Physics Based Methodology for the Estimation of Bearings' RUL: Physics-Based Models, Diagnostic Methods and Experiments

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.

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.

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

Accurate remaining useful life (RUL) estimation of rolling bearings can significantly improve the safety, availability, reliability and productivity of a rotating machinery system. In this article, a new approach of RUL estimation for rolling bearings based upon the fractional-order spatiotemporal sparse low-rank matrix (FST-SLRM) and augmented quaternion least mean p-power with correntropy induced metric (AQLMP-CIM) is originally proposed. Specifically, the proposed approach includes three modules: the construction of the fused health indicator, which fuses the classical features and spectral kurtosis derived indices; the decomposition of the static and dynamic components, the fused health indicator time series (FHITS) is decomposed by the FST-SLRM algorithm, thus low- and high- frequency trend components (i.e., LFCs, HFCs) are obtained, respectively; and the prognostics of degradation trajectory and RUL estimation, the degradation trajectories are obtained by the AQLMP-CIM algorithm via integrating the predicted LFC and HFC, and the RUL is eventually acquired. Two experimental cases are conducted on run-to-failure fatigue test of rolling bearings, the results demonstrate that the proposed approach is able to achieve better performance compared with state-of-the-art benchmarks.

In industrial applications, nearly half the failures of motors are caused by the degradation of rolling element bearings (REBs). Therefore, accurately estimating the remaining useful life (RUL) for REBs is of crucial importance to ensure the reliability and safety of mechanical systems. To tackle this challenge, model-based approaches are limited by the complexity of mathematical modeling. Conventional data-driven approaches, on the other hand, require massive efforts to extract the degradation features and construct the health index. In this article, a novel data-driven framework is proposed to exploit the adoption of deep convolutional neural networks (CNNs) in predicting the RULs of bearings. More concretely, raw vibrations of training bearings are first processed using the Hilbert–Huang transform to construct a novel nonlinear degradation energy indicator which can be used as the training label. The CNN is then employed to identify the hidden pattern between the extracted degradation energy indicator and the raw vibrations of training bearings, which makes it possible to estimate the degradation of the test bearings automatically. Finally, testing bearings’ RULs are predicted through using an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -support vector regression model. The superior performance of the proposed RUL estimation framework, compared with the state-of-the-art approaches, is demonstrated through the experimental results. The generality of the proposed CNN model is also validated by performance test on other bearings undergoing different operating conditions.

Rolling element bearings (REBs) are key components in rotating machines. 40% of the failures in electrical motors occur due to bearing faults. Consequently, monitoring the health stage and estimating the remaining useful life (RUL) of the REBs is essential. Additionally, maintenance of rotating machines can be scheduled based on the RUL estimation, which will mitigate potential time wasting, economic losses and hazards. In this summary, several issues that exist in current research are highlighted. Then a series of preliminary explorations have been performed, and some results have been already obtained. Finally, a systematic methodology is expected to be proposed by combining the state estimation techniques and physical models to facilitate the development of the PHM.

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.

Fault diagnosis of rolling element bearings is a critical aspect of machine maintenance and reliability. Bearings are extensively used in various industrial applications, and their failure can lead to costly downtime and equipment damage. Rotating machinery under continuous overload conditions can indeed significantly degrade bearing life and lead to various other issues. To identify issues in rolling element bearings (REB), several techniques and methods are employed. Diagnosing faults in ball bearings while simultaneously estimating the Remaining Useful Life (RUL) of the bearing is a crucial aspect of predictive maintenance. This can be achieved through a combination of signal processing techniques, machine learning methods, and RUL prediction models. The estimation of a bearing Remaining Useful Life (RUL) is of significant importance in predictive maintenance strategies to avoid unexpected failures, reduce downtime, and optimize maintenance costs. This literature review aims to explore the methodologies, techniques, and advancements in predicting the remaining useful life of bearings.

We describe the approach – submitted as part of the 2018 PHM Data Challenge – for estimating time-to-failure or Remaining Useful Life (RUL) of Ion Mill Etching Systems in an online fashion using data from multiple sensors. RUL estimation from multi-sensor data can be considered as learning a regression function that maps a multivariate time series to a real-valued number, i.e. the RUL. We use a deep Recurrent Neural Network (RNN) to learn the metric regression function from multivariate time series. We highlight practical aspects of the RUL estimation problem in this data challenge such as i) multiple operating conditions, ii) lack of knowledge of exact onset of failure or degradation, iii) different operational behavior across tools in terms of range of values of parameters, etc. We describe our solution in the context of these challenges. Importantly, multiple modes of failure are possible in an ion mill etching system; therefore, it is desirable to estimate the RUL with respect to each of the failure modes. The data challenge considers three such modes of failures and requires estimating RULs with respect to each one, implying learning three metric regression functions - one corresponding to each failure mode. We propose a simple yet effective extension to existing methods of RUL estimation using RNN based regression to learn a single deep RNN model that can simultaneously estimate RULs corresponding to all three failure modes. Our best model is an ensemble of two such RNN models and achieves a score of 1:91 X 10^7 on the final validation set..

Remaining useful life estimation based on discriminating shapelet extraction

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.

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

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.

A cutting-edge solution enables accurate prediction of the remaining useful life (RUL) of drill string components before deployment in the field. This proactive approach allows informed decisions about such components to be made prior to actual drilling, significantly reducing the risk of field fatigue-related failures. The solution provides an efficient and cost-effective method for extending the lifespan of critical components, such as BHA connectors, ultimately improving overall operational efficiency. The solution seamlessly integrates drill plan data with results from offset well analysis to estimate the RUL of various drill string components, particularly different BHA connectors. By examining offset wells with similar equipment and geological conditions, it extracts essential anticipated operational parameters. Combining a physics-based model of the relevant drill string components with a data-driven approach and modeling capabilities, the solution ensures reliable decision-making regarding the suitability of specific components for particular drilling operations. Additionally, it facilitates the optimal selection of drill string components for the intended job. This innovative solution has undergone extensive testing, leveraging historical data to validate its reliability and effectiveness. A comprehensive comparison of predicted RUL for monitored components before field runs with actual post-job RUL estimates based on recorded drilling time consistently demonstrates favorable outcomes. This rigorous validation confirms the accuracy and dependability of the approach. By implementing this solution, drilling engineers can optimize drill string component selection, configurations, and maintenance operations, minimizing uncertainties in RUL estimation and reducing the risk of costly failures. Integrating predicted RUL estimates into routine post-job maintenance before starting new drilling runs enables well-informed decisions, preventing unnecessary maintenance and mitigating premature component retirements. The solution is now thoroughly validated and ready for seamless integration into a comprehensive drilling platform, encompassing maintenance systems, well construction planning, and execution. This unified strategy for drill string component management maximizes equipment utilization, enhances drilling performance, and ensures reliability throughout the drilling process. Operators adopting this integrated approach can optimize fleet management, reduce nonproductive time, minimize associated costs, and ultimately maximize revenue. This solution highlights the significant value digital technology brings to traditional mechanical systems in the oil and gas industry by enhancing functionality and creating new service opportunities. The described algorithm and its validation process are novel to the industry. Several instances analyzed demonstrate the methodology's application, providing valuable comparisons to post-job results and underscoring the approach's robustness.

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.