nonstationary signa. Waveet packet transform is preferred over waveet transform (WT) because it presents a more precise frequency band partitioning over the entire anayzed frequency band by spitting both high frequency and ow frequency bands, hence, enhancing the frequency resoution. Whereas, WT ony spits ow frequency bands and eaves out the high frequency information. Fig. 1 iustrates a 3-eve WPT decomposition tree with symbos L and H representing approximation (ow frequency) and detai (high frequency) components n W ( ) respectivey. The waveet packet function jk, t is expressed mathematicay as: n j n j W, ( ) t W t k jk (1) Where j and k are the scae and transation parameters respectivey; n= 0, 1, is the osciation parameter. The n jk waveet packet coefficients, foowing equation: S are obtained by the j j j () S( j, k) 1 s t t k dt The raw vibration signa is convoved with both ow and high pass fiters and then down samped by two to give two vectors of approximate coefficients L1 and detai coefficients H1 with haf the ength of the origina signa. The process is repeated for the second eve decomposition j = to give four sub-bands (LL, LH, HL, HH). The process continues for a eves required and at each subsequent resoution, the number of packets doubes whie the number of data points is reduced by haf. Literature on WPT can be seen in [10] The seection of an appropriate waveet function (mother waveet) can significanty infuence the efficiency of WPT. After carefu investigation, the mother waveet that correate we with the shape of the vibration signa under investigation is Daubechies 4 (db4) [11]. Figure 1 Waveet packet transform decomposition tree of three eves Using db4 mother waveet, the vibration signa is decomposed into 4 waveet eves giving a tota of 16 waveet sub-bands at the termina node (4 th eve). The percentage distribution of energy for a frequency band is used to seect the optima sub-band for further anaysis. The ratio of different frequency band energy to the tota energy of the origina vibration signa is defined as: Where and xk x j, n, x j, n, E(n) x 100% k (3) is the energy of each sub-band on eve j is the energy of the origina vibration signa. Enveope anaysis is then performed on the sub-band with the greatest energy distribution and finay harmonics changes with severa operating oads for a conditions (norma and fauty cases) is used for faut cassification. III. EMPIRICAL MODE DECOMPOSITION Empirica mode decomposition (EMD) is another popuar nontraditiona signa processing technique proposed by [] in 1998. EMD decomposes a signa into severa intrinsic mode functions (IMFs) [1]. An IMF is a function that satisfy two conditions [6]: 1. In the whoe anaysis dataset, the number of extrema and the number of zero-crossings must either equa or differ at most by one.. At any point, the mean vaue of the enveope defined by oca maxima and the enveope defined by the oca minima is zero. An IMF consists of a simpe osciatory mode buried in the signa. The assumption is that a given signa has different simpe IMFs. Therefore, EMD is designed to decompose a signa into a coection of IMF components and a fina residue r L, which is the mean c, c,..., cl trend of the origina signa. The IMFs 1 have different frequency bands ranging from high to ow. Theory on EMD can be found in [6].The sum of a IMFs and the fina residue gives the equation: L x(t) c rl (4) 1
In this study, the optima IMF is chosen by obtaining the Pearson correation coefficients between each IMF and the origina vibration signa. Like WPT anaysis process, enveope anaysis of the optima IMF is then used for further cassification [4]. IV. EXPERIMENTAL SETUP To compare the two techniques under investigation, vibration signas from high pressure cyinder (second stage) were coected from the experimenta test rig of a reciprocating compressor given in Fig.. The compressor deivers high pressured air to the receiver tank with a maximum capacity of about 1.38 MPa (approximatey 00 psi). The -stroke type reciprocating compressor with four vaves (two on each cyinder) competes one crankshaft revoution in 360 degrees and an intercooer coi is connected between the two cyinders (first and second stage) to reduce the temperature from the first stage pressure cyinder, hence improving the efficiency of the compressor. Vibration signas are coected using an acceerometer A. Data coection Procedure To investigate the efficiency of both techniques for faut diagnosis, vibration signas anayzed are coected from the acceerometer mounted on the pressure cyinder through the data acquisition system. The vibration data is coected at a set samping frequency of 49kHz and the data ength is set at 3768 sampes for each operating pressure range investigated (0.55,0.6,0.69,0.76,and0.83) MPa, approximatey (80,90,100,110,and10) psi. Therefore the time duration of 3768 sampes is 0.66seconds over five cyces. The focus of this paper is on findings from ony the second stage (high-pressure) cyinder because effects from the seeded fauts are more prominent at this stage. Fig. 3 presents the vibration waveform of heathy case and three faut cases at the maximum tank pressure condition studied (0.8MPa). Figure 3 Vibration waveform of a) baseine case b) intercooer eakage faut case c) discharge vave eakage faut case d) discharge vave eakage and intercooer eakage faut case Figure Two-cyinder reciprocating compressor test rig (YD-5-) mounted on each side of the cyinder. Specifications of the compressor and specific features of the acceerometer are isted in Tabe 1. TABLE 1 COMPONENT SPECIFICATIONS Reciprocating Compressor Specifications Components Eectric motor Speed 