A Novel Method for Predicting Tensile Strength of Friction Stir Welded AA6061 Aluminium Alloy Joints Based on Hybrid Random Vector Functional Link and Henry Gas Solubility Optimization

Aluminum alloys have low weldability by conventional fusion welding processes. Friction stir welding (FSW) is a promising alternative to traditional fusion welding techniques for producing high quality aluminum joints. The quality of the welded joints is highly dependent on the process parameters used during welding. In this research, a new approach was developed to predict the process parameters and mechanical properties of AA6061-T6 aluminium alloy joints in terms of ultimate tensile strength (UTS). A new hybrid artificial neural network (ANN) approach has been proposed in which Henry Gas Solubility Optimization (HGSO) algorithm has been incorporated to improve the performance of Random Vector Functional Link (RVFL) network. The HGSO-RVFL model was constructed with four parameters; rotational speed, welding speed, tilt angle, and pin profile. The validity of the model was tested, and it was demonstrated that the HGSO-RVFL model is a powerful technique for predicting the UTS of friction stir welded (FSWD) joints. In addition, the effects of process parameters on UTS of welded joints were discussed, where a significant agreement was observed between experimental results and predicted results which indicates the high performance of the model developed to predict the appropriate welding parameters that achieve optimal UTS.


I. INTRODUCTION
AA6061 is a precipitation-hardened aluminum alloy. It has a relatively high strength with good toughness and high corrosion resistance. Furthermore, it offers excellent weldability. Therefore, AA6061 has enormous applications, especially The associate editor coordinating the review of this manuscript and approving it for publication was Fan Zhang . in aerospace, automotive, and marine industries [1], [2]. Intensive structural applications of AA6061 such as truck roofs, side panels, and ship bodies require feasible and efficient welding techniques. Conventional fusion welding of aluminum alloys is unsuitable due to creation of intermetallic compounds, oxide layers, hot cracks in molten weld pool which consequently deteriorate the joint mechanical properties such as strength, hardness, toughness, stiffness, and ductility [3]. Friction stir welding (FSW) was first introduced by The Welding Institute, United Kingdom, in 1991, as a new joining technique [4], which initially applied for joining aluminum alloys instead of the conventional fusion welding technique [5]. FSW process has been proposed as a solid state welding technique to weld similar, dissimilar, and composite materials [6]- [8]. FSW process has many advantages over conventional fusion welding methods such as avoiding solidification cracks and porosity as well as the absence of parent metal melting which make this method capable of producing defect-free joints with high mechanical properties. Moreover, the rapid progress in FSW associated technologies such as welding machines, tool design, and tool materials is another advantage of FSW over other conventional techniques. FSW has been widely used in car, ship and airplane industries. In a typical FSW process, a non-consumable rotating tool is used to join two adjacent workpieces without melting the workpiece material. The primary motion is provided by rotating the tool, and the feed motion is provided by traversing the tool along the joint line. The tool starts rubbing onto the workpiece surfaces and heat is generated under friction action. The material around the tool is heated up and a softened material zone is formed. The softened material zone is stirred by the rotating tool to create a solid phase weld.
Rajendran et al. [9] studied the influence of tool tilt angle (0 • -4 • ) on the strength of friction welded AA2014-T6 aluminum alloy. It was recommended to use tool tilt angle less than 3 • to avoid weld joint defects. The optimum shear strength of the joint (14.42 kN) was obtained at tool tilt angle of 2 • . Palanivel et al. [10] investigated the effect of the tool profile (straight square, tapered square, straight octagon, tapered octagon, and straight hexagon) and its rotational speed (600 rpm, 950 rpm and 1300 rpm) on the tensile strength and microstructure during FSW of two dissimilar aluminum alloys: AA6351-T6 and AA5083-H111 using a tool made of high carbon chromium steel. It was reported that tensile strength of the welded joint is affected by cold work losses in the heat affected zone of the welded workpieces, flow behavior of the softened material, and defects formed in the weld region. The highest tensile strength of the joint (273 MPa) was obtained using straight square tool profile rotated at 950 rpm. This highest tensile strength is less than the ultimate tensile strength of AA6351-T6 and AA5083-H111 by 11.9% and 11.3%, respectively. The effects of tool geometry (cylindrical and conical) on a FSW lap joint made of two dissimilar aluminum alloys (AA 6082-T6 and AA 5754-H22) have been investigated by Costa et al. [11]. The use of a