Hierarchical procedures for distributed design of engineering systems

Satish Radhakrishnan, Purdue University


In this thesis, a hierarchical procedure termed "Distributed design" is developed for the design of complex physical systems in a distributed manner. The distributed design procedure is based on physical decomposition of the system as against the functional decomposition of the system (used in concurrent engineering, multidisciplinary optimization and collaborative design) that currently exists in the literature. A system representation technique based on binary tree used in Constructive Solid Geometry (CSG) is developed for the distributed design procedure. The CSG representation is extended to model the assembly of sub-systems through operators that represent kinematic constraints. System decomposition procedures based on graph partitioning are applied to identify the sub-systems based on functional or physical hierarchy. Three example problems are consistently used to demonstrate techniques developed in this thesis. The example problems are: a three-bar truss, a ten-bar truss and a "real-life" fiber-optic system. Design techniques to improve the system performance in the presence of variable uncertainty are developed. A novel min-max robust design formulation is developed to minimize the solution sensitivity to system performance. The developed procedure does not rely on linearized function form and is therefore more general than techniques proposed in the literature. Monte Carlo Simulation, First Order Second Moment and Second Order Second Moment techniques are applied to study uncertainty in system performance. A novel distributed design procedure that addresses the issues of data security, feasibility and design variability is developed. A formal theory is proposed, that a system level function can be partitioned and mapped onto the sub-systems if the behavior field can be analogously partitioned. The partitioning procedure allows evaluation of the system functions locally enabling distributed design. The local evaluation of system functions is the means by which data security and feasibility are ensured. Further, a local sensitivity analysis procedure based on the partitioned functions is developed. The sensitivity procedure enables one to study effects of sub-system design changes or uncertainty on system performance. Formal procedures for representing the system and formal theory to ensure encapsulation of "local" design data do not appear to have been studied heretofore in the literature.




Subbarayan, Purdue University.

Subject Area

Mechanical engineering

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