Remaining Useful Life Estimation Research Articles

An Adaptive Prognostic Approach for Partially Observable Degrading Products With Random Shocks

This paper proposes an adaptive remaining useful life (RUL) estimation method for partially observable degrading products with time-varying random shocks. In the modeling aspect of the proposed method, a shock degradation model is proposed to characterize the degradation process of the product, in which the continuous degradation process is described by the Wiener process, and the random shock process with a time-varying intensity is described by the non-homogeneous compound Poisson process (NHCPP). In the proposed model, to characterize the effect of random shocks on the degradation process, the degradation rate is related to the number of shocks and the magnitude of cumulative shocks. In the estimating aspect, we utilize a strong tracking filtering (STF) algorithm to estimate partially observable degradation states and a two-step expectation conditional maximization (ECM) algorithm to estimate the model parameters. In the prognostic aspect, the approximated analytical RUL distribution under the concept of the first hitting time (FHT) is obtained by incorporating the unit-to-unit variability and the uncertainty of the partially observable degradation state estimation from observations into the RUL estimation. As such, the RUL distribution can be updated according to the latest available degradation observation, thereby realizing the adaptive RUL estimation. Finally, the accuracy and effectiveness of the proposed approach is verified by a numerical example and a practical case study for the furnace wall, which provides higher estimation accuracy and better online capability than existing approaches.

Generative adversarial networks based remaining useful life estimation for IIoT

Artificial intelligence (AI) and Predictive Maintenance (PdM) become productive using IIoT-data with zero-downtime for maintenance in industries by estimating the remaining useful life (RUL). Most reported works consider training data availability with an equal number of normal and fault samples concerning different machine health conditions. However, practical scenarios have to deal with fault-data unavailability, resulting in an imbalanced training dataset. This problem can lead to inaccuracies with missed fault-prediction in RUL estimation approaches. This paper proposes a novel prognostics framework based on conditional generative adversarial network (CGAN) and deep gated recurrent unit (DGRU) network. The framework can generate multi-variate fault instances, solve data imbalance, and predict the RUL of complex systems with the least latency. We observed that the learning of fault samples using underlying noise distribution, data augmentation, and training DGRU improves the RUL prediction accuracy by at least 15% compared to reported imbalanced work on the C-MAPSS dataset.

A data-driven approach based on deep neural networks for lithium-ion battery prognostics

Remaining useful life estimation is gaining attention in many real-world applications to alleviate maintenance expenses and increase system reliability and efficiency. Deep learning approaches have recently provided a significant improvement in the estimation of remaining useful life (RUL) and degradation progression concerning machinery prognostics. This research presents a new data-driven approach for RUL estimation using a hybrid deep neural network that combines CNN, LSTM, and classical neural networks. The presented CNN–LSTM neural network aims to extract the spatio-temporal relations in multivariate time series data and capture nonlinear characteristics to achieve better RUL prediction accuracy. To improve the proposed model's performance, PSO is handled to simultaneously optimize the hyperparameters of the network consisting of the number of epochs, the number of convolutional and LSTM layers, the size of units (or filters) in each convolutional, and LSTM layers. Besides, the proposed model in this paper, called the CNN–LSTM–PSO, realizes the multi-step-ahead prediction. In the experimental studies, the popular lithium-ion battery dataset presented by NASA is selected to verify the CNN–LSTM–PSO approach. The experimental consequences revealed that the presented CNN–LSTM–PSO model gives better results than other state-of-the-art machine learning techniques and deep learning approaches considering various performance criteria.

