# Rotating machine bearing health prognosis using a data driven approach based on KS-density and BiLSTM

Houssem Habbouche, Tarak Benkedjouh, Yassine Amirat, Mohamed Benbouzid

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Houssem Habbouche, Tarak Benkedjouh, Yassine Amirat, Mohamed Benbouzid. Rotating machine bearing health prognosis using a data driven approach based on KS-density and BiLSTM. IET Science Measurement and Technology, 2024, 10.1049/smt2.12215. hal-04695365

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# Rotating machine bearing health prognosis using a data driven approach based on KS-density and BiLSTM

Houssem Habbouche<fnref n="1" />

Tarak Benkedjouh<fnref n="1" />

Yassine Amirat<fnref n="2" />

Mohamed Benbouzid<fnref n="3" />,<fnref n="4" />

<figure><img src="image_2.png" /></figure>

**Correspondence**

Mohamed Benbouzid, University of Brest, UMR CNRS 6027, 29238 Brest, France.

Email: Mohamed.Benbouzid@univ-brest.fr

**Abstract**

Rolling element bearings are vital components within rotating machinery, making them a central focus of maintenance in the prognostics and health management sector. This involves closely monitoring their condition to accurately predict the remaining useful life, increasing reliability while minimizing unexpected breakdowns, thereby enabling cost savings through planned maintenance, and enhancing operational stability and security. To achieve this goal, it is necessary to build an online intelligent system for degradation monitoring and failure prognosis by the construction of a robust health indicator and making quantitative measure for bearing degradation. In this paper, an efficient and reliable approach is proposed to estimate the remaining useful life of bearing. A new prediction method is presented by the combination of kernel smoothing density (KS-density) and bidirectional long short-term memory (BiLSTM). Firstly, KS-density smoothens the preliminarily estimated probability distribution function using machinery degradation data. Secondly, the obtained KS-density is used in feed deep learning technique based on BiLSTM models. On this basis, the variation of the signal distribution models between the current faulty state and the normal conditions state is quantified for bearing health assessment. The effective recognition of bearing degradation by the proposed Weibull-based health index is demonstrated through experimental validations utilizing run-to-failure datasets, provided by the centre for intelligent maintenance systems. The comparison with the literature's review show that the prediction results of the proposed approach are more accurate.

## 1 | INTRODUCTION

The country's economic progress is intricately tied to its industrial sector, essential for fulfilling its requirements. This requires a competitive industry in terms of quality and quantity. To achieve these objectives, it is essential to have reliable machines to ensure continuous production without interruptions [1]. However, the reality is that no such machine exists, as maintenance is always necessary. The problem arises with unplanned failures of some key components such as bearings, gears etc. According to numerous research studies, rolling element bearings (REBs) are widely recognized as essential components in rotating machinery [2]. They can lead to unscheduled production outages or even accidents, highlighting the importance of following maintenance strategies to address these issues [3, 4].

The most commonly used maintenance strategies in the industry are corrective maintenance, preventive maintenance, and condition-based maintenance (CBM) [5]. The first strategy, corrective maintenance, is not always effective as it is primarily suitable for components that do not significantly impact production. The second one requires the systematization of maintenance and can be expensive since the components are not consumed and can be changed before the end of their life. However, CBM allows the consumption of components until the end, planning of necessary maintenance personnel, and management of necessary stock [6].

Prognostic and health management (PHM) is an extension of condition-based maintenance (CBM). It proves its efficiency in the industrial field by following different steps to achieve an accurate estimation of remaining useful life (RUL) [7]. It

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

© 2024 The Author(s). *IET Science, Measurement & Technology* published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.

<footnote n="1">¹Ecole Militaire Polytechnique, Mechanical Structures Laboratory, Bordj Elbahri, Algiers, Algeria</footnote>

<footnote n="2">²ISEN Yncrea Ouest, L@blsen, Brest, France</footnote>

<footnote n="3">³University of Brest, UMR CNRS 6027, Brest, France</footnote>

<footnote n="4">⁴Shanghai Maritime University, Logistics Engineering College, Shanghai, China</footnote>
starts with monitoring signal acquisition using necessary hardware and software. Signals are usually noisy and need to be analysed to extract useful information and build health indicators (HIs) expressing the evolution of component degradation [8]. In this strategy, three approaches are used: model-based, data-driven, and hybrid approach [9]. The first requires mathematical modelling and knowledge of the physical phenomena of degradation. The second requires a lot of data for training and knowledge in signal processing to extract useful information. The last approach presents a compromise between the first two, as it requires a degradation model in addition to data monitoring [10]. Among these approaches, the data-driven approach has proven its effectiveness in the industrial field because it does not require extensive expert knowledge about the degradation process model. The data-driven approach is the most adequate for the smart industry 4.0, as it enables remote monitoring by connecting different physical devices, synchronization between different services (maintenance, stock etc.), and real-time communication between them [11, 12]. Moreover, the integration of data-driven approach plays a crucial role in the effective deployment of digital twins. By leveraging advanced data collection and analysis techniques, the data-driven approach enables the creation of accurate and informative digital twins [13].

