scholarly journals Gradient-based multifidelity optimisation for aircraft design using Bayesian model calibration

2011 ◽  
Vol 115 (1174) ◽  
pp. 729-738 ◽  
Author(s):  
A. March ◽  
K. Willcox ◽  
Q. Wang
Keyword(s):  
Bayesian Model ◽  
Model Calibration ◽  
Trust Region Method ◽  
Trust Region ◽  
Aircraft Design ◽  
High Fidelity ◽  
First Order ◽  
Gradient Based ◽  
Quadratic Programming Method ◽  
Optimisation Methods

Abstract Optimisation of complex systems frequently requires evaluating a computationally expensive high-fidelity function to estimate a system metric of interest. Although design sensitivities may be available through either direct or adjoint methods, the use of formal optimisation methods may remain too costly. Incorporating low-fidelity performance estimates can substantially reduce the cost of the high-fidelity optimisation. In this paper we present a provably convergent multifidelity optimisation method that uses Cokriging Bayesian model calibration and first-order consistent trust regions. The technique is compared with a single-fidelity sequential quadratic programming method and a conventional first-order trust-region method on both a two-dimensional structural optimisation and an aerofoil design problem. In both problems adjoint formulations are used to provide inexpensive sensitivity information.

scholarly journals Distributed Trust-Region Method With First Order Models

2019 ◽  
Author(s):  
Aleksandar Armacki ◽  
Dusan Jakovetic ◽  
Natasa Krejic ◽  
Natasa Krklec Jerinkic
Keyword(s):  
Trust Region Method ◽  
Trust Region ◽  
First Order ◽  
Region Method

scholarly journals An Active Set Trust-Region Method for Bound-Constrained Optimization

2021 ◽  
Author(s):  
Morteza Kimiaei
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Positive Definiteness ◽  
Active Set ◽  
Sufficient Descent Condition ◽  
Critical Measure ◽  
Complexity Result ◽  
Bound Constrained Optimization

AbstractThis paper discusses an active set trust-region algorithm for bound-constrained optimization problems. A sufficient descent condition is used as a computational measure to identify whether the function value is reduced or not. To get our complexity result, a critical measure is used which is computationally better than the other known critical measures. Under the positive definiteness of approximated Hessian matrices restricted to the subspace of non-active variables, it will be shown that unlimited zigzagging cannot occur. It is shown that our algorithm is competitive in comparison with the state-of-the-art solvers for solving an ill-conditioned bound-constrained least-squares problem.

Based on GA Mixed with Trust Region Method Solving Nonlinear Least Square Problems

2011 ◽  
Vol 141 ◽  
pp. 92-97
Author(s):  
Miao Hu ◽  
Tai Yong Wang ◽  
Bo Geng ◽  
Qi Chen Wang ◽  
Dian Peng Li
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Least Square ◽  
Search Range ◽  
Genetic Search ◽  
Region Method ◽  
Unconstrained Optimization Problems ◽  
Least Square Problems

Nonlinear least square is one of the unconstrained optimization problems. In order to solve the least square trust region sub-problem, a genetic algorithm (GA) of global convergence was applied, and the premature convergence of genetic algorithms was also overcome through optimizing the search range of GA with trust region method (TRM), and the convergence rate of genetic algorithm was increased by the randomness of the genetic search. Finally, an example of banana function was established to verify the GA, and the results show the practicability and precision of this algorithm.

Automatic Three-Dimensional Optimisation of a Modern Tandem Compressor Vane

2014 ◽  
Author(s):  
R. C. Schlaps ◽  
S. Shahpar ◽  
V. Gümmer
Keyword(s):  
Pressure Ratio ◽  
Three Dimensional ◽  
Trust Region ◽  
Automatic Generation ◽  
Navier Stokes ◽  
Design Parameters ◽  
High Fidelity ◽  
Stall Margin ◽  
Design Choice ◽  
Multipoint Approximation

In order to increase the performance of a modern gas turbine, compressors are required to provide higher pressure ratio and avoid incurring higher losses. The tandem aerofoil has the potential to achieve a higher blade loading in combination with lower losses compared to single vanes. The main reason for this is due to the fact that a new boundary layer is generated on the second blade surface and the turning can be achieved with smaller separation occurring. The lift split between the two vanes with respect to the overall turning is an important design choice. In this paper an automated three-dimensional optimisation of a highly loaded compressor stator is presented. For optimisation a novel methodology based on the Multipoint Approximation Method (MAM) is used. MAM makes use of an automatic design of experiments, response surface modelling and a trust region to represent the design space. The CFD solutions are obtained with the high-fidelity 3D Navier-Stokes solver HYDRA. In order to increase the stage performance the 3D shape of the tandem vane is modified changing both the front and rear aerofoils. Moreover the relative location of the two aerofoils is controlled modifying the axial and tangential relative positions. It is shown that the novel optimisation methodology is able to cope with a large number of design parameters and produce designs which performs better than its single vane counterpart in terms of efficiency and numerical stall margin. One of the key challenges in producing an automatic optimisation process has been the automatic generation of high-fidelity computational meshes. The multi block-structured, high-fidelity meshing tool PADRAM is enhanced to cope with the tandem blade topologies. The wakes of each aerofoil is properly resolved and the interaction and the mixing of the front aerofoil wake and the second tandem vane are adequately resolved.

A BFGS trust-region method for nonlinear equations

Computing ◽  
2011 ◽  
Vol 92 (4) ◽  
pp. 317-333 ◽  
Author(s):  
Gonglin Yuan ◽  
Zengxin Wei ◽  
Xiwen Lu
Keyword(s):  
Nonlinear Equations ◽  
Trust Region Method ◽  
Trust Region ◽  
Region Method

scholarly journals A Nonmonotone Weighting Self-Adaptive Trust Region Algorithm for Unconstrained Nonconvex Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yunlong Lu ◽  
Weiwei Yang ◽  
Wenyu Li ◽  
Xiaowei Jiang ◽  
Yueting Yang
Keyword(s):  
Nonconvex Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Search Technique ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Line Search Technique ◽  
Self Adaptive

A new trust region method is presented, which combines nonmonotone line search technique, a self-adaptive update rule for the trust region radius, and the weighting technique for the ratio between the actual reduction and the predicted reduction. Under reasonable assumptions, the global convergence of the method is established for unconstrained nonconvex optimization. Numerical results show that the new method is efficient and robust for solving unconstrained optimization problems.

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