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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. Phased Array Ultrasonic Transducers. - PowerPoint PPT Presentation
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Towards the Automated Design of Phased Array Ultrasonic Transducers – Using Particle Swarms to find “Smart” Start Points
Stephen Chen, York UniversitySarah Razzaqi, University of
QueenslandVincent Lupien, Acoustic Ideas
Inc.
June 26, 2007 IEA/AIE 2007
Phased Array Ultrasonic Transducers
A non-mechanical way to direct an energy beam Useful for Non-Destructive Evaluation
June 26, 2007 IEA/AIE 2007
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
June 26, 2007 IEA/AIE 2007
Continuum Probe Designer™ Components
Cost function generator uses exclusive patent-pending technology to design an optimized probe
Continuum Probe Designer™
GUI
Optimization solver
Cost function generator
June 26, 2007 IEA/AIE 2007
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”
June 26, 2007 IEA/AIE 2007
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
June 26, 2007 IEA/AIE 2007
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
June 26, 2007 IEA/AIE 2007
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+λ)-ES
76.2 32.5
70.8 3.9
5 18
June 26, 2007 IEA/AIE 2007
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+λ)-ESFour
parallel
32.5 31.3
3.9 2.9
18 22
June 26, 2007 IEA/AIE 2007
“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
June 26, 2007 IEA/AIE 2007
Analyzing “Smart” Start Points
Is perceived correlation significant? From 120 random start points, apply the (1+λ)-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
June 26, 2007 IEA/AIE 2007
“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%
June 26, 2007 IEA/AIE 2007
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%
June 26, 2007 IEA/AIE 2007
Improve Coarse Search
Generate 50 random points Use best 4 to seed 4 PSOs Design PSOs to favour exploration
over convergence
June 26, 2007 IEA/AIE 2007
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
June 26, 2007 IEA/AIE 2007
Exploiting Global Convexity
Search space is globally convex Seek centre of search space by coordinating individual ESs with crossover
PSOWith
Crossover
29.2 28.5
1.9 1.3
27 30
June 26, 2007 IEA/AIE 2007
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
June 26, 2007 IEA/AIE 2007
Rastrigin function
Globally convex Average value of each “well” is directly related to the quality of the local optima
June 26, 2007 IEA/AIE 2007
Schwefel function
NOT globally convex Average value of each “well” should still be directly related to the quality of the local optima
June 26, 2007 IEA/AIE 2007
Summary
Achieved important level of performance on benchmark test suite for a difficult real-world problem
Demonstrated potential of coarse search-greedy search combinations