As mentioned before, data-driven is based on monitoring signals which are noisy and require processing to extract useful information. Among the statistical indicators employed for monitoring the turnover's health, kurtosis and skewness stand out [14]. These two metrics are intricately linked to the shape of the density curve. Kurtosis is utilized to measure the flattening of the density curve, while skewness assesses its symmetry. Given that these indicators are responsive to signal stationarity, it is advisable to directly apply them to the density function. Among the available density functions, kernel smoothing density holds a highly regarded position. The combination of signal processing with machine learning has proven successful in monitoring by adopting machine learning techniques for learning features [15].

Numerous competitive architectures have been developed to cater to diverse fields such as medicine, maintenance, aerospace, and more. These architectures encompass probabilistic neural networks, multi-layer perceptrons, convolutional neural networks, and recurrent neural networks (RNNs). For instance, in one study [16], wavelet packet transform (WPT) was combined with support vector machines (SVM) for signal decomposition and fault diagnosis, with validation conducted on both experimental and numerically emulated faults. Similarly, in another study [17], the challenge of data scarcity was tackled by utilizing acquired signals. This approach involved simulating defects and adapting them to measured signals using generative adversarial networks (GANs), alongside classification employing convolutional neural networks (CNNs). Additionally, another research effort [18] directly confronted the issue of imbalanced data by leveraging GANs to generate synthetic data, thus enhancing learning by incorporating simulated data. Recurrent neural networks (RNNs) offer the advantage of learning temporal relations from time series sequences, aligning well with the nature of prognosis data. However, a notable drawback of RNNs

is the gradient vanishing problem, which may result in the loss of long-term information [19]. To address this limitation, the long short-term memory (LSTM) architecture has been proposed, capable of learning both long and short-term dependencies effectively [20]. Recently, LSTM has been successful because of their performance in several fields of research such as, speech recognition, medicine, maintenance etc. This part is dedicated to expose some frameworks based on LSTM network in maintenance field. [21] proposed an architecture based on CNN and LSTM for REB monitoring, where CNN layers are used for features extraction by the use of convolution operations, in the other hand, LSTM is used because of its capacity of learning long and short-term dependencies, the proposed approach is compared with simple CNN and simple LSTM on IMS dataset, by calculating evaluation metrics (MSE and MAE), which showed the superiority of this architecture over others. [22] got much more interested in the classification of defects using a machine learning technique based on LSTM also, and to make this task more practical and useful, a synchronization is planned, allowing to provide a decision support tool (keep or remove damaged parts and even stock management) for the maintenance policy (dynamic predictive maintenance). [23] proposed a machine learning network based on BiLSTM for health monitoring, this network allows from statistical indicators to estimate RUL, at the end, this article compared the proposed network with other architectures (SVR, MLP, BD-RNN, CNN, and LSTM) to show its effectiveness. [24] proposed a new approach based on two different machine learning type (supervised and unsupervised), RBM is used as unsupervised and in the other hand LSTM is used as supervised machine learning, to get better results and for an optimal architecture, GA is used for designing network and the choice of 14 hyperparameters, after, this architecture was tested on an experimental dataset C-MAPSS and compared with previous work by the estimation of RMSE. [25] proposed to enhance the quality of bearing fault diagnosis by integrating data from the physical model. [26] designed a health indicator based on multiple features to ensure the prognosis of bearing faults. Ultimately, they conclude with training based on GRU with optimized parameters.

The previously cited frameworks have focused on improving learning to achieve a more reliable prognosis and health monitoring. However, before initiating the learning process and fine-tuning hyperparameters, it is advisable to test the predictability of the data. For studies based on statistical indicators, several criteria are employed, including monotonicity, trendability, and prognosability [27]. Prognosis based on statistical indicators is known for its unreliability because of the non-stationarity of monitoring signals. This drawback highlights the need for suitable signal processing techniques for nonstationary data, like Kernel smoothing density, which enables the assessment of signal evolution. Another critique regarding the mentioned research is the absence of fitting health indicators such as Weibull fitting function, which plays a crucial role in ensuring repeatability and adaptability to various degradation phenomena, such as bearing faults. Practically speaking, unnecessary data storage can rapidly overwhelm memory resources, an aspect overlooked by prior referenced
studies. This underscores the need for implementing thresholds to trigger signal processing upon fault detection.

