Remaining useful life estimation based on discriminating shapelet extraction

The remaining useful life (RUL) estimation is an important metric that helps in condition-based maintenance. Damage data obtained from the diagnostics techniques are often noisy, and the RUL estimated from the data is less reliable. Estimating the probabilistic RUL by quantifying the uncertainty in the predictive model parameters using the noisy data increases confidence in the predicted values. In this work, Bayesian inference is used to inversely quantify the uncertainty in the model parameters of the predictive damage model in adhesively bonded joints, and quantified parameter uncertainty is represented by a probability distribution function (PDF). It is difficult to obtain a closed-form solution for the RUL from the PDF of model parameters due to the nonlinearity of the damage models. Instead, statistical simulations are used to generate the model parameter samples from the PDF, and the RUL is estimated from the samples. In the statistical simulations, the predictive damage model is evaluated for each parameter sample. Using a physics-based model as the predictive model increases computational time, which makes the statistical techniques to be computationally expensive. It is essential to reduce the computational time to estimate the RUL in a feasible time. In this work, real-time probabilistic RUL estimation is demonstrated in adhesively bonded joints using the Sequential Monte Carlo (SMC) sampling method and cloud-based computations. The SMC sampling method is an alternative to traditional Markov Chain Monte Carlo (MCMC) methods, which enables generating statistical parameter samples in parallel. The parallel computational capabilities of the SMC methods are exploited by running the SMC simulation on multiple cloud calls. This approach is demonstrated by estimating fatigue RUL in the adhesively bonded joint. The accuracy of probabilistic RUL estimated by SMC is validated by comparing it with RUL estimated by the MCMC and the experimental values. The SMC simulation is run on the cloud and the computational speedup of the SMC is demonstrated.

Remaining Useful Life (RUL) estimation of rotating machinery based on their degradation data is vital for machine supervisors. Deep learning models are effective and popular methods for forecasting when rotating machinery such as bearings may malfunction and ultimately break down. During healthy functioning of the machinery, however, RUL is ill-defined. To address this issue, this study recommends using anomaly monitoring during both RUL estimator training and operation. Essential time-domain data is extracted from the raw bearing vibration data, and deep learning models are used to detect the onset of the anomaly. This further acts as a trigger for data-driven RUL estimation. The study employs an unsupervised clustering approach for anomaly trend analysis and a semi-supervised method for anomaly detection and RUL estimation. The novel combined deep learning-based anomaly-onset aware RUL estimation framework showed enhanced results on the benchmarked PRONOSTIA bearings dataset under non-varying operating conditions. The framework consisting of Autoencoder and Long Short Term Memory variants achieved an accuracy of over 90% in anomaly detection and RUL prediction. In the future, the framework can be deployed under varying operational situations using the transfer learning approach.

Ball bearings are one of the most critical components of rotating machines. They ensure shaft support and friction reduction, thus their malfunctioning directly affects the machine’s performance. As a consequence, it is necessary to monitor the health conditions of such a component to avoid major degradations which could permanently damage the entire machine. In this context, HMS (Health Monitoring Systems) and PHM (Prognosis and Health Monitoring) methodologies propose a wide range of algorithms for bearing diagnosis and prognosis. The present article proposes an end-to-end PHM approach for ball bearing RUL (Remaining Useful Life) estimation. The proposed methodology is composed of three main steps: HI (Health Indicator) construction, bearing diagnosis and RUL estimation. The HI is obtained by processing non-stationary vibration data with the MODWPT (Maximum Overlap Discrete Wavelet Packet Transform). After that, a degradation profile is defined and coupled with crack initiation and crack propagation fatigue models. Lastly, a MB-HMM (Hidden Markov Model) is trained to capture the bearing degradation dynamics. This latter model is used to estimate the current degradation state as well as the RUL. The obtained results show good RUL prediction capabilities. In particular, the fatigue models allowed a reduction of the ML (Machine Learning) model size, improving the algorithms training phase.

