Remaining Useful Life Prediction Method Research Articles

A weighted time embedding transformer network for remaining useful life prediction of rolling bearing

Data-driven remaining useful life (RUL) prediction is of vital importance to industrial equipment prognostics health management (PHM). The transformer algorithms have been applied for RUL prediction recently. RUL prediction is a typically time-correlated task. However, in most transformer-based RUL prediction methods, one of the main procedures, patch embedding, is usually implemented by linear-based or convolution-based approaches, which lacks consideration for time correlation feature extraction. Moreover, the time correlation features at different degradation states may be variable, which will make different contributions to RUL prediction. To this end, in this paper, a novel framework for RUL prediction named weighted time embedding transformer (WTE-Trans) is proposed. A WTE module is designed to enhance the capacity of the model to extract more discriminative time correlation features and impose different weights automatically. Concretely, the peak-to-peak values are calculated from input and transformed firstly to provide prior knowledge information, and then multiplied by a learnable mask to generate an adaptive weight. Afterwards, the adaptive weight is used to impose constraints on the transformed input. Secondly, multiple 3D convolution (3D-conv) modules are designed to integrate the deep features through the time axis. Finally, the shifted-window transformer block is adopted to complete the RUL prediction task. Experiments are carried out on the widely used PHM 2012 bearing dataset and an actual industrial bearing full-lifecycle dataset to verify the effectiveness and application value. The results and analysis have shown that lower prediction error can be achieved by the proposed method.

Remaining useful life prediction across operating conditions based on deep subdomain adaptation network considering the weighted multi-source domain

As one of the core contents of transfer learning, domain adaptation (DA) has been widely used to predict of the remaining useful life (RUL) of rolling bearings across operating conditions. However, existing RUL prediction methods often adopt single-source DA and do not consider the sample's drift phenomenon and migration degree in the source domain. At the same time, the distribution of bearing samples in different subdomains (degradation stages) differs, forcing global adaptation to inevitably lead to negative migration. Therefore, a deep subdomain adaptation network considering weighted multi-source domain (DSAN-WM) is proposed to improve the prediction accuracy of RUL across operating conditions. Firstly, a migration metric is developed to measure the migration degree of samples in the source domain, and a high-quality multi-source domain sample set is constructed. Secondly, a fine-grained feature distribution alignment strategy for subdomains based on adaptive degradation stage identification is proposed to reduce the difference in sample distribution in the same subdomain. Thirdly, for each decision boundary obtained by the multi-source domain model, consistent alignment and degradation constraints based on physical knowledge are established to improve the consistency and prediction accuracy of each regressor output. Lastly, the effectiveness of the proposed method is verified using eight migration scenarios of two bearing data sets, and the superiority of the method is proven through a comparison with advanced deep learning and transfer learning approaches.

Remaining useful life prediction method based on stacked autoencoder and generalized wiener process for degrading bearing

Abstract Remaining Useful Life (RUL) prediction using deep learning networks primarily produces point estimates of RUL, but capturing the inherent uncertainty in RUL prediction is difficult. The use of the stochastic process approach can reflect the uncertainty in RUL predictions. However, the amount of data generated during equipment operation cannot be effectively utilized. This paper aims to propose an adaptive RUL prediction method tailored for extensive datasets and prediction uncertainty, effectively harnessing the strengths of deep learning methods in managing massive data and stochastic process techniques in quantifying uncertainties. RUL prediction method, based on Stacked Autoencoder (SAE) combined with Generalized Wiener Process, employs SAE to extract profound underlying features from the monitoring signals. Principal Component Analysis (PCA) is then used to select highly trending features as inputs. The output of PCA accurately reflects health status. A Generalized Wiener Process is used to construct a model for the evolution of the health indicators. The estimation values for the model parameters are determined using the Maximum Likelihood Estimation method. Furthermore, an adaptive update is performed based on Bayesian theory. Utilizing the sense of the first hitting time concept, the Probability Density Function for RUL prediction is derived accurately. Finally, the effectiveness and superiority of the proposed method is verified using numerical simulations and experimental studies of bearing degradation data. The method improves the life prediction accuracy while reducing the prediction uncertainty.

