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Remaining useful life ( RUL ) estimation approaches on the basis of the degradation data have been greatly developed, and significant advances have been witnessed. Establishing an applicable degradation model of the system is the foundation and key to accurately estimating its remaining useful life. Most current researches focus on age-dependent degradation models, but it has been found that some degradation processes in engineering are also related to the degradation states themselves. In addition, due to different working conditions and complex environments in engineering, the problems of the unit-to-unit variability in the degradation process of the same batch of systems and actual degradation states cannot be directly observed will affect the estimation accuracy of the remaining useful life. In order to solve the above issues jointly, we develop an age-dependent and state-dependent nonlinear degradation model taking into consideration the unit-to-unit variability and hidden degradation states. Then, the Kalman filter ( KF ) is utilized to update the hidden degradation states in real time, and the expectation-maximization ( EM ) algorithm is applied to adaptively estimate the unknown model parameters. Besides, the approximate analytical remaining useful life distribution can be obtained from the concept of the first hitting time. Once the new observation is available, the remaining useful life distribution can be updated adaptively on the basis of the updated degradation states and model parameters. The effectiveness and accuracy of the proposed approach are shown by a numerical simulation and case studies for Li-ion batteries and rolling element bearings.

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.

Remaining useful life (RUL) prediction is extremely significant to ensure the safe and reliable operation for bearing suffering from the deterioration. The main focus of the RUL prediction is to accurately predict the future failure event, and thus, how to quantify the prediction uncertainty will be a major concern. However, current deep learning based RUL prediction methods are difficult to reflect the uncertainty of the RUL prediction results. Toward this end, we propose a RUL prediction model based on the deep belief network (DBN) and diffusion process (DP) in this article. The proposed method consists of two parts: feature extraction combining DBN and locally linear embedding (LLE), DP-based RUL prediction. In the first part, DBN is used to extract deep hidden features behind the monitoring signals, and then the features with higher tendency are screened as the input of LLE. The health index that can truly reflect the bearing health condition is further determined through LLE. In the second part, a health index evolving model based on DP is presented and the probability density function (PDF) of the predicted RUL is accordingly derived in the sense of the first hitting time (FHT). As such, the proposed method holds promise to improve the prediction accuracy and facilitate the prognostic uncertainty. Finally, experimental studies on the bearing degradation data and the associated comparative analysis verify the effectiveness and superiority of the proposed method.

As the fundamental and prerequisite work of remaining useful life (RUL) prediction, degradation modeling directly affects the accuracy of RUL prediction. Existing degradation models are all developed under a single time scale, and less research has been carried out to consider the impact of multiple time scales on the degradation model. Toward this end, we mainly study a nonlinear degradation modeling and RUL prediction method for nonlinear stochastic degraded equipment with bivariate time scales in this paper. Firstly, a nonlinear degradation model considering the influence of two time scales is constructed based on the diffusion process. At the same time, the relationship between the two scales is quantitatively characterized by random proportional coefficient. Then, the analytical expressions of the life and RUL for nonlinear degraded equipment are derived under the concept of first passage time (FPT). In order to realize the adaptive estimation of parameters, the model parameters estimation method based on maximum likelihood estimation (MLE) and Kalman filtering algorithm is developed in this paper. Finally, numerical simulation and the monitoring data of gyroscope verify the effectiveness and superiority of the proposed method. The experimental results show that the method proposed in this paper can effectively improve the accuracy of RUL prediction, and has a broad engineering application space.

In the absence of sufficient degradation data of long-lifetime and highly reliable products, a step-stress accelerated degradation model based on nonlinear diffusion process is proposed to estimate the remaining useful life (RUL), with the advantage of requiring small sample size and short test time. For multiple uncertainties caused by inherent properties, individual differences, measurement equipment performance and artificial deviations in the degradation process, this model considers the temporal variability, unit-to-unit variability and measurement errors in both performance degradation and covariates. To estimate the RUL, we derive an analytical approximation to the first hitting time (FHT) of the nonlinear diffusion process crossing a predetermined threshold with the consideration of measurement errors. Based on maximum likelihood estimation (MLE), a modified simulation and extrapolation (SIMEX) method, called MLE-SIMEX, is developed for estimating unknown parameters in the established model. The usefulness of the proposed model is demonstrated by a simulation case and a real-world example. The results reveal that considering nonlinearity and multiple sources of variability in the step-stress accelerated degradation process can improve the model fitting and the accuracy of RUL estimation.

As the central component of prognostic and health management (PHM) field, remaining useful life (RUL) estimation approaches based on degradation modeling have played an extremely significant role in recent years. For the newly developed systems working in complex environments, the associated degradation processes not only lack historical data and prior information but also have strong nonlinearity and three-source variability. Therefore, this paper proposes an adaptive RUL estimation approach for the newly developed system based on a nonlinear model. Specifically, a general nonlinear Wiener-process-based degradation model is established to simultaneously characterize three-source variability and nonlinearity, and the associated RUL distribution is derived with an explicit form. In order to utilize the condition monitoring (CM) data of the service system up to date, we present a parameter estimation method based on the expectation maximization algorithm to adaptively estimate and update the model parameters online. As such, the RUL distribution can be updated once the new CM data are available. Finally, the effectiveness and superiority of the proposed method are demonstrated by the numerical example an empirical study for battery data. The results show that the proposed method can provide accurate and robust RUL prediction for the newly developed system.

