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Predictive modelling for quality analysis becomes one of the most critical requirements for a continuous improvement of reliability, efficiency and safety of laser welding process. Accurate and effective model to perform non-destructive quality estimation is an essential part of this assessment. This paper presents a structured approach developed to design an effective artificial neural network based model for predicting the weld bead dimensional characteristic in laser overlap welding of low carbon galvanized steel. The modelling approach is based on the analysis of direct and interaction effects of laser welding parameters such as laser power, welding speed, laser beam diameter and gap on weld bead dimensional characteristics such as depth of penetration, width at top surface and width at interface. The data used in this analysis was derived from structured experimental investigations according to Taguchi method and exhaustive FEM based 3D modelling and simulation efforts. Using a factorial design, different neural network based prediction models were developed, implemented and evaluated. The models were trained and tested using experimental data, supported with the data generated by the 3D simulation. Hold-out test and k-fold cross validation combined to various statistical tools were used to evaluate the influence of the laser welding parameters on the performances of the models. The results demonstrated that the proposed approach resulted successfully in a consistent model providing accurate and reliable predictions of weld bead dimensional characteristics under variable welding conditions. The best model presents prediction errors lower than 7% for the three weld quality characteristics.

Laser welding is an assembly process widely used in the industry, including the automotive industry. Overlap welding of galvanized steels enables joining of body car elements from different thicknesses. The disadvantage of the overlap configuration is the premature vaporization of zinc, which generates pressure at the interface of the overlapped sheets. These pressurized vapors eventually eject the metal out of the melting pool or trapped as blowers after solidification.

Several experimental studies have shown the possibility of overcoming this situation by controlling the welding process parameters. Like the keyhole welding, which creates a channel permitting the evacuation of zinc vapors, an optimal gap between the parts to be welded also allows the lateral evacuation of these vapors. This means that a good control of welding parameters and conditions (laser power, welding speed, focal diameter, Gap between sheets and sheet thicknesses) can produce the desired welds characteristics.

Laser welding parameters play an important role in determining the mechanical characteristics of the weld seam [

In contrast, thanks to their strong learning ability, artificial neural networks (ANNs) can establish nonlinear deterministic relationships between the inputs and the outputs of any system regardless of their complexity. ANNs are inspired by the human brain, they can learn and experience from examples, as they have a powerful ability to classify and recognize patterns. ANNs are used in many different fields of business, industry and science [

Synthia et al. [

Frason et al. [

Olabi et al. [

Depending on their architecture and their fields of application, several types of ANN exist. A broader description of different neural networks is presented in the literature review made by Zhang et al. [

Only a few studies used ANNs to predict the quality of laser welding of galvanized steels and even less in overlap configurations. The few attempts revealed in the literature are focussed on specific application of the ANNs without explicit and detailed references to the nature of the data used in the models training and validation and criteria adopted for the model performance evaluation. These fundamental ideas that constitute the basic ingredients of any models optimization procedure are indispensable to build an efficient predictive modeling approach.

The present paper presents an artificial neural network based model for predicting the weld bead dimensional characteristic in laser overlap welding of low carbon galvanized steel. The modelling approach is based on laser welding parameters such as laser power, welding speed, laser beam diameter and the gap between the overlapped parts to estimate specific weld bead dimensional characteristics such as depth of penetration, width at top surface and width at interface. A series of data provided from experiments using a 3KW Nd-YAG laser source in a well-structured Taguchi design are combined with simulation data provided by a 3D finite element model to train and test the ANN built using variables selection based factorial design. Hold-out test and k-fold cross validation combined to various improved statistical criteria are used for assessing the models performance.