This original framework makes it possible to provide an REB tracking tool with RUL estimation. The proposed methodology is based on the use of kernel smoothing density (KS-density) for the processing of degradation signals, which allows extracting useful information. A machine learning model based on BiLSTM is utilized for learning dependencies between different REBs' degradation states. The proposed methodology was tested on an experimental dataset [28], with an estimation of different metrics evaluations, to demonstrate its effectiveness concerning fault prognosis in the industry. The main contribution insights of this study are summarized as follows:

(1) Development of an intelligent prognostic methodology for assessing the health of bearings and estimating remaining useful life (RUL) through the analysis of historical vibration data.

(2) Demonstration of the efficacy of the kernel density and extracted health indicator (HI) based on the Weibull function in accurately characterizing the bearing degradation process.

(3) Introduction of BiLSTM model that facilitates the utilization of extensive historical data for training, effectively addressing the challenge of overfitting.

(4) Validation of the proposed methodology through testing on an experimental dataset sourced from the Centre of Intelligent Maintenance Systems.

This paper is organized as follows; the second section is reserved for the presentation of the proposed prognosis methodology with a brief exposition of the necessary background. The third section discusses the obtained results from the application of the proposed methodology on an experimental dataset. Finally, a conclusion is provided along with propositions for future scope.

## 2 | THE PROPOSED METHODOLOGY

The proposed methodology is part of the PHM activities, applied to REB monitoring and RUL estimation. Based on data-driven approach and health indicator assessment, to provide a decision support tool for the smart industry.

Figure 1 shows the detailed of the proposed methodology. Firstly, the acceleration signal is collected from run to failure of bearing in a certain operating condition. Secondly, the KS-density was applied from the raw signals to obtain the probability distribution. Then the deep learning used to construct the Health Indicator and being capable to reflect the full lifetime degradation, by optimizing the function parameters used in deep learning, signal distribution models with good performance have been obtained.

This prognosis methodology is based on PHM steps. Starting by signal acquisition which are noisy and can't be exploited as it is. Signal analysis techniques are used to extract necessary information's, HI construction based on time analysis, and

KS-density to track the evolution degradation. The use of intelligent system to learn features and automatic recognition based on BiLSTM network. At the end, calculate statistical metrics to evaluate the quality of the prediction, and testing this methodology on an experimental dataset as shown in the flowchart of Figure 2.

### 2.1 | Data acquisition & preprocessing

The first step in this framework is the data acquisition, using necessary instruments such as data acquisition modules and sensors (microphone, accelerometer etc.). With the setting of acquisition conditions (sampling frequency, transducer sensitivities etc.), the recorded data will be stored for further processing which can be expensive in time and stockage [29]. To avoid retaining data unnecessarily, it is preferable to use triggers. The first trigger is called incipient threshold (IT), estimated using the ISO 10816 standard. Second trigger is called failure threshold (FT), to end the monitoring and stop the machine immediately [30].

The second step, which is health indicator (HI) construction, seeks to find an indicator reflecting the REB health state from the acquired signal. This indicator should exhibit the most monotonicity and accurately reflect the degradation of the component under study [31]. Unfortunately, the indicators commonly used often exhibit fluctuations, as shown in Figure 3. These fluctuations can influence the quality of the prediction and necessitate the use of fitting techniques to enhance monitoring accuracy. For this purpose, several techniques can be employed, such as exponential and Weibull fitting [32]. The Weibull function is particularly suitable for irreversible degradation phenomena, which is the case under consideration in our study of REB degradation [33]. This holds true whether there is a defect in the outer ring, inner ring, or even the ball. Based on these hypotheses, the Weibull failure rate function (WFRF) in this framework is formulated as shown in Equation (1).

$$ \lambda(t) = Y + K \frac{\beta}{\eta^{\beta}} t^{\beta-1} \quad (1) $$

### 2.2 | Data processing

At this stage, it's necessary to use signal processing techniques to extract useful information. This framework proposes using the kernel smoothing density technique. The kernel distribution is a probabilistic statistical technique used to estimate the probability function of a random variable by approximating the samples with a Gaussian bell curve. This smooth shape is achieved by adjusting the bandwidth to filter out noise. The formula for the kernel density estimator is given by Equation (2) [34].

