A Multiobjective Adaptive Surrogate Modeling-Based Optimization (MO-ASMO) Framework Using Efficient Sampling Strategies

2017 ◽  
Author(s):  
Yong Hoon Lee ◽  
R. E. Corman ◽  
Randy H. Ewoldt ◽  
James T. Allison
Keyword(s):  
Surrogate Model ◽  
Design Space ◽  
Surrogate Modeling ◽  
Pareto Set ◽  
Test Problems ◽  
High Fidelity ◽  
Sampling Strategies ◽  
Nsga Ii ◽  
Sample Points ◽  
Fidelity Model

A novel multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) framework is proposed to utilize a minimal number of training samples efficiently for sequential model updates. All the sample points are enforced to be feasible, and to provide coverage of sparsely explored sparse design regions using a new optimization subproblem. The MO-ASMO method only evaluates high-fidelity functions at feasible sample points. During an exploitation sample phase, samples are selected to enhance solution accuracy rather than the global exploration. Sampling tasks are especially challenging for multiobjective optimization; for an n-dimensional design space, a strategy is required for generating model update sample points near an (n − 1)-dimensional hypersurface corresponding to the Pareto set in the design space. This is addressed here using a force-directed layout algorithm, adapted from graph visualization strategies, to distribute feasible sample points evenly near the estimated Pareto set. Model validation samples are chosen uniformly on the Pareto set hypersurface, and surrogate model estimates at these points are compared to high-fidelity model responses. All high-fidelity model evaluations are stored for later use to train an updated surrogate model. The MO-ASMO algorithm, along with the set of new sampling strategies, are tested using two mathematical and one realistic engineering problems. The second mathematical test problems is specifically designed to test the limits of this algorithm to cope with very narrow, non-convex feasible domains. It involves oscillatory objective functions, giving rise to a discontinuous set of Pareto-optimal solutions. Also, the third test problem demonstrates that the MO-ASMO algorithm can handle a practical engineering problem with more than 10 design variables and black-box simulations. The efficiency of the MO-ASMO algorithm is demonstrated by comparing the result of two mathematical problems to the results of the NSGA-II algorithm in terms of the number of high fidelity function evaluations, and is shown to reduce total function evaluations by several orders of magnitude when converging to the same Pareto sets.

Enhanced multi-fidelity model for flight simulation using global exploration and the Kriging method

2016 ◽  
Vol 231 (4) ◽  
pp. 606-620 ◽  
Author(s):  
Daeyeon Lee ◽  
Nhu Van Nguyen ◽  
Maxim Tyan ◽  
Hyung-Geun Chun ◽  
Sangho Kim ◽  
...  
Keyword(s):  
Surrogate Model ◽  
Cross Validation ◽  
Vortex Lattice ◽  
Flight Simulation ◽  
High Fidelity ◽  
Analysis Tool ◽  
Kriging Method ◽  
Flight Vehicles ◽  
Aerodynamic Database ◽  
Fidelity Model

Using the global exploration and Kriging-based multi-fidelity analysis methods, this study developed a multi-fidelity aerodynamic database for use in the performance analysis of flight vehicles and for use in flight simulations. Athena vortex lattice, a program based on vortex lattice method, was used as the low-fidelity analysis tool in the multi-fidelity analysis method. The in-house high-fidelity AADL-3D code was based on the Navier–Stokes equations. The AADL-3D code was validated by comparing the data and the analysis results of the Onera M-6 wing and NACA TN 3649. The design of experiment method and the Kriging method were applied to integrate low- and high-fidelity analysis results. General data tendencies were established from the low-fidelity analysis results. The high-fidelity analysis results and the Kriging method were used to generate a surrogate model, from which the low-fidelity analysis results were interpolated. To reduce repeated calculations, three design points were simultaneously added for each calculation. The convergence of three design points was avoided by considering only the peak points as additional design points. The reliability of the final surrogate model was determined by applying the leave-one-out cross-validation method and by obtaining the cross-validation root mean square error. Using the multi-fidelity model developed in this study, a multi-fidelity aerodynamic database was constructed for use in the three degrees of freedom flight simulation of flight vehicles.

