Modeling of uncertain geometry of cold formed steel members based on laser measurements and machine learning

Abstract

This research focuses on modeling of as-true geometric uncertainty of cold-formed steel (CFS) members with a multidimensional Gaussian process, the coefficients of which are trained by a maximum-likelihood machine-learning method. The stochasticity and correlations of geometric features, including geometric imperfections, are embedded in the model. An optimization-based feature-recognition algorithm is devised to process general CFS members, by which the processed features are used as the benchmark data, and the entire geometry of a CFS member is reconstructed by the parameterized features. A multidimensional Gaussian process is used to model a joint distribution of feature parameters along the longitudinal direction, where some decorrelations in space and features are assumed to reduce the dimension of the process due to difficulties of acquiring massive samples. The Gaussian process model is trained by geometric features of 112 samples and tested by 48 samples, and results were satisfactory for the proposed method. Finite element analysis with different geometric uncertainty modeling methods applied are conducted and compared. The as-true geometric uncertainty provides more robust and accurate simulation, such as strength and failure modes, as a result. Thus, the proposed method provides a new way in geometric uncertainty modeling for advanced structural analysis and design, which thoroughly considers nonlinear geometric and material conditions.