$$ \hat{f}_b(x) = \frac{1}{nb} \sum_{i=1}^{n} K \left( \frac{x - x_i}{b} \right) \quad (2) $$
<figure><img src="image_3.png" /><figcaption>FIGURE 1 Proposed methodology for failure prognostics.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>FIGURE 2 Probability distribution evolution.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>FIGURE 3 RMS fluctuation.</figcaption></figure>

where $x_1, x_2, ..., x_n$ are random samples from an unknown distribution, $n$ is the sample size, $K(.)$ is the kernel smoothing function, and $b$ is the bandwidth (smoothing parameter). Kernel smoothing density is a non-parametric technique that works well with the approach adopted (data-driven), given the unavailability of a precise model expressing the degradation of REBs [34, 35].

## 2.3 | Learning & regression

In order to automate the REB monitoring process, it's necessary to apply a learning algorithm to build an intelligent system that minimizes human intervention and enables real-time monitoring. Given the nature of time-series data, which requires an algorithm capable of learning dependencies between data, the most widely used networks for the time-series domain are the RNNs. Unfortunately, they present a vanishing gradient problem, in addition to their inability for long-term dependency learning. To address these issues, a new variety of RNNs emerged, known as LSTM, which has demonstrated its competence in time-series monitoring [36]. This is achieved through the inclusion of new gates compared to the simple RNN (input, output, and forget gates). These additions have made it possible to solve the problems associated with traditional RNNs.

The architecture of the LSTM node is illustrated in Figure 4, and the equations governing the flow of information within it are formulated from Equations (3) to (8) [30].

Input gate

$$i^t = \sigma(W_i x_t + U_i b_{t-1} + b_i) \quad (3)$$

forget gate

$$f^t = \sigma(W_f x_t + U_f b_{t-1} + b_f) \quad (4)$$
<figure><img src="image_6.png" /><figcaption>FIGURE 4 LSTM bloc.</figcaption></figure>

output gate

$$d = \sigma(W_o x_t + U_o b_{t-1} + b_o) \quad (5)$$

candidate state of the memory unit

$$\tilde{c}_t = \tanh(W_c x_t + U_c b_{t-1} + b_c) \quad (6)$$

updated internal state

$$c_t = f_t \circ c_{t-1} + i_t \circ \tilde{c}_t \quad (7)$$

LSTM unit's final output

$$b_t = o_t \circ \tanh(c_t) \quad (8)$$

where $W$, $U$, and $b$ represent the network parameters to be learnt. The symbol $\circ$ denotes Hadamard product, and two types of activation function were used, $\sigma(x)$ as logistic sigmoid and $g(x)$, $b(x)$ as hyperbolic tangent.

In the same context of improving time-series learning, a new variant of LSTM named BiLSTM has emerged. While LSTM ensures dependencies from the past to the present, the BiLSTM network ensures a dual dependency from the past to the future and vice versa, as depicted in Figure 5. It retains the same architecture as the unidirectional LSTM but differs in how information flows across layers. The equations describing this aspect are presented below [30].

$$\vec{b}_t = \text{LSTM}(x_t, \vec{b}_{t-1}) \quad (9)$$

$$\tilde{b}_t = \text{LSTM}(x_t, b_{t+1}) \quad (10)$$

$$y_t = W_{by}^z \vec{b}_t + W_{by} \tilde{b}_t + b_y \quad (11)$$

where $\vec{b}_t$ and $\tilde{b}_t$ represent forward and backward hidden state respectively. LSTM(.) is the application of equations from Equations (3) to (8), $W_{by}^z$ and $W_{by}$ represent forward and backward LSTM weights.

<figure><img src="image_7.png" /><figcaption>FIGURE 5 Bidirectional process.</figcaption></figure>

## 2.4 | Remaining useful life estimation

The proposed network is trained to estimate HI, and RUL is calculated through temporal inversion and subtraction from the end of life (EoL) limit, as shown in Equation (12). The obtained results exhibit fluctuations that lack physical meaning and can be reduced through simple smoothing techniques, such as applying a moving average window.

$$RUL(t) = t_{EoL} - \text{HI}^{-1}(t) \quad (12)$$

To facilitate comparison with previous work, various metrics for assessing the quality of prediction are utilized, including RMSE, MSE, MAE etc. [37].

# 3 | EXPERIMENTAL VALIDATION

## 3.1 | Experimental dataset

In this framework, an experimental NASA dataset [28] is used to test the proposed methodology. The used test rig consists of an engine linked by a belt with a shaft supported by four bearings, while two are subjected to radial loading (Figure 6). Equipped with accelerometers to record vibrations at bearings, in addition to the presence of a thermocouple.

