Bayesian Stochastic Neural Network Model for Turbomachinery Damage Prediction
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Published
Nov 19, 2020
Shuhua Yang
Xiaomo Jiang
Shengli Xu
Xiaofang Wang
Abstract
Turbomachinery often suffers various defects such as impeller cracking, resulting in forced outage, increased maintenance costs, and reduced productivity. Condition monitoring and damage prognostics has been widely used as an increasingly important and powerful tool to improve the system availability, reliability, performance, and maintainability, but still very challenging due to multiple sources of data uncertainties and the complexity of analytics modeling. This paper presents an intelligent probabilistic methodology for anomaly prediction of high-fidelity turbomachine, considering multiple data imperfections and multivariate correlation. The proposed method adeptly integrates several advanced state-of-the-art signal processing and artificial intelligence techniques: wavelet multi-resolution decomposition, Bayesian hypothesis testing, probabilistic principal component analysis, and fuzzy stochastic neural network modeling. The advanced signal processing is employed to reduce dimensionality and to address multivariate correlation and data uncertainty for damage prediction. Instead of conventionally using raw time series data, principal components are utilized in the establishment of stochastic neural network model and anomaly prediction. Bayesian interval hypothesis testing metric is then presented to quantitatively compare the predicted and measured data for model validation and anomaly evaluation, thus providing a confidence indicator to judge the model quality and evaluate the equipment status. Bayesian method is developed in this study for denoising the raw data with multiresolution wavelet decomposition, quantifying the model accuracy, and assessing the equipment status. The dynamic stochastic neural network model is established via the nonlinear autoregressive moving average with exogenous inputs approach. It seamlessly integrates the fuzzy clustering and independent Bernoulli random function into radial basis function neural network. A natural gradient method based on Kullback-Leibler distance criterion is employed to maximize the log-likelihood loss function. The effectiveness of the proposed methodology and procedure is demonstrated with the 11-variable time series data and the forced outage event of a real-world centrifugal compressor.
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Keywords
Wavelet, Bayesian hypothesis testing, Probabilistic PCA, Stochastic neural network, Damage prediction, Turbomachinery
References
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Al-Badour, F., Sunar, M., & Cheded, L. (2011). Vibration analysis of rotating machinery using time–frequency analysis and wavelet techniques, Mechanical Systems and Signal Processing, 25(6), 2083–2101. doi: 10.1016/j.ymssp.2011.01.017.
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Burrus, C.S., Gopinath, R.A., & Guo, H. (1998). Introduction to Wavelets and Wavelet Transforms: a Primer, New Jersey: Prentice Hall.
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Chen, P., Taniguchi, M., Toyota, T., & He, Z. (2005). Fault diagnosis method for machinery in unsteady operating condition by instantaneous power spectrum and genetic programming, Mechanical Systems and Signal Processing, 19(1), 175–194. doi: 10.1016/j.ymssp.2003.11.004.
Coifman, R.R. & Donoho, D.L. (1995). Translation-invariant de-noising. In Antoniadis, A. & Oppenheim, G. (Eds.), Wavelets and Statistics, Lecture Notes in Statistics, 103 (125 – 150), New York: Springer-Verlag.
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Eftekharnejad, B., Carrasco, M.R., Charnley, B., & Mba, D. (2011). The application of spectral kurtosis on acoustic emission and vibrations from a defective bearing, Mechanical Systems and Signal Processing, 25(1), 266–284. doi: 10.1016/j.ymssp.2010.06.010.
Galka, T. & Tabaszewski, M. (2011). An application of statistical symptoms in machine condition diagnostics, Mechanical Systems and Signal Processing, 25(1), 253–265. doi:10.1016/j.ymssp.2010.07.006.
Ghanem, R. & Shinozuka, M. (1995). Structural system identification; parts I and II, ASCE Journal of Engineering Mechanics, 121(2), 255–273. doi: 10.1061/(ASCE)0733-9399(1995)121:2(255).
