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Penetration quality prediction of asymmetrical fillet root welding based on optimized BP neural network
Journal of Manufacturing Processes 50 (2020) 247–254
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Penetration quality prediction of asymmetrical fillet root welding based on optimized BP neural network
T
Yushuo Chang, Jianfeng Yue*, Rui Guo, Wenji Liu, Liangyu Li School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Asymmetrical fillet weld Penetration forming BPNN Mind Evolutionary Algorithm
Penetration morphology has an important influence on the weld quality. Due to the nonlinear and strong coupling characteristics of welding process, neural network is often used to predict weld formation and quality. However, the prediction method of fillet weld penetration needs further exploration due to the difficulty in quality evaluation. More intricately, fillet welds of the medium-thickness plate with one-side V-groove are structurally asymmetrical, which makes the penetration quality difficult to guarantee. In this study, the penetration quality of asymmetrical fillet welds is depicted by two characteristic quantities: penetration depth and penetration deflection. The penetration deflection can be reflected by leg length on both sides. After correlation analysis, a back-propagation neural network(BPNN) optimized by Mind Evolutionary Algorithm (MEA) is proposed. The welding current, welding speed, torch work angle and real-time molten pool width were chosen as input parameters, and the penetration of blunt edge and the leg length on both sides of the weld were chosen as output parameters. The results demonstrated that it is feasible and reasonable to predict the penetration of asymmetrical fillet welds by this model. Experimental comparison showed that the optimized model has a significant improvement in predictive performance. The prediction error of blunt edge penetration is controlled within 0.1 mm, and the prediction error rate of leg length is less than 7 %. It satisfies the accurate prediction of penetration quality of asymmetrical fillet welds, and lays the foundation for the study of penetration morphology control of asymmetrical fillet automatic welding.
1. Introduction There are many fillet welds of the medium-thickness plate in large construction machinery such as ship, mine equipment, airplane body and so on [1–3]. Among them, some fillet welds of box girder structure can only be welded from the front because it is difficult to turn over or inconvenient to weld inside [4–6]. The welding process usually needs three processes: root, filling and cover welding, in which root welding is the most critical process but relatively difficult to control efficiently [7]. In order to improve welding efficiency, the one-side V-groove is usually adopted [8,9]. However, the following problem is that the single Vgroove makes the welds have different structures on both sides, especially the root welding with the most obvious difference. Structural difference creates obvious heat conduction difference, which further leads to unstable control of penetration and affects welding quality. Therefore, the key to solve this welding problem is to achieve good shaping of asymmetrical fillet root welding. Due to the asymmetry of the structure, the desirable penetration quality can not be guaranteed by only adjusting the heat input. Too low
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heat input (too low welding current or too high welding speed) leads to incomplete penetration of the blunt edge. However, relatively excessive heat input makes incomplete fusion of the blunt edge and back pit [10,14]. In manual welding of asymmetrical fillet root welding of the medium-thickness plate, welders control the interior penetration quality of the welding by adjusting the torch work angle [11,12]. In the preliminary research, the extracted deviation between the welding torch and the molten pool center is studied, which proves that there is a close correlation between the torch work angle and the deflection of the molten center [13]. Based on previous research, the author propose to control penetration quality by adjusting heat input and torch work angle to affect heat distribution on both sides of the weld. Then, the relationship model between the above welding parameters and penetration morphology is established. Through this model, the penetration depth and deflection are controlled in a small reasonable range, and the welding quality is improved. The quality of root welding of fillet welds directly affects the strength and longevity of joint. Achieving good penetration of that is conductive to ensuring product quality [14–16]. However, the interior
Corresponding author. E-mail address: [email protected] (J. Yue).
https://doi.org/10.1016/j.jmapro.2019.12.022 Received 15 September 2019; Received in revised form 9 December 2019; Accepted 16 December 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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penetration morphology can’t be measured directly in real time, there are many scholars have tried a variety of indirect methods for the detection and control of that [17–22]. The core of their research is mostly to fit by mathematical equation and multiple regression methods or to predict the weld bead geometry by artificial neural networks. In the subsequent relevant studies, some researchers compared the regression method with the artificial neural network. The results showed that the multivariate regression model is only speculative about which factors and expressions are used. It is likely to ignore the coupling effect of welding parameters and the non-linear causality, consequently the prediction accuracy is relatively low [23–26]. Especially for asymmetrical fillet welds, the variation of heat input parameters leads to worse regularity of penetration forming under the influence of torch angle. The more complex nonlinear relationship and coupling effect make it difficult to obtain high accuracy with traditional fitting equation, and the neural network prediction has more advantages and adaptability. In the current research, in order to control penetration quality at the root of fillet welds, low frequency pulse TIG welding with filler wire is adopted, which is easy to control heat input accurately and has advantages of small deformation [27]. The molten pool visual sensing contains abundant information and can directly reflect the dynamic behavior of molten metal in welding process. It has been widely studied and applied in automatic and intelligent welding [28,29]. Considering that the back of asymmetrical fillet weld is usually inconvenient to weld, only the front molten pool is monitored by the industrial camera. This paper focuses on a BPNN-based model for predicting the penetration morphology of asymmetrical fillet welds, in which input parameters synthesize welding parameters and real-time molten pool characteristics. To solve the problem that the prediction effect of asymmetrical fillet weld forming is not satisfactory, the MEA is introduced to optimize the model. The verification experiment show that the predictive performance of the optimized model is significantly improved by combining the MEA in swarm intelligence algorithms. The prediction accuracy is able to meet the requirements of quality evaluation and subsequent penetration control. The optimized model can accurately reflect the nonlinear relationship between welding parameters and penetration morphology, which is helpful to ensure the penetration quality of asymmetric fillet root welding.
Fig. 1. The experimental setup.
Fig. 2. Schematic of welding position and torch work angle.