The purpose of this study is to set up a model able to predict accurately and quickly three geometrical characteristics of the weld seams: depth of penetration (DOP), weld width at the top surface (WS) and at the interface (WI) as defined in

In order to know the most influential laser welding parameters on the model accuracy, as well as the effects of these parameters on the quality of the of weld characteristics prediction, 16 models are built according to a full factorial design including the variables known for their influence on the variation of the geometrical characteristics of the weld. As shown in

To eliminate the maximum random error sources, the learning data inputs, and the testing data inputs must represent the same population, i.e. both should be contained in the same variation range. This is the case in the present study, as shown in

The database generated by simulations is structured in a full factorial design of 4 factors, each at three levels, while experimental data are planned in three L9

Model | Gap | Power | Speed | Diameter |
---|---|---|---|---|

M_{1} | 1 | 1 | 1 | 1 |

M_{2} | 0 | 1 | 1 | 1 |

M_{3} | 1 | 0 | 1 | 1 |

M_{4} | 1 | 1 | 0 | 1 |

M_{5} | 1 | 1 | 1 | 0 |

M_{6} | 0 | 0 | 1 | 1 |

M_{7} | 0 | 1 | 0 | 1 |

M_{8} | 0 | 1 | 1 | 0 |

M_{9} | 1 | 0 | 0 | 1 |

M_{10} | 1 | 0 | 1 | 0 |

M_{11} | 1 | 1 | 0 | 0 |

M_{12} | 1 | 0 | 0 | 0 |

M_{13} | 0 | 1 | 0 | 0 |

M_{14} | 0 | 0 | 1 | 0 |

M_{15} | 0 | 0 | 0 | 1 |

M_{16} | 0 | 0 | 0 | 0 |

Level | Gap | Power | Speed | Diameter |
---|---|---|---|---|

1 | 0.05 | 2000 | 40 | 300 |

2 | 0.10 | 2500 | 55 | 395 |

3 | 0.15 | 3000 | 70 | 490 |

orthogonal matrix. For each gap value, to determine the true prediction errors of an ANN model and its accuracy for future predictions, new unused data in learning stage should be used in model testing phase, because learning errors are often inferior to validation errors. To do this, two validation methods are adopted: “hold-out set method” and “k-fold crossvalidation method”. The hold-out set method consists of using the large part of the data to train the model and the remaining data to test it. The k-fold cross validation method consists of sampling all the n data after its randomization in k segments, the model is then trained by n-k data and tested by k remaining data. The procedure is repeated k times by changing the testing sample each time. The validation errors are estimated by various statistical tools for the k variants, then averaged to determine the real prediction errors of the model.

The neural network modeling procedure used in this study consists first in confirming the reliability of the data provided by the 3D finite element model. Using the hold-out set method, the ANN models are trained by the entire simulation data and then tested by the experimental data. Second, all the data are mixed and randomized, then the k-fold cross validation method is applied, with k = 6.

There are several kinds of networks according to their architectures, their internal mechanisms and their application objectives. In the present study, the interest is focused on multilayer feedforward back propagation perceptron for its prediction capability. As illustrated in

The artificial neuron is an integrator that performs the weighted sum of its inputs originate from the previous layer (Equation (1)). The resulted sum is then transformed by a transfer function to provide the neuron output. The transfer function used for neurons of the input and hidden layer, is a sigmoid (Equation

(2)), and that used for the output layer neurons is a linear function (Equation (3)) where x, w^{T} and b denote respectively neuron input, Wight matrix and bias.

a = f ( s ) = f ( x W T − b ) (1)

f ( s ) = 1 / ( 1 + e − s ) (2)

f ( s ) = s (3)

The outputs of last layer neurons are then compared to the target values (dependent variables), if the difference is greater than the tolerated deviation, the network updates the weights associated to each neuron by means of a backpropagation technique and therefore starts a new computing loop, to help minimize the gap between the network output and the target value. Thus, the iterations continue until reaching a tolerated value of the error. The networks are assembled using the built in Matlab NetfitingToolbox. The function used for the training of the various networks is the Levenberg-Marquardt function. This function use an algorithm for supervised learning considered the fastest available algorithm by virtue of the validation vectors, which enables the network learning to stop prematurely if the performance in the validation matrix fails to reduce the error.

