Integrating Bayesian Inference into Structural Parameter Estimation: A Python-Based Approach Using OpenSeesPy and PyMC

In structural engineering, accurate prediction of structural behavior is crucial for ensuring safety and reliability. Traditional parameter estimation methods often rely on deterministic approaches, which may overlook inherent uncertainties in real-world structures. This paper presents a comprehensive manual on utilizing a Bayesian framework to update structural model parameters, offering a robust strategy for quantifying uncertainties and enhancing predictive accuracy. The methodology employs Python, leveraging Open-SeesPy for finite element modeling and PyMC for probabilistic inference. Five distinct examples are provided to illustrate the workflow, ranging from fundamental parameter estimation in structural frames to advanced Hierarchical Stochastic Models (HSMs) for constitutive material calibration. This work serves as a practical guide for structural engineers seeking to adopt novel probabilistic techniques. By integrating Bayesian inference, engineers can effectively account for both measurement noise and intrinsic physical variability, thereby improving the fidelity of predictive models. The use of open-source tools streamlines the implementation process, making these advanced methods accessible to a wider audience in engineering practice.