scholarly journals An approximate high-dimensional optimization method using hierarchical design space reduction strategy

2021 ◽  
Vol 39 (2) ◽  
pp. 292-301
Author(s):  
Pengcheng Ye ◽  
Congcong Wang ◽  
Guang Pan
Keyword(s):  
Design Space ◽  
Optimization Method ◽  
Surrogate Models ◽  
Black Box ◽  
High Dimensional ◽  
Hierarchical Design ◽  
Reduction Strategy ◽  
Space Reduction ◽  
Ensemble Of Surrogates ◽  
Dimensional Optimization

To overcome the complicated engineering model and huge computational cost, a hierarchical design space reduction strategy based approximate high-dimensional optimization(HSRAHO) method is proposed to deal with the high-dimensional expensive black-box problems. Three classical surrogate models including polynomial response surfaces, radial basis functions and Kriging are selected as the component surrogate models. The ensemble of surrogates is constructed using the optimized weight factors selection method based on the prediction sum of squares and employed to replace the real high-dimensional black-box models. The hierarchical design space reduction strategy is used to identify the design subspaces according to the known information. And, the new promising sample points are generated in the design subspaces. Thus, the prediction accuracy of ensemble of surrogates in these interesting sub-regions can be gradually improved until the optimization convergence. Testing using several benchmark optimization functions and an airfoil design optimization problem, the newly proposed approximate high-dimensional optimization method HSRAHO shows improved capability in high-dimensional optimization efficiency and identifying the global optimum.

Aerodynamic Optimization of the Low-Pressure Turbine Module: Exploiting Surrogate Models in a High-Dimensional Design Space

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Lieven Baert ◽  
Emmanuel Chérière ◽  
Caroline Sainvitu ◽  
Ingrid Lepot ◽  
Arnaud Nouvellon ◽  
...  
Keyword(s):  
Data Mining ◽  
Design Space ◽  
Low Pressure ◽  
Surrogate Models ◽  
High Dimensional ◽  
Efficiency Gain ◽  
Aerodynamic Optimization ◽  
Component Design ◽  
Efficient Data ◽  
Lp Turbine

Abstract Further improvement of state-of-the-art low-pressure (LP) turbines (LPTs) has become progressively more challenging. LP design is more than ever confronted to the need to further integrate complex models and to shift from single-component design to the design of the complete LPT module at once. This leads to high-dimensional design spaces and automatically challenges their applicability within an industrial context, where computing resources are limited and the cycle time is crucial. The aerodynamic design of a multistage LP turbine is discussed for a design space defined by 350 parameters. Using an online surrogate-based optimization (SBO) approach, a significant efficiency gain of almost 0.5pt has been achieved. By discussing the sampling of the design space, the quality of the surrogate models, and the application of adequate data mining capabilities to steer the optimization, it is shown that despite the high-dimensional nature of the design space, the followed approach allows to obtain performance gains beyond target. The ability to control both global as well as local characteristics of the flow throughout the full LP turbine, in combination with an agile reaction of the search process after dynamically strengthening and/or enforcing new constraints in order to adapt to the review feedback, not only illustrates the feasibility but also the potential of a global design space for the LP module. It is demonstrated that intertwining the capabilities of dynamic SBO and efficient data mining allows to incorporate high-fidelity simulations in design cycle practices of certified engines or novel engine concepts to jointly optimize the multiple stages of the LPT.

