Parameterized Design Optimization of a Magnetohydrodynamic Liquid Metal Active Cooling Concept

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Darren J. Hartl ◽  
Edgar Galvan ◽  
Richard J. Malak ◽  
Jeffrey W. Baur
Keyword(s):  
Liquid Metal ◽  
Design Optimization ◽  
Optimization Problems ◽  
Material Design ◽  
Element Model ◽  
Algebraic Model ◽  
Engineering Problem ◽  
Computationally Efficient ◽  
Design Selection ◽  
Computationally Intensive

The success of model-based multifunctional material design efforts relies on the proper development of multiphysical models and advanced optimization algorithms. This paper addresses both in the context of a structure that includes a liquid metal (LM) circuit for integrated cooling. We demonstrate for the first time on a complex engineering problem the use of a parameterized approach to design optimization that solves a family of optimization problems as a function of parameters exogenous to the subsystem of interest. This results in general knowledge about the capabilities of the subsystem rather than a restrictive point solution. We solve this specialized problem using the predictive parameterized Pareto genetic algorithm (P3GA) and show that it efficiently produces results that are accurate and useful for design exploration and reasoning. A “population seeding” approach allows an efficient multifidelity approach that combines a computationally efficient reduced-fidelity algebraic model with a computationally intensive finite-element model. Using data output from P3GA, we explore different design scenarios for the LM thermal management concept and demonstrate how engineers can make a final design selection once the exogenous parameters are resolved.

Application of the Ritz Method to the Optimization of Vibrating Structures

2012 ◽  
Author(s):  
J. Gregory McDaniel ◽  
Andrew S. Wixom
Keyword(s):  
Optimization Problems ◽  
Ritz Method ◽  
Global Optimum ◽  
Vibration Characteristics ◽  
Exhaustive Search ◽  
Computationally Efficient ◽  
Convergence Properties ◽  
Vibrating Structures ◽  
Computationally Intensive ◽  
Made In

This work presents an application of the Ritz Method to the optimization of vibrating structures. The optimization problems considered here involve local design choices made in various regions of the structure in hopes of improving the vibration characteristics of the structure. In order to find the global optimum, one must perform an exhaustive search over all combinations of such choices. Even a modest number of design choices may give rise to a large number of combinations, so that an exhaustive search becomes computationally intensive. In the present work, the Ritz Method is employed to efficiently compute cost functions related to the vibration characteristics of the structure. Since the Ritz Method is based on integral expressions of the potential and kinetic energies of the structure, one may naturally divide these integrals over regions of the structure. In doing so, the concept of substructuring appears naturally in the formulation without explicitly considering boundary conditions between regions. This advantage, combined with the well-known convergence properties of the Ritz Method, provide for a computationally efficient approach for optimization problems. Numerical examples related to the optimization of a vibrating plate illustrate the approach.

Embedded magnetohydrodynamic liquid metal thermal transport: validated analysis and design optimization

2016 ◽  
Vol 28 (7) ◽  
pp. 862-877 ◽  
Author(s):  
Darren J Hartl ◽  
Geoffrey J Frank ◽  
Jeffery W Baur
Keyword(s):  
Finite Element ◽  
Liquid Metal ◽  
Design Optimization ◽  
Transport System ◽  
Thermal Transport ◽  
Algebraic Model ◽  
System Response ◽  
Reduced Order ◽  
Analysis And Design ◽  
Multi Objective

This work addresses the multi-fidelity analysis-driven design of a thermal transport system based on the flow of liquid metal through a structural laminate as induced by a solid-state magneto-hydro-dynamic (MHD) pump. A full three-dimensional model of the thermal transport system is both simplified to a reduced-order algebraic model, which correctly captures trends in the global system response, and alternatively implemented in an finite element framework, which captures essential global and local aspects of the system response not attainable via reduced-order modeling. The predictions of each model are validated against previously published experimental data. It is shown in detail for the first time in the context of MHD systems that a multi-fidelity approach to the multi-objective design optimization problem can leverage both the speed of the algebraic model and the accuracy of the finite element model, leading to effective predictions of optimal system designs in a reasonable amount of time. A relatively new algorithm for multi-objective and parameterized Pareto optimization is employed, and a clear path of continued development is identified.

scholarly journals A Sequential Linearization Approach for Solving Mixed-Discrete Nonlinear Design Optimization Problems

1991 ◽  
Vol 113 (3) ◽  
pp. 325-334 ◽  
Author(s):  
Han Tong Loh ◽  
P. Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Continuous Variables ◽  
New Approach ◽  
Design Variables ◽  
Nonlinear Design ◽  
Discrete Problems ◽  
Computationally Intensive ◽  
Discrete Values ◽  
Sequential Linearization

Design optimization models of often contain variables that must take only discrete values, such as standard sizes. Nonlinear optimization problems with a mixture of discrete and continuous variables are very difficult, and existing algorithms are either computationally intensive or applicable to models with special structure. A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables. It involves solving a sequence of mixed-discrete linear approximations of the original nonlinear model. In this article, a review of previous approaches is followed by description of the resulting algorithm, its convergence properties and limitations. Several illustrative examples are given. A sequel article presents a detailed algorithmic implementation and extensive computational results.

