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This paper is concerned with estimating remaining useful life (RUL) for a class of stochastic degrading systems with surviving degradation paths and uncertain measurements. The motivation comes from two engineering facts: the system's degradation state is discretely monitored and the measured degradation signals are taken from a survival degradation path, i.e., its lifetime is greater than the latest observation time, and the underlying degradation state cannot be perfectly observed due to the noise, disturbance, nonideal instruments, etc. Thus, the measured degradation signals are uncertain, but related to the underlying degradation state. Toward this end, we first present a general stochastic degradation modeling approach to account for the abovementioned facts. Then, a non-Gaussian degradation state transition equation is derived considering the constraint of the survival path and thus the particle filtering algorithm is used to estimate the underlying degradation state in real time from uncertain measurements. Furthermore, we derive the RUL distribution based on the first-passage time concept which incorporates the uncertainty of the estimation for the degradation state and can be real-time updated based on the available surviving yet uncertain measurements. The novelty of this paper is to allow us to exclude the probability of failure between discrete monitoring times and to account for the impacts of surviving and uncertain measurements on estimating both the degradation state and the RUL. To apply the presented methodology, a maximum likelihood estimation framework is provided to determine the model parameters based on the expectation maximization algorithm together with particle filtering and smoothing methods. As a special case fallen into the presented framework, a linear degradation modeling and prognostic realization is discussed. Finally, we demonstrate the proposed approach by a case study. [ABSTRACT FROM AUTHOR]

• Prognosis for stochastic degrading systems with massive data is investigated. • A prognosis method is proposed from a data-model interactive perspective. • Deep health indicator extraction and model-driven prognosis are handled interactively. • The remaining life is predicted by modeling the progression of the extracted health indicator. • Advantages in the improvement of the prognosis accuracy are justified. Fast development of various advanced sensing techniques has provided the possibility acquiring massive monitoring data of stochastic degrading systems. In this circumstance, deep learning techniques have become the emerging topic in prognostics under massive data. However, the capability of quantifying the prognosis uncertainty is limited by such methods. In addition, existing studies have attempted to combine deep learning methods and stochastic degradation model based methods, but they are basically handled separately, which cannot guarantee that the extracted health indicator (HI) by deep learning method match the adopted degradation model. To address prognostic issues under massive data, this paper proposes a data-model interaction based prognostic method by constructing a closed-loop prediction mechanism between the HI extraction and degradation modeling. The main idea is to construct a novel optimization objective function related with the prognosis performance so as to establish an interactive linkage among the HI extraction, degradation modeling and prognosis. To do so, the extracted HI is hopefully matching the adopted degradation model. In the implementation process, the stacked denoising autoencoder is used to extract the HI from massive data while the Wiener process is used to model the extracted HI for prognosis. Based on the proposed interactive mechanism, these two parts are synchronously optimized. As such, the proposed method hold promise to integrate the advantages of the deep learning in handling the massive data and stochastic process method in quantifying the prognosis uncertainty. Finally, the effectiveness and superiority of the proposed method are demonstrated by a case study associated with turbofan engines. [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]