The objective in the hook design is to identify an optimal shape that enhances the stiffness while adhering to specific volume constraints and loads. This can be achieved by minimizing the strain energy. The physical boundary conditions are as follows.
We model the half of the hook by lofting 11 2D sections along a guideline, the procedure for constructing a hook is as follows, see Appendix G for more details.
For maintaining a naturalistic semblance characterized by smoothness and minimal undulation, we apply mean filter to each section once or two at random (each section are generated independently and randomly), considering its neighboring sections.
Finally, we generate a total of 222,141 shape data points. All data are stored in data.
We employ the mean-teacher-based active learning algorithm on this dataset, to select 50,000 shapes for labeling and train the physical model, the corresponding labels are obtained by COMSOL.
Run the following code under the directory mean-teacher-al.
python main.py
The trained model is stored in net_best_teacher.tar, and the learning results is as follows.
| 4.308E-3 | 1.818E-3 |
Firstly, run the following code to compute the intrinsic dimension.
python lpca.py
The results should be 68 (round up). For verifying that the value is sufficient, we examine the reconstruction error as a function of the dimension of latent space, which are shown as follows.
We choose 68 as the dimension of the latent space in the auto-encoder. Run the following code for training.
python main_ae.py --embed-dim 68
The trained model are stored in results_aeID=68. The learning results of auto-encoder are documented in the following table.
| ReconErr mean | ReconErr variance |
|---|---|
| 1.143E-2 | 9.055E-5 |
We perform two kinds of optimization problem with a given initial hook.
- P1:
$\min E$ s.t.$V\leq0.5V_{\text{init}}$ - P2:
$\min V$ s.t.$E\leq0.5E_{\text{init}}$
Run the following code
python shape_opt_pysparse.py --prob minEconV # problem 1
python shape_opt_pysparse.py --prob minVconE # problem 2
Both optimized results are located in optimize_results. The following figure shows the comparison of our optimized results and the COMSOL's optimized results.
