An expert system for the diagnosis of faults in rotating machinery using adaptive order-tracking algorithm Expert Systems with Applications 36 (2009) 5424–5431 Contents lists available at ScienceDirect Expert Systems with Applications j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e s w a An expert system for the diagnosis of faults in rotating machinery using adaptive order-tracking algorithm Jian-Da Wu a,*, Mingsian R. Bai b, Fu-Cheng Su b, Chin-Wei Huang c a Institute of Vehicle Engineering, National Changhua University of Education, 1 Jin-De Road, Changhua City, Changhua 500, Taiwan, ROC b Department of Mechanical Engineering, National Chiao-Tung University, Hsin-Chu, Taiwan, ROC c Department of Mechanical and Automation Engineering, Da-Yeh University, Changhua, Taiwan, ROC a r t i c l e i n f o a b s t r a c t Keywords: Signal processing Fault diagnosis Order-tracking Adaptive RLS filter 0957-4174/$ - see front matter � 2008 Elsevier Ltd. A doi:10.1016/j.eswa.2008.06.059 * Corresponding author. E-mail address: jdwu@cc.ncue.edu.tw (J.-D. Wu). This paper describes an application of an adaptive order-tracking technique for the diagnosis of faults in rotating machinery. Conventional methods of order-tracking are primarily based on Fourier analysis with reference to shaft speed. Unfortunately, in some applications of order-tracking performance is limited, such as when a smearing problem arises and also in a multiple independent shaft system. In this study, the proposed fault diagnostic system is based on a recursive least-square (RLS) filtering algorithm. The problem is treated as the tracking of various frequency bandpass signals. Order amplitudes can be calcu- lated with high-resolution in real-time implementation. The algorithm is implemented on a digital signal processor (DSP) platform for diagnosis and evaluated by experimental investigation. An experimental investigation is implemented to evaluate the proposed system in two applications of gear-set defect diag- nosis and in the diagnosis of damaged engine turbocharger blades. The results of the experiments indi- cate that the proposed algorithm is effective in fault diagnosis for both experimental cases. Furthermore, a characteristic analysis and experimental comparison of a vibration signal and a sound emission signal for the present algorithm are also presented in this report. � 2008 Elsevier Ltd. All rights reserved. 1. Introduction Traditionally, the condition of rotating machinery such as fans, compressors, motors and engines can be monitored by measuring the respective vibration signal or sound emission signal. These sig- nals normally consist of a combination of the basic frequency with discrete or narrowband frequency components and the harmonics thereof, most of which are related to the revolution of the machin- ery. The sound emission and vibration energy are increased when the machinery is damaged. An example result of a sound emission power spectrum level measured from the wheel-blades of an inter- nal combustion (IC) engine turbocharger is shown in Fig. 1. The conventional fault diagnostic technique is to observe the ampli- tude difference in the time or the frequency domain for diagnosis of damage. Recently, the order-tracking technique has become an impor- tant approach for diagnosing fault in rotating machinery. Interest in diagnosis using the order-tracking technique has grown signifi- cantly, having advanced with the progress of digital signal process- ing algorithms and technology in the last two decades (Biswas, Pandey, Bluni, & Samman, 1994; Chen, Du, & Qu, 1995; Gelle, Colas, ll rights reserved. & Serviere, 2001; Lin & Qu, 2000; Shibata, Takahashi, & Shirai, 2000). The conventional order-tracking method is primarily based on Fourier analysis with reference to shaft revolution (Lee & White, 1998; Vold & Leuridan, 1993). Unfortunately, re-sampling process- ing is generally required in the fast Fourier transform (FFT) meth- ods to compromise between time and frequency resolution for varying revolutions. However, in the conventional FFT methods, a