Predicting the ultimate tensile strength of AISI 1045 steel and 2017-T4 aluminum alloy joints in a laser-assisted rotary friction welding process using machine learning: a comparison with response surface methodology

Welding metal alloys with dissimilar melting points makes conventional welding processes not feasible to be used. Friction welding, on the other hand, has proven to be a promising technology. However, obtaining the welded joint’s mechanical properties with characteristics similar to the base materials remains a challenge. In the development of this work, several of the machine learning (ML) regressors (e.g., Gaussian process, decision tree, random forest, support vector machines, gradient boosting, and multi-layer perceptron) were evaluated for the prediction of the ultimate tensile strength (UTS) in joints of AISI 1045 steel and 2017-T4 aluminum alloy produced by rotary friction welding with laser assistance. A mixed design of experiments was employed to assess the effect of the rotation speed, friction pressure, and laser power over the UTS. Furthermore, the response surface methodology (RSM) was employed to determine an empirical equation for predicting the UTS, and contours maps determine the main interactions. A total of 48 specimens were employed to train the regressors; the 5-fold cross-validation methodology was used to find the algorithm with greater precision. The gradient boosting regressor (GBR), support vector regressor (SVR), and Gaussian processes regressors present the highest precision with a less than 3% percentage error for the laser-assisted rotary friction welding process. The GBR and SVR capability exceed the RSM’s accuracy with a coefficient of determination (R2) greater than 90.9 versus 83.2%, respectively.


