Machine Learning-based Second-order Analysis of Beam-columns through Physics-Informed Neural Networks

The second-order analysis of slender steel members can be challenging, particularly when large deflections are involved. This research introduces a novel Machine Learning-based Structural Analysis (MLSA) method for the second-order analysis of beam-columns. This method presents a promising alternative to prevailing solutions that rely on oversimplified analytical equations or traditional finite-element-based methods.

The effectiveness of conventional machine learning methods heavily depends on the quality and quantity of the provided data. However, such data are often scarce and costly to obtain in structural engineering practices. To address this issue, we employ a new and explainable machine learning-based method called Physics-informed Neural Networks (PINN). This method uses physical information to guide the learning process, creating a self-supervised learning procedure. This approach makes it possible to train the neural network with few or even no predefined datasets, achieving an accurate approximation.

This research extends the PINN method to the problems of second-order analysis of slender beam-columns. The source code for the PINN program used in this paper is available on this GitHub page. We encourage readers to explore the code to gain a deeper understanding of the implementation details.

If you find our research and the provided source code useful, please consider citing our paper in your work.

Developed by:

• Siwei Liu - Assistant Professor, The Hong Kong Polytechnic University. si-wei.liu@polyu.edu.hk.
• Liang Chen - Postdoctoral Fellow, The Hong Kong Polytechnic University. liang17.chen@connect.polyu.hk.
• Haoyi Zhang - PhD Student, The Hong Kong Polytechnic University. haoyi.zhang@connect.polyu.hk.

Requirements

All codes were developed and tested on a Windows 11 machine with Python 3.8. The following packages are required to run the codes:

• numpy: (For numerical computation)
• torch: (For neural network)
• matplotlib: (For plotting)
• tqdm: (For progress bar)

Please install the required packages via:

pip install -r requirements.txt

Package compatibility has been checked with versions specified in "requirements.txt".

How to Use

• To run the examples in this study, please first clone the repository via:

git clone https://github.com/zsulsw/mlsa.git

• Run the "Main.py" file located in the "Source" folder.
• Input the filename of the example from the "Examples" folder. You will see a list of file names showing the data files in the "Examples" folder. Please ensure that the data file is in JSON format and has been placed into the "Examples" folder.
• For further information, please check this publication.

Citation

If the source codes are useful, please cite the paper. Click Here.

• Chen, L, Zhang H.Y., Liu, S.W. & Chan, S.L.: "Second-order Analysis of Beam-columns by Machine Learning-based Structural Analysis through Physics-Informed Neural Networks", Advanced Steel Construction, 2023. 19, 411-420. DOI

@article{Chen-Liang-2023,
author = {Liang Chen, Hao-Yi Zhang, Si-Wei Liu and Siu-Lai Chan},
doi = {10.18057/IJASC.2023.19.4.10},
issn = {1816-112X},
journal = {Advanced Steel Construction},
pages = {411-420},
title = {{Second-order Analysis of Beam-columns by Machine Learning-based Structural Analysis through Physics-Informed Neural Networks}},
url = {http://dx.doi.org/10.18057/IJASC.2023.19.4.10},
volume = {19},
year = {2023}
}