To prevent unexpected failures of complex engineering systems, multiple sensors have been widely used to simultaneously monitor the degradation process and make inference about the remaining useful life in real time. As each of the sensor signals often contains partial and dependent information, data-level fusion techniques have been developed that aim to construct a health index via the combination of multiple sensor signals. While the existing data-level fusion approaches have shown a promise for degradation modeling and prognostics, they are limited by only considering a linear fusion function. Such a linear assumption is usually insufficient to accurately characterize the complicated relations between multiple sensor signals and the underlying degradation process in practice, especially for complex engineering systems considered in this study. To address this issue, this study fills the literature gap by integrating kernel methods into the data-level fusion approaches to construct a health index for better characterizing the degradation process of the system. Through selecting a proper kernel function, the nonlinear relation between multiple sensor signals and the underlying degradation process can be captured. As a result, the constructed health index is expected to perform better in prognosis than existing data-level fusion methods that are based on the linear assumption. In fact, the existing data-level fusion models turn out to be only a special case of the proposed method. A case study based on the degradation signals of aircraft gas turbine engines is conducted and finally shows the developed health index by using the proposed method is insensitive for missing data and leads to an improved prognostic performance.

In condition monitoring, multiple sensors have been widely used to simultaneously collect measurements from the same unit to estimate the degradation status and predict the remaining useful life. In this paper, we propose a generic framework for multisensor degradation modeling, which can be viewed as an extension of the degradation models from one-dimensional space to multi-dimensional space. Specifically, we model each sensor signal based on random-effect models and characterize failure events by a multi-dimensional failure surface which is an extension of the conventional definition of the failure threshold for a single sensor signal. To overcome the challenges in estimating the failure surface, we transform the degradation modeling problem into a supervised classification problem, where a variety of classifiers can be incorporated to estimate the degradation status of the unit based on the underlying signal paths, i.e., the collected sensor signals after removing the noises. As a result, the proposed method gains great flexibility. It is also capable for sensor selection, able to handle asynchronous sensor signals, and easy to implement in practice. Simulation studies and a case study on the degradation of aircraft engines are conducted to evaluate the performance of the proposed framework in parameter estimation and prognosis.

To monitor the degradation status of units and prevent unexpected failures in engineering systems, health index (HI)-based data fusion technologies have been rapidly developed by combining multiple sensor signals, which are helpful to understand the degradation processes of units and predict their remaining useful lifetime (RUL). Although promising, existing HI-based data fusion models for degradation modeling are still limited due to the restrictive assumptions made during the fusion or the degradation modeling processes, e.g., assuming the fusion model as a linear or kernel-based function from multiple sensor signals, or modeling the degradation process by a preselected basis function. Such assumptions are often invalid in industrial practice and may fail to accurately characterize the complicated relationships between multiple sensor signals and the underlying degradation process. To address the issue, this article proposes a generic indirect deep learning method that constructs an HI by combining multiple sensor signals to better characterize the degradation process. In particular, our innovative idea is to seamlessly integrate a deep neural network (DNN) and a long short term memory (LSTM) model to construct the HI by fusing multiple sensor signals and characterize the degradation process, which can be applied to the degradation modeling of various engineering systems. Domain knowledge including the concept of failure threshold and monotonicity of the degradation process is also considered to enhance the interpretability of the proposed method. For parameter estimation, we develop an indirect gradient descent (IGD) algorithm to train the proposed method. Simulation studies and a case study on the degradation of aircraft gas turbine engines are presented to validate the performance of the proposed method. Note to Practitioners —The article aims to develop a generic health index (HI)-based data fusion method for degradation modeling when multiple sensors are available to monitor the degradation status of a unit. Specifically, the developed method addresses two challenging questions in practice: 1) how to effectively combine multiple sensor signals to construct an HI that accurately characterizes the underlying degradation status and 2) how to flexibly model the degradation evolution based on the constructed HI. To implement this method in practice, four steps are included as follows: First , collecting multiple sensor signals and failure time of historical units. Second , constructing the HI and describing the underlying degradation process by training a deep neural network (DNN) model and a long short term memory (LSTM) model, respectively. Third , estimating model parameters using the proposed IGD algorithm. Fourth , constructing the HI of in-service units and predicting their remaining useful lifetime (RUL) using the constructed HI. The proposed method is expected to be able to characterize various degradation processes and be applied to the degradation modeling of different engineering systems.