conical tool produced similar strengths welds for retreating and advancing sides. Xu et al. [12]studied the fracture behavior of a FSW joint made of AA7085 Al alloy aluminum alloy. The tensile strength under a tool rotational speed of 600 rpm decreases by about 33.3% compared with that of base material. Rajakumar et al. [13] investigated the effect of rotational speed (900-1800 rpm), traverse speed (20-100 mm/min) and axial tool force (6-10 KN), tool hardness (33-56 HRC), tool shoulder diameter (9-21 mm), and pin diameter (3-7 mm) on the tensile strength of FSWD joints made of AA7075-T6 alloy. The maximum tensile strength of 373 MPa and joint efficiency of 77% were obtained at rotational speed of 1400 rpm, welding speed of 60 mm/min, axial force of 8 kN, tool hardness of 45 HRC, shoulder diameter of 15 mm, and pin diameter of 5 mm. The enhancement in the tensile properties of the welded joints is due to the fine-grained microstructure with no defects and uniformly distributed finer MgZn 2 particles.
The selection and control of FSW process parameters is highly required to enhance the quality of FSWD in terms of mechanical properties. Many artificial intelligence methods have been proposed to predict the process response (output) based on some process inputs by establishing prediction models such as Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS).
ANN based modeling is one of the most significant areas of research in recent decades. It is an artificial intelligence-based system that mimics the function, mechanism and structure of the human brain [14]. Complex problems of a nonlinear nature can be modeled using ANN [15]. It is a complex system consists of many neurons that form the main component of the ANN model and generally composed of input, hidden and output layers. The first layer acts as a receiver to the input parameters. Then the data is processed from the input layer in the hidden layer, and the output is finally computed in the output layer, the number of neurons in the first and last layer is equal to the inputs and outputs of the ANN. ANNs are particularly suitable for identifying highly complex nonlinear phenomena and have been widely used in the study of material constitutive relations [16], [17]. ANN has outstanding generalization capabilities in modeling non-linear mathematical problems [18]- [22]. ANN has been proposed to model different welding processes. Andersen et al. [23] developed an ANN model to predict the bead shape during arc tungsten gas welding. Nagesh and Datta [24] used ANN for predicting weld bead geometry and penetration in shielded metal-arc welding and in TIG welding of pure aluminum [25]. Sukhomay et al. [26] constructed an ANN model to predict the UTS of inert gas-welded plates and the results of the developed model had a better agreement with experimental ones compared with those obtained by multiple regression analysis. Palanivel et al. [27] established an ANN model to predict the UTS of FSWD titanium tubes and compared the results with RSM, and concluded that ANN produced the most accurate predictions. Dehabadi et al. [28] used the same technique to predict the microhardness of FSWD AA6061 joints. ANN was also applied to predict the mechanical properties of FSWD aluminum plates including hardness, strength, and elongation [29]. Recently, various metaheuristic optimization algorithms, such as genetic algorithms, particle swarm optimization, artificial bee colony, cat swarm optimization, Harris hawks optimization, and whale optimization algorithm, have been integrated with ANN to determine the optimal ANN structure and parameters [15], [30]- [35].
Genetically optimized neural network systems have been applied to model FSW process. It has been used to search the optimized parameters of the FSW process [36]. Furthermore, the hybrid multi-objective optimization has been applied to improve the microstructural and mechanical properties of B4C/A356 composites fabricated by FSP [37], and aluminum composites reinforced with different reinforcing particles type [38]. Additional studies on ANN applications to model FSW process have been carried out [29], [36], [39]- [42]. Since the FSW process has many variables, which makes it difficult to reach the appropriate parameters that achieve the best results, therefore this work focuses on predicting the optimal output by specifying the appropriate parameters for the welding process to obtain the best mechanical properties. In this study, a new approach to predict UTS of AA6061-T6 FSWD joints is presented. The proposed approach is constructed by integrating ANN with a new metaheuristic algorithm called Henry gas solubility optimization (HGSO) [43] to improve the performance of the Random Vector Functional Link (RVFL) that used to predict the UTS of the FSWD joints under different welding parameters. The use of RVFL avoids the problem that faces the traditional ANN such as overfitting since RVFL connects the input data with the output which improves the prediction accuracy of the output. Moreover, HGSO helps to obtain the optimal RVFL parameters that maximize the prediction accuracy of the model.