Hung, S.L., Huang, C.S., Wen, C.M., & Hsu, Y.C. (2003). Nonparametric identification of a building structure from experimental data using wavelet neural network. Computer-Aided Civil and Infrastructure Engineering, 18(5), 358–370. doi: 10.1111/1467-8667.t01-1-00313.
Jardine, A.K.S., Lin, D. & Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mechanical Systems and Signal Processing, 20(7), 1483–1510. doi: 10.1016/j.ymssp.2005.09.012.
Jiang, X. & Adeli, H. (2005). Dynamic wavelet neural network for nonlinear system identification, Computer-Aided Civil and Infrastructure Engineering, 20(4), 316–330. doi: 10.1111/j.1467-8667.2005.00399.x.
Jiang, X. & Adeli, H. (2007). Psuedospectra, MUSIC, and dynamic wavelet neural network for damage detection of high-rise buildings, International Journal for Numerical Methods in Engineering, 71(5), 606-629. doi: 10.1002/nme.1964.
Jiang, X. & Foster, C. (2013). Remote thermal performance monitoring: Turning data to solution, ASME Power Conference (V002T13A004), Jul 29 – Aug 1, Boston, Massachusetts. doi:10.1115/POWER2013-98246.
Jiang, X. & Foster C. (2014). Plant performance monitoring and diagnostics: remote, automated, and real-time, ASME Turbo Expo (V006T06A034), Jun 16 – 20, Düsseldorf, Germany. doi: 10.1115/GT2014-27314.
Jiang, X. & Mahadevan, S. (2008a). Bayesian wavelet methodology for structural damage detection, Structural Control and Health Monitoring, 15(7), 974-991. doi: 10.1002/stc.230. Jiang, X. & Mahadevan, S. (2008b). Bayesian probabilistic inference for nonparametric damage detection of structures, ASCE Journal of Engineering Mechanics, 134(10), 820-831. doi: 10.1061/(ASCE)0733-9399(2008)134:10(820).
Jiang, X., Mahadevan, S., & Adeli, H. (2007). Bayesian wavelet packet denoising for structural system identification, Structural Control and Health Monitoring, 14(2), 333–356. doi: 10.1002/stc.161.
Jiang, X., Mahadevan, S., & Yuan, Y. (2017). Fuzzy stochastic neural network model for structural system identification. Mechanical Systems and Signal Processing, 82(1), 394-411. doi: 10.1016/j.ymssp.2016.05.030.
Juang, J.N. (1994). Applied system identification. NJ: Prentice Hall, Englewood Cliffs.
Kamitsuji, S. & Shibata, R. (2003). Effectiveness of stochastic neural network for prediction of fall or rise of TOPIX, Asia-Pacific Financial Markets, 10(2), 187–204. doi: 10.1007/s10690-005-6010-4.
Kass, R. & Raftery, A. (1995). Bayes factors, Journal of the American Statistical Association, 90(430), 773–795. doi: 10.1080/01621459.1995.10476572.
Kennel, M.B., Brown, R., & Abarbanel, H.D.I. (1992), Determining embedding dimension for phase-space reconstruction using a geometrical construction, Physical Review A, 45: 3403–3411. doi: 10.1103/PhysRevA.45.3403.
Lai, T.L. & Wong, S.P.S. (2001). Stochastic neural networks with applications to nonlinear time series, Journal of the American Statistical Association, 96(455), 968–981. doi: 10.1198/016214501753208636.
Lee, J., Wu, F., Zhao, W., Ghaffari, M., Liao, L., & Siegel, D. (2014). Prognostics and health management design for rotary machinery systems - Reviews, methodology and applications, Mechanical Systems and Signal Processing, 42(1-2), 314–334. doi: 10.1016/j.ymssp.2013.06.004.
Lei, Y., Jiang Y., & Xu Z. (2012), Structural damage detection with limited input and output measurement signals, Mechanical Systems and Signal Processing, 28, 229-243. doi: 10.1016/j.ymssp.2011.07.026.
Li, H., Zhang, X., & Xu, F. (2013). Experimental investigation on centrifugal compressor blade crack classification using the squared envelope spectrum, Sensors, 13(9), 12548–63. doi: 10.3390/s130912548.
