**1. Introduction**

Modern machines with rotating components tend to use rolling bearings for their bearing arrangements. For reasons of energy efficiency and limited design space, the bearings are laid out as small as possible, which can lead to them being operated at the limits of their durability. An unforeseen failure of a bearing can cause considerable damage to the entire machine and its environment. Especially in the case of safety-relevant systems, an unforeseen failure must be avoided in any case. In order to prevent such unforeseen failures, condition monitoring and predictive maintenance are becoming increasingly important [1]. Condition monitoring involves using suitable sensors to record measurement data during operation, which is then processed to draw conclusions about the condition of the component [2]. If the condition is judged to be critical in this process, corrective actions such as maintenance can be planned. To be able to carry out such planning with as little risk as possible, it is essential to estimate the remaining useful life (RUL) of components [3].

Rolling bearing damage can occur in various ways. The damage can be caused by lack of lubrication, short-term overload or material fatigue due to long-term stress. Material fatigue usually manifests itself in the form of propagating pitting within the raceway surfaces [4]. Recently, for bearing damage detection, traditional condition monitoring methods have been increasingly combined with Artificial Intelligence (AI). Machine learning (ML), as a subfield of AI, plays an essential role here. ML algorithms can be used to recognize complex structures in data and to evaluate these structures [5]. This offers the possibility of automated inference from the data. Applied to the challenge of RUL prediction, these are

**Citation:** Bienefeld, C.; Kirchner, E.; Vogt, A.; Kacmar, M. On the Importance of Temporal Information for Remaining Useful Life Prediction of Rolling Bearings Using a Random Forest Regressor. *Lubricants* **2022**, *10*, 67. https://doi.org/10.3390/ lubricants10040067

Received: 14 February 2022 Accepted: 7 March 2022 Published: 14 April 2022

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approaches to automatically draw conclusions about the RUL from the data measured at the component. Among the machine learning algorithms used for RUL predictions there are different variants of neural networks, such as convolutional neural networks (CNN) [6], recurrent neural networks (RNN) [7], long short-term memory (LSTM) [8], and generative adversarial networks (GAN) [9]. Furthermore, there are contributions to state detection using random forest algorithms [10]. Machine learning is therefore becoming increasingly relevant, not least in the field of tribology [11].

When using machine learning, the achievable prediction quality is highly dependent on the type and quality of the data as well as the preprocessing used. Targeted data preprocessing has a significant impact on both the achievable prediction accuracy and the computational speed of the implemented algorithms [12,13]. In the context of rotating machinery, the measurement of structure-borne sound has proven particularly useful for drawing conclusions about the components' condition [14–16]. Therefore, the present article will also use structure-borne sound measurements to investigate the condition of rolling bearings and to predict their RUL.

Recent approaches for predictive maintenance based on electrical impedance measurements of rolling bearings can complement or even replace structure-borne sound measurements with in situ information [17]. The quality of the underlying model is continuously increased by considering unloaded rolling elements and modeling the detailed rolling contact geometry [18]. ML approaches are used to further enhance the predictive capabilities [19].

In a previous paper presented by the present authors, the influence of feature engineering on condition monitoring of rolling bearings was shown using a random forest regressor [20]. A feature engineering approach is presented in the previous work, which, compared to features from Lei et al. [21], achieves particularly good results in structureborne sound-based condition detection. Based on these results, the feature-engineering approach is optimized and extended in this study regarding the prediction of remaining useful life. The aim is to develop a methodology that leads to a RUL prediction model with high accuracy and good traceability. Therefore, the investigations are focused on feature engineering and the consideration of information from the temporal past. In order to predict the RUL of rolling bearings, a methodology based on a random forest condition regression is presented.

#### **2. Materials and Methods**

To evaluate the developed feature engineering methods in the context of RUL predictions, a methodology in which all other model components and their parameters remain constant as boundary conditions is used. The approach used for this purpose is illustrated in Figure 1. The individual model parts are described in more detail within the subsequent sections.

**Figure 1.** Overview of the methodology used.
