Generative Design for Catalan Vaults for Multi-storey Seismic Construction

Abstract

This paper explores the scope of using a deep learning framework for shape optimization of Catalan vaults for medium seismic areas. Catalan vaults are thin tile vaults that optimize the material usage of a floor slab without form-work and thus, additional material and labour. These structures can be constructed from tiles made from locally sourced earth which can provide an alternate to steel, timber, and concrete for areas with poor access to such materials, bringing down transportation, material, and carbon costs, providing opportunity to accommodate the consequences of rapid population growth. Seismic optimization of these vaults usually requires topology optimization and shape optimization tools. However, conventionally, these are computationally expensive and time-consuming - making them unsuitable for initial design explorations where a vast array of designs need to be quickly explored. As an alternative, a deep learning framework is explored as a design generation and optimization tool. This uses a Variational Autoencoder (VAE) trained on a dataset of 10,000 samples to extract novel meshes whose seismic performance is then predicted with the help of fully-connected dense Neural Network (NN) surrogate models trained on the results of a Linear Dynamic analysis in Karamba (in Grasshopper). An optimization loop is set-up through Gradient Descent Optimization where the gradient of the predicted score is minimized with respect to the latent space of the VAE - for single and multi-objective optimization. Conditioning the latent space of the VAE is further explored (Conditional VAE) so that the user is able to extract samples from the latent space with particular desirable characteristics such as a desirable height of the vault. This opens up opportunities to gain better control of the latent space and generate meaningful new samples that are able to incorporate user specifications. The geometry of the Catalan vault is represented in terms of polyedge force-densities that allow a 99.91% reduction in dimensionality and thus, faster convergence, as compared to other data structuring techniques explored in the literature as half-adjacency matrices.