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An asynchronous RUL fusion estimation algorithm is presented for the hidden degradation process with multiple asynchronous monitoring sensors based on multisource information fusion. Firstly, a state-space type model is established by modeling the stochastic degradation as a Wiener process and transforming asynchronous indirectly observations in the fusion period to the fusion time. The statistical characteristics of involved noises and their correlations are analyzed. Secondly, the estimate of the hidden degradation state is obtained by applying Kalman filtering with correlated noises to the established state-space model, where the synchronized observations are fused. Also, the unknown model parameters are recursively identified based on the Expectation-Maximization (

Modern engineering systems are becoming large in scale, huge in investment, and more and more sophisticated in structure with the development of science and technology. As a result, once an accident occurs in these systems, it would cause tremendous damage and enormous loss of property [

The complexity of the system itself and the running environment makes it hard to establish a mechanism model for RUL estimation. In recent years, the RUL estimation based on monitoring data attracts a lot of research attentions due to its wide application range and the ability to quantify the uncertainties of the estimation results [

Although there are fruitful researches on RUL estimation based on stochastic modeling with monitoring data, most of works are specific to single sensor. However, the complexity of the system itself and the running environment makes the RUL prediction have large uncertainties. At the same time, the information from single source tends to be quite limited. In response to the above issues, multiple sensors are usually utilized to monitor the condition of the system in order to reduce the uncertainties of the system and improve the accuracy of the RUL estimation [

Observations from multiple sensors.

Synchronous

Asynchronous

Consequently, motivated by the above discussions, the asynchronous RUL fusion estimation problem is studied in this paper. We assume that the hidden degradation which is modeled as Wiener process with unknown model parameters is observed by an arbitrary number of asynchronous sensors, whose sampling frequencies and initial sampling times are all arbitrary. The asynchronous sensor observations are firstly synchronized to the fusion time and then fused using the Kalman filtering technology to get the fused estimate of the latent degradation state with the correlations between various noises introduced by the synchronization process analyzed. The unknown model parameters are also recursively identified using the synchronized observations based on the

The organization of this paper is as follows. The fusion estimation problem of RUL for stochastic degradation process with multiple asynchronous sensors is formulated in Section

Wiener process is widely used to model the stochastic degradation of a system attributed to its good mathematical characteristics such as the infinite separability. In general, a linear Wiener-process-based degradation model can be represented as

We assume the degradation process (

Consequently, the objective of this paper is to predict the distribution of RUL of degradation process (

From the degradation process (

From (

Then, by applying the Kalman filtering with correlated noises to the degradation process (

Firstly, the predicted estimate and its error covariance are given by

Secondly, the updated estimate and its error covariance are got by fusing the asynchronous indirect observations

Note from (

As we know, in real applications, the only information we have is the indirect observations

The joint log-likelihood function at time

As we said, the

The iteration of the

From (

In this section, a simulation example is provided to illustrate the feasibility and effectiveness of the proposed asynchronous RUL fusion estimation algorithm.

The stochastic degradation is formulated by (

The proposed asynchronous RUL fusion estimation algorithm is used to estimate the RUL of the hidden degradation process. Figure

The actual degradation path and the estimated.

In the simulation, the failure threshold

The PDFs of RUL at different time instants.

The PDFs of RUL at 36 hours.

In addition, it can be seen from Figure

Comparison of the proposed algorithm and the approach in [

In this paper, an asynchronous RUL fusion estimation algorithm has been proposed for the latent degradation process with multiple asynchronous monitoring sensors. The asynchronous indirect observations are firstly synchronized to the fusion time and then fused using the Kalman filtering technology to get the estimate of the latent degradation state with the correlations between the involved noise considered and the unknown model parameters identified by the

Due to the noise correlation introduced by the synchronization process,

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China under Grants 61304105 and 61520106009 and in part by the Fundamental Research Funds for the Central Universities of China with Grant FRF-TP-16-029A3.