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A deep learning-based remaining useful life prediction approach for bearings

Cheng Cheng, Guijun Ma, Yong Zhang, Mingyang Sun, Fei Teng, Han Ding, Ye Yuan

arXiv:1812.03315v2cs.LGeess.SPstat.ML

TL;DR

Bearing degradation is a major source of motor failures, making reliable RUL estimation important for mechanical-system safety and reliability. The paper proposes an HHT–CNN–ε-SVR framework with a nonlinear degradation indicator and reports strong experimental prediction performance.

  • Problem

    Bearing degradation contributes to nearly half of motor failures, motivating accurate RUL estimation for mechanical-system safety and reliability.

    Source: §I · p. 1

  • Method

    The framework extracts a nonlinear degradation indicator from raw vibrations using HHT, trains a CNN to estimate degradation automatically, and uses ε-SVR to predict bearing RUL.

    Source: §IV · p. 10

  • Results

    The proposed approach achieves an average score Smean = 0.87, with MAE = 46.2 and NRMSE = 0.05, while reporting Er% values of -0.29%, 6.83%, and -1.37% for three bearings.

    Source: E. Comparison and discussion · pp. 9–10

  • Takeaways & Limitations

    The experiments validate the proposed data-driven framework for bearing RUL prediction using an accelerated degradation platform.

    Source: §IV · p. 10

Abstract

from arXiv · show

In industrial applications, nearly half the failures of motors are caused by the degradation of rolling element bearings (REBs). Therefore, accurately estimating the remaining useful life (RUL) for REBs are of crucial importance to ensure the reliability and safety of mechanical systems. To tackle this challenge, model-based approaches are often limited by the complexity of mathematical modeling. Conventional data-driven approaches, on the other hand, require massive efforts to extract the degradation features and construct health index. In this paper, a novel online data-driven framework is proposed to exploit the adoption of deep convolutional neural networks (CNN) in predicting the RUL of bearings. More concretely, the raw vibrations of training bearings are first processed using the Hilbert-Huang transform (HHT) and a novel nonlinear degradation indicator is constructed as the label for learning. The CNN is then employed to identify the hidden pattern between the extracted degradation indicator and the vibration of training bearings, which makes it possible to estimate the degradation of the test bearings automatically. Finally, testing bearings' RULs are predicted by using a $ε$-support vector regression model. The superior performance of the proposed RUL estimation framework, compared with the state-of-the-art approaches, is demonstrated through the experimental results. The generality of the proposed CNN model is also validated by transferring to bearings undergoing different operating conditions.

NOMENCLATURE

The paper frames bearing RUL prediction as important for industrial reliability, while contrasting model-based and data-driven approaches and introducing an HHT-CNN-ε-SVR framework with nonlinear degradation indicators.

  • Rolling element bearing degradation is linked to nearly half of motor failures, making RUL estimation important for system safety and reliability.Source: §I · p. 1
  • Model-based approaches are limited by the difficulty of constructing precise physical degradation models under noisy operating environments.Source: §I · p. 2
  • HHT provides efficient, high-resolution time-frequency analysis by decomposing vibration signals into intrinsic mode functions.Source: §I · p. 2
  • The proposed framework uses HHT to construct a nonlinear DEI, CNN to learn vibration-to-DEI mappings, and ε-SVR to forecast bearing RUL.Source: §I · p. 2
  • The proposed CNN architecture is reported as transferable across different operating conditions without changing its hyperparameters or layer depth.Source: §I · pp. 2–3
  • The nonlinear DEI models a long stable period followed by sharp degradation and is presented as more effective for RUL estimation than a linear time indicator.Source: Figure 1 · p. 3

II. DEGRADATION INDICATOR TRAINING AND RUL

The framework extracts a degradation indicator from bearing vibrations using EMD, Hilbert analysis, and component frequencies, then uses it to train and apply a CNN-based RUL pipeline.

A. Degradation indicator extraction

B. DEI pattern learning

The CNN learns to map raw vibration signals to normalized DEI labels through stacked convolutional, pooling, fully connected, and regression layers. ReLU activations, max-pooling, and sigmoid-normalized output support DEI estimation.

B. DEI pattern learning

  • The CNN stacks convolutional, pooling, fully connected, and regression layers to learn DEI patterns from raw vibration data.The architecture contains six layers, including two convolutional and two max-pooling layers.Source: B. DEI pattern learning · p. 4, Figure 3 · p. 5
  • Convolutional filters transform local patches from the previous layer using learned weights, bias, and convolution operations.For the first layer, the input sub-vectors come directly from the raw vibration signal.Source: B. DEI pattern learning · p. 4
  • ReLU is used after convolutional layers to provide nonlinear activation and reduce vanishing-gradient problems during training.The passage links vanishing gradients with longer training or non-convergence.Source: B. DEI pattern learning · p. 4
  • Max-pooling downsamples feature maps by retaining maximum values, reducing computation and parameters while supporting shift invariance.The method selects max-pooling as an algorithmic choice intended to support neural-network generalization.Source: B. DEI pattern learning · p. 4
  • The trained six-layer CNN maps raw vibration data Si to normalized DEI labels and directly estimates Ltest for new bearings.The sigmoid output is used because the learning label is normalized DEI.Source: Figure 3 · p. 5, B. DEI pattern learning · p. 5

C. RUL prediction

The RUL prediction stage forecasts future degradation from CNN-estimated DEI sequences using sliding-window features and ε-SVR. Predicted DEI progression is converted into failure time through the recording interval.

