Towards the Automated Design of Phased Array Ultrasonic Transducers

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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.

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Phased Array Ultrasonic Transducers

• A non-mechanical way to direct an energy beam
• Useful for Non-Destructive Evaluation

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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

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Continuum Probe Designer Components

• Cost function generator uses exclusive
  patent-pending technology to design an optimized
  probe

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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

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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

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An Evolution Strategy for the Optimization Solver
(CEC2006)

• Standard (1?)-ES with ? 3
• Performs significantly better than gradient
  descent (i.e. fmincon)
• Note fmincon takes about an hour and uses about
  300 evaluations

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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

fmincon (1?)-ES
76.2 32.5
70.8 3.9
5 18
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Independent Parallel Runs

• High standard deviation suggests that using
  multiple runs will lead to easy improvements
• Results are better, but still not good enough

(1?)-ES Four parallel
32.5 31.3
3.9 2.9
18 22
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Smart Start Points

• High correlation between ES solution and quality
  of random start point
• Use random search to find smart points
• Better results again

Four parallel Smart start pts
31.3 30.1
2.9 3.2
22 25
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Analyzing Smart Start Points

• Is perceived correlation significant?
• From 120 random start points, apply the (1?)-ES
  to the 30 worst and best

30 Worst 30 Best 30 Worst 30 Best
770.5 121.5 34.1 31.7
87.1 66.3 5.7 3.1
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Smart Start Points on the TSP

• Is correlation an obvious/trivial observation?
• Correlation does not exist on TSP

30 Worst 30 Best 30 Worst 30 Best
1230 1128 11 11
18 16 1.3 2.4
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Coarse Search does not Help on TSP

• Coarse search for better starting points does
  not improve the performance of two-opt on the TSP

Four parallel Smart start pts
9.2 8.8
1.1 1.4
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Improve Coarse Search

• Generate 50 random points
• Use best 4 to seed 4 PSOs
• Design PSOs to favour exploration over convergence

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PSO vs. Random Searchto find Smart Start Points

• PSO finds even better start points
• Improved smart start points lead to an even
  better performance

Random search PSO
30.1 29.2
3.2 1.9
25 27
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Exploiting Global Convexity

• Search space is globally convex
• Seek centre of search space by coordinating
  individual ESs with crossover

PSO With Crossover
29.2 28.5
1.9 1.3
27 30
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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

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Rastrigin function

• Globally convex
• Average value of each well is directly related
  to the quality of the local optima

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Schwefel function

• NOT globally convex
• Average value of each well should still be
  directly related to the quality of the local
  optima

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Summary

• Achieved important level of performance on
  benchmark test suite for a difficult real-world
  problem
• Demonstrated potential of coarse search-greedy
  search combinations