II. PROPOSED APPROACH A. RANDOM VECTOR FUNCTIONAL LINK
In the last decades, the single layer feed forward neural network (SLFNN) has been extended to other more versions, for example, in 1994, Pao et al. [44] supposed the Random Vector Functional Link Network, noted as RVFL. The main difference between them that in the RVFL, the input layer and output layer are connected to each other directly, as shown in Fig.1. Such connection can assist the RVFL network to be able to avert the problems of overfitting. The RVFL network can be mathematically modeled as following, there is a number N of data samples, where each sample can be symbolized as (x i , y i ), where x i ∈ R n , y i ∈ R m , i = 1, . . . , N . Such samples are transferred through another layer unlike the input layer, in which they can be enhanced as in the following equation: where α j and β j are weights between layers, input layer and improved one, and the bias respectively. In addition, S is the parameter tuning coefficient and is a scale factor. The RVFL output layer after that can have an output obtained through the weight w as follows where F represents the samples of the input data matrix that contains F 1 and F 2 represents the output of the improving layer.
The output weight w is updated by the ridge regression [45] or by the Moore-Penrose pseudo-inverse [45], [46].
where I , † and C are, the identity matrix, the Moore-Penrose pseudo-inverse and a coefficient of the trading-off, respectively.

B. HENRY GAS SOLUBILITY OPTIMIZATION
In this section, we introduce the steps of the HGSO which simulates the physical behavior defined by Henr's law. The HGSO, like other Physics-based algorithms, starts by constructing a set of N positions for the gases (X ) and this process is formulated as where Lb and Ub are the lower and upper values in the search space, respectively. The second step is to cluster the solutions in equal groups equivalent to the number of gas types and each group has the same number of gases. In addition, each of them has the same Henry's constant that defined as where r 1 is a random number and l is a constant value set to 5E-2, while N g represents the number of groups. The next step is to assess the gas in each group to determine the best gas in each group. Followed by determining the best gas overall the groups. Thereafter, the Henr's coefficient for the j-th group will be updated using the following equation where T , T θ , and iter are the temperature, constant value (set to 298.15), and the maximum number of iterations. The next step in HGSO is to update the solubility of each solution among all groups (S ij ) using the following equation.
where K is a constant and P ij (t) represents the partial pressure on i-th gas on j-th cluster j and its defined as The HGSO go to update the position of the i-th gas in the j-th group using the following equation: In Equation (10), the F ij is the fitness value of the solution i on the group j and F b is the best fitness value. F is a flag to change the direction gas. η represents the ability of the i-th gas in the group j to interact with other gases in the same group. Whereas, the α = 1 represents the influence of other gases on the i-th gas in the j-th group. The HGSO use the following equation to escape the local point which determine the worst N w solutions.
Then those solutions are updated using the following equation G ij is the solution i in the group j which belongs to the worst solutions.

C. THE PROPOSED HGSO-RVFL METHOD
The proposed model for predicting UTS of FSW is based on improving RVFL performance using a new swarm algorithm called HGSO. The proposed HGSO-RVFL contains two phases, in the first phase, the training phase, the initial values for the parameters of HGSO, and RVFL are received as well as the training set, then the initial values for N solutions (X ) are generated which represent the parameters of the RVFL. Each one of these solutions refers to an RVFL configuration and to evaluate the quality of this configuration, it is learned using the training set and the performance of its output is computed using the root mean square error.
After, computing the fitness value for all configurations (solutions), the best configuration is determined which has the smallest fitness value. The next step is to compute updating other configurations using HGSO operators. This process is performed until the stop conditions are satisfied and return by the best configuration. Then, the testing set is applied to this best configuration to assess its performance. Details of these two phases are given in the following sections.