For the condition-based maintenance decision of the degrading equipment, the existing methods usually only consider the impact of maintenance activities on equipment degradation rate or degradation level, ignoring the impact of shocks existing in the life cycle. Toward this end, this paper concentrates on how to make optimal maintenance decision policy for degraded equipment subjected to random shocks under imperfect maintenance. Firstly, we propose a multi-stage degradation model based on the Wiener process and incorporate the influence of shocks and maintenance into the degradation model. The remaining useful life(RUL) is predicted under the concept of the first hitting time (FHT). Secondly, we establish a condition-based maintenance decision model on the basis of the prognostic information and determine the monitoring interval and the preventive maintenance (PM) threshold. Finally, a numerical simulation is provided to substantiate the condition-based maintenance decision model proposed in the paper.

This article addresses the problem of estimating the remaining useful life (RUL) of degrading products by fusing the accelerated degradation data and condition monitoring (CM) data. The proposed model differs from the existing models in adopting the non-conjugate prior distributions for random-effect parameters. First, a nonlinear diffusion process model is developed to characterize the degradation process of a product. Next, the relationship between the model parameters and accelerated stress level is established, and the accelerated degradation data are used to determine the prior distribution types and estimate the hyperparameters in the prior distributions. Then, to fuse the accelerated degradation data and CM data, the Bayesian inference is used to update the posterior distributions of model parameters once the new degradation observations are available. In addition, the Markov Chain Monte Carlo (MCMC) method based on Gibbs sampling is used to obtain the Bayesian solution numerically. Finally, the approximate RUL distribution considering the randomness of model parameters is obtained by the MCMC method based on the concept of the first hitting time. The proposed method is verified by the practical case study of accelerometers. Comparison results demonstrate that the proposed method can obtain higher RUL estimation accuracy and less uncertainty.

SAR ship detection based on deep learning has wide application, however there exist the following three problems for SAR ship detection. Firstly, the ships in the port are seriously disturbed by the onshore buildings. The existing detection methods cannot effectively distinguish the target from the background. Secondly, the algorithm cannot accurately locate the closely arranged ship targets. Finally, the ships in SAR images have a variety of scales, and the existing algorithms have poor positioning effect on ship targets of different scales. To solve the above problems, this paper proposes an object detection network which combines attention mechanism to enhance the network’s ability to accurately locate targets in complex background. To deal with the diversity of ship target scales, we propose a loss function that incorporates Generalized Intersection over Union (GIoU) loss to reduce the sensitivity of the algorithm to scale. The proposed algorithm achieves good results for ship target detection in complex backgrounds based on the extended SAR Ship Detection Dataset (SSDD), while maintaining a fast detection speed.

Accelerated degradation testing and modeling is an effective way to predict the lifetime when the failure data are rare and the testing is costly. Under this consideration, we first proposed a novel method of lifetime estimation by integrating nonlinear accelerated degradation model and hazard rate model. Then, the parameters of acceleration model are estimated based on the accelerated degradation data, which can be used to obtain the relationship between acceleration model parameters and stresses. Further, we provide a lifetime estimation approach fusing the failure data and censored data based on Cox proportional hazards model. In addition, to facilitate the practical usage of our model, we introduce a two-step method of model identification based on MLE (Maximum Likelihood Estimation). Finally, a practical case is adopted for illustration.

Due to the environment changing, working state switch, and physical mutation, the degradation process often exhibits multi-phase feather and the random jump usually exists at the change point, which may make traditional lifetime estimation approach for single-stage degradation process unsuitable. In this paper, we concentrate on how to model the multi-phase degradation process and estimate its lifetime. Under this consideration, we firstly formulate a general degradation framework based on the multi-phase Wiener model to describe such the degradation process. Unlike traditional methods, we provide an analytical form of lifetime estimation for two-phase model with fixed jump, and a single-integral form for two-phase model with random jump via taking full advantage of the uncertainty of the degradation state at the change point. In addition, we extend these results from two-phase model to multi-phase model and obtain a general result of lifetime estimation. Finally, a numerical case is provided for illustration.

For the Optimal tracking problem of a class affine non-linear system, based on discrete-time State Dependent Riccati Equation(DSDRE), an optimal tracking sample-data control method is proposed. Moreover, the optimization is discussed with relation between HJBE and DSDRE; stability of close-loop system is investigated with Lyapunov theorem. Finally, the method is the verified in numerical simulations.

Considering bounded torque and the existence of parameter uncertainties, the trajectory tracking control of joint and the active suppression of flexible vibration for a free-floating flexible space robot (FFFSR) are discussed. Based on singular perturbation method, the FFFSR system is decomposed into a slow subsystem tracking joint trajectory and a fast subsystem describing flexible vibration. Then a combination controller including a slow and a fast control component is proposed. For the slow subsystem, an optimized control method is proposed based on State-Dependent Riccati Equation (SDRE), making it possible to optimize the performance index function constituted by the output torque and the tracking error to ensure tracking accuracy while reducing their energy consumption as much as possible. For the fast subsystem, an extended state observer is adopted to estimate the coordinate derivatives of flexible modal and uncertain disturbance that are difficult to measure, and then LQR is used to suppress the flexible vibration. The numerical simulation results show that the combination controller can suppress the flexible vibration effectively while tracking the desired joint trajectory stably with bounded torque.