Some Further Results for a Reduction Method in Nonhierarchical Optimization-Based Design

1992 ◽  
Author(s):  
Bi-Chu Wu ◽  
Shapour Azarm
Keyword(s):  
Optimality Conditions ◽  
Reduction Method ◽  
Numerical Test ◽  
Verification And Validation ◽  
Previous Article ◽  
Test Problems ◽  
Engineering Systems ◽  
Test Results ◽  
Simple Reduction ◽  
Optimization Based Design

Abstract In a previous article, a new and simple reduction method was presented for optimization-based design of nonhierarchically decomposed engineering systems. As a sequel to that work, in this paper we first examine some significant issues in relation to the reduction method: the optimality conditions when the method is applied, the reason why move limits are not required, and some of the factors that might affect the robustness of the cumulative constraints. For verification and validation, we then present some numerical test results in which the method is applied to twenty-one (21) test problems. Based on the test results reported, some guidelines for applying the method are suggested.

scholarly journals The Direct Simulation of Third Order Linear Problems on Single Step Block Method

2021 ◽  
pp. 1-12
Author(s):  
J. Sabo ◽  
Y. Skwame ◽  
T. Y. Kyagya ◽  
J. A. Kwanamu
Keyword(s):  
Reduction Method ◽  
Direct Method ◽  
Numerical Test ◽  
Single Step ◽  
Test Problems ◽  
Direct Simulation ◽  
Block Method ◽  
Third Order ◽  
Order Linear ◽  
Linear Problems

In this article, the direct simulation of third order linear problems on single step block method has been proposed. In order to overcoming the setbacks in reduction method, direct method has been proposed using power series to reduce computational burden that occur in the reduction method. Numerical properties for the block method are established and the method developed is consistent, convergent and zero-stable. To validate the accuracy of the block method, certain numerical test problems were considered, the results shown that the accuracy of our method are more accurate over the existing method in literature.

Chemical equilibrium systems as numerical test problems

1990 ◽  
Vol 16 (2) ◽  
pp. 143-151 ◽  
Author(s):  
Keith Meintjes ◽  
Alexander P. Morgan
Keyword(s):  
Chemical Equilibrium ◽  
Numerical Test ◽  
Test Problems

scholarly journals Construction and investigation of new numerical algorithms for the heat equation : Part 2

2020 ◽  
Vol 10 (4) ◽  
pp. 339-348
Author(s):  
Mahmoud Saleh ◽  
Ádám Nagy ◽  
Endre Kovács
Keyword(s):  
Heat Conduction ◽  
Numerical Methods ◽  
Heat Conduction Equation ◽  
Space Dimension ◽  
Numerical Test ◽  
Numerical Algorithms ◽  
Heat Conducting ◽  
Heat Sources ◽  
Test Results ◽  
New Algorithms

This paper is the second part of a paper-series in which we create and examine new numerical methods for solving the heat conduction equation. Now we present numerical test results of the new algorithms which have been constructed using the known, but non-conventional UPFD and odd-even hopscotch methods in Part 1. Here all studied systems have one space dimension and the physical properties of the heat conducting media are uniform. We also examine different possibilities of treating heat sources.

scholarly journals A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 904 ◽  
Author(s):  
Afshin Babaei ◽  
Hossein Jafari ◽  
S. Banihashemi
Keyword(s):  
Order Of Convergence ◽  
Additive Noise ◽  
Numerical Solutions ◽  
Numerical Test ◽  
Test Problems ◽  
Heat Equations ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Stochastic Heat Equations ◽  
Collocation Approach

A spectral collocation approach is constructed to solve a class of time-fractional stochastic heat equations (TFSHEs) driven by Brownian motion. Stochastic differential equations with additive noise have an important role in explaining some symmetry phenomena such as symmetry breaking in molecular vibrations. Finding the exact solution of such equations is difficult in many cases. Thus, a collocation method based on sixth-kind Chebyshev polynomials (SKCPs) is introduced to assess their numerical solutions. This collocation approach reduces the considered problem to a system of linear algebraic equations. The convergence and error analysis of the suggested scheme are investigated. In the end, numerical results and the order of convergence are evaluated for some numerical test problems to illustrate the efficiency and robustness of the presented method.

Comprehensive Study of Typical Metamodel Methods Applied in Aircraft Multidisciplinary Design Optimization

2011 ◽  
Vol 110-116 ◽  
pp. 3031-3039 ◽  
Author(s):  
Teng Long ◽  
Li Liu
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Least Squares Method ◽  
Numerical Test ◽  
Kriging Model ◽  
Multidisciplinary Design ◽  
Test Problems ◽  
Comparison Results ◽  
Moving Least Squares Method ◽  
Comprehensive Study

—Metamodels have been widely applied in aircraft multidisciplinary design optimization (MDO) to alleviate the computation burden and improve the optimization efficiency. At present, there are various metamodel methods available, such as response surface method, Kriging model, moving least squares method, radial basis function, neural networks and so on. However, it is difficult to confirm which metamodel method is more promising, which is also an interesting question puzzled most designers. In this article, by using a series of numerical test problems with different inherent features, a comprehensive study is employed to compare five typical metamodel methods commonly applied in aircraft MDO under multiple metrics. In term of the comparison results, the conclusions are drawn and recommendations for selecting suitable metamodels in aircraft MDO practice are also summarized.