140 rpm Eectric motor power.5/3 kw Piston Diameter [first stage 93.6 mm cyinder] Piston diameter [second stage 55.6 mm cyinder] Max working pressure 1.38 MPa Number of cyinders (90 opposed) Piston stroke 76 mm Crank shaft speed 40 440 rpm Specification of Acceerometer Type YD-5- Frequency range 0 to 40kHz Temperature Up to 50⁰ C Sensitivity 45mv/ms B. Case description The four different cases investigated are: baseine (BL), intercooer eakage (ICL), second stage discharge vave eakage (DVL), and a combined faut of intercooer eakage and the second-stage discharge vave (ICL+DVL) under a wide tank pressure range. Data for the heathy condition was coected when a components within the compressor system are working normay. Intercooer eakage faut is simuated by oosening the intercooer nut connected to the second stage compression chamber; discharge vave eakage is produced by seeding a mm diameter hoe on the second stage discharge vave whie the combined faut (DVL+ICL) is impemented by running the compressor with the second stage discharge vave eakage and intercooer eakage. Fig. 4 presents the fow chart of signa processing using WPT and EMD. V. FAULT DIAGNOSIS USING WPT The frequency of the vibration signa coected is resamped to 16384Hz reducing the number of data points to 10953 over five cyces within the same time duration of 0.66seconds. WPT is performed on each raw vibration signa at eve 4 using Daubechies 4 (db4) mother waveet and therefore sixteen frequency band signas are obtained. Subsequenty, the optima frequency sub-band is seected
by cacuating the percentage energy distribution of the termina sub-bands as described in section (II) of this paper. The first termina sub-band has the greatest percentage energy for a cases and for each tank pressure range as seen in Fig. 5. This termina node corresponds to the frequency range of 0 51 Hz and is therefore seected and used for further anaysis. Start Raw vibration signa WPT Extract sixteen termina nodes Cacuate the percentage energy Distribution of each termina node to the origina signa Seect node with the greatest energy distribution as the optima termina node Decompose the signa using WPT/EMD Cacuate the enveope of optima termina node /IMF EMD Extract a IMFs and residua Cacuate the correation coefficient vaues for a IMFs Seect the IMF with the highest correation vaue as the optima Figure 5 Percentage energy distribution of termina nodes for a studied cases and pressure range The fundamenta frequency is seen at 7.3Hz, and this frequency corresponds to the compressor running speed (40-440 rpm). Other frequencies are mutipes of the fundamenta frequency (x7.3 Hz, 3x7.3Hz, 4x7.3Hz etc.). The fundamenta frequency and the third harmonic frequency are used for faut cassification. The resut from cassification is seen in Fig. 8.The faut cases are ceary cassified, giving an acceptabe faut separation. Cassification using harmonics changes Diagnosis resut Figure 4 Fow chart of processing vibration signa using WPT and EMD Enveope anaysis of the optima sub band is computed for a conditions, however, because of space imitations, ony the enveope at 0.8 MPa for a cases is shown in Fig. 6. Furthermore, Fourier transform of the enveoped signa is computed and the frequencies are used for cassification. Fig.7 presents the frequencies of the enveoped signa for tank pressure at 0.8MPa. Figure 6 Enveope anaysis of optima termina node at 0.83 MPa for a four cases
Figure 7 Frequency Spectrum of Enveoped optima node at 0.83 MPa for a cases Figure 8 Faut diagnosis (a) 3rd harmonic and fundamenta frequency (b) residua and fundamenta frequency VI. FAULT DIAGNOSIS USING EMD EMD uses the oca characteristics of a signa to robusty decompose the signa into severa intrinsic mode functions (IMF). The samping frequency of the vibration signa is 49 khz and the data ength is set at 3768 sampes EMD of the signa is processed to give 6 IMFs for each operating pressure range and a cases however, because of space constraints, ony four IMFs are presented in Fig. 9 for baseine case at 10 psi. The correation coefficients of each IMF are cacuated and resuts show that the first IMF (IMF1) had the greatest correation coefficient as seen in Fig 10. Therefore, IMF1 is seected as the optima IMF and used for further anaysis. Figure 10 Correation coefficients of each IMF for a cases and a pressure range The resuts in Fig. 1 ceary show the fundamenta frequency of 7.3Hz and its harmonics. However, it is observed that the frequency ampitudes for baseine case, which is the heathy condition is greater than the frequencies of a faut cases. Figure 11 FFT of enveoped IMF signa at 0.83MPa for a cases Figure 9 Waveform of the origina vibration signa and its four corresponding IMF components at 10 psi (0.83MPa) Enveope anaysis of the optima IMF is computed and its Fourier transform for a cases and tank pressure range are obtained for faut cassification. Because of space imitations, enveope anaysis of the optima IMF at tank pressure of 0.83MPa is presented in Fig 11 for a conditions, that is, baseine and a three fauts. Aso, Fig. 1 gives FFT resuts of the enveoped signa. The reationship between the fundamenta frequency and its harmonics for tank pressure ranging from 0.6 MPa to 0.83 MPa (90 psi to 10 psi) were compared. Ony the comparison between the fundamenta and nd harmonic gave the best separation as seen in Fig. 13. The discharge vave faut (DVL) and combined faut (DVL + ICL) are we separated from the baseine (BL) and intercooer faut (ICL) but not from each other. Aso, the intercooer faut (ICL) cassification does not show good separation from the baseine (BL) condition.