smearing problem generally arises in practical implementation, particularly at low revolution speeds. In addition, the conventional methods are ineffective for application to certain critical conditions such as a fixed sampling frequency, and FFT analysis with a track- ing technique is ineffective when the shaft speed varies rapidly. In this study, an adaptive order-tracking fault diagnostic tech- nique using both vibration signals and sound emissions is applied to the diagnosis of damage in gear-sets and engine turbocharger blades. According to recent studies by Haykin (1996) and Bai, Jeng, and Chen (2002) there exists some conclusions for adaptive filter- ing algorithms and their application to order-tracking techniques. The proposed adaptive fault diagnostic system is based on the recursive least-square (RLS) algorithm (Bai et al., 2002). Similar to conventional methods, the RLS method also requires informa- tion on shaft or engine revolution. The algorithm is essentially sample-based; thus, order amplitudes can be calculated in a real- time fashion. The method is well suited for high-resolution mailto:jdwu@cc.ncue.edu.tw http://www.sciencedirect.com/science/journal/09574174 http://www.elsevier.com/locate/eswa Fig. 1. Sound power spectrum level of sound emissions from turbocharger blades. A solid line depicts blades without damage; broken lines depict blades of which one is damaged. J.-D. Wu et al. / Expert Systems with Applications 36 (2009) 5424–5431 5425 tracking of closely spaced orders or crossing orders. The filter algo- rithm is implemented in a TMS320C32 DSP platform for evaluating the performance in a practical application of the diagnosis of dam- age in gear-sets and IC engine turbocharger blades. In fault diagnostic techniques to date, measurement of the vibration signal has become most widely used when a reference signal is available. Unfortunately, in some practical applications, such a vibration signal is unavailable. Measurement of high-fre- quency sound emissions serves as a promising alternative to con- dition monitoring of many types of rotating machinery (Mba, 2002; Toutountzakis & Mba, 2003). During operation of the machinery, defects at different locations will generate characteris- Transversal filter ˆ ( 1)w n − Adaptive weight control mechanism Input vector ( )u n *ξ (n) k(nΣ Σd*(n) + _ )1()(H − ∧ nn wu Gain a b Fig. 2. Representations of RLS algorithm. (a) B tic frequencies. However, in the present study, both vibration sig- nals and sound emission signals are used to evaluate the proposed diagnostic technique. The details of the proposed adap- tive filtering with an RLS algorithm are described in the following section. 2. Principle of adaptive order-tracking technique using RLS algorithm The conventional algorithms used in fault diagnostic techniques fall into two categories. One is Fourier transform with a fixed sam- pling rate for obtaining frequency domain information; the other is - + Desired response d(n) Output ˆ ( 1) ( )Hw n u n− Error ( )nξ z -1I Σ uH(n) Negative unity feedback )(n ∧ w )1( − ∧ nw lock diagram and (b) signal-flow graph. 0 1000 2000 3000 4000 5000 6000 7000 8000 -350 -300 -250 -200 -150 -100 -50 0 50 Iteration Number E rr o r (d B ) Fig. 3. A comparison of convergence speeds and estimation errors in various adaptive filters. A solid line depicts the Kalman filter; a dash-dot line depicts the RLS; a dotted line depicts the LMS. DSP controller Mic. Gear 2 Gear 1Coupling Frequency converter Accelerometer Fiber optical sensor Motor D/A A/D A/DA/D Fig. 4. Experimental arrangement of gear-set defect diagnosis. Tim 0 2 4 S p e e d ( rp m ) 700 800 900 1000 1100 1200 1300 1400 1500 1600 Fig. 5. Revolution of gear-se 5426 J.