1) TRAINING PHASE
This phase starts by receiving the input set and dividing it into training (70%) and testing set (30%). Then, the initial value for the parameters of the proposed HGSO-RVFL model such as number of solutions (N ), dimension of each solution N par (number of parameters), number of iterations are set. Thereafter, construct the initial solutions X using the following equation where u j and l j are the upper and lower boundaries at j th parameter, respectively. r ∈ [0, 1] random value. For clarity, assume the i-th solution [1,2000] represents the number of hidden neuron; the value of x i2 ∈ {0, 1} indicates either there is a bias in the output layer or not. The value of x i3 ∈ {0, 1} is used if there is a direct link to output layer or not; while, the value of x i4 ∈ {1, 2, 3, 4, 5} represents the type of the objective function (i.e., sig, tribas, radbas, hardlim, sin, and sign). The x i5 ∈ {1, 2} is used to determine the kind of the randomization approach that applied to set the value of the weights (Uniform, and Gaussian);x i6 ∈ {1, 2} is the approach used to improve the weights (Moore-Penrose pseudoinverse, and regularized least square). The value of x i7 ∈ {1, 2, 3} is applied to determine the type of scaling the features here; and there are three types a) all neurons, b) each hidden neuron separately, and c) the randomization range of the uniform distribution. For example, x i = [200, 1, 1, 3, 1, 2, 2] indicates that the current configuration of RVFL contains 200 neurons with bias and direct link. In addition, radbas is used as an activation function, while weights are generated according to a uniform distribution. The regularized least square is sued to update weights with scale the features for each hidden neuron separately.
To assess the quality of each configuration, the training set is passed through the neurons and the final output (Y P ) is computed then the quality of this output is computed by using the following equatio where Y T is the original output, and Ns represents the number of samples in the training set. Thereafter, the best configuration (X b ) is determined and according to its value, the other VOLUME 8, 2020 configurations will be updated, in addition to using the operators of the HGSO as discussed in section B. Then the terminal conditions are checked; if they are met, then return by the best configuration otherwise, repeat the previous steps again.

2) TESTING PHASE
In this phase, the testing set is applied to assess the performance of the best configuration X b by passing its samples to the input neurons and computing the final output. Then evaluate the output quality by computing the RMSE as defined in Equation (14). The HGSO-RVFL framework is shown in Fig.2.

III. MATERIALS AND METHOD
In order to collect data to construct the HGSO-RVFL model, experimental information of literature [47] has been used as well as the regression model given in Eq. 15 for UTS. Two 5 mm thickness AA6061-T6 aluminum alloys plates have been used to produce FSWD butt joints as shown in Fig. 3. The chemical composition of AA6061-T6 is shown in Table 1. UTS of AA6061-T6 aluminum alloys is 312 MPa. Five tools with different pin geometries made of molybdenum-based high-speed steel were used to produce the FSWD joints: simple square (SS), simple cylindrical (SC), simple tapered (ST), cylindrical with threads (CT), and tapered with threads (TT) as shown in Fig. 4. All tools had the same dimension of shoulder diameter of 18 mm with a concave of 6 • , pin diameter of 6 mm and pin length of 4.7 mm.  The base of the pin and the tip diameter of TT and ST were 4 and 6 mm, respectively, while the plunge depth was 0.1 mm. FSW parameters used in the proposed model and working  range are shown in Table 2. Tensile samples were prepared based on ASTM E8M-04 standard dimensions as described in Fig. 5. Each experiment had three replicates and the mean was computed for each experimental set. Table 3 shows the FSW parameters for the welded AA6061-T6 plates and the measured UTS used to create the HGSO-RVFL model. In this study, we proposed HGSO-RVFL as the main algorithm. However, we added two other algorithms to compare their results with the result of HGSO-RVFL and demonstrate the accuracy of the proposed model. The measured UTS results are compared with the predicted results by RVF-HGOS model as shown in Fig. 6. The HGSO-RVFL model showed a high correlation with experimental results due to its high prediction rate. To confirm the strength of the HGSO-RVFL model in the prediction process, ANFIS and K Nearest Neighbor algorithm (KNN) models have been constructed with the same input data and then compared with the experimental data. The ANFIS model displayed less predictability than HGSO-RVFL model as shown in Fig.7, while KNN model had the lowest degree of predictability as shown in Fig.8. This indicates that the KNN suffers from overfitting and needs more experiments as training set. Therefore, the correlation between HGSO-RVFL predicted data and the corresponding experimental data is better than those obtained by ANFIS or KNN thanks to the integration between advanced ANN technique (RVFL) and robust metaheuristic technique (HGSO) that successfully predicts the UTS of FSW process. Since the HGSO aims to find the optimal configuration that provides RVFL with a suitable tool to avoid the limitations in traditional ANFIS and KNN such as absence of direct link between input and output which leads to overfitting. In addition, the percentage error E i and the average percentage error E av have been used to assess the performance of HGSO-RVFL algorithm. The E i and E av are defined   in equations. (16) and (17) respectively. where, i is the experiment number, E i is the percentage error; UTS i and UTS P i are the experimental and predicted UTS, respectively. E av denotes the average value of the percentage error. Fig. 9 demonstrate the prediction error for HGSO-RVFL, ANFIS, and KNN models which are 0 %, 2.139 %, and 2.693 %, respectively. This indicates that ANFIS and KNN models suffer from overfitting. Therefore, HGSO-RVFL model can be used to predict UTS values better than other investigated models. From the abovementioned discussion, the HGSO-RVFL is proved to be a reliable and strong algorithm to predict mechanical properties of FSWD.  Fig. 10 (a), which indicates the accuracy and fitness of the model because of the ability of HGSO algorithm to discover the optimal configuration that provides RVFL a suitable tool for avoiding constraints in conventional ANFIS and KNN such as there is no direct link between inputs and outputs leading to overfitting, while values are less uniformly distributed around the line for ANFIS model as shown in Fig. 10 (b), they are also randomly distributed around the line for KNN model as shown in Fig. 10 (c) which indicates the worst fitness among all investigated models. The above discussion illustrates an excellent prediction capability of the HGSO-RVFL model.