Each test involves capturing vibration signals from all four bearings, with one or more bearings intentionally run to failure. The signals are acquired with a sampling frequency of 20 kHz, and every 10 min, a 1-s signal is recorded. This paper is based on the use of the vibration signal from the first bearing of the second experiment, which consists of 9840 min of recordings.

## 3.2 | Data preprocessing

The construction of the health indicator is based on temporal analysis, utilizing RMS as a statistical indicator. This indicator is frequently used for prognosis needs due to its sensitivity to degradation [38], as demonstrated in Figure 3. Statistical
<figure><img src="image_8.png" /><figcaption>FIGURE 6 NASA REB test bench [28].</figcaption></figure>

<table><caption>TABLE 1 Fitting parameters.</caption><thead><tr><th></th><th>η</th><th>β</th><th>Y</th><th>K</th></tr></thead><tbody><tr><td>RMS</td><td>281.021</td><td>12.092</td><td>0.0773</td><td>1.38 × 10<sup>-5</sup></td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>FIGURE 7 Health indicator.</figcaption></figure>

indicators frequently display fluctuations, prompting the utilization of fitting techniques like the Weibull failure rate function, as formulated in Equation (1). Weibull model parameters are obtained from the literature [30] and summarized in Table 1. The fitting results are depicted in Figure 7, facilitating the preparation of the outputs of the learning model.

## 3.3 | Data processing

KS-Density is used for features extraction from sample vector data, to returns a probability density function. The estimation is based on a normal kernel function for 100 points, and is evaluated at equally-spaced points xi. Figure 8 shows the obtained

<figure><img src="image_10.png" /><figcaption>FIGURE 8 KS-density signals samples.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>FIGURE 9 Proposed BiLSTM network.</figcaption></figure>

belts of samples (702nd, 730th, 758th, 786th, 814th, 842th, 870th, 898th, 926th, 954th, and 982th) from REB degraded. Shows an evolution over time, and makes it possible to conclude that this signal processing technique can provide useful information about the evolution of the degradation.

Prognosis activity is based on manipulating time-series data, which represents temporal dependencies and necessitates the use of deep neural networks with memory effects. This justifies the utilization of the BiLSTM network to capitalize on the dual temporal dependency learning. The proposed network in Figure 9 consists of an input layer stacked with two layers of BiLSTM, with 160 and 135 nodes, respectively. These layers are separated by two dropout layers with a rate of 0.2 to mitigate
<figure><img src="image_12.png" /><figcaption>FIGURE 10 Training process.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>FIGURE 11 Health indicator prediction (training data).</figcaption></figure>

overfitting. The network is then finalized with two fully connected layers of 135 nodes each, followed by a regression layer for RUL estimation.

Arriving at this step, HI can be predicted by training the proposed network and specifying training options: SGD optimizer, learning rate = 0.0001, minibatch size = 32, and a GPU environment for execution. The training process is depicted in Figure 10, which demonstrates satisfactory learning progress without overfitting.

After the training of the proposed model, the obtained results are shown in Figures 11 and 12, for the prediction of HI. Remarkably, the two curves are nearly identical, highlighting the performance of the proposed methodology. To provide a clearer presentation of the results, a temporal projection is employed using Equation (12). This enables estimation of the RUL, as depicted in Figures 13 and 14, which demonstrate accurate RUL prediction through the proposed methodology.

<figure><img src="image_14.png" /><figcaption>FIGURE 12 Health indicator prediction (test data).</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>FIGURE 13 RUL training prediction (training data).</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>FIGURE 14 RUL test prediction (test data).</figcaption></figure>
<table><caption>TABLE 2 Metrics evaluation.</caption><thead><tr><th></th><th>MAE</th><th>MSE</th><th>RMSE</th></tr></thead><tbody><tr><td>Training</td><td>0.0149</td><td>0.0005</td><td>0.0176</td></tr><tr><td>Test</td><td>0.0173</td><td>0.0007</td><td>0.0267</td></tr><tr><td>[21]</td><td>0.0403</td><td>0.0029</td><td>/</td></tr><tr><td>[39]</td><td>0.0240</td><td>0.0011</td><td>0.0326</td></tr><tr><td>[40]</td><td>0.0017</td><td>/</td><td>0.0297</td></tr><tr><td>[30]</td><td>0.0049</td><td>/</td><td>/</td></tr><tr><td>[41]</td><td>/</td><td>/</td><td>0.0686</td></tr></tbody></table>