Liu, Y., Guo, L., Wang, Q., An, G., Guo, M., & Lian, H. (2010). Application to induction motor faults diagnosis of the amplitude recovery method combined with FFT, Mechanical Systems and Signal Processing, 24(8), 2961–2971. doi: 10.1016/j.ymssp.2010.03.008.
Mallat, S. (1989). A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674–693. doi: 10.1109/34.192463.
Masri, S.F., Nakamura, M., Chassiakos, A.G., & Caughey, T.K. (1996). Neural network approach to the detection of changes in structural parameters. ASCE Journal of Engineering Mechanics, 122(4), 350–360. doi: 10.1061/(ASCE)0733-9399(1996)122:4(350).
Masri, S.F., Smyth, A.W., Chassiakos, A.G., Caughey, T.K., & Hunter, N.F. (2000). Application of neural networks for detection of changes in nonlinear systems, ASCE Journal of Engineering Mechanics, 126(7), 666–676. doi: 10.1061/(ASCE)0733-9399(2000)126:7(666).
Migon, H.S. & Gamerman, D. (1999). Statistical Inference-An Integrated Approach. London, UK: Arnold, a Member of the Holder Headline Group.
McFadden, P.D. & Toozhy, M.M. (2000). Application of synchronous averaging to vibration monitoring of rolling element bearings, Mechanical Systems and Signal Processing, 14(6), 891–906. doi: 10.1006/mssp.2000.1290.
Moody, J. & Darken, C.J. (1989). Fast learning in networks of locally-tuned processing units, Neural Computation, 1, 281–294. doi: 10.1162/neco.1989.1.2.281.
Nakamura1, M., Masri, S.F., Chassiakos, A.G., & Caughey, T.K. (1998). A method for non-parametric damage detection through the use of neural network, Earthquake Engineering and Structural Dynamics, 27(9), 997–1010. doi: 10.1002/(SICI)1096-9845(199809)27:9<997::AID-EQE771>3.0.CO;2-7.
Peeters, B. & Roeck, G.D. (2001). Stochastic system identification for operational modal analysis: A review, ASME Journal of Dynamic Systems, Measurement, and Control, 10(4), 659–667. doi: 10.1115/1.1410370.
Percival, D.B. & Walden, A.T. (2000). Wavelet Methods for Time Series Analysis, New York: Cambridge University Press.
Rai, V.K. & Mohanty, A.R. (2007). Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert–Huang transform, Mechanical Systems and Signal Processing, 21(6), 2607–2615. doi: 10.1016/j.ymssp.2006.12.004.
Samanta, B. & Al-Balushi, K.R. (2003). Artificial neural network based fault diagnostics of rolling element bearings using time-domain features, Mechanical Systems and Signal Processing, 17(2), 317–328. doi: 10.1006/mssp.2001.1462.
Stoica, P. & Moses, R.L. (1997). Introduction to Spectral Analysis. New Jersey: Prentice-Hall, Englewood Cliffs.
Tipping, M.E. & Bishop, C.M. (1999). Probabilistic principal component analysis, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61(3), 611–622. doi: 10.1111/1467-9868.00196.
Vidakovic, B. (1998). Nonlinear wavelet shrinkage with Bayes rules and Bayes factors, Journal of the American Statistical Association, 93(441), 173 – 179. doi: 10.1080/01621459.1998.10474099.
Wang, W.J., Chen, J., Wu, X.K., & Wu, Z.T. (2001). The application of some non-linear methods in rotating machinery fault diagnosis, Mechanical Systems and Signal Processing 15(4), 697–705. doi: 10.1006/mssp.2000.1316.
Wang, W.Q., Golnaraghi, M.F., & Ismail, F. (2004). Prognosis of machine health condition using neuro-fuzzy systems, Mechanical Systems and Signal Processing, 18(4), 813–831. doi: 10.1016/S0888-3270(03)00079-7.
Wu, Z.S., Xu, B., & Yokoyama, K. (2002). Decentralized parametric damage detection based on neural networks, Computer-Aided Civil-Infrastructure Engineering, 17(3), 175–184. doi: 10.1111/1467-8667.00265.
