Machine learning for structural design models of continuous beam systems via influence zones

TL;DR

This work develops a machine learned structural design model for continuous beam systems from the inverse problem perspective based on the recently developed influence zone concept to conceptualise a non-iterative structural design model that predicts cross-section requirements for continuous beam systems of arbitrary system size.

Abstract

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.

Figures (16)

• Figure 1: The inverse problem perspective for structural design, which relies on known priors such as design brief details of loading and span requirements along with observations of utilisation ratios that represent structural adequacy to evaluate the model parameters of a solution, such as size, shape and topology of a viable structure. Structural analysis is treated as the forward problem.
• Figure 2: Types of machine learning (ML) components from the inverse problem perspective. Shapes in each sub-figure; ellipses: inverse problem (top), forward problem (bottom); rectangles: observations (left), known priors (middle), causal factors (right).
• Figure 3: Design process of a continuous beam system from the inverse problem perspective.
• Figure 4: A figurative influence zone of $k_\mathrm{max}=2$ for design beam $g=3$ within a $m=7$ continuous beam system with $\epsilon_{\mathrm{max}} = 0.02$ limit.
• Figure 5: An illustration demonstrating the structuring of the neural network inputs using influence zones and zero-padding with $k_\mathrm{max} = 2$, leading to $n=4 k_\mathrm{max} + 2 = 10$ inputs.