Skip to content

v1.0.4

Choose a tag to compare

View all tags
@luclaurent luclaurent released this 06 Dec 16:23
· 33 commits to main since this release
v1.0.4
a227ef6

BO-HBM-ex

GitHub license GitHub release GitHub stars DOI

Description

The Python's tool BO-HBM-ex shows an example of the application of Bayesian Optimization [1] on a Duffing problem [2]. The Duffing's oscillator problem is here solved using Harmonic Balance Method and a continuation technique.



Duffing oscillator scheme.

The optimization problem can be written:

Find $(k_{nl}^*,\xi^*)$ such as

$(k_{nl}^*,\xi^*)=\underset{(k_{nl},\xi)\in\mathcal{D}}{\arg\min}\,\underset{\omega\in[\omega_l,\omega_u]}{\max} \ddot{q}_{\mathrm{RMS}}(k_{nl},\xi,\omega)$

Installation

Get the source code from this repository. The example can be run after installation of dependencies with pip install -r requirements.txt.

Usage

The Python's scripts can be run only with Python 3.

Run solver of Duffing oscillator

The file respDuffing.py provides frequencies responses for displacement and acceleration on PDF pictures for $\xi=\{0.15, 0.3, 0.5, 1.\}$ ($[\mathrm{kg}\cdot\mathrm{s}^{-1}]$) and $k_{nl}=\{0.25,0.5,0.75,...,2\}$ ($[\mathrm{N}\cdot\mathrm{m}^{-3}]$) . Pictures are stored in ParamDuffing folder.

Following pictures show $\ddot{q}_ {\mathrm{RMS}}$ for a few values of $k_ {nl}$ for $\xi=0.15\,\mathrm{kg}\cdot\mathrm{s}^{-1}$ (a), $\xi=0.3\,\mathrm{kg}\cdot\mathrm{s}^{-1}$ (b), $\xi=0.5\,\mathrm{kg}\cdot\mathrm{s}^{-1}$ (c) and $\xi=1\,\mathrm{kg}\cdot\mathrm{s}^{-1}$ (d).

(a) (b)
Arms_xi15 Arms_xi30
(c) (d)
Arms_xi50 Arms_xi100

Animations of $q_ {\mathrm{RMS}}$ (a) and $\ddot{q}_ {\mathrm{RMS}}$ (b) of large set of values of $k_{nl}$ for $\xi=0.15\,\mathrm{kg}\cdot\mathrm{s}^{-1}$:

(a) (b)
anim_Drms anim_Arms

Run Bayesian Optimization on Duffing oscillator

The file OptiExp.py generates data of Bayesian Optimization's iterations. These data will be available on the directory ExpOptimDuffing which contains data for sample sets containing 10, 20 and 25 samples. Results are provided along BO iterations on CSV files and acquisition and objective functions are plotted in 2D and 3D.

The following pictures show the evolution of the acquisition and objective functions along BO's iterations applied on the Optimization of the Duffing Oscillator (minimization of the maximum of the acceleration along the frequency bandwidth $[0,2.5]$ ($\mathrm{rad}\cdot\mathrm{s}^{-1}$)). The initial sampling obtained with LHS contains 10 sample points.

Acquisition function Objective function
anim_10_contourEI anim_10_contourObj
anim_10_surfaceEI anim_10_surfaceObj

Versions

The code has been executed without any issues with the following versions of Python and libraries:

- Python 3.10.9
- numpy 1.26.2
- matplotlib 3.8.2
- pandas 2.1.3
- torch 2.1.1
- botorch 0.9.4
- gpytorch 1.11
- pydoe 0.3.8

How to cite

This repo is relative to the PhD thesis of Quentin Ragueneau achieved at LMSSC under the supervision of Antoine Legay and Luc Laurent in collaboration with Ingeliance Technologies and founded by ANRT (Cifre 2020/0272).

Please use the following citation reference if you use the code:

Ragueneau, Q., Laurent, L. & Legay, A. (2023). BO-HBM-ex (vxxx). Zenodo. https://doi.org/10.5281/zenodo.102592910

Bibtex entry:

@software{BO-HBM-ex-soft,
author       = {Ragueneau, Quentin and Laurent, Luc and Legay, Antoine},
title        = {{BO-HBM-ex}},
month        = dec,
year         = 2023,
publisher    = {Zenodo},
version      = {vxxx}
doi          = {10.5281/zenodo.10259290},
url          = {https://doi.org/10.5281/zenodo.10259290}
}

NB: version number and DOI must be adapted from Zenodo's repository.

License

MIT License

Copyright (c) 2023 - Quentin Ragueneau (quentin.ragueneau@ingeliance.com)

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

References

[1] D. R. Jones, M. Schonlau, and W. J. Welch. Efficient Global Optimization of Expensive Black-Box Functions. Journal of Global Optimization, 13(4):455–492, Dec. 1998.

[2] B. Balaram, M. D. Narayanan, and P. K. Rajendrakumar. Optimal design of multi-parametric nonlinear systems using a parametric continuation based Genetic Algorithm approach. Nonlinear Dynamics, 67(4):2759–2777, Mar. 2012.

What's Changed

Full Changelog: v1.0.3...v1.0.4

Contributors

luclaurent
Assets 2
Loading