CDS&E: ECCS: Accurate and Efficient Uncertainty Quantification and Reliability Assessment for Computational Electromagnetics and Engineering

Colorado State University, Fort Collins CO

Investigators

Abstract

Uncertainty quantification (UQ) permits analyses of sensitivity and reliability, which is of critical importance in all areas of engineering. Indeed, uncertainty is unavoidable in all engineering applications. Just as one example, UQ in biomedical computational electromagnetics (CEM) applications involves studies of electromagnetic field’s sensitivity to uncertainties in position and orientation of field exciters as well as dimensions and materials of biological objects. Through rigorous UQ, the effectiveness and reliability of analyses and designs may be improved drastically. With the growing demand for high-precision components, devices, and systems for consumer use (e.g., cellphones) or national security (e.g., stealth technology), the analysis of uncertainty is extremely important. In fact, in the design of practical systems and methods, the low-probability but high-risk events often dominate design concerns. To achieve these critical objectives, this project will conduct a cohesive analysis and treatment of deterministic and statistical errors to enhance engineering designs through automatic and rigorous techniques. The proposed methodology for error control and UQ in CEM and computational engineering enhances both quality and confidence in designs and simulation data while also increasing efficiency. Although the project focuses on safety-critical and mission-critical applications requiring high-quality rigorous UQ, the proposed new approach can also provide significant advantages in other CEM and numerical modeling applications. Compared to existing techniques facing challenges of severe limitations in the dimension of uncertain parameter space, the computational expense, and the ability to reliably and accurately model and calculate failure probabilities, particularly for high-risk events, the proposed approach has advantages of extensive adaptivity, achieving accuracy for high-dimensional problems, and computing the probabilities of arbitrary events rapidly. The project’s educational activities include advising and training of graduate students, developing new educational and course materials, and participating in various retention/outreach programs. The principal objective of this project is to formulate, develop, analyze, and demonstrate a novel synergistic approach of fully adaptive error control (both deterministic and statistical) and uncertainty quantification to greatly enhance the efficiency, accuracy, and usability of reliability assessment for engineering applications including electromagnetic systems and devices. The project develops a comprehensive approach to constrain deterministic error (to eliminate significant error propagation effects) and statistical error (to ensure high-quality resolution of success and failure probabilities). The novel approach promises significant savings in computational resources and enhanced performance for high-dimensional uncertainty. The approach will significantly improve the analysis of safety-critical and mission-critical problems demanding high-quality UQ. The analysis of uncertain events, particularly those with low-probability and high-risk, is untenable in practical applications through existing UQ approaches. Compared to existing methods, the proposed novel adaptive local resolution with dimension reduction UQ method has several unique features: (A) comprehensive deterministic and statistical error control synergy, as opposed to independent processes, to efficiently drive local resolution enhancements; (B) integral support for multiple objectives in the automated UQ processes with accelerated convergence to specified error tolerances; (C) novel adjoint-based similarity indicators to conduct significant efficiency enhancements through quantity of interest clustering; (D) high-resiliency to high-dimensional uncertainty while supporting multiple objectives and providing significantly enhanced convergence rates; (E) failure-probability-aware dimension reduction techniques through adjoint data indicators and parametric sensitivity metrics; and (F) identification of critical points in the parameter space to drive intelligent resource allocations and identify unstable regions. Overall, the proposed approach has a strong potential to fulfill the needs of rigorous, automatic, and efficient uncertainty quantification. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.