Machine Learning-Based Data and Model Driven Bayesian Uncertanity Quantification of Inverse Problems for Suspended Non-structural System

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and control strategies based on simulation or prediction results. However, in the surrogate model, preventing overfitting and incorporating reasonable prior knowledge of embedded physics and models is a challenge. Suspended Nonstructural Systems (SNS) pose a significant challenge in the inverse problem. Research on their seismic performance and mechanical models, particularly in the inverse problem and uncertainty quantification, is still lacking. To address this, the author conducts full-scale shaking table dynamic experiments and monotonic & cyclic tests, and simulations of different types of SNS to investigate mechanical behaviors. To quantify the uncertainty of the inverse problem, the author proposes a new framework that adopts machine learning-based data and model driven stochastic Gaussian process model calibration to quantify the uncertainty via a new black box variational inference that accounts for geometric complexity measure, Minimum Description length (MDL), through Bayesian inference. It is validated in the SNS and yields optimal generalizability and computational scalability

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Water-drive gas reservoir: sensitivity analysis and simplified prediction

Water influx and well completions affect recovery from water-drive gas reservoir. Material balance, aquifer models and well inflow equations are used to examine and predict the pressure depletion, water influx, and production rates of water-drive gas reservoirs. The parameters of these simple, lumped models are estimated from simulation results using response surfaces and experimental designs for eight varying geologic and engineering factors. Eleven simulated responses (including maximum gas rate, aquifer and well constants, and water breakthrough) are analyzed using ANOVA and response models. A sensitivity analysis of aquifer productivity index, gas production factor, and sweep efficiency reveals that permeability is the dominating factor. In contrast to earlier investigations, this study indicates that water-drive gas recovery is often higher for higher permeability water-drive gas reservoirs. The high gas mobility more than offsets the high aquifer mobility. The other seven factors are statistically significant for many responses, but much less important in determining reservoir behavior. The proposed approach combines simple analytic expressions with more complete but difficult-to-use reservoir simulation models. The response models can be used to make quick, accurate predictions of water-drive gas reservoirs that include the effects of changing geologic and engineering variables. These simple, approximate models are appropriate for prospect screening, sensitivity analysis and uncertainty analysis