*3.6. Others/General*

Apart from aforementioned areas, a wide variety of studies can be found in fields which also related to tribology, but that were not assigned to the traditional core and are therefore not included in more detail in this review. The tribology of driven piles in clay [127], plate tectonics and earthquakes [128], or motion control [129,130] can be mentioned as examples. Nevertheless, some selected research shall be presented that did not necessarily fit into one of the upper categories but had a rather general scope. As such, already in 2002, Ao et al. [131] introduced an ANN to predict the evolution of surface topography during the wear process. The proposed approach utilized surface measurements at a finite number of time intervals during tribological experiments in a conformal block-on-ring configuration. The back-propagation ANN with sigmoid transfer functions was trained with the LM algorithm and statistical surface parameters (RMS roughness, skewness, kurtosis, and autocorrelation). Together with initial surface parameters, the corresponding 3D topography in worn conditions could be estimated by surface synthesis. Thereby, good prediction quality could be achieved, especially if

the autocorrelation function did not experience stronger changes. So, this was not just about predicting and optimizing target variables but was rather already a step towards semi-physical modeling. Thereby, the usage of ML/AI in the field of tribology may not be limited to forward approaches, which predict the tribological behavior based on some input data sets in the context of an experimental design. Accordingly, Haviez et al. [132] later developed a modified ANN model, which was used to solve actual physical equations describing the phenomena of fretting wear. Interestingly, this eliminated the necessity for iterative learning, e.g., by back propagation, or other regularization techniques. Thus, the fretting wear damage could be predicted with higher efficiency and accuracy than by a conventional back propagation ANN trained with experimental data, highlighting the ability of generalization albeit the rather low level of complexity. Similarly, Argatov and Chai [133] suggested an ANN-based modeling framework for analyzing the dry sliding wear during running-in from pin-on-disk tribometer tests. The authors attempted to derive the true wear coefficient instead of the specific wear rate at given conditions, contact pressures and sliding velocities. This was based upon the integral and differential forms of the Archard's wear equation as well as single-hidden layer ANN with sigmoid transfer functions. They applied their approach to various data from the literature ranging from cermet coatings, zirconia reinforced aluminum hybrid composites to nickel–chromium alloys and reported good efficiency and agreement. Very recently, Almqvist [134] derived a physics informed neural network (PINN) to solve the initial and boundary value problems described by linear ordinary differential equations and to solve the second order Reynolds differential equation. Thereby, comparable results to analytical solutions were obtained. The advantage of the present approach is not in accuracy or efficiency, but in the fact that it is a mesh-free method that is not data-driven. The author hypothesized that this concept could be generalized in the future and lead to a more accurate and efficient solution of related but nonlinear problems than the currently available routines.

Finally, two papers shall be highlighted that addressed other approaches than ANNs and/or other scales as well. Bucholz et al. [135] used a dataset from dry sliding pin-on-disk tests with different ceramic pairings having different intrinsic properties and inorganic minerals to develop a predictive model. The latter was generated by the recursive partitioning method, resulting in a graphical expression of the classification of observations according to similarities determined by variable importance in projection and the error some of squares. The obtained regression tree as illustrated in Figure 7a) demonstrated a satisfactory coefficient of determination above 0.89 when comparing prediction and experiment (Figure 7b). Finally, Perˇcic et al. [136] recently trained various ML/AI approaches to predict the nanoscale friction of alumina (Al2O3), titanium dioxide (TiO2), molybdenum disulphide (MoS2), and aluminum (Al) thin films in dependency of several process parameters, including normal forces, sliding velocities, and temperature. The data were acquired by lateral force microscopy (LFM) within a centroidal Voronoi tessellation (CVT) design of experiments, whereas 2/3 of the data were generally used for training and 1/3 for validation. The study employed MLP ANN, random DT and RF, support vector regression (SVR), age-layered population structure (ALPS), grammatical evolution (GE), and symbolic regression multi-gene programming (SRMG). The suitability for predicting the frictional force for these approaches was further evaluated with respect to the mean absolute error, the root mean squared error and the coefficient of determination. Thereby, the SRMG model showed the best performance with prediction accuracies (determination coefficient) between 72% and 91%, depending on the sample type. This allowed to derive simple functional descriptions of the nanoscale friction for studied variable process parameters.