C. RUL prediction

  • The trained CNN automatically generates estimated DEI values for each historical unit of a test bearing.These values form the input sequence for subsequent RUL forecasting.Source: C. RUL prediction · p. 5
  • ε-SVR forecasts upcoming degradation from estimated DEI sequences using features extracted over overlapping sliding windows.Each feature stores the mean and variance of a sampling window.Source: C. RUL prediction · p. 5
  • The CNN training procedure uses normalized DEI labels and raw vibration data, with ReLU, max-pooling, sigmoid output, MSE loss, and Adam updates.The algorithm repeats parameter updates until the maximum number of iterations is reached.Source: C. RUL prediction · p. 5
  • The SVR model forecasts future DEI values by repeatedly shifting the same sliding window across predicted values.The framework uses an RBF kernel for nonlinear prediction and manually set distance and penalty parameters.Source: C. RUL prediction · pp. 5–6
  • Predicted failure time is calculated as bTfailure = U × τ, where U is the number of predicted units and τ is the recording interval.The predicted sequence reaches the failure threshold between consecutive forecasted DEI values.Source: C. RUL prediction · p. 6

A. Data description

The framework is validated on the PRONOSTIA bearing platform using vibration recordings collected under controlled rotational and loading conditions. The experimental setup accelerates degradation and evaluates ε-SVR forecasting across selected bearings and operating conditions.

A. Data description

  • PRONOSTIA combines rotating, loading, and measurement parts to test bearings under applied radial force and monitored vibration.The applied force exceeds the bearing’s allowable dynamic load, accelerating degradation behavior.Source: A. Data description · p. 6, Figure 5 · p. 7
  • Bearing1_2 provides DEI extraction and CNN training, while Bearing1_6 are used to estimate DEIs and predict RULs.Results for Bearing2 under different rotational frequencies and external dynamic loads are also compared.Source: A. Data description · p. 6
  • The ε-SVR framework uses an RBF kernel with distance limit ε and penalty parameter C to construct a nonlinear regression model.The model represents regression as f(x) = wT φ(x) + b, with the kernel expressing mapped-feature inner products.Source: A. Data description · p. 6
  • Vibration is sampled at 25.6 kHz, with 0.1-second signals recorded every τ = 10 s and 2560 measurements per recording phase.These settings define the sensor data used by the framework.Source: A. Data description · p. 7

B. Degradation indicator extraction

The degradation indicator DEI is extracted from bearing-component frequency responses and defined as the maximum component-specific magnitude. Its evolution is illustrated for the first bearing.

B. Degradation indicator extraction

  • For bearing1, the extracted DEI uses fouter = 168 Hz, finner = 221 Hz, and fball = 215.4 Hz.The resulting DEI evolution is shown in Fig. 6(a).Source: B. Degradation indicator extraction · p. 7
  • Each DEI magnitude equals the maximum among the intermediate features Mi(finner), Mi(fouter), and Mi(fball) at the same time point.The intermediate feature evolutions are shown separately in Fig. 7.Source: B. Degradation indicator extraction · p. 7

C. Degradation indicator estimation

The CNN uses raw vibration from a training bearing and normalized DEI labels to estimate degradation indicators. The estimated DEI follows the labeled degradation evolution, with a defined failure threshold for test bearings.

D. RUL prediction

Because test-bearing DEIs do not reach the fault limit, an ε-SVR forecasts their degradation to failure. RUL is then obtained from the predicted threshold-crossing time.

  • ε-SVR is applied to forecast test-bearing DEIs beyond the observed data until end-of-life.Source: D. RUL prediction · p. 7
  • The forecasting setup uses a sampling window of 50 and moving size 1 with an RBF kernel.Source: D. RUL prediction · p. 7
  • Predicted DEIs are extended 1000 steps and limited using the maximum predicted DEI of bearing1 2, Ltf = 0.9756.Source: D. RUL prediction · p. 8
  • RUL equals the difference between the final time when DEI reaches the failure threshold and the last known test-bearing point.Source: D. RUL prediction · p. 8
  • The predicted RULs are 340 s for bearing1 4, 1500 s for bearing1 5, and 1480 s for bearing1 6.Source: D. RUL prediction · p. 8

E. Comparison and discussion

The proposed DEI–CNN framework produces smaller RUL prediction errors than the tested and published approaches. Its CNN modeling reduces noise and computational burden, while transfer to different operating conditions remains effective.

IV. CONCLUSION

The paper presents an HHT–CNN–ε-SVR framework that learns nonlinear bearing degradation from vibration data and forecasts RUL. Experiments report smaller prediction errors than previous published approaches, while future work targets broader validation and alternative labels.

  • The framework extracts a nonlinear DEI with HHT, trains a CNN to predict DEI from raw vibration, and uses ε-SVR to forecast RUL.Source: §IV · p. 10
  • The proposed framework achieves much smaller RUL prediction errors than previous published approaches.Source: §IV · p. 10
  • Future work will examine more experimental case studies in other applications and alternative degradation labels for higher RUL-estimation accuracy.Source: §IV · p. 10
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