Physics-informed machine learning for predicting building structure strength in fire tests

1. Introduction and motivation

Virtual fire tests (e.g., see this article) are important for designing and testing novel materials and structures. It is common to place sensors to measure the temperature and displacement (or deformation) at sensor locations during fire tests. However, we would like to know the temperature and displacement everywhere in the domain for a more accurate analysis.

The challenge with classical methods and simulation software (e.g., finite element methods) is that they are computationally expensive and require so many trial and error.

To overcome this challenge, I introduce a physics-informed machine learning framework.

Given the temperature and deformation at sensor locations, the physics-informed machine learning framework predicts the temperature and deformation everywhere in the domain.

2. Physics-informed machine learning framework

Physics-informed machine learning falls in the category of weakly supervised learning. Specifically, physics-informed neural networks were first introduced by Raissi et al. in 2019 and cited more than 2700 times so far! I specifically apply this framework to fire tests for predicting temperature and displacements of a building structure.

In this framework, the input of the neural network is the spatial coordinates of the building structure and the output is the displacement and temperature fields of the structure. I use the automatic differentiation technology of TensorFlow to buildup the governing equations that describes the physics of the problem. Afterwards, I enforce the physics and the sparse data to the loss function of the neural network.

Loss function = conservation of energy + conservation of momentum for linear elasticity + sparse observations at sensor locations

I train the neural network to minimize this loss function!

3. Neural network setup and performance

  • Gradient decent optimization with Adam
  • Coding in Python along with TensorFlow, NumPy, and MatPlotLib libraries
  • Sherlock cluster with V100-24GB memory and clock Rate of 1.38 GHz
  • GPU clock time of approximately 1 hour
  • Twice differentiable activation functions such as hyperbolic tangent

4. Accomplishments

  • A good agreement between the prediction by the introduced physics-informed machine learning framework and the ground truth is observed.
  • My framework successfully predicts the Von Mises stress and compares it to the yield strength in the fire test.
  • This framework can be commercialized and be a core idea for a startup company.

5. Next steps

  • Extending the framework to unsteady and three-dimensional problems
  • Involving spatially varying material properties in the framework to test more complicated structures
  • Incorporating plasticity equations

Poster

For the full visual and quantitative results and discussion, please click on the top figure and then save it on your computer. By opening this figure, you will see the poster presentation of my work with high quality.

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