scholarly journals Variable Fidelity Modeling as Applied to Trajectory Optimization for a Hydraulic Backhoe

2009 ◽  
Author(s):  
Roxanne A. Moore ◽  
Christiaan J. J. Paredis
Keyword(s):  
Trajectory Optimization ◽  
Design Space Exploration ◽  
Design Space ◽  
Optimization Process ◽  
High Fidelity ◽  
Simulation And Optimization ◽  
Variable Fidelity ◽  
Computational Resources ◽  
The Cost ◽  
Fidelity Model

Modeling, simulation, and optimization play vital roles throughout the engineering design process; however, in many design disciplines the cost of simulation is high, and designers are faced with a tradeoff between the number of alternatives that can be evaluated and the accuracy with which they are evaluated. In this paper, a methodology is presented for using models of various levels of fidelity during the optimization process. The intent is to use inexpensive, low-fidelity models with limited accuracy to recognize poor design alternatives and reserve the high-fidelity, accurate, but also expensive models only to characterize the best alternatives. Specifically, by setting a user-defined performance threshold, the optimizer can explore the design space using a low-fidelity model by default, and switch to a higher fidelity model only if the performance threshold is attained. In this manner, the high fidelity model is used only to discern the best solution from the set of good solutions, so computational resources are conserved until the optimizer is close to the solution. This makes the optimization process more efficient without sacrificing the quality of the solution. The method is illustrated by optimizing the trajectory of a hydraulic backhoe. To characterize the robustness and efficiency of the method, a design space exploration is performed using both the low and high fidelity models, and the optimization problem is solved multiple times using the variable fidelity framework.

scholarly journals Selection of Existing Sail Designs for Multi-Fidelity Surrogate Models

2022 ◽  
Vol 7 (01) ◽  
pp. 31-51
Author(s):  
Tanya Peart ◽  
Nicolas Aubin ◽  
Stefano Nava ◽  
John Cater ◽  
Stuart Norris
Keyword(s):  
Surrogate Model ◽  
Lift Coefficient ◽  
Simulation Method ◽  
Surrogate Models ◽  
High Fidelity ◽  
Data Points ◽  
Velocity Prediction ◽  
The Difference ◽  
Fidelity Model ◽  
Selection Of

Velocity Prediction Programs (VPPs) are commonly used to help predict and compare the performance of different sail designs. A VPP requires an aerodynamic input force matrix which can be computationally expensive to calculate, limiting its application in industrial sail design projects. The use of multi-fidelity kriging surrogate models has previously been presented by the authors to reduce this cost, with high-fidelity data for a new sail being modelled and the low-fidelity data provided by data from existing, but different, sail designs. The difference in fidelity is not due to the simulation method used to obtain the data, but instead how similar the sail’s geometry is to the new sail design. An important consideration for the construction of these models is the choice of low-fidelity data points, which provide information about the trend of the model curve between the high-fidelity data. A method is required to select the best existing sail design to use for the low-fidelity data when constructing a multi-fidelity model. The suitability of an existing sail design as a low fidelity model could be evaluated based on the similarity of its geometric parameters with the new sail. It is shown here that for upwind jib sails, the similarity of the broadseam between the two sails best indicates the ability of a design to be used as low-fidelity data for a lift coefficient surrogate model. The lift coefficient surrogate model error predicted by the regression is shown to be close to 1% of the lift coefficient surrogate error for most points. Larger discrepancies are observed for a drag coefficient surrogate error regression.

scholarly journals Design Space Exploration of Turbulent Multiphase Flows Using Machine Learning-Based Surrogate Model

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4565 ◽  
Author(s):  
Himakar Ganti ◽  
Manu Kamin ◽  
Prashant Khare
Keyword(s):  
Machine Learning ◽  
Surrogate Model ◽  
Momentum Flux ◽  
Design Space Exploration ◽  
Design Space ◽  
Machine Learning Techniques ◽  
Dispersed Phase ◽  
High Fidelity ◽  
Test Conditions ◽  
Learning Techniques