Spatiotemporal non-negative projected convolutional network with bidirectional NMF and 3DCNN for remaining useful life estimation of bearings

Remaining useful life (RUL) estimation for bearings is crucial in guaranteeing the reliability of rotating machinery. With the rapid development of information science, deep-learning-based RUL estimation has become more appealing as it can automatically establish the mapping relationship between the monitored data and the degradation states through feature learning. Vibration analysis via time–frequency representation (TFR) has shown great advantages for the detection of bearing damage in deep-learning-based prognostics. However, the following two problems remain: 1) insufficient or ineffective utilization of the data feature information, and 2) the requirement for huge computational resources, which still present challenges for the accuracy and efficiency of TFR-based prognostics. A novel RUL estimation approach called spatiotemporal non-negative projected convolutional network (SNPCN) is hence proposed. The approach can fully learn the spatiotemporal degradation features of bearing TFRs with high computational efficiency. In detail, the continuous wavelet transform (CWT) was applied as a TFR analysis method to reveal the nonstationary properties of the bearing degradation signals. Then, a newly proposed bidirectional non-negative matrix factorization (BiNMF) method was used to obtain the low-rank eigenmatrices of the TFRs and greatly compress the calculations in TFR-based prognostics. A three-dimensional convolutional neural network (3DCNN) was next constructed to learn the spatiotemporal degradation features in adjacent BiNMF eigenmatrices and construct the mapping relationship between the bearing RUL and current monitored data. Experiments on the PRONOSTIA platform demonstrate the feasibility and superiority of the proposed SNPCN-based bearing RUL estimation approach.

A sample entropy based prognostics method for lithium-ion batteries using relevance vector machine

Over the increasing number of charging and discharging cycling processes of lithium-ion batteries, the aging and even failure of lithium-ion batteries may occur. If anomalies are not detected in time, lithium-ion batteries could cause major safety accidents. In this paper, a prognostics method integrating the sample entropies and relevance vector machine (RVM) is proposed to estimate the remaining useful life (RUL) of lithium-ion batteries. First, RUL prediction using multiple inputs, including the voltage sample entropy and the current sample entropy, are compared with prediction methods based on a single entropy input. The multiple entropy input method indicates better capability of describing the battery degradation process. In addition, the wavelet denoising method is used to pre-process the inputs to remove sudden and unusual changes in the battery capacity degradation data. A prediction model using the denoised entropy inputs is constructed through linearly weighting the entropy inputs in the RVM model. The weight for each input is assigned according to the individual contribution to the prediction accuracy. Experimental data from lithium-ion battery testing are applied to three prediction models with different entropy inputs. The results indicate that the proposed method has higher prediction accuracy than those in existing models only using a single sample entropy. The proposed method has potentials for the RUL estimation of industrial machinery in manufacturing.

LSTM-based multi-layer self-attention method for remaining useful life estimation of mechanical systems

Accurate remaining useful life (RUL) estimation is significant in reducing maintenance costs and avoiding catastrophic failures of mechanical systems like an aeroengine. To effectively estimate the RUL of mechanical systems, the long short-term memory (LSTM)-based multi-layer self-attention (MLSA) (LSTM-MLSA) method is proposed by designing MLSA mechanism and LSTM, to improve the modeling precision and computing efficiency. In the MLSA mechanism, the multi-layer is respected to extract the effective features of system degradation data in different subspace, and self-attention is employed to establish the accurate correlation of time steps in raw time series data by parallel computation. The LSTM is used to process the extracted features and capture the degradation process of the mechanical system. The RUL estimation of an aeroengines with life degradation data is implemented, to validate the proposed LSTM-MLSA method by comparing with other RUL estimation methods. The results illustrate that the LSTM-MLSA method has high computational efficiency theoretically, high accuracy, and strong robustness in the RUL estimation of an aeroengines. The efforts of this paper provide a highly-efficient method for the RUL estimation of complex mechanical systems, which is promising to enhance the operation and maintenance of the mechanical system by reducing costs and improving RUL estimation precision.

