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Effectiveness and Efficiency of Particle Swarm Optimization Technique in Inverse Heat Conduction Analysis   ,[object Object],[object Object],[object Object],[object Object],[object Object]
Inverse Problems ,[object Object],Background   >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
Inverse Heat Transfer Problem Finding Surface Values from Readings of Thermocouples Inside the Plate Background   >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
Classical Approach ,[object Object],[object Object],Background  >   Classical Methods   >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion [ See:  “ Inverse Heat Conduction: Ill-Posed Problems”; By Beck, et al.]
Objective Function ,[object Object],T direct solution Obtained Using Direct Solution  with Assumed Boundary Conditions T experiment Experimentally Obtained Solution N Number of Data Points Background  >   Classical Methods   >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
Our Problems with Classical Approach ,[object Object],[object Object],[object Object],[object Object],If you don’t experience these problems: Stick  to the classical approaches Background  >   Classical Methods   >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion If you experience these problems: You may want to try stochastic methods, such as  Particle Swarm
Particle Swarm Optimization (PSO) ,[object Object],[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >   Particle Swarm Optimization   >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
Basic Particle Swarm Optimization  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >   Particle Swarm Optimization   >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
Update Equations i ’s best performance x i p g p i v i overall  best performance Background  >  Classical Methods  >   Particle Swarm Optimization   >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
Some Variations of the PSO ,[object Object],[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >   Particle Swarm Optimization   >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
Test Case I: 1D Transient Problem without regularization with regularization Background  >  Classical Methods  >  Particle Swarm Optimization  >   Test Cases and Results   >  Efficiency  >  Effectiveness  >  Conclusion
Test Case II: 2D Problem Axisymmetric around the left side Similar to a thermocouple hole inside a plate Top surface is subjected to a heat flux similar to those happening in real cooling of hot steel Background  >  Classical Methods  >  Particle Swarm Optimization  >   Test Cases and Results   >  Efficiency  >  Effectiveness  >  Conclusion
Classical Approach & Large Time Step Background  >  Classical Methods  >  Particle Swarm Optimization  >   Test Cases and Results   >  Efficiency  >  Effectiveness  >  Conclusion
Classical Approach & Small Time Step Background  >  Classical Methods  >  Particle Swarm Optimization  >   Test Cases and Results   >  Efficiency  >  Effectiveness  >  Conclusion
PSO Is Stable for Small Time Steps Background  >  Classical Methods  >  Particle Swarm Optimization  >   Test Cases and Results   >  Efficiency  >  Effectiveness  >  Conclusion
Comparing the Efficiency ,[object Object],[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >   Efficiency   >  Effectiveness  >  Conclusion
t  – Test Results critical  t -value = 1.73   If  t -value > 1.73, Method 2 performs better than Method 1 in at least 95% of cases GA : Genetic Algorithm Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >   Efficiency   >  Effectiveness  >  Conclusion CRPSO RPSO 6 CRPSO PSO 5 RPSO PSO 4 CRPSO GA 3 RPSO GA 2 PSO GA 1 Method 2 Method 1 Test # 7.75 3.45 3.04 Test 6 7.92 7.59 4.63 Test 5 1.27 3.32 1.49 Test 4 13.41 17.76 10.78 Test 3 9.41 12.52 6.60 Test 2 8.26 10.08 4.88 Test 1 Test Case 3 Test Case 2 Test Case 1
Observations ,[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >   Efficiency   >  Effectiveness  >  Conclusion
Effectiveness in Handling Noisy Data ,[object Object],[object Object],r  : normally distributed random variable with zero mean and unit standard deviation  σ  is the standard deviation  Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Effect of Self-Confidence Parameter (1) Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Effect of Self-Confidence Parameter (1) Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Effect of Self-Confidence Parameter (2) Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Effect of Self-Confidence Parameter (3) Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Advantages of PSO ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >   Conclusion
Disadvantages of PSO ,[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >   Conclusion
Future Works ,[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >   Conclusion
[object Object]
Future Works ,[object Object],[object Object],[object Object],[object Object],Background  >  Inverse Problem  >  Particle Swarm Optimization  >  Results  >  Conclusion  >   Future Work
What do we get from our experiments? Background   >  Inverse Problem  >  Particle Swarm Optimization  >  Results  >  Conclusion  >  Future Work
Motivations for Controlled Cooling ,[object Object],[object Object],Background   >  Inverse Problem  >  Particle Swarm Optimization  >  Results  >  Conclusion  >  Future Work
Motivations for Controlled Cooling ,[object Object],Controlled Cooling Background   >  Inverse Problem  >  Particle Swarm Optimization  >  Results  >  Conclusion  >  Future Work
Improved Objective Function Regularization Penalizing nonphysical oscillations in the results Background  >   Inverse Problem   >  Particle Swarm Optimization  >  Results  >  Conclusion  >  Future Work q i  : Heat Flux Component
World Crude Steel Production Background   >  Inverse Problem  >  Particle Swarm Optimization  >  Results  >  Conclusion  >  Future Work "World Steel in Figures, 2007", http://www.worldsteel.org/
