Douglas L. Allaire

Multifidelity DDDAS Methods with Application to a Self-aware Aerospace Vehicle☆

Abstract A self-aware aerospace vehicle can dynamically adapt the way it performs missions by gathering information about itself and its surroundings and responding intelligently. We consider the specific challenge of an unmanned aerial vehicle that can dynamically and autonomously sense its structural state and re-plan its mission according to its estimated current structural health. The challenge is to achieve each of these tasks in real time–executing online models and exploiting dynamic data streams–while also accounting for uncertainty. Our approach combines information from physics-based models, simulated offline to build a scenario library, together with dynamic sensor data in order to estimate current flight capability. Our physics-based models analyze the system at both the local panel level and the global vehicle level.

A variance-based sensitivity index function for factor prioritization

Abstract Among the many uses for sensitivity analysis is factor prioritization—that is, the determination of which factor, once fixed to its true value, on average leads to the greatest reduction in the variance of an output. A key assumption is that a given factor can, through further research, be fixed to some point on its domain. In general, this is an optimistic assumption, which can lead to inappropriate resource allocation. This research develops an original method that apportions output variance as a function of the amount of variance reduction that can be achieved for a particular factor. This variance-based sensitivity index function provides a main effect sensitivity index for a given factor as a function of the amount of variance of that factor that can be reduced. An aggregate measure of which factors would on average cause the greatest reduction in output variance given future research is also defined and assumes the portion of a particular factors variance that can be reduced is a random variable. An average main effect sensitivity index is then calculated by taking the mean of the variance-based sensitivity index function. A key aspect of the method is that the analysis is performed directly on the samples that were generated during a global sensitivity analysis using rejection sampling. The method is demonstrated on the Ishigami function and an additive function, where the rankings for future research are shown to be different than those of a traditional global sensitivity analysis.

An Information-Theoretic Metric of System Complexity With Application to Engineering System Design

System complexity is considered a key driver of the inability of current system design practices to at times not recognize performance, cost, and schedule risks as they emerge. We present here a denition of system complexity and a quantitative metric for measuring that complexity based on information theory. We also derive sensitivity indices that indicate the fraction of complexity that can be reduced if more about certain factors of a system can become known. This information can be used as part of a resource allocation procedure aimed at reducing system complexity. Our methods incorporate Gaussian process emulators of expensive computer simulation models and account for both model inadequacy and code uncertainty. We demonstrate our methodology on a candidate design of an infantry ghting vehicle.

An Offline/Online DDDAS Capability for Self-Aware Aerospace Vehicles

In this paper we develop initial offline and online capabilities for a self-aware aerospace vehicle. Such a vehicle can dynamically adapt the way it performs missions by gathering information about itself and its surroundings via sensors and responding intelligently. The key challenge to enabling such a self-aware aerospace vehicle is to achieve tasks of dynamically and autonomously sensing, planning, and acting in real time. Our first steps towards achieving this goal are presented here, where we consider the execution of online mapping strategies from sensed data to expected vehicle capability while accounting for uncertainty. Libraries of strain, capability, and maneuever loading are generated offline using vehicle and mission modeling capabilities we have developed in this work. These libraries are used dynamically online as part of a Bayesian classification process for estimating the capability state of the vehicle. Failure probabilities are then computed online for specific maneuvers. We demonstrate our models and methodology on decisions surrounding a standard rate turn maneuver.

Compositional Uncertainty Analysis via Importance Weighted Gibbs Sampling for Coupled Multidisciplinary Systems

This paper presents a novel compositional multidisciplinary uncertainty analysis methodology for systems with feedback couplings, and model discrepancy. Our approach incorporates aspects of importance resampling, density estimation, and Gibbs sampling to ensure that, under mild assumptions, our method is provably convergent in distribution. A key feature of our approach is that disciplinary models can all be executed offline and independently. Offline data is synthesized in an online phase that does not require any further model evaluations or any full coupled system level evaluations. We demonstrate our approach on a simple aerodynamics-structures system.

Methodology for Dynamic Data-Driven Online Flight Capability Estimation

United States. Air Force Office of Scientific Research. Dynamic Data-Driven Application Systems Program (Grant FA9550-11-1-0339)

A Bayesian-Based Approach to Multifidelity Multidisciplinary Design Optimization

Design processes for complex systems often begin with low-fidelity models and progressively incorporate higher fidelity tools. Existing multifidelity optimization approaches generally attempt to calibrate low-fidelity models or replace low-fidelity analysis results using data from higher fidelity analyses. This paper proposes a fundamentally dierent approach that uses the tools of estimation theory to fuse together information from multifidelity analyses. This approach is combined with maximum entropy characterizations of model inadequacy and global sensitivity analysis for fidelity management, resulting in a Bayesian-based approach to mitigating risk in multifidelity multidisciplinary design optimization. The method is demonstrated on a wing-sizing problem for a high altitude, long endurance vehicle.

Quantifying the Impact of Different Model Discrepancy Formulations in Coupled Multidisciplinary Systems

In this paper, we quantify the impact of different formulations of model discrepancy propagation in coupled multidisciplinary systems. Standard Gaussian process formulations of model discrepancy leave room for interpretation when incorporated into coupled system analyses. The objective of this work is to analyze resulting coupling variable distributions under different assumptions regarding these model discrepancy interpretations. The goal is to identify efficient, implementation independent, methods and rationale for the rigorous propagation of uncertainty in coupled systems. We demonstrate our methodology on an aerostructural wing analysis problem.

A Decomposition Approach to Uncertainty Analysis of Multidisciplinary Systems

To support eective decision making, engineers should comprehend and manage various uncertainties throughout the design process. Unfortunately, in today’s modern systems, uncertainty analysis can become cumbersome and computationally intractable for one individual or group to manage. This is particularly true for systems comprising multiple components described by a large number of models. In many cases, these models may be developed by dierent groups and even run on dierent computational platforms. This paper proposes an approach for decomposing and distributing the uncertainty analysis task amongst the various components comprising a system. The mathematical approach draws on concepts and algorithms from multidisciplinary analysis and optimization, density estimation, and sequential Monte Carlo methods. The distributed multidisciplinary uncertainty analysis approach is provably convergent and is compared to a traditional allat-once Monte Carlo uncertainty analysis approach. The proposed method is illustrated on a mathematical example and two aerospace system applications|a beam loading example and a gas turbine design example.

Multifidelity Optimization using Statistical Surrogate Modeling for Non-Hierarchical Information Sources

United States. Air Force. Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550- 09-0613)