Actions for The Quadratic Point Estimate Method for Probabilistic Moment and Distribution Estimation for Uncertainty Quantification : Applications in Structural and Geotechnical Engineering

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The Quadratic Point Estimate Method for Probabilistic Moment and Distribution Estimation for Uncertainty Quantification : Applications in Structural and Geotechnical Engineering

Author
Ko, Minhyeok
Published
[University Park, Pennsylvania] : Pennsylvania State University, 2023.
Physical Description
1 electronic document
Additional Creators
Papakōnstantinou, Kōstas
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Restricted (PSU Only).
Summary
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.
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Dissertation Note
Ph.D. Pennsylvania State University 2023.
Technical Details
The full text of the dissertation is available as an Adobe Acrobat .pdf file ; Adobe Acrobat Reader required to view the file.
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