A novel prognostic method for degrading devices with nonlinear degradation processes indexed by both continuous and discrete time scales

Remaining useful life (RUL) prediction techniques based on degradation modeling to ensure the safety and reliability of stochastic degraded devices are of critical value. However, although the performance degradation of various devices in engineering practice is affected by multi-timescales, there are few RUL prediction methods for stochastic degraded devices with dual time scales in the existing literature. The research of prediction methods considering continuous and discrete time scales is blank. Toward this end, this paper proposes a novel prognostic method for nonlinear degradation devices based on the continuous-discrete dual time scales. First, the performance degradation with a discrete timescale is determined with a compound Poisson process and integrated into the diffusion process model to establish a nonlinear dual-timescale degradation model. Subsequently, the joint expression of the dual-timescale RUL distribution of the device in the first hitting time sense solves with threshold transformation. Finally, the effectiveness and superiority of the proposed method are verified through a numerical simulation and a gyroscope example. The experimental results show that the proposed method can provide more comprehensive information about the life distribution and effectively improve the accuracy of the RUL prediction.

Multi-task learning mixture density network for interval estimation of the remaining useful life of rolling element bearings

Existing remaining useful life (RUL) predictions of rolling element bearings have the following shortcomings. 1) Model-driven methods typically employ a sole model for processing the data of an individual, making it challenging to accommodate the variety of degradation behaviors and susceptible to abnormal interference. 2) Data-driven methods place greater emphasis on training data, and in reality, it can be challenging to acquire comprehensive data covering the lifecycle. 3) Many studies fail to give adequate attention to the assessment of RUL uncertainty. This paper proposes a multi-task learning mixture density network (MTL-MDN) method to address these issues. Firstly, the peak-of-Histogram (PoHG) is extracted and served as the novel health indicators. Secondly, multi-task learning dictionaries are constructed based on the evolution law of PoHG, thus combining both model-driven and data-driven strategies. Finally, a multi-task learning strategy is proposed with mixture density networks. It effectively accomplishes the collaborative learning objective of numerous degradation samples in the regression problem and accomplishes the uncertainty assessment of RUL. After analyzing the experimental and real-world degradation data of rolling element bearings throughout their lifecycle, and comparing it to other modern RUL prediction methods, it becomes evident that the proposed MTL-MDN method offers superior prediction accuracy and robustness.

Data-model-linked remaining useful life prediction method with small sample data: A case of subsea valve

Remaining useful life (RUL) prediction is essential for strategic maintenance planning and enhancing overall operational efficiency. To address the challenges posed by limited data and deteriorated models, this paper introduces an innovative method for RUL prediction using small sample data, leveraging the integration of data and models. This approach utilizes intermittent monitoring data from industrial equipment, capturing extended intervals of small sample data, to establish the equipment's health index (HI). The dataset associated with the HI is expanded to improve model fitting. By converting the HI into reliability metrics, the method tackles data challenges through life analysis based on the Weibull distribution. The interaction between data and the model is used to assess the reliability and RUL of the equipment. The method's application is demonstrated through a case study of a subsea valve. By constructing an RUL prediction framework that integrates data and models and incorporating a parameter uncertainty prediction model, the method provides probabilistic expressions of parameters and results for the entire prediction period, thereby enhancing the accuracy of the prediction results.

