Improving Prediction of Springback in Sheet Metal Forming Using Multilayer Perceptron-Based Genetic Algorithm
Abstract
:1. Introduction
2. Experimental
2.1. Material
2.2. Method
3. Establishment of an Artificial Neural Network Model
3.1. Background
3.2. ANN Modelling
4. Results and Discussion
4.1. Experimental Springback
4.2. ANN-Based Springback Prediction
- Adopting a method of coding the real parameters of the adaptation function in the form of a chromosome (interconnected binary numbers representing subsequent parameters which form a chromosome).
- Determining the form of the adaptation function.
- Random selection of starting points—the process of searching for the optimal set of parameters begins with the random selection of starting points.
- Selection of chromosomes for a new population—the selection of individuals for the new population is carried out according to the roulette wheel rule in which each individual corresponds to a segment of a circle of a size proportional to the value of the adaptation function, and then a random point is selected on the wheel and the chromosome to which the randomly drawn part of the circle corresponds is transferred to the new population. This process is repeated until the number of chromosomes in the new population is equal to the number of chromosomes in the old population.
- Genetic operators are used for individuals from the new population, the most common of which are: crossover and mutation.
5. Conclusions
- The specimens cut transverse to the rolling direction exhibit lower values of springback coefficient Ks compared to the specimens cut along the rolling direction. The difference between the springback coefficients measured for both directions does not exceed 2.3%.
- An increase in the bend angle γl leads to a nonlinear increase in the springback coefficient Ks. The higher the bend angle γl, the smaller the difference between the springback coefficients Ks measured for both sample orientations.
- The Young’s modulus E and ultimate tensile stress σm are variables which have no significant effect on the coefficient of springback.
- The smallest RMS error value for a training set is seen in the network trained with the QN and LM algorithms. RMS error values for both networks trained by these algorithms are very similar for all the network architectures tested.
- The network trained with the BP algorithm (MLP 5:5-7-1:1) had the highest value of correlation coefficient in connection with the lowest value of SD ratio.
- For each network, the RMS error for the training set was less than the RMS error determined for the validation set. This is due to the different number of learning sets on the basis of which the network gains the ability to generalise data.
- The MLP trained by the BP, CG and LM algorithms favoured the punch bend depth under load fl as the most important variable affecting the springback coefficient Ks.
- It was found that the anisotropic coefficient r was the least important parameter.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Orientation of Specimen | E, MPa | σy, MPa | σm, MPa | K, MPa | n | r |
---|---|---|---|---|---|---|
0° | 1.98·105 | 186.7 | 324.1 | 558.9 | 0.211 | 1.74 |
90° | 1.92·105 | 194.3 | 318.6 | 542.6 | 0.223 | 1.82 |
Parameter | fl | E | σy | σm | K | n | r |
---|---|---|---|---|---|---|---|
Useful at δ = 0.0005 | Yes | Yes | Ignore | Ignore | Yes | Yes | Ignore |
Useful at δ = 0.001 | Yes | Ignore | Yes | Ignore | Yes | Yes | Yes |
Useful at δ = 0.002 | Yes | Ignore | Yes | Ignore | Yes | Yes | Yes |
Useful at δ = 0.005 | Yes | Yes | Ignore | Ignore | Yes | Yes | Yes |
Useful at δ = 0.01 | Yes | Ignore | Yes | Ignore | Yes | Yes | Ignore |
BP | CG | QN | LM | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
MLPs | RMS(T) | RMS(V) | SD Ratio | Correlation | RMS(T) | RMS(V) | SD Ratio | Correlation | RMS(T) | RMS(V) | SD Ratio | Correlation | RMS(T) | RMS(V) | SD Ration | Correlation |
MLP 5:5-6-1:1 | 0.085 | 0.129 | 0.270 | 0.962 | 0.769 | 0.113 | 0.269 | 0.963 | 0.068 | 0.128 | 0.240 | 0.970 | 0.068 | 0.126 | 0.239 | 0.971 |
MLP 5:5-7-1:1 | 0.084 | 0.107 | 0.254 | 0.967 | 0.077 | 0.118 | 0.265 | 0.964 | 0.068 | 0.129 | 0.237 | 0.971 | 0.067 | 0.129 | 0.235 | 0.972 |
MLP 5:5-9-1:1 | 0.112 | 0.165 | 0.262 | 0.965 | 0.073 | 0.124 | 0.257 | 0.967 | 0.067 | 0.145 | 0.235 | 0.972 | 0.068 | 0.129 | 0.239 | 0.971 |
BP | CG | QN | LM | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Test MLPs | fl | σy | K | n | r | fl | σy | K | n | r | fl | σy | K | n | r | fl | σy | K | n | r |
MLP 5:5-6-1:1 | ••••• | •• | ••• | •••• | • | ••••• | • | ••• | •••• | •• | •••• | ••• | ••••• | •• | • | ••••• | ••• | •••• | • | •• |
MLP 5:5-7-1:1 | ••••• | ••• | •••• | •• | • | •••• | ••••• | ••• | •• | • | • | ••••• | •• | ••• | •••• | •••• | • | ••• | ••••• | •• |
MLP 5:5-9-1:1 | •••• | • | ••••• | •• | ••• | ••••• | •• | •••• | ••• | • | ••• | •••• | • | ••••• | •• | ••••• | • | •••• | ••• | •• |
Case | Input Parameter | Springback Coefficient Ks | |||||
---|---|---|---|---|---|---|---|
fl, mm | σy, MPa | K | n | r | ANN | Experiment | |
1 | 3 | 186.7 | 558.9 | 0.211 | 1.74 | 0.867 | 0.869 |
13 | 12 | 186.7 | 558.9 | 0.211 | 1.74 | 0.914 | 0.907 |
17 | 24 | 186.7 | 558.9 | 0.211 | 1.74 | 0.953 | 0.956 |
18 | 27 | 186.7 | 558.9 | 0.211 | 1.74 | 0.952 | 0.954 |
28 | 3 | 194.3 | 542.6 | 0.223 | 1.82 | 0.834 | 0.832 |
31 | 12 | 194.3 | 542.6 | 0.223 | 1.82 | 0.914 | 0.918 |
37 | 3 | 194.3 | 542.6 | 0.223 | 1.82 | 0.831 | 0.832 |
41 | 15 | 194.3 | 542.6 | 0.223 | 1.82 | 0.862 | 0.876 |
51 | 18 | 194.3 | 542.6 | 0.223 | 1.82 | 0.939 | 0.928 |
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Trzepieciński, T.; Lemu, H.G. Improving Prediction of Springback in Sheet Metal Forming Using Multilayer Perceptron-Based Genetic Algorithm. Materials 2020, 13, 3129. https://doi.org/10.3390/ma13143129
Trzepieciński T, Lemu HG. Improving Prediction of Springback in Sheet Metal Forming Using Multilayer Perceptron-Based Genetic Algorithm. Materials. 2020; 13(14):3129. https://doi.org/10.3390/ma13143129
Chicago/Turabian StyleTrzepieciński, Tomasz, and Hirpa G. Lemu. 2020. "Improving Prediction of Springback in Sheet Metal Forming Using Multilayer Perceptron-Based Genetic Algorithm" Materials 13, no. 14: 3129. https://doi.org/10.3390/ma13143129