Danny Smyl

Adrien Gallet, Andrew Liew, Iman Hajirasouliha et al.

This work develops a machine learned structural design model for continuous beam systems from the inverse problem perspective. After demarcating between forward, optimisation and inverse machine learned operators, the investigation proposes a novel methodology based on the recently developed influence zone concept which represents a fundamental shift in approach compared to traditional structural design methods. The aim of this approach is to conceptualise a non-iterative structural design model that predicts cross-section requirements for continuous beam systems of arbitrary system size. After generating a dataset of known solutions, an appropriate neural network architecture is identified, trained, and tested against unseen data. The results show a mean absolute percentage testing error of 1.6% for cross-section property predictions, along with a good ability of the neural network to generalise well to structural systems of variable size. The CBeamXP dataset generated in this work and an associated python-based neural network training script are available at an open-source data repository to allow for the reproducibility of results and to encourage further investigations.

Bozhou Zhuang, Sashank Rana, Brandon Jones et al.

Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of interest (e.g. at finite element nodes). The lack of explicit model error approximators has been addressed recently with the emergence of machine learning (ML), which closes the loop between numerical model features/solutions and explicit model error approximations. In this paper, we propose physics-informed neural networks (PINNs) for simultaneous numerical model error approximation and superresolution. To test our approach, numerical data was generated using finite element simulations on a two-dimensional elastic plate with a central opening. Four- and eight-node quadrilateral elements were used in the discretization to represent the reduced-order and higher-order models, respectively. It was found that the developed PINNs effectively predict model errors in both x and y displacement fields with small differences between predictions and ground truth. Our findings demonstrate that the integration of physics-informed loss functions enables neural networks (NNs) to surpass a purely data-driven approach for approximating model errors.

Xiangxiong Kong, Danny Smyl

On June 24, 2021, a 12-story condominium building (Champlain Towers South) in Surfside, Florida partially collapsed, resulting in one of the deadliest building collapses in United States history with 98 people confirmed deceased. In this work, we analyze the collapse event using a video clip that is publicly available from social media. In our analysis, we apply computer vision algorithms to corroborate new information from the video clip that may not be readily interpreted by human eyes. By comparing the differential features against different video frames, our proposed method is used to quantify the falling structural components by mapping the directions and magnitudes of their movements. We demonstrate the potential of this video processing methodology in investigations of catastrophic structural failures and hope our approach may serve as a basis for further investigations into structure collapse events.

Danny Smyl, Tyler N. Tallman, Dong Liu et al.

Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as perturbation techniques, which ultimately limits the use for time-sensitive applications. In particular, in nonlinear inverse problems Gauss-Newton methods are used that require iterative updates to be computed from the Jacobian. Computationally more efficient alternatives are Quasi-Newton methods, where the repeated computation of the Jacobian is replaced by an approximate update. Here we present a highly efficient data-driven Quasi-Newton method applicable to nonlinear inverse problems. We achieve this, by using the singular value decomposition and learning a mapping from model outputs to the singular values to compute the updated Jacobian. This enables a speed-up expected of Quasi-Newton methods without accumulating roundoff errors, enabling time-critical applications and allowing for flexible incorporation of prior knowledge necessary to solve ill-posed problems. We present results for the highly non-linear inverse problem of electrical impedance tomography with experimental data.

Danny Smyl, Dong Liu

Electrical Impedance Tomography (EIT) is a powerful tool for non-destructive evaluation, state estimation, and process tomography - among numerous other use cases. For these applications, and in order to reliably reconstruct images of a given process using EIT, we must obtain high-quality voltage measurements from the target of interest. As such, it is obvious that the locations of electrodes used for measuring plays a key role in this task. Yet, to date, methods for optimally placing electrodes either require knowledge on the EIT target (which is, in practice, never fully known) or are computationally difficult to implement numerically. In this paper, we circumvent these challenges and present a straightforward deep learning based approach for optimizing electrodes positions. It is found that the optimized electrode positions outperformed "standard" uniformly-distributed electrode layouts in all test cases. Further, it is found that the use of optimized electrode positions computed using the approach derived herein can reduce errors in EIT reconstructions as well as improve the distinguishability of EIT measurements.