A Few-Shot Learning-Based Crashworthiness Analysis and Optimization for Multi-Cell Structure of High-Speed Train
Abstract
:1. Introduction
2. Materials and Methods
2.1. Materials
2.1.1. Theoretical Analysis
- Film deformation energy: The film deformation energy E_{m} of each flange plate can be calculated by integrating the triangular cells of a folded wavelength.$${E}_{\mathrm{m}}={{\displaystyle \int}}_{s}{\sigma}_{0}t\mathrm{d}s=\frac{1}{8}{\sigma}_{0}t{L}^{2}=\frac{1}{2}{M}_{0}\frac{{L}^{2}}{t},$$$${\sigma}_{0}=\sqrt{\frac{{\sigma}_{y}{\sigma}_{u}}{1+n}},$$$${E}_{\mathrm{m}}^{{90}^{\circ}}=2{E}_{\mathrm{m}}={M}_{0}\frac{{L}^{2}}{t},$$
- Bending deformation energy: Using the SSFE theory, where buckling wavelength L and wall thickness t are assumed to be constant, we can divide the energy absorption region of each corner unit into a thin film deformation zone and a bending deformation zone. For each of the flange plates, bending deformation energy is calculated as follows:$${E}_{\mathrm{b}}={{\displaystyle \sum}}_{i=1}^{3}{M}_{0}{\theta}_{i}c=2\pi {M}_{0}{B}_{0},$$
- Mean crushing forces: Five-cell structures with the cross-section configuration honeycomb tubes consist of 16 V-shaped elements, 4 Y-I-shaped elements, and 4 Y-II-shaped elements. We can then substitute Equations (5) and (7)–(9) into Equation (1) to obtain Equation (10).$${F}_{\mathrm{m}}\mathrm{L}\eta ={E}_{\mathrm{b}3}+16{E}_{\mathrm{m}}^{\mathrm{V}}+4{E}_{\mathrm{m}}^{\mathrm{Y}-\mathrm{I}}+4{E}_{\mathrm{m}}^{\mathrm{Y}-\mathrm{II}},$$
2.1.2. Finite Element Model
2.1.3. Test Set-Up
2.1.4. Crashworthiness Analysis
2.2. Few-Shot Learning
2.2.1. Data Augmentation
2.2.2. Model Framework
- Wide component
- 2.
- Deep component
- 3.
- Joint training
Algorithm 1. Few-shot learning pseudo code. |
Few-Shot Learning in This Study |
hybrid data augmentation to obtain dataset |
initialize all variables by the random value |
for loop from 1 to num_epoch |
choose x_{i} from X data as the wide model input |
choose x_{j} from X data as the deep model input |
compute the y_{j} of the wide model output |
$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{y}_{j}:={\displaystyle \sum}_{i=1}^{n}{\mathit{w}}_{i,j}{x}_{i}+{b}_{1}$ |
compute the output of the deep model output-layer a^{(l+1)} |
for l = L to 5: |
compute the a^{(l + 1)} based on a^{(l)} and W^{(l)} and b^{(l)} |
$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{a}^{\left(l+1\right)}=f\left({W}^{\left(l\right)}{a}^{\left(l\right)}+{b}^{\left(l\right)}\right)$ |
concatenate the wide output and deep output, and compute the model output |
$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\left(Y=1\mid x\right)=\sigma \left({w}_{wide}^{T}\left[x,\varphi \left(x\right)\right]+{w}_{\mathrm{deep}}^{T}{a}^{\left({l}_{f}\right)}+b\right)$ |
2.3. Problem Set-Up
2.3.1. Optimization Problem
