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A hybrid-driven remaining useful life prediction method combining asymmetric dual-channel autoencoder and nonlinear Wiener process

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Abstract

Remaining Useful Life (RUL) prediction is an essential aspect of Prognostics and Health Management (PHM), facilitating the assessment of mechanical components’ health statuses and their times to failure. Currently, most deep learning-based RUL prediction methods can achieve accurate RUL point estimations. However, due to sample variability and degradation randomness, point estimations may contain uncertainties. To obtain both RUL prediction values and their corresponding uncertainty estimations, this paper proposes a novel hybrid-driven prediction method that effectively combines an Asymmetric Dual-Channel AutoEncoder and the Nonlinear Wiener Process (ADCAE-NWP). To achieve comprehensive feature extraction, two feature extraction channels are parallelly combined in the encoder. Moreover, to reduce the space-time overhead of the model training process, an asymmetric form of the autoencoder is composed by using only the fully connected layer in the decoder. Subsequently, the ADCAE model is trained to construct health indicators in an unsupervised manner. Finally, the RUL Probability Density Functions (PDFs) are calculated using the NWP. RUL predictions containing uncertainty estimations are obtained by calculating expectations over confidence intervals. The proposed model is experimentally validated and compared on two datasets, and the results demonstrate that the proposed scheme achieves better prediction performance than competing approaches.

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Data Availability

The Train wheel data that support the findings of this study are available from Shenhua Group but restrictions apply to the availability of these data, which were used under licence for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of Shenhua Group. The public milling data can be found in https://www.nasa.gov/content/prognostics-center-of-excellence-data-set-repository.

Abbreviations

ADCAE-NWP:

Asymmetric Dual-Channel AutoEncoder and Nonlinear Wiener Process

BiLSTM:

Bidirectional LSTM

CNN:

Convolutional Neural Network

FHT:

First Hitting Time

FPT:

First Passage Time

HI:

Health Indicator

LSTM:

Long Short-Term Memory

MAPE:

Mean Absolute Percent Error

PDF:

Probability Density Function

RMSE:

Root Mean Square Error

RNN:

Recurrent Neural Network

RUL prediction:

Remaining Useful Life prediction

STFT:

Short-Time Fourier Transform

TWDS:

Train Wheel Detection System

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Acknowledgements

This research is supported by the Technology Innovation Project of Shenhua Group (Grant No. SHGF-17-56) and National Key Research and Development Program of China (Grant number 2019YFB2102500).

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Authors and Affiliations

  1. School of Computer and Information Technology, Beijing Jiaotong University, 100044, Beijing, China

    Yuhang Duan, Zhen Liu, Honghui Li, Chun Zhang & Ning Zhang

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  1. Yuhang Duan
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  3. Honghui Li
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Correspondence to Honghui Li.

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Appendix A Key hyperparameter learning search

Appendix A Key hyperparameter learning search

This section explores the effects of Transformer layers, attention heads, Transformer nodes, and LSTM nodes on the RUL prediction results. We use the violin plot to display the evaluation metrics for RUL prediction visually. The violin plot can well reflect the data distribution, where the white dots represent the median value, the thick black bars indicate the interquartile range, the thin black bars represent the 95% confidence interval, and the edge contours indicate the density of the data distribution.

Fig. 13
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The effect of different Transformer layers on RUL prediction results

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Fig. 14
figure 14

The effect of different attention heads on RUL prediction results

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Fig. 15
figure 15

The effect of different Transformer nodes on RUL prediction results

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Fig. 16
figure 16

The effect of different LSTM nodes on RUL prediction results

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1.1 A.1 Transformer layers

The number of Transformer network layers affects the feature extraction capability and model complexity of the attention channel. The prediction results with different Transformer layers are shown in Fig. 13. When the Transformer layer is 1, the evaluation metrics take a wide range of values, and the performance of prediction results is volatile. When the number of Transformer layers is 3 and 6, the performance of the evaluation metrics is very close and reaches the best. To simplify the complexity of the model and improve the computational efficiency, we finally choose the number of Transformer layers to be 3.

1.2 A.2 Attention heads

Attention heads can be understood as the model extracting critical information about the time series from different perspectives. For a certain number of hidden nodes, an increase in the number of attention heads decreases the number of attention vector dimensions, which is equal to Transformer nodes divided by attention heads. In Fig. 14, it can be observed that the RMSE and score of RUL prediction results are higher when the attention head is 2 or 8. When the attention head is selected as 4, the median performance of RMSE and score is lower. The median accuracy is slightly higher than the other two.

1.3 A.3 Transformer nodes

The number of Transformer nodes affects the attention dimension calculated for each attention head. As seen in Fig. 15, the median performance of the evaluation metrics score and accuracy is better when the Transformer nodes are set as 128. However, compared to the smaller Transformer node value, 64, the prediction performance does not significantly improve. It may mean that increasing the dimension of attention does not bring a significant RUL prediction advantage.

1.4 A.4 LSTM nodes

The LSTM is used as the temporal feature extraction channel in the proposed model, complementing the attention channel to achieve long-dependency information extraction and information supplementation. In Fig. 16, we can observe that the median of the evaluation metrics is very close and reaches the best when the number of LSTM nodes is 50 or 100. When the LSTM nodes are set as 25, the prediction result has a large range of evaluation metrics, and the stability of the prediction model is poor. Considering the issue of computational efficiency, we selected smaller LSTM nodes for experiments and statistics.

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Duan, Y., Liu, Z., Li, H. et al. A hybrid-driven remaining useful life prediction method combining asymmetric dual-channel autoencoder and nonlinear Wiener process. Appl Intell 53, 25490–25510 (2023). https://doi.org/10.1007/s10489-023-04855-3

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