Christina Bloebaum

NON-HIERARCHIC SYSTEM DECOMPOSITION IN STRUCTURAL OPTIMIZATION

Decomposition methods provide a systematic approach for decoupling large engineering systems into smaller, coupled subsystems identified by disciplines or by engineering tasks. The paper develops a general decomposition approach for multidisciplinary optimization that is applicable for non-hierarchic systems in which a distinct system hierarchy is difficult to identify. The approach is implemented in a structural synthesis problem for verification purposes. The optimal design of a ten-bar truss for minimum weight subject to displacement and stress constraints is considered. Subsystems are defined in terms of sizing and space variables. The approach allows for implementation of specialized methods for analysis in each subsystem and the ability to incorporate human intervention and decision making. Results demonstrate that the Concurrent Subspace Optimization approach is a versatile method that potentially offers exceptional computational as well as data management advantages.

Ordering design tasks based on coupling strengths

The design process associated with large engineering systems requires an initial decomposition of the complex system into modules of design tasks which are coupled through the transference of output data. In analyzing or optimizing such a coupled system, it is essential to be able to determine which interactions figure prominently enough to significantly affect the accuracy of the system solution. Many decomposition approaches assume the capability is available to determine what design tasks and interactions exist and what order of execution will be imposed during the analysis process. Unfortunately, this is often a complex problem and beyond the capabilities of a human design manager. A new feature for DeMAID (Design Managers Aid for Intelligent Decomposition) will allow the design manager to use coupling strength information to find a proper sequence for ordering the design tasks. In addition, these coupling strengths aid in deciding if certain tasks or couplings could be removed (or temporarily suspended) from consideration to achieve computational savings without a significant loss of system accuracy. New rules are presented and two small test cases are used to show the effects of using coupling strengths in this manner.

Sensitivity of control-augmented structure obtained by a system decomposition method

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beams dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The methods principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

Application of global sensitivity equations in multidisciplinary aircraft synthesis

The present paper investigates the applicability of the Global Sensitivity Equation (GSE) method in the multidisciplinary synthesis of aeronautical vehicles. The GSE method provides an efficient approach for representing a large coupled system by smaller subsystems and accounts for the subsystem interactions by means of first-order behavior sensitivities. This approach was applied in an aircraft synthesis problem with performance constraints stemming from the disciplines of structures, aerodynamics, and flight mechanics. Approximation methods were considered in an attempt to reduce problem dimensionality and to improve the efficiency of the optimization process. The influence of efficient constraint representations, the choice of design variables, and design variable scaling on the conditioning of the system matrix was also investigated. 10 refs.

A genetic tool for optimal design sequencing in complex engineering systems

Methods in multidisciplinary design optimization rely on computer tools to manage the large amounts of information involved. One such tool is DeMAID (DEsign Managers Aide for Intelligent Decomposition), which incorporates planning and scheduling functions to analyse the effect of the information coupling between design tasks in complex systems on the efficiency of the design process. Scheduling involves the formation of circuits of interdependent design tasks, and the minimization of feedbacks within these circuits. Recently there has been interest in the incorporation of other considerations in the sequencing of tasks within circuits. This study presents the program Gendes (GENetic DEsign Sequencer), a sequencing tool based on a genetic algorithm. The program currently has the capability to minimize feedbacks as well as crossovers (intersections in the flow of design information which obscure straightforward evaluation), and allows the potential for other considerations in the sequencing function.This paper presents the development of this tool and the methods used. The results of computational studies to determine the most effective settings of the genetic algorithm for the task sequencing problem are presented, including population size, objective function weighting for the tradeoff between feedbacks and crossovers, mutation rate, and choice of selection operator and fitness function form. The incorporation of Gendes into the DeMAID scheduling function is explored, and the method is applied to two test systems to show its feasibility.

Coupling strength-based system reduction for complex engineering design

The design process associated with large engineering systems requires an initial decomposition of the complex system into subsystem modules which are coupled through transference of output data. The implementation of such a decomposition approach assumes that the ability exists to determine what subsystems and interactions exist and what order of execution will be imposed during the analysis process. Unfortunately, this is quite often an extremely complex task which may be beyond human ability to efficiently achieve. Further, in optimizing such a coupled system, it is essential to be able to determine which interactions figure prominently enough to significantly affect the accuracy of the optimal solution. The ability to determine “weak” versus “strong” coupling strengths would aid the designer in deciding which couplings could be permanently removed from consideration or which could be temporarily suspended so as to achieve computational savings with minimal loss in solution accuracy. An approach that uses normalized sensitivities to quantify coupling strengths is presented. The approach is applied to a coupled system composed of analytical equations for verification purposes.

