Uncertainty quantification in model verification and validation as applied to large scale historic masonry monuments

This publication focuses on the Verification and Validation (V&V) of numerical models for establishing confidence in model predictions, and demonstrates the complete process through a case study application completed on the Washington National Cathedral masonry vaults. The goal herein is to understand where modeling errors and uncertainty originate from, and obtain model predictions that are statistically consistent with their respective measurements. The approach presented in this manuscript is comprehensive, as it considers all major sources of errors and uncertainty that originate from numerical solutions of differential equations (numerical uncertainty), imprecise model input parameter values (parameter uncertainty), incomplete definitions of underlying physics due to assumptions and idealizations (bias error) and variability in measurements (experimental uncertainty). The experimental evidence necessary for reducing the uncertainty in model predictions is obtained through in situ vibration measurements conducted on the masonry vaults of Washington National Cathedral. By deploying the prescribed method, uncertainty in model predictions is reduced by approximately two thirds.

► Developed a finite element model of Washington National Cathedral masonry vaults.
► Carried out code and solution verification to address numerical uncertainties.
► Conducted in situ vibration experiments to identify modal parameters of the vaults.
► Calibrated and validated model to mitigate parameter uncertainty and systematic bias.
► Demonstrated a two thirds reduction in the prediction uncertainty through V&V.