-D. Wu et al. / Expert Systems with Applications 36 (2009) 5424–5431 tracking with various sampling rates. The second method employs a re-sampling scheme synchronous with the shaft revolution. The time domain data are hence converted to revolution-domain data. Then the FFT is also applied to obtain the order spectrum with re- spect to engine speed. Both the time and the frequency resolution of this approach are essentially varied with the shaft speed. This FFT order-tracking method relies on accurate measurement of the tachometer signal. In general, the vibration signal or the sound emission signal generated by rotating machinery essentially con- sists of a combination of the basic frequency with narrowband fre- quency components and its harmonic frequencies, most of which are related to the revolution of the machine. Bai et al. (2002) pro- posed an RLS algorithm for adaptive order-tracking technique. In this work, the vibration signal x(t) containing k orders generated by one rotating shaft can be written as xðtÞ¼ ½cos½hðtÞ�� sin½hðtÞ�cos½2hðtÞ�� sin½2hðtÞ� � � �cos½khðtÞ� � sin½khðtÞ�� A1I A1Q A2I A2Q .. . AkI AkQ 2 6666666664 3 7777777775 ð1Þ e (sec) 6 8 10 12 t in experimental case. J.-D. Wu et al. / Expert Systems with Applications 36 (2009) 5424–5431 5427 where AkI and AkQ denote the in-phase and quadrature components, respectively, of kth order. Note that AkI ¼ Ak cos /k; AkQ ¼ Ak sin /k: ð2Þ The amplitude of kth order can be written as jAkj ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A2kIi þ A 2 kQ q : ð3Þ and the phase of the kth order is obtained by /k ¼ tan�1 AkQ AkI � � : ð4Þ For a discrete-time system, Eq. (1) can be expressed as Time (sec) *1 0 2 4 6 8 10 12 0 1 2 3 x 10 -3 *2 0 2 4 6 8 10 12 0 1 2 3 x 10 -3 *3 0 2 4 6 8 10 12 0 1 2 3 x 10 -3 *4 0 2 4 6 8 10 12 0 1 2 3 x 10 -3 A m pl it ud e Fig. 6. Order figures of vibration signals for gear-set using adaptive RLS filter. A solid line depicts gear without defect; a dashed line depicts gear with a defect. xðnÞ¼ ½cos½hðnÞ�� sin½hðnÞ�cos½2hðnÞ�� sin½2hðnÞ� � � �cos½khðnÞ� � sin½khðnÞ�� A1I A1Q A2I A2Q .. . AkI AkQ 2 6666666666664 3 7777777777775 ð5Þ where n is the discrete-time index (Oppenheim & Schafer, 1999). To solve Eq. (5), collect 2k samples of xðnÞ to form *1 0 2 4 6 8 10 12 0 2 4 x 10 -4 *2 0 2 4 6 8 10 12 0 2 4 6 x 10 -4 *3 0 2 4 6 8 10 12 0 2 4 6 x 10 -4 *4 0 2 4 6 8 10 12 0 2 4 6 x 10 -4 Time(sec) A m pl it ud e Fig. 7. Order figures of sound emission signals for gear-set using adaptive RLS filter. A solid line depicts gear without defect; a dashed line depicts gear with a defect. xðnÞ xðn þ 1Þ .. . xðn þ kÞ xðn þ 2k � 1Þ 2 66666664 3 77777775 ¼ cos½hðnÞ� �sin½hðnÞ� � � � cos½khðnÞ� �sin½khðnÞ� cos½hðn þ 1Þ� �sin½hðn þ 1Þ� � � � cos½khðn þ 1Þ� �sin½khðn þ 1Þ� .. . .. . � � � .. . .. . cos½hðn þ 2kÞ� �sin½hðn þ 2kÞ� � � � cos½khðn þ 2kÞ� �sin½khðn þ 2kÞ� cos½hðn þ 2k � 1Þ� �sin½hðn þ 2k � 1Þ� � � � cos½khðn þ 2k � 1Þ� �sin½khðn þ 2k � 1Þ� 2 66666664 3 77777775 A1I A1Q .. . AkI AkQ 2 66666664 3 77777775 ð6Þ 5428 J.-D. Wu et al. / Expert Systems with Applications 36 (2009) 5424–5431 Here it is assumed that the 2k amplitude parameters AI and AQ remain constant within the interval ½n; n þ 2k � 1�. In view of the special structure of the signal described in Eq. (1), the order-track- ing problem can be recast into a parameter identification form. The estimation error eðnÞ¼ xðnÞ� wTðnÞuðnÞ; ð7Þ uTðnÞ¼ ½cos½hðnÞ�� sin½hðnÞ�cos½2hðnÞ� � sin½2hðnÞ� � � �cos½khðnÞ�� sin½khðnÞ�� ð8Þ is the regressor; WTðnÞ¼ ½A1IðnÞ A1QðnÞ A2IðnÞ A2QðnÞ � � � AkIðnÞ AkQ ðnÞ� ð9Þ is the parameter vector; x(n) is the measurement error. Note that the vector u(n) consists of angular displacements of the shaft; the Fig. 8. (a) Damaged turbocharger compress-wheel-blades. (b) Make sure that turbocharg Anglin, 1993). Turbocharger Acoustic signal A/D A/D Tachometer Microphone Digital si Dynam Fig. 9. Experimental arrangement for diagno vector w(n) consists of the in-phase and quadrature components of all orders to be identified. The parameter identification problem in Eq. (7) can be solved by the method of least-squares (Denbigh, 1998). The problem amounts to finding optimal parameters ŵðnÞ so that the perfor- mance index f(n) is minimized as fðnÞ¼ Xn i¼1 kn�ijeðiÞj2; ð10Þ where the forgetting factor k exponentially weighs the estimation error from the present to the past. Fig. 2 shows the block diagram and signal-flow graph of the RLS algorithm. The optimal solution of the problem can be recursively solved by using the following RLS algorithm (Haykin, 1996): kðnÞ¼ k�1Pðn � 1ÞuðnÞ 1 þ k�1uHðnÞPðn � 1ÞuðnÞ ð11Þ er shaft-wheel assembly turns freely and smoothly by rotating it by hand (Crouse & gnal processor Data recorder Algorithms (RLS) (FFT) Diagnostic system ic signal analyzer sis of turbocharger wheel-blade faults. J.