Development of a Changeable Airfoil Optimization Model for Use in the Multidisciplinary Design of Unmanned Aerial Vehicles

2009 ◽  
Author(s):  
Scott Ferguson ◽  
Andrew H. Tilstra ◽  
Carolyn C. Seepersad ◽  
Kristin L. Wood
Keyword(s):  
Optimization Problem ◽  
Design Research ◽  
Optimization Problems ◽  
Mathematical Optimization ◽  
Operating Conditions ◽  
Multidisciplinary Optimization ◽  
System Level ◽  
Airfoil Optimization ◽  
Design Variables ◽  
Subsystem Design

Complex systems need to perform in a variety of functional states and under varying operating conditions. Therefore, it is important to manage the different values of design variables associated with the operating states for each subsystem. The research presented in this paper uses multidisciplinary optimization (MDO) and changeable systems methods together in the design of a reconfigurable Unmanned Aerial Vehicle (UAV). MDO is a useful approach for designing a system that is composed of distinct disciplinary subsystems by managing the design variable coupling between the subsystem and system level optimization problems. Changeable design research addresses how changes in the physical configuration of products and systems can better meet distinct needs of different operating states. As a step towards the development of a realistic reconfigurable UAV optimization problem, this paper focuses on the performance advantage of using a changeable airfoil subsystem. Design principles from transformational design methods are used to develop concepts that determine how the design variables are allowed to change in the mathematical optimization problem. The performance of two changeable airfoil concepts is compared to a fixed airfoil design over two different missions that are defined by a sequence of mission segments. Determining the configurations of the static and changeable airfoils is accomplished using a genetic algorithm. Results from this study show that aircraft with changeable airfoils attain increased performance, and that the manner by which the system transforms is significant. For this reason, the changeable airfoil optimization developed in this paper is ready to be integrated into a complete MDO problem for the design of a reconfigurable UAV.

Multidisciplinary collaborative optimization based on relaxation method for solving complex problems

2020 ◽  
Vol 28 (4) ◽  
pp. 280-289
Author(s):  
Hamda Chagraoui ◽  
Mohamed Soula
Keyword(s):  
Optimization Problems ◽  
Inequality Constraints ◽  
Relaxation Method ◽  
Multidisciplinary Optimization ◽  
Collaborative Optimization ◽  
System Level ◽  
Dynamic Relaxation ◽  
Dynamic Relaxation Method ◽  
Feasible Solutions ◽  
The Impact

The purpose of the present work is to improve the performance of the standard collaborative optimization (CO) approach based on an existing dynamic relaxation method. This approach may be weakened by starting design points. First, a New Relaxation (NR) method is proposed to solve the difficulties in convergence and low accuracy of CO. The new method is based on the existing dynamic relaxation method and it is achieved by changing the system-level consistency equality constraints into relaxation inequality constraints. Then, a Modified Collaborative Optimization (MCO) approach is proposed to eliminate the impact of the information inconsistency between the system-level and the discipline-level on the feasibility of optimal solutions. In the MCO approach, the impact of the inconsistency is treated by transforming the discipline-level constrained optimization problems into an unconstrained optimization problem using an exact penalty function. Based on the NR method, the performance of the MCO approach carried out by solving two multidisciplinary optimization problems. The obtained results show that the MCO approach has improved the convergence of CO significantly. These results prove that the present MCO succeeds in getting feasible solutions while the CO fails to provide feasible solutions with the used starting design points.

