Design Space Description through Adaptive Sampling and Symbolic Computation

In this paper, we propose a novel solution strategy to explicitly describe the design space in which no recourse is considered for the realization of the parameters. First, to smooth the boundary of the design space, the Kreisselmeier-Steinhauser (KS) function is applied to aggregate all inequality constraints, and project them into the design space. Next, for creating a surrogate polynomial model of the KS function, we focus on finding the sampling points on the boundary of KS space. After testing the feasibility of Latin hypercube sampling points, two methods are presented to efficiently extend the set of boundary points. Finally, a symbolic computation method, cylindrical algebraic decomposition, is applied to transform the surrogate model into a series of explicit and triangular subsystems that can be further converted to describe the KS space. Two case studies are considered to show the efficiency of the proposed algorithm.

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On Adaptive Sampling for Single and Multi-Response Bayesian Surrogate Models

Volume 1: 32nd Design Automation Conference, Parts A and B ◽

10.1115/detc2006-99210 ◽

2006 ◽

Cited By ~ 9

Author(s):

David A. Romero ◽

Cristina H. Amon ◽

Susan Finger

Keyword(s):

Experimental Design ◽

Adaptive Sampling ◽

Design Space Exploration ◽

A Priori ◽

Computer Experiments ◽

Latin Hypercube Sampling ◽

Surrogate Models ◽

Sampling Techniques ◽

Design And Optimization ◽

Sampling Points

In order to reduce the time and resources devoted to design-space exploration during simulation-based design and optimization, the use of surrogate models, or metamodels, has been proposed in the literature. Key to the success of metamodeling efforts are the experimental design techniques used to generate the combinations of input variables at which the computer experiments are conducted. Several adaptive sampling techniques have been proposed to tailor the experimental designs to the specific application at hand, using the already-acquired data to guide further exploration of the input space, instead of using a fixed sampling scheme defined a priori. Though mixed results have been reported, it has been argued that adaptive sampling techniques can be more efficient, yielding better surrogate models with less sampling points. In this paper, we address the problem of adaptive sampling for single and multi-response metamodels, with a focus on Multi-stage Multi-response Bayesian Surrogate Models (MMBSM). We compare distance-optimal latin hypercube sampling, an entropy-based criterion and the maximum cross-validation variance criterion, originally proposed for one-dimensional output spaces and implemented in this paper for multi-dimensional output spaces. Our results indicate that, both for single and multi-response surrogate models, the entropy-based adaptive sampling approach leads to models that are more robust to the initial experimental design and at least as accurate (or better) when compared with other sampling techniques using the same number of sampling points.

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

International Journal of Turbo and Jet Engines ◽

10.1515/tjj-2016-0080 ◽

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.

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Beyond the Known: Detecting Novel Feasible Domains Over an Unbounded Design Space

Journal of Mechanical Design ◽

10.1115/1.4037306 ◽

2017 ◽

Vol 139 (11) ◽

Cited By ~ 9

Author(s):

Wei Chen ◽

Mark Fuge

Keyword(s):

Real World ◽

Adaptive Sampling ◽

Design Space ◽

Fundamental Problem ◽

Domain Boundary ◽

Sampling Technique ◽

Standard Test ◽

Worst Case ◽

Trade Offs ◽

Design Variables

To solve a design problem, sometimes it is necessary to identify the feasible design space. For design spaces with implicit constraints, sampling methods are usually used. These methods typically bound the design space; that is, limit the range of design variables. But bounds that are too small will fail to cover all possible designs, while bounds that are too large will waste sampling budget. This paper tries to solve the problem of efficiently discovering (possibly disconnected) feasible domains in an unbounded design space. We propose a data-driven adaptive sampling technique—ε-margin sampling, which learns the domain boundary of feasible designs and also expands our knowledge on the design space as available budget increases. This technique is data-efficient, in that it makes principled probabilistic trade-offs between refining existing domain boundaries versus expanding the design space. We demonstrate that this method can better identify feasible domains on standard test functions compared to both random and active sampling (via uncertainty sampling). However, a fundamental problem when applying adaptive sampling to real world designs is that designs often have high dimensionality and thus require (in the worst case) exponentially more samples per dimension. We show how coupling design manifolds with ε-margin sampling allows us to actively expand high-dimensional design spaces without incurring this exponential penalty. We demonstrate this on real-world examples of glassware and bottle design, where our method discovers designs that have different appearance and functionality from its initial design set.