Based on the modeling process results, three statistical variables are estimated to evaluate the performance of each model: 1) Coefficient of determination R^{2} which is commonly applied to training errors. Its main defect is its growth with the addition of input variables to the model, whereas an excess of variables does not always lead to robust models. This is why one is interested in the adjusted coefficient R 2 ¯ . 2) Root mean squared error (RMSE) is the standard deviation of prediction errors (residuals), it measures the extent of these residuals and indicates the concentration of data around the line of best fit, and 3) mean absolute percentage error (MAPE) is a useful measure of forecasting accuracy. It is easy to interpret because it is expressed in percentage. The criteria are expressed mathematically as:

R 2 = 1 − ∑ i = 1 n ( y i − y ^ i ) 2 ∑ i = 1 n ( y i − y ¯ ) 2 (4)

R 2 ¯ = 1 − ( 1 − R 2 ) ( n − 1 ) ( n − p − 1 ) (5)

MAPE = ( 1 n ∑ i = 1 n | y i − y ^ i y i | ) 100 ( % ) (6)

RMSE = 1 n ∑ i = 1 n ( y i − y ^ i ) 2 (7)

where n, p, y i , y ^ and y ¯ denote respectively sample size, number of input process parameter, actual output, predicted output and the mean actual output.

The evaluation of the training and testing performances of the 16 models are based on the three statistical criteria applied to the two validation methods. First, the models training and testing performances using the hold-out set method are evaluated and the contributions of the laser welding parameters to ANN model improvement are estimated. In this case, as the models are trained using numerical simulation data and tested by means of experimental data, the major part of the training errors are due to the laser welding parameters not considered as variables in the ANN model building and to the possible bias in the 3D numerical model predictions, while the observed testing errors are related to experimental errors.

_{1}, which contains the four process variables. The relative errors of DOP, WS and WI Prediction are 2.1%, 1.1% and 2.6% respectively. The M_{2} model, which does not include the gap as input, also shows high performances in the prediction of