Remaining useful life prediction method of rolling bearings based on improved 3σ and DBO-HKELM

Abstract An improved 3σ method and dung beetle algorithm optimization hybrid kernel extreme learning machine-based (DBO-HKELM) approach for predicting the remaining useful life (RUL) of rolling bearings was suggested in order to increase prediction accuracy. Firstly, multi-dimensional degradation feature data is extracted from bearing vibration data. Considering the influence of noise signal on the prediction accuracy, an improved kernel principal component analysis method is proposed to reduce the noise of degraded features. Then, an improved 3σ method is proposed to determine the starting point of bearing degradation by combining bearing vibration signal data. Lastly, a DBO-HKELM life prediction model was put forth. The parameters of hybrid kernel extreme learning machine were optimized by dung beetle algorithm, and appropriate kernel parameters and regularization coefficient were selected. The feature set of degradation indicators is input into the trained model to output the bearing RUL prediction results starting from the determined degradation starting point. Multiple data sets were used to verify that the new RUL prediction method significantly improves the prediction accuracy.

Remaining useful life prediction for are cracked rotor system via moving feature fusion based deep learning approach

This study proposes a novel approach for predicting the remaining useful life (RUL) of a cracked rotor system by using a moving fusion gated recurrent unit (MFGRU) model. Firstly, 12 multi-domain features were extracted from the raw collected vibration signals, which were then fused and distributed adaptively using bidirectional exponential moving average (EMA) and multi-head attention (MHA). Then a bidirectional gated recurrent unit network combined with moving feature fusion method was proposed to capture the long-term dependence relationship in the monitoring data of the cracked rotor for RUL prediction. Finally, the model’s performance was validated through accelerated life experiments, with the measured values of root mean square error (RMSE) and mean absolute error (MAE) below 3.17 and 2.60, respectively. This study offers a dynamic RUL prediction method with certain significance and valuable reference for designing deep learning models.

Task-orientated probabilistic damage model with interdependent degradation behaviors for RUL prediction of traction converter systems

Remaining useful life (RUL) prediction is crucial for the safety and reliability of engineering systems with stringent requirements, like high-speed trains. Previous studies on fixed or phased conditions ignore the effects of time-varying operations on survivability. Additionally, the stochastic dependence among units is often neglected. To address the above problems, a task-oriented probabilistic damage model with interdependent degradation behaviors (TPDM-IDB) and an RUL prediction method based on TPDM-IDB are proposed. The model integrates three relations: the fundamental relation from load to damage, the task-oriented relation from task to load, and the interdependence relation. First, the degradation process and variability of the failure unit are tracked based on failure physics, mapping load to damage. Next, a task-oriented thermal loading translation is proposed to dynamically update load under time-varying operations. Then, to address the underestimation of life caused by interdependent degradation behaviors, the degradation factor is adjusted by thermal load redistribution. Finally, considering the failure stochasticity, a decision simulation method based on structural reliability is employed to predict the RUL. The effectiveness of the proposed method is validated through simulation examples and actual case studies. Notably, the method uses system tasks as inputs, which is more suitable for practical engineering applications.

Change point detection of health stage and remaining useful lifetime prediction for electro-mechanical brake unit on trains

Electro-mechanical brake units (EMBUs) have complex degradation process. There are challenges such as component fault coupling, unclear degradation characteristics, random disturbance and so on. A remaining useful life (RUL) framework for EMBUs is developed in this paper. To eliminate the issue of time lag, a data pre-processing method based on zero-phase filtering is proposed for health indicator (HI) construction. Then, the 3 health stages (HSs) characteristics of degradation process is proposed, and is modeled using the Wiener process. To overcome perturbation of large diffusion coefficient and random fluctuation, the change point (CP) detection methods based on the variance ratio hypothesis test and maximal overlap discrete wavelet transform — multi-resolution analysis (MODWT-MRA) are developed. Besides, a consecutive anomaly window detection strategy using sliding windows is employed. Finally, the MODWT-MRA-based RUL prediction methods is proposed. The proposed methods are verified by the durability test data. The proposed data pre-processing method can avoid 10% time error compared to the common difference method. The proposed MODWT-MRA-based CP detection and RUL prediction method can overcome the interference of large random fluctuations in the non-healthy state of EMBU.