Aerodynamic Optimisation of the Low Pressure Turbine Module: Exploiting Surrogate Models in a High-Dimensional Design Space

2019 ◽  
Author(s):  
Lieven Baert ◽  
Ingrid Lepot ◽  
Caroline Sainvitu ◽  
Emmanuel Chérière ◽  
Arnaud Nouvellon ◽  
...  
Keyword(s):  
Data Mining ◽  
Design Space ◽  
Low Pressure ◽  
Surrogate Models ◽  
High Dimensional ◽  
Efficiency Gain ◽  
Component Design ◽  
Efficient Data ◽  
Complex Models ◽  
Lp Turbine

Abstract Further improvement of state-of-the-art Low Pressure (LP) turbines has become progressively more challenging. LP design is more than ever confronted to the need to further integrate complex models and to shift from single component design to the design of the complete LPT module at once. This leads to high-dimensional design spaces and automatically challenges its applicability within an industrial context, where CPU resources are limited and the cycle time crucial. The aerodynamic design of a multistage LP turbine is discussed for a design space defined by 350 parameters. Using an online surrogate-based optimisation (SBO) approach a significant efficiency gain of almost 0.5pt has been achieved. By discussing the sampling of the design space, the quality of the surrogate models, and the application of adequate data mining capabilities to steer the optimisation, it is shown that despite the high-dimensional nature of the design space the followed approach allows to obtain performance gains beyond target. The ability to control both global as well as local characteristics of the flow throughout the full LP turbine, in combination with an agile reaction of the search process after dynamically strengthening and/or enforcing new constraints in order to adapt to the review feedback, illustrates not only the feasibility but also the potential of a global design space for the LP module. It is demonstrated that intertwining the capabilities of dynamic SBO and efficient data mining allows to incorporate high-fidelity simulations in design cycle practices of certified engines or novel engine concepts to jointly optimise the multiple stages of the LPT.

High-Dimensional Constrained Multiobjective Optimization of a Fan Stage

2011 ◽  
Author(s):  
Marcel Aulich ◽  
Ulrich Siller
Keyword(s):  
Design Space ◽  
Surrogate Models ◽  
Expected Improvement ◽  
High Dimensional ◽  
Process Chain ◽  
Fast Evaluation ◽  
New Members ◽  
Stall Margin ◽  
Advantages And Disadvantages ◽  
The Right

A high-dimensional design space, different objectives, many constraints and a time-consuming process chain result in a complex task for any optimization tool. This paper shows methods and strategies used at DLR, Institute of Propulsion Technology, to handle this kind of problem. The present optimization task is a rotor-stator configuration with more than two hundred free design variables, two objective functions (efficiency, stall margin) and mechanical and aerodynamic constraints (mass flow, eigenfrequencies, etc.). The process chain consists of geometry and mesh generation, FEM-and 3D-CFD calculations for different operating points. After defining the setup and explaining the initial already 3-D-preoptimized configuration, the CFD/FEM optimization tool is described. This tool calculates the complete CFD/FEM process chain and creates new designs (also called members) by using an evolutionary algorithms. Parallel to the CFD/FEM optimization a program based on surrogate models is running. By using surrogate models a fast evaluation of new members is enabled. So a database of new members can be created quickly. Based on this database a set of new members is built. This is send to the CFD/FEM optimization tool, where the complete CFD/FEM process chain is applied. After the CFD/FEM evaluation process, these member are used to train the surrogate models again. This procedure repeats until the optimization goals are reached. In the next part of this paper the implemented surrogate models are discussed. Both neural networks and Kriging models have advantages and disadvantages compared to each other. It is important to understand them to choose the right model at the right time of optimization. The main focus of this paper is on the selection criterion for new members. This criterion has two targets: push the performance of the fan stage and enhance the surrogate models. At first sight these targets seem to be contrary, but the surrogate models do not predict a single mean value for an objective. They offer a density distribution of the potential objective values. That allows calculation of the Paretofront enhancement (ParetoEnSet) for a set of new members. ParetoEnSet is the expected area gain of a set of members to the current Paretofront. This criterion based on the already known expected improvement. It is shown, that ParetoEnSet can rise, when the uncertainty of an prediction increases. The uncertainty is estimated by a surrogate model. So new members tend to explore the design space, where the predicted uncertainty is huge. These members are favorable for improving the surrogate models. In addition, it is easy to couple constraints with ParetoEnSet. In the last section the results of the optimization are illustrated. Compared to baseline design the optimized stage accomplishes a notable improvement in efficiency by obtaining the stall margin and fulfilling multi aerodynamical and mechanical constraints.

