3.1.1. Thermoset Matrix Composites

In this way, Padhi and Satapathy [39] applied a Taguchi experimental design of experiments (DoE, 16 data points) in combination with a back propagation ANN to train multi-layered feed-forward networks, predicting the tribological behavior of epoxy composites with short glass fibers (SGF) and/or micro-sized blast furnaces slag (BFS) particles. Based on data obtained from tests in a pin-on-disk setup under dry sliding conditions against a hardened ground steel counter-body and divided into training, test and validation categories and operational and material parameters with significance for the resulting wear rate were thus identified. Thereby, the ANN was able to predict the specific wear rate with low errors between 2.5% and 6.9% for composites without BFS and between 0.9% and 5.1% for composites with BFS. Epoxy composites were also investigated recently by Egala et al. [40] with newly developed natural short castor oil fibers (ricinus communis) as unidirectional reinforcements of different lengths and at a constant volume fraction of 40%. The database consisting of 36 data points was acquired from experiments utilizing a flat pin-on-disk tribometer under dry sliding conditions against a hardened steel disk as a counter-body. Besides fiber lengths, the normal force as well as the sliding distance were varied and the influence on gravimetric wear, interfacial heat, and COF were studied within a full factorial DoE. The experiments were carried out in duplicate and averaged values were used in further data processing. Thereby, the relationships between variation parameters and target values were expressed by linear regression as well as by hidden layer ANNs. For the training of the latter, the data set was randomly split into training (60%), validation (20%), and test (20%) data. To find the best prediction, 73 different ANNs (cascade forward back propagation, feed forward back propagation and layer recurrent) with Levenberg-Marquardt (LM) training function and a varying number of hidden layers (1–4), number of neurons (7–15), and different transfer functions (Logsig, Purelin) were tested stepwise (see Figure 3a–d). It was found that the linear regressions were able to describe the results within errors of ±8%. The best predictions however were provided by a cascade forward back propagation network as well as a feed forward back propagation ANN with architectures as illustrated in Figure 3e,f using Trainlm and Purelin as training and transfer functions. Thereby, the errors were ±5% and ±4.5%, respectively,

indicating higher efficiency and reliability in predicting the tribological behavior of studied composites than common regression models.

**Figure 3.** Average total errors for the wear prediction of different ANN architectures when optimizing the transfer function (**a**), the network type and the number of neurons in the single-hidden layer ANN (**b**) as well as the network type and the number of layers (**c**) and the number of neurons in the multi-hidden layer ANN (**d**). Illustration of the architectures of the single- (**e**) and multi-hidden layer ANN (**f**) with least errors. Redrawn from [40] with permission by CC BY 4.0 (Springer).

Nirmal [41] attempted to predict the friction coefficient of treated betelnut fiber reinforced polyester composites by an ANN trained with data from 492 experimental sets of a block-on-disk tribometer against stainless steel under dry sliding conditions with varying normal loads, sliding distances and three different fiber orientations (parallel, antiparallel and normal). In trial-and-error variations of neuron, layer, and transfer function, an ANN consisting of two hidden layers with 30 and 20 neurons, respectively, trained by LM function and utilizing logsig transfer functions between the hidden layers and a pure linear transfer function to the output layer was found as most capable of predicting the COF based upon the inputs. Albeit other training algorithms (gradient descent back propagation, with momentum and adaptive learning rate, with adaptive learning rate and conjugate gradient back propagation with Powell-Beale restarts) resulted in significantly faster convergence, the LM function featured the lowest errors compared to the test data, especially after repeated training. Thus, sum squared errors (SSE) of less than 10−<sup>2</sup> were obtained. Similarly, Nasir et al. [42] identified the LM function as most suitable compared to others when training ANNs to predict the COF from 7389 data sets attained in experiments on multi-layered glass fiber reinforced polyester resin rubbing against stainless steel using a disk-on-flat tribometer under different fiber orientations, loads, sliding speeds, and test durations. The prediction model was able to reproduce the trends of the experiments well and accuracies up to 90% were achieved. It was stated, however, that performance was lower compared to other studies due to the large amount of input data as well as larger deviations and fluctuations in the experimental results, especially during running-in periods. Furthermore, it was emphasized that the number of layers as well as neurons have a decisive influence on the results. While multi-hidden layer ANNs mapped partial areas of the input data (e.g., only one fiber orientation) very well, the entire data area was best represented by a single-hidden layer ANN with comparatively many neurons.

