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A Mixed Integer Efficient Global Optimization Algorithm with Multiple Infill Strategy - Applied to a Wing Topology Optimization Problem

With the advancement in high performance computing and numerical optimization techniques,engineering design optimization problems are becoming more complex, larger scale,higher fidelity, and computationally more demanding, requiring longer run times than ever before. There exists methodologies and techniques that can address some of these challenges but very few can address all, and most are limited in the extent that these concerns can be addressed. With the goal of addressing such challenging engineering problems, we developed anew optimization framework, named AMIEGO, that combines concepts from surrogate-based optimization approaches, gradient-based numerical methods, Partial Least Squares, evolutionary algorithms, and Branch-and-Bound, providing newer capabilities that were not previouslyperceived. However, the original version of this framework, in the process of adaptive samplingto explore and exploit the design space, finds only a single sample point per iteration. The efforthere builds upon this previously developed optimization framework to include multiple infillsampling capability that combines the concept of generalized expected improvement function,unsupervised learning, and multi-objective evolutionary technique. To demonstrate, AMIEGOwith the multiple infill capability (called AMIEGO-MIMOS) solves a series of increasingly difficultengineering design optimization problems. The results reveal the performance of the newapproach is problem dependent. When applied to a ten-bar truss problem, the newly proposedmultiple infill strategy consistently leads to a better design solutions when compared to theexisting CPTV method (implemented with the context of the AMIEGO framework). On theother hand, when applied to a mixed-integer high fidelity wing topology optimization problem- MIMOS, despite showing a steeper convergence at the start, eventually leads to an inferiorsolution as compared to CPTV approach. These results also reveal that a small number ofstarting points, in general, are sufficient to lead to a good overall solution.

Mixed-integer optimization↗

Sizing and Layout Design of an Aeroelastic Wingbox Through Nested Optimization

The goals of this work are to 1) develop an optimization algorithm that can simultaneously handle a large number of sizing variables and topological layout variables for an aeroelastic wingbox optimization problem and 2) utilize this algorithm to ascertain the benefits of curvilinear wingbox components. The algorithm used here is a nested optimization, where the outer level optimizes the rib and skin stiffener layouts with a surrogate-based optimizer, and the inner level sizes all of the components via gradient-based optimization. Two optimizations are performed: one restricted to straight rib and stiffener components only, the other allowing curved members. A moderate 1.18% structural mass reduction is obtained through the use of curvilinear members.

Stanford, Bret K.↗

Numerical Investigation and Optimization of a Flushwall Injector for Scramjet Applications at Hypervelocity Flow Conditions

An investigation utilizing Reynolds-averaged simulations (RAS) was performed in order to find optimal designs for an interdigitated flushwall injector suitable for scramjet applications at hypervelocity conditions. The flight Mach number, duct height, spanwise width, and injection angle were the design variables selected to maximize two objective functions: the thrust potential and combustion efficiency. A Latin hypercube sampling design-of-experiments method was used to select design points for RAS. A methodology was developed that automated building geometries and generating grids for each design. The ensuing RAS analysis generated the performance database from which the two objective functions of interest were computed using a one-dimensional performance utility. The data were fitted using four surrogate models: an artificial neural network (ANN) model, a cubic polynomial, a quadratic polynomial, and a Kriging model. Variance-based decomposition showed that both objective functions were primarily driven by changes in the duct height. Multiobjective design optimization was performed for all four surrogate models via a genetic algorithm method. Optimal solutions were obtained at the upper and lower bounds of the flight Mach number range. The Kriging model obtained an optimal solution set that predicted high values for both objective functions. Additionally, three challenge points were selected to assess the designs on the Pareto fronts. Further sampling among the designs of the Pareto fronts are required in order to lower the errors and perform more accurate surrogate-based optimization. sed optimization.

Shenoy, Rajiv R.↗

Surrogate-based Analysis and Optimization

A major challenge to the successful full-scale development of modem aerospace systems is to address competing objectives such as improved performance, reduced costs, and enhanced safety. Accurate, high-fidelity models are typically time consuming and computationally expensive. Furthermore, informed decisions should be made with an understanding of the impact (global sensitivity) of the design variables on the different objectives. In this context, the so-called surrogate-based approach for analysis and optimization can play a very valuable role. The surrogates are constructed using data drawn from high-fidelity models, and provide fast approximations of the objectives and constraints at new design points, thereby making sensitivity and optimization studies feasible. This paper provides a comprehensive discussion of the fundamental issues that arise in surrogate-based analysis and optimization (SBAO), highlighting concepts, methods, techniques, as well as practical implications. The issues addressed include the selection of the loss function and regularization criteria for constructing the surrogates, design of experiments, surrogate selection and construction, sensitivity analysis, convergence, and optimization. The multi-objective optimal design of a liquid rocket injector is presented to highlight the state of the art and to help guide future efforts.

Queipo, Nestor V.↗

Optimal Reference Strain Structure for Studying Dynamic Responses of Flexible Rockets

In the proposed paper, the optimal design of reference strain structures (RSS) will be performed targeting for the accurate observation of the dynamic bending and torsion deformation of a flexible rocket. It will provide the detailed description of the finite-element (FE) model of a notional flexible rocket created in MSC.Patran. The RSS will be attached longitudinally along the side of the rocket and to track the deformation of the thin-walled structure under external loads. An integrated surrogate-based multi-objective optimization approach will be developed to find the optimal design of the RSS using the FE model. The Kriging method will be used to construct the surrogate model. For the data sampling and the performance evaluation, static/transient analyses will be performed with MSC.Natran/Patran. The multi-objective optimization will be solved with NSGA-II to minimize the difference between the strains of the launch vehicle and RSS. Finally, the performance of the optimal RSS will be evaluated by checking its strain-tracking capability in different numerical simulations of the flexible rocket.

finite-element (FE)↗

Computer-Simulation Surrogates for Optimization: Application to Trapezoidal Ducts and Axisymmetric Bodies

Engineering design and optimization efforts using computational systems rapidly become resource intensive. The goal of the surrogate-based approach is to perform a complete optimization with limited resources. In this paper we present a Bayesian-validated approach that informs the designer as to how well the surrogate performs; in particular, our surrogate framework provides precise (albeit probabilistic) bounds on the errors incurred in the surrogate-for-simulation substitution. The theory and algorithms of our computer{simulation surrogate framework are first described. The utility of the framework is then demonstrated through two illustrative examples: maximization of the flowrate of fully developed ow in trapezoidal ducts; and design of an axisymmetric body that achieves a target Stokes drag.

Otto, John C.↗