Multi-objective particle swarm optimization of a modified Bernstein polynomial for curved phased array synthesis using Bézier curves, surfaces, and volumes

Open Access
Boeringer, Daniel Wilharm
Graduate Program:
Electrical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
July 01, 2004
Committee Members:
  • Douglas Henry Werner, Committee Chair
  • Kultegin Aydin, Committee Member
  • Anthony J Ferraro, Committee Member
  • Pingjuan Li Werner, Committee Member
  • David Carl Swanson, Committee Member
  • Bernstein polynomial
  • particle swarm
  • optimization
  • multi-objective
  • phased array
  • Bézier
This dissertation develops the multi-objective particle swarm optimization of a modified Bernstein polynomial for curved phased array synthesis. Chapter 1 states the goals of the dissertation, discusses the background and current state of the art, and outlines the original contributions. Chapter 2 defines the far field patterns and the aperture efficiency of a curved array, and develops performance criteria for sidelobe level and main beam quality. Chapter 2 also introduces the novel modified Bernstein polynomial, which provides a new way to specify a variety of smooth, realizable, and unimodal array amplitude distributions using just five parameters. On curved arrays, the modified Bernstein polynomial outperforms Taylor weights. Chapter 3 introduces particle swarm optimization, a relatively new method of evolutionary optimization only recently applied to electromagnetics. A method is shown where the particle swarm optimizer constrains the aperture efficiency to a specified value while finding the array distribution providing the best sidelobe and main beam performance. This optimization is extremely efficient because the optimizer need only determine five parameters. Chapter 4 combines the independent sidelobe optimization outcomes for various aperture efficiencies to implement e-constraint multi-objective optimization, providing the modified Bernstein polynomial parameters for the best sidelobe performance as a function of aperture efficiency. Either the optimized parameters or the resulting weights can be interpolated to provide smooth transitions between optimized distributions and generate intermediate solutions. A convenient way to represent the array weights as a function of aperture efficiency is with a Bézier surface. This is a new approach, both for phased array synthesis and multi-objective optimization in general. Chapter 5 extends this approach to two independent variables, optimizing the best sidelobe performance for a given aperture efficiency and scan angle. In this case the optimized array weights as a function of aperture efficiency and scan angle can be represented with a Bézier volume. Chapter 6 adds the dimension of array curvature and Chapter 7 adds the variable of element spacing. Chapter 7 also illustrates the various trends and interactions among these four independent parameters. Finally, Chapter 8 gives some conclusions and ideas for future work.