#### 3.1.2. Thermoplastic Matrix Composites

Already in the early 2000s, Velten et al. [43,44] evaluated the ability of ANNs to predict tribological properties of short fiber thermoplastic matrix (PA) composites and aid in the

material design. Here, the decisive role of the data sets as well as the ANN architecture was emphasized as well. Later, Gyurova et al. [45] modeled the tribological behavior of PPS composites with short carbon fibers (SCF), graphite, PTFE, and titanium dioxide (TiO2) fillers with over 90 data sets obtained from dry-running pin-on-disk tribometer tests at constant test duration and varied loads and sliding speeds. The data were split into 80% training and 20% testing data and included the material composition (matrix volume fraction, filler, reinforcing agents and lubricants), testing conditions (pressure and sliding speed), as well as characteristic thermo-mechanical properties (tensile and compressive properties) as inputs and the specific wear and the friction coefficient as outputs. For the latter, separate ANNs were trained by a gradient descent back propagation algorithm with momentum and adaptive learning rate to minimize the mean relative error (MRE). These consisted of two hidden layers with 9 and 3 (wear rate) as well as 3 and 1 (COF) neurons, respectively. Thus, most significant inputs could be identified, and it was observed that the MRE for the wear rate (0.60–0.78) was higher than for the sliding friction (0.10–0.12), which was attributed to the rather small database. Furthermore, a so-called optimal brain surgeon (OBS) method was used to prune the ANN through the identification and removal of irrelevant nodes (weight elimination). The architectures as well as exemplary 3D profiles for predicting the wear rate in dependency of the SCF and the TiO2 content before and after pruning are illustrated in Figure 4. Apparently, both cases matched adequately with the experimental data. Besides higher computational efficiency, the pruned network featured superior prediction accuracy in some areas of the parameter space. Finally, optimal compositions with higher SCF and lower TiO2 concentrations around 10–15% as well as 3–5%, respectively, could be derived with considerably reduced experimental efforts, which corresponded well to the observations from Jiang et al. [46]. Gyurova and Friedrich [47] evaluated the influence of the data set size on the prediction capabilities of trained ANNs. Utilizing a newly measured database consisting of 124 independent pin-on-disk dry sliding wear tests on PPS matrix composites, the mean relative errors were reduced from above 0.72 to below 0.55 (specific wear rate) and from above 0.11 to beneath 0.10 (COF) compared to previous studies [45,48]. Later, the approach was further enhanced by Busse and Schlarb [49] using the same data, most notably by utilizing a LM training algorithm with mean squared error regularization as performance function, which significantly improved the computational efficiency and, in particular, the accuracy. Independently of the inputs, the wear rate prediction quality was found to be six times higher compared to the comparative studies [45,47].

Zhu et al. [50] also emphasized the crucial role of data set size and reported better agreement of experimental data with the prediction of the friction coefficient than with the volumetric wear losses when applying an ANN to carbon fiber and TiO2 reinforced PTFE. 12 Different compositions were therefore investigated in block-on-disk dry sliding tests under varying sliding velocities and normal loads. A network trained by gradient search and consisting of three hidden layers (15, 10, and 5 neurons) and tan-sigmoid transfer functions between the input and the hidden layers as well as pure linear transfer functions to the output layer was found to deliver the least mean square errors. Li et al. [51] applied a Monte Carlo-based ANN to predict the tribological behavior of PTFE resin with aramid pulp, potassium titanate whisker (PTW), mica, copper (Cu) as well as silicon dioxide (SiO2) for ultrasonic motors and compared the performance to a back propagation ANN. The database, an orthogonal table by variation of the composition, was generated from experiments conducted in triplicate on a quasi-static test rig where the specimens were fixed on a dynamic rotor and slid against a phosphor bronze stator at constant speed and load. In combination with a grey relational analysis, it was shown that especially mica and SiO2 exerted significant roles for friction and wear improvements. The Monte Carlo-based ANN was particularly suitable for predictions with more limited amount of data due to repeated random sampling and the utilization of combinations of different transfer functions (sigmoid, polynomial, tanh, and gauss functions). The authors reported that, in the context of the variation and volatility of the underlying data, the Monte Carlo ANN

performed better than the conventional back propagation ANN with root mean squared errors of 0.97 (specific wear rate) and 0.007 (COF) compared to 2.08 and 0.019.

**Figure 4.** ANN architecture as well as 3D profiles for the specific wear rate in dependency of the SCF and the TiO2 concentration without (**a**) and with (**b**) pruning. Redrawn from [45] with permission (Elsevier).

Kurt and Oduncuoglu [52] utilized 125 data sets extracted from established literature sources to study the effects of normal load and sliding speed in dry sliding experiments as well as the type and weight fraction of various reinforcements in ultrahigh molecular weight PE (UHMWPE) composites by a feed forward back propagation ANN. This involved zinc oxide (ZnO), zeolite, carbon nanotubes (CNT), carbon fibers (CF), graphene oxide (GO), and wollastonite additives, leading to a total number of 11 inputs, whereas the volumetric wear loss was considered as target/output value. In a trial-and-error search, an ANN with a single-hidden layer consisting of 12 neurons and logistic sigmoid transfer functions trained by a LM algorithm was selected. With *R*<sup>2</sup> values for training and testing above 0.8 as well as mean absolute errors not exceeding 4.1%, it was thus shown that sliding speed and load determined the wear losses more significantly than the particle types and fractions. Recently, Vinoth and Datta [53] also used 153 experimental data sets from literature to predict mechanical properties of UHMWPE composites with multi-walled carbon nanotubes (MWCNT) and graphene reinforcements in dependency of seven input variables comprising composite composition, particle size, and mechanical bulk properties. A feed forward ANN with scaled conjugate gradient back propagation, hyperbolic tangent transfer functions and 3 (for Young's modulus) or 5 (for the ultimate tensile strength) hidden layers were utilized, achieving correlation coefficients for the outputs of 0.93 and 0.97, respectively. Subsequently, a multi-objective (pareto) optimization of the input variables was performed with a non-dominated sorting genetic algorithm. On this basis, samples (pins) of UHMWPE composites with MWCNT and graphene filler ratios considered as optimal were fabricated accordingly and characterized mechanically as well as in tribological tests under dry sliding conditions against cobalt chromium alloy disks. It was actually possible to demonstrate improved properties compared to references and, in particular, excellent wear behavior due to the formation of wear-protecting transfer films on the counter-body.

#### 3.1.3. Metal Matrix Composites

Some successful studies using ML and AI can also be found for composites with soft metals as matrix [54], for example aluminum, copper or zinc and their alloys [55–59]. As such, Stojanovi´c et al. [60] investigated the friction and wear behavior of aluminum hybrid composites with Al-Si alloy matrix and 10 wt.% silicon carbide (SiC) as well as 0, 1, and 3 wt.% graphite. The data sets were generated in lubricated block-on-disk tribometer tests at three sliding speeds, the normal loads and at constant sliding distance with the application of Taguchi's robust orthogonal array design method (27 data points). This was reported to be a simple and efficient methodology. Besides performing ANOVA factor variance analysis and the fitting of a linear regression model, a feed forward back propagation

ANN was developed. Therefore, 70% of the data were used for training, 15% for testing and 15% for validation. The model was trained by LM optimization and consisted of two hidden layers of 20 and 30 neurons, respectively, as well as logarithmic sigmoid and pure linear transfer functions. The values predicted by the ANN provided sufficient agreement with the experiments and were more precise than those provided by the statistical methods used. Similarly, Thankachan et al. [61] compared the performance of a feed forward back propagation ANN with statistical regression analysis when investigating the wear behavior of hybrid copper composites with aluminum nitride and boron nitride particles in dry-running pin-on-disk tribometer tests at different volumetric fractions, loads, sliding speeds and sliding distances by applying Taguchi's orthogonal array. The ANN featured the 4 inputs, one hidden layer with 7 neurons, the specific wear rate as output and was trained by the LM function to optimize the mean absolute error. Thus, the neural network reached higher accuracy than the reference regression model.

Gangwar and Pathak [62] introduced a novel improved bat algorithm (IBA) to train an ANN for predicting the wear behavior of marble dust reinforced zinc-aluminum (Zn-Al) alloy by optimizing the weights, biases and neurons as well as finding minimum mean squared errors, see Figure 5a). The main advantage of the IBA compared to other training algorithms (e.g., back propagation, genetic algorithms or particle swarm optimization) was in the flexibility and stable training through the introduction of a new velocity, position search equation and sugeno inertia weights. This overcame local optima stagnation and enhanced the convergence speed. The evaluation of the specific wear rate was based on data from pin-on-disk experiments with varied filler content, normal load, sliding velocity and distance, as well as ambient temperature (5 levels each) by means of a Taguchi orthogonal array (25 data sets). Thereby, an ANN with 7 neurons in the single-hidden layer was found to be optimal, with a mean squared error of 0.26 and an average prediction accuracy of 97%. Exemplary 3D plots of the wear rate as a function of the variation parameters are shown in Figure 5b). Obtained results and the suggested IBA-ANN approach can thus help to save resources when searching for beneficial stress or material combinations with limited experimental database.

**Figure 5.** Schematic representation of encoding bat individuals to train the ANN (**a**) as well as 3D response surfaces of influencing factors on the specific wear rate (**b**). Redrawn from [62] with permission (Elsevier).

Very recently, Hasan et al. [63,64] compared five different ML techniques when predicting the friction and wear behavior of aluminum base alloys and graphite composites: ANN, kNN, SVM, gradient boosting machine (GBM), and RF. The 852 data sets were obtained from experimental studies in literature. It was shown that basically all ML approaches

were able to adequately describe the tribological behavior from material and tribological test data. Thereby, RF outperformed the other algorithms in predicting the wear behavior, while GBM and KNN had the highest accuracy for the friction behavior for the base alloy and the composite, respectively. This underlines that the right choice of the ML approach is highly dependent on the respective problem formulation.

The works in the area of composite materials are summarized in Table 1 according to the subject, the database, the inputs and outputs, and the ML approach.
