**1. Introduction**

Predictive maintenance has been a topic of increasing interest in research and industry over the past few years [1]. As part of predictive maintenance techniques, condition monitoring [2–4] is used to detect anomalies and to predict the health of machinery in real time. It uses both sensor data and monitoring software to establish whether a component failure is likely. While some types of failure occur gradually and can be prevented by routine examinations, sudden failures are of course very difficult to forecast. This is the reason why artificial intelligence (AI), especially machine learning (ML) techniques, has gained increasing popularity in the recent years. ML algorithms are trained to learn from the available data and help identify certain behaviours or parameters that contribute to failure with high accuracy. ML algorithms can be divided into two main groups, namely supervised and unsupervised learning [5], differing in whether prior knowledge on the expected output is considered or not. The prerequisite for supervised learning is a set of labelled training data, while unsupervised learning aims at uncovering features on its own.

In tribology research, AI has already been applied to various fields, including inprocess tool condition monitoring [3], anomaly detection [6–8], failure prediction [9], classification of the lubrication regime [10], optimisation of tribological performance of copper composites [11], as well as AI-based lubricant design [12]. Deshpande et al. [13] give a good summary of the most common machine learning algorithms used in the classification of tribological states of operation and prediction of wear, depending on the

**Citation:** Prost, J.; Cihak-Bayr, U.; Neacs,u, I.A.; Grundtner, R.; Pirker, F.; Vorlaufer, G. Semi-Supervised Classification of the State of Operation in Self-Lubricating Journal Bearings Using a Random Forest Classifier. *Lubricants* **2021**, *9*, 50. https://doi.org/10.3390/ lubricants9050050

Received: 26 March 2021 Accepted: 30 April 2021 Published: 4 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

application. Classical ML techniques, such as Support Vector Machine (SVM) [3,6,14], Random Forest (RF) [9,15] and Radial Base Function (RBF) methods [16] are widely used. An approach for fast bearing fault diagnosis in rolling elements, combining traditional pattern recognition methods with meta-heuristic search and ML, was presented by Sun et al. [17]. Additionally, deep-learning techniques based on Artificial Neural Networks (ANN) have gained increased popularity over the past few years [10,18,19]. The recently published article by Rosenkranz et al. [20] gives a comprehensive overview of the various application fields and methods in tribology and shows the extended use of AI and ML techniques in the field of tribology as a future perspective.

Acoustic emission (AE), both airborne [8] and structure-borne [9,14], have proven to provide well-suited datasets for training ML algorithms. Other datasets used in tribologyrelated applications include torque [10] and force [2] data, accelerometer signals [21], as well as images of worn tool surfaces [22]. Thermal imaging has also been applied successfully to fault diagnosis [23].

RF classifiers may have a slightly lower prediction accuracy compared to ANN-based classifiers. However, ANN algorithms require careful parameter tuning and large training datasets. RF classifiers already give good prediction accuracy without or with little fine tuning of their hyperparameters. This makes RF models very suitable for industrial use, as they are easier to adopt for specific applications [24].

In general, self-lubricating sliding elements are composed of porous sintered materials filled with a lubricant [25]. Often, the bearing itself is made out of a porous material, such as sintered metal compounds [26–28] or oil-bearing self-lubricating layers [29], as well as polymer composites [30]. Another variant of self-lubricating elements is the use of solid lubricants as coatings, e.g., PTFE in roller bearings [31].

In contrast, the bearings used in this study consist of a base material equipped with a grid of bores, which are filled with a porous polymer compound infiltrated with lubricant. This kind of bearing is common in industrial applications. However, scientific literature on these specific systems is not very widely available; e.g., [32,33], information on this topic is often restricted to company-owned empirical know-how. Consequently, precise knowledge of the main acting mechanisms has not been reported publicly. It is assumed that the variety of commercially available products is based on proprietary know-how and engineering experience.

In 2007, Jisa [34] performed a fundamental review and studied sliding elements in the shape of plates and bearings with different copper-based alloys forming the supporting structure. Jisa has shown that the thermal expansion of the liquid lubricant in the gap between the two sliding components, assisted by capillary effects of the pore and surface topography structures, determine friction levels and lifetime. Generally, the lubricating effect is assisted by a moderate rise of temperature, as the bearing is most likely to operate in boundary or mixed friction conditions. This made a stepwise increase of loading necessary during the run-in phase of the experiment, as a too-high temperature would lead to inferior lubrication due to lower oil viscosity, resulting in adhesive wear and finally end of lifetime by increase of the friction force up to the limit of the specific machine.

For axial sliding operation conditions as studied in the current work, wear is predominantly taking place at the bearing edges and at the edges of the lubricant macrodepots. The wear debris generated at these positions causes abrasive wear in the whole contact zone, leading to gradually growing grooves. As long as the lubricant macrodepots are in contact with the counterbody, these grooves are no lifetime-limiting feature, and most of the wear debris particles are quickly transported out of the contact zone. The re-disposition of wear debris particles into the lubricant macrodepots may lead to a temporary strong increase of the friction force. These events occur rather statistically, accompanied by friction peaks, but they do not result in permanent damage of the lubricant macrodepots and eventually the removal of the loosened wear debris from the sliding contact. Due to these mechanisms, this type of bearings shows self-recovery effects [34].

The judgment of critical operation and useful remaining lifetime in industrial applications relies on specific experience and empirical data exhibiting large variance. The system studied in this work is interesting for application of ML techniques to explore the opportunities of ML for a self-recovering complex tribological system.