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Multiple Lump Solutions of the (4+1)-Dimensional Fokas Equation

Advances in Mathematical Physics ◽

10.1155/2020/3407676 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Hongcai Ma ◽

Yunxiang Bai ◽

Aiping Deng

Keyword(s):

Symbolic Computation ◽

Bilinear Form ◽

Three Dimensional ◽

Structural Features ◽

Computation Method ◽

Lump Solutions ◽

Wave Solutions ◽

Lump Wave

In this paper, we investigate multiple lump wave solutions of the new (4+1)-dimensional Fokas equation by adopting a symbolic computation method. We get its 1-lump solutions, 3-lump solutions, and 6-lump solutions by using its bilinear form. Moreover, some basic characters and structural features of multiple lump waves are explained by depicting the three-dimensional plots.

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General Surrogate Adaptive Sampling using Interquartile Range for Design Space Exploration

AIAA Scitech 2019 Forum ◽

10.2514/6.2019-2213 ◽

2019 ◽

Cited By ~ 3

Author(s):

Yiming Zhang ◽

Nam Ho Kim ◽

Raphael T. Haftka

Keyword(s):

Adaptive Sampling ◽

Design Space Exploration ◽

Design Space ◽

Space Exploration ◽

Interquartile Range

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Shape Optimization of Microchannels Using Surrogate Modelling

Volume 8B: Heat Transfer and Thermal Engineering ◽

10.1115/imece2018-87780 ◽

2018 ◽

Author(s):

Muhammad Ansab Ali ◽

Tariq S. Khan ◽

Saqib Salam ◽

Ebrahim Al Hajri

Keyword(s):

Shape Optimization ◽

Heat Sink ◽

Pareto Front ◽

Sampling Method ◽

Design Space ◽

Latin Hypercube Sampling ◽

Optimum Shape ◽

Microchannel Heat Sink ◽

Objective Functions ◽

Computational Resources

To minimize the computational and optimization time, a numerical simulation of 3D microchannel heat sink was performed using surrogate model to achieve the optimum shape. Latin hypercube sampling method was used to explore the design space and to construct the model. The accuracy of the model was evaluated using statistical methods like coefficient of multiple determinations and root mean square error. Thermal resistance and pressure drop being conflicting objective functions were selected to optimize the geometric parameters of the microchannel. Multi objective shape optimization of design was conducted using genetic algorithm and the optimum design solutions are presented in the Pareto front. The application of the surrogate methods has predicted the performance of the heat sink with the sufficient accuracy employing significantly lower computational resources.

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Reliability-Based Optimal Design and Tolerancing for Multibody Systems Using Explicit Design Space Decomposition

Journal of Mechanical Design ◽

10.1115/1.4000760 ◽

2010 ◽

Vol 132 (2) ◽

Cited By ~ 16

Author(s):

Henry Arenbeck ◽

Samy Missoum ◽

Anirban Basudhar ◽

Parviz Nikravesh

Keyword(s):

Multibody Systems ◽

Adaptive Sampling ◽

Design Space ◽

Limit State ◽

Uniform Design ◽

Probability Of Failure ◽

Support Vector ◽

State Function ◽

Nominal System ◽

Truncated Normal

This paper introduces a new approach for the optimal geometric design and tolerancing of multibody systems. The approach optimizes both the nominal system dimensions and the associated tolerances by solving a reliability-based design optimization (RDBO) problem under the assumption of truncated normal distributions of the geometric properties. The solution is obtained by first constructing the explicit boundaries of the failure regions (limit state function) using a support vector machine, combined with adaptive sampling and uniform design of experiments. The use of explicit boundaries enables the treatment of systems with discontinuous or binary behaviors. The explicit boundaries also allow for an efficient calculation of the probability of failure using importance sampling. The probability of failure is subsequently approximated over the whole design space (the nominal system dimensions and the associated tolerances), thus making the solution of the RBDO problem straightforward. The proposed approach is applied to the optimization of a web cutter mechanism.

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