COLLABORATIVE OPTIMIZATION WITH DIMENSION REDUCTION

2010 ◽  
Vol 01 (02) ◽  
pp. 179-198 ◽  
Author(s):  
ZHENXIAO GAO ◽  
TIANYUAN XIAO ◽  
WENHUI FAN
Keyword(s):  
Dimension Reduction ◽  
Multidisciplinary Design Optimization ◽  
Optimization Problem ◽  
Convergence Property ◽  
Extreme Points ◽  
Optimization Methods ◽  
Collaborative Optimization ◽  
System Level ◽  
Design Variables ◽  
Feasible Domain

Collaborative optimization (CO) method is widely used in solving multidisciplinary design optimization (MDO) problems, yet its computation requirement has been an obstacle to the applications, leading to doubts about CO's convergence property. The feasible domain of CO problem is first examined and it is proven that feasible domain remains the same during the CO formulation. So is the same with extreme points. Then based on contemporary research conclusion that the system-level optimization problem suffers from inherent computational difficulties, it is further pointed out that the employment of meta-heuristic optimization methods in CO could eliminate these difficulties. To make CO more computational feasible, a new method collaborative optimization with dimension reduction (CODR) is proposed. It focused on optimization dimension reduction and lets local copy of common shared design variables equal system shared design variables directly. Thus, the number of dimensions that CODR could reduce equal the number of common shared design variables. Numerical experiment suggests that CODR reduces computations greatly without losing of optimization accuracy.

scholarly journals Interaction Prediction Optimization in Multidisciplinary Design Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Debiao Meng ◽  
Xiaoling Zhang ◽  
Hong-Zhong Huang ◽  
Zhonglai Wang ◽  
Huanwei Xu
Keyword(s):  
Interaction Design ◽  
Large Scale ◽  
Optimization Problems ◽  
Collaborative Optimization ◽  
System Level ◽  
Design Parameters ◽  
Large Scale Systems ◽  
Interaction Prediction ◽  
Design Variables ◽  
Subsystem Level

The distributed strategy of Collaborative Optimization (CO) is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM), is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO) method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables) are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO.

scholarly journals Nonconvex and game theory optimization for resource allocation in wireless communications

2021 ◽  
Author(s):  
Kandasamy Illanko
Keyword(s):  
Wireless Communication ◽  
Power Allocation ◽  
Communication Systems ◽  
Optimization Problem ◽  
Polynomial Complexity ◽  
Optimization Problems ◽  
Stackelberg Game ◽  
Mathematical Optimization ◽  
Simultaneous Optimization ◽  
Theoretical Development

Designing wireless communication systems that efficiently utilize the resources frequency spectrum and electric power, leads to problems in mathematical optimization. Most of these optimization problems are difficult to solve because the objective functions are nonconvex. While some problems remain unsolved, the solutions proposed in the literature for the others are of somewhat limited use because the algorithms are either unstable or have too high a computational complexity. This dissertation presents several stable algorithms, most of which have polynomial complexity, that solve five different nonconvex optimization problems in wireless communication. Two centralized and two distributed algorithms deal with the power allocation that maximizes the throughput in the Gaussian interference channel (GIC)with various constraints. The most valuable of these algorithms, the one with the minimum rate constraints became possible after a significant theoretical development in the dissertation that proves that the throughput of the GIC has a new generalized convex structure called invexity. The fifth algorithm has linear complexity, and finds the power allocation that maximizes the energy efficiency (EE) of OFDMA transmissions, for a given subchannel assignment. Some fundamental results regarding the power allocation are then used in the genetic algorithm for determining the subchannel allocation that maximizes the EE. Pricing for channel subleasing for ad-hoc wireless networks is considered next. This involves the simultaneous optimization of many functions that are interconnected through the variables involved. A composite game, a strategic game within a Stackelberg game, is used to solve this optimization problem with polynomial complexity. For each optimization problem solved, numerical results obtained using simulations that support the analysis and demonstrate the performance of the algorithms are presented.

