Uncertainty Quantification in Structural Dynamics

Overview

This series of Jupyter Notebooks is based on the book Quantificação de Incerteza e Estimação de Parâmetros em Dinâmica Estrutural: Uma Introdução Baseada em Exemplos Computacionais by Daniel Alves Castello and Thiago Gamboa Ritto.

Project Objectives

• Summarize the theoretical contents of the book
• Explore the underlying mathematical formulae and their derivations
• Translate the original MATLAB codes to Python

Computational Approach

Probability Theory and Static Problem

We begin by introducing fundamental concepts in Probability Theory and tackle a static problem to determine the model's stiffness using experimental data.

Dynamic System Analysis

Next, we analyze a dynamical system represented by a mass-spring-damper model.

Frequency Response Exploration

For this dynamical system, we identified upper and lower limits for the Frequency Response based on a probability distribution of the uncertain parameter.

Parameter Identification

Using experimental data and a reference model, we identified the uncertain parameter.

Complementary Topics

Throughout the project, we developed additional notebooks to provide insights into:

• Frequency Response Function and Fourier Transform
• Least-Squares Method
• Levenberg-Marquardt Method for Error Minimization

References

1. Castello, D. A., & Ritto, T. G. (2016). Quantificação de Incerteza e Estimação de Parâmetros em Dinâmica Estrutural: Uma Introdução Baseada em Exemplos Computacionais. [Notas em Matemática Aplicada Vol. 81]
2. Riley, K. F., & Hobson, M. P. (2006). Mathematical Methods for Physics and Engineering: Third Edition. [Cambdrige University Press]
3. Mary L. Boas, (2005). Mathematical Methods in the Physical Sciences: Third Edition. [Wiley]