Probabilistic remaining useful life prediction without lifetime labels: A Bayesian deep learning and stochastic process fusion method

Trustworthy remaining useful life (RUL) predictions are critical for the long-term safe and reliable operation of degradation systems. The existing deep learning-based methods for RUL prediction are attracting increasing attention but typically face three main challenges. One is the absence of complete run-to-failure data, implying a lack of lifetime labels. Second, it is difficult to directly measure the health indicators (HIs) for field degradation systems. Third, the prediction models output point estimates without uncertainty. To this end, this paper proposes a Bayesian deep learning and stochastic process fusion method for probabilistic RUL prediction without lifetime labels. First, a model-free Bayesian neural network (BNN) is constructed to integrate the quantification of epistemic and aleatoric uncertainties in deep learning. Based on the constructed BNN, it is possible to predict the probability features of HIs. Then, degeneracy modeling is conducted using a nonlinear Wiener process to derive the probability density function of the RUL. Furthermore, model evolution can be achieved through parameter updating during online operations. Finally, the effectiveness and superiority of the proposed prediction method are verified on CALCE battery degradation data.

A hybrid data- and model-driven learning framework for remaining useful life prognostics

The efficient and safe production of machinery equipment relies on the health of its mechanical components, making prognostics and health management (PHM) a critical aspect of production processes. One key PHM measure is the remaining useful life (RUL), which estimates the expected lifespan of a component in a production line before requiring repair or replacement. However, state-of-the-art RUL prediction methods, including data-driven, model-based, and hybrid approaches, face limitations such as incomplete/imprecise physical models, uncertainties in degradation processes, and measurement data noise. To address these limitations, this paper proposes a novel hybrid RUL prediction framework that combines the strengths of data-based and model-driven approaches. The framework includes an exponential model to leverage physical knowledge and a multi-head attention transformer to extract information from data. An extended Kalman filter is used to estimate unknown degradation process parameters and provide physical model information for the prediction process. A regression token is introduced to efficiently fuse the deep learning model and the stochastic filtering method. Numerical tests using real-world rolling bearing degradation datasets demonstrate the superiority of the proposed method over competitive alternatives.

Adaptive Framework for Maintenance Scheduling Based on Dynamic Preventive Intervals and Remaining Useful Life Estimation

Data-based prognostic methods exploit sensor data to forecast the remaining useful life (RUL) of industrial settings to optimize the scheduling of maintenance actions. However, implementing sensors may not be cost-effective or practical for all components. Traditional preventive approaches are not based on sensor data; however, they schedule maintenance at equally spaced intervals, which is not a cost-effective approach since the distribution of the time between failures changes with the degradation state of other parts or changes in working conditions. This study introduces a novel framework comprising two maintenance scheduling strategies. In the absence of sensor data, we propose a novel dynamic preventive policy that adjusts intervention intervals based on the most recent failure data. When sensor data are available, a method for RUL prediction, designated k-LSTM-GFT, is enhanced to dynamically account for RUL prediction uncertainty. The results demonstrate that dynamic preventive maintenance can yield cost reductions of up to 51.8% compared to conventional approaches. The predictive approach optimizes the exploitation of RUL, achieving costs that are only 3–5% higher than the minimum cost achievable while ensuring the safety of critical systems since all of the failures are avoided.

A hybrid residual correction method with auxiliary particle filter and conditional kernel density estimation for remaining useful life prediction

Predicting the remaining useful life (RUL) is crucial for prognosis and health management and provides an essential foundation for maintenance decisions. This study constructed a hybrid RUL prediction method based on residual correction to enhance prediction accuracy, minimize uncertainty, and mitigate errors caused by local fluctuations in the degeneration state within complex environments. This approach combined an auxiliary particle filter (APF), complementary ensemble empirical mode decomposition (CEEMD), and conditional kernel density estimation (CKDE). First, a Wiener degradation model was established, and the APF was used to acquire the initial state estimate of the equipment and residual difference between actual observations. Second, CEEMD was used to reconstruct the residual sequence and reduce interference. Subsequently, the nonparametric CKDE predicted the residual to correct the filter estimation. The corrected degeneration state value elucidated the local details of the system degradation process, and the point prediction of the RUL at the current time was obtained. The probability density distribution of the remaining life was estimated by substituting the modified degeneration state values into the kernel density estimation (KDE) model. Finally, the method was tested using an aircraft engine dataset. The results demonstrated the efficacy of the proposed method and its superiority over alternative approaches.

