arXiv subjects

John F. Quindlen

Publications and source records attributed to John F. Quindlen.

4 recordsLinked to original sources

arXiv2019

Multi-Fidelity modeling of Probabilistic Aerodynamic Databases for Use in Aerospace Engineering

Explicit quantification of uncertainty in engineering simulations is being increasingly used to inform robust and reliable design practices. In the aerospace industry, computationally-feasible analyses for design optimization purposes often introduce significant uncertainties due to deficiencies in the mathematical models employed. In this paper, we discuss two recent improvements in the quantification and combination of uncertainties from multiple sources that can help generate probabilistic aerodynamic databases for use in aerospace engineering problems. We first discuss the eigenspace perturbation methodology to estimate model-form uncertainties stemming from inadequacies in the turbulence models used in Reynolds-Averaged Navier-Stokes Computational Fluid Dynamics (RANS CFD) simulations. We then present a multi-fidelity Gaussian Process framework that can incorporate noisy observations to generate integrated surrogate models that provide mean as well as variance information for Quantities of Interest (QoIs). The process noise is varied spatially across the domain and across fidelity levels. Both these methodologies are demonstrated through their application to a full configuration aircraft example, the NASA Common Research Model (CRM) in transonic conditions. First, model-form uncertainties associated with RANS CFD simulations are estimated. Then, data from different sources is used to generate multi-fidelity probabilistic aerodynamic databases for the NASA CRM. We discuss the transformative effect that affordable and early treatment of uncertainties can have in traditional aerospace engineering practices. The results are presented and compared to those from a Gaussian Process regression performed on a single data source.

physics.flu-dyn↗

arXiv2018

Active Sampling-based Binary Verification of Dynamical Systems

Nonlinear, adaptive, or otherwise complex control techniques are increasingly relied upon to ensure the safety of systems operating in uncertain environments. However, the nonlinearity of the resulting closed-loop system complicates verification that the system does in fact satisfy those requirements at all possible operating conditions. While analytical proof-based techniques and finite abstractions can be used to provably verify the closed-loop system's response at different operating conditions, they often produce conservative approximations due to restrictive assumptions and are difficult to construct in many applications. In contrast, popular statistical verification techniques relax the restrictions and instead rely upon simulations to construct statistical or probabilistic guarantees. This work presents a data-driven statistical verification procedure that instead constructs statistical learning models from simulated training data to separate the set of possible perturbations into "safe" and "unsafe" subsets. Binary evaluations of closed-loop system requirement satisfaction at various realizations of the uncertainties are obtained through temporal logic robustness metrics, which are then used to construct predictive models of requirement satisfaction over the full set of possible uncertainties. As the accuracy of these predictive statistical models is inherently coupled to the quality of the training data, an active learning algorithm selects additional sample points in order to maximize the expected change in the data-driven model and thus, indirectly, minimize the prediction error. Various case studies demonstrate the closed-loop verification procedure and highlight improvements in prediction error over both existing analytical and statistical verification techniques.

eess.SY↗

arXiv2017

Active Sampling for Constrained Simulation-based Verification of Uncertain Nonlinear Systems

Increasingly demanding performance requirements for dynamical systems motivates the adoption of nonlinear and adaptive control techniques. One challenge is the nonlinearity of the resulting closed-loop system complicates verification that the system does satisfy the requirements at all possible operating conditions. This paper presents a data-driven procedure for efficient simulation-based, statistical verification without the reliance upon exhaustive simulations. In contrast to previous work, this approach introduces a method for online estimation of prediction accuracy without the use of external validation sets. This work also develops a novel active sampling algorithm that iteratively selects additional training points in order to maximize the accuracy of the predictions while still limited to a sample budget. Three case studies demonstrate the utility of the new approach and the results show up to a 50% improvement over state-of-the-art techniques.

eess.SY↗

arXiv2017

Closed-Loop Statistical Verification of Stochastic Nonlinear Systems Subject to Parametric Uncertainties

This paper proposes a statistical verification framework using Gaussian processes (GPs) for simulation-based verification of stochastic nonlinear systems with parametric uncertainties. Given a small number of stochastic simulations, the proposed framework constructs a GP regression model and predicts the system's performance over the entire set of possible uncertainties. Included in the framework is a new metric to estimate the confidence in those predictions based on the variance of the GP's cumulative distribution function. This variance-based metric forms the basis of active sampling algorithms that aim to minimize prediction error through careful selection of simulations. In three case studies, the new active sampling algorithms demonstrate up to a 35% improvement in prediction error over other approaches and are able to correctly identify regions with low prediction confidence through the variance metric.

eess.SY↗