Recurrent neural networks (RNNs) have been widely adopted in research areas concerned with sequential data, such as text, audio, and video. However, RNNs consisting of sigma cells or tanh cells are ...unable to learn the relevant information of input data when the input gap is large. By introducing gate functions into the cell structure, the long short-term memory (LSTM) could handle the problem of long-term dependencies well. Since its introduction, almost all the exciting results based on RNNs have been achieved by the LSTM. The LSTM has become the focus of deep learning. We review the LSTM cell and its variants to explore the learning capacity of the LSTM cell. Furthermore, the LSTM networks are divided into two broad categories: LSTM-dominated networks and integrated LSTM networks. In addition, their various applications are discussed. Finally, future research directions are presented for LSTM networks.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
•A Wiener-process-inspired semi-stochastic filtering approach is developed.•The proposed method is applied to prognostics of stochastic degrading systems.•No resort to negatively correlated ...assumption is achieved by the developed method.•The parameters in the established model are estimated from measurements.•Advantages of the developed method are validated by two case studies.
Semi-stochastic filtering method has been termed as one of the typical methods for predicting remaining useful life (RUL). Despite of its simple and direct framework, selecting or determining the conditional distribution of the condition monitoring (CM) measurements given the RUL is a challenging task remaining to be solved. To address this issue, this paper presents a novel Wiener-process-inspired semi-stochastic filtering approach for prognostics. First, the relationship between the degradation monitoring data modeled by Wiener process and the RUL of the system is explored. Inspired this relation, the conditional distribution of the CM measurements give the RUL is directly established and used as the observation equation in semi-stochastic filtering based prognosis method, and the parameters in Wiener process and semi-stochastic filtering model are estimated by the maximum likelihood estimation method. Then, the RUL of the concerned in-service system can be predicted with a probabilistic distribution based on the constructed state equation and the estimated model parameters using the CM data to date. To do so, the proposed prognosis method has an ability to integrate the historical data and the real-time CM data of the in-service system. Finally, the developed method is validated by the wear data of milling cutters and Lithium-ion button cells.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
•A state-space model based method is proposed to predict RUL under time-varying operating conditions.•Two factors are analyzed separately: changes in degradation rate and jumps in degradation ...signals.•A time-scale transformation is applied to a Wiener process to describe the time-varying degradation rates.•A signal transformation function is applied to smooth the jumps in degradation signals.
The growth of the Industrial Internet of Things (IIoT) has generated a renewed emphasis on research of prognostic degradation modeling whereby degradation signals, such as vibration signals, temperature and acoustic emissions, are used to estimate the state-of-health and predict the remaining useful life (RUL). Besides the inherent system state, external operating conditions, such as the rotational speed and load also play a significant role in the behavior of degradation signals. Time-varying operating conditions often cause two major effects on the degradation signals. First, they change the degradation rate of systems. Second, they cause signal jumps at condition change-points. These two factors make RUL prediction more difficult under time-varying operating conditions. This paper proposes a RUL prediction method by introducing these two factors into a state-space model. Changes in the degradation rate are introduced into a state transition function, and jumps in the degradation signals are introduced into a measurement function. The separate analysis of these two factors makes it possible to distinguish their own contributions to RUL prediction, thus avoiding false alarms and improving the prediction accuracy. The effectiveness of the proposed method is demonstrated using both a simulation study and an accelerated degradation test of rolling element bearings.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Remaining useful life (RUL) prediction is central to the prognostics and health management (PHM) of lithium-ion batteries. This paper proposes a novel RUL prediction method for lithium-ion batteries ...based on the Wiener process with measurement error (WPME). First, we use the truncated normal distribution (TND) based modeling approach for the estimated degradation state and obtain an exact and closed-form RUL distribution by simultaneously considering the measurement uncertainty and the distribution of the estimated drift parameter. Then, the traditional maximum likelihood estimation (MLE) method for population based parameters estimation is remedied to improve the estimation efficiency. Additionally, we analyze the relationship between the classic MLE method and the combination of the Bayesian updating algorithm and the expectation maximization algorithm for the real time RUL prediction. Interestingly, it is found that the result of the combination algorithm is equal to the classic MLE method. Inspired by this observation, a heuristic algorithm for the real time parameters updating is presented. Finally, numerical examples and a case study of lithium-ion batteries are provided to substantiate the superiority of the proposed RUL prediction method.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
Over the past few decades, condition-based maintenance (CBM) has attracted many researchers because of its effectiveness and practical significance. This paper deals with mission-oriented systems ...subject to gradual degradation modeled by a Wiener stochastic process within the context of CBM. For a mission-oriented system, the mission usually has constraints on availability/reliability, the opportunity for maintenance actions, and the monitoring type (continuous or discrete). Furthermore, in practice, a mission-oriented system may undertake some preventive maintenance (PM) and after such PM, the system may return to an intermediate state between an as-good-as new state and an as-bad-as old state, i.e., the PM is not perfect and only partially restores the system. However, very few CBM models integrated these mission constraints together with an imperfect nature of the PM into the course of optimizing the PM policy. This paper develops a model to optimize the PM policy in terms of the maintenance related cost jointly considering the mission constraints and the imperfect PM nature. A numerical example is presented to demonstrate the proposed model. The comparison with the simulated results and the sensitivity analysis show the usefulness of the optimization model for mission-oriented system maintenance presented in this paper.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Remaining useful life (RUL) prediction has great importance in prognostics and health management (PHM). Relaxation effect refers to the capacity regeneration phenomenon of lithium-ion batteries ...during a long rest time, which can lead to a regenerated useful time (RUT). This paper mainly studies the influence of the relaxation effect on the degradation law of lithium-ion batteries, and proposes a novel RUL prediction method based on Wiener processes. This method can simplify the modeling complexity by using the RUT to model the recovery process. First, the life cycle of a lithium-ion battery is divided into the degradation processes that eliminate the relaxation effect and the recovery processes caused by relaxation effect. Next, the degradation model, after eliminating the relaxation effect, is established based on linear Wiener processes, and the model for RUT is established by using normal distribution. Then, the prior parameters estimation method based on maximum likelihood estimation and online updating method under the Bayesian framework are proposed. Finally, the experiments are carried out according to the degradation data of lithium-ion batteries published by NASA. The results show that the method proposed in this paper can effectively improve the accuracy of RUL prediction and has a strong engineering application value.