scholarly journals A Sequential Linearization Approach for Solving Mixed-Discrete Nonlinear Design Optimization Problems

1990 ◽  
Author(s):  
Han Tong Loh ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Continuous Variables ◽  
New Approach ◽  
Design Variables ◽  
Nonlinear Design ◽  
Discrete Problems ◽  
Computationally Intensive ◽  
Discrete Values ◽  
Sequential Linearization

Abstract Design optimization models often contain variables that must take only discrete values, such as standard sizes. Nonlinear optimization problems with a mixture of discrete and continuous variables are very difficult, and existing algorithms are either computationally intensive or applicable to models with special structure. A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables. It involves solving a sequence of mixed-discrete linear approximations of the original nonlinear model. In this article, a review of previous approaches is followed by description of the resulting algorithm, its convergence properties and limitations. Several illustrative examples are given. A sequel article presents a detailed algorithmic implementation and extensive computational results.

A Comprehensive Investigation of Ensembles of Gaussian-Based and Gradient-Based Transformed Reliability Analyses: When and How to Use Them

2016 ◽  
Author(s):  
Po Ting Lin ◽  
Wei-Hao Lu ◽  
Shu-Ping Lin
Keyword(s):  
Design Optimization ◽  
Design Space ◽  
Optimization Problems ◽  
Nonlinear Problems ◽  
Kernel Functions ◽  
Sensitivity Analyses ◽  
Normal Space ◽  
Highly Nonlinear ◽  
Standard Normal ◽  
Gradient Based

In the past few years, researchers have begun to investigate the existence of arbitrary uncertainties in the design optimization problems. Most traditional reliability-based design optimization (RBDO) methods transform the design space to the standard normal space for reliability analysis but may not work well when the random variables are arbitrarily distributed. It is because that the transformation to the standard normal space cannot be determined or the distribution type is unknown. The methods of Ensemble of Gaussian-based Reliability Analyses (EoGRA) and Ensemble of Gradient-based Transformed Reliability Analyses (EGTRA) have been developed to estimate the joint probability density function using the ensemble of kernel functions. EoGRA performs a series of Gaussian-based kernel reliability analyses and merged them together to compute the reliability of the design point. EGTRA transforms the design space to the single-variate design space toward the constraint gradient, where the kernel reliability analyses become much less costly. In this paper, a series of comprehensive investigations were performed to study the similarities and differences between EoGRA and EGTRA. The results showed that EGTRA performs accurate and effective reliability analyses for both linear and nonlinear problems. When the constraints are highly nonlinear, EGTRA may have little problem but still can be effective in terms of starting from deterministic optimal points. On the other hands, the sensitivity analyses of EoGRA may be ineffective when the random distribution is completely inside the feasible space or infeasible space. However, EoGRA can find acceptable design points when starting from deterministic optimal points. Moreover, EoGRA is capable of delivering estimated failure probability of each constraint during the optimization processes, which may be convenient for some applications.

scholarly journals A computationally efficient hybrid 2D–3D subwoofer model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ahmad H. Bokhari ◽  
Martin Berggren ◽  
Daniel Noreland ◽  
Eddie Wadbro
Keyword(s):  
Hybrid Model ◽  
3D Model ◽  
Element Model ◽  
Acoustic Properties ◽  
Computational Time ◽  
Average Response ◽  
Frequency Range ◽  
Computationally Efficient ◽  
Lumped Element ◽  
Lumped Element Model

AbstractA subwoofer generates the lowest frequency range in loudspeaker systems. Subwoofers are used in audio systems for live concerts, movie theatres, home theatres, gaming consoles, cars, etc. During the last decades, numerical simulations have emerged as a cost- and time-efficient complement to traditional experiments in the design process of different products. The aim of this study is to reduce the computational time of simulating the average response for a given subwoofer design. To this end, we propose a hybrid 2D–3D model that reduces the computational time significantly compared to a full 3D model. The hybrid model describes the interaction between different subwoofer components as interacting modules whose acoustic properties can partly be pre-computed. This allows us to efficiently compute the performance of different subwoofer design layouts. The results of the hybrid model are validated against both a lumped element model and a full 3D model over a frequency band of interest. The hybrid model is found to be both accurate and computationally efficient.

Study on Mix-Variable Collaborative Design Optimization

2012 ◽  
Vol 215-216 ◽  
pp. 592-596
Author(s):  
Li Gao ◽  
Rong Rong Wang
Keyword(s):  
Design Optimization ◽  
Product Design ◽  
Optimization Algorithm ◽  
Collaborative Design ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Collaborative Optimization ◽  
Continuous Variables ◽  
Complex Product ◽  
Divide And Rule

In order to deal with complex product design optimization problems with both discrete and continuous variables, mix-variable collaborative design optimization algorithm is put forward based on collaborative optimization, which is an efficient way to solve mix-variable design optimization problems. On the rule of “divide and rule”, the algorithm decouples the problem into some relatively simple subsystems. Then by using collaborative mechanism, the optimal solution is obtained. Finally, the result of a case shows the feasibility and effectiveness of the new algorithm.

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