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Stephen Chen, York University Sarah Razzaqi, University of Queensland

Towards the Automated Design of Phased Array Ultrasonic Transducers – Using Particle Swarms to find “Smart” Start Points. Stephen Chen, York University Sarah Razzaqi, University of Queensland Vincent Lupien, Acoustic Ideas Inc. Phased Array Ultrasonic Transducers.

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Stephen Chen, York University Sarah Razzaqi, University of Queensland

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  1. Towards the Automated Design of Phased Array Ultrasonic Transducers – Using Particle Swarms to find “Smart” Start Points Stephen Chen, York University Sarah Razzaqi, University of Queensland Vincent Lupien, Acoustic Ideas Inc.

  2. Phased Array Ultrasonic Transducers • A non-mechanical way to direct an energy beam • Useful for Non-Destructive Evaluation IEA/AIE 2007

  3. Continuum Probe Designer™ • Product of Acoustic Ideas Inc. • Automated design tool that creates an optimized probe for a given inspection task • Removes “art” of design IEA/AIE 2007

  4. Continuum Probe Designer™ Components • Cost function generator uses exclusive patent-pending technology to design an optimized probe IEA/AIE 2007

  5. Optimization Solver • The optimized probe is developed for a given probe geometry • Finding the best probe geometry is another optimization task • In this paper, the probe designer is treated as a “cost function generator” IEA/AIE 2007

  6. Optimization Objective • Probe costs are directly related to the number of elements used in a design • Existing instrumentation can only control 32 independent channels at a time IEA/AIE 2007

  7. An Evolution Strategy for the Optimization Solver (CEC2006) • Standard (1+λ)-ES with λ = 3 • Performs significantly better than gradient descent (i.e. fmincon) • Note: fmincon takes about an hour and uses about 300 evaluations IEA/AIE 2007

  8. Evolution Strategy vs. fmincon • Tested on one expert selected and 29 random start points • ES results are much better and more consistent • ES results are still not good enough IEA/AIE 2007

  9. Independent Parallel Runs • High standard deviation suggests that using multiple runs will lead to easy improvements • Results are better, but still not good enough IEA/AIE 2007

  10. “Smart” Start Points • High correlation between ES solution and quality of random start point • Use random search to find “smart” points • Better results again IEA/AIE 2007

  11. Analyzing “Smart” Start Points • Is perceived correlation significant? • From 120 random start points, apply the (1+λ)-ES to the 30 worst and best IEA/AIE 2007

  12. “Smart” Start Points on the TSP • Is correlation an obvious/trivial observation? • Correlation does not exist on TSP IEA/AIE 2007

  13. Coarse Search does not Help on TSP • Coarse search for better starting points does not improve the performance of two-opt on the TSP IEA/AIE 2007

  14. Improve Coarse Search • Generate 50 random points • Use best 4 to seed 4 PSOs • Design PSOs to favour exploration over convergence IEA/AIE 2007

  15. PSO vs. Random Searchto find “Smart” Start Points • PSO finds even better start points • Improved “smart” start points lead to an even better performance IEA/AIE 2007

  16. Exploiting Global Convexity • Search space is globally convex • Seek centre of search space by coordinating individual ESs with crossover IEA/AIE 2007

  17. Current Work • Exploring Coarse Search – Greedy Search • Inspired by WoSP (CEC2005) • Different from memetic algorithms (which apply greedy search to every search point) • Useful for expensive evaluations • Useful for non-globally convex search spaces IEA/AIE 2007

  18. Rastrigin function • Globally convex • Average value of each “well” is directly related to the quality of the local optima IEA/AIE 2007

  19. Schwefel function • NOT globally convex • Average value of each “well” should still be directly related to the quality of the local optima IEA/AIE 2007

  20. Summary • Achieved important level of performance on benchmark test suite for a difficult real-world problem • Demonstrated potential of coarse search-greedy search combinations IEA/AIE 2007

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