Introduction
Metal joining processes are an essential need for various industries. Proper selection of materials and procedures and safety and quality standards are important aspects in the manufacturing industry [1]. For the union of materials with different characteristics, conventional fusion welding is not feasible due to the difference between their melting points; besides, intermetallic compounds with brittle characteristics are generated [2]. Solid-state welding is a novel joining process in which two workpieces are joined under pressure, generating frictional heat, but at temperatures below the base materials' melting point [3]. Friction welding (FW) is a solid-state joining method that produces the coalescence of materials under a compressive force when workpieces rotate or move in contact with each other, producing heat and plastically displacing the material creating a welding interface [4]. Filler metal, flux, and shielding gas are not required in this process. Due to its versatility, FW has promising industrial applicability as a mass production process for joining metals [5].
Manufacturing processes in automotive and aeronautical industries require welded cylindrical elements with good mechanical properties, low specific weight, and good corrosion resistance [6]. Joining steels and other materials in fusion welding processes can have unexpected phase propagation, grain boundary corrosion, or generation of delta and sigma ferrite phases at the weld interface [7]. The use of steel and aluminum parts in rotating systems and steel structures requires developing reliable, efficient, and economic joining processes. Therefore, it is necessary to take certain precautions, such as using heat treatments or higher welding speeds, since, in this way, a certain homogeneity in the welding interface will be achieved [8]. Yilmaz, Çöl, and Acet [9] applied a preheat of approximately 900°C at the interface of a steel shaft joined to an aluminum alloy. They determined that the intermetallic layer's thickness depends linearly on the friction time's square root, which indicates that growth occurs by diffusion. Nevertheless, Winiczenko, Goroch, Krzyńska, and Kaczorowski [10] reported that the FW joints' nature is rather adhesive than diffusive for a couple of heavy weight alloy with aluminum alloy. For aluminum-aluminum joints, Campanelli, Casalino, Casavola, and Moramarco [11] found that laser treatment induces higher microhardness values and lower longitudinal residual stress on the surface of the aluminum weld zone.
The proper selection of the processing parameters influences the mechanical properties of the joints. Wang, Li, Li, and Varis [12] conclude that during the conventional rotational friction welding (RFW) process, the heat generation is mainly determined by the rotation speed, the friction pressure, and the friction time. Thus, the heating energy is minimal, especially for thin shaft welding. Wang, Qin, Geng, and Ma [13] reached a joint efficiency of 88% by continuous drive friction welding at a low friction time and high upset pressure. Li, Yu, Li, Zhang, and Wang [14] developed a friction heatassisted electric arc welding process to join austenitic stainless steel (21-4N) and martensitic stainless steel (4Cr9Si2) from 4mm-diameter valves, achieving short welding times, otherwise tough to achieve using a conventional friction welding process. When analyzing the thermo-mechanically affected area and the heat-affected zone (HAZ), they found that the plasticized area became more uniform than that achieved with the conventional RFW technique. Jabbari [15] showed that an increase in the preheating time leads to a decrease in the processing time. For joints of dissimilar materials, Kutsuna, Yamagami, Rathod, and Ammar [16] studied the laser's effect on a joint of low-carbon steel and an AA5052 aluminum alloy. They found a uniform layer of intermetallic compounds, FeAl 2 , FeAl 3 , and Fe 2 Al 5 , which are reduced by increasing welding speed. Similar results were reported by Taban, Gould, and Lippold [17] in the joining of 6061-T6 aluminum and AISI 1018 steel. Therefore, laser preheating presents many advantages; it is possible to use lower rotational speeds and friction pressures, thus reducing total welding time. Laserassisted friction welding (LAFW) has been implemented in friction stir welding (FSW), but in RFW, it has been seldom explored. Recently, Mullo, Ramos-Grez, and Barrionuevo [18] demonstrated that LAFW could increase the interlayer bonding thickness by 4-fold, accelerating the diffusion process by 25%, and thus increasing the ultimate tensile strength (UTS) of aluminum-steel bars.
On the other hand, thanks to the increase in computational power and the development of new machine learning (ML) algorithms. ML has been employed to learn information directly from the data without relying on a predetermined model [19]. Supervised ML algorithms map a function from known input-output pairs to estimate relationships between them. Some of the commonly employed ML algorithms for regression task are artificial neural networks (ANN) or multi-layer perceptron (MLP) [20], decision tree (DTR) [21], support vector machines (SVM) [22], Gaussian process (GP), ensembled methods (EM), among others. EM combines several base estimators' predictions with a given learning algorithm to produce one optimal predictive model [23] and reduce overfitting risk [24]. Some of the commonly applied EM include bagging methods, random forests (RFR) [25], and boosting methods such as AdaBoost and extreme gradient boosting regressor (XGBR) [26]. Boosting ML algorithms provides new opportunities for optimizing advanced manufacturing systems, turning weak algorithms into strong ones, while reducing bias and variance.
The applicability of ML in FW has been little explored; there are just a few publications about it, and most of them are concentrated in FSW [27]. Hartl, Vieltorf, Benker, and Zaeh [28] applied GP to predict the UTS in 6082-T6 joints of aluminum alloy processed by FSW. They concluded that GP could replace the tensile test for known materials by applying GP. The idea of replacing destructive testing with ML looks promising; however, experimentation will always be necessary to corroborate the predictions. One of the advantages of ML is that it is capable of predicting highly non-linear processes, and its application could optimize experimental designs to save material consumption and reduce the number of trials. Zhang and Xu [29] compared GP, ANN, and response surface methodology (RSM) to predict the material removal rate during the electrical discharge diamond surface grinding of Inconel-718. They recommended combined approaches to reduce experimental trials. Alternatively, Winiczenko [30] applied a hodology combining RSM and genetic algorithm to optimize the FW process's UTS. He developed a quadratic equation for the UTS prediction as a function of the friction force, friction time, and upset force. The accuracy was determined from the coefficient of determination (R 2 ). Therefore, this work will contribute to the selection of a suitable ML algorithm to predict UTS; in that sense, the first objective is to evaluate several ML algorithms to determine which one has greater precision to predict UTS in a laser-assisted rotary friction welding (LARFW) process. To achieve this goal, 48 AISI 1045 steel and 2017-T4 aluminum alloy joints produced by LARFW were subjected to a uniaxial tensile test varying the rotation speed, friction pressure, and laser power during the welding process. Second, the response surface methodology is applied to evaluate the contribution of each study parameter, and the statistical significance in the performance of UTS, the contour maps characterize the significant interactions. Finally, the ability of ML vs. RSM is evaluated by comparing the coefficient of determination.  Table 1. The mechanical properties of the base materials are presented in Table 2.