Remaining useful life estimation via transformer encoder enhanced by a gated convolutional unit

Remaining Useful Life (RUL) estimation is a fundamental task in the prognostic and health management (PHM) of industrial equipment and systems. To this end, we propose a novel approach for RUL estimation in this paper, based on deep neural architecture due to its great success in sequence learning. Specifically, we take the Transformer encoder as the backbone of our model to capture short- and long-term dependencies in a time sequence. Compared with convolutional neural network based methods, there is no limitation from the kernel size for a complete receptive field of all time steps. While compared with recurrent neural network based methods, we develop our model based on dot-product self-attention, enabling it to fully exploit parallel computation. Moreover, we further propose a gated convolutional unit to facilitate the model’s ability of incorporating local contexts at each time step, for the attention mechanism used in the Transformer encoder makes the output high-level features insensitive to local contexts. We conduct experiments on the C-MAPSS datasets and show that, the performance of our model is superior or comparable to those of other existing methods. We also carry out ablation studies and demonstrate the necessity and effectiveness of each component used in the proposed model.

A nonlinear-drift-driven Wiener process model for remaining useful life estimation considering three sources of variability

The estimation of remaining useful life (RUL) for a degrading system has gained increasing attention both in academia and in industry for decades. In this study, a nonlinear-drift-driven Wiener process model considering three common sources of uncertainty is constructed by an age-dependent state-space model for the RUL estimation of degrading systems. Analytical expressions approximating the probability distribution function of RUL of the above-described model are derived for both online estimation and offline estimation scenarios. It is shown that the derived expressions are more general and cover the simplified cases discussed in previous woks. A model parameter estimation method is proposed based on unbalanced historical degradation measurements, and a down-sampling strategy is introduced to avert the underflow issue. The prognostic performance of the proposed method against previous similar works under the online and offline estimation scenarios is demonstrated on two publicly available datasets by comparisons in terms of three prognostic metrics and the probabilistic distribution of RUL at different condition monitoring points. The results show that it is necessary to include the nonlinear degradation characteristics and the three sources of uncertainty into the RUL estimation especially for the offline estimation scenario.

Remaining Useful Life Prediction Using Temporal Convolution with Attention

Prognostic techniques attempt to predict the Remaining Useful Life (RUL) of a subsystem or a component. Such techniques often use sensor data which are periodically measured and recorded into a time series data set. Such multivariate data sets form complex and non-linear inter-dependencies through recorded time steps and between sensors. Many current existing algorithms for prognostic purposes starts to explore Deep Neural Network (DNN) and its effectiveness in the field. Although Deep Learning (DL) techniques outperform the traditional prognostic algorithms, the networks are generally complex to deploy or train. This paper proposes a Multi-variable Time Series (MTS) focused approach to prognostics that implements a lightweight Convolutional Neural Network (CNN) with attention mechanism. The convolution filters work to extract the abstract temporal patterns from the multiple time series, while the attention mechanisms review the information across the time axis and select the relevant information. The results suggest that the proposed method not only produces a superior accuracy of RUL estimation but it also trains many folds faster than the reported works. The superiority of deploying the network is also demonstrated on a lightweight hardware platform by not just being much compact, but also more efficient for the resource restricted environment.

Remaining Useful life Estimation: A Review on Stochastic Process-based Approaches

Background: Remaining Useful Life (RUL) estimation is the central mission to the complex systems’ prognostics and health management. During the last decades, numbers of developments and applications of the RUL estimation have proliferated. Objective: As one of the most popular approaches, stochastic process-based approach has been widely used for characterizing the degradation trajectories and estimating RULs. This paper aimed at reviewing the latest methods and patents on this topic. Methods: The review is concentrated on four common stochastic processes for degradation modelling and RUL estimation, i.e., Gamma process, Wiener process, inverse Gaussian process and Markov chain. Results: After a brief review of these four models, we pointed out the pros and cons of them, as well as the improvement direction of each method. Conclusion: For better implementation, the applications of these four approaches on maintenance and decision-making are systematically introduced. Finally, possible future trends are concluded tentatively.