Remaining Useful Life Prediction Method Enhanced by Data Augmentation and Similarity Fusion

Precise prediction of the remaining useful life (RUL) of rolling bearings is crucial for ensuring the smooth functioning of machinery and minimizing maintenance costs. The time-domain features can reflect the degenerative state of the bearings and reduce the impact of random noise present in the original signal, which is often used for life prediction. However, obtaining ideal training data for RUL prediction is challenging. Thus, this paper presents a bearing RUL prediction method based on unsupervised learning sample augmentation, establishes a VAE-GAN model, and expands the time-domain features that are calculated based on the original vibration signals. By combining the advantages of VAE and GAN in data generation, the generated data can better represent the degradation state of the bearings. The original data and generated data are mixed to realize data augmentation. At the same time, the dynamic time warping (DTW) algorithm is introduced to measure the similarity of the dataset, establishing the mapping relationship between the training set and target sequence, thereby enhancing the prediction accuracy of supervised learning. Experiments employing the XJTU-SY rolling element bearing accelerated life test dataset, IMS dataset, and pantograph data indicate that the proposed method yields high accuracy in bearing RUL prediction.

A novel evidence reasoning-based RUL prediction method integrating uncertainty information

The remaining useful life (RUL) prediction plays an essential role in maintenance decision making to ensure safe operation of mechanical equipment. However, it still remains challenges to mine and utilize the uncertainty information hidden behind the running data and to enhance the interpretability of the prediction process, which leads to inaccurate and unreasonable prediction results. Therefore, a novel evidence reasoning-based RUL prediction method integrating uncertainty information is proposed to overcome these limitations. First, a sample casting method is presented to transform the historical sample set of an input feature sequence into the corresponding referential life evidence matrix (RLEM), achieving almost lossless transformation from RUL about the input feature sequence to life evidence. Second, the real-time samples of multiple input features activate their corresponding RLEMs to obtain the activated life evidence, and use evidence reasoning (ER) rule to fuse these activated life evidence to ultimately obtain integrated life evidence. Then, to further improve the accuracy of integrated life evidence, the reliability of activated life evidence is calculated online through sample entropy method, and the weight of life evidence is optimized offline using genetic algorithm. Finally, the integrated life evidence is transformed into predicted values of RUL based on utility theory. Two case studies on rolling bearing and hydrogen fuel cell show the superiority of the proposed RUL prediction method.

Predicting the remaining useful life of rails based on improved deep spiking residual neural network

the remaining useful life (RUL) of rails is important to ensure safe and reliable operation of railway transportation lines. However, the severity of deterioration of rails from different types of damage varies. Multichannel vibrational data collected by sensors can be utilized to identify the relevant complex correlations and temporal relationships; however, existing methods struggle to predict rail damage accurately. Thus, this paper proposes a RUL prediction method for rails based on an improved deep spiking residual neural network. First, multichannel data collected by sensors are used directly as input to the predictive network without requiring a separate feature extraction step. Additionally, an encoding module is designed to adaptively convert the temporal sequences of data into spiking signals to reduce the information loss during the encoding process. Second, a spiking residual convolutional neural network (CNN) is incorporated into the proposed method to extract optimal features. The separable, spiking CNN can model the relationships among multichannel data accurately, and an attention mechanism is implemented to recalibrate the spiking feature maps such that the predictive network can distinguish between items of information effectively. Third, the spiking residual connections are altered to mitigate network degradation caused by the incompatibility between the conventional residual connections and the spiking neural network. Finally, the obtained spiking features are input to a fully connected layer to predict the rail RUL. Experimental results demonstrated that the proposed method can predict the rail RUL accurately, and validation results obtained on a rolling bearing dataset demonstrated the high generalizability of the proposed method.