This study focuses on establishing a surrogate model based on machine learning techniques to predict the time-averaged spatially distributed behaviors of vaporizing liquid jets in turbulent air crossflow for momentum flux ratios between 5 and 120. This surrogate model extends a previously developed Gaussian-process-based framework applicable to laminar flows to accommodate turbulent flows and demonstrates that in addition to detailed fields of primitive variables, second-order turbulence statistics can also be predicted using machine learning techniques. The framework proceeds in 3 steps—(1) design of experiment studies to identify training points and conducting high-fidelity calculations to build the training dataset; (2) Gaussian process regression (supervised training) for the range of operating conditions under consideration for gaseous and dispersed phase quantities; and (3) error quantification of the surrogate model by comparing the machine learning predictions with the truth model for test conditions (i.e., conditions not used for training). The framework was trained using data generated by high-fidelity large eddy simulation (LES)-based calculations (also referred to as the truth model), which solves the complete set of conservation equations for mass, momentum, energy, and species in an Eulerian reference frame, coupled with a Lagrangian solver that tracks the dispersed phase. Simulations were conducted for the range of momentum flux ratios between 5 and 120 for liquid water injected into crossflowing air at a pressure of 1 atm and temperature of 600 K. Results from the machine-learned surrogate model, also called emulations, were compared with the truth model under testing conditions identified by momentum flux ratios of 7 and 40. L1 errors for time-averaged field quantities, including velocity magnitudes, pressure, temperature, vapor fraction of the evaporated liquid, and turbulent kinetic energy in the gas phase, and spray penetration and Sauter mean diameters in the dispersed phase are reported. Speedup of 65 was achieved with this emulator when compared against LES simulation of the same test conditions with errors for all quantities below 14%, thus demonstrating the potential benefits of using machine learning techniques for design space exploration of devices that are based on turbulent multiphase fluid flows. This is the first effort of its kind in the literature that demonstrates the application of machine learning techniques on turbulent multiphase flows.

Prediction of Flow Properties on Turbine Vane Airfoil Surface From 3D Geometry With Convolutional Neural Network

2019 ◽  
Author(s):  
Yuan Jin ◽  
Shan Li ◽  
Olivier Jung
Keyword(s):  
Neural Network ◽  
Surrogate Model ◽  
Design Space ◽  
Flow Fields ◽  
High Fidelity ◽  
Flow Properties ◽  
Cfd Simulations ◽  
Airfoil Surface ◽  
3D Geometry ◽  
Turbine Vane

Abstract Nowadays, Computational Fluid Dynamics (CFD) simulations play an increasingly important role for turbine airfoil design. This high-fidelity approach is capable to provide accurate information of flow fields. Meanwhile, the calculation accuracy is always gained at the expense of numerical cost. This gap limits opportunities for design space exploration. To address this problem, surrogate models (also known as metamodels) are introduced to approximate high-fidelity CFD models. However, traditional surrogate models, such as Kriging or Radial Basis Function, construct response surface on a design space with limited dimensions. This prevents users from predicting the flow fields directly from the geometry and performing interactive design of airfoil. In the present work, we propose a Convolutional Neural Network (CNN) based surrogate model to predict flow properties on turbine vane airfoil surface from 3D airfoil profile defined by point cloud. The proposed CNN architecture adopts a symmetric expanding path that is similar to the so-called U-Net. The geometries in the training and testing dataset are generated via varying the parameters defined by the Free-Form Deformation approach. The corresponding flow fields are obtained through high-fidelity CFD simulations performed in a finite volume context. Furthermore, a gaussian process based Bayesian optimization technique is utilized to tune automatically the hyperparameters of the network. In this work, we trained the CNN based surrogate model with static pressure and temperature on the mean section of turbine vane airfoil surface. The trained model is able to predict in a reliable and efficient way the corresponding property directly from the 3D geometry, which allows engineers to agilely adjust their airfoil design.