Deep learning has been used to train neural networks to estimate the Remaining Useful Life (RUL) of a machine given sensor signals from that machine. This has resulted in some accurate state-of-the-art RUL estimation models. Here we present a novel way to construct a generative model to estimate the RUL and quantify its uncertainty. It takes the form of a Linear Gaussian State Space Model (LGSSM) and is trained using the Kalman Filter; hence, uncertainty is quantified using this LGSSM instead of by other popular methods like Monte Carlo Dropout or Deep Ensembles. This means we can train by directly using the marginal log-likelihood loss and don’t require multiple samples to represent the uncertainty. However, this method is limited to using Gaussian distributions to quantify uncertainty. We avoid needing to use non-linear variants of the filter by processing the sensors using a neural network to represent noncausal sensor sequences as a “control variable” in the LGSSM. This noncausal representation is shown to be important for achieving state-of-the-art performance. The model is tested on a turbofan engine and dust filter dataset. The code can be found on GitHub. 1 1 https://github.com/StarMarco/Kalman_DVAE • Deep Neural Networks encode time window of sensor signals. • These are used as control/forcing variables of a Linear Gaussian State Space Model (LGSSM). • The “observables" of the LGSSM are the Remaining Useful Life (RUL) values of the machine. • The Kalman filtering algorithm is used to estimate the marginal log-likelihood of these RUL estimates. • After training the LGSSM can be evaluated over time to estimate the RUL trajectories.

Prognostics and health management (PHM) is one of the research hotspots in reliability, where remaining useful life (RUL) estimation is a typical application scenario. In this article, a feature learning method based on dynamic Bayesian networks (DBNs) is proposed to improve the RUL estimation accuracy of the regression models. The best feature set is obtained with the conditional dependencies represented by the DBN structure. A local modeling method is applied here to reduce the computation for high-order DBN construction. The strength of the connections between variables together with a contribution index of variables in the DBN structure are defined to represent the feature importance of the variables. Feature transfer is carried out with feature importance under different operating conditions for a further improvement. Nonlinear regression models such as support vector regression (SVR) and Gaussian mixture regression (GMR) are built based on the learned features and used to estimate the RUL. The turbofan engine dataset C-MAPSS is used to validate the effectiveness of the proposed method. Compared with other recent RUL estimation models, the proposed method has a faster modeling speed and higher prediction accuracy.

Prognostics, in other words, remaining useful life (RUL) estimation is a core task of prognostics and health management (PHM). Reliable RUL predictions can reduce maintenance costs, improve production efficiency, and avoid unexpected downtime. Lots of models for RUL predictions have been proposed; however, noise and the nonlinear nature of degradation phenomena often leads to poor prognostics results, and the acquired engineered system data are usually subject to a high level of uncertainty. This makes the RUL estimation models less than satisfactory. Accurate RUL estimation and prediction not only rely on an accurate model but also depend on the adjustments of model parameters to track the variation. In this paper, an ensemble model combining the health index synthesis (HIS) approach and improved particle filtering (PF) is introduced. HIS approach was used to obtain the synthesized health index (SHI) for an engineered system with multiple sensors, which indicated the system's degradation model, while the improved PF approach was used to adjust the parameters of the degradation model obtained from the HIS approach and optimized the RUL estimation results. The performance of the prognostics approach introduced in this paper was demonstrated by using turbofan engine degradation data sets, which was supplied by NASA Ames, and results were compared with several usually used methods.

Prognostics or Remaining Useful Life (RUL) Estimation from multi-sensor time series data is useful to enable condition-based maintenance and ensure high operational availability of equipment. We propose a novel deep learning based approach for Prognostics with Uncertainty Quantification that is useful in scenarios where: (i) access to labeled failure data is scarce due to rarity of failures (ii) inherent noise ispresent in the sensor readings. The two scenarios mentioned are unavoidable sources of uncertainty in the RUL estimation process, often resulting in unreliable RUL estimates. To address (i), we formulate RUL estimation as an Ordinal Regression (OR) problem and propose LSTM-OR: deep Long Short Term Memory (LSTM) network-based approach to learn the OR function. We show that LSTM-OR naturally allows for the incorporation of censored operational instances in training along with the failed instances, leading to more robust learning. To address (ii), we propose a simple yet effectiveapproach to quantify predictive uncertainty in the RUL estimation models by training an ensemble of LSTM-OR models. Through empirical evaluation on the publicly available turbofan engine benchmark datasets, we demonstrate that LSTMOR is at par with commonly used deep metric regressionbased approaches for RUL estimation when sufficient failed instances are available for training. Importantly, LSTM-OR outperforms these metric regression-based approaches in the practical scenario where failed training instances are scarce, but sufficient operational (censored) instances are additionally available. Furthermore, our uncertainty quantification approach yields high-quality predictive uncertainty estimateswhile also leading to improved RUL estimates compared to single best LSTM-OR models.

