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Application of Kalman filter to Model-based Prognostics for Solenoid Valve

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Abstract

Solenoid valves (SVs) are electromechanical components, which are used as actuators in various application environments and play crucial roles in control systems, and their breakdown may result in a system crash. Therefore, this paper explores a Kalman filter (KF)-based method to predict the remaining useful life (RUL) of SVs, so that the SVs can be replaced or maintained before their failure bringing a catastrophic consequence for engineering system. In this paper, a degradation signal is extracted from the driven current, which can be monitored conveniently with a non-contact current sensor. Based on an empirical linear degradation model, the KF is adopted to track the degradation state and the degradation rate and to capture the uncertainties. The Monte Carlo sampling and kernel density estimation are used to propagate the uncertainties and estimate the probability distribution of RUL, respectively. To verify our methods, a degradation experiment is designed. The experiment results show that the degradation signal extracted from the driven current can indeed reflect the degradation state of SVs. By comparing the proposed method with other state of the arts prognostic approaches, it shows that the proposed KF method preforms better and has a higher prediction accuracy than other methods.

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Abbreviations

\(I_\mathrm{temp}\) :

The template dynamic current waveform when the SV operate at the best state

\(I_k\) :

The dynamic current waveform when the SV works at kth operation cycle

\(i_{kn}\) :

The nth sample of dynamic current waveform at kth operation cycle

\(d_k\) :

The Euclidean distance between the dynamic current waveform at the kth operation cycle and the template one, which represents the degradation state

\(b_k\) :

The degradation rate at kth operation cycle

\(k_\mathrm{p}\) :

Operation cycle when the prediction begins

\(R(k_\mathrm{p})\) :

The remaining useful life (RUL) when the prediction starting time is kth operation cycle

\(f_\mathrm{R}(r)\) :

The probability distribution function (PDF) of remaining useful life (RUL)

\(k_\mathrm{EOL}\) :

Operation cycle at End-of-Life (EoL)

\(w_k\) :

The process uncertainty at kth operation cycle

\(w_k^d\) :

The process uncertainty of degradation state at kth operation cycle

\(w_k^b\) :

The process uncertainty of degradation rate at kth operation cycle

\(v_k\) :

The measurement uncertainty at kth operation cycle

\(x_k\) :

The system state at kth operation cycle, including degradation state and degradation rate

\(y_k\) :

The observed degradation state at kth operation cycle

\({\hat{x}}_k\) :

The estimated system state at kth operation cycle

W :

The covariance of process uncertainty

V :

The covariance of measurement uncertainty

\(P_k\) :

The estimated covariance of system state at kth operation cycle

SV:

Solenoid valve

RUL:

Remaining useful life

KF:

Kalman filter

EOL:

End-of-life

PDF:

Probability distribution function

ANN:

Artificial neural network

ARMA:

Autoregressive moving average model

PF:

Particle filter

References

  • An D, Choi JH, Kim NH (2013) Prognostics 101: a tutorial for particle filter-based prognostics algorithm using matlab. Reliab Eng Syst Saf 115(1):161–169

    Article  Google Scholar 

  • An D, Kim NH, Choi JH (2015) Practical options for selecting data-driven or physics-based prognostics algorithms with reviews. Reliab Eng Syst Saf 133:223–236

    Article  Google Scholar 

  • Angadi SV, Jackson RL, Choe SY, Flowers GT, Suhling JC, Chang YK, Ham JK (2009a) Reliability and life study of hydraulic solenoid valve. Part 1: a multi-physics finite element model. Eng Fail Anal 16(3):874–887

    Article  Google Scholar 

  • Angadi SV, Jackson RL, Choe SY, Flowers GT, Suhling JC, Chang YK, Ham JK, Bae JI (2009b) Reliability and life study of hydraulic solenoid valve. Part 2: experimental study. Eng Fail Anal 16(3):944–963

    Article  Google Scholar 

  • Benkedjouh T, Medjaher K, Zerhouni N, Rechak S (2013a) Remaining useful life estimation based on nonlinear feature reduction and support vector regression. Eng Appl Artif Intell 26(7):1751–1760

    Article  Google Scholar 

  • Benkedjouh T, Medjaher K, Zerhouni N, Rechak S (2013b) Remaining useful life estimation based on nonlinear feature reduction and support vector regression. Eng Appl Artif Intell 26(7):1751–1760