2. Experimental equipment and process In the experiment, a TDW series pulse welding machine of TIME Inc. is adopted to adjust welding current and other welding parameters, the electrode polarity is DCEN. The welding process adopts the way of keeping the position of the workpiece unchanged and making the torch move. The welding torch is fixed on the fixture with adjustable angle, and its moving speed is controlled by the welding operator. Restricted by the space size of the structure, the range of welding torch work angle θ (the angle between the torch and groove) in the experiment is 18° -42°.The workpiece is placed on a self-designed welded bracket for ship welding. In order to facilitate the welding and ensure the uniform length of the weld bead, the workpiece support is adjusted so that the un-grooved plate is at an angle of 60° to the horizontal, and the grooved plate is at an angle of 30° to the horizontal. The experimental setup and workpiece placement are shown in Figs. 1 and 2. A Canadian XIRIS XVC-1000 camera is mounted on the beam of welding manipulator and moves with welding torch. The angle between industrial camera and horizontal direction is 45° to achieve the image acquisition of front molten pool. The collected images are processed to extract the edge of the molten pool and calculate the width of the molten pool. The welding parameters and other parameters involved in the experiment are shown in Table 1. During the pulse period, the size of the molten pool changes at any time. In order to ensure the matching of the molten pool width and the penetration morphology of the corresponding position, the starting welding position should be marked before welding. Sampling points are
selected by combining welding speed and time series of camera sampling. The pulse frequency is constant at 2 Hz from previous experiments. Under this condition, capturing images within 0.15 s in the middle of the pulse base value can not only avoid the unclear edge of the molten pool caused by strong arc interference, but also ensure the relative stability of the molten pool size in the obtained image. Taking the average width of the molten pool in this period as the weld width at current sampling points is able to avoid accidental errors and make the experimental results more scientific and precise. After welding, the weldment is cut, polished and etched along the section of the image sampling point by a wire cutting machine. Under the Leica DVM6 microscope, the macroscopic metallography of the fusion line is observed and photographed to measure the relevant penetration characteristics. The experimental results show that within the experimental range, as the angle of the welding torch increases, the penetration deflection increases and the growth rate increases. The penetration deflection has an influence on the size of weld legs. As can be seen from Fig. 3, with the increase of penetration deflection, the size of leg length of the grooved side increases, and the change on the other side is opposite. Fig. 3 shows the experimental results when the peak current is 180A and the welding speed is 1.5 mm/s. The penetration deflection η is the angle between the penetration center and the groove. Therefore, in order to describe penetration deflection conveniently and evaluate fillet weld forming quality better, the leg length on both 248
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Table 1 Welding parameters and other information. Welding parameters
Variables
Peak current(A) Welding speed(mm/s) Torch work angle(°) Distance from electrode to weld root(mm) Wire feed rate(mm/s) Argon flow(L/min) Impulse frequency(Hz) Duty ratio ER50-6, φ0.8mm WC20, φ2.4mm Q235, 180 × 50 × 8 mm. Groove angle is 60°,blunt edge is 2 mm.
Constants
Otherinformation
Wire type and size Electrode type and size Workpiece material and dimension
180/190/200/210/220 1.0/1.5/2.0 18/24/30/36/42 3.5 6.5 12 2 50 %
Table 2 Some experimental parameters and measurement results.
Fig. 3. Influence of torch work angle on penetration deflection and leg length.
sides of the fillet weld (L1 and L2) and the penetration depth of blunt edge (PD) are selected as target parameters to study. The macroscopic metallographic diagram and dimensional measurement of the weldment sampling are shown in Fig. 4. A part of experimental data of the neural network samples are shown in Table 2.
No.
I(A)
v(mm/s)
θ(°)
W(mm)
L1(mm)
L2(mm)
PD(mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
180 180 180 180 180 180 200 200 200 200 200 200 220 220 220 220 220 220
1.00 1.00 1.50 1.50 2.00 2.00 1.00 1.00 1.50 1.50 2.00 2.00 1.00 1.00 1.50 1.50 2.00 2.00
18 30 18 42 30 42 18 30 18 42 30 42 18 30 18 42 30 42
4.172 4.398 3.610 4.080 3.320 3.546 4.636 4.898 4.118 4.633 3.717 4.055 5.012 5.333 4.628 5.230 4.308 4.536
4.391 4.834 3.587 4.566 3.304 3.906 4.745 5.201 3.751 4.924 3.622 4.036 4.957 5.443 4.094 5.426 3.988 4.544
4.882 4.552 4.336 3.620 3.231 2.904 5.184 4.743 4.534 3.548 3.427 3.129 5.364 4.999 4.956 3.821 3.630 3.157
0.221 0.323 0.020 0.191 0.023 0.069 0.652 0.799 0.422 0.657 0.214 0.325 0.992 1.098 0.872 1.063 0.704 0.778
prediction of joint strength and welding deformation [32–34]. 3.1. Determination of input and output nodes The first step to establishing the neural network prediction model of penetration morphology of asymmetrical fillet welds is to select reasonable inputs and outputs. At present, there are great differences in the selection of input parameters in the relevant research on the prediction of weld formation using neural network, but most of them are based on different combinations of welding parameters. According to the welding characteristics of asymmetrical fillet welds, correlation analysis was carried out on the preliminary experimental data, and the results were shown in Fig. 5. In the range of parameter adjustment in actual welding, the peak current of welding is
3. Establishment and prediction of BPNN model The excellent non-linear processing ability and non-limitation of the neural network have obvious advantages in predicting weld forming and mechanical properties [30,31]. BP neural network has the advantages of simple structure, stable working state and easy hardware implementation, and it is mature in network theory and performance optimization after a long period of development. Therefore, in the field of welding, there are many research and applications based on this, especially in the control of weld formation,
Fig. 4. Macroscopical metallographic and characteristics measurement diagram of weldment section sampling. 249
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Fig. 5. Correlation analysis between model inputs and outputs.
the most significant factor affecting the penetration depth of blunt edge in the welding parameters. The welding speed has a greater influence on the leg length of welds than current. The change of welding torch work angle has an obvious effect on the leg length, and also has a certain adjustment effect on the penetration depth of blunt edge. In addition, the formation of molten pool is the result of the interaction of welding parameters and heat conduction and accumulation at the current welding spot. It is defective to use welding parameters as input only. Therefore, adding real-time molten pool characteristic information to the input parameters can not only make up for this defect, but also comprehensively reflect the influence of other factors on welding, such as the weld gap error, arc length variation error and so on. Therefore, in order to predict the penetration morphology of asymmetrical fillet welds accurately and reliably, the real-time molten pool width (W) is introduced together with the welding parameters (peak welding current I, welding speed v and torch work angle θ) as the input parameters of the neural network. The leg length on both sides of the weld (L1 and L2) and penetration depth of blunt edge (PD) are taken as the output parameters.
