From Gaussian to Lognormal: Improving Material Property Modeling forPrecise Structural Predictions.

Accurate prediction of material properties is essential in structural engineering design to ensure re-liability and safety. Traditional approaches often rely on Gaussian distributions to model materialvariability. However, our research reveals limitations with Gaussian assumptions, particularly whencovariance parameters exceed certain thresholds, leading to physically unrealistic negative values formaterial properties.To overcome these limitations, we investigate an alternative approach using lognormal distribu-tions for material property modeling. Through Monte Carlo simulations employing Cholesky decom-position, we compare the performance of lognormal distributions with Gaussian counterparts. Ourfindings demonstrate that lognormal distributions offer a viable alternative, providing more accuraterepresentations of material variability while maintaining computational efficiency.Furthermore, we utilize finite element method (FEM) data from Monte Carlo simulations to predictbeam deflection using deep neural networks (DNNs). Leveraging inverse modeling techniques, weshowcase the ability to predict elastic modulus from beam deflection data under both normal andlognormal distribution assumptions.By integrating lognormal modeling and inverse modeling techniques into structural analysis, weenhance the realism and accuracy of predictions, thereby improving reliability in engineering design.This paper discusses the implications of our findings and emphasizes the importance of consideringalternative probability distributions for material property modeling in structural engineering applica-tions.