    Article  Google Scholar 

  • Celaya J, Saxena A, Goebel K (2012) Uncertainty representation and interpretation in model-based prognostics algorithms based on kalman filter estimation. In: Annual conference of the prognostics and health management society

  • Chen Z (2003) Bayesian filtering: from kalman filters to particle filters and beyond. Statistics 182(1):1–69

    Article  Google Scholar 

  • Chen YS (2019) Performance identification in large-scale class data from advanced facets of computational intelligence and soft computing techniques. Int J High Perform Comput Netwo 13(3):283–293

    Article  Google Scholar 

  • Dietterich TG (1995) Overfitting and undercomputing in machine learning. ACM Comput Surv 27(3):326–327

    Article  Google Scholar 

  • Dong HC, Zhang ST, Li QH, Wang CH (2012) A new approach to battery capacity prediction based on hybrid arma and ann model. Appl Mech Mater 190–191:241–244

    Article  Google Scholar 

  • Dong H, Jin X, Lou Y, Wang C (2014) Lithium-ion battery state of health monitoring and remaining useful life prediction based on support vector regression-particle filter. J Power Sources 271:114–123

    Article  Google Scholar 

  • Fan J, Yung KC, Pecht M (2014) Prognostics of lumen maintenance for high power white light emitting diodes using a nonlinear filter-based approach. Reliab Eng Syst Saf 123(3):63–72

    Article  Google Scholar 

  • Hu Y, Baraldi P, Maio FD, Zio E (2015) A particle filtering and kernel smoothing-based approach for new design component prognostics. Reliab Eng Syst Saf 134:19–31

    Article  Google Scholar 

  • Jardine AKS, Lin D, Banjevic D (2006) A review on machinery diagnostics and prognostics implementing condition-based maintenance. Mech Syst Signal Process 20(7):1483–1510

    Article  Google Scholar 

  • Jerónimo Andrés A, Luciano M (2010) Increasing the reliability of solution exchanges by monitoring solenoid valve actuation. J Neurosci Methods 185(2):280–283

    Article  Google Scholar 

  • Jin G, Matthews DE, Zhou Z (2013) A bayesian framework for on-line degradation assessment and residual life prediction of secondary batteries inspacecraft. Reliab Eng Syst Saf 113(1):7–20

    Article  Google Scholar 

  • Jing W, Tao JXZLZ (2019) The optimisation of speech recognition based on convolutional neural network. Int J High Perform Comput Netw 13(2):222–231

    Article  MathSciNet  Google Scholar 

  • Jouin M, Gouriveau R, Hissel D (2016) Particle filter-based prognostics: review, discussion and perspectives. Mech Syst Signal Process 72:2–31

    Article  Google Scholar 

  • Lall P, Lowe R, Kai G (2012) Extended kalman filter models and resistance spectroscopy for prognostication and health monitoring of leadfree electronics under vibration. IEEE Trans Reliab 61(4):858–871

    Article  Google Scholar 

  • Lazib L, Zhao Y, Qin B, Liu T (2016) Negation scope detection with recurrent neural networks models in review texts. In: International conference of pioneering computer scientists. Springer, pp 494–508

  • Lee J, Ni J, Djurdjanovic D, Qiu H, Liao H (2006) Intelligent prognostics tools and e-maintenance. Comput Ind 57(6):476–489

    Article  Google Scholar 

  • Liu ZH, Gao Q, Niu HL (2014) The fault diagnosis of electromagnetic valves based on driving current detection. Acta Armamentarii pp 1083–1090

  • Liu Q, Bo H, Qin B (2010) Experimental study and numerical analysis on electromagnetic force of direct action solenoid valve. Nucl Eng Des 240(12):4031–4036

    Article  Google Scholar 

  • Mercer JR (1969) Reliability of solenoid valves. In: Presented at safety and failure of components pp 89–94

  • Peng CY, Tseng ST (2009) Mis-specification analysis of linear degradation models. IEEE Trans Reliab 58(3):444–455

    Article  Google Scholar 

  • Peng BH, Zhou JL, Feng J, Liu XM (2011) Residual lifetime prediction of metallized film pulse capacitors. Syst Eng Electr Technol 39(11):2674–2679