Fig. 6. Structure of the BPNN. model.
most of them have determined a small number of samples and then made network prediction. In fact, the number of hidden layer nodes and training samples must satisfy some conditions, one of which is that the number of training samples should be more than the connection weight of network model, generally 2–10 times. Otherwise, "rotation training" is required to obtain reliable prediction results. For the model in this study, at least 2*(4*5 + 5*3) = 70 training samples are needed. Therefore, 80 sets of samples were selected for training through experiments, and another 20 groups were used to test prediction accuracy. After training for many times, the root mean square error (RMSE) of each training is recorded to evaluate the stability of the network prediction, and the minimum RMSE is taken as the optimal result. Comparing the optimal prediction results with the actual measurement results, the error rates of the predicted leg length L1 and L2 are shown in Fig. 7. Since the value of PD is too close to 0 when the small penetration depth of blunt edge is acquired, a large error rate is caused. Therefore, the absolute error of PD prediction is used as a reference to evaluate the prediction accuracy, and the result is shown in Fig. 8. The change of torch work angle makes the coupling effect of parameters in asymmetrical fillet root welding more complex. According to the prediction results of Figs. 7 and 8, it can be seen that the maximum error rate of leg length prediction is about 15 %, and the maximum error of penetration depth of blunt edge is about 0.27 mm. Although a certain prediction ability is able to prove the rationality of the modeling method, the current accuracy can not meet the future research on penetration control and quality evaluation, which may lead to misjudgement due to the large errors of individual points. In order to further improve the adaptability and prediction effect of the model for penetration forming prediction of asymmetrical fillet welds, swarm
3.2. Determination of the network model structure In the current related research, it is inconclusive whether increasing the number of hidden layers can reduce the network error, but it will undoubtedly complicate the network structure and greatly increase the network training time and data occupation space. Therefore, the threelayer network with a single hidden layer is generally preferred in design, and the number of hidden layer nodes is changed by trial and error method to obtain the network structure with the smallest error. The selection of the number of hidden layer nodes also has a great influence on the performance of the neural network model, which is the direct cause of "over-fitting" in training. At present, the formulas given in most literatures are for any number of samples and most of them are for the most disadvantageous situation, so they are not recommended for practical engineering applications. Based on the basic principle that the network structure should be as compact as possible on the premise of meeting the accuracy requirements. Comprehensively considering the complexity of the network structure, the size of the error and the number of samples, this model has been trained many times using the node deletion method. After performance comparison, the optimal number of hidden layer nodes is determined to be 5. So far, BP neural network model for predicting penetration morphology of asymmetrical fillet welds is determined, and the topological structure of the model is shown in Fig. 6. 3.3. Sample processing and data prediction In the research of the application of neural network in welding field, 250
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information, which is more conducive to quickly and accurately find the global optimal solution [35–37]. Based on these characteristics, this paper uses MEA to optimize the initial weight and threshold of the BPNN model, aiming to avoid the neural network falling into local optimum and improve the search speed of the optimal solution, thereby improving the prediction accuracy and stability of the model. The main steps to realize the optimization of BPNN model by MEA are as follows. The algorithm flow chart is shown in Fig. 9.
4.1. Weight and threshold encoding According to the topological structure of BPNN, the initial weights and thresholds to be solved need to be numerically coded. For a network structure with N inputs M outputs and L hidden layer nodes, the coding length X equals the sum of the initial weights and the number of thresholds: X=N*L+L*M+L+M,
Fig. 7. Prediction error rate of L1 and L2.
(1)
where N, L and M are respectively the node number of input layer, hidden layer and output layer. Therefore, after iterative optimization by evolutionary algorithm, each solution corresponds to a coding, and ultimately the optimal solution X = 4*5 + 5*3 + 5+3 = 43.
4.2. Set initial population and scoring rules Set parameters of the initial population and generate a random initial population. In this paper, the initial population size is set to 200(initial random generation of 200 codes), the number of superior and temporary sub-populations is 5, and the number of iterations is 10. The score of each solution is calculated according to the network calculation rules. In order to evaluate the quality of a solution, the reciprocal of the mean square error between the output value and the expected value of the solution acting on the network is usually used as the final score.
score = Fig. 8. Prediction absolute error of PD.
1 mse(expectation − calculation)
(2)
Where score is the score for each solution; expectation is the ideal value, that is, the definite value given in the experimental sample; calculation is the calculated value output by the network according to the group of weights and thresholds. This means that the higher the score, the smaller the proof error, the better the solution set.
intelligence algorithms were used to optimize BP neural network. The results show that the BP neural network optimized by the mind evolution algorithm (MEA) can significantly improve the prediction effect of the model. 4. Methodology of mind evolution algorithm
4.3. Convergence and alienation
The mathematic principle of BP neural network determines its inherent defect that it is easy to fall into local optimum. In addition, its training effect depends too much on the initial random weights and thresholds. With the purpose of making up for the deficiency of BP neural network, many scholars try to use optimization algorithm to improve the applicability of BP neural network [16,24].Compared with traditional optimization methods, intelligent optimization algorithms generally do not need a very clear objective function and the continuity and convexity of constraints. They have weak theoretical requirements and strong adaptability, and have advantages in solving speed and global optimization. The MEA is derived from the shortcomings of low search efficiency and prematurity of Genetic Algorithm. The core idea of that is still population evolution. It only uses two new operators, “convergence” and “alienation”, to coordinate and cooperate in the realization process. The parallel feature improves the search efficiency, and this algorithm can memorize multi-generation evolutionary
According to the score, the individuals are ranked from high to low, the top 5 constitutes the winner sub-population, and the second 5 constitutes the temporary sub-population. With these 10 individuals as the center, new individuals are generated according to normal distribution. Convergence operations (Individual competition produces winners.) are carried out within each subgroup until no new winners are generated to represent the subgroup maturity. At this time, the highest score of the individual within the subgroup is taken as the subgroup score. If the score of temporary subgroup is higher than that of the winner subgroup, the alienation operation (mainly substitution or abandonment between the two subgroups) will be performed until all the temporary subgroup scores are lower than that of the winner subgroup, and the evolution is completed. 251
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Fig. 9. Optimization flow chart for prediction model.
depth of blunt edge are recorded after some training. The results are shown in Fig. 10. It can be seen that, compared with the optimized model, the RMSE of the unoptimized model fluctuates obviously. Ten times in training, the RMSE of the leg length fluctuates more than 0.1 mm, and the RMSE of the penetration depth of blunt edge fluctuates about 0.06 mm, which means that the predicted results of the model fluctuate greatly, and the unstable predictive performance may have a greater impact on the later work. The predictive stability of the model is improved obviously by combining the MEA. The RMSE fluctuations of the leg length of and the penetration depth of blunt edge are controlled at 0.05 mm and 0.03 mm, respectively.