means that WPT is more suitabe for arge size signa anaysis as EMD gives too many IMFs REFERENCES Figure 1 Frequency spectrum of enveoped IMF at 0.83MPa Figure 13 Faut diagnosis (a) nd frequency and fundamenta frequency (b) residua and fundamenta frequency VII. CONCLUSION This paper considers the cassification of common reciprocating compressor fauts using harmonics changes extracted from the enveope of decomposed optima signas from WPT and EMD. The purpose of this work is to compare the efficiency of WPT and EMD for diagnosis of common reciprocating compressor fauts. Empoying the WPT method for faut diagnosis; the fundamenta frequency and the third harmonic were used for faut cassification and resuts show good separation between a conditions investigated. On the other hand, EMD was used to decompose the raw vibration signa into six IMFs. A simpe but effective IMF seection method is used to seect the most usefu IMF for further studies. The fundamenta and second frequencies were used for faut cassification, but faied to separate a cases (baseine, intercooer eakage faut, discharge vave eakage faut and the combined faut). Comparing the two techniques the foowing concusions are drawn: 1. Faut diagnosis of the common reciprocating compressor fauts investigated are more effective using the fundamenta frequency and the third harmonics of the WPT optima sub band compared to resuts from using the EMD method.. Both methods show the characteristic frequency 7Hz corresponding to the rotationa speed of the reciprocating compressor 40 440 rpm and its harmonics. 3. The WPT method has better computing efficiency than the EMD method, which [1] D. T. Lee and A. Yamamoto, "Waveet Anaysis: Theory and Appications," Hewett-Packard journa, vo. 3, pp. 44-5, 1994. [] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung and H. H. Liu, "The Empirica Mode Decomposition and the Hibert Spectrum for Noninear and NonStationary Time Series Anaysis," in Proceedings: Mathematica, Physica and Engineering Sciences, 1998. [3] R. Gao and R. Yan, "Non-stationary signa processing for bearing heath monitoring," Internationa journa of manufacturing research, vo. 1, pp. 18-40, 006. [4] Z. K. Peng, P. W. Tse and F. L. Chu, "A Comparison study of improved Hibert-Huang transform and waveet transform: Appication to faut diagnosis for roing bearing," Mechanica systems and signa processing, vo. 19, pp. 974-988, 005. [5] Q. Gao, C. Duan, H. Fan and Q. Meng, "Rotating machine faut diagnosis using empirica mode decomposition," in Mechanica Systems and Signa Processing, 008. [6] Y. Lei, J. Lin, Z. He and M. J. Zuo, "A review on empirica mode decomposition in faut diagnosis of rotating machinery," Mechanica Systems and Signa Processing, vo. 35, pp. 108-16, 013. [7] J. L. Luo, Y. Yan and P. Xie, "Hibert-Huaug transform,hurst and Chaotic anaysis based fow regime identification method for an aircraft reactor," Chemica Engineering Journa, pp. 181-18, 01. [8] P. Xu, W. F. Tian and L. Qian, "EMD-and SVMbased temperature drift modeing and compensation for a dynamicay tuned gyroscope (DTG)," mechanica system signa process, vo. 1, p. 318 3188, 007. [9] C. V. Sonia, G. C. Ramo n, and C. L. Georgina,, "Cracke sounds anaysis by empirica mode decomposition," IEEE, vo. 6, pp. 40-47, 007. [10] Z. Kunpeng, W. Y. San and H. G. Soon, "Waveet anaysis of sensor signas for too condition monitoring: A review and some new resuts," Internationa Journa of Machine Toos & Manufacture, vo. 49, p. 537 553, 009. [11] Y. Lei,,. Z. He and Y. Zi, "Appication of an inteigent cassification method to mechanica faut diagnosis," Expert Systems with Appications, vo. 36, pp. 9941-9948, 009. [1] Z. Li, X. Yan, Z. Tian, C. Yuan, Z. Peng and L. Li, "Bind vibration component separation and noninear feature extraction appied to the nonstationary vibration signas for the gearbox
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