Transfer remaining useful life estimation of bearing using depth-wise separable convolution recurrent network

Rolling bearing is a vital part of the machinery, whose remaining useful life (RUL) estimation plays a critical role in ensuring the safety and maintenance decision-making. However, in most industrial applications, it is difficult to obtain run-to-failure data under complex operating conditions, which is inefficient for deep learning approaches. To solve the above problem, a new approach using transfer depth-wise separable convolution recurrent network (TDSCRN) for RUL estimation of bearing is presented. A novel prediction model so-called depth-wise separable convolution recurrent network (DSCRN) is designed and trained by the source-domain dataset. The parameters and model of DSCRN are transferred to the target-domain, and then TDSCRN is obtained for RUL estimation task. Two public run-to-failure datasets are used to validate the performance of the presented method. The results indicate that this framework can improve estimation accuracy and robustness in complex operating conditions.

A Risk-Averse Remaining Useful Life Estimation for Predictive Maintenance

Remaining useful life (RUL) prediction is an advanced technique for system maintenance scheduling. Most of existing RUL prediction methods are only interested in the precision of RUL estimation; the adverse impact of over-estimated RUL on maintenance scheduling is not of concern. In this work, an RUL estimation method with risk-averse adaptation is developed which can reduce the over-estimation rate while maintaining a reasonable under-estimation level. The proposed method includes a module of degradation feature selection to obtain crucial features which reflect system degradation trends. Then, the latent structure between the degradation features and the RUL labels is modeled by a support vector regression (SVR) model and a long short-term memory (LSTM) network, respectively. To enhance the prediction robustness and increase its marginal utility, the SVR model and the LSTM model are integrated to generate a hybrid model via three connection parameters. By designing a cost function with penalty mechanism, the three parameters are determined using a modified grey wolf optimization algorithm. In addition, a cost metric is proposed to measure the benefit of such a risk-averse predictive maintenance method. Verification is done using an aero-engine data set from NASA. The results show the feasibility and effectiveness of the proposed RUL estimation method and the predictive maintenance strategy.

Adaptive Particle Filter-Based Approach for RUL Prediction Under Uncertain Varying Stresses With Application to HDD

In recent years, the estimation of the remaining useful life (RUL) has become an increasingly important topic. Existing RUL estimation studies mainly focus on linear degradation cases or degradation processes that can be linearized. A few nonlinear degradation models often rely on a training process based on a batch of samples obtained from the same population. Consequently, large bias or uncertainties may often occur under varying stress conditions. To address this problem, this article proposes a prognostic approach based on an adaptive particle filter (PF) to predict the RUL of the dynamic degradation systems using system degradation records. First, a nonlinear degradation model based on the fusion of an exponential item and a power law wear model were derived to capture the wear process under varying stress conditions. Second, the PF method was used to update the model parameters by treating the parameters as hidden state variables. Third, an adaptive strategy was derived based on the expectation-maximization algorithm and particle smoother algorithm to recursively update the hidden variables. Finally, an actual magnetic head wear dataset obtained from an actual manufacturing plant is used to verify the effectiveness of the proposed approach. The results reveal that the proposed approach significantly improves the prediction accuracy compared with the PF-based approach and extends Kalman-filter-based approach.

Multiscale deep bidirectional gated recurrent neural networks based prognostic method for complex non-linear degradation systems

Reliable estimation of the remaining useful life (RUL) of complex engineered systems plays a vital role in avoiding undue maintenance situations while guaranteeing system safety. However, efficient tracking of RUL often gets hampered by the prerequisite for prior knowledge regarding degradation characteristics of critical components, which are not available in most cases. Additionally, machine learning techniques face difficulties in adapting and modeling degradation trends in the presence of equipment’s complex working environments. To address these issues, we present a novel data-driven feature learning approach based on a multi-scale deep bidirectional gated recurrent neural network (MDBGRU). The MDBGRU network can: i) automatically learns both local and global information in addition to temporal variations in the multivariate sensor data; ii) capture salient discriminative features characterizing the system complexity; iii) overcome the pre-expertise requirement on multiple sub-components of the system; and iv) curb shortcomings of machine learning methods. Extensive experiments are performed on the C-MAPSS dataset to evaluate the prognostic capability of the proposed method. Compared with the existing works, our network attains enhanced prediction accuracy with an overall improvement of 13.54%, suggesting this as a new and promising RUL estimation approach.