4.4. Decode and complete optimization The best individual in the best subgroup gained by iterations are found and decoded, and the optimal initial weight and threshold are obtained for BP neural network training. 5. Results and discussion The optimal weights and thresholds optimized by the mind evolutionary algorithm are applied to BP neural network, and the same sample data, parameters and methods are used to train and predict the network. The effects before and after optimization are compared from the three aspects of model prediction stability, convergence speed and prediction accuracy.
5.2. Comparison of convergence speed of network training By comparing the convergence steps of training for many times, the optimized network model can basically achieve the target error within 20 steps. It not only improves obviously than before optimization, but also has no occasional large number of iterations to converge after
5.1. Comparison of stability results of model prediction The root mean square error of the leg length and the penetration
Fig. 10. RMSE of the prediction of leg length and PD. 252
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Fig. 11. Comparison of iteration steps before and after optimization.
optimization, which can be inferred from Fig. 11. It shows that the initial weights and thresholds obtained by evolutionary algorithm optimization are closer to the optimum, only a few iterations are needed to meet the target accuracy, and generally do not fall into local optimum, resulting in occasional poor prediction performance. It is concluded that the optimized model has better performance and greatly improves the convergence speed of the model.
Fig. 13. Comparison of prediction absolute error of PD. Table 3 Comparison of the R2 and RMSE of outputs.
R2 before optimization R2 after optimization RMSE before optimization RMSE after optimization
5.3. Validation of prediction accuracy of optimized model The two models are trained with the same sample data, and choosing two models with the best training effect (the least RMSE) to predict the test samples. The comparison of the prediction results is as follows. Fig. 12 displays the comparison of predicted relative error rates of leg length L1 and L2. The prediction result of the penetration depth of blunt edge is shown in Fig. 13, which contrast with absolute error. It can be seen from the figures that the relative error rate of leg length has been increased by more than five percentage points after model optimization. The prediction error rates of leg length L1 and L2 are stable within 5 % and 7 % respectively. The prediction absolute error of PD is also controlled within 0.08 mm, which can meet the accuracy requirements of penetration control and quality evaluation. The determination coefficient (R2) and root mean square error (RMSE) are commonly used model evaluation indicators, but they are very sensitive to outliers. The forecasting results above show that the error of 20 groups of validation samples is small, and there is no abnormal point, which provides conditions for using these two evaluation indicators. Therefore, in order to evaluate the performance of the model more intuitively, the R2 and RMSE of the three outputs before and after optimization are compared. The result is shown in Table 3. The result shows that the R2 of three parameters are all above 0.94
L1
L2
PD
0.8526 0.9630 0.2582 0.0955
0.8614 0.9453 0.2559 0.1206
0.8360 0.9579 0.1357 0.0476
after optimization, which proves that the optimized model has good forecasting performance. The RMSE of leg length is about 0.1 mm, and that of PD is 0.0476 mm, which shows that the model has high prediction accuracy. 6. Conclusions In this paper, the general rule of penetration forming is obtained by analyzing a large number of asymmetrical fillet welds experimental results. Based on this, a neural network model for predicting penetration forming is established. Further, the model is optimized by Mind Evolutionary Algorithm. The results demonstrate that the optimized model has good predictive performance. Through the analysis of experiments and predictive results, the main conclusions are as follows: 1 The sensitivity analysis of the inputs and outputs of the neural network shows that the peak welding current is the most important factor affecting the penetration depth of blunt edge (PD). The welding speed has a greater influence on the leg length (L1 and L2)
Fig. 12. Comparison of prediction error rate of leg length(L1 and L2). 253
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than the peak current. The torch work angle not only has a significant effect on the leg length, but also has a certain adjustment role in PD. 2 The width of molten pool can synthetically reflect some potential factors that may affect the forming process, and it is highly correlated with L1, L2 and PD. Taking it as one of the input parameters of the model can improve the accuracy of the model prediction. 3 The BP neural network model based on peak welding current, welding speed, torch work angle and molten pool width as inputs, leg length on both sides and penetration depth of blunt edge as outputs can be used to predict penetration forming of asymmetrical fillet welds. However, more accurate penetration control and quality evaluation still need to be further optimized. 4 It is an effective attempt to use swarm intelligence algorithm to optimize the classical neural network model for predicting the relatively complex weld penetration forming. In this study, the stability, accuracy and convergence rate of prediction are significantly improved by MEA optimization. The error rate of leg length is less than 7 %, the error of penetration depth of blunt edge is within 0.08 mm. Good prediction performance makes it possible to control penetration and evaluate quality of asymmetrical fillet welds, which lays a foundation for realizing automatic welding of asymmetrical fillet welds. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (Grant No. U1733125) and the Natural Science Foundation of Tianjin Municipal, China (Grant Nos. 17JCZDJC38700 and 18JCYBJC19100). References [1] Teng TL, et al. Analysis of residual stresses and distortions in T-joint fillet welds. Int J Press Vessel Pip 2001;78(8):523–38. [2] Deng Dean, Liang W, Murakawa H. Determination of welding deformation in filletwelded joint by means of numerical simulation and comparison with experimental measurements. J Mater Process Technol 2007;183(2–3):219–25. [3] Unt Anna, Poutiainen I, Salminen A. Effects of sealing run welding with defocused laser beam on the quality of T-joint fillet weld. Phys Procedia 2014;56:497–506. [4] Kozak Janusz, Kowalski Jakub. Problems of determination of welding angular distortions of T-fillet joints in ship hull structures. Polish Marit Res 2015;22(2):79–85. [5] GONG Shui-li, et al. Formation, microstructure and mechanical properties of double-sided laser beam welded Ti–6Al–4V T-joint. Trans Nonferrous Met Soc China 2016;26(3):729–35. [6] Abe Takamasa, et al. Fatigue properties and fracture mechanism of load carrying type fillet joints with one-sided welding. Frat Ed Integritã Strutt 2016;35:424. [7] Chen Ji, et al. Predicting the influence of groove angle on heat transfer and fluid flow for new gas metal arc welding processes. Int J Heat Mass Transf 2012;55(1–3):102–11. [8] Fricke Wolfgang, Kahl Adrian, Paetzold Hans. Fatigue assessment of root cracking of fillet welds subject to throat bending using the structural stress approach. Weld World 2006;50(7–8):64–74. [9] Gyasi Emmanuel Afrane, et al. Study of adaptive automated GMAW process for full penetration fillet welds in offshore steel structures. The 27th International Ocean and Polar Engineering Conference. International Society of Offshore and Polar Engineers 2017. [10] Kumar A, DebRoy Tarasankar. Guaranteed fillet weld geometry from heat transfer model and multivariable optimization. Int J Heat Mass Transf 2004;47(26):5793–806.