<table><caption>TABLE 3 Metrics comparison.</caption><thead><tr><th></th><th>Proposed (BiLSTM)</th><th>RNN</th><th>LSTM</th></tr></thead><tbody><tr><td>MAE</td><td>0.0173</td><td>0.0283</td><td>0.0221</td></tr><tr><td>MSE</td><td>0.0007</td><td>0.0015</td><td>0.0011</td></tr><tr><td>RMSE</td><td>0.0267</td><td>0.0388</td><td>0.0326</td></tr></tbody></table>

For a quantitative evaluation, some metrics are calculated to compare with previous prognosis frameworks. The used metrics are already illustrated in the previous section, and present in Table 2, which shows the performance of this proposed methodology compared to a recent frameworks [21] based on CNN-LSTM for RUL prediction, [39] used stacked autoencoder for health indicator estimation and LSTM for RUL prediction, [40] based on CWT for signal processing and GAM-CNN for RUL prediction, [30] WPD for signal processing and BiLSTM for RUL prediction, and [41] based on features fusion and CNN-LSTM for RUL prediction.

Another comparison was conducted between the proposed methodology and other networks of the same nature, designed for learning time series (simple LSTM and RNN). The results obtained presented in Table 3 highlight the superiority of BiLSTM over RNN, considering that it represents an enhanced version that addresses the issue of gradient vanishing. Additionally, the comparison between BiLSTM and LSTM demonstrates the efficacy of bidirectional learning, as discussed in the corresponding Section 2.3.

The results presented in this part show the strength of the proposed methodology for health assessment and RUL estimation, by the qualitative results shown on the figures above, as well as the quantitative results in Tables 2 and 3 with a comparison with a framework in the literature.

## 4 | CONCLUSION

In this paper, a new methodology has been proposed that fits into the field of PHM based on a data-driven approach for REB health state monitoring and RUL estimation. This methodology follows the steps of PHM, commencing with signals from an experimental dataset of intelligent maintenance systems. Subsequently, an HI is constructed to express

the degraded state of the REB. In parallel, signal processing is performed using KS-density to extract useful information related to bearing degradation. The outputs of these two techniques are employed to train an intelligent system based on BiLSTM for real-time monitoring automation. To render this framework useful, various metrics evaluations are estimated to evaluate the quality of prediction and to enable comparison with other frameworks. The obtained results underscore the value of deploying the proposed methodology in the smart industry for health monitoring.

Looking ahead, the future scope beyond this framework involves enhancing prediction quality through the use of an optimization algorithm, which facilitates the optimal design of the learning network. Another compelling objective for the emerging industry is to integrate this endeavour with a physical model of bearing degradation, thereby facilitating the development of digital twin technology. Furthermore, considering the problem of imbalanced data to ensure accurate predictions.

## AUTHOR CONTRIBUTIONS

**Houssem Habbouche:** Conceptualization; formal analysis; methodology; software; visualization; writing—original draft.

**Tarak Benkedjouh:** Formal analysis; methodology; validation; visualization; writing—review and editing. **Yassine Amirat:** Formal analysis; methodology; validation; visualization; writing—review and editing. **Mohamed Benbouzid:** Formal analysis; methodology; validation; visualization; writing—review and editing.

## CONFLICTS OF INTEREST STATEMENT

The authors declare no conflicts of interest.

## DATA AVAILABILITY STATEMENT

The data that support the findings of this study are openly available in the Prognostics Data Repository at https://www.nasa.gov/intelligent-systems-division/discovery-and-systems-health/pcoe/pcoe-data-set-repository/.

## ORCID

Mohamed Benbouzid https://orcid.org/0000-0002-4844-508X

## REFERENCES

1. Yan, W., Wang, J., Lu, S., Zhou, M., Peng, X.: A review of real-time fault diagnosis methods for industrial smart manufacturing. Processes 11(2), 369 (2023)

2. Berghout, T., Mouss, L.-H., Bentrcia, T., Benbouzid, M.: A semi-supervised deep transfer learning approach for rolling-element bearing remaining useful life prediction. IEEE Trans. Energy Convers. 37(2), 1200–1210 (2021)

3. Saini, K., Dhami, S., Vanraj: Predictive monitoring of incipient faults in rotating machinery: a systematic review from data acquisition to artificial intelligence. Arch. Comput. Methods Eng. 29(6), 4005–4026 (2022)

4. Xiaoqiao, W., Mingzhou, L., Conghu, L., Lin, L., Xi, Z.: Data-driven and knowledge-based predictive maintenance method for industrial robots for the production stability of intelligent manufacturing. Expert Syst. Appl. 121136 (2023)

