*3.5. Lubricants*

ML/AI approaches have also been used in the development and formulation of lubricants [118] and their additives [119] intended for the use in tribological systems. As such, Durak et al. [120] analyzed the effects of PTFE-based additives in mineral oil onto the frictional behavior of hydrodynamic journal bearings (252 data sets) by the aid of a feed forward back propagation ANN. An architecture with three inputs as studied in respective experiments (load, velocity, additive concentration), two hidden layers of 5 and 3 neurons, and the COF as output resulted in an accuracy of 98%. Therefore, optimal concentrations depending on the load case could be identified with rather little

experimental effort. Humelnicu et al. [121] applied an ANN to investigate the tribological behavior of vegetable oil-diesel fuel mixtures. The data were generated in pin-on-disk tests at constant conditions, whereas the concentration of rapeseed and sunflower oil was varied and the averaged COF values of five repetitions of each combination was used for further processing. The neural network was trained with a back propagation algorithm and tangential transfer functions and the architecture considered as most suitable with relative deviations between 0.2% and 2.3% was built of three hidden layers with 2, 6, and 9 neurons, respectively. Bhaumik et al. [122,123] also applied a multi-hidden layer feed forward ANN to design lubricant formulations with vegetable oil blends (coconut, castor and palm oil) and various friction modifiers (MWCNT and graphene) based upon 80 data sets obtained from four-ball-tests as well as 120 data sets from pin-on-disk tests as reported in various literature. The respective material and test conditions were also included as influencing factors. For building the ANN, hyperbolic tangent transfer functions and a scaled conjugate gradient back propagation algorithm were used. Good prediction quality was thus achieved for the 11 and 13 inputs in the four-ball- and pin-on-disk tests, respectively, with accuracies over 92%. In addition to the influences of the lubricant and material properties, significant differences were also revealed due to the test setup. In an optimization based on the ANN using a genetic algorithm, it was also possible to derive ideal lubricant formulations, the suitability of which was actually demonstrated by subsequent preparation and corresponding experimental validation. Lately, Mujtaba et al. [124] utilized a Cuckoo search algorithm to optimize an extreme learning machine (ELM) and a response surface methodology (RSM) in predicting the tribological behavior of biodiesel from palm-sesame oil in dependency of ultrasound-assisted transesterification process variables. Based on a Box-Behnken experimental design, the biodiesel yield was predicted, whereby the ELM featured a better performance than RSM, and optimized. In tribological experiments on a four-ball-tester, improved friction and wear behavior compared to reference lubricants was also demonstrated with the derived blend.

In addition to these more macro-tribological approaches, some studies can also be found that tend to target even smaller scales [125]. For example, Sattari Baboukani et al. [126] employed a Bayesian modeling and transfer learning approach to predict maximum energy barriers of the potential surface energy, which corresponds to intrinsic friction, of various 2D materials from the graphene and the transition metal dichalcogenide (TMDC) families when sliding against a similar material with the aim of application as lubricant additives. The input variables for the model in the form of different descriptors (structural, electronic, thermal, electron-phonon coupling, mechanical and chemical effects) were extracted from density function theory (DFT) and molecular dynamics (MD) simulation studies in literature. The applied Bayesian model accommodated the sparse and noisy data set and estimated the maximum energy barrier as target variable as well as its uncertainty and potentially missing data. The predictions were validated against MD simulations, whereas excellent agreement with mean squared errors mostly below 0.25 were found. Thus, the application of the ML approach not only allowed for the prediction estimation of the applicability for tribological purposes of ten previously underexplored 2D materials, but also initiated discussion on novel empirical correlations and physical mechanisms.

The works in the area of lubricant formulation are summarized in Table 5 according to the subject, the database, the inputs and outputs, and the ML approach.


**Table 5.** Overview of ML approaches successfully applied in the area of lubricant formulation.