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Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Penetration quality prediction of asymmetrical fillet root welding based on optimized BP neural network
T
Yushuo Chang, Jianfeng Yue*, Rui Guo, Wenji Liu, Liangyu Li School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Asymmetrical fillet weld Penetration forming BPNN Mind Evolutionary Algorithm
Penetration morphology has an important influence on the weld quality. Due to the nonlinear and strong coupling characteristics of welding process, neural network is often used to predict weld formation and quality. However, the prediction method of fillet weld penetration needs further exploration due to the difficulty in quality evaluation. More intricately, fillet welds of the medium-thickness plate with one-side V-groove are structurally asymmetrical, which makes the penetration quality difficult to guarantee. In this study, the penetration quality of asymmetrical fillet welds is depicted by two characteristic quantities: penetration depth and penetration deflection. The penetration deflection can be reflected by leg length on both sides. After correlation analysis, a back-propagation neural network(BPNN) optimized by Mind Evolutionary Algorithm (MEA) is proposed. The welding current, welding speed, torch work angle and real-time molten pool width were chosen as input parameters, and the penetration of blunt edge and the leg length on both sides of the weld were chosen as output parameters. The results demonstrated that it is feasible and reasonable to predict the penetration of asymmetrical fillet welds by this model. Experimental comparison showed that the optimized model has a significant improvement in predictive performance. The prediction error of blunt edge penetration is controlled within 0.1 mm, and the prediction error rate of leg length is less than 7 %. It satisfies the accurate prediction of penetration quality of asymmetrical fillet welds, and lays the foundation for the study of penetration morphology control of asymmetrical fillet automatic welding.
1. Introduction There are many fillet welds of the medium-thickness plate in large construction machinery such as ship, mine equipment, airplane body and so on [1–3]. Among them, some fillet welds of box girder structure can only be welded from the front because it is difficult to turn over or inconvenient to weld inside [4–6]. The welding process usually needs three processes: root, filling and cover welding, in which root welding is the most critical process but relatively difficult to control efficiently [7]. In order to improve welding efficiency, the one-side V-groove is usually adopted [8,9]. However, the following problem is that the single Vgroove makes the welds have different structures on both sides, especially the root welding with the most obvious difference. Structural difference creates obvious heat conduction difference, which further leads to unstable control of penetration and affects welding quality. Therefore, the key to solve this welding problem is to achieve good shaping of asymmetrical fillet root welding. Due to the asymmetry of the structure, the desirable penetration quality can not be guaranteed by only adjusting the heat input. Too low
⁎
heat input (too low welding current or too high welding speed) leads to incomplete penetration of the blunt edge. However, relatively excessive heat input makes incomplete fusion of the blunt edge and back pit [10,14]. In manual welding of asymmetrical fillet root welding of the medium-thickness plate, welders control the interior penetration quality of the welding by adjusting the torch work angle [11,12]. In the preliminary research, the extracted deviation between the welding torch and the molten pool center is studied, which proves that there is a close correlation between the torch work angle and the deflection of the molten center [13]. Based on previous research, the author propose to control penetration quality by adjusting heat input and torch work angle to affect heat distribution on both sides of the weld. Then, the relationship model between the above welding parameters and penetration morphology is established. Through this model, the penetration depth and deflection are controlled in a small reasonable range, and the welding quality is improved. The quality of root welding of fillet welds directly affects the strength and longevity of joint. Achieving good penetration of that is conductive to ensuring product quality [14–16]. However, the interior
Corresponding author. E-mail address: [email protected] (J. Yue).
https://doi.org/10.1016/j.jmapro.2019.12.022 Received 15 September 2019; Received in revised form 9 December 2019; Accepted 16 December 2019 1526-6125/ © 2019 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
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penetration morphology can’t be measured directly in real time, there are many scholars have tried a variety of indirect methods for the detection and control of that [17–22]. The core of their research is mostly to fit by mathematical equation and multiple regression methods or to predict the weld bead geometry by artificial neural networks. In the subsequent relevant studies, some researchers compared the regression method with the artificial neural network. The results showed that the multivariate regression model is only speculative about which factors and expressions are used. It is likely to ignore the coupling effect of welding parameters and the non-linear causality, consequently the prediction accuracy is relatively low [23–26]. Especially for asymmetrical fillet welds, the variation of heat input parameters leads to worse regularity of penetration forming under the influence of torch angle. The more complex nonlinear relationship and coupling effect make it difficult to obtain high accuracy with traditional fitting equation, and the neural network prediction has more advantages and adaptability. In the current research, in order to control penetration quality at the root of fillet welds, low frequency pulse TIG welding with filler wire is adopted, which is easy to control heat input accurately and has advantages of small deformation [27]. The molten pool visual sensing contains abundant information and can directly reflect the dynamic behavior of molten metal in welding process. It has been widely studied and applied in automatic and intelligent welding [28,29]. Considering that the back of asymmetrical fillet weld is usually inconvenient to weld, only the front molten pool is monitored by the industrial camera. This paper focuses on a BPNN-based model for predicting the penetration morphology of asymmetrical fillet welds, in which input parameters synthesize welding parameters and real-time molten pool characteristics. To solve the problem that the prediction effect of asymmetrical fillet weld forming is not satisfactory, the MEA is introduced to optimize the model. The verification experiment show that the predictive performance of the optimized model is significantly improved by combining the MEA in swarm intelligence algorithms. The prediction accuracy is able to meet the requirements of quality evaluation and subsequent penetration control. The optimized model can accurately reflect the nonlinear relationship between welding parameters and penetration morphology, which is helpful to ensure the penetration quality of asymmetric fillet root welding.
Fig. 1. The experimental setup.
Fig. 2. Schematic of welding position and torch work angle.