Accelerating the estimation of collisionless energetic particle confinement statistics in stellarators using multifidelity Monte Carlo

2021 ◽  
Author(s):  
Frederick Law ◽  
Antoine J Cerfon ◽  
Benjamin Peherstorfer
Keyword(s):  
Monte Carlo ◽  
Surrogate Model ◽  
Energetic Particle ◽  
Small Time ◽  
Point Of View ◽  
High Fidelity ◽  
Monte Carlo Studies ◽  
Long Time ◽  
Particle Confinement ◽  
Fidelity Model

Abstract In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo analyses are highly expensive because a large number of particle trajectories need to be integrated over long time scales, and small time steps must be taken to accurately capture the features of the wide variety of trajectories. Even when they are based on guiding center trajectories, as opposed to full-orbit trajectories, these standard Monte Carlo studies are too expensive to be included in most stellarator optimization codes. We present the first multifidelity Monte Carlo scheme for accelerating the estimation of energetic particle confinement in stellarators. Our approach relies on a two-level hierarchy, in which a guiding center model serves as the high-fidelity model, and a data-driven linear interpolant is leveraged as the low-fidelity surrogate model. We apply multifidelity Monte Carlo to the study of energetic particle confinement in a 4-period quasi-helically symmetric stellarator, assessing various metrics of confinement. Stemming from the very high computational efficiency of our surrogate model as well as its sufficient correlation to the high-fidelity model, we obtain speedups of up to 10 with multifidelity Monte Carlo compared to standard Monte Carlo.

scholarly journals Elite Exploitation: A Combination of Mathematical Concept and EMO Approach for Multi-Objective Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 136
Author(s):  
Wenxiao Li ◽  
Yushui Geng ◽  
Jing Zhao ◽  
Kang Zhang ◽  
Jianxin Liu
Keyword(s):  
Decision Making ◽  
Optimization Problems ◽  
Hybrid Genetic Algorithm ◽  
Decision Makers ◽  
Superior Performance ◽  
Test Problems ◽  
Mathematical Function ◽  
Hyperbolic Tangent ◽  
Nsga Ii ◽  
Multi Objective

This paper explores the combination of a classic mathematical function named “hyperbolic tangent” with a metaheuristic algorithm, and proposes a novel hybrid genetic algorithm called NSGA-II-BnF for multi-objective decision making. Recently, many metaheuristic evolutionary algorithms have been proposed for tackling multi-objective optimization problems (MOPs). These algorithms demonstrate excellent capabilities and offer available solutions to decision makers. However, their convergence performance may be challenged by some MOPs with elaborate Pareto fronts such as CFs, WFGs, and UFs, primarily due to the neglect of diversity. We solve this problem by proposing an algorithm with elite exploitation strategy, which contains two parts: first, we design a biased elite allocation strategy, which allocates computation resources appropriately to elites of the population by crowding distance-based roulette. Second, we propose a self-guided fast individual exploitation approach, which guides elites to generate neighbors by a symmetry exploitation operator, which is based on mathematical hyperbolic tangent function. Furthermore, we designed a mechanism to emphasize the algorithm’s applicability, which allows decision makers to adjust the exploitation intensity with their preferences. We compare our proposed NSGA-II-BnF with four other improved versions of NSGA-II (NSGA-IIconflict, rNSGA-II, RPDNSGA-II, and NSGA-II-SDR) and four competitive and widely-used algorithms (MOEA/D-DE, dMOPSO, SPEA-II, and SMPSO) on 36 test problems (DTLZ1–DTLZ7, WGF1–WFG9, UF1–UF10, and CF1–CF10), and measured using two widely used indicators—inverted generational distance (IGD) and hypervolume (HV). Experiment results demonstrate that NSGA-II-BnF exhibits superior performance to most of the algorithms on all test problems.

