My research interests are in the area of probabilistic methods, including reliability analysis, Monte Carlo methods, Bayes networks, uncertainty quantification (model verification, validation, and calibration), system identification, and structural health monitoring. The results of uncertainty quantification are used to guide in risk-informed decision making under uncertainty. I have worked on a variety of applications in Aerospace, Civil, Electrical, and Mechanical engineering, including multi-level, multi-disciplinary systems.
Statistical Modeling
Data mining: Supervised (regression, trees, etc.) vs. unsupervised learning (clustering methods)
Regression: Linear/non-linear regression, and regularization methods (ridge, Lasso, etc.), trees
Classification: Logistic regression, classification trees, support/relevance vector machine classifiers
Inference methods: Parameter estimation, confidence intervals, credibility intervals, etc.
Hypothesis testing: Classical testing methods, A/B testing, Bayes factor (likelihood ratio-test), etc.
Sampling methods: Monte Carlo sampling, importance sampling, adaptive sampling, MCMC sampling, etc.
Machine learning: Gaussian processes, splines, radial basis kernels, support/relevance vector machines
Decision trees: Resampling, bootstrapping, bagging, random forests and boosting for bias/variance reduction
Uncertainty Quantification
Probabilistic methods
Risk and reliability analysis
Inverse problems and parameter estimation
Monte Carlo methods
Bayesian networks and probabilistic inference
Epistemic uncertainty
Diagnostics, Prognostics, and Health Monitoring
Model-based approaches for diagnosis and prognosis
Online system health monitoring and management
Bayesian tracking methods - Kalman filtering, particle filtering, etc.
Uncertainty quantification in diagnosis and prognosis
Uncertainty management in prognosis
Fault mitigation
Decision-Making under Uncertainty
Model verification, validation, and calibration
Design optimization under uncertainty
Resource allocation for testing and model refinement
Applications
Electrical and electronic components (lithium ion battery, MOSFET capacitor)
Damage mechanics (fatigue and fracture, energy dissipation)
Structural, mechanical, and aerospace systems (rotor craft mast, hydraulic actuator, space telescope, satellites, etc.)
Multi-disciplinary systems (fluid-structure interaction, thermal-structural interaction, thermal-electrical interactions, etc.)
System of systems (Satellite system)