C. STATISTICS FOR HGSO-RVFL MODEL COMPARED WITH ANFIS, AND KNN MODELS
The obtained results by different models are checked using different statistical criteria such as the root mean square error (RMSE), the mean absolute error (MAE), the coefficient of determination (R2), the mean relative estimate error (MRE), and the coefficient of variance (COV). The values of these statistical coefficients are tabulated in Table 4. R2 equals 1, 1, and 0.9997 for the HGSO-RVFL, ANFIS, and KNN models  technique has much adequacy to predict the UTS of FSWD joints with high accuracy.

D. PREDICTION OF FSW PROCESS PARAMETERS
The developed HGSO-RVFL model was applied to study and predict the parameters of FSW process as shown in Fig.11 (a-c) where a significant agreement was observed between the predicted results and the experimental results, indicating the high ability of the developed model to predict the ideal welding parameters that achieve the optimal UTS. Fig. 11a illustrates the effects of rotational speed and welding speed on UTS. It was observed that base material UTS (312 MPa) is higher than the UTS for all investigated joints regardless of rotational speed and welding speed used in the FSW process. Increasing the rotational speed and decreasing the welding speed increases the tensile stress to reach the maximum value (288.1 MPa) at (1150 rpm -70 mm / min), and (286.72 MPa) at (1150 rpm -30 mm / min), then gradually decreases with increasing welding speed due to the increase in heat input to the welding region. Increasing the rotational speed of the welding tool increases the heat input and affects the uniform flow behavior of the material. At the same time, the lower rotational speed produces less heat input, which results in the lack of stirring action. Therefore, excessive grain growth, solubilization and reprecipitating lead to a decrease in UTS of AA6061 FS welded aluminum alloys. Fig. 11b shows the effect of rotational speed and tool pin profile where simple cylindrical pin profile produces maximum UTS at 1450 rpm whereas tensile stress gradually decreases at a rotation speed of 1150 rpm using a tapered pin with threading, cylindrical pin with threading, and simple tapered screw, respectively to reach minimum value using simple square pin profile. Fig. 11c shows the effects of rotational speed and tool tilt angle. UTS increases with increasing tilt angle and rotational speed to reach peak value at 3 • and 1450 rpm then decreases with increasing these parameters more than these values. Increasing the tilt angle causes poor bonding due to excessive reduction of frictional heat generation which increases average grain size while decreasing tilt angle leads to poor bonding because of high frictional heat generation [48]. Fig. 11d plots the effect of tool pin profile and welding speed on the UTS of the FSWD joints. The plot shows that simple cylindrical pin profile gives the maximum UTS at 30 mm/min, while a gradual decrease of tensile stress is observed at welding speed of 70 mm/min using tapered pin VOLUME 8, 2020 with threads, cylindrical pin with threads, and simple tapered pin profile respectively to reach minimum value using simple square pin profile. Finer grain size is achieved for taper tools compared to other tools as a result of better flow of plasticized material, thereby producing a sound joint [49].
The effects of welding speed and tool tilt angle on UTS are shown in Fig. 11e. As welding speed increases, UTS decreases. Increasing in tilt angle results in increasing the UTS to reach the maximum value at 3 • and 30 mm/min, and then gradually decreases as these two parameters increase. Increasing the tilt angle of the welding tool leads to an increase in the vertical force and torque, this may lead to an increase in the contact between the tool and the workpiece and then the highest heat inputs are achieved which causes a thermal softening of the deformed material and an increase in the flow of downward materials, where the restoration of grains are obtained in stir zone that occurs in conjunction with the deformation, and this process is called dynamic recrystallization, which leads to the grain refinement during welding [50]. Fig. 11f shows the effect of tool tilt angle and tool pin profile. Maximum UTS value is achieved by simple cylindrical tool pin profile and tilt angle of 3 • while this value gradually decreases at the same tilt angle for cylindrical pin with threads and simple tapered pin profile, respectively until it reaches the minimum value using simple square pin profile.