Parametric Optimization for Structural Design Problems

2019 ◽  
Author(s):  
Krupakaran Ravichandran ◽  
Nafiseh Masoudi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Structural Design ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Nonlinear Constraint ◽  
Computational Performance ◽  
Design Variables ◽  
Input Parameters ◽  
Parametric Optimization Problem ◽  
Objective Function Values

Abstract Parametric Optimization is used to solve problems that have certain design variables as implicit functions of some independent input parameters. The optimal solutions and optimal objective function values are provided as functions of the input parameters for the entire parameter space of interest. Since exact solutions are available merely for parametric optimization problems that are linear or convex-quadratic, general non-convex non-linear problems require approximations. In the present work, we apply three parametric optimization algorithms to solve a case study of a benchmark structural design problem. The algorithms first approximate the nonlinear constraint(s) and then solve the optimization problem. The accuracy of their results and their computational performance are then compared to identify a suitable algorithm for structural design applications. Using the identified method, sizing optimization of a truss structure for varying load conditions such as a varying load direction is considered and solved as a parametric optimization problem to evaluate the performance of the identified algorithm. The results are also compared with non-parametric optimization to assess the accuracy of the solution and computational performance of the two methods.

Multilevel Hierarchical Decomposition: Identification Procedures for Edge of Design Space Feasibility

2006 ◽  
Author(s):  
Somanath Nagendra ◽  
Jeff Midgley ◽  
Joseph B. Staubach
Keyword(s):  
High Performance ◽  
Design Space ◽  
Optimization Problems ◽  
Functional Dependence ◽  
Minimum Weight ◽  
Design Feature ◽  
Turbine Disk ◽  
System Level ◽  
Optimum Shape ◽  
Design Variables

In high performance machines, multiple active MDO constraints dictate the edge of feasibility, i.e. boundary of the design space. It is essential to have an accurate description of the boundary in terms of design variables. Given a sample of data, the recognition of a design feature (e.g. design shape) is not usually familiar to the design domain experts but must be extracted based on data-driven procedures. The “edge of feasibility” could be evaluated as a continuous or piece wise continuous function of active constraints. In this work, the focus is on a class of quasiseparable optimization problems. The subsystems for these problems involve local design shape variables and global system variables, but no variables from other subsystems. The system in this particular case is the engine component (i.e. HPT) and the subsystem is the turbine disk. The system is hierarchically decomposed to the system and subsystem components respectively. The HPT flowpath and its defined thermodynamic and geometric parameters define the system. The subsystem is the HPT turbine disk and its associated geometric shape variables. A system level DOE determines the design space of the HPT system. The optimized subsystem turbine disk is the solution to the DOE of the system and feasible disk designs are the shapes that can withstand the design loads and stresses. The focus of the paper is to develop a methodology that would systematically utilize minimum weight optimum shape designs across the design space and predict new designs close to being optimal in performance for a specified range of design conditions. The shape of minimum weight disks are identified as a solution of a system of inverse response surface equations that can determine disk shapes with good confidence. The methodology is developed using synthetic turbine disk problems with known regions of feasibility and infeasibility. The edge of feasibility is determined and the functional dependence on the design variables estimated.

A Two Level Parallel Evolution Strategy for Solving Mixed-Discrete Structural Optimization Problems

1995 ◽  
Author(s):  
Georg Thierauf ◽  
Jianbo Cai
Keyword(s):  
Parallel Computing ◽  
Structural Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Parallel Evolution ◽  
Evolution Strategy ◽  
Parallel Computer ◽  
Computing Architecture ◽  
Design Variables

Abstract A method for the solution of mixed-discrete structural optimization problems based on a two level parallel evolution strategy is presented. On the first level, the optimization problem is divided into two subproblems with discrete and continuous design variables, respectively. The two subproblems are solved simultaneously on a parallel computing architecture. On the second level, each subproblem is further parallelized by means of a parallel sub-evolution-strategy. Periodically, the design variables in the two groups axe exchanged. Examples are included to demonstrate the implementation of this method on a 8 nodes parallel computer.

scholarly journals Gradient Span Analysis Method: Application to the Multipoint Aerodynamic Shape Optimization of a Turbine Cascade