Multi-objective pareto concurrent subspace optimization for multidisciplinary design

Most real-world design problems are complex and multidisciplinary, with almost always more than one objective (cost) function to be extremized simultaneously. The primary goal of this research is to develop a framework to enable multi-objective optimization of multidisciplinary design applications, wherein each discipline is able to retain substantial autonomous control during the process. To achieve this end, we have extended the capability of the concurrent subspace optimization method to handle multi-objective optimization problems in a multidisciplinary design optimization context Although the conventional concurrent subspace optimization approach is easily able to deal with multi-objective optimization problems by applying the weighted sum approach, the main disadvantage is that the weighted sum cannot capture Pareto points on any nonconvex part of the Pareto frontier. Moreover, an aggregate objective function simply cannot reflect the true spirit of the concurrent subspace optimization method, which was developed to allow groups of specialists to independently have more control over their own design criteria and goals, even while maintaining system level coordination. In this paper, the multi-objective Pareto concurrent subspace optimization method is proposed in which each discipline has substantial control over its own objective function during the design process, while still ensuring responsibility for constraint satisfaction in coupled subspaces. The proposed approach is particularly useful given the realities of geographical distribution, computational platform variation, and dependence upon legacy codes within individual disciplines that so predominates the design of large-scale products such as aircraft and automobiles. As part of the multi-objective Pareto concurrent subspace optimization method developed here, it is demonstrated that the endpoints of the Pareto frontier can be easily identified, together with an ability to generate Pareto points within prescribed limits to ensure a reasonably even distribution across the entire frontier. The approach is validated (using three multidisciplinary design optimization test problems) against Pareto frontiers generated using the weighted sum approach.

Integrating a Genetic Algorithm Into a Knowledge-Based System for Ordering Complex Design Processes

The design cycle associated with large engineering systems requires an initial decomposition of the complex system into design processes which are coupled through the transference of output data. Some of these design processes may be grouped into iterative subcycles. In analyzing or optimizing such a coupled system, it is essential to be able to determine the best ordering of the processes within these subcycles to reduce design cycle time and cost. Many decomposition approaches assume the capability is available to determine what design processes and couplings exist and what order of execution will be imposed during the design cycle. Unfortunately, this is often a complex problem and beyond the capabilities of a human design manager. A new feature, a genetic algorithm, has been added to DeMAID (Design Manager’s Aid for Intelligent Decomposition) to allow the design manager to rapidly examine many different combinations of ordering processes in an iterative subcycle and to optimize the ordering based on cost, time, and iteration requirements. Two sample test cases are presented to show the effects of optimizing the ordering with a genetic algorithm.

Development of multiple cycle coupling suspension in the optimization of complex systems

Abstract.The design of complex engineering systems requires an initial decomposition of the system into subsystems. These systems are linked together by couplings, which represent output data transference from one subsystem to another. Because complex engineering systems can have hundreds or thousands of such couplings, the optimization of these systems is often quite difficult, if not impossible. To reduce the optimization time, it becomes important that a system designer have the ability to select couplings that have little effect on the solution accuracy, and temporarily remove them. Previous coupling strength analysis methods have not related the effect of a coupling’s removal for multiple cycles to solution accuracy. The method presented here identifies weak couplings based on their relationship to the objective function and constraints in the overall system optimization problem. The couplings are then suspended for multiple cycles of the multidisciplinary design optimization process. Discussion of the application of this new method follows, as well as implementation on a decomposed analytical problem. The method significantly reduces the number of subsystem analyses required to optimize the decomposed problem by suspending couplings for multiple design cycles. As a result of the system reduction, considerable computational saving are made without introducing significant error into the results of the optimization. The trade-offs between computational savings and solution accuracy are also shown and discussed.

Intuitive Design Selection using Visualized n-Dimensional Pareto Frontier

A visualization methodology is presented in which a Pareto Frontier can be visualized in an intuitive and straightforward manner for an n-dimensional performance space. An approach for preference incorporation is presented that enables a designer to quickly identify ‘good’ points and regions of the performance spaces for a multi-objective optimization application, regardless of space complexity, numbers of objectives, or numbers of Pareto points. Visualizing Pareto solutions for more than three objectives has long been a significant challenge to the multi-objective optimization community. The Hyper-space Diagonal Counting (HSDC) method described here enables the lossless visualization to be implemented to achieve a hyperspace Pareto frontier. In this paper, we demonstrate the incredible power of using the hyperspace Pareto frontier as a visualization tool for design concept selection in a multiobjective optimization environment.