Research articleAn automated health indicator construction methodology for prognostics based on multi-criteria optimization
Introduction
In recent years, companies facing with fierce global competition must continuously innovate to improve their performances and avoid downtime and loss of revenue. One of the levers to achieving these goals is to develop autonomous systems from the viewpoint of system health management [1]. This can be done, in the first step, by using intelligent sensors, which provide reliable solutions for systems monitoring in real time. Then, monitoring data are treated and analyzed in the second step to extract health indicators (HI) for maintenance and operation decisions.
The health indicator construction is generally based on feature engineering process. This process involves selecting relevant features in data and transforming them to generate new powerful indicators which are then used for system health management. In early studies, the principal component analysis (PCA) was proposed to find lower dimensional representation of features for condition and performance assessment [2]. However, this method, which is based on linear combination of original variables, shows its limitations when facing nonlinearities and time-varying behaviors of system degradations. Thus, numerous PCA variations were developed to handle data with nonlinearity and multi-modality properties such as Kernel-PCA, PCA-based KNN and PCA-based Gaussian mixture model [3]. Besides, other non-linear combination techniques such as Isomap or Linear Locally Embedding (LLE), which allow finding manifold embedding of lower dimensionality, are also used to extract useful features for monitoring system states [4], [5]. However, the new features created by these mentioned statistical projection methodologies are not interpretable, which can lead to a deal-breaker in some settings. In addition, they are usually used for diagnostic problem [6], [7], but rarely for prognostics issue which requires more signal processing techniques [4], [8].
Considering HI construction methods that are dedicated to prognostics domain, they can be generally classified in two groups: mathematical model based and deep learning based. For model based methods, the authors in [9] evaluate the distance between the vibration signals of degraded bearing and nominal bearing, and then smooth it by an exponential model. In [10], the authors manually chose the relevant features, and then construct the HI using a weighted average combination of the chosen features. The HI is also developed based on expertise knowledge about physical behaviors of system [1], [11] and about the relevant features used for creating effective HI [12]. In a recent study [13], the authors propose to use the multivariate state estimation method, which is a non-parametric regression modeling technique, to generate useful HI. However, the above studies are based on assumptions about degradation forms over time or the expertise knowledge about signal processing techniques, data analysis, and system behaviors. In practice, it is usually difficult to obtain these information, especially for complex systems. Then, an automatic process end-to-end is preferable. Deep learning (DL) models, that provide alternative solutions, become one of the most popular trends in recent studies. In fact, they allow automatically extracting and creating useful features by themselves without the expertise knowledge while traditional machine learning approaches require features to be predetermined by users. This ability helps users to save an important amount of work. Furthermore, they are cable of using different data formats to train models without a manual processing and still obtain useful results. Once trained properly, a DL model can perform accurately many repetitive tasks within a short time-period. Hence, in literature numerous studies develop different DL models to construct HI for prognostics. For example, the authors in [14] propose the Encoder–Decoder based on Long Short Term Memory (LSTM) while a Recurrent Neural Network (RNN) Encoder–Decoder is used in [15]. Besides, the Convolution Neural Network (CNN) is also applied to create HI using raw vibration signals [16], [17] or using time–frequency features extracted from data [18], [19]. From these studies, it can be seen that the DL models can take advantage of abundant data to automatically generate health indicators without much expert knowledge about the system. Nevertheless, the deep features created by these works are difficult to understand and cannot be interpreted as physical characteristics of the system.
Developing an automated HI construction method that requires minimal user effort and allows creating interpreted HI is challenging. In [20], the authors present a genetic programming (GP) method to automatically find the best mathematical formulation that combines low-level features to form more abstract high-level prognostic features. This method does not require any analytical knowledge about the HI formulation and is flexible in discovering new mathematical combinations of features for HI construction. The created HI, which is an explicit mathematical function of low-level features, can be interpreted for further studies. In other words, it offers the interpretability of the physical meaning of the created HI. Thanks to these mentioned advantages, GP can be considered as a promising solution to develop the automated HI construction method. However, as GP finds the optimal mathematical formulation based on the fitness function, the performance of created solutions strictly depends on the evaluation criteria. To our humble knowledge, various evaluation criteria for creating prognostics features are proposed in literature but no paper provides an insightful overview on which criteria are appropriate and when a combination of these criteria could be useful. In addition, the existing work based on GP [20] only considers low-level features, that are manually extracted using signal processing experiences of the authors, and does not construct an automated feature extraction (FE) phase with various flexible options of FE operators.
Therefore, the first contribution of this work, presented in Section 2, aims to fill the literature gap by a brief overview of the HI evaluation criteria for prognostics purpose. It also addresses an interesting question, whether the multi-criteria is necessary to create HI or a simple criterion is sufficient, through different case studies. The second contribution, that is also the main contribution, concerns the development of a new HI construction framework. In our humble knowledge, this is the first work that proposes a complete automated process from extraction of low-level features to construction of useful HI when tanking into account multi evaluation criteria. To inherit the positive properties such as the flexibility in creating new mathematical functions and the result interpretability, the proposed framework is developed based on two stage GP. The first stage aims to automatically extract pertinent low-level features from raw sensor measurements, while the second stage is dedicated to construct effective HI using the first stage’s output. An overview of the proposed framework will be presented in Section 3.1. Then, the details of the feature extraction step and the HI construction step will be respectively described in Sections 3.2 Automated feature extraction stage, 3.3 Automated health indicator construction step. Next, the performance of the proposed methodology will be examined in Section 4. Finally, the conclusion and further works will be discussed in Section 5.
Section snippets
Health indicator evaluation criteria
The choice of the appropriate criteria is essential to construct powerful HI for the prognostics purpose. Therefore, this section aims to present an overview of the HI evaluation criteria. Its main points are drawn from our comprehensive survey of the studies that developed HI in prognostics field.
In summary, according to the final objective, which is prognostics, the HI evaluation criteria can be generally classified in two principal groups. The first group only focuses on the performance
Two stage GP based automated-HI-construction methodology
The characteristics of the HI construction methods reported in literature are summarized in Table 3. Each method has its own advantages and weaknesses. To inherit the advantages and overcome the weaknesses of these methods, this work aims to develop a new methodology that allows:
- 1.
automatically extracting reasonable low-level features, and automatically combining them to form high-level abstract features;
- 2.
not requiring the expertise knowledge but facilitating its integration if available;
- 3.
taking
Real case study applications
In this section, two benchmark datasets are considered to highlight the performance of the proposed methodology that allows addressing main challenges of the automated HI constructions. The first database having different sensor measurements is dedicated to present the ability to correctly chose the relevant measurements among various sensor sources. The second one is used to show the capability to handle raw data from high-frequency sensors. These two datasets are described hereinafter.
- •
Case 1
Conclusion
In this paper, a new automated HI construction methodology based on genetic programming was presented. It is a complete process from extracting low-level features to creating effective HI for prognostics. The proposed methodology does not require any expertise knowledge about system degradation trends but allows easily integrating this information if available. Hence, it can be widely used in practical applications even for complex systems when model-based approaches are infeasible. In
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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