scholarly journals Design of Mechanical Metamaterials via Constrained Bayesian Optimization

2018 ◽  
Author(s):  
Conner Sharpe ◽  
Carolyn Conner Seepersad ◽  
Seth Watts ◽  
Dan Tortorelli
Keyword(s):  
Design Space ◽  
Engineering Problem ◽  
Bayesian Optimization ◽  
Probabilistic Constraints ◽  
Objective Functions ◽  
Bulk Properties ◽  
New Class ◽  
Naturally Occurring ◽  
Design Variables ◽  
Mechanical Metamaterials

Advances in additive manufacturing processes have made it possible to build mechanical metamaterials with bulk properties that exceed those of naturally occurring materials. One class of these metamaterials is structural lattices that can achieve high stiffness to weight ratios. Recent work on geometric projection approaches has introduced the possibility of optimizing these architected lattice designs in a drastically reduced parameter space. The reduced number of design variables enables application of a new class of methods for exploring the design space. This work investigates the use of Bayesian optimization, a technique for global optimization of expensive non-convex objective functions through surrogate modeling. We utilize formulations for implementing probabilistic constraints in Bayesian optimization to aid convergence in this highly constrained engineering problem, and demonstrate results with a variety of stiff lightweight lattice designs.

scholarly journals Bayesian optimization with adaptive surrogate models for automated experimental design

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Bowen Lei ◽  
Tanner Quinn Kirk ◽  
Anirban Bhattacharya ◽  
Debdeep Pati ◽  
Xiaoning Qian ◽  
...  
Keyword(s):  
Experimental Design ◽  
Design Space ◽  
Materials Science ◽  
Scientific Discovery ◽  
Surrogate Models ◽  
Multivariate Adaptive Regression Splines ◽  
Bayesian Optimization ◽  
Objective Functions ◽  
Additive Regression ◽  
Efficient Exploration

AbstractBayesian optimization (BO) is an indispensable tool to optimize objective functions that either do not have known functional forms or are expensive to evaluate. Currently, optimal experimental design is always conducted within the workflow of BO leading to more efficient exploration of the design space compared to traditional strategies. This can have a significant impact on modern scientific discovery, in particular autonomous materials discovery, which can be viewed as an optimization problem aimed at looking for the maximum (or minimum) point for the desired materials properties. The performance of BO-based experimental design depends not only on the adopted acquisition function but also on the surrogate models that help to approximate underlying objective functions. In this paper, we propose a fully autonomous experimental design framework that uses more adaptive and flexible Bayesian surrogate models in a BO procedure, namely Bayesian multivariate adaptive regression splines and Bayesian additive regression trees. They can overcome the weaknesses of widely used Gaussian process-based methods when faced with relatively high-dimensional design space or non-smooth patterns of objective functions. Both simulation studies and real-world materials science case studies demonstrate their enhanced search efficiency and robustness.

Bayesian Optimization for Multi-Objective High-Dimensional Turbine Aero Design

2021 ◽  
Author(s):  
Yiming Zhang ◽  
Sayan Ghosh ◽  
Thomas Vandeputte ◽  
Liping Wang
Keyword(s):  
Design Space Exploration ◽  
Design Space ◽  
Industrial Applications ◽  
Bayesian Optimization ◽  
High Dimensional ◽  
Multi Objective Optimization ◽  
Loop Optimization ◽  
Multi Objective ◽  
Input Design ◽  
Design Variables

Abstract Industrial design fundamentally relies on high-dimensional multi-objective optimization. Bayesian Optimization (BO) based on Gaussian Processes (GPs) has been shown to be effective for this practice where new designs are picked in each iteration for varying objectives including optimization and model refinement. This paper introduces two industrial applications of BO for turbine aero design. The first application is GE’s Aviation & Power DT4D Turbo Aero Design with 32 design variables. It has a single objective to maximize with 32 input/design variables and thus considered high-dimensional in terms of the input space. BO has significantly succeeded the traditional design schemes. It has been shown that finding the maximum-EI points (inner-loop optimization) could be critical and the influence of inner-loop optimization was evaluated. The second application is for multi-objective optimization. Each simulation run is the aggregate result from multiple CFD runs tuning geometry and took 24 hours to complete. BO has been capable to extend the existing Pareto front with a few additional runs. BO has been searching along the border of the design space and therefore motivate the open-up of design space exploration. For both applications, BO successfully guide the CFD run and allocate design variables more optimum than previous design approaches.

