2,132 research outputs found
Investigation of robust optimization and evidence theory with stochastic expansions for aerospace applications under mixed uncertainty
One of the primary objectives of this research is to develop a method to model and propagate mixed (aleatory and epistemic) uncertainty in aerospace simulations using DSTE. In order to avoid excessive computational cost associated with large scale applications and the evaluation of Dempster Shafer structures, stochastic expansions are implemented for efficient UQ. The mixed UQ with DSTE approach was demonstrated on an analytical example and high fidelity computational fluid dynamics (CFD) study of transonic flow over a RAE 2822 airfoil.
Another objective is to devise a DSTE based performance assessment framework through the use of quantification of margins and uncertainties. Efficient uncertainty propagation in system design performance metrics and performance boundaries is achieved through the use of stochastic expansions. The technique is demonstrated on: (1) a model problem with non-linear analytical functions representing the outputs and performance boundaries of two coupled systems and (2) a multi-disciplinary analysis of a supersonic civil transport.
Finally, the stochastic expansions are applied to aerodynamic shape optimization under uncertainty. A robust optimization algorithm is presented for computationally efficient airfoil design under mixed uncertainty using a multi-fidelity approach. This algorithm exploits stochastic expansions to create surrogate models utilized in the optimization process. To reduce the computational cost, output space mapping technique is implemented to replace the high-fidelity CFD model by a suitably corrected low-fidelity one. The proposed algorithm is demonstrated on the robust optimization of NACA 4-digit airfoils under mixed uncertainties in transonic flow. --Abstract, page iii
Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport
The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport. An approach based on non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected by any number of high-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability of the multifidelity polynomial chaos approach, two model problems were explored. The first was supersonic airfoil with three levels of modeling fidelity, each capturing an additional level of physics. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Both problems illustrate the applicability and significant computational savings of the multifidelity polynomial chaos method
Optimizing the Safety Margins Governing a Deterministic Design Process while Considering the Effects of a Future Test and Redesign on Epistemic Model Uncertainty
At the initial design stage, engineers often rely on low-fidelity models that have high uncertainty. Model uncertainty is reducible and is classified as epistemic uncertainty; uncertainty due to variability is irreducible and classified as aleatory uncertainty. In a deterministic safety-margin-based design approach, uncertainty is implicitly compensated for by using fixed conservative values in place of aleatory variables and ensuring the design satisfies a safety-margin with respect to design constraints. After an initial design is selected, testing (e.g. physical experiment or high-fidelity simulation) is performed to reduce epistemic uncertainty and ensure the design achieves the targeted levels of safety. Testing is used to calibrate low-fidelity models and prescribe redesign when tests are not passed. After calibration, reduced epistemic model uncertainty can be leveraged through redesign to restore safety or improve design performance; however, redesign may be associated with substantial costs or delays. In this work, the possible effects of a future test and redesign are considered while the initial design is optimized using only a low-fidelity model. The goal is to develop a general method for the integrated optimization of the design, testing, and redesign process that allows for the tradeoff between the risk of future redesign and the associated performance and reliability benefits. This is accomplished by formulating the design, testing, and redesign process in terms of safety-margins and optimizing these margins based on expected performance, expected probability of failure, and probability of redesign. The first objective of this study is to determine how the degree of conservativeness in the initial design relates to the expected design performance after a test and possible redesign. The second objective is to develop a general method for modeling epistemic model uncertainty and calibration when simulating a possible future test and redesign. The third objective is to apply the method of simulating a future test and redesign to a sounding rocket design example
Adaptive Multi-Fidelity Modeling for Efficient Design Exploration Under Uncertainty
This thesis work introduces a novel multi-fidelity modeling framework, which is designed to address the practical challenges encountered in Aerospace vehicle design when 1) multiple low-fidelity models exist, 2) each low-fidelity model may only be correlated with the high-fidelity model in part of the design domain, and 3) models may contain noise or uncertainty. The proposed approach approximates a high-fidelity model by consolidating multiple low-fidelity models using the localized Galerkin formulation. Also, two adaptive sampling methods are developed to efficiently construct an accurate model. The first acquisition formulation, expected effectiveness, searches for the global optimum and is useful for modeling engineering objectives. The second acquisition formulation, expected usefulness, identifies feasible design domains and is useful for constrained design exploration. The proposed methods can be applied to any engineering systems with complex and demanding simulation models
Surrogate-Assisted Unified Optimization Framework for Investigating Marine Structural Design Under Information Uncertainty.
Structural decisions made in the early stages of marine systems design can have a large impact on future acquisition, maintenance and life-cycle costs. However, owing to the unique nature of early stage marine system design, these critical structure decisions are often made on the basis of incomplete information or knowledge about the design. When coupled with design optimization analysis, the complex, uncertain early stage design environment makes it very difficult to deliver a quantified trade-off analysis for decision making. This work presents a novel decision support method that integrates design optimization, high-fidelity analysis, and modeling of information uncertainty for early stage design and analysis. To support this method this dissertation improves the design optimization methods for marine structures by proposing several novel surrogate modeling techniques and strategies.
The proposed work treats the uncertainties that are sourced from limited information in a non-statistical interval uncertainty form. This interval uncertainty is treated as an objective function in an optimization framework in order to explore the impact of information uncertainty on structural design performance. In this examination, the potential structural weight penalty regarding information uncertainty can be quickly identified in early stage, avoiding costly redesign later in the design. This dissertation then continues to explore a balanced computational structure between fidelity and efficiency. A proposed novel variable fidelity approach can be applied to wisely allocate expensive high-fidelity computational simulations. In achieving the proposed capabilities for design optimization, several surrogate modeling methods are developed concerning worst-case estimation, clustered multiple meta-modeling, and mixed variable modeling techniques. These surrogate methods have been demonstrated to significantly improve the efficiency of optimizer in dealing with the challenges of early stage marine structure design.PhDNaval Architecture and Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133365/1/yanliuch_1.pd
Epistemic Modeling Uncertainty of Rapid Neural Network Ensembles for Adaptive Learning
Emulator embedded neural networks, which are a type of physics informed
neural network, leverage multi-fidelity data sources for efficient design
exploration of aerospace engineering systems. Multiple realizations of the
neural network models are trained with different random initializations. The
ensemble of model realizations is used to assess epistemic modeling uncertainty
caused due to lack of training samples. This uncertainty estimation is crucial
information for successful goal-oriented adaptive learning in an aerospace
system design exploration. However, the costs of training the ensemble models
often become prohibitive and pose a computational challenge, especially when
the models are not trained in parallel during adaptive learning. In this work,
a new type of emulator embedded neural network is presented using the rapid
neural network paradigm. Unlike the conventional neural network training that
optimizes the weights and biases of all the network layers by using
gradient-based backpropagation, rapid neural network training adjusts only the
last layer connection weights by applying a linear regression technique. It is
found that the proposed emulator embedded neural network trains
near-instantaneously, typically without loss of prediction accuracy. The
proposed method is demonstrated on multiple analytical examples, as well as an
aerospace flight parameter study of a generic hypersonic vehicle
- …