Orientation Capability, Error Analysis, and Dimensional Optimization of Two Articulated Tool Heads With Parallel Kinematics

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Xin-Jun Liu ◽  
Ilian A. Bonev
Keyword(s):  
Design Space ◽  
Optimization Method ◽  
Thin Wall ◽  
Optimal Solutions ◽  
Parallel Kinematics ◽  
Spherical Joint ◽  
Increasing Demand ◽  
Error Index ◽  
Three Degree Of Freedom ◽  
Dimensional Optimization

Because of the increasing demand in industry for A/B-axis tool heads, particularly in thin wall machining applications for structural aluminium aerospace components, the three-degree-of-freedom articulated tool head with parallel kinematics has become very popular. This paper addresses the dimensional optimization of two types of tool head with 3-P̱VPHS and 3-P̱VRS parallel kinematics (P, R, and S standing for prismatic, revolute, and spherical joint, respectively; the subscripts V and H indicating that the direction of the P joint is vertical or horizontal, and the joint symbol with underline means the joint is active) by considering their orientation capability and positioning accuracy. We first investigate the tilt angle of the spherical joint, the orientation capability, and the error of one point from the mobile platform caused by input errors. Optimization of the 3-P̱VPHS tool head is easy. For the 3-P̱VRS tool head, a design space is developed to illustrate how the orientation capability and error index are related to the link lengths. An optimization process is accordingly presented. Using the optimization method introduced here, it is not difficult to find all the possible optimal solutions.

Optimization of the Vibration Response of a Longitudinal-Transverse Stiffened Conical Shell Based on an Ensemble of Surrogates

2018 ◽  
Author(s):  
Jiachang Qian ◽  
Enen Yu ◽  
Jinlan Zhang ◽  
Dawei Zhan ◽  
Yuansheng Cheng
Keyword(s):  
Conical Shell ◽  
Design Space ◽  
Computational Cost ◽  
Kriging Model ◽  
Surrogate Models ◽  
Vibration Response ◽  
Support Vector ◽  
Conical Shells ◽  
Design Variables ◽  
Ensemble Of Surrogates

The acceleration responses at certain points of the longitudinal-transverse stiffened conical shells in special frequency region are major matters of concern. Because the finite element models of the longitudinal-transverse stiffened conical shells have to be employed to calculate the vibration response of the structure at all frequencies under consideration, it requires a large amount of computational cost when the optimization is conducted. In order to optimize the vibration response of the longitudinal-transverse stiffened conical shell, the surrogate modeling method is used in this study to approximate the frequency-acceleration response function which makes the vibration response optimization affordable. Since different surrogate models often perform differently in different regions of the design space, an ensemble of surrogate models is utilized to maximize the overall accuracy over the whole design space. The ensemble of surrogates is a weighted combination of Kriging model, radial basis function (RBF) and support vector regression (SVR). The weights of the ensemble of surrogates vary in different regions and are determined by the estimated errors of the surrogate models at the study point. The smaller the estimated error is, the higher the weight is. Then the prediction of ensemble of surrogates is compared to the individual surrogate’s, and the results show that the accuracies of the ensemble of surrogates in peak regions are significant higher than its components. Based on the ensemble of surrogates, a vibration optimization of a longitudinal-transverse stiffened conical shell is conducted using genetic algorithm (GA). The design variables of the optimization are the thickness of the longitudinal-transverse stiffened conical shell and the height of stiffened structure. The objective is to minimize the highest acceleration of the shell and the calculations of the peak accelerations are approximated by the built ensemble of the surrogates. The constraints include the weight of the stiffened conical shell and structure size combination. The optimization results show that the proposed approach is efficient in optimization of the vibration response of longitudinal-transverse stiffened conical shells.

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