Principal-feature-guided degradation trend prediction algorithm based on gear fault dynamics model

The long-term remaining useful life (RUL) prediction of gears is one of the key technologies for gear failure prediction and health management, which has significant practical significance for maintenance decision-making in the traditional mechanical industry. However, due to the lack of sufficient failure data, most RUL prediction methods face significant challenges when predicting gear degradation trends under different fault conditions. The purpose of this article is to solve the dependency of predictive models on data. The paper proposes a principal-feature-guided degradation trend prediction algorithm based on the gear fault dynamics model. Based on the degradation mechanisms under different failure modes, this paper establishes a high-fidelity faulty gears dynamic model. The accuracy of the dynamic model for two failure modes has reached 90% and 88%. The model can provide adequate failure data for RUL faulty gear prediction. Furthermore, a principal-feature-guided Transformer-TCN-ATT (TTA) algorithm was proposed to achieve trend prediction of faulty gears. The prediction algorithm introduces a principal feature reinforcement to reduce the impact of high-frequency fluctuations on feature extraction. Compared with the various typical methods, the proposed algorithm improves prediction accuracy by 76% and 77% for two failure modes.

A dual-model adaptive Kalman filtering for remaining useful life prediction method based on feature fusion and online TSP recognition

Remaining Useful Life (RUL) prediction is of significant importance for the safe operation of machines. However, the Health Indicators (HIs) constructed by a single feature of machines cannot precisely describe the non-stationary and accelerating degradation operation. Moreover, poor identification of Time to Start Prediction (TSP), and the limited adaptability of models restrict the accuracy of RUL prediction. A Dual-Model Adaptive Kalman Filter (DMAKF) RUL prediction method based on feature fusion and online TSP recognition is proposed. Firstly, a feature-fusion strategy is proposed, integrating various information to construct distinguishing HIs. Secondly, a statistic-based change-point detection approach is investigated to online recognize TSP, balancing the sensitivity and interference immunity. Finally, the DMAKF is conducted for adaptive adjustment of RUL prediction in real-time. The proposed method is validated on two sets of bearing datasets from different sources. Comparison with four other methods demonstrates the effectiveness of the proposed method.

A nonparametric degradation modeling method for remaining useful life prediction with fragment data

Condition-based maintenance (CBM) is an effective way to keep the safety of industrial equipment by predicting the remaining useful life (RUL) and scheduling the maintenance plan before failure. Condition monitoring data is the basis of health state evaluation and RUL prediction. In ideal cases, the monitoring data are collected consecutively starting from the healthy stage until the end of the lifetime. In real industrial cases, however, fragment data often exist due to the interruption of monitoring and/or the loss of sensor readings. The major characteristic of fragment data is that they only record a random period of degradation process. The initial degradation time information is generally lost. Therefore, it is unable to be modeled using the common time-dependent modeling framework. To deal with the above issue, this paper proposes a nonparametric degradation modeling method for RUL prediction with fragment data. In this method, a new state-dependent degradation modeling framework is constructed via two-step axis transform. It formulates the RUL using a function depending on the health state. Based on functional principle component analysis (FPCA), a principal analysis via maximum likelihood estimation (PAMLE) algorithm is developed to recover the missing data of failed units. In addition, a RUL prediction-oriented optimization (POO) algorithm is proposed to predict the RUL of in-service units based on a piece of fragment data. Consequently, the proposed method is capable of dealing with the issues of both data recovery and RUL prediction. The effectiveness of the method is demonstrated using a fatigue crack growth dataset and a lithium-ion (Li-ion) battery degradation dataset.