A Gaussian Process Based Method for Data- Efficient Remaining Useful Life Estimation

The task of remaining useful life (RUL) estimation is a major challenge within the field of prognostics and health management (PHM). The quality of the RUL estimates determines the economical feasibility of the application of predictive maintenance strategies, that rely on accurate predictions. Hence, many effective methods for RUL estimation have been developed in the recent years. Especially deep learning methods have been among the best performing ones setting new record accuracies on bench mark data sets. However, those approaches often rely on numerous and representative run-to-failure sequences of the components under investigation. In real-world use cases, this kind of data (i.e. run-to-failure sequences and RUL labels) is hardly ever present. Therefore, this paper proposes a new, data-efficient method, which is based on Gaussian process classification to derive abstract health indicator (HI) values in a first step, and warped, monotonic Gaussian process regression for indirect RUL estimation in a second step. The proposed approach does neither rely on entire run-to-failure sequences nor on any RUL labels and was tested on the benchmark C-MAPSS turbo fan and FEMTO bearing data sets, achieving comparable results to the state-of-the art whilst using only a small fraction of the available training data. Hence, the proposed approach allows RUL estimation in use cases, in which gathering enough failure data for the application of deep learning models is infeasible.

Cross-Operating Condition Degradation Knowledge Learning for Remaining Useful Life Estimation of Bearings

As one of the most crucial issues in the condition monitoring of mechanical systems, the remaining useful life (RUL) estimation of bearings suffers from the limitation of run-to-failure data, which makes the cross-operating condition RUL estimation of bearings a challenging subject. To address this issue, a cross-operating condition degradation knowledge learning method is proposed by constructing a shared latent feature space across different operating conditions, in which the bearing degradation features are effectively extracted and the cross-domain feature differences are weakened. Focusing on learning the cross-operating condition degradation knowledge, the time-frequency representation (TFR) samples generated by the continuous wavelet transform (CWT) method in both the source and target domains were projected onto a shared latent feature space constructed by a novel joint dictionary matrix factorization (JDMF) method. The joint-domain dictionaries solved by the JDMF method have played a core role in extracting the domain-invariant features that do not change along with the operating conditions of bearings. As a result, the convolutional neural network (CNN) model trained with the source samples in the shared latent feature space can be directly generalized to the target bearings for the degradation indicator (DI) modeling and RUL estimation. The cross-operating condition bearing RUL estimation experiment executed in the PRONOSTIA platform has demonstrated the effectiveness and superiority of the proposed JDMF-CNN framework.

Hybrid Particle Filter Trained Neural Network for Prognosis of Lithium-Ion Batteries