-D. Wu et al. / Expert Systems with Applications 36 (2009) 5424–5431 5429 nðnÞ¼ dðnÞ� ŵ H ðn � 1ÞuðnÞ; ð12Þ ŵðnÞ¼ ŵðn � 1Þþ kðnÞn�ðnÞ; ð13Þ PðnÞ¼ k�1Pðn � 1Þ� k�1kðnÞuHðnÞPðn � 1Þ: ð14Þ In this procedure, matrix P(n) is the inverse of the auto-correla- tion matrix of input vector u, nðnÞ is the a priori estimation error, and k(n) is the gain vector. To initialize the RLS algorithm, the ini- tial conditions are generally taken to be ŵð0Þ¼ 0M�1, where M is the number of parameters and Pð0Þ¼ d�1I, where I is an M � M identity matrix and d is a small positive constant. One reason for using the RLS order-tracking technique is that the rate of conver- gence of the RLS algorithm is typically an order of magnitude faster than the traditional LMS algorithm. In order to provide valid understand of the characteristic in adaptive filtering algorithms. A comparison of convergence speeds and the mean-square-error (MSE) in various adaptive filters, i.e., Fig. 10. Order figures of sound emission signals for engine speed at 800 rpm using adaptive RLS filter. A solid line depicts blades without any damage; dashed line depicts blades with one fault. LMS, RLS, and Kalman filter in simulation is shown as Fig. 3. The re- sults have shown that the Kalman filter has the quickest conver- gence speed, converging at the iteration number of 800, the RLS converges at 1500, and LMS converges at 2800. That is because the Kalman filter algorithm takes into account the noise factor and is well structured with sophisticated considerations. However, the Kalman filter may be exploited as the basis for deriving an adaptive filtering algorithm appropriate to the complex calculation situations. In particular, each updated estimate of the state is com- puted from the previous estimate and the new input data, so the previous estimate requires storage. Comparatively, the RLS filter algorithm is rather simple in filtering design. 3. Experimental verification of fault diagnostic systems In the experimental investigation, two experiments are imple- mented to evaluate the proposed RLS filtering algorithm. One is a gear-set defect diagnosis using both the vibration signal and the sound emission signal; the other is a diagnosis of damaged IC en- gine turbocharger wheel-blades by using a sound emission signal. 3.1. Application 1: gear-set defect diagnosis The experimental setup for the gear-set defect diagnostic sys- tem is shown in Fig. 4. The horsepower of the DC servo motor is 0.5 with a maximum revolution of 3000 rpm. The motor can be controlled by using a DSP controller. An optical fiber sensor (LM339) is used to detect motor revolution and angular displace- ment as reference signals in the diagnostic system. The vibration signal and sound emission are measured by using an accelerometer (PCB 353B15) and a condenser microphone (ACO P4012). The pro- posed diagnostic system is implemented on a 60 MHz floating- point TMS320C32 DSP equipped with two 16-bit analog I/O chan- nels by using the adaptive RLS algorithm. In applying the proposed high-resolution order-tracking methods, some parameters need to be determined, such as the number of tracking orders N ^order and forgetting factor k in the proposed RLS algorithm. In addition, the experimental implementation of the gear-set is at various speed conditions. The experimental conditions are indi- cated in Fig. 5, where the gear-set is operated as a running-up schedule. The experimental results from order figures using a vibration signal are shown in Fig. 6; the order figures using a sound Fig. 11. Sound pressure amplitude in test schedule for diagnosis of faults in turbocharger blades. A solid line depicts blades without any damage; a dashed line depicts blades with one fault. 