Model | DOP | WS | WI | ||||||
---|---|---|---|---|---|---|---|---|---|

RMSE | MAPE | R 2 ¯ | RMSE | MAPE | R 2 ¯ | RMSE | MAPE | R 2 ¯ | |

M_{1} | 68.9 | 2.1 | 1 | 20.2 | 1.1 | 1.01 | 53.5 | 2.6 | 0.99 |

M_{2} | 142.3 | 4.2 | 0.95 | 35.5 | 2 | 0.97 | 80 | 4.6 | 0.89 |

M_{3} | 263 | 9.3 | 0.79 | 119.3 | 7.1 | 0.50 | 179 | 10.4 | 0.53 |

M_{4} | 440.4 | 16.4 | 0.29 | 111.1 | 4.1 | 0.58 | 193 | 10.8 | 30.9 |

M_{5} | 237.9 | 8.2 | 0.82 | 47.8 | 2.8 | 0.93 | 79.8 | 4.5 | 0.89 |

M_{6} | 281.5 | 9.7 | 0.74 | 124 | 7.4 | 0.48 | 191 | 11.2 | 0.48 |

M_{7} | 449.2 | 16.2 | 0.27 | 107.6 | 6.2 | 50.8 | 196.8 | 11.4 | 0.36 |

M_{8} | 268.9 | 8.9 | 0.77 | 57.5 | 3.2 | 0.89 | 105.3 | 6.1 | 0.83 |

M_{9} | 476.2 | 16.9 | 0.16 | 147.6 | 8.4 | 0.17 | 238.9 | 13.3 | 0.064 |

M_{10} | 330.1 | 11.1 | 0.64 | 130.4 | 7.8 | 0.36 | 184.2 | 11 | 0.48 |

M_{11} | 476.7 | 17.0 | 0.16 | 117.7 | 6.8 | 0.50 | 191.3 | 11 | 0.375 |

M_{12} | 507.6 | 18.1 | 0.03 | 161 | 9.1 | 0.02 | 242.3 | 13.2 | 0.047 |

M_{13} | 487.1 | 17.2 | 0.12 | 121.8 | 7 | 0.47 | 204.6 | 11.8 | 0.32 |

M_{14} | 347.8 | 1.8 | 0.59 | 137.1 | 8.1 | 0.33 | 199 | 11.9 | 0.43 |

M_{15} | 486.1 | 17 | 0.12 | 151.7 | 8.5 | 0.15 | 250.9 | 14 | 0.018 |

M_{16} | 517.3 | 18.3 | 0 | 165.6 | 9.3 | 0 | 253.8 | 14.2 | 0 |

the three weld seam attributes with respectively a relative error of 4.2%, 2% and 4.6%. In third place comes the M_{5} model, which does not consider the focal diameter as input with prediction errors of 8.2%, 2.8% and 4.5% for DOP, WS and WI respectively. Among the two-variable models, the model M_{8}, which considers only the power and the welding speed as inputs, shows relatively good performance during learning stage. The DOP, WS and WI relative prediction errors are 8.9%, 3.2% and 6.1% respectively.

Variance analysis (ANOVA) results in

Despite their percentage differences, the graphs of effect reveal that all welding parameters have a positive effect on improving the prediction quality of the three geometric attributes of the weld. This asserts that the most accurate and reliable model is indeed the M_{1} which considers all the variables.

The P-value and F-value express the reliability of ANOVA results. For example, for P = 0.03, the Gap contribution of 1.2% is a reliable result with 97% confidence. As we can see, the confidence interval for the effects of laser power, welding speed and focal diameter is about 99%, and that associated with the gap effect is 94%, this is most likely due to difficulty maintaining a constant Gap along the welding line.

A comparison between validation errors and learning errors shows how well an ANN model can predict the geometric attributes of the weld for any laser welding parameters combination. The comparison is applied to the models that show better performances during the learning process, namely models M_{1}, M_{2}, M_{5} and M_{8}.

Source | RMSE_DOP | RMSE_WS | RMSE_WI | ||||||
---|---|---|---|---|---|---|---|---|---|

