Solution of ordinary differential equations in gradient-based multidisciplinary design optimization

2018 ◽  
Author(s):  
John T. Hwang ◽  
Drayton Munster
Keyword(s):  
Differential Equations ◽  
Design Optimization ◽  
Ordinary Differential Equations ◽  
Multidisciplinary Design Optimization ◽  
Multidisciplinary Design ◽  
Gradient Based

Multidisciplinary Design Optimization of a Naval Surface Combatant

2003 ◽  
Vol 47 (01) ◽  
pp. 1-12 ◽  
Author(s):  
Daniele Peri ◽  
Emilio F. Campana
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Optimization Methods ◽  
Ship Design ◽  
Multidisciplinary Design ◽  
Construction Costs ◽  
Gradient Based ◽  
Numerical Tools ◽  
Surface Combatant ◽  
Hydrodynamic Optimization

Whereas shape optimal design has received considerable attention in many industrial contexts, the application of automatic optimization procedures to hydrodynamic ship design has not yet reached the same maturity. Nevertheless, numerical tools, combining together modern computational fluid dynamics and optimization methods, can aid in the ship design, enhancing the operational performances and reducing development and construction costs. This paper represents an attempt of applying a multidisciplinary design optimization (MDO) procedure to the enhancement of the performances of an existing ship. At the present stage the work involves modeling, development, and implementation of algorithms only for the hydrodynamic optimization. For a naval surface combatant, the David Taylor Model Basin (DTMB) model ship 5415, a three-objective functions optimization for a two-discipline design problem is devised and solved in the framework of the MDO approach. A simple decision maker is used to order the Pareto optimal solutions, and a gradient-based refinement is performed on the selected design.

Reliability-Based Multidisciplinary Design Optimization Using Probabilistic Gradient-Based Transformation Method

2012 ◽  
Vol 135 (2) ◽  
Author(s):  
Po Ting Lin ◽  
Hae Chang Gea
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Transformation Method ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Multidisciplinary Design ◽  
Sensitivity Analyses ◽  
Chance Constrained Programming ◽  
Complex Design ◽  
Gradient Based

Recently, solving the complex design optimization problems with design uncertainties has become an important but very challenging task in the communities of reliability-based design optimization (RBDO) and multidisciplinary design optimization (MDO). The MDO algorithms decompose the complex design problem into the hierarchical or nonhierarchical optimization structure and distribute the workloads to each discipline (or subproblem) in the decomposed structure. The coordination of the local responses is crucial for the success of finding the optimal design point. The problem complexity increases dramatically when the existence of the design uncertainties is not negligible. The RBDO algorithms perform the reliability analyses to evaluate the probabilities that the random variables violate the constraints. However, the required reliability analyses build up the degree of complexity. In this paper, the gradient-based transformation method (GTM) is utilized to reduce the complexity of the MDO problems by transforming the design space to multiple single-variate monotonic coordinates along the directions of the constraint gradients. The subsystem responses are found using the monotonicity principles (MP) and then coordinated for the new design points based on two general principles. To consider the design uncertainties, the probabilistic gradient-based transformation method (PGTM) is proposed to adapt the first-order probabilistic constraints from three different RBDO algorithms, including the chance constrained programming (CCP), reliability index approach (RIA), and performance measure approach (PMA), to the framework of the GTM. PGTM is efficient because only the sensitivity analyses and the reliability analyses require function evaluations (FE). The optimization processes of monotonicity analyses and the coordination procedures are free of function evaluations. Several mathematical and engineering examples show the PGTM is capable of finding the optimal solutions with desirable reliability levels.

Optimization Algorithms and ODE’s in MDO

2013 ◽  
Author(s):  
C. Bakker ◽  
G. T. Parks ◽  
J. P. Jarrett
Keyword(s):  
Differential Geometry ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Multidisciplinary Design Optimization ◽  
Optimization Algorithms ◽  
Optimization Methods ◽  
Multidisciplinary Design ◽  
Theoretical Understanding ◽  
Solution Methods ◽  
Systems Of Odes

There is a need for a stronger theoretical understanding of Multidisciplinary Design Optimization (MDO) within the field. Having developed a differential geometry framework in response to this need, we consider how standard optimization algorithms can be modeled using systems of ordinary differential equations (ODEs) while also reviewing optimization algorithms which have been derived from ODE solution methods. We then use some of the framework’s tools to show how our resultant systems of ODEs can be analyzed and their behaviour quantitatively evaluated. In doing so, we demonstrate the power and scope of our differential geometry framework, we provide new tools for analyzing MDO systems and their behaviour, and we suggest hitherto neglected optimization methods which may prove particularly useful within the MDO context.

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