2. Experimental equipment and process In the experiment, a TDW series pulse welding machine of TIME Inc. is adopted to adjust welding current and other welding parameters, the electrode polarity is DCEN. The welding process adopts the way of keeping the position of the workpiece unchanged and making the torch move. The welding torch is fixed on the fixture with adjustable angle, and its moving speed is controlled by the welding operator. Restricted by the space size of the structure, the range of welding torch work angle θ (the angle between the torch and groove) in the experiment is 18° -42°.The workpiece is placed on a self-designed welded bracket for ship welding. In order to facilitate the welding and ensure the uniform length of the weld bead, the workpiece support is adjusted so that the un-grooved plate is at an angle of 60° to the horizontal, and the grooved plate is at an angle of 30° to the horizontal. The experimental setup and workpiece placement are shown in Figs. 1 and 2. A Canadian XIRIS XVC-1000 camera is mounted on the beam of welding manipulator and moves with welding torch. The angle between industrial camera and horizontal direction is 45° to achieve the image acquisition of front molten pool. The collected images are processed to extract the edge of the molten pool and calculate the width of the molten pool. The welding parameters and other parameters involved in the experiment are shown in Table 1. During the pulse period, the size of the molten pool changes at any time. In order to ensure the matching of the molten pool width and the penetration morphology of the corresponding position, the starting welding position should be marked before welding. Sampling points are
selected by combining welding speed and time series of camera sampling. The pulse frequency is constant at 2 Hz from previous experiments. Under this condition, capturing images within 0.15 s in the middle of the pulse base value can not only avoid the unclear edge of the molten pool caused by strong arc interference, but also ensure the relative stability of the molten pool size in the obtained image. Taking the average width of the molten pool in this period as the weld width at current sampling points is able to avoid accidental errors and make the experimental results more scientific and precise. After welding, the weldment is cut, polished and etched along the section of the image sampling point by a wire cutting machine. Under the Leica DVM6 microscope, the macroscopic metallography of the fusion line is observed and photographed to measure the relevant penetration characteristics. The experimental results show that within the experimental range, as the angle of the welding torch increases, the penetration deflection increases and the growth rate increases. The penetration deflection has an influence on the size of weld legs. As can be seen from Fig. 3, with the increase of penetration deflection, the size of leg length of the grooved side increases, and the change on the other side is opposite. Fig. 3 shows the experimental results when the peak current is 180A and the welding speed is 1.5 mm/s. The penetration deflection η is the angle between the penetration center and the groove. Therefore, in order to describe penetration deflection conveniently and evaluate fillet weld forming quality better, the leg length on both 248
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Table 1 Welding parameters and other information. Welding parameters
Variables
Peak current(A) Welding speed(mm/s) Torch work angle(°) Distance from electrode to weld root(mm) Wire feed rate(mm/s) Argon flow(L/min) Impulse frequency(Hz) Duty ratio ER50-6, φ0.8mm WC20, φ2.4mm Q235, 180 × 50 × 8 mm. Groove angle is 60°,blunt edge is 2 mm.
Constants
Otherinformation
Wire type and size Electrode type and size Workpiece material and dimension
180/190/200/210/220 1.0/1.5/2.0 18/24/30/36/42 3.5 6.5 12 2 50 %
Table 2 Some experimental parameters and measurement results.
Fig. 3. Influence of torch work angle on penetration deflection and leg length.
sides of the fillet weld (L1 and L2) and the penetration depth of blunt edge (PD) are selected as target parameters to study. The macroscopic metallographic diagram and dimensional measurement of the weldment sampling are shown in Fig. 4. A part of experimental data of the neural network samples are shown in Table 2.
No.
I(A)
v(mm/s)
θ(°)
W(mm)
L1(mm)
L2(mm)
PD(mm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
180 180 180 180 180 180 200 200 200 200 200 200 220 220 220 220 220 220
1.00 1.00 1.50 1.50 2.00 2.00 1.00 1.00 1.50 1.50 2.00 2.00 1.00 1.00 1.50 1.50 2.00 2.00
18 30 18 42 30 42 18 30 18 42 30 42 18 30 18 42 30 42
4.172 4.398 3.610 4.080 3.320 3.546 4.636 4.898 4.118 4.633 3.717 4.055 5.012 5.333 4.628 5.230 4.308 4.536
4.391 4.834 3.587 4.566 3.304 3.906 4.745 5.201 3.751 4.924 3.622 4.036 4.957 5.443 4.094 5.426 3.988 4.544
4.882 4.552 4.336 3.620 3.231 2.904 5.184 4.743 4.534 3.548 3.427 3.129 5.364 4.999 4.956 3.821 3.630 3.157
0.221 0.323 0.020 0.191 0.023 0.069 0.652 0.799 0.422 0.657 0.214 0.325 0.992 1.098 0.872 1.063 0.704 0.778
prediction of joint strength and welding deformation [32–34]. 3.1. Determination of input and output nodes The first step to establishing the neural network prediction model of penetration morphology of asymmetrical fillet welds is to select reasonable inputs and outputs. At present, there are great differences in the selection of input parameters in the relevant research on the prediction of weld formation using neural network, but most of them are based on different combinations of welding parameters. According to the welding characteristics of asymmetrical fillet welds, correlation analysis was carried out on the preliminary experimental data, and the results were shown in Fig. 5. In the range of parameter adjustment in actual welding, the peak current of welding is
3. Establishment and prediction of BPNN model The excellent non-linear processing ability and non-limitation of the neural network have obvious advantages in predicting weld forming and mechanical properties [30,31]. BP neural network has the advantages of simple structure, stable working state and easy hardware implementation, and it is mature in network theory and performance optimization after a long period of development. Therefore, in the field of welding, there are many research and applications based on this, especially in the control of weld formation,
Fig. 4. Macroscopical metallographic and characteristics measurement diagram of weldment section sampling. 249
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Fig. 5. Correlation analysis between model inputs and outputs.
the most significant factor affecting the penetration depth of blunt edge in the welding parameters. The welding speed has a greater influence on the leg length of welds than current. The change of welding torch work angle has an obvious effect on the leg length, and also has a certain adjustment effect on the penetration depth of blunt edge. In addition, the formation of molten pool is the result of the interaction of welding parameters and heat conduction and accumulation at the current welding spot. It is defective to use welding parameters as input only. Therefore, adding real-time molten pool characteristic information to the input parameters can not only make up for this defect, but also comprehensively reflect the influence of other factors on welding, such as the weld gap error, arc length variation error and so on. Therefore, in order to predict the penetration morphology of asymmetrical fillet welds accurately and reliably, the real-time molten pool width (W) is introduced together with the welding parameters (peak welding current I, welding speed v and torch work angle θ) as the input parameters of the neural network. The leg length on both sides of the weld (L1 and L2) and penetration depth of blunt edge (PD) are taken as the output parameters.