Xu, S., Jiang, X., Huang, J., Yang, S., & Wang. X. (2016). Bayesian wavelet PCA methodology for turbomachinery damage diagnosis under uncertainty, Mechanical Systems and Signal Processing, 80(1), 1-18. doi: 10.1016/j.ymssp.2016.04.031.
Adeli, H. & Jiang, X. (2006). Dynamic fuzzy wavelet neural network model for structural system identification, ASCE Journal of Structural Engineering, 132(1), 102–111. doi: 10.1061/(ASCE)0733-9445(2006)132:1(102).
Al-Badour, F., Sunar, M., & Cheded, L. (2011). Vibration analysis of rotating machinery using time–frequency analysis and wavelet techniques, Mechanical Systems and Signal Processing, 25(6), 2083–2101. doi: 10.1016/j.ymssp.2011.01.017.
Baydar, N., Chen, Q., Ball, A., & Kruger, U. (2001). Detection of incipient tooth defect in helical gears using multivariate statistics, Mechanical Systems and Signal Processing, 15(2), 303–321. doi: 10.1006/mssp.2000.1315.
Bezdek, J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. New York: Plenum.
Burrus, C.S., Gopinath, R.A., & Guo, H. (1998). Introduction to Wavelets and Wavelet Transforms: a Primer, New Jersey: Prentice Hall.
Chatfield, C. (2004). The Analysis of Time Series: an Introduction. 6th edition. Boca Raton, FL: Chapman & Hall/CRC.
Chen, P., Taniguchi, M., Toyota, T., & He, Z. (2005). Fault diagnosis method for machinery in unsteady operating condition by instantaneous power spectrum and genetic programming, Mechanical Systems and Signal Processing, 19(1), 175–194. doi: 10.1016/j.ymssp.2003.11.004.
Coifman, R.R. & Donoho, D.L. (1995). Translation-invariant de-noising. In Antoniadis, A. & Oppenheim, G. (Eds.), Wavelets and Statistics, Lecture Notes in Statistics, 103 (125 – 150), New York: Springer-Verlag.
Coifman, R.R. & Wickerhauser, M.V. (1992), Entropy-based algorithms for best basis selection, IEEE Transaction on Information Theory, 38(2), 713–718. doi: 10.1109/18.119732.
Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets, Communication on Pure and Applied Mathematics, 41(7), 909 – 996. doi: 10.1002/cpa.3160410705.
Edwards, S., Lee, A.W., & Friswell, M.I. (1998). Fault Diagnosis of Rotating Machinery, Shock and Vibration, 30(1), 4-13. doi: 10.1177/058310249803000102.
Eftekharnejad, B., Carrasco, M.R., Charnley, B., & Mba, D. (2011). The application of spectral kurtosis on acoustic emission and vibrations from a defective bearing, Mechanical Systems and Signal Processing, 25(1), 266–284. doi: 10.1016/j.ymssp.2010.06.010.
Galka, T. & Tabaszewski, M. (2011). An application of statistical symptoms in machine condition diagnostics, Mechanical Systems and Signal Processing, 25(1), 253–265. doi:10.1016/j.ymssp.2010.07.006.
Ghanem, R. & Shinozuka, M. (1995). Structural system identification; parts I and II, ASCE Journal of Engineering Mechanics, 121(2), 255–273. doi: 10.1061/(ASCE)0733-9399(1995)121:2(255).
Hung, S.L., Huang, C.S., Wen, C.M., & Hsu, Y.C. (2003). Nonparametric identification of a building structure from experimental data using wavelet neural network. Computer-Aided Civil and Infrastructure Engineering, 18(5), 358–370. doi: 10.1111/1467-8667.t01-1-00313.
Jardine, A.K.S., Lin, D. & Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance, Mechanical Systems and Signal Processing, 20(7), 1483–1510. doi: 10.1016/j.ymssp.2005.09.012.
