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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

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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

Authors
  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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Communicated by B. B. Gupta.

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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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