E. MAIN EFFECTS OF FSW WELDING PARAMETERS ON UTS
The main effect plot of different FSW parameters on the process response (UTS) is shown in Fig.12. In order to realize the maximum UTS, it is recommended to use a rotation speed of 1450 rpm or 1150 rpm and avoid using a rotation speed of 1300 rpm as it leads to minimal UTS. It is also recommended to use a welding speed of 30 mm/min to obtain maximum UTS. It can also be noted that the use of a simple cylindrical pin profile or a cylindrical tapered pin profile can attain maximum UTS while simple square pin profile leads to impair UTS. A tilt angle of 3 • can achieve maximal UTS while 5 • leads to minimal UTS. Generally, the HGSO-RVFL model can successfully confirm that the use of a simple cylindrical tool, a tilt angle of 3 • , a rotation speed of 1150 rpm, and a welding speed of 30 mm/min can achieve a high quality AA6061-T6 aluminum alloy welding joint.

V. CONCLUSION
In this paper, we proposed a novel ANN model to predict UTS of the FSWD joints of aluminum alloy AA6061-T6 as functions of welding speed, rotational speed, tilt angle, and tool pin profile. HGSO algorithm was used to optimize the performance of RVFL network, the validity of the model was checked, and the effect of the process parameters on the mechanical properties of the joint was discussed. The following conclusions can be drawn: • HGSO technique can successfully find the optimal configuration that provides RVFL with a suitable tool to avoid the limitations in traditional algorithms such as absence of direct link between input and output which leads to overfitting.
• The developed HGSO-RVFL model can be used to predict the responses of experimental values at R2 of 1.
• The HGSO-RVFL model can successfully confirm that using simple cylindrical tool, 3 • tilt angle, rotation speed 1150 rpm, and welding speed 30mm / min can achieve high quality aluminum alloy AA6061-T6 FSWD joint.
• The HGSO-RVFL model has high predictability of FSW parameters to reach the optimum mechanical properties and is recommended for other engineering applications.  XIAOYUAN JI was born in 1986. He received the Ph.D. degree from the Huazhong University of Science and Technology, in 2013. He is currently a Lecturer with the School of Materials Science and Engineering. He developed the InteCAST-ERP software. He has published more than 50 articles, won two provincial and ministerial level awards, five software copyrights, and one patent. His research interests include algorithms, deep learning, artificial intelligence, data mining, big data, information management, and ERP for foundry enterprises.
XU SHEN received the M.S. and Ph.D. degrees from the Huazhong University of Science and Technology, in 2008 and 2016, respectively. He is currently a Lecturer with the School of Materials Science and Engineering. His research interests include numerical simulation, titanium alloys, solidification, modeling of casting processes, and software development. He has published more than ten articles, won four scientific research awards, two software copyrights, and five patents.