5. Aujoux, C., Mesnil, O.: Environmental impact assessment of guided wave-based structural health monitoring. Struct. Health Monit. 22(2), 913–926 (2023)
6. Zhang, J., Zhao, X., Song, Y., Qiu, Q.: Joint optimization of condition-based maintenance and spares inventory for a series-parallel system with two failure modes. Comput. Ind. Eng. 168, 108094 (2022)

7. Benbouzid, M., Berghout, T.: Quo vadis machine learning-based systems condition prognosis—a perspective. Electronics 12(3), 527 (2023)

8. Ma, W., Yu, Y., Guo, L., Qian, M., Gao, H.: RFIS-HI: a new health indicator for quantitative condition monitoring of the bearing under variable speed conditions. Struct. Health Monit. (2023). https://doi.org/10.1177/14759217231203244

9. Gougam, F., Chemseddine, R., Benazzouz, D., Benaggoune, K., Zerhouni, N.: Fault prognostics of rolling element bearing based on feature extraction and supervised machine learning: application to shaft wind turbine gearbox using vibration signal. Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 235(20), 5186–5197 (2021)

10. Hagmeyer, S., Zeiler, P.: A comparative study on methods for fusing data-driven and physics-based models for hybrid remaining useful life prediction of air filters. IEEE Access 11, 35737–35753 (2023)

11. Jieyang, P., Kimmig, A., Dongkun, W., Niu, Z., Zhi, F., Jiahai, W., Liu, X., Ovtcharova, J.: A systematic review of data-driven approaches to fault diagnosis and early warning. J. Intell. Manuf. 34, 3277–3304 (2022)

12. Correa-Jullian, C., Groth, K.M.: Opportunities and data requirements for data-driven prognostics and health management in liquid hydrogen storage systems. Int. J. Hydrogen Energy 47(43), 18748–18762 (2022)

13. Feng, K., Ji, J., Zhang, Y., Ni, Q., Liu, Z., Beer, M.: Digital twin-driven intelligent assessment of gear surface degradation. Mech. Syst. Sig. Process. 186, 109896 (2023)

14. Li, X., Wang, Y., Tang, B., Qin, Y., Zhang, G.: Canonical correlation analysis of dimension reduced degradation feature space for machinery condition monitoring. Mech. Syst. Sig. Process. 182, 109603 (2023)

15. Xin, Y., Li, S., Wang, J., An, Z., Zhang, W.: Intelligent fault diagnosis method for rotating machinery based on vibration signal analysis and hybrid multi-object deep CNN. IET Sci. Meas. Technol. 14(4), 407–415 (2020)

16. Xiang, J., Zhong, Y.: A novel personalized diagnosis methodology using numerical simulation and an intelligent method to detect faults in a shaft. Appl. Sci. 6(12), 414 (2016)

17. Lou, Y., Kumar, A., Xiang, J.: Machinery fault diagnosis based on domain adaptation to bridge the gap between simulation and measured signals. IEEE Trans. Instrum. Meas. 71, 1–9 (2022)

18. Gao, Y., Liu, X., Xiang, J.: Fault detection in gears using fault samples enlarged by a combination of numerical simulation and a generative adversarial network. IEEE/ASME Trans. Mechatron. 27(5), 3798–3805 (2021)

19. Ni, Q., Cao, X.: Mbgan: An improved generative adversarial network with multi-head self-attention and bidirectional RNN for time series imputation. Eng. Appl. Artif. Intell. 115, 105232 (2022)

20. Zhang, L.: The evaluation on the credit risk of enterprises with the CNN-LSTM-ATT model. Comput. Intell. Neurosci. 2022, 6826573 (2022)

21. Du, W., Wang, Y.: Stacked convolutional LSTM models for prognosis of bearing performance degradation. In: 2019 Prognostics and System Health Management Conference (PHM-Qingdao), pp. 1–6. IEEE, Piscataway, NJ (2019)

22. Nguyen, K.T., Medjaher, K.: A new dynamic predictive maintenance framework using deep learning for failure prognostics. Reliab. Eng. Syst. Saf. 188, 251–262 (2019)

23. Zhang, J., Wang, P., Yan, R., Gao, R.X.: Long short-term memory for machine remaining life prediction. J. Manuf. Syst. 48, 78–86 (2018)

24. Ellefsen, A.L., Bjorlykhaug, E., Æsoy, V., Ushakov, S., Zhang, H.: Remaining useful life predictions for turbofan engine degradation using semi-supervised deep architecture. Reliab. Eng. Syst. Saf. 183, 240–251 (2019)