Enhanced Multi-Objective Optimization of a Microchannel Heat Sink Using Multiple Surrogates Modeling

2009 ◽  
Author(s):  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Heat Sink ◽  
Design Space ◽  
Surrogate Models ◽  
Pareto Optimal ◽  
Microchannel Heat Sink ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Design Variables

A liquid flow microchannel heat sink has been studied and optimized with the help of three-dimensional numerical analysis and multiple surrogate methods. Two objective functions, thermal resistance and pumping power have been selected to assess the performance of the microchannel heat sink. The design variables related to the microchannel top and bottom widths, depth and fin width, which contribute to objective functions, have been identified and design space has been explored through some preliminary calculations. Design of experiments was performed and a three-level full factorial design was selected to exploit the design space. The numerical solutions obtained at these design points were utilized to construct surrogate models namely Response Surface Approximations and Kriging. A hybrid multi-objective evolutionary algorithm coupled with surrogate models and a gradient-based search algorithm is applied to find global Pareto-optimal solutions. Since, the surrogate models are highly problem-dependent, the accuracy of the two surrogate models has been discussed in view of their predictions at on- and off-Pareto-optimal front. The trade-off analysis was performed in view of the two competing objectives. The Pareto-optimal sensitivity (change in value along the Pareto-optimal front) of the design variables has been found out to economically compromise with the design variables contributing relatively less to the objective functions. The application of the multiple surrogate methods not only improves quality of multi-objective optimization but also gives the feedback of the fidelity of the model near the optimum region.

Multi-Objective Design Problem of Tire Wear and Visualization of Its Pareto Solutions2

2006 ◽  
Vol 34 (3) ◽  
pp. 170-194 ◽  
Author(s):  
M. Koishi ◽  
Z. Shida
Keyword(s):  
Inverse Problems ◽  
Conceptual Design ◽  
Dimensional Space ◽  
Design Stage ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Design Problems ◽  
Multi Objective ◽  
Design Engineers ◽  
Design Variables

Abstract Since tires carry out many functions and many of them have tradeoffs, it is important to find the combination of design variables that satisfy well-balanced performance in conceptual design stage. To find a good design of tires is to solve the multi-objective design problems, i.e., inverse problems. However, due to the lack of suitable solution techniques, such problems are converted into a single-objective optimization problem before being solved. Therefore, it is difficult to find the Pareto solutions of multi-objective design problems of tires. Recently, multi-objective evolutionary algorithms have become popular in many fields to find the Pareto solutions. In this paper, we propose a design procedure to solve multi-objective design problems as the comprehensive solver of inverse problems. At first, a multi-objective genetic algorithm (MOGA) is employed to find the Pareto solutions of tire performance, which are in multi-dimensional space of objective functions. Response surface method is also used to evaluate objective functions in the optimization process and can reduce CPU time dramatically. In addition, a self-organizing map (SOM) proposed by Kohonen is used to map Pareto solutions from high-dimensional objective space onto two-dimensional space. Using SOM, design engineers see easily the Pareto solutions of tire performance and can find suitable design plans. The SOM can be considered as an inverse function that defines the relation between Pareto solutions and design variables. To demonstrate the procedure, tire tread design is conducted. The objective of design is to improve uneven wear and wear life for both the front tire and the rear tire of a passenger car. Wear performance is evaluated by finite element analysis (FEA). Response surface is obtained by the design of experiments and FEA. Using both MOGA and SOM, we obtain a map of Pareto solutions. We can find suitable design plans that satisfy well-balanced performance on the map called “multi-performance map.” It helps tire design engineers to make their decision in conceptual design stage.