C% | F-Value | P-Value | C% | F-Value | P-Value | C% | F-Value | P-Value | |

Gap | 0.51 | 5.18 | 0.057 | 0.29 | 5.22 | 0.06 | 1.18 | 20.46 | 0.003 |

P | 8.28 | 84.63 | 0.000 | 54.4 | 988.6 | 0.00 | 41 | 711.54 | 0.000 |

S | 77.5 | 792.4 | 0.000 | 34.4 | 624.5 | 0.00 | 50.1 | 868.69 | 0.000 |

D | 6.42 | 65.6 | 0.000 | 2.70 | 48.9 | 0.00 | 0.43 | 7.43 | 0.030 |

P*S | 3.25 | 3.25 | 0.001 | 7.34 | 133.3 | 0.00 | 6.18 | 107.2 | 0.000 |

P*D | 0.72 | 7.34 | 0.030 | 0.10 | 1.89 | 0.21 | 0.18 | 3.21 | 0.116 |

S*D | 2.05 | 20.98 | 0.003 | 0.17 | 3.08 | 0.12 | 0.34 | 5.84 | 0.046 |

P*S*D | 0.53 | 5.42 | 0.053 | 0.23 | 4.2 | 0.08 | 0.17 | 3 | 0.127 |

Error | 0.69 | - | - | 0.39 | - | - | 0.40 | - | - |

Total | 100 | - | - | 100 | - | - | 100 | - | - |

Model | Limits | RMSE_DOP | MAPE_DOP | RMSE_WS | MAPE_WS | RMSE_WI | MAPE_WI |
---|---|---|---|---|---|---|---|

M_{1} | Train | 68.9 | 2.1 | 20.2 | 1.1 | 53.5 | 2.6 |

Val_{1} | 134.01 | 6.05 | 48.51 | 3.1 | 133.4 | 6.81 | |

Val_{2} | 163.1 | 6.8 | 35.2 | 2.2 | 101.5 | 6.6 | |

M_{2} | Train | 142.3 | 4.2 | 35.5 | 2.8 | 79.8 | 4.5 |

Val_{1} | 194.6 | 8.2 | 62.4 | 4.2 | 166.4 | 8.7 | |

Val_{2} | 203.3 | 8.8 | 50.5 | 3.4 | 117.4 | 8.4 | |

M_{5} | Train | 237.9 | 8.2 | 47.8 | 2.8 | 79.8 | 4.5 |

Val_{1} | 330.2 | 12.9 | 68.7 | 4.2 | 152.3 | 7.6 | |

Val_{2} | 366.4 | 17.4 | 65.2 | 4.8 | 115.4 | 7.8 | |

M_{8} | Train | 268.9 | 8.9 | 57.5 | 3.2 | 105.4 | 6.1 |

Val_{1} | 337.2 | 13.6 | 80.5 | 4.9 | 168.4 | 8.7 | |

Val_{2} | 308.5 | 13.0 | 66.8 | 4.4 | 126.6 | 8.5 |

The results do not show a large deviation between training errors and validation errors, as the maximum gap between these two has been proved to not exceed 4%. The validation errors obtained by the two methods are almost identical. In the light of the results shown in _{1}, a precision greater than 91% by the M_{2} model and a prediction error exceeding 10% for the two other models. WS can be estimated with a precision greater than 95% by the four models. WI can be predicted by the model M_{1} with an accuracy greater than 93% and a precision of 91% for other models. _{1} Vs actual values, respectively of DOP, WS and WI. _{2} and _{5}. The contour of the cross section of a weld bead can be deduced from the three predicted geometric attributes DOP, WS and WI.

This paper presents a structured approach developed to design an effective artificial neural network based model for predicting the weld bead dimensional characteristic in laser overlap welding of low carbon galvanized steel. Based on a fused data provided by structured experimental investigations using Taguchi method and in-depth FEM based 3D simulations, the possible relationships between welding parameters such as laser power, welding speed, laser beam diameter and gap, and weld bead dimensional characteristics such as depth of penetration, width at top surface and width at interface are analyzed and their sensitivity to the welding conditions are evaluated using relevant statistical tools. Based on these results, a factorial design is used to develop, implement and evaluate different neural network based prediction models. The proposed models

are trained and tested using experimental data, supported by the data generated by the 3D simulation. Hold-out test and k-fold cross validation combined to improved statistical criteria are used to evaluate the influence of the laser welding parameters on the performances of the models. Analyses of variance results reveal that all the welding parameters have a positive contribution to the improvement of the prediction quality. The laser power and the welding speed contributions are much more important compared to the contribution of the laser beam diameter. The gap contribution appears to be insignificant.

The achieved predictive modelling results demonstrate that the resulting models present excellent performances and can effectively predict the weld bead dimensional characteristics with average predicting errors less than 10%. The validation process reveals that the WS can be predicted with an accuracy of 96% while the prediction accuracy of DOP and WI is about 93%. These results demonstrate that the proposed ANN based prediction approach can effectively lead to a consistent model able to accurately and reliably provide an appropriate prediction of weld bead dimensional characteristics in laser overlap welding of low carbon galvanized steel under variable welding parameters and conditions.

With the encouraging results achieved using this modelling strategy, the laser overlap welding of low carbon galvanized steel will be the subject of additional and exhaustive investigations to produce more numerical simulation and experimental data as well as to test others neural networks approach in order to develop more efficient ANN predictive modelling method.

The authors declare no conflicts of interest regarding the publication of this paper.

Oussaid, K. and El Ouafi, A. (2019) A Study on Prediction of Weld Geometry in Laser Overlap Welding of Low Carbon Galvanized Steel Using ANN-Based Models. Journal of Software Engineering and Applications, 12, 509-523. https://doi.org/10.4236/jsea.2019.1212031