25. Ni, Q., Ji, J., Halkon, B., Feng, K., Nandi, A.K.: Physics-informed residual network (PIResNet) for rolling element bearing fault diagnostics. Mech. Syst. Sig. Process. 200, 110544 (2023)

26. Ni, Q., Ji, J., Feng, K., Zhang, Y., Lin, D., Zheng, J.: Data-driven bearing health management using a novel multi-scale fused feature and gated recurrent unit. Reliab. Eng. Syst. Saf. 242, 109753 (2024)

27. de Pater, I., Mitici, M.: Developing health indicators and RUL prognostics for systems with few failure instances and varying operating conditions using a LSTM autoencoder. Eng. Appl. Artif. Intell. 117, 105582 (2023)

28. Lee, J., Qiu, H., Yu, G., Lin, J.: Rexnord technical services, bearing data set. IMS, University of Cincinnati. NASA AMES Prognostics Data Repository. NASA AMES, Moffett Field, CA. https://www.nasa.gov/ intelligent-systems-division/discovery-and-systems-health/pcoe/pcoe-data-set-repository/ (2007). Accessed Jan 2024

29. Ou, J., Ji, H., Liu, B., Peng, D.: Deep transfer residual variational autoencoder with multi-sensors fusion for tool condition monitoring in impeller machining. Measurement 204, 112028 (2022)

30. Habbouche, H., Benkedjouh, T., Zerhouni, N.: Intelligent prognostics of bearings based on bidirectional long short-term memory and wavelet packet decomposition. Int. J. Adv. Manuf. Technol. 114(1-2), 145–157 (2021)

31. Broer, A., Galanopoulos, G., Benedictus, R., Loutas, T., Zarouchas, D.: Fusion-based damage diagnostics for stiffened composite panels. Struct. Health Monit. 21(2), 613–639 (2022)

32. Ramezani, S., Moini, A., Riahi, M.: Prognostics and health management in machinery: a review of methodologies for RUL prediction and roadmap. Int. J. Ind. Eng. Manage. Sci. 6(1), 38–61 (2019)

33. Yan, M., Wang, X., Wang, B., Chang, M., Muhammad, I.: Bearing remaining useful life prediction using support vector machine and hybrid degradation tracking model. ISA Trans. 98, 471–482 (2019)

34. Mandala, V., Senthilnathan, T., Suganyadevi, S., Gobhinath, S., Selvaraj, D., Dhanapal, R.: An optimized back propagation neural network for automated evaluation of health condition using sensor data. Meas.: Sens. 29, 100846 (2023)

35. Huang, C.-G., Huang, H.-Z., Peng, W., Huang, T.: Improved trajectory similarity-based approach for turbofan engine prognostics. J. Mech. Sci. Technol. 33(10), 4877–4890 (2019)

36. Zhao, H., Jiang, X., Wang, B., Cheng, X., Xu, S.: Towards smart monitoring of systems: an integrated non-parametric Bayesian KDE and LSTM approach for anomaly detection of rotating machinery under uncertainties. Struct. Health Monit. 22(3), 1984–2001 (2023)

37. Qu, Y., Zhao, H., Zhao, S., Ma, L., Li, Z.: Evaluation method for insulation degradation of power transformer windings based on incomplete internet of things sensing data. IET Sci. Meas. Technol. 18(3), 130–144 (2024)

38. Ying, J., Yang, Z., Chen, C., Liu, Z., Li, S., Chen, H.: Remaining useful life prediction of rolling element bearing based on hybrid drive of data-driven and dynamic model. Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. (2022)

39. Han, T., Pang, J., Tan, A.C.: Remaining useful life prediction of bearing based on stacked autoencoder and recurrent neural network. J. Manuf. Syst. 61, 576–591 (2021)

40. Du, X., Jia, W., Yu, P., Shi, Y., Gong, B.: RUL prediction based on GAM-CNN for rotating machinery. J. Braz. Soc. Mech. Sci. Eng. 45(3), 142 (2023)

41. Zhang, H., Shuai, L., Hu, S.: A parallel feature fusion network for simultaneous bearing fault detection and remaining useful life prediction. In: 2023 IEEE International Conference on Mechatronics and Automation (ICMA), pp. 2064–2069. IEEE, Piscataway, NJ (2023)

**How to cite this article:** Habbouche, H., Benkedjouh, T., Amirat, Y., Benbouzid, M.: Rotating machine bearing health prognosis using a data driven approach based on KS-density and BiLSTM. IET Sci. Meas. Technol. 1–9 (2024). https://doi.org/10.1049/smt2.12215