2.3.2. Optimization Algorithm
3. Results and Discussion
3.1. Model Training
3.2. Parametric Study
3.3. Optimisation Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Property | Units | Value |
---|---|---|
Density | kg/m^{3} | 2700 |
Young’s modulus | MPa | 71,000 |
Poisson’s ratio | - | 0.33 |
Yield stress | MPa | 121 |
Ultimate tensile strength | MPa | 183 |
Fracture strain | % | 7.71 |
Fracture stress | MPa | 175 |
Methods | F_{m} (kN) | Displacement (mm) | EA (KJ) | SEA (KJ/kg) |
---|---|---|---|---|
Experimental | 874.0 | 278 | 243.0 | 26.9 |
Simulation | 905.7 | 269 | 243.6 | 25.75 |
Theorical | 903.3 | 279 | 252.0 | 26.6 |
Simulation Error (%) | 3.6 | 3.2 | 0.2 | 4.2 |
Theorical Error (%) | 3.4 | 3.5 | 3.3 | 3.1 |
Test | t (mm) | a (mm) | b (mm) | c (mm) | F_{m} (kN) | SEA | ||||
---|---|---|---|---|---|---|---|---|---|---|
Actual | Predicted | Eror | Actual | Predicted | Error | |||||
1 | 4.2 | 57 | 67 | 44 | 761.11 | 749.03 | 0.015 | 26.078 | 28.034 | −0.07 |
2 | 5.7 | 69 | 41 | 46 | 1116.38 | 1114.536 | 0.002 | 28.729 | 31.34 | −0.09 |
3 | 4.7 | 70 | 67 | 68 | 931.48 | 952.34 | −0.025 | 29.2 | 32.456 | −0.111 |
4 | 5.7 | 47 | 48 | 69 | 1006.12 | 1007.639 | −0.001 | 33.272 | 36.299 | −0.09 |
5 | 3.6 | 61 | 69 | 63 | 629.65 | 651.34 | −0.034 | 23.16 | 28.67 | −0.237 |
6 | 5.9 | 69 | 63 | 64 | 1231.12 | 1218.28 | 0.01 | 32.29 | 34.85 | −0.08 |
7 | 5.4 | 69 | 98 | 67 | 1140.87 | 1134.53 | 0.006 | 35.88 | 36.5 | −0.017 |
8 | 3.6 | 70 | 67 | 68 | 668.87 | 700.87 | −0.047 | 21.8 | 28.82 | −0.322 |
9 | 4.2 | 42 | 58 | 48 | 666.69 | 668.17 | −0.002 | 29.77 | 29.16 | 0.02 |
10 | 3.8 | 79 | 31 | 63 | 749.89 | 776.08 | −0.03 | 21.67 | 28.35 | −0.30 |
11 | 4.3 | 47 | 68 | 70.5 | 741.17 | 756.45 | −0.02 | 28.07 | 32.37 | −0.15 |
12 | 1.33 | 11 | 4 | 82 | 71.022 | 131.23 | −0.84 | 28.02 | 30.23 | −0.07 |
Design | t (mm) | a (mm) | b (mm) | c (mm) | F_{m} (kN) | EA (kJ) | SEA (kJ/kg) | M (kg) |
---|---|---|---|---|---|---|---|---|
Initial | 5 | 56 | 56 | 51 | 905.7 | 243.6 | 25.75 | 9.46 |
Optimal | 6 | 49 | 0 | 37 | 1060.9 | 333.9 | 36.86 | 9.06 |
Change | 0.20 | −0.125 | - | −0.274 | 0.171 | 0.371 | 0.301 | −0.040 |
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Dong, S.; Jing, T.; Zhang, J. A Few-Shot Learning-Based Crashworthiness Analysis and Optimization for Multi-Cell Structure of High-Speed Train. Machines 2022, 10, 696. https://doi.org/10.3390/machines10080696
Dong S, Jing T, Zhang J. A Few-Shot Learning-Based Crashworthiness Analysis and Optimization for Multi-Cell Structure of High-Speed Train. Machines. 2022; 10(8):696. https://doi.org/10.3390/machines10080696
Chicago/Turabian StyleDong, Shaodi, Tengfei Jing, and Jianjun Zhang. 2022. "A Few-Shot Learning-Based Crashworthiness Analysis and Optimization for Multi-Cell Structure of High-Speed Train" Machines 10, no. 8: 696. https://doi.org/10.3390/machines10080696