Jiang, X. & Adeli, H. (2005). Dynamic wavelet neural network for nonlinear system identification, Computer-Aided Civil and Infrastructure Engineering, 20(4), 316–330. doi: 10.1111/j.1467-8667.2005.00399.x.
Jiang, X. & Adeli, H. (2007). Psuedospectra, MUSIC, and dynamic wavelet neural network for damage detection of high-rise buildings, International Journal for Numerical Methods in Engineering, 71(5), 606-629. doi: 10.1002/nme.1964.
Jiang, X. & Foster, C. (2013). Remote thermal performance monitoring: Turning data to solution, ASME Power Conference (V002T13A004), Jul 29 – Aug 1, Boston, Massachusetts. doi:10.1115/POWER2013-98246.
Jiang, X. & Foster C. (2014). Plant performance monitoring and diagnostics: remote, automated, and real-time, ASME Turbo Expo (V006T06A034), Jun 16 – 20, Düsseldorf, Germany. doi: 10.1115/GT2014-27314.
Jiang, X. & Mahadevan, S. (2008a). Bayesian wavelet methodology for structural damage detection, Structural Control and Health Monitoring, 15(7), 974-991. doi: 10.1002/stc.230. Jiang, X. & Mahadevan, S. (2008b). Bayesian probabilistic inference for nonparametric damage detection of structures, ASCE Journal of Engineering Mechanics, 134(10), 820-831. doi: 10.1061/(ASCE)0733-9399(2008)134:10(820).
Jiang, X., Mahadevan, S., & Adeli, H. (2007). Bayesian wavelet packet denoising for structural system identification, Structural Control and Health Monitoring, 14(2), 333–356. doi: 10.1002/stc.161.
Jiang, X., Mahadevan, S., & Yuan, Y. (2017). Fuzzy stochastic neural network model for structural system identification. Mechanical Systems and Signal Processing, 82(1), 394-411. doi: 10.1016/j.ymssp.2016.05.030.
Juang, J.N. (1994). Applied system identification. NJ: Prentice Hall, Englewood Cliffs.
Kamitsuji, S. & Shibata, R. (2003). Effectiveness of stochastic neural network for prediction of fall or rise of TOPIX, Asia-Pacific Financial Markets, 10(2), 187–204. doi: 10.1007/s10690-005-6010-4.
Kass, R. & Raftery, A. (1995). Bayes factors, Journal of the American Statistical Association, 90(430), 773–795. doi: 10.1080/01621459.1995.10476572.
Kennel, M.B., Brown, R., & Abarbanel, H.D.I. (1992), Determining embedding dimension for phase-space reconstruction using a geometrical construction, Physical Review A, 45: 3403–3411. doi: 10.1103/PhysRevA.45.3403.
Lai, T.L. & Wong, S.P.S. (2001). Stochastic neural networks with applications to nonlinear time series, Journal of the American Statistical Association, 96(455), 968–981. doi: 10.1198/016214501753208636.
Lee, J., Wu, F., Zhao, W., Ghaffari, M., Liao, L., & Siegel, D. (2014). Prognostics and health management design for rotary machinery systems - Reviews, methodology and applications, Mechanical Systems and Signal Processing, 42(1-2), 314–334. doi: 10.1016/j.ymssp.2013.06.004.
Lei, Y., Jiang Y., & Xu Z. (2012), Structural damage detection with limited input and output measurement signals, Mechanical Systems and Signal Processing, 28, 229-243. doi: 10.1016/j.ymssp.2011.07.026.
Li, H., Zhang, X., & Xu, F. (2013). Experimental investigation on centrifugal compressor blade crack classification using the squared envelope spectrum, Sensors, 13(9), 12548–63. doi: 10.3390/s130912548.
Liu, Y., Guo, L., Wang, Q., An, G., Guo, M., & Lian, H. (2010). Application to induction motor faults diagnosis of the amplitude recovery method combined with FFT, Mechanical Systems and Signal Processing, 24(8), 2961–2971. doi: 10.1016/j.ymssp.2010.03.008.
Mallat, S. (1989). A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674–693. doi: 10.1109/34.192463.