Prognostics and Health Management (PHM) plays a key role in Industry 4.0 revolution by providing smart predictive maintenance solutions. Early failure detection and prediction of remaining useful life (RUL) of critical industrial machines/components are the main challenges addressed by PHM methodologies. In literature, model-based and data-driven methods are widely used for RUL estimation. Model-based methods rely on empirical/phenomenological degradation models for RUL prediction using Bayesian formulations. In many cases, the lack of accurate physics-based models emphasizes the need to resort to machine learning based prognostic algorithms. However, data-driven methods require extensive machine failure data incorporating all possible operating conditions along with all possible failure modes pertaining to that particular machine/component, which are seldom available in their entirety. In this work, we propose a three-stage hybrid prognostic algorithm (HyA) combining model-based (Particle Filters-PF) and data-driven (Neural Networks-NN) methods in a unique way. The proposed method aims to overcome the need for accurate degradation modeling or extensive failure data sets. In the first stage, a feedforward neural network is used to formulate lithium-ion battery’s degradation trends and the corresponding NN model parameters are used to define the initial prior distribution of PF algorithm. In the second stage, the PF algorithm optimizes the model parameters and the posterior model parameter distributions are utilized to ‘ warm-start ’ the neural network used for prognosis and the third/final stages focuses on prognosis and RUL estimation using the trained NN model leveraging on the posterior distributions of the PF fine-tuned weights and biases. The proposed method is demonstrated on CALCE and NASA lithium-ion battery capacity degradation datasets. The efficacy of the proposed hybrid algorithm is evaluated using root mean square error (RMSE) values and alpha-lambda prognostic metrics. Also, the impact of the NN architecture on the prediction accuracy and computational load are analyzed.

Remaining Useful Life Prediction of Nonlinear Wiener Process-Based Degradation Model Based on Multi Source Information with Considering Random Effects

Accurate parameters estimation is the premise of accurate remaining useful life (RUL) prediction. This paper proposes a RUL prediction method of nonlinear Wiener process based on multi source information with considering random effects. First, a nonlinear Wiener process with considering random effects is used to model the degradation process of equipment. Then, according to the nature of parameters estimation, nonlinear parameter can be obtained based on historical degradation data. After that, the expectation maximization (EM) algorithm is used to calculate fixed parameter and random coefficient in model with fusing prior degradation information and prior failure time data information. Finally, fatigue crack data are used for experimental verification. Compared with the method based on historical degradation data or failure time data, the method based on multi source information with considering random effects can effectively improve the accuracy of parameters estimation and RUL estimation.

Remaining Useful Life Estimation Combining Two-Step Maximal Information Coefficient and Temporal Convolutional Network With Attention Mechanism

Remaining useful life (RUL) estimation has received extensive attention in many fields, which provides improved decision-making for condition-based maintenance (CBM) and enhances the stability of engineered systems. However, the effective construction of the feature set and design of the high-accuracy prediction model are the main challenges in RUL estimation. Consequently, a novel RUL estimation method is proposed in this paper. Initially, to extract the deep characteristics of the raw sensor data, the modified ensemble empirical mode decomposition (MEEMD), combined with the correlation coefficient threshold to select the sensitive intrinsic mode function (IMF) components, is proposed to reconstruct more representative features. Additionally, maximal information coefficient-based two-step feature selection (TSMIC) method is used to select the optimal feature subset. Ultimately, temporal convolutional network with attention mechanism (TCNA) is proposed to capture long-term time-series information and achieves more precise prediction results. The proposed framework is verified through a case study on aircraft turbofan engines, and comparisons with other state-of-the-art methods are presented. The experimental results of the case study show the effectiveness and superiority of the proposed approach.

Degradation-Aware Remaining Useful Life Prediction With LSTM Autoencoder

The remaining useful life (RUL) prediction plays a pivotal role in the predictive maintenance of industrial manufacturing systems. However, one major problem with the existing RUL estimation algorithms is the assumption of a single health degradation trend for different machine health stages. To improve the RUL prediction accuracy with various degradation trends, this article proposes an algorithm dubbed degradation-aware long short-term memory (LSTM) autoencoder (AE) (DELTA). First, the Hilbert transform is adopted to evaluate the degradation stage and factor with the real-time sensory signal. Second, we adopt LSTM AE to predict RUL based on multisensor time-series data and the degradation factor. Distinct from the existing studies, the proposed framework is able to dynamically model the degradation factor and explore latent variables to improve RUL prediction accuracy. The performance of DELTA is evaluated with the open-source FEMTO bearing data set. Compared with the existing algorithms, DELTA achieves appreciable improvements in the RUL prediction accuracy.