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Hadrien Montanelli ◽  
Marc Montagnac ◽  
François Gallard
Keyword(s):  
Cost Function ◽  
Optimization Problem ◽  
Stokes Equations ◽  
Single Point ◽  
Operating Conditions ◽  
Design Variables ◽  
Wide Range ◽  
The Cost ◽  
Multipoint Optimization ◽  
Utopia Point

This paper presents the application of the gradient span analysis (GSA) method to the multipoint optimization of the two-dimensional LS89 turbine distributor. The cost function (total pressure loss) and the constraint (mass flow rate) are computed from the resolution of the Reynolds-averaged Navier–Stokes equations. The penalty method is used to replace the constrained optimization problem with an unconstrained problem. The optimization process is steered by a gradient-based quasi-Newton algorithm. The gradient of the cost function with respect to design variables is obtained with the discrete adjoint method, which ensures an efficient computation time independent of the number of design variables. The GSA method gives a minimal set of operating conditions to insert into the weighted sum model to solve the multipoint optimization problem. The weights associated to these conditions are computed with the utopia point method. The single-point optimization at the nominal condition and the multipoint optimization over a wide range of conditions of the LS89 blade are compared. The comparison shows the strong advantages of the multipoint optimization with the GSA method and utopia-point weighting over the traditional single-point optimization.

scholarly journals Harris Hawks Optimization for Optimum Design of Truss Structures with Discrete Variables

2021 ◽  
Vol 6 (4) ◽  
pp. 1157-1173
Author(s):  
Mustafa Al-Bazoon
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Population Based ◽  
Truss Structures ◽  
Discrete Variables ◽  
Structural Problems ◽  
Collaborative Behavior ◽  
Design Variables ◽  
Predatory Birds ◽  
The Mathematical Model

This article investigates the use of Harris Hawks Optimization (HHO) to solve planar and spatial trusses with design variables that are discrete. The original HHO has been used to solve continuous design variables problems. However, HHO is formulated to solve optimization problems with discrete variables in this research. HHO is a population-based metaheuristic algorithm that simulates the chasing style and the collaborative behavior of predatory birds Harris hawks. The mathematical model of HHO uses a straightforward formulation and does not require tuning of algorithmic parameters and it is a robust algorithm in exploitation. The performance of HHO is evaluated using five benchmark structural problems and the final designs are compared with ten state-of-the-art algorithms. The statistical outcomes (average and standard deviation of final designs) show that HHO is quite consistent and robust in solving truss structure optimization problems. This is an important characteristic that leads to better confidence in the final solution from a single run of the algorithm for an optimization problem.

An Embedded Multi-Phase Tactic of Scheduling Autoimmunization for Complex Correlated Production System

2010 ◽  
Vol 439-440 ◽  
pp. 505-509 ◽  
Author(s):  
Ya Bo Luo ◽  
Ming Chun Tang
Keyword(s):  
Optimization Problem ◽  
Job Shop ◽  
Optimization Problems ◽  
Scheduling System ◽  
Design Variables ◽  
Complex Optimization ◽  
Feasible Solutions ◽  
Optimum Solution ◽  
Multi Phase ◽  
Machine Allocation

The schedule for job shop system involving the complex correlated constraints is a complex combinatorial optimization problem, for which currently there is no a methodology claiming to have capability to find the optimum solution. Current research concentrate on the search of acceptable feasible solutions. This research proposes an embedded multi-phase methodology to find the acceptable feasible solutions in a higher efficiency. The thinking of the methodology is to decompose the complex optimization problem into two sub problems of the operation sequence and the machine allocation to lower the complexity of the scheduling system and improve the searching efficiency. The two sub problems are solved orderly respectively, and the results of the first sub problem are embedded into the second sub problem as the original values of design variables. Thus these two sub optimization problems are integrated into a searching loop to ensure the feasibility of solution and improve the searching efficiency in the complex correlated system.

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