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The Nonparametric Probabilistic Meth...

Azzi, Marie Jose,

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The Nonparametric Probabilistic Method for Model-Form Uncertainty Quantification, Model Updating and Digital Twinning /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Nonparametric Probabilistic Method for Model-Form Uncertainty Quantification, Model Updating and Digital Twinning // Marie Jose Azzi.
Author:	Azzi, Marie Jose,
Description:	1 electronic resource (156 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-05, Section: B.
Contained By:	Dissertations Abstracts International86-05B.
Subject:	Digital twins. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31643410
ISBN:	9798346385950

The Nonparametric Probabilistic Method for Model-Form Uncertainty Quantification, Model Updating and Digital Twinning /
Azzi, Marie Jose,

The Nonparametric Probabilistic Method for Model-Form Uncertainty Quantification, Model Updating and Digital Twinning /Marie Jose Azzi. - 1 electronic resource (156 pages)

Source: Dissertations Abstracts International, Volume: 86-05, Section: B.

Digital twins are virtual representations of physical systems that enable monitoring, diagnostics, and prognostics. They have been gaining popularity due to their potential to transform industries such as manufacturing, aerospace, healthcare, and urban planning. One specific type of digital twin, the Digital Twin Instance (DTI), is created through the real-time integration of data with computer simulations. DTIs facilitate the continuous and dynamic exchange of data between physical and virtual representations, enabling operations such as real-time system monitoring and predictive maintenance.To achieve their goals, DTIs must be founded on robust methodologies capable of performing model updates efficiently. Additionally, to ensure reliability and accuracy and to provide valid updates resilient to incomplete environmental knowledge, any modeling approach underlying a digital twin must incorporate uncertainty quantification.This thesis presents the development and application of the Nonparametric Probabilistic Method (NPM) for uncertainty quantification and model updating as a foundational methodology for digital twins, specifically DTIs. NPM is a physics-based, computationally tractable machine learning method designed to model and quantify model-form uncertainties. It extracts information from data not captured by a high-dimensional deterministic model and integrates it into a "hyperparameterized" stochastic, hyperreduced, projection-based reduced-order model by solving an inverse statistical problem formulated using a loss function and a few hyperparameters. The loss function ensures that the mean value and statistical fluctuations of quantities of interest predicted by the real-time stochastic model match target values obtained from reference data.NPM's performance hinges on the efficient minimization of the loss function, which is challenging due to factors such as stochasticity, non-convexity, and potential data scarcity. This thesis addresses these challenges, enabling a tractable and robust solution for the minimization and the inverse problem, thus maturing NPM into a foundational method for DTIs.The research introduces a two-pronged approach to enhance the efficiency and tractability of NPM. First, it analytically computes the sensitivities of the stochastic loss function with respect to hyperparameters, tracking the complex web of operations underlying its construction. Second, it reduces the theoretical number of hyperparameters from O(n2) to O(n)by developing a network of variational autoencoders that provide a nonlinear approximation of the SHPROM dependence on the hyperparameters.Additionally, the thesis addresses issues related to the robustness of the optimization problem, including scenarios plagued by data scarcity. This is achieved by adopting an adapted version of the squared quadratic Wasserstein distance as a measure of dissimilarity between data sets and reformulating the inverse statistical problem into a multimodal data-assimilation framework to handle potential ill-posedness. These advancements improve the reliability of the optimization process.The enhanced NPM is demonstrated through applications in structural dynamics, including real-time structural health monitoring. A practical example showcases Level 1 damage detection in a mockup aircraft wing, highlighting the potential of digital twins to revolutionize structural health monitoring by providing real-time insights and enabling predictive maintenance.This work lays a solid foundation for future research applying NPM to complex, nonlinear multiscale dynamics, setting the stage for integrating NPM with emerging technologies to tackle increasingly sophisticated engineering challenges.

English

ISBN: 9798346385950Subjects--Topical Terms:

3816704
Digital twins.

The Nonparametric Probabilistic Method for Model-Form Uncertainty Quantification, Model Updating and Digital Twinning /
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502 $b Ph.D. $c Stanford University $d 2024.
520 $a Digital twins are virtual representations of physical systems that enable monitoring, diagnostics, and prognostics. They have been gaining popularity due to their potential to transform industries such as manufacturing, aerospace, healthcare, and urban planning. One specific type of digital twin, the Digital Twin Instance (DTI), is created through the real-time integration of data with computer simulations. DTIs facilitate the continuous and dynamic exchange of data between physical and virtual representations, enabling operations such as real-time system monitoring and predictive maintenance.To achieve their goals, DTIs must be founded on robust methodologies capable of performing model updates efficiently. Additionally, to ensure reliability and accuracy and to provide valid updates resilient to incomplete environmental knowledge, any modeling approach underlying a digital twin must incorporate uncertainty quantification.This thesis presents the development and application of the Nonparametric Probabilistic Method (NPM) for uncertainty quantification and model updating as a foundational methodology for digital twins, specifically DTIs. NPM is a physics-based, computationally tractable machine learning method designed to model and quantify model-form uncertainties. It extracts information from data not captured by a high-dimensional deterministic model and integrates it into a "hyperparameterized" stochastic, hyperreduced, projection-based reduced-order model by solving an inverse statistical problem formulated using a loss function and a few hyperparameters. The loss function ensures that the mean value and statistical fluctuations of quantities of interest predicted by the real-time stochastic model match target values obtained from reference data.NPM's performance hinges on the efficient minimization of the loss function, which is challenging due to factors such as stochasticity, non-convexity, and potential data scarcity. This thesis addresses these challenges, enabling a tractable and robust solution for the minimization and the inverse problem, thus maturing NPM into a foundational method for DTIs.The research introduces a two-pronged approach to enhance the efficiency and tractability of NPM. First, it analytically computes the sensitivities of the stochastic loss function with respect to hyperparameters, tracking the complex web of operations underlying its construction. Second, it reduces the theoretical number of hyperparameters from O(n2) to O(n)by developing a network of variational autoencoders that provide a nonlinear approximation of the SHPROM dependence on the hyperparameters.Additionally, the thesis addresses issues related to the robustness of the optimization problem, including scenarios plagued by data scarcity. This is achieved by adopting an adapted version of the squared quadratic Wasserstein distance as a measure of dissimilarity between data sets and reformulating the inverse statistical problem into a multimodal data-assimilation framework to handle potential ill-posedness. These advancements improve the reliability of the optimization process.The enhanced NPM is demonstrated through applications in structural dynamics, including real-time structural health monitoring. A practical example showcases Level 1 damage detection in a mockup aircraft wing, highlighting the potential of digital twins to revolutionize structural health monitoring by providing real-time insights and enabling predictive maintenance.This work lays a solid foundation for future research applying NPM to complex, nonlinear multiscale dynamics, setting the stage for integrating NPM with emerging technologies to tackle increasingly sophisticated engineering challenges.
546 $a English
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