Deep Gaussian Process and Deep Sigma Point Process Applied to Aerodynamic Optimization Problem

2022 ◽  
Author(s):  
Kaoruko Eto ◽  
Satoshi Takanashi ◽  
Shinsuke Nishimura
Keyword(s):  
Gaussian Process ◽  
Point Process ◽  
Optimization Problem ◽  
Aerodynamic Optimization ◽  
Sigma Point

On the weak convergence of a class of estimators of the variance-time curve of a weakly stationary point process

1977 ◽  
Vol 14 (01) ◽  
pp. 114-126 ◽  
Author(s):  
A. M. Liebetrau
Keyword(s):  
Weak Convergence ◽  
Gaussian Process ◽  
Point Process ◽  
Stationary Point ◽  
Stationary Gaussian Process ◽  
Time Curve ◽  
Second Moment ◽  
Stationary Point Process ◽  
Class Of Estimators

The second-moment structure of an estimator V*(t) of the variance-time curve V(t) of a weakly stationary point process is obtained in the case where the process is Poisson. This result is used to establish the weak convergence of a class of estimators of the form Tβ (V*(tTα ) – V(tTα )), 0 < α < 1, to a non-stationary Gaussian process. Similar results are shown to hold when α = 0 and in the case where V(tTα ) is replaced by a suitable estimator.

On the weak convergence of a class of estimators of the variance-time curve of a weakly stationary point process

1977 ◽  
Vol 14 (1) ◽  
pp. 114-126 ◽  
Author(s):  
A. M. Liebetrau
Keyword(s):  
Weak Convergence ◽  
Gaussian Process ◽  
Point Process ◽  
Stationary Point ◽  
Stationary Gaussian Process ◽  
Time Curve ◽  
Second Moment ◽  
Stationary Point Process ◽  
Class Of Estimators

The second-moment structure of an estimator V*(t) of the variance-time curve V(t) of a weakly stationary point process is obtained in the case where the process is Poisson. This result is used to establish the weak convergence of a class of estimators of the form Tβ(V*(tTα) – V(tTα)), 0 < α < 1, to a non-stationary Gaussian process. Similar results are shown to hold when α = 0 and in the case where V(tTα) is replaced by a suitable estimator.

A Gaussian Process Modeling Approach for Fast Robust Design With Uncertain Inputs

2018 ◽  
Author(s):  
Kevin M. Ryan ◽  
Jesper Kristensen ◽  
You Ling ◽  
Sayan Ghosh ◽  
Isaac Asher ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Problem ◽  
Robust Design Optimization ◽  
Design Parameters ◽  
Input Uncertainty ◽  
Single Level ◽  
Output Uncertainty ◽  
Gp Model

Many engineering design and industrial manufacturing applications are tasked with finding optimum designs while dealing with uncertainty in the design parameters. The performance or quality of the design may be sensitive to the input variation, making it difficult to optimize. Probabilistic and robust design optimization methods are used in these scenarios to find the designs that will perform best under the presence of known input uncertainty. Robust design optimization algorithms often require a two-level optimization problem (double-loop) to find a solution. The design optimization outer-loop repeatedly calls a series of inner loops that calculate uncertainty measures of the outputs. This nested optimization problem is computationally expensive and can sometimes render the task infeasible for practical engineering robust design problems. This paper details a single-level metamodel-assisted approach for probabilistic and robust design. An enhanced Gaussian Process (GP) metamodel formulation is used to provide exact values of output uncertainty in the presence of uncertain inputs. The GP model utilizes a squared-exponential kernel function and assumes normally distributed input uncertainty. These two factors together allow for an exact calculation of the first and second moments of the marginal predictive distribution. Predictions of output uncertainty are directly calculated, creating an efficient single-level robust optimization problem. We demonstrate the effectiveness of the single-level GP-assisted robust design approach on multiple engineering example problems, including a beam vibration problem, a cantilevered beam with multiple constraints, and a robust autonomous aircraft flight controller design problem. For the optimization problems investigated in this study, the single-level framework found the robust optimum with a 99.9% savings in function evaluations over the standard two-level approach.

scholarly journals Wing Section Optimization for Supersonic Viscous Flow

1998 ◽  
Vol 120 (1) ◽  
pp. 102-108 ◽  
Author(s):  
Cem C. Item ◽  
Oktay Baysal
Keyword(s):  
Optimization Problem ◽  
Stokes Equations ◽  
Design Method ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Navier Stokes ◽  
Test Cases ◽  
Aerodynamic Optimization ◽  
Wing Section ◽  
Problem Formulations