5430 J.-D. Wu et al. / Expert Systems with Applications 36 (2009) 5424–5431 emission signal are shown in Fig. 7. The experimental results dem- onstrate that the proposed diagnostic system is effective in defect diagnosis by using both vibration and sound emission signals. The ordered figures can be saved as a data bank for practical fault diag- nosis. Furthermore, order-tracking is one of the important tools for feature extraction of rotating machinery. The order amplitude fig- ure gives the information of the harmonic order signal in the mechanical system. Ordinarily, the amplitude of fault conditions is higher than without fault condition. So it is very easy to distin- guish the fault and without fault conditions. 3.2. Application 2: diagnosis of damaged IC engine turbocharger wheel-blades An IC engine can produce more power at the same speed if a forced induction system is used to improve volumetric efficiency. Such a system consists of air pumps or blowers that force more Fig. 12. Order figures of sound emission signals for engine run-up test. A solid line depicts blades without any damage; a dashed line depicts blades with one fault. air-fuel mixture into the engine combustion chamber. Normally they may produce 35–60% more power than a naturally-aspirated engine (Crouse & Anglin, 1993). However, the turbocharger system requires periodic maintenance to prevent early failure. Frequent causes of turbocharger failure are sand and other particles striking the blades, as in the case of the turbo blades shown in Fig. 8a. Con- ventional diagnosis of damaged blades is to conduct a visual inspection when the engine is cool or check to make sure that the turbocharger shaft-wheel assembly turns freely and smoothly by rotating it by hand, as shown in Fig. 8b. Obviously, the conven- tional inspection is not a precision approach for diagnosis of dam- age; it also is not a suitable method for diagnosis when the engine is running. The conventional FFT methods with a fixed sampling frequency also are ineffective for this application because normal operation of the engine varies rapidly. In fault diagnostic techniques to date, the vibration signal has become the most widely used method when a vibration signal is available. Unfortunately, in some applications of fault diagnostic systems, a vibration reference signal is unavailable. In this applica- tion, only the sound emission signal is used to evaluate the pro- posed system in the diagnosis of a damaged turbocharger under fixed revolution, acceleration and deceleration conditions. The experimental arrangement for the diagnosis of damaged turbo- charger wheel-blades is depicted in Fig. 9. A four-cylinder, four- stroke, 2.8-l IC engine with a turbocharger system is used in this application. A fiber-optic sensor is utilized to detect the revolution signal that is related to the sound emission from the wheel-blades. In this experimental implementation, the related reference signal from the engine can be measured by the ignition system or the wheel-blade signal. However, the ignition system may have sub- stantial interference that will affect the performance; therefore, the reference signal is picked up near the wheel-blades by using a fiber-optic sensor. To verify the filtering algorithm in order-track- ing, a preliminary test was conducted in an engine with a fixed rev- olution of 800 rpm. The order figures using a sound emission signal are shown in Fig. 10. In a practical condition, an engine may be operated by running-up or casting down. Although the high sweep rates make accurate order measurement difficult, the proposed adaptive order-tracking is suitable for such a condition. In order to verify the adaptive filter, the test schedule for the diagnosis of damaged turbocharger blades is shown in Fig. 11. The ordered fig- ures using a sound emission signal are shown in Fig. 12. The exper- imental results demonstrate that the proposed diagnostic system is effective in fault diagnosis by using sound emission signals. The or- dered figures and data also can be saved as a data bank for practical fault diagnosis. 