    Google Scholar 

  • Raffo A, Falco SD, Sozzi G, Menozzi R, Schreurs MP, Vannini G (2011) Analysis of the gate current as a suitable indicator for fet degradation under nonlinear dynamic regime. Microelectron Reliab 51(2):235–239

    Article  Google Scholar 

  • Sankararaman S (2015) Significance, interpretation, and quantification of uncertainty in prognostics and remaining useful life prediction. Mech Syst Signal Process 52–53(1):228–247

    Article  Google Scholar 

  • Sankararaman S, Goebel K (2013) Why is the remaining useful life prediction uncertain? In: Annual conference of the prognostics and health management society

  • Saxena A, Celaya J, Balaban E, Kai G, Saha B, Saha S, Schwabacher M (2008) Metrics for evaluating performance of prognostic techniques. In: International conference on prognostics and health management

  • Sclater N, Chironis NP (2001) Mechanisms and mechanical devices sourcebook, vol 3. McGraw-Hill, New York

    Google Scholar 

  • Sharieh A, Albdour L (2017) A heuristic approach for service allocation in cloud computing. Int J Cloud Appl Comput 7(4):60–74

    Google Scholar 

  • Si XS, Wangbde W, Zhouc DH (2011) Remaining useful life estimation–a review on the statistical data driven approaches. Eur J Oper Res 213(1):1–14

    Article  MathSciNet  Google Scholar 

  • Sikorska J, Hodkiewicz M, Ma L (2011) Prognostic modelling options for remaining useful life estimation. Mech Syst Signal Process 25(5):1803–1836

    Article  Google Scholar 

  • Tao G, Chen HY, Jin YY, Zhong-Bo HE (2002) Optimal design on the magnetic field of the high-speed response solenoid valve. J Mater Process Technol 129(s1):555–558

    Article  Google Scholar 

  • Tian Z (2012) An artificial neural network method for remaining useful life prediction of equipment subject to condition monitoring. J Intell Manuf 23(2):227–237

    Article  Google Scholar 

  • Wang X (2010) Wiener processes with random effects for degradation data. J Multivar Anal 101(2):340–351

    Article  MathSciNet  MATH  Google Scholar 

  • Wang Q, Yang F, Qian Y, Chen J, Guan H (2011a) Experimental analysis of new high-speed powerful digital solenoid valves. Energy Convers Manag 52(5):2309–2313

    Article  Google Scholar 

  • Wang Q, Yang F, Qian Y, Chen J, Guan H (2011b) Experimental analysis of new high-speed powerful digital solenoid valves. Energy Convers Manag 52(5):2309–2313

    Article  Google Scholar 

  • Wang D, Tsui KL, Wang D, Tsui KL (2017) Statistical modeling of bearing degradation signals. IEEE Trans Reliab 66(4):1331–1344

    Article  Google Scholar 

  • Welch G, Bishop G (1995) An introduction to the kalman filter. Technical report, Chapel Hill, NC, USA

  • Wu J, Song G, Jie L, Zeng D (2016) Big data meet green challenges: big data toward green applications. IEEE Syst J 10(3):888–900

    Article  Google Scholar 

  • Wu J, Guo S, Huang H, Liu W, Xiang Y (2018) Information and communications technologies for sustainable development goals: state-of-the-art, needs and perspectives. IEEE Commun Surv Tutor 20:2389–2406. https://doi.org/10.1109/comst.2018.2812301

  • Xilang T, Mingqing X, Yajun L, Bin H, Lei Z, Srikanta P (2018) Application of particle filter technique to online prognostics for solenoid valve. J Intell Fuzzy Syst 35(1):523–532

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. ATS Lab, Air Force Engineering University, Xi’an, China

    Xilang Tang & Mingqing Xiao

  2. China Mobile Communications Corporation, Xiangtan, China

    Bin Hu

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  1. Xilang Tang
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  2. Mingqing Xiao
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  3. Bin Hu
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Correspondence to Xilang Tang.

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Tang, X., Xiao, M. & Hu, B. Application of Kalman filter to Model-based Prognostics for Solenoid Valve. Soft Comput 24, 5741–5753 (2020). https://doi.org/10.1007/s00500-019-04311-w

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