Discrete degradation stage modelling is faced with the challenge of identifying multiple degradation stages. Methods such as hidden Markov models [11] or Mahalanobis Taguchi System [12] are used to characterize bearing degradation stages based on observations. These approaches consider low dimensional feature vector inputs since model parameter estimation in high dimensional settings is challenging [13]. Low dimensional inputs reduce model predictive power, as information is lost when bearing vibration signal is embedded intpo lower dimensions. Our work is different from these models as we attempt to build a decision-support system that can provide a health assessment of each bearing as continuum, which serves as feature required for ranking-comparison of bearing status at any given moment. The continuous degradation is often referred as health index [14] and is typically calculated from a single feature, or a combination of features derived from bearing vibration data and fused together, using e.g., RMS [15], kurtosis values [16], power densities [17], or statistical methods [18]. A fault is detected when the health index exceeds a predefined threshold value. This is a critical decision in the system, yet setting the threshold value is not a trivial task. The work describes this body of literature and builds upon the aforementioned methods. 3. DOMAIN KNOWLEDGE The Cross Industry Standard Process for Data Mining (CRISP-DM) is a widely recognized model for data mining, which emphasizes the importance of having technical knowledge to effectively classify the results of a data science approach and its underlying process [19]. For instance, when dealing with bearing faults, having an understanding of the technical background of bearings is crucial for properly identifying, assessing and characterizing different types of faults that may occur. Therefore, this section provides an in-depth exploration of the structural components of a bearing and the various types of faults that can manifest within the bearing system Bearings consist of four essential components, namely the rolling elements, cage, inner ring, and outer ring. Rolling elements, typically steel balls, are located between the outer and inner rings and are responsible for reducing friction between moving parts as shown in Figure 1. The cage maintains the relative positions of the rolling elements, reducing friction and therefore preventing them from colliding or rubbing against each other. While a bearing fault can arise from any of the four components, approximately 90% of faults are associated with the inner and outer rings [20]. This may be attributed to the permanent stress that the rings are subjected to, whereas the rolling elements are in continuous motion, causing their contact area to continually change. In addition, the cage does not bear any load [21]. Fault can occur in three different forms [22]: A) Single-point defects, B) Multiple-point defects, C) Distributed faults. In the event of a defect occurring at a singular location on a bearing, all other components of the bearing remain in sound condition, with the exception of the specific point where the defect arises, resulting in an amplified magnitude of the characteristic frequencies associated with the particular fault type. Examples of this fault classification include the emergence of pits, spalls, and cracks on the outer and inner ring, balls, and cage of the bearing. The majority of contemporary research articles are primarily on the investigation of single point defects [23].
The term multiple-point defects refers to the occurrence of more than one single point defect in a bearing. This type of fault results in variations in the magnitude of the frequency in the frequency domain. The position of the defects can either reinforce or oppose these frequency variations [24].
Figure 1 - Structure of a rolling bearing Finally, distributed faults typically result from contamination, loss of lubrication, or coupling misalignment. These faults lead to a roughening of the bearing surface, also known as "generalized roughness". Unlike multiple-point defects, distributed faults cannot be decomposed into distinct single-point defects. As a consequence, characteristic frequencies may not be readily detectable, or they may not exist at all [25]. 4. METHODOLGY The basic scheme of a machinery health prognostic program is composed of following technical processes [26]: data acquisition, health indicator (HI) construction, health stage (HS) division. 4.1 Data acquisition Data acquisition is the procedure of acquiring and recording various types of monitoring data from a multitude of sensors that are installed on the equipment under surveillance. This crucial process serves as the initial step in machinery prognostics, and provides fundamental condition monitoring information that forms the basis for subsequent analysis. A data acquisition system consists of several components, including sensors that measure and capture data, data transmission devices that transmit the data to a storage location, as well as data storage devices that store the captured information. In order to build a predictive maintenance model, the most important data to acquire has to capture breakdown events of the equipment. However, acquiring high-quality run-to- failure data for academic research on machinery remains a challenge due to several reasons [26]. Firstly, machinery undergoes a prolonged degradation process from a healthy state to failure, which can last several months or even years. Gathering complete run-to-failure data during this extended period can be both time- consuming and expensive. Secondly, practical considerations prohibit allowing machinery to run to failure, as unexpected failure can result in machine breakdown or catastrophic accidents. This makes it difficult to capture run-to-failure data in industrial settings. Thirdly, machinery, such as gearboxes, engines or bearings, operates in harsh environments that introduce significant external interferences to monitoring data, thereby reducing its quality. Fourthly, much monitoring data are collected during out-of-service periods, such as downtime or restart, which exhibit different behaviours compared to in-service period measurements, further reducing the quality of the monitoring data. In our research, the authors reached out to all paper mills and plants within the Mondi Group, to identify where the best data were available and collaborated with local expert to ensure the highest possible quality
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