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.

June 26, 2007IEA/AIE 2007 Phased Array Ultrasonic Transducers  A non-mechanical way to direct an energy beam  Useful for Non-Destructive Evaluation

June 26, 2007IEA/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, 2007IEA/AIE 2007 Continuum Probe Designer™ Components  Cost function generator uses exclusive patent- pending technology to design an optimized probe

June 26, 2007IEA/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, 2007IEA/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, 2007IEA/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, 2007IEA/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

June 26, 2007IEA/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)-ES Four parallel

June 26, 2007IEA/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

June 26, 2007IEA/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 Worst30 Best30 Worst30 Best

June 26, 2007IEA/AIE 2007 “Smart” Start Points on the TSP  Is correlation an obvious/trivial observation?  Correlation does not exist on TSP 30 Worst30 Best30 Worst30 Best 1230%1128%11% 18%16%1.3%2.4%

June 26, 2007IEA/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, 2007IEA/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, 2007IEA/AIE 2007 PSO vs. Random Search to find “Smart” Start Points  PSO finds even better start points  Improved “smart” start points lead to an even better performance Random search PSO

June 26, 2007IEA/AIE 2007 Exploiting Global Convexity  Search space is globally convex  Seek centre of search space by coordinating individual ESs with crossover PSO With Crossover

June 26, 2007IEA/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, 2007IEA/AIE 2007 Rastrigin function  Globally convex  Average value of each “well” is directly related to the quality of the local optima

June 26, 2007IEA/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, 2007IEA/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