Fig. 6. Structure of the BPNN. model.
most of them have determined a small number of samples and then made network prediction. In fact, the number of hidden layer nodes and training samples must satisfy some conditions, one of which is that the number of training samples should be more than the connection weight of network model, generally 2–10 times. Otherwise, "rotation training" is required to obtain reliable prediction results. For the model in this study, at least 2*(4*5 + 5*3) = 70 training samples are needed. Therefore, 80 sets of samples were selected for training through experiments, and another 20 groups were used to test prediction accuracy. After training for many times, the root mean square error (RMSE) of each training is recorded to evaluate the stability of the network prediction, and the minimum RMSE is taken as the optimal result. Comparing the optimal prediction results with the actual measurement results, the error rates of the predicted leg length L1 and L2 are shown in Fig. 7. Since the value of PD is too close to 0 when the small penetration depth of blunt edge is acquired, a large error rate is caused. Therefore, the absolute error of PD prediction is used as a reference to evaluate the prediction accuracy, and the result is shown in Fig. 8. The change of torch work angle makes the coupling effect of parameters in asymmetrical fillet root welding more complex. According to the prediction results of Figs. 7 and 8, it can be seen that the maximum error rate of leg length prediction is about 15 %, and the maximum error of penetration depth of blunt edge is about 0.27 mm. Although a certain prediction ability is able to prove the rationality of the modeling method, the current accuracy can not meet the future research on penetration control and quality evaluation, which may lead to misjudgement due to the large errors of individual points. In order to further improve the adaptability and prediction effect of the model for penetration forming prediction of asymmetrical fillet welds, swarm
3.2. Determination of the network model structure In the current related research, it is inconclusive whether increasing the number of hidden layers can reduce the network error, but it will undoubtedly complicate the network structure and greatly increase the network training time and data occupation space. Therefore, the threelayer network with a single hidden layer is generally preferred in design, and the number of hidden layer nodes is changed by trial and error method to obtain the network structure with the smallest error. The selection of the number of hidden layer nodes also has a great influence on the performance of the neural network model, which is the direct cause of "over-fitting" in training. At present, the formulas given in most literatures are for any number of samples and most of them are for the most disadvantageous situation, so they are not recommended for practical engineering applications. Based on the basic principle that the network structure should be as compact as possible on the premise of meeting the accuracy requirements. Comprehensively considering the complexity of the network structure, the size of the error and the number of samples, this model has been trained many times using the node deletion method. After performance comparison, the optimal number of hidden layer nodes is determined to be 5. So far, BP neural network model for predicting penetration morphology of asymmetrical fillet welds is determined, and the topological structure of the model is shown in Fig. 6. 3.3. Sample processing and data prediction In the research of the application of neural network in welding field, 250
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information, which is more conducive to quickly and accurately find the global optimal solution [35–37]. Based on these characteristics, this paper uses MEA to optimize the initial weight and threshold of the BPNN model, aiming to avoid the neural network falling into local optimum and improve the search speed of the optimal solution, thereby improving the prediction accuracy and stability of the model. The main steps to realize the optimization of BPNN model by MEA are as follows. The algorithm flow chart is shown in Fig. 9.
4.1. Weight and threshold encoding According to the topological structure of BPNN, the initial weights and thresholds to be solved need to be numerically coded. For a network structure with N inputs M outputs and L hidden layer nodes, the coding length X equals the sum of the initial weights and the number of thresholds: X=N*L+L*M+L+M,
Fig. 7. Prediction error rate of L1 and L2.
(1)
where N, L and M are respectively the node number of input layer, hidden layer and output layer. Therefore, after iterative optimization by evolutionary algorithm, each solution corresponds to a coding, and ultimately the optimal solution X = 4*5 + 5*3 + 5+3 = 43.
4.2. Set initial population and scoring rules Set parameters of the initial population and generate a random initial population. In this paper, the initial population size is set to 200(initial random generation of 200 codes), the number of superior and temporary sub-populations is 5, and the number of iterations is 10. The score of each solution is calculated according to the network calculation rules. In order to evaluate the quality of a solution, the reciprocal of the mean square error between the output value and the expected value of the solution acting on the network is usually used as the final score.
score = Fig. 8. Prediction absolute error of PD.
1 mse(expectation − calculation)
(2)
Where score is the score for each solution; expectation is the ideal value, that is, the definite value given in the experimental sample; calculation is the calculated value output by the network according to the group of weights and thresholds. This means that the higher the score, the smaller the proof error, the better the solution set.
intelligence algorithms were used to optimize BP neural network. The results show that the BP neural network optimized by the mind evolution algorithm (MEA) can significantly improve the prediction effect of the model. 4. Methodology of mind evolution algorithm
4.3. Convergence and alienation
The mathematic principle of BP neural network determines its inherent defect that it is easy to fall into local optimum. In addition, its training effect depends too much on the initial random weights and thresholds. With the purpose of making up for the deficiency of BP neural network, many scholars try to use optimization algorithm to improve the applicability of BP neural network [16,24].Compared with traditional optimization methods, intelligent optimization algorithms generally do not need a very clear objective function and the continuity and convexity of constraints. They have weak theoretical requirements and strong adaptability, and have advantages in solving speed and global optimization. The MEA is derived from the shortcomings of low search efficiency and prematurity of Genetic Algorithm. The core idea of that is still population evolution. It only uses two new operators, “convergence” and “alienation”, to coordinate and cooperate in the realization process. The parallel feature improves the search efficiency, and this algorithm can memorize multi-generation evolutionary
According to the score, the individuals are ranked from high to low, the top 5 constitutes the winner sub-population, and the second 5 constitutes the temporary sub-population. With these 10 individuals as the center, new individuals are generated according to normal distribution. Convergence operations (Individual competition produces winners.) are carried out within each subgroup until no new winners are generated to represent the subgroup maturity. At this time, the highest score of the individual within the subgroup is taken as the subgroup score. If the score of temporary subgroup is higher than that of the winner subgroup, the alienation operation (mainly substitution or abandonment between the two subgroups) will be performed until all the temporary subgroup scores are lower than that of the winner subgroup, and the evolution is completed. 251
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Fig. 9. Optimization flow chart for prediction model.
depth of blunt edge are recorded after some training. The results are shown in Fig. 10. It can be seen that, compared with the optimized model, the RMSE of the unoptimized model fluctuates obviously. Ten times in training, the RMSE of the leg length fluctuates more than 0.1 mm, and the RMSE of the penetration depth of blunt edge fluctuates about 0.06 mm, which means that the predicted results of the model fluctuate greatly, and the unstable predictive performance may have a greater impact on the later work. The predictive stability of the model is improved obviously by combining the MEA. The RMSE fluctuations of the leg length of and the penetration depth of blunt edge are controlled at 0.05 mm and 0.03 mm, respectively.
