Thesis overview
A comprehensive overview of my thesis research
If I had to define the motivation behind my Ph.D. thesis using a few words, I would use Certification by Analysis.
Certification by Analysis (CbA) is transformative approach in aviation where validated computational simulations are used to satisfy compliance with certification requirements, reducing the need for expensive and time taking physical testing.
To give an example, consider the controlled impact demonstration project conducted jointly by NASA and Boeing in 1984, where they crashed a remotely controlled Boeing 720 aircraft to accquire data. Millions of dollars was spent in collecting a single crash point data. Repeating this process for different data points obviously does not make sense.
This is where CbA comes in. By carefully quantifying the uncertianty or error present in the numerical modeling tools, one can completely avoid these expensive tests or aid in deciding only a minimal set of required tests to implement.
The critical enabling technology is Uncertainty Qunatification (UQ), where aleatoric and epistemic uncertainties are completely quantified through probablistic tools and analyses.
The Big Picture
- Broder problem: CbA has the potential to dramatically reduce certification costs for next generation aerospace systems.
- Key challenges: Quantifying uncertainties in numerical simulations is computationally expensive because of the number and amount of uncertainties involved.
- How does my work help: Developing novel methods that address the computational challenge while maintaining accuracy or confidence.
Thesis Structure
My thesis is organized into the following main research areas. Click on each project to explore the detailed work, or visit individual subprojects for specific techniques and case studies.
Multi-fidelity inverse problems
Multi-fidelity inverse problems leverage cheap, low-accuracy models to accelerate quantifying uncertainty of parameters in expensive, high-accuracy models.
Related Projects:
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Multilevel Markov chain Monte Carlo
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Multi-fidelity Kalman filtering
Adaptive surrogates for Multi-Disciplinary Analysis
Strategy for building and refining fast and accurate surrogate models to enable outer loop applications in coupled multi-disciplinary systems.
Related Projects:
Multi-sacle closure modeling
Learning physics based, data-driven closure models that allow for resolving expensive full scale simulations
Related Projects:
Future ideas
Some possible future extensions involve stochastic multi-fidelity optimization and reinforcement learning