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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]

This paper addresses the problem of how to estimate the remaining useful life (RUL) for partially observed linear stochastic degrading systems with survival measurements. The motivation of this paper arises from two engineering facts—the measured degradation signals are taken from a survival degradation path and the degradation progression of the system is inevitably affected by multisource variability. To do so, we first revisit the linear degradation modeling framework driven by the Wiener process to account for the above two facts, and a new state-space model with non-Gaussian state transitions is constructed based on the constraint of survival measurements. Then, the particle filtering algorithm is applied to real-time estimate the non-Gaussian degradation state and random-effect parameter from measurements. Furthermore, we derive the probabilistic distribution of the RUL which can be real-time updated based on the available measurements. To apply the presented method, a two-stage estimation procedure based on particle expectation maximization algorithm is presented to determine and update the model parameters. The novelty of the presented method is to exclude the probability of failure before the current monitoring time and account for both impacts of the multisource variability and surviving degradation path on the RUL estimation. Finally, we demonstrate the proposed approach by a case study on gyros in the inertial platform. [ABSTRACT FROM AUTHOR]

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]

Condition-based maintenance for a degrading system has been attached great importance in reducing unexpected failures and enabling the safe operation of the system. In this paper, we consider a condition-based replacement problem with observed degradation signals for the determination of the optimal replacement time of the system. The observed degradation signals contain some health related information of the system so that the system's health state may be more accurately estimated and the future degradation progression of the system can be predicted. Based on the predicted degradation state, the concerned replacement problem is formulated in the framework of the Markov decision process and then a new degradation-modeling framework based on maximum likelihood estimation is proposed to analyze the degradation signals and to predict the future degradation state of the system. To solve the proposed condition-based replacement decision problem, we analyze structural properties of the optimal replacement policy and an optimal monotonic control limit solution policy is developed for condition-based replacement. Finally, a case study is provided to illustrate the proposed optimal replacement method. [ABSTRACT FROM AUTHOR]

Reliability estimation is central to enhance safety, availability, and effectiveness of phased-mission systems (PMSs). With the development of information and sensing technologies, condition monitoring (CM) data are now available in many real-world PMSs, and then a more interesting question: how can we dynamically estimate the reliability of PMSs using the in-situ CM data, is of considerable significance to industrial practitioners. In this paper, using the CM data and degradation data of PMS, we present a novel condition-based approach to resolve this question under dynamic operating scenarios. This paper differs from most existing methods which only consider the static scenario without using real-time information, and estimate the reliability only for a population of PMSs but not for an individual PMS in service. To establish a linkage between the historical data and real-time data of the individual PMS, a stochastic filtering model is first utilized to model the phase duration. As such, the updated estimation of the mission time can be obtained by Bayesian law at each phase. To account for the dependency of the degradation progression of PMS on the mission process, the degradation process of PMS is modeled by a Brownian motion with a mission phase-dependent drift coefficient. The corresponding lifetime is derived and the lifetime distribution of PMS can be updated under Bayesian framework once new information is available. Unique to this paper is the union of the CM data and degradation data of PMS to real-time estimate the mission reliability through the estimated distribution of the mission time in conjunction with the estimated lifetime distribution, in which the estimated lifetime considers the dependency of the degradation rate of PMS on mission phase. The effectiveness of the proposed approach is verified by a numerical simulation and a case study. [ABSTRACT FROM PUBLISHER]

• 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]