For health prognostic task, ever-increasing efforts have been focused on machine learning based methods, which are capable of yielding accurate remaining useful life (RUL) estimation for industrial equipment or components without exploring the degradation mechanism. A prerequisite ensuring the success of these methods depends on a wealth of run-to-failure data; however, run-to-failure data may be insufficient in practice. That is, conducting a substantial amount of destructive experiments not only is of high cost but also may cause catastrophic consequences. Out of this consideration, an enhanced RUL framework focusing on data self-generation is put forward for both noncyclic and cyclic degradation patterns for the first time. It is designed to enrich data from a data-driven way, generating realistic-like time-series to enhance current RUL methods. First, high-quality data generation is ensured through the proposed convolutional recurrent generative adversarial network, which adopts a two-channel fusion convolutional recurrent neural network. Next, a hierarchical framework is proposed to combine generated data into current RUL estimation methods. Finally, in this article the efficacy of the proposed method is verified through both noncyclic and cyclic degradation systems. With the enhanced RUL framework, an aero-engine system following noncyclic degradation has been tested using three typical RUL models. State-of-the-art RUL estimation results are achieved by enhancing capsule network with generated time-series. Specifically, estimation errors evaluated by the index score function have been reduced by 21.77$\%$ and 32.67$\%$ for the two employed operating conditions, respectively. Besides, the estimation error is reduced to zero for the lithium-ion battery system, which presents cyclic degradation.

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.

A multi-model data-fusion based deep transfer learning for improved remaining useful life estimation for IIOT based systems

Rolling element bearing (REB) is one of the basic mechanical components in a rotating machinery. REBs’ remaining useful life (RUL) estimation allows not only to assess time for maintenance actions but also can prevent a critical failure of the mechanical system. Usually, REB damage occurs in two stages, damage initiation and damage propagation. In the current work, it is assumed that spall is generated on the surface of the raceway during the initiation stage. The spall generation process is modeled based on continuum damage mechanics with the representation of material grain structure and implemented using a Finite Element (FE) software. The results of the model are in a good agreement with published theoretical and experimental data. However, after the first spall formation, the bearing might be fully operational for millions of cycles. For estimation of the bearing RUL it is important to understand the damage propagation process. The material behavior at the trailing edge of the spall during the rolling element (RE) impact is analyzed. The analysis is carried out by using a hybrid modeling approach. This approach integrates non-linear dynamic modeling and FE simulations. The paper also includes a discussion on the ongoing research and the methodology for the development of the prognostic method. Implementation of the proposed methodology has the potential to provide a complete estimation of the bearing’s RUL: from first spall formation to the un-operational bearing.

Intelligent framework for degradation monitoring, defect identification and estimation of remaining useful life (RUL) of bearing

Remaining useful life (RUL) estimation via degradation modeling is considered as one of the most central components in prognostics and health management. Current RUL estimation studies mainly focus on linear stochastic models, and the results under nonlinear models are relatively limited in literature. Even in nonlinear degradation modeling, the estimated RUL is aimed at a population of systems of the same type or depend only on the current degradation observation. In this paper, an adaptive and nonlinear prognostic model is presented to estimate RUL using a system's history of the observed data to date. Specifically, a general nonlinear stochastic process with a time-dependent drift coefficient is first adopted to characterize the dynamics and nonlinearity of the degradation process. In order to render the RUL estimation depending on the degradation history to date, a state-space model is constructed, and Kalman filtering is applied to update one key parameter in the drifting function through treating this parameter as an unobserved state variable. To update the hidden state and other parameters in the state-space model simultaneously and recursively, the expectation maximization algorithm is used in conjunction with Kalman smoother to achieve this aim. The probability density function of the estimated RUL is derived with an explicit form, and some commonly used results under linear models turn out to be its special cases. Finally, the implementation of the presented approach is illustrated by numerical simulations, and an application for estimating the RUL of lithium-ion batteries is used to demonstrate the superiority of the method.

Satellite lithium-ion battery remaining useful life estimation with an iterative updated RVM fused with the KF algorithm

Due to the growing necessity for a reliable power supply and the aging of distribution transformers (DTs), estimating the remaining useful life (RUL) of these transformers has gained wide attention in the power industry. However, there is an inevitable data shortage that restricts the performance of the estimation. In addition, data sharing sometimes tends to result in the leakage of sensitive information. These are the main issues that need to be resolved currently. For this purpose, a privacy-preserving cross-silo federated learning (FL) method is developed for the RUL estimation of DTs, namely ADP-FedRUL. Specifically, a cross-silo FL architecture enables different data silos to train a global model without the need to share raw data. In this way, it extracts composite health index from multi-source sensor data and integrates the advantages of data to facilitate accurate RUL estimation while preserving privacy. Moreover, a user-level adaptive differential privacy (ADP) strategy is adopted to address potential problems of excessive and insufficient perturbations. Case studies show that the proposed method achieves a favorable balance between privacy budget and estimation performance, with estimation accuracy as high as 98.7 %.