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SCIENTIA SINICA Informationis, Volume 51 , Issue 6 : 997(2021) https://doi.org/10.1360/SSI-2020-0382

Incipient fault diagnosis for high-speed train traction systems via improved LSTM

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  • ReceivedMay 28, 2020
  • AcceptedOct 30, 2020
  • PublishedMay 18, 2021

Abstract


Funded by

国家自然科学基金项目(61922042,61973140)

江苏高校“青蓝工程”

111 引智基地(B20007)


Author information





References

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  • Figure 1

    The framework of improved LSTM cell

  • Figure 1

    The framework of improved LSTM cell

  • Figure 3

    (Color online) The framework of improved LSTM encoder-decoder model

  • Figure 3

    (Color online) The framework of improved LSTM encoder-decoder model

  • Figure 4

    (Color online) The loss $J_{\rm~ed}$ of the encoders based on improved LSTM, LSTM, and GRU. (a) First 1500 iterations; (b) last 500 iterations

  • Figure 4

    (Color online) The loss $J_{\rm~ed}$ of the encoders based on improved LSTM, LSTM, and GRU. (a) First 1500 iterations; (b) last 500 iterations

  • Figure 5

    (Color online) The dimensionality reduction results. (a) t-SNE; (b) PCA; (c) Isomap

  • Figure 5

    (Color online) The dimensionality reduction results. (a) t-SNE; (b) PCA; (c) Isomap

  • Table 1   The sensor signals
    Symbol Description Unit
    ${U_{\rm~net}}$ Transformer input voltage V
    ${U_{d1,d2}}$ Bridge arm voltage V
    ${T_{\rm~oq}}$ Motor torque N$\cdot$m
    ${I_{a,b,c}}$ A current of the three-phase input current of the motor A
    ${\omega~_m}$ Motor speed rpm
  •   

    Algorithm 1 The improved LSTM-based auto-encoder algorithm

    Process and normalize the initial data signals to push their values between 0 and 1 as $X~=~\{x_1,~x_2,~\ldots, x_{L~-~1},~x_L\}$;

    Repeat

    Input the data signal $X~=~\{x_1,~x_2,~\ldots,~x_{L~-~1},~x_L\}$ to train the improved LSTM encoder;

    Extract the cell state $C_t$ from the improved LSTM encoder;

    Input cell state $C_t$ to the GRU decoder and output the predicted state $\hat{X}~=~\{\hat{x}_L, \hat{x}_{L~-~1},~\ldots,~\hat{x}_2,~\hat{x}_1\}$;

    Calculate the object function through the error between $X$ and $\hat{X}$;

    Update parameters $W$ with SGD (stochastic gradient descent);

    Update the cell state $C_t$ as the trained feature vectors;

    Until Convergence of parameters $W$;

    Return $W$ and obtain the final $C_t$;

    Dimension reduction

    Utilize the t-SNE approach on $C_t$ to get a low dimensional vector $z$;

    Clusting

    Apply the DBSCAN approach tocluster the low-dimensional feature vectors to achieve the incipient fault diagnosis.

  •   

    Algorithm 1 The improved LSTM-based auto-encoder algorithm

    Process and normalize the initial data signals to push their values between 0 and 1 as $X~=~\{x_1,~x_2,~\ldots, x_{L~-~1},~x_L\}$;

    Repeat

    Input the data signal $X~=~\{x_1,~x_2,~\ldots,~x_{L~-~1},~x_L\}$ to train the improved LSTM encoder;

    Extract the cell state $C_t$ from the improved LSTM encoder;

    Input cell state $C_t$ to the GRU decoder and output the predicted state $\hat{X}~=~\{\hat{x}_L, \hat{x}_{L~-~1},~\ldots,~\hat{x}_2,~\hat{x}_1\}$;

    Calculate the object function through the error between $X$ and $\hat{X}$;

    Update parameters $W$ with SGD (stochastic gradient descent);

    Update the cell state $C_t$ as the trained feature vectors;

    Until Convergence of parameters $W$;

    Return $W$ and obtain the final $C_t$;

    Dimension reduction

    Utilize the t-SNE approach on $C_t$ to get a low dimensional vector $z$;

    Clusting

    Apply the DBSCAN approach tocluster the low-dimensional feature vectors to achieve the incipient fault diagnosis.

  • Table 2   The considered four kinds of faults
    Category Typical description Parameter Fault type
    Health Healthy data None Health
    Fault I $C_f~=~C_h~{\rm~e}^{-\alpha~t_f}$ $\alpha$ = 0.01, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.5 Incipient time-varying fault
    Fault II $R_f~=~R_h~{\rm~e}^{-\beta~t_f}$ $\beta$ = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1 Incipient time-varying fault
    Fault III $N_f~=\gamma~\log~({t_f}~+~1)$ $\gamma$ = 1, 3, 5, 7, 10, 13, 15, 17 Incipient time-varying fault
    Fault IV $\Omega_f=~\Omega_h(1+\lambda)$ $\lambda$ = 0.005, 0.01, 0.02, 0.05, 0.1, 0.2 Abrupt fault
  • Table 3   The mean and variance of the loss in the encoders
    Model Mean Variance
    GRU encoder-decoder model 0.0513 0.00007
    LSTM encoder-decoder model 0.0175 0.00002
    Improved LSTM encoder-decoder model 0.0062 0.00006
  • Table 4   The fault diagnosis scheme for the known faults (health, fault I, fault II cases)
    Category Number Testing accuracy (%) False alarm rate (%) Missed alarm rate (%)
    Health 1480 100 0.00 0.00
    Fault I 990 85.86 0.00 14.14
    Fault II 935 95.62 0.21 4.17
  • Table 5   The fault diagnosis results for the unknown faults (health, fault I$\sim$IV cases)
    Category Number Testing accuracy (%) False alarm rate (%) Missed alarm rate (%)
    Health 1480 100 0.00 0.00
    Fault I 990 85.86 0.00 14.14
    Fault II 935 95.62 0.21 4.17
    Fault III 1175 98.04 0.00 1.96
    Fault IV 1175 100 0.00 0.00
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