**Figure 7.** Dendrogram for the COF estimation from recursive partitioning (**a**) and comparison between experimental and predicted values (**b**). Redrawn from [135] with permission (Springer).

#### **4. Summary and Concluding Remarks**

Tribology naturally involves multiple interacting features and processes, where machine learning and artificial intelligence approaches are feasible to support sorting through the complexity of patterns and identifying trends on a much larger scale than the human brain is capable of. Computers are able to fit thousands of properties, which enables for a much wider search of the available solution space and allows quantitative fits to a broad range of properties. Predictions do not have to be limited to averaged or global values/outputs but could also cover locally and timely resolved evolutions and bridge the gap between different scales. Therefore, ML and AI might change the landscape of what is possible going beyond the mere understanding of mechanisms towards designing novel and/or potentially smart tribological systems. As is also evident from the quantified survey, ML has hence already been employed in many fields of tribology, from composite materials and drive technology to manufacturing, surface engineering, and lubricants. The intent of ML might not necessarily be to create conclusive predictive models but can be seen as complementary tool to efficiently achieve optimum designs for problems, which elude other physically motivated mathematical and numerical formulations. We assume that, besides the availability of larger amounts of experimental data, this is the reason for the comparatively large number of investigations on composite materials.

The challenge is that a ML approach does not necessarily guide towards the specific problem solution and the selection as well as optimization of a qualified algorithm is of decisive importance. Accordingly, there is a wide variety of approaches that have already been successfully applied to answer tribological research questions. A summary is provided in Table 6, which is—together with Tables 1–5—intended to support researchers in identifying initial selections.


**Table 6.** Overview of ML approaches successfully applied in various areas of tribology.

Apparently, a large share of the research discussed in this article (roughly three quarters) was based on ANNs. However, even still, there are manifold possibilities concerning architecture, training algorithms, or transfer functions. Other ML approaches are still less commonly used for tribological issues but are justifiably coming more into focus and can be more effective for some problems. The reproducibility and comparability of the prediction quality from the various approaches and studies is frequently hampered by the sometimes ambiguous underlying database and the lack of information on the implementation of ML approaches withing publications as well as the use of different error/accuracy measures. Most of the works also comprised forward ML models, which were developed to predict the tribological behavior as output based on various input parameters such as material or test conditions. In principle, however, inverse models to characterize the materials and surfaces [54] or physics-informed ML approaches [134] can also be applied. With a closer assessment of the intentions and objectives of the studies, as well as the overrepresentation of ANNs, one might get the impression that ML is in many cases being used to serve its own ends. The added value compared to physical modeling or statistical evaluation based on more classical regressions is not always evident. A few studies, however, manage to extract real insights and thus additional knowledge from a large and broad database. The comprehensive works in the field of composite materials from Kurt and Oduncuoglu [52], Vinoth and Datta [53], and Hasan et al. [63,64] utilizing literature-extracted databases may be highlighted here and can serve as excellent examples. The current showstopper is still the availability of sufficient and comparable datasets as well as the handling of uncertainties regarding test conditions and deviations. In this respect, we would like to encourage authors to also publish the underlying databases and the corresponding models in appendices or data repositories. Moreover, there is great potential to automatize and optimize the data acquisition and processing, which is presently still very manual in the field of tribology, in order to unfold the knowledge already available in institutes, enterprises or in the literature by means of machine learning.

**Author Contributions:** Conceptualization, M.M.; methodology, M.M. and S.T.; formal analysis and investigation, M.M. and S.T.; data curation, M.M.; visualization, M.M.; writing—original draft preparation, review and editing, M.M. and S.T. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data on the quantitative evaluation are available upon request from the corresponding author.

**Acknowledgments:** The authors kindly acknowledge the continuous support of Friedrich-Alexander-University Erlangen-Nuremberg (FAU) and University of Bayreuth, Germany.

**Conflicts of Interest:** The authors declare no conflict of interest.