Nested and Simultaneous Solution Strategies for General Combined Plant and Control Design Problems

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Daniel R. Herber ◽  
James T. Allison
Keyword(s):  
Optimality Conditions ◽  
Design Theory ◽  
Control Design ◽  
System Level ◽  
Test Problems ◽  
Design Problems ◽  
Closed Form Solutions ◽  
Solution Strategies ◽  
Solution Methods ◽  
And Control

In this paper, general combined plant and control design or co-design problems are examined. The previous work in co-design theory imposed restrictions on the type of problems that could be posed. This paper lifts many of those restrictions. The problem formulations and optimality conditions for both the simultaneous and nested solution strategies are given. Due to a number of challenges associated with the optimality conditions, practical solution considerations are discussed with a focus on the motivating reasons for using direct transcription (DT) in co-design. This paper highlights some of the key concepts in general co-design including general coupling, the differences between the feasible regions for each strategy, general boundary conditions, inequality path constraints, system-level objectives, and the complexity of the closed-form solutions. Three co-design test problems are provided. A number of research directions are proposed to further co-design theory including tailored solution methods for reducing total computational expense, better comparisons between the two solution strategies, and more realistic test problems.

Design and Simulation of an Improved Particle Swarm Optimization

2010 ◽  
Vol 20-23 ◽  
pp. 1280-1285
Author(s):  
Jian Xiang Wei ◽  
Yue Hong Sun
Keyword(s):  
Particle Swarm Optimization ◽  
Dimensional Space ◽  
Numerical Test ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Population Diversity ◽  
Test Problems ◽  
Local Optimum ◽  
Swarm Optimization ◽  
Improved Pso

The particle swarm optimization (PSO) algorithm is a new population search strategy, which has exhibited good performance through well-known numerical test problems. However, it is easy to trap into local optimum because the population diversity becomes worse during the evolution. In order to overcome the shortcoming of the PSO, this paper proposes an improved PSO based on the symmetry distribution of the particle space position. From the research of particle movement in high dimensional space, we can see: the more symmetric of the particle distribution, the bigger probability can the algorithm be during converging to the global optimization solution. A novel population diversity function is put forward and an adjustment algorithm is put into the basic PSO. The steps of the proposed algorithm are given in detail. With two typical benchmark functions, the experimental results show the improved PSO has better convergence precision than the basic PSO.

P3GA: An Algorithm for Technology Characterization

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Edgar Galvan ◽  
Richard J. Malak
Keyword(s):  
Design Automation ◽  
Design Space Exploration ◽  
Design Space ◽  
Space Exploration ◽  
Numerical Test ◽  
Pareto Frontier ◽  
Test Problems ◽  
Genetic Optimization ◽  
Technology Evaluation ◽  
Mathematical Basis

It is important for engineers to understand the capabilities and limitations of the technologies they consider for use in their systems. However, communicating this information can be a challenge. Mathematical characterizations of technical capabilities are of interest as a means to reduce ambiguity in communication and to increase opportunities to utilize design automation methods. The parameterized Pareto frontier (PPF) was introduced in prior work as a mathematical basis for modeling technical capabilities. One advantage of PPFs is that, in many cases, engineers can model a system by composing frontiers of its components. This allows for rapid technology evaluation and design space exploration. However, finding the PPF can be difficult. The contribution of this article is a new algorithm for approximating the PPF, called predictive parameterized Pareto genetic algorithm (P3GA). The proposed algorithm uses concepts and methods from multi-objective genetic optimization and machine learning to generate a discrete approximation of the PPF. If needed, designers can generate a continuous approximation of the frontier by generalizing beyond these data. The algorithm is explained, its performance is analyzed on numerical test problems, and its use is demonstrated on an engineering example. The results of the investigation indicate that P3GA may be effective in practice.

A Reshaping Method for Wind Turbine RCS Reduction

2015 ◽  
Vol 764-765 ◽  
pp. 457-461 ◽  
Author(s):  
Shyh Kuang Ueng ◽  
Yao Hong Chan
Keyword(s):  
Wind Turbine ◽  
Cross Section ◽  
Wind Turbines ◽  
Electromagnetic Waves ◽  
Reduction Method ◽  
Radar Cross Section ◽  
Modeling Method ◽  
Test Results ◽  
Wind Turbine Tower

This paper presents a Radar Cross Section (RCS) reduction method for wind turbines. In the proposed method, a reshaping procedure is utilized to generate waves or bumps on the surface of the wind-turbine tower. As the tower is illuminated by electromagnetic waves, the reflected rays are perturbed by the convex structures and the RCS of the wind turbine is decreased. Test results conclude that our modeling method reduces the average RCS values. The scatterings in the directions of the convex structures are significantly declined.

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