To improve the performance of a highly swept supersonic wing, it is desirable to have an automated design method that also includes a higher fidelity to the flow physics. With this impetus, an aerodynamic optimization methodology incorporating the thin-layer Navier-Stokes equations and sensitivity analysis had previously been developed. Prior to embarking upon the full wing design task, the present investigation concentrated on the identification of effective optimization problem formulations and testing the feasibility of the employed methodology, by defining two-dimensional test cases. Starting with two distinctly different initial airfoils, two independent optimizations resulted in shapes with similar features: cambered, parabolic profiles with sharp leading- and trailing-edges. Secondly, an outboard wing section normal to the subsonic portion of the leading edge, which had a high normal angle-of attack, was considered. The optimization resulted in a shape with twist and camber that eliminated the adverse pressure gradient, hence, exploiting the leading-edge thrust. The wing section shapes obtained in all the test cases included the features predicted by previous studies. This was considered as a strong indication that the flow field analyses and sensitivity coefficients were computed and provided to the present gradient-based optimizer correctly. Also, from the results of the present study, effective optimization problem formulations could be deduced to start a full wing shape optimization.

Training a Neural-Network-Based Surrogate Model for Aerodynamic Optimization Using a Gaussian Process

2021 ◽  
Author(s):  
Nahla Alhazmi ◽  
Yousef Ghazi ◽  
Mohammed N. Aldosari ◽  
Radek Tezaur ◽  
Charbel Farhat
Keyword(s):  
Neural Network ◽  
Gaussian Process ◽  
Surrogate Model ◽  
Aerodynamic Optimization

Multi-objective aerodynamic optimization using active multi-output Gaussian process and mesh deformation method

2021 ◽  
pp. 095441002110221
Author(s):  
Fan Yang ◽  
Zhaolin Chen
Keyword(s):  
Active Learning ◽  
Gaussian Process ◽  
Process Model ◽  
Learning Algorithm ◽  
Mesh Deformation ◽  
Aerodynamic Optimization ◽  
Deformation Method ◽  
Nsga Ii ◽  
Gaussian Process Model ◽  
Multi Objective

A wing is an important part of the aircraft to improve aerodynamic performance. The current study is focused on an adaptive surrogate algorithm for airfoil aerodynamic optimization, which is based on a multi-output Gaussian process model. The conventional design method seriously relies on wind tunnel experiments and expensive computational simulations. The metamodels can significantly improve design efficiency and hence reduce the overall design costs. An active learning algorithm is proposed to improve the effectiveness of the multi-output Gaussian process model. The NSGA-II algorithm is adopted to obtain the optimal Pareto set with the optimization objectives of lift and drag coefficients for adaptive airfoil shapes. Besides, the Bezier curve and radial basis function are utilized in this study for airfoil mesh deformation. The results show that the airfoil shape can be obtained effectively by integrating the metamodel, active learning algorithm, and multi-objective optimization algorithm. The optimized results are of great engineering applications.

scholarly journals Improved Gaussian Process Acquisition for Targeted Bayesian Optimization

2021 ◽  
pp. 12-18
Author(s):  
Peter Mitic ◽  
Keyword(s):  
Gaussian Process ◽  
Optimization Problem ◽  
Bayesian Optimization ◽  
Stochastic Algorithm ◽  
Confidence Bound ◽  
Noise Component ◽  
Simple Modification ◽  
Lower Confidence ◽  
Lower Confidence Bound ◽  
Long Time

A black-box optimization problem is considered, in which the function to be optimized can only be expressed in terms of a complicated stochastic algorithm that takes a long time to evaluate. The value returned is required to be sufficiently near to a target value, and uses data that has a significant noise component. Bayesian Optimization with an underlying Gaussian Process is used as an optimization solution, and its effectiveness is measured in terms of the number of function evaluations required to attain the target. To improve results, a simple modification of the Gaussian Process ‘Lower Confidence Bound’ (LCB) acquisition function is proposed. The expression used for the confidence bound is squared in order to better comply with the target requirement. With this modification, much improved results compared to random selection methods and to other commonly used acquisition functions are obtained.

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