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A multi-fidelity approach to predict stress fields in elastic structures with random pores through Bayesian deep learning

Krokos, Vasileios 2023. A multi-fidelity approach to predict stress fields in elastic structures with random pores through Bayesian deep learning. PhD Thesis, Cardiff University.
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Multiscale structures, although being prevalent in engineering applications, are challenging to analyse due to the high computational cost involved in simulating them using direct numerical simulations. This increased cost is the result of the very fine mesh that needs to be used to capture the effect of the smallest geometrical features. Common approaches to tackle multiscale problems fall either in the homogenisation or domain decomposition techniques. Homogenisation, that is computationally less expensive, assumes that the macroscale displacement gradients vary slowly over the structure. That assumption is commonly violated in real world applications, thus it is necessary to employ domain decomposition techniques, which are computationally more expensive and practically more intrusive. The objective of this study is to develop a multiscale surrogate modelling technique that can be used to perform fast stress predictions in structures exhibiting spatially random microscopic features. The proposed approach does not assume separation of scales and it does not require prior geometrical parametrisation of the multiscale problem. The input to the developed framework is an inexpensively calculated macroscale solution obtained using a coarse finite element mesh that ignores the microscale features. The framework outputs corrections to the macroscale field that take into account the existence of the microscale features. A Neural Network (NN) is utilised to perform these fine scale corrections. As opposed to classical surrogate models like Gaussian Processes, NNs can efficiently learn and operate on image and graph data. In contrast to the relevant literature, in this thesis we are primarily interested in cases where multiple fine scale features are interacting with each other and/or the boundaries of the structure. Another area of focus is the exploration of Bayesian NNs (BNNs). As opposed to deterministic NNs, BNNs can be used to provide uncertainty information for their prediction, which is crucial in engineering applications. Nonetheless, most of the works found in the relevant literature are deterministic. In this thesis we use the Bayes By Backprop method to convert the developed NNs to BNNs. Additionally, we show how this uncertainty can be utilised to solve problems reported by NN practitioners. Firstly, using efficient Bayesian conditioning algorithms we impose physics-based corrections to the output of the network, leading to improved performance in cases where training data are sparse. Additionally, we adopt selective learning which is commonly used to reduce the need for labelled data in segmentation tasks. In this work we show how it can be used in the context of regression tasks. Lastly, we adopt two techniques from the computer vision domain to reduce the training data requirements. To this end, we use mechanically consistent rotations as data augmentation technique and transfer learning to efficiently train models with limited number of data. The conducted experiments show that the proposed approach manages to accurately predict both the stress distribution and the maximum equivalent stress in the examined structures, as long as these lay inside the training data distribution. Additionally, the uncertainty of the prediction is quantified and shown to positively correlate with the prediction error. Finally, in terms of data requirements we show that with a dataset of reasonable size, below 500 FE simulations, the performance of the networks is satisfactory

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Engineering
Uncontrolled Keywords: 1) Bayesian machine learning 2) Surrogate modelling 3) Multiscale stress analysis 4) Graph neural network 5) Convolutional neural network 6) Porous media
Date of First Compliant Deposit: 31 January 2024
Last Modified: 31 Jan 2024 13:52

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