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The tracking control of a multi-input multioutput nonlinear nonminimum phase system in general form is discussed. This system is assumed to be suffering from parameter uncertainties and unmodeled ...dynamics, and the priori information of them is unknown. By considering both the exact model and uncertain model, the sliding mode-based learning controller is proposed. By designing an appropriate sliding surface and a learning controller, the stability of the closed-loop system is guaranteed for both the exact model and uncertain model. To overcome the disadvantage caused by parameter uncertainties and unmodeled dynamics, a fuzzy logical system is adopted here. A numerical simulation result carried on vertical takeoff and landing aircraft is taken as an example to validate the effectiveness of the presented controller.
Generalized eigendecomposition problem has been widely employed in many signal processing applications. In this paper, we propose a unified and self-stabilizing algorithm, which is able to extract ...the first principal and minor generalized eigenvectors of a matrix pencil of two vector sequences adaptively. Furthermore, we extend the proposed algorithm to extract multiple generalized eigenvectors. The performance analysis shows that only the desired equilibrium point of the proposed algorithm is stable and all others are (unstable) repellers or saddle points. Convergence analysis based on the deterministic discrete-time approach shows that, for a step size within a certain range, the norm of the principal/minor state vector converges to a fixed value that relates to the corresponding principal/minor generalized eigenvalue. Thus, the proposed algorithm is a generalized eigenpairs (eigenvectors and eigenvalues) extraction algorithm. Finally, the simulation experiments are carried to further demonstrate the efficiency of the proposed algorithm.
Owing to operating condition changing, physical mutation, and sudden shocks, degradation trajectories usually exhibit multi-phase features, and the abrupt jump often appears at the changing time, ...which makes the traditional methods of lifetime estimation unavailable. In this paper, we mainly focus on how to estimate the lifetime of the multi-phase degradation process with abrupt jumps at the change points under the concept of the first passage time (FPT). Firstly, a multi-phase degradation model with jumps based on the Wiener process is formulated to describe the multi-phase degradation pattern. Then, we attain the lifetime's closed-form expression for the two-phase model with fixed jump relying on the distribution of the degradation state at the change point. Furthermore, we continue to investigate the lifetime estimation of the degradation process with random effect caused by unit-to-unit variability and the multi-phase degradation process. We extend the results of the two-phase case with fixed parameters to these two cases. For better implementation, a model identification method with off-line and on-line parts based on Expectation Maximization (EM) algorithm and Bayesian rule is proposed. Finally, a numerical case study and a practical example of gyro are provided for illustration.
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State-of-Health (SOH) is an intuitive reflection to the capacity during the degradation of lithium-ion batteries. Accurate SOH estimation can not only grasp the battery performance but also achieve a ...better balance between the safety and economic benefits for lithium-ion battery application system. Relaxation effect refers to the capacity regeneration phenomenon of lithium-ion batteries during long rest time. This paper mainly studies the impact of relaxation effect on the degradation law of lithium-ion batteries, and proposes a novel SOH estimation method based on the Wiener process. First, the life cycle of a lithium-ion battery is divided into three parts, i.e., the degradation process that eliminates the relaxation effect, the capacity regeneration process during the rest time, and the degradation process of the regenerated capacity. Next, the degradation model after eliminating the relaxation effect is established based on linear Wiener process, the capacity regenerated model is developed by the normal distribution, and the degradation model of regenerated capacity is established based on a nonlinear Wiener process. Then, for the degradation model based on nonlinear Wiener process, a two-step maximum likelihood estimation (MLE) method for prior parameters is proposed, and the random variables representing the personality features are updated online under the Bayesian framework. For the capacity regenerated model, a parameter estimation method based on MLE is proposed. In addition, a one-step and a multi-step SOH prediction method based on piecewise modeling are developed. Finally, the experiments are carried out based on the degradation data of lithium-ion batteries published by the NASA, and the results show that the method proposed in this paper can effectively improve the accuracy of the SOH estimation.
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