Experimental Setup at UBC Background   >  Inverse Problem  >  Particle Swarm Optimization  >  Results  >  Conclusion  >  Future Work
Test Case I: 1D Problem
Speedup 1.22 19611.40 1.36 9938.90 1.22 4155.40 CRPSO 1.15 20872.30 1.27 10658.60 1.15 4426.70 RPSO 1.13 21118.70 1.19 11382.10 1.11 4582.40 PSO 1.00 23903.10 1.00 13498.90 1.00 5074.70 GA Speedup Cost Speedup Cost Speedup Cost Test Case 3 Test Case 2 Test Case 1
Motivations for Controlled Cooling ,[object Object],[object Object],[object Object],Background   >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
Measurement Errors Background   >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
What to Expect? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Background   >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >  Conclusion
Statistical  t –  Test A significance level of  5%, and a 10+10-2=18 degrees of freedom  a critical  t­ -value of 1.73 Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >   Efficiency   >  Effectiveness  >  Conclusion
Effect of the Regularization Parameter (1) Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Effect of the Regularization Parameter (2) Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Effect of the Regularization Parameter (3) Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Effect of Using PSO Variants Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Key Points To Remember ,[object Object],[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >   Conclusion
PSO Is Stable for Small Time Steps Background  >  Classical Methods  >  Particle Swarm Optimization  >   Test Cases and Results   >  Efficiency  >  Effectiveness  >  Conclusion
Test Case III: 3D Steady Problem Background  >  Classical Methods  >  Particle Swarm Optimization  >   Test Cases and Results   >  Efficiency  >  Effectiveness  >  Conclusion
3D Results ,[object Object],[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >   Test Cases and Results   >  Efficiency  >  Effectiveness  >  Conclusion
Effect of the Regularization Parameter (4) ,[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
Effect of Self-Confidence Parameter (4) ,[object Object],[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >   Effectiveness   >  Conclusion
PSO Variants ,[object Object],[object Object],[object Object],[object Object],Background  >  Classical Methods  >  Particle Swarm Optimization  >  Test Cases and Results  >  Efficiency  >  Effectiveness  >   Conclusion
What Is an Inverse Problem? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Inverse Problems   >  Particle Swarm Optimization  >  Test  Cases  >  Performance Studies  >  Conclusion  >  Future Work

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Effectiveness and Efficiency of Particle Swarm Optimization Technique in Inverse Heat Conduction Analysis

  • 1.
  • 2.
  • 3. Inverse Heat Transfer Problem Finding Surface Values from Readings of Thermocouples Inside the Plate Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9. Update Equations i ’s best performance x i p g p i v i overall best performance Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 10.
  • 11. Test Case I: 1D Transient Problem without regularization with regularization Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 12. Test Case II: 2D Problem Axisymmetric around the left side Similar to a thermocouple hole inside a plate Top surface is subjected to a heat flux similar to those happening in real cooling of hot steel Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 13. Classical Approach & Large Time Step Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 14. Classical Approach & Small Time Step Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 15. PSO Is Stable for Small Time Steps Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 16.
  • 17. t – Test Results critical t -value = 1.73 If t -value > 1.73, Method 2 performs better than Method 1 in at least 95% of cases GA : Genetic Algorithm Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion CRPSO RPSO 6 CRPSO PSO 5 RPSO PSO 4 CRPSO GA 3 RPSO GA 2 PSO GA 1 Method 2 Method 1 Test # 7.75 3.45 3.04 Test 6 7.92 7.59 4.63 Test 5 1.27 3.32 1.49 Test 4 13.41 17.76 10.78 Test 3 9.41 12.52 6.60 Test 2 8.26 10.08 4.88 Test 1 Test Case 3 Test Case 2 Test Case 1
  • 18.
  • 19.
  • 20. Effect of Self-Confidence Parameter (1) Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 21. Effect of Self-Confidence Parameter (1) Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 22. Effect of Self-Confidence Parameter (2) Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 23. Effect of Self-Confidence Parameter (3) Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 24.
  • 25.
  • 26.
  • 27.
  • 28.
  • 29. What do we get from our experiments? Background > Inverse Problem > Particle Swarm Optimization > Results > Conclusion > Future Work
  • 30.
  • 31.
  • 32. Improved Objective Function Regularization Penalizing nonphysical oscillations in the results Background > Inverse Problem > Particle Swarm Optimization > Results > Conclusion > Future Work q i : Heat Flux Component
  • 33. World Crude Steel Production Background > Inverse Problem > Particle Swarm Optimization > Results > Conclusion > Future Work "World Steel in Figures, 2007", http://www.worldsteel.org/
  • 34. Experimental Setup at UBC Background > Inverse Problem > Particle Swarm Optimization > Results > Conclusion > Future Work
  • 35. Test Case I: 1D Problem
  • 36. Speedup 1.22 19611.40 1.36 9938.90 1.22 4155.40 CRPSO 1.15 20872.30 1.27 10658.60 1.15 4426.70 RPSO 1.13 21118.70 1.19 11382.10 1.11 4582.40 PSO 1.00 23903.10 1.00 13498.90 1.00 5074.70 GA Speedup Cost Speedup Cost Speedup Cost Test Case 3 Test Case 2 Test Case 1
  • 37.
  • 38. Measurement Errors Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 39.
  • 40. Statistical t – Test A significance level of 5%, and a 10+10-2=18 degrees of freedom a critical t­ -value of 1.73 