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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. [ABSTRACT FROM AUTHOR]

• An age- and state-dependent nonlinear degradation model is proposed for prognosis. • Nonlinearity between measurements and hidden degradation is characterized by a state space model. • Extended Kalman filtering and expectation-maximization algorithm are jointly applied to update the model. • Analytical distribution of remaining useful life is derived and updated for online prognosis. • Advantages in the prognosis accuracy are justified by numerical example and case study. To deal with age- and state-dependent degradation, unit-to-unit variability and partially observable or hidden degradation in remaining useful life prediction jointly, this paper proposes a condition-based prognostic approach for age- and state-dependent partially observable nonlinear degrading system. The dynamics and nonlinearity of the system degradation process are described by the age- and state-dependent nonlinear diffusion process. The nonlinear relationship between observations and the hidden degradation state is characterized by a state space model. To derive the distribution of the remaining useful life, we apply the extended Kalman filtering and expectation-maximization algorithm to adaptively estimate the degradation states and the unknown model parameters. Based on the estimated degradation states and model parameters, we derive the approximately analytical distribution of remaining useful life in the concept of the first hitting time. Furthermore, the distribution of remaining useful life can be updated according to the newly available data, thereby realizing real-time remaining useful life estimation. An illustrative example is given to explain the application of the proposed approach in the specific age- and state-dependent nonlinear degradation model. Finally, a numerical example and a case study for bearing degradation data are presented to verify the accuracy and effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

• Prognosis for multi-sensor monitored stochastic degrading devices is investigated. • A data-model interactive prognosis method is proposed by a closed-loop feedback mechanism. • Data-driven health index construction and model-driven prognosis are handled interactively. • The model parameters and remaining useful life distribution are updated by the Bayesian method. • Advantages in the improvements of the signal quality and prognosis accuracy are justified. With advances in sensing and monitoring techniques, real time multi-sensor monitoring data of stochastic degrading devices has become the reality. How to effectively fuse these multi-sensor monitoring data to first construct the composite health index (CHI) and then model its degradation evolving process has become the emerging topic in the field of the remaining useful life (RUL) prediction. However, existing works treat the CHI construction and degradation modeling for prognostics under multi-sensor data as the disjoint problems rather than both though they are closely related in nature. To address this issue, this paper presents a novel data-model interactive RUL prediction method for multi-sensor monitored stochastic degrading devices. In the proposed method, based on the CHI extracted from multi-sensor historical data and the associated lifetime prediction via stochastic degradation modeling, an optimization objective function synthesizing the mean squared error between the predicted life and the actual life as well as the variance of the predicted life is constructed. As such, a closed-loop feedback mechanism is established for the CHI constructing and stochastic degradation modeling. Based on this feedback mechanism, the fusion coefficients for multi-sensor data and the failure threshold of the associated CHI are reversely optimized to realize the collaborative interaction between the CHI constructing and stochastic degradation modeling. To do so, the goal of making the constructed CHI automatically match the adopted stochastic degradation model can be achieved naturally. To make the degradation model accurately reflect the current reality of the in-service device, a sequential Bayesian method is proposed to update the degradation model parameters. Based on the updated model, the RUL distribution can be derived under the concept of the first passage time to achieve the prognosis. Finally, through multi-sensor data of aircraft gas turbine engines, we justify the necessity of applying the proposed method in prognosis and show its advantages in the improvements of the signal quality and prognosis accuracy. [ABSTRACT FROM AUTHOR]

• Box-Cox transformation is introduced in nonlinear degradation modeling. • Transformed degradation data are modeled by wiener process. • Two-stage estimation procedure is presented to identify the model parameters. • Closed-form remaining useful life distribution is derived for prognostics. • The proposed method is validated by degradation data of batteries and LCDs. Transforming nonlinear degradation paths into nearly linear ones has been widely used for nonlinear degradation modeling and prognostics. However, types of the current transformation functions are difficult to determine. This paper addresses issues in nonlinear stochastic degradation modeling and prognostics from a Box-Cox transformation (BCT) perspective. Specifically, the BCT is first used to transform the nonlinear degradation data into nearly linear data, and then the Wiener process with random drift is utilized to model the evolving process of the transformed data. To determine the model parameters, a two-stage estimation procedure is developed including offline stage and online stage. In the offline stage, the parameters are determined via maximum likelihood estimation method based on the historical degradation data and such estimated values are used to initialize the online stage. During the online stage, the Bayesian method is adopted to update the model parameters using the data of the degrading system in service, in which the hyperparameters are updated by the expectation maximization algorithm. A closed-form solution to remaining useful life with updated model parameters is further derived for prognostics. Finally, case studies for lithium-ion batteries and liquid coupling devices are provided to demonstrate the proposed approach. [ABSTRACT FROM AUTHOR]

• Physics-informed data-driven remaining useful life prediction methods are reviewed. • Physics-informed machine learning based prognosis methods are detailed. • Individual strengths and weaknesses of different kinds of methods are discussed. • Challenges and possible opportunities are provided to steer the future development. Remaining useful life (RUL) prediction, known as 'prognostics', has long been recognized as one of the key technologies in prognostics and health management (PHM) to maintain the safety and reliability of the system, and reduce the operating and management costs. Particularly, thanks to great advances in sensing and condition monitoring techniques, data-driven RUL prediction has attracted much attention and various data-driven RUL prediction methods have been reported. Despite the extensive studies on data-driven RUL prediction methods, the successful applications of such methods depend heavily on the volume and quality of the data, and purely data-driven methods possibly generate physically infeasible/inconsistent RUL prediction results and have the limited generalizability and interpretability. It is noted that there is an increasing consensus that embedding the physics or the domain knowledge into the data-driven methods and developing physics-informed data-driven methods will hold promise to improve the interpretability and efficiency of the RUL prediction results and lower the requirement of the volume and quality of the data. In this context, physics-informed data-driven RUL prediction has become an emerging topic in the prognostics field. However, there has not been a systematic review particularly focused on this emerging topic. To fill this gap, this paper reviews recent developments of physics-informed data-driven RUL prediction methods. In this review, current methods fallen into this type are broadly divided into three categories, i.e. physical model and data fusion methods, stochastic degradation model based methods, and physics-informed machine learning (PIML) based methods. Particularly, this review is centered on the PIML based methods since the fast development of such methods have been witnessed in the past five years. Through discussing the pros and cons of existing methods, we provide discussions on challenges and possible opportunities to steer the future development of physics-informed data-driven RUL prediction methods. [ABSTRACT FROM AUTHOR]