2,2-Dialkylacetic Acids -A New Class of Naturally Occurring Lipid Constituents

1995 ◽  
Vol 50 (1-2) ◽  
pp. 123-126 ◽  
Author(s):  
Gottfried Raab ◽  
Jürgen Jacob
Keyword(s):  
Retention Time ◽  
Relative Retention Time ◽  
Methyl Esters ◽  
South American ◽  
Time Data ◽  
New Class ◽  
The Past ◽  
Relative Retention ◽  
Naturally Occurring ◽  
Acetic Acids

Abstract The uropygial gland waxes of the South American red-legged Seriema (Cariama cristata (L., 1766)) were found to be composed of unbranched alcohols and 2,2′-dialkyl-substituted acetic acids which so far have not been found in skin lipids. When used as a chemosystematic character, the occurrence of this lipid class separates the order Cariamiformes (Seriemas) from all other avian orders hitherto investigated, especially from the Gruiformes (cranes and rails) to which they have been tentatively attributed in the past. From the GC retention time data now available for a series of 2-alkyl-substituted fatty acid methyl esters relative retention time indices for other compounds may be predicted.

Multi-Objective Optimization of an Autonomous Underwater Vehicle

2009 ◽  
Vol 43 (2) ◽  
pp. 48-60 ◽  
Author(s):  
M. Martz ◽  
W. L. Neu
Keyword(s):  
Design Space ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Design Problems ◽  
Single Measure ◽  
Design Variables ◽  
Complex Design ◽  
Final Design ◽  
Undersea Vehicle ◽  
Hierarchy Process

AbstractThe design of complex systems involves a number of choices, the implications of which are interrelated. If these choices are made sequentially, each choice may limit the options available in subsequent choices. Early choices may unknowingly limit the effectiveness of a final design in this way. Only a formal process that considers all possible choices (and combinations of choices) can insure that the best option has been selected. Complex design problems may easily present a number of choices to evaluate that is prohibitive. Modern optimization algorithms attempt to navigate a multidimensional design space in search of an optimal combination of design variables. A design optimization process for an autonomous underwater vehicle is developed using a multiple objective genetic optimization algorithm that searches the design space, evaluating designs based on three measures of performance: cost, effectiveness, and risk. A synthesis model evaluates the characteristics of a design having any chosen combination of design variable values. The effectiveness determined by the synthesis model is based on nine attributes identified in the U.S. Navy’s Unmanned Undersea Vehicle Master Plan and four performance-based attributes calculated by the synthesis model. The analytical hierarchy process is used to synthesize these attributes into a single measure of effectiveness. The genetic algorithm generates a set of Pareto optimal, feasible designs from which a decision maker(s) can choose designs for further analysis.

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.

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

2017 ◽  
Vol 139 (11) ◽  
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.

A Deep Adversarial Learning Methodology for Designing Microstructural Material Systems

2018 ◽  
Author(s):  
Xiaolin Li ◽  
Zijiang Yang ◽  
L. Catherine Brinson ◽  
Alok Choudhary ◽  
Ankit Agrawal ◽  
...  
Keyword(s):  
Latent Variables ◽  
Materials Design ◽  
Information Loss ◽  
Bayesian Optimization ◽  
Generative Adversarial Networks ◽  
Microstructural Characteristics ◽  
Significant Information ◽  
Adversarial Learning ◽  
Design Variables ◽  
Microstructural Design

In Computational Materials Design (CMD), it is well recognized that identifying key microstructure characteristics is crucial for determining material design variables. However, existing microstructure characterization and reconstruction (MCR) techniques have limitations to be applied for materials design. Some MCR approaches are not applicable for material microstructural design because no parameters are available to serve as design variables, while others introduce significant information loss in either microstructure representation and/or dimensionality reduction. In this work, we present a deep adversarial learning methodology that overcomes the limitations of existing MCR techniques. In the proposed methodology, generative adversarial networks (GAN) are trained to learn the mapping between latent variables and microstructures. Thereafter, the low-dimensional latent variables serve as design variables, and a Bayesian optimization framework is applied to obtain microstructures with desired material property. Due to the special design of the network architecture, the proposed methodology is able to identify the latent (design) variables with desired dimensionality, as well as capturing complex material microstructural characteristics. The validity of the proposed methodology is tested numerically on a synthetic microstructure dataset and its effectiveness for materials design is evaluated through a case study of optimizing optical performance for energy absorption. Additional features, such as scalability and transferability, are also demonstrated in this work. In essence, the proposed methodology provides an end-to-end solution for microstructural design, in which GAN reduces information loss and preserves more microstructural characteristics, and the GP-Hedge optimization improves the efficiency of design exploration.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

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