4. Conclusions An order-tracking technique exploiting adaptive filtering based on an RLS algorithm for tracking the orders of vibration and sound emission signals in the diagnosis of defects in a gear-set and in damaged engine turbocharger wheel-blades has been applied. In this method, the order-tracking problem was treated as parameter identification and calculated at a high-resolution. Although, the Kalman filter is the alternative method when the uncertainty fac- tors of the entire system are taken into consideration. However, in some cases the design is more complex than the RLS algorithm. In the present study, the contribution is emphasized in the practi- cal application of gear-set defect diagnosis and diagnosis of dam- aged IC engine turbocharger wheel-blades by using the proposed RLS filtering algorithm. The results of the experiments indicated that the RLS algorithm is effective in fault diagnosis for both exper- imental cases. Various adaptive filtering algorithms are expected to be used in different applications; future research should focus on J.-D. Wu et al. / Expert Systems with Applications 36 (2009) 5424–5431 5431 the development of a robust adaptive filtering algorithm to accom- modate perturbation as well as uncertainties in the diagnostic system. Acknowledgements This study was supported by the National Science Council of Taiwan, the Republic of China, under project number NSC-93- 2212-E-018-004. The authors also wish to express appreciation to Dr. Cheryl Rutledge for her editorial assistance. References Bai, M. R., Jeng, J., & Chen, C. (2002). Adaptive order tracking technique using recursive least-square algorithm. Transactions of the ASME, Journal of Vibrations and Acoustics, 124, 502–511. Biswas, M., Pandey, A. K., Bluni, S. A., & Samman, M. M. (1994). Modified chain-code computer vision techniques for interrogation of vibration signatures for structural fault detection. Journal of Sound and Vibration, 175, 89–104. Chen, Y. D., Du, R., & Qu, L. S. (1995). Fault features of large rotating machinery and diagnosis using sensor fusion. Journal of Sound and Vibration, 188, 227–242. Crouse, W. H., & Anglin, D. L. (1993). Automotive mechanics. McGraw-Hill. Denbigh, P. (1998). System analysis and signal processing. Addison Wesley. Gelle, G., Colas, M., & Serviere, C. (2001). Blind source separation: a tool for rotating machine monitoring by vibration analysis. Journal of Sound and Vibration, 248, 865–885. Haykin, S. (1996). Adaptive filter theory. Prentice-Hall. Lee, S. K., & White, P. R. (1998). The enhancement of impulsive noise and vibration signals for fault detection in rotating and reciprocating machinery. Journal of Sound and Vibration, 217, 485–505. Lin, J., & Qu, L. (2000). Feature extraction based on morlet wavelet and its application for mechanical fault diagnosis. Journal of Sound and Vibration, 234, 135–148. Mba, D. (2002). Applicability of acoustic emissions to monitoring the mechanical integrity of bolted structures in low speed rotating machinery: Case study. NDT and E International, 35(5), 293–300. Oppenheim, A. V., & Schafer, R. W. (1999). Discrete-time signal processing. Prentice-Hall. Shibata, K., Takahashi, A., & Shirai, T. (2000). Fault diagnosis of rotating machinery through visualization of sound signals. Mechanical Systems and Signal Processing, 14, 229–241. Toutountzakis, T., & Mba, D. (2003). Observations of acoustic emission activity during gear defect diagnosis. NDT and E International, 36, 471–477. Vold, H., & Leuridan, J. (1993). High resolution order tracking at extreme slew rates, using Kalman filters. SAE Paper 931288 (pp. 219–226).. An expert system for the diagnosis of faults in rotating machinery using adaptive order-tracking algorithm Introduction Principle of adaptive order-tracking technique using RLS algorithm Experimental verification of fault diagnostic systems Application 1: gear-set defect diagnosis Application 2: diagnosis of damaged IC engine turbocharger wheel bladeswheel-blades Conclusions Acknowledgements References