Application programming interface for electron beam welding of Inconel 718 thin plates

In this paper the simulation of electron beam welding of Inconel 718 thin plates by a moving linear heat source is considered. Neural network models are developed and used for the description of the dependence of the molten pool geometry characteristics on the process parameters - electron beam power, welding velocity, and the plate thickness. Neural network models, based on a multi-layered feedforward neural network, trained with Levenberg-Marquardt error backpropagation algorithm are compared with estimated regression models. The neural networks are trained, tested and validated using a set of experimental data. The resulting models are implemented for developing of an application programming interface for electron beam welding of Inconel 718 thin plates, which is used for prediction, investigation and graphical optimization of the molten pool geometry characteristics of the obtained electron beam welds.


Introduction
Inconel 718 is a high-strength, corrosion-resistant nickel-based superalloy known for its exceptional physical and chemical properties [1].This alloy primarily consists of nickel, chromium, and small amounts of other elements like iron, niobium, and molybdenum.These elements contribute to its unique characteristics.
Inconel 718 exhibits excellent mechanical properties, making it suitable for high-temperature applications.It has a high tensile strength, fatigue resistance, and creep-rupture strength, making it suitable for use in extreme conditions.It is highly resistant to oxidation and corrosion, even at elevated temperatures.This resistance is due to its chromium content, which forms a protective oxide layer on the surface.It also has good resistance to various corrosive environments, such as acids, salts, and sea water.
Inconel 718 possesses remarkable physical and chemical properties, including high strength, corrosion resistance, and heat resistance, which make it a versatile material for demanding applications across a wide range of industries, particularly in aerospace, oil and gas, nuclear, chemical processing, marine, automotive, and racing sectors.Its ability to perform under extreme conditions has solidified its reputation as a top choice for critical engineering applications [2].
In this paper simulation of electron beam welding of Inconel 718 thin plates by a moving linear heat source [3,4] is considered.Artificial neural network (ANN) models for the molten pool geometry characteristics: H -molten pool length (mm) along the axis x, W -molten pool width (mm) along the axis y and S -molten pool transverse cross-section area (mm 2 ) in y-z plane, depending on the electron beam power, welding velocity, and the thickness of the plates are trained, tested and validated.These ANN models are based on a multi-layered feedforward neural network, trained with Levenberg-Marquardt error backpropagation algorithm [5,6].They are compared with estimated regression models [7].The resulting models are implemented to develop an application programming interface for electron beam welding of Inconel 718 thin plates, which is used for prediction, investigation and graphical optimization of the molten pool geometry characteristics of the obtained electron beam welds.

Experimental conditions
Simulation electron beam welding (EBW) experiments of Inconel 718 thin plates with thickness of 0.5 to 1.5 mm and dimensions of 60 mm × 100 mm were conducted.These experiments were carried out using the Desktop Weld Optimization Software SmartWeld [8].The study was focused on varying specific process parameters, shown in table 1.In the table P represents the electron beam power, v corresponds to the welding velocity, and h is the plate thickness within the selected regions for parameter variation.The following geometric characteristics of the molten pool are investigated: H -molten pool length (mm) along the axis x, W -molten pool width (mm) along the axis y and S -molten pool transverse cross-section area (mm 2 ) in y-z plane.40 randomly generated experiments of electron beam welding of Inconel 718 thin plates in SmartWeld, were simulated.The obtained experimental data were used to train ANNs with varying numbers of hidden neurons (3, 6, and 9) and different number of outputs (1 and 3).

Artificial neural network models
Artificial neural networks are versatile function approximators that determine robustness to errors, making them advantageous in various application domains [5,9].
In order to construct an expert system, two types of structures of ANN models are used: with one output describing a single geometric characteristic of the molten pool and with three outputs simulating all three considered geometric characteristics simultaneously, all trained ANNs have 3, 6, or 9 hidden neurons in their hidden layer.
For the training, testing, and validation of ANNs, the available 40 experiments were divided into 3 datasets, respectively: 70% for training, 15% for validation, and 15% for testing.Training was conducted for 200 neural networks of each type.For the final selection of ANNs, the best values of the following criteria were considered: • Multiple Correlation Coefficient (R) -closer to 1 value indicates that the ANN model works more accurately.• Mean Squared Error (MSE), which is calculated using an equation 1, where yi represents the measured value of the i-th output quality characteristic (H, W and S),  ̂ is its predicted value by the ANN model, and N is the number of used datasets. (1) The results for the ANNs with 1 output are shown in table 2, and the results for those with 3 outputs are provided in table 3. Tables 2 and 3 show that all selected ANN models have high values of R and values of MSE close to 0.

