The Quadratic Point Estimate Method for Probabilistic Moment and Distribution Estimation for Uncertainty Quantification: Applications in Structural and Geotechnical Engineering
Restricted (Penn State Only)
- Author:
- Ko, Minhyeok
- Graduate Program:
- Civil Engineering (PHD)
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- November 07, 2023
- Committee Members:
- Puneet Singla, Outside Unit & Field Member
Gordon Warn, Major Field Member
Kostas Papakonstantinou, Chair & Dissertation Advisor
Farshad Rajabipour, Program Head/Chair
Pinlei Chen, Major Field Member
Gregory Banyay, Special Member - Keywords:
- Uncertainty Quantification
Quadratic Point Estimate Method
Moment Estimation
Vine-copula
Polynomial Chaos Expansion
Point Estimate Method
Unscented Transformation
Structural Engineering
Geotechnical Engineering
Uncertainty Propagation - Abstract:
- The study of probabilistic engineering mechanics has witnessed significant advancements, particularly in the domain of moment estimation and probability distribution evaluation. This work introduces and rigorously develops a novel method, the Quadratic Point Estimate Method (QPEM), which is verified to effectively evaluate moments of any input random variables up to the fifth order. The Monte Carlo (MC) method, a prevalent sampling-based technique for evaluating probabilistic integrals, has limitations, notably the slow convergence of estimation error. This work explores variance reduction techniques like Quasi-Monte Carlo and Latin Hypercube Sampling to enhance MC's efficiency. It also delves into Sparse Grid Quadrature, with a focus on the Smolyak scheme, addressing challenges in multidimensional integrals. QPEM’s robustness and innovative approach in capturing moments stand out, offering a superior alternative to existing Point Estimate Methods (PEM) and the Unscented Transformation (UT). It presents an enhanced capability in numerical evaluation of probabilistic integrals, showing adaptability and precision across various applications in civil engineering, especially structural and geotechnical engineering. Integrated with the Rosenblatt transformation, the QPEM addresses applications involving complex multivariate input dependencies effectively. The work also examines the Pearson/Johnson Distribution Systems in relation to QPEM. These systems classify probability distributions using their moments, providing a framework to categorize various distributions. Integrating the QPEM with these systems facilitates both output distribution estimation and moments evaluation. Subsequently, the work explores the Polynomial Chaos Expansion (PCE) framework, a spectral representation of random processes. By leveraging the strengths of QPEM in estimating higher-order moments and the flexibility of PCE in representing random outputs, this combined approach aims to offer a more comprehensive solution for uncertainty quantification. In conclusion, this work offers a holistic view of the significance of the QPEM and its integration with renowned distribution systems. The versatility of the QPEM is further underscored by its successful application across problems in structural and geotechnical engineering. From statics to dynamics, elasticity to plasticity, and even for random fields, the methodologies presented in this work have proven their efficacy.