Ben Grocholsky Doctor of Philosophy The University of Sydney March 2002 Information-Theoretic Control of This thesis is concerned with the development of a consistent, information-theoretic basis for understanding of coordination and cooperation decentralised multi-sensor multi-platform systems. Autonomous systems composed of multiple sensors and multiple platforms potentially have significant importance in applications such as defence, search and rescue, mining or intelligent manufacturing. However, the e#ective use of multiple autonomous systems requires that an understanding be developed of the mechanisms of coordination and cooperation between component systems in pursuit of a common goal. A fundamental, quantitative, understanding of coordination and cooperation between decentralised autonomous systems is the main goal of this thesis.

Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for large-scale distributed analysis applications. In this approach, a complex problem is hierarchically decomposed along disciplinary boundaries into a number of subproblems which are brought into multidisciplinary agreement by a system-level coordination process. When applied to problems in a multidisciplinary design environment, this scheme has several advantages over traditional solution strategies. These advantageous features include reducing the amount of information transferred between disciplines, the removal of large iteration-loops, allowing the use of different subspace optimizers among the various analysis groups, an analysis framework which is easily parallelized and can operate on heterogenous equipment, and a structural framework that is well-suited for conventional disciplinary organizations. In this article, the collaborative architectu...

The dimensionality and complexity of typical multidisciplinary systems hinders the use of formal optimization techniques in application to this class of problems. The use of approximations to represent the system design metrics and constraints has become vital for achieving good performance in many multidisciplinary design optimization (MDO) algorithms. This paper reports resent research efforts on the use of variable fidelity response surface approximations (RSA) to drive the convergence of MDO problems using a trust region model management algorithm. The present study focuses on a comparative study of different response sampling strategies based on design of experiment (DOE) approaches within the disciplines to generate the zero order data to build the RSAs. Two MDO test problems that have complex coupling between disciplines are used to benchmark the performance of each sampling strategy. The results show that these types of variable fidelity RSAs can be eectively managed by the trust region model management strategy to drive convergence of MDO problems. It is observed that the efficiency of the optimization algorithm depends on the sampling strategy used. A comparison of the DOE approaches with those obtained using a optimization based sampling strategy (i.e., concurrent subspace optimization - CSSO) show the DOE methodologies to be competitive with the CSSO based sampling methodology in some cases. However, the CSSO based sampling strategy was found to be...

The use of Response Surface Approximation (RSA) within an approximate optimization framework for the design of complex systems has increased as designers are challenged to develop better designs in reduced times. Traditionally, statistical sampling techniques (i. e., experimental design) have been used for constructing RSA's. These statistical sampling techniques are designed to be space filling, so that the response surface approximations are predictive across the range of the design sample space. When used in sequential approximate optimization strategies, a portion of the samples can be in the infeasible and/or ascent regions of the design space. These samples can bias the resulting RSA and make it less predictive in the usable feasible region where the optimization takes place. In the response surface based concurrent subsace optimization approach the design sampling strategy for RSA construction is optimization based. This optimization based sampling has proved to be effective due to the fact it samples in the linearized usable feasible region. In the present research, an experimental design strategy for projecting data points in the linearized usable feasible region is developed for constructing RSA's. The technique is implemented in a Sequential Approximate Optimization framework and tested in application to two multidisciplinary design optimization (MDO) test problems. Results show that the proposed technique pro-

Decomposition of large engineering system models is desirable since increased model size reduces reliability and speed of numerical solution algorithms. The article presents a methodology for optimal model-based decomposition (OMBD) of design problems, whether or not initially cast as optimization problems. The overall model is represented by a hypergraph and is optimally partitioned into weakly connected subgraphs that satisfy decomposition constraints. Spectral graph-partitioning methods together with iterative improvement techniques are proposed for hypergraph partitioning. A known spectral K-partitioning formulation, which accounts for partition sizes and edge weights, is extended to graphs with also vertex weights. The OMBD formulation is robust enough to account for computational demands and resources and strength of interdependencies between the computational modules contained in the model. KEYWORDS: Model decomposition, multidisciplinary design, hypergraph partitioning, larges...

Sequential Approximate Optimization (SAO) is a class of methods available for the multidisciplinary design optimization (MDO) of complex systems that are composed of several disciplines coupled together. One of the approaches used for SAO, is based on a quadratic response surface approximation, where zero and first order information are required. In these methods, designers must generate and query a database of order O(n²) in order to compute the second order terms of the quadratic response surface approximation. As the number of design variables grows, the computational cost of generating the required database becomes a concern. In this paper, we present an new approach in which we require just O(n) parameters for constructing a second order approximation. This is accomplished by transforming the matrix of second order terms into the canonical form. The method periodically requires an order O(n²) update of the second order approximation to maintain accuracy. Results show

The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of reproducible experiments. In the first phase of the study, three MDO methods were implemented in the iSIGHT z framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, preliminary numbers suggest that the performance of the methods tends to be consistent with their predicted theoretical properties. Key Words: Multidisciplinary Design Optimization, Method Evaluation AMS Subject Classification: 65K05, 49M37 Introduction Multidisciplinary Design Optimization (MDO) problems are optimization problems that desc...

The analysis of engineering systems must often be conducted using complex, non-hierarchic, coupled, discipline-specific methods. When the cost of performing these individual analyses is high, it is impractical to apply many current optimization methods to this type of system to achieve improved designs. Consequently, methods are being developed which attempt to reduce the cost of designing or optimizing non-hierarchic systems. This paper details the application of an extension of the Concurrent Subspace Optimization (CSSO) approach through the use of neural network based response surface mappings. The response surface mappings are used to allow the discipline designer to account for discipline coupling and the impact of design decisions on the system at the discipline level as well as for system level design coordination. The ability of this method to identify globally optimal designs is discussed using two example system design problems. Comparisons between this algorithm and full sys...

Design engineers often employ numerical optimization techniques to assist in the evaluation and comparison of new aircraft configurations. While the use of numerical optimization methods is largely successful, the presence of numerical noise in realistic engineering optimization problems often inhibits the use of many gradient-based optimization techniques. Numerical noise causes inaccurate gradient calculations which in turn slows or prevents convergence during optimization. The problems created by numerical noise are particularly acute in aircraft design applications where a single aerodynamic or structural analysis of a realistic aircraft configuration may require tens of CPU hours on a supercomputer. The computational expense of the analyses coupled with the convergence difficulties created by numerical noise are significant obstacles to performing aircraft multidisciplinary design optimization. To address these issues, a procedure has been developed to create two types of noise-free mathematical models for use in aircraft optimization studies. These two methods use elements of statistical analysis and the overall procedure for using the methods is made computationally affordable by the application of parallel computing techniques. The first

A multidisciplinary design optimization framework suitable for application to mixed continuous/discrete systems has been developed. This framework, called Concurrent Subspace Design, employs artificial neural networks to provide response surface approximations. A concise metric indicating how accurately a neural network is able to approximate the design space was defined and used to assess different networks, which were obtained by varying the amount of data considered in their construction and the means by which discrete design variables are represented in them. Results demonstrate that this framework is able to locate optimal designs and that its computational requirements are related to some degree to the database used in formulating the neural network approximations.