Masri, S.F., Nakamura, M., Chassiakos, A.G., & Caughey, T.K. (1996). Neural network approach to the detection of changes in structural parameters. ASCE Journal of Engineering Mechanics, 122(4), 350–360. doi: 10.1061/(ASCE)0733-9399(1996)122:4(350).
Masri, S.F., Smyth, A.W., Chassiakos, A.G., Caughey, T.K., & Hunter, N.F. (2000). Application of neural networks for detection of changes in nonlinear systems, ASCE Journal of Engineering Mechanics, 126(7), 666–676. doi: 10.1061/(ASCE)0733-9399(2000)126:7(666).
Migon, H.S. & Gamerman, D. (1999). Statistical Inference-An Integrated Approach. London, UK: Arnold, a Member of the Holder Headline Group.
McFadden, P.D. & Toozhy, M.M. (2000). Application of synchronous averaging to vibration monitoring of rolling element bearings, Mechanical Systems and Signal Processing, 14(6), 891–906. doi: 10.1006/mssp.2000.1290.
Moody, J. & Darken, C.J. (1989). Fast learning in networks of locally-tuned processing units, Neural Computation, 1, 281–294. doi: 10.1162/neco.1989.1.2.281.
Nakamura1, M., Masri, S.F., Chassiakos, A.G., & Caughey, T.K. (1998). A method for non-parametric damage detection through the use of neural network, Earthquake Engineering and Structural Dynamics, 27(9), 997–1010. doi: 10.1002/(SICI)1096-9845(199809)27:9<997::AID-EQE771>3.0.CO;2-7.
Peeters, B. & Roeck, G.D. (2001). Stochastic system identification for operational modal analysis: A review, ASME Journal of Dynamic Systems, Measurement, and Control, 10(4), 659–667. doi: 10.1115/1.1410370.
Percival, D.B. & Walden, A.T. (2000). Wavelet Methods for Time Series Analysis, New York: Cambridge University Press.
Rai, V.K. & Mohanty, A.R. (2007). Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert–Huang transform, Mechanical Systems and Signal Processing, 21(6), 2607–2615. doi: 10.1016/j.ymssp.2006.12.004.
Samanta, B. & Al-Balushi, K.R. (2003). Artificial neural network based fault diagnostics of rolling element bearings using time-domain features, Mechanical Systems and Signal Processing, 17(2), 317–328. doi: 10.1006/mssp.2001.1462.
Stoica, P. & Moses, R.L. (1997). Introduction to Spectral Analysis. New Jersey: Prentice-Hall, Englewood Cliffs.
Tipping, M.E. & Bishop, C.M. (1999). Probabilistic principal component analysis, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 61(3), 611–622. doi: 10.1111/1467-9868.00196.
Vidakovic, B. (1998). Nonlinear wavelet shrinkage with Bayes rules and Bayes factors, Journal of the American Statistical Association, 93(441), 173 – 179. doi: 10.1080/01621459.1998.10474099.
Wang, W.J., Chen, J., Wu, X.K., & Wu, Z.T. (2001). The application of some non-linear methods in rotating machinery fault diagnosis, Mechanical Systems and Signal Processing 15(4), 697–705. doi: 10.1006/mssp.2000.1316.
Wang, W.Q., Golnaraghi, M.F., & Ismail, F. (2004). Prognosis of machine health condition using neuro-fuzzy systems, Mechanical Systems and Signal Processing, 18(4), 813–831. doi: 10.1016/S0888-3270(03)00079-7.
Wu, Z.S., Xu, B., & Yokoyama, K. (2002). Decentralized parametric damage detection based on neural networks, Computer-Aided Civil-Infrastructure Engineering, 17(3), 175–184. doi: 10.1111/1467-8667.00265.
Xu, S., Jiang, X., Huang, J., Yang, S., & Wang. X. (2016). Bayesian wavelet PCA methodology for turbomachinery damage diagnosis under uncertainty, Mechanical Systems and Signal Processing, 80(1), 1-18. doi: 10.1016/j.ymssp.2016.04.031.
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