4.4. Decode and complete optimization The best individual in the best subgroup gained by iterations are found and decoded, and the optimal initial weight and threshold are obtained for BP neural network training. 5. Results and discussion The optimal weights and thresholds optimized by the mind evolutionary algorithm are applied to BP neural network, and the same sample data, parameters and methods are used to train and predict the network. The effects before and after optimization are compared from the three aspects of model prediction stability, convergence speed and prediction accuracy.
5.2. Comparison of convergence speed of network training By comparing the convergence steps of training for many times, the optimized network model can basically achieve the target error within 20 steps. It not only improves obviously than before optimization, but also has no occasional large number of iterations to converge after
5.1. Comparison of stability results of model prediction The root mean square error of the leg length and the penetration
Fig. 10. RMSE of the prediction of leg length and PD. 252
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Fig. 11. Comparison of iteration steps before and after optimization.
optimization, which can be inferred from Fig. 11. It shows that the initial weights and thresholds obtained by evolutionary algorithm optimization are closer to the optimum, only a few iterations are needed to meet the target accuracy, and generally do not fall into local optimum, resulting in occasional poor prediction performance. It is concluded that the optimized model has better performance and greatly improves the convergence speed of the model.
Fig. 13. Comparison of prediction absolute error of PD. Table 3 Comparison of the R2 and RMSE of outputs.
R2 before optimization R2 after optimization RMSE before optimization RMSE after optimization
5.3. Validation of prediction accuracy of optimized model The two models are trained with the same sample data, and choosing two models with the best training effect (the least RMSE) to predict the test samples. The comparison of the prediction results is as follows. Fig. 12 displays the comparison of predicted relative error rates of leg length L1 and L2. The prediction result of the penetration depth of blunt edge is shown in Fig. 13, which contrast with absolute error. It can be seen from the figures that the relative error rate of leg length has been increased by more than five percentage points after model optimization. The prediction error rates of leg length L1 and L2 are stable within 5 % and 7 % respectively. The prediction absolute error of PD is also controlled within 0.08 mm, which can meet the accuracy requirements of penetration control and quality evaluation. The determination coefficient (R2) and root mean square error (RMSE) are commonly used model evaluation indicators, but they are very sensitive to outliers. The forecasting results above show that the error of 20 groups of validation samples is small, and there is no abnormal point, which provides conditions for using these two evaluation indicators. Therefore, in order to evaluate the performance of the model more intuitively, the R2 and RMSE of the three outputs before and after optimization are compared. The result is shown in Table 3. The result shows that the R2 of three parameters are all above 0.94
L1
L2
PD
0.8526 0.9630 0.2582 0.0955
0.8614 0.9453 0.2559 0.1206
0.8360 0.9579 0.1357 0.0476
after optimization, which proves that the optimized model has good forecasting performance. The RMSE of leg length is about 0.1 mm, and that of PD is 0.0476 mm, which shows that the model has high prediction accuracy. 6. Conclusions In this paper, the general rule of penetration forming is obtained by analyzing a large number of asymmetrical fillet welds experimental results. Based on this, a neural network model for predicting penetration forming is established. Further, the model is optimized by Mind Evolutionary Algorithm. The results demonstrate that the optimized model has good predictive performance. Through the analysis of experiments and predictive results, the main conclusions are as follows: 1 The sensitivity analysis of the inputs and outputs of the neural network shows that the peak welding current is the most important factor affecting the penetration depth of blunt edge (PD). The welding speed has a greater influence on the leg length (L1 and L2)
Fig. 12. Comparison of prediction error rate of leg length(L1 and L2). 253
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than the peak current. The torch work angle not only has a significant effect on the leg length, but also has a certain adjustment role in PD. 2 The width of molten pool can synthetically reflect some potential factors that may affect the forming process, and it is highly correlated with L1, L2 and PD. Taking it as one of the input parameters of the model can improve the accuracy of the model prediction. 3 The BP neural network model based on peak welding current, welding speed, torch work angle and molten pool width as inputs, leg length on both sides and penetration depth of blunt edge as outputs can be used to predict penetration forming of asymmetrical fillet welds. However, more accurate penetration control and quality evaluation still need to be further optimized. 4 It is an effective attempt to use swarm intelligence algorithm to optimize the classical neural network model for predicting the relatively complex weld penetration forming. In this study, the stability, accuracy and convergence rate of prediction are significantly improved by MEA optimization. The error rate of leg length is less than 7 %, the error of penetration depth of blunt edge is within 0.08 mm. Good prediction performance makes it possible to control penetration and evaluate quality of asymmetrical fillet welds, which lays a foundation for realizing automatic welding of asymmetrical fillet welds. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (Grant No. U1733125) and the Natural Science Foundation of Tianjin Municipal, China (Grant Nos. 17JCZDJC38700 and 18JCYBJC19100). References [1] Teng TL, et al. Analysis of residual stresses and distortions in T-joint fillet welds. Int J Press Vessel Pip 2001;78(8):523–38. [2] Deng Dean, Liang W, Murakawa H. Determination of welding deformation in filletwelded joint by means of numerical simulation and comparison with experimental measurements. J Mater Process Technol 2007;183(2–3):219–25. [3] Unt Anna, Poutiainen I, Salminen A. Effects of sealing run welding with defocused laser beam on the quality of T-joint fillet weld. Phys Procedia 2014;56:497–506. [4] Kozak Janusz, Kowalski Jakub. Problems of determination of welding angular distortions of T-fillet joints in ship hull structures. Polish Marit Res 2015;22(2):79–85. [5] GONG Shui-li, et al. Formation, microstructure and mechanical properties of double-sided laser beam welded Ti–6Al–4V T-joint. Trans Nonferrous Met Soc China 2016;26(3):729–35. [6] Abe Takamasa, et al. Fatigue properties and fracture mechanism of load carrying type fillet joints with one-sided welding. Frat Ed Integritã Strutt 2016;35:424. [7] Chen Ji, et al. Predicting the influence of groove angle on heat transfer and fluid flow for new gas metal arc welding processes. Int J Heat Mass Transf 2012;55(1–3):102–11. [8] Fricke Wolfgang, Kahl Adrian, Paetzold Hans. Fatigue assessment of root cracking of fillet welds subject to throat bending using the structural stress approach. Weld World 2006;50(7–8):64–74. [9] Gyasi Emmanuel Afrane, et al. Study of adaptive automated GMAW process for full penetration fillet welds in offshore steel structures. The 27th International Ocean and Polar Engineering Conference. International Society of Offshore and Polar Engineers 2017. [10] Kumar A, DebRoy Tarasankar. Guaranteed fillet weld geometry from heat transfer model and multivariable optimization. Int J Heat Mass Transf 2004;47(26):5793–806.
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