Adaptive response prediction for aerodynamic shape optimization

2017 ◽  
Vol 34 (5) ◽  
pp. 1485-1500
Author(s):  
Leifur Leifsson ◽  
Slawomir Koziel
Keyword(s):  
Shape Optimization ◽  
Adaptive Response ◽  
Simulation Models ◽  
Response Prediction ◽  
High Fidelity ◽  
High Fidelity Simulation ◽  
Aerodynamic Shape Optimization ◽  
Content Type ◽  
Aerodynamic Shape ◽  
Fidelity Model

Purpose The purpose of this paper is to reduce the overall computational time of aerodynamic shape optimization that involves accurate high-fidelity simulation models. Design/methodology/approach The proposed approach is based on the surrogate-based optimization paradigm. In particular, multi-fidelity surrogate models are used in the optimization process in place of the computationally expensive high-fidelity model. The multi-fidelity surrogate is constructed using physics-based low-fidelity models and a proper correction. This work introduces a novel correction methodology – referred to as the adaptive response prediction (ARP). The ARP technique corrects the low-fidelity model response, represented by the airfoil pressure distribution, through suitable horizontal and vertical adjustments. Findings Numerical investigations show the feasibility of solving real-world problems involving optimization of transonic airfoil shapes and accurate computational fluid dynamics simulation models of such surfaces. The results show that the proposed approach outperforms traditional surrogate-based approaches. Originality/value The proposed aerodynamic design optimization algorithm is novel and holistic. In particular, the ARP correction technique is original. The algorithm is useful for fast design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search spaces, which is challenging using conventional methods because of excessive computational costs.

Aerodynamic Efficiency Optimization of the 1st Stage of Transonic High Pressure Turbine through Lean and Sweep Angles

2019 ◽  
Vol 36 (3) ◽  
pp. 245-256
Author(s):  
Yoonki Kim ◽  
Sanga Lee ◽  
Kwanjung Yee ◽  
Young-Seok Kang
Keyword(s):  
High Pressure ◽  
Surrogate Model ◽  
Design Space ◽  
Latin Hypercube Sampling ◽  
Expected Improvement ◽  
Total Efficiency ◽  
High Pressure Turbine ◽  
Sweep Angle ◽  
Design Variables ◽  
Optimal Latin Hypercube Sampling

Abstract The purpose of this study is to optimize the 1st stage of the transonic high pressure turbine (HPT) for enhancement of aerodynamic performance. Isentropic total-to-total efficiency is designated as the objective function. Since the isentropic efficiency can be improved through modifying the geometry of vane and rotor blade, lean angle and sweep angle are chosen as design variables, which can effectively alter the blade geometry. The sensitivities of each design variable are investigated by applying lean and sweep angles to the base nozzle and rotor, respectively. The design space is also determined based on the results of the parametric study. For the design of experiment (DoE), Optimal Latin Hypercube sampling is adopted, so that 25 evenly distributed samples are selected on the design space. Sequentially, based on the values from the CFD calculation, Kriging surrogate model is constructed and refined using Expected Improvement (EI). With the converged surrogate model, optimum solution is sought by using the Genetic Algorithm. As a result, the efficiency of optimum turbine 1st stage is increased by 1.07 % point compared to that of the base turbine 1st stage. Also, the blade loading, pressure distribution, static entropy, shock structure, and secondary flow are thoroughly discussed.

Multi-Objective Design and Optimisation of Bypass Outlet-Guide Vanes

2003 ◽  
Author(s):  
Shahrokh Shahpar ◽  
David Giacche ◽  
Leigh Lapworth
Keyword(s):  
Design Space ◽  
Guide Vane ◽  
Automated Design ◽  
Analysis Procedure ◽  
High Fidelity ◽  
Cfd Analysis ◽  
Optimization System ◽  
Multi Objective ◽  
Cluster Of Workstations ◽  
Stagger Angle

This paper describes the development of an automated design optimization system that makes use of a high fidelity Reynolds-Averaged CFD analysis procedure to minimize the fan forcing and fan BOGV (bypass outlet guide vane) losses simultaneously taking into the account the down-stream pylon and RDF (radial drive fairing) distortions. The design space consists of the OGV’s stagger angle, trailing-edge recambering, axial and circumferential positions leading to a variable pitch optimum design. An advanced optimization system called SOFT (Smart Optimisation for Turbomachinery) was used to integrate a number of pre-processor, simulation and in-house grid generation codes and postprocessor programs. A number of multi-objective, multi-point optimiztion were carried out by SOFT on a cluster of workstations and are reported herein.

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