Expert system
The trained ANN models and estimated in [7] regression models were utilized to develop an application programming interface (API) within the MATLAB environment.This interface enables the simulation of geometric characteristics of the molten pool, with the ability to perform the following tasks: calculation of specific operating conditions, investigation of the dependencies of the molten pool geometry on the EBW process parameters (using predefined value of one of the input parameters), or definition of the zone with optimal process parameter settings aiming to fulfil specified requirements for the fusion geometric characteristics.
When the software is started, the window shown in figure 1 is loaded.The user has the possibility to choose between calculator, investigation and optimization options for simulation the molten pool geometry characteristics.If the operator selects "Calculator" from the start window, the window shown in figure 3 opens.The calculator has a pop-up menu, where the operator can choose between the following methodologies for calculating the H -molten pool length (mm), W -molten pool width (mm), and Smolten pool transverse cross-section area (mm 2 ): • Regression models; • ANNs models shown in table 2 and 3.The Calculator has also three functional buttons: • Calculate -After the operator selects a methodology from the pop-up menu and enters values into the input parameters within the specified ranges, he/she can press the "Calculate" button and the geometric characteristics of the molten pool will be calculated and presented in "Geometry characteristics" field; • Clear Results -all results are cleared by pressing this button, but the input process parameters stay for further investigation; • Clear all -all the results and the input parameters are cleared.The "Investigation" window is shown on figure 3. It includes a pop-up with the same methodologies.The input parameters are in the form of radio buttons and the user has to choose and set a value for only one of them.Here, again there are three buttons: • Plot -by pressing the buttons, the program calculates the geometric characteristics depending on the chosen parameter and methodology, and presents the result in the form of a contour plot; • Clear Plot -pressing this button clears the contour plot in the graphic window; • Clear All -clears the contour plot and the set value for the input parameter.In order to demonstrate the functionality of "Optimization" (figure 4) the following multi-criteria optimization problem has been solved: simultaneous fulfillment of the requirements for all molten pool geometric characteristics -1.5 mm ≤ H ≤ 3.8 mm; 1.8 mm ≤ W ≤ 3.5 mm and 2 mm 2 ≤ S ≤ 3 mm 2 .
Again, the methodology and parameter are chosen, the minimum and maximum constraints for each geometric characteristic are entered into their respective fields, and upon pressing the button "Calculate", the results are presented in the form of contour plots.The highlighted in yellow area in figure 4 indicates all operating conditions, resulting in meeting the superimposed constraints for all geometric characteristics.

Comparing artificial neural network models with regression models
In order to compare the methodologies used in the developed application, 10 new experiments were simulated in SmartWeld, and the obtained data were compared with the results obtained using all 7 predefined methodologies.MSE values were calculated, and the results are presented in table 4. In table 4, the lowest MSE values for each of the studied geometric characteristics are indicated in bold.It can be observed that the regression models are the most accurate for calculating W and S, while ANN-4, which has 3 outputs and 3 hidden neurons, exhibits the least deviation in simulating H.

Conclusions
In this paper, the simulation of electron beam welding of Inconel 718 thin plates by a moving linear heat source is considered.Randomly simulated experiments were performed and used for investigation of the influence of the process parameters: electron beam power, welding velocity and plate thickness on the geometrical characteristics of the molten pool -length, width and the transverse cross-section.Training has been performed on artificial neural network models with experimental data, varying the number of hidden neurons and the number of outputs.
The trained ANNs models and estimated regression models were used to develop a custom graphical user interface in MATLAB.This interface can be used to explore and optimize the geometric characteristics of the molten pool obtained during electron beam welding of Inconel 718 thin plates.
Verification and comparison of the trained ANNs and evaluated regression models were performed using data from 10 new experiments.It was found that all assessed models produced results close to the experimental data.
Based on the conducted comparison, it was determined that the ANNs model with 3 outputs and 3 hidden neurons provided the closest results to the experimental values for the molten pool length.For the other two geometric characteristics, the regression models had best performance.

Figure 1 .
Figure 1.Starting window.Figure 2. Calculator window for the geometry of the molten pool characteristics.

Figure 2 .
Figure 1.Starting window.Figure 2. Calculator window for the geometry of the molten pool characteristics.

Figure 3 .
Figure 3. Investigation window for the geometry of the molten pool characteristics.

Figure 4 .
Figure 4. Optimization window for the geometry of the molten pool characteristics.

Table 1 .
Process parameter variation regions.

Table 2 .
Results from the training, validation, and testing of ANNs with 1 output.

Table 3 .
Results from the training, validation, and testing of ANNs with 3 outputs.

Table 4 .
Results from the MSE.