Materials and method
A laser-assisted rotary friction welding (LARFW) procedure was employed, where a conventional lathe machine was adapted to a CO 2 laser (Oerlikon OPL3500) of 3.5 kW max power, wavelength of 10.6 μm, and TEM 00 (Figure 1). The lathe has 3 HP of power, 2000 RPM of rotation speed, and a distance between centers of 1000 mm. Furthermore, a hydraulic operated pressure system has been implemented that allows pressing the friction joints at two pressure levels. The pressure mechanism consists of a 5-ton capacity hydraulic cylinder driven by a 300-cc hydraulic pump. The pressure mechanism also has a pressure gauge that allows visualizing the friction and forging pressures.
The joining process consists of preheating the steel rod for 40 s; the friction process starts until the rotational speed (N) is reached at 1600/1800 rpm, and then the axial friction pressure  Table 3.
The ASTM E-8 standard was applied to test the ultimate tensile strength of the welded specimens. The tensile test was performed using a universal testing machine (Instron 3368) with a 50-kN capacity of 0.02 s − 1 strain rate.

Design of experiments
The rotational speed and friction pressure were evaluated at two levels due to the experimental setup's limitations. The study's parameters and levels were selected from the results reported in our previous work [18]. The laser power was controlled at four levels, from no laser assistance (0 W) up to 600, 800, and 1000 W. The experiments were repeated three times for each set of parameters with a total of 48 produced specimens. The obtained results were processed statistically with Minitab 19®, where an analysis of variance (ANOVA) was conducted to analyze the main effects and their interactions to determine each factor's contribution. The main effects were defined as the mean response difference, which describes a single independent variable's action on the dependent variable (UTS).

Machine learning algorithms
Several of the most powerful algorithms were used in this study. Decision tree, random forest, support vector regression, gradient boosting, Gaussian process, and multi-layer perceptron were accurately detailed in [31]. Extreme gradient boosting regressor (XGBR) is an optimized distributed gradient boosting library designed to be highly efficient, flexible, and portable [32]. The employed hyperparameters are described in Table 4.
The computations were performed in the Google Colaboratory (Colab) environment using Scikit-learn and XGBoost libraries on a CPU Intel® Core™ i7-7700HQ 2.8 GHz, with 12 Gb of RAM installed.

Accuracy evaluation
A total of 48 samples were employed; the dataset was randomized and then split into training (80%) and testing (20%) portions. The input parameters were the rotation speed (N), friction pressure (FP), and laser power (LP), while the target value was the UTS. Before initiating the training process, the data were scaled using zero mean and unit variance. Five-fold cross-validation (CV) was employed to avoid overfitting during the training process [33]. Barrionuevo et al. [31]   introduced an index of merit (IM) to assess the prediction accuracy, which combines multiple metrics to get a unique metric of the algorithms' accuracy. As the magnitude of the index approaches zero, the lower the error is achieved. The IM is calculated in the form of Eq. (1), whose components are the coefficient of determination (R 2 ), the mean squared error (MSE), and the mean absolute error (MAE) obtained from Eqs. (2), (3), and (4), respectively.
Once it was identified which algorithm presents the higher accuracy (lower IM), feature importance (FI) analysis was employed. FI assigns a score to input features based on how useful they are at predicting a target variable (UTS). Moreover, FI provides scores that help us obtain insight into the data, and the model can improve the efficiency and effectiveness of a predictive model on the predictions.

Ultimate tensile strength evaluation
During the welding process, a flux formation around the aluminum rod was observed (Figure 2). The flash formation is mainly influenced by the friction pressure, leading to a more significant deformation of the aluminum side [34], causing a greater flash effect due to the higher mechanical pressure [17]. After the RFW process, the specimens were prepared for the tensile test. Figure 3 shows the specimens after welding, later machined for the tensile test and after the tensile test. Furthermore, it is possible to observe that the failure occurred at the welding interface. Figure 4 illustrates the range of UTS values obtained as a function of the process parameters. For the specimens manufactured by RFW without laser assistance (S1, S2, S3, and S4), the higher the friction pressure, the lower the UTS value. While for the LARFW process, the dominant parameter is laser power. The higher the laser power, the higher the UTS. For the RFW, the highest UTS value was 175.7 MPa in specimen S3. While for the LARFW, the highest UTS was 215.4 MPa, denoting the usefulness of the laser assistance.  Figure 5 illustrates the main effects of the rotational speed (N), friction pressure (FP), and laser power (LP) over the ultimate tensile strength. The main effects plot is used to observe how one or more factors influence a continuous response, here the UTS. For this study, the most statistically significant factor was the laser power. N and FP do not significantly affect the UTS value. Figure 6 summarizes the interaction effects between N, FP, and LP values for the UTS impact. The most significant effect is observed for N and LP interactions, as indicated by the curve's slope.

Statistical analysis
The analysis of variance (ANOVA) is reported in Table 5. Each factor's significance is determined using the p value; a p value of less than 0.05 indicates that the factors or their interaction are statistically significant. Therefore, FP and LP and their interactions are statistically significant. Furthermore, the rotational speed does not play a significant role in LARFW, but it influences FP interaction. An empirical equation has been derived The goodness of the model given by Eq. (5) is reported in Table 6. The coefficient of determination reaches a value   superior to 83% for the predicted UTS. Adjusted R 2 (R 2 (adj)), a modified version of R 2 , adds precision and reliability by considering the impact of additional independent variables that tend to skew the results of R 2 measurements. S is measured in the UTS units representing the variation of how far the data values fall from the true response surface. Figures 7, 8, and 9 show contour plots of the interaction between the welding parameters N, FP, and LP. Figure 7 shows that the highest UTS is obtained in the region where the highest laser power is combined with the highest friction pressure. In Figure 8, the interaction between speed and laser power is observed. It shows a quadratic response for the N as a function of LP; through the contour plot, it is possible to distinguish a range where the laser power achieves the lowest UTS (200-600 W). The interaction between rotational speed and friction pressure is depicted in the contour plot in Figure 9. In this case, the higher the speed and lower friction pressure produced the lowest UTS. While at the highest FP, and N the UTS performance was improved.
Additionally, a Pareto chart shows the standardized effect of the parameters, where the laser power contributes the most to the variability in the UTS response (Fig. 10). The reference line on the chart indicates which effects are significant. Figure 11 illustrates the ML algorithms' behavior for predicting the UTS; the vertical axis shows the predicted value and the measured value's horizontal axis. In Table 7, it is listed the metrics obtained for the CV and testing procedures. For the CV, GBR appears the most accurate algorithm with the highest R 2 , the lowest RMSE, MAE, and the corresponding lowest IM. SVR and GPs also show good performance with low IM. The remaining algorithms show lower R 2 than GBR and SVR and higher RMSE and MAE, with IMs higher than 0.5345. Almost every algorithm performance shows good accuracy; only the RFR shows poor accuracy, with the highest IM.   Figure 12 shows the performance during training and testing for the GBR algorithm. This observation provides insight into the algorithm's excellent performance for the UTS prediction in laser-assisted rotary friction welding. Figure 13 shows the feature importance analysis results, where the laser power represents the main factor for predicting the UTS. The rotation speed (N) represents less than 9.42 % of the model predictivity, friction pressure (FP) represents around 28.35 %, while laser power (P) appears to be the most significant parameter, with a score superior to 62.23%.

Feature importance analysis
The Feature Importance results agree with the Pareto chart, corroborating that the laser power represents the most statistically significant factor for the UTS prediction in laser-assisted rotary friction welding.

Conclusions
This paper evaluates several machine learning regressors to predict the UTS, resulting from a laser-assisted rotary friction welding process between 2017-T4 aluminum and AISI 1045 steel. The following conclusions can be drawn: 1) The application of the laser improves the ultimate tensile strength. For the conventional rotary friction welding process, there is an average UTS value of 119 MPa, while for the laser-assisted process, there is a UTS value of 152 MPa, which represents an increase of near to 28%. 2) The algorithms that better perform predicting the UTS were gradient boosting regressor and support vector regressor, which show the highest coefficient of determination, the lowest root mean squared error, and the lowest mean absolute error.
3) The ML algorithms' accuracy was examined through the index of merit (IM), which appears as a robust estimator since it groups three metrics in one. The lower the IM, the more accurate the algorithm predicts the UTS. GBR reported an IM = 0.3449, and SVR IM = 0.3479. 4) The empirical equation obtained through the response surface methodology explains 83.64% of the UTS performance variation, denoting the importance of the laser power factor on the UTS prediction. It is important to note that this empirical relationship only represents this particular LARFW setup and materials system used.

5)
The GBR and SVR algorithms outperform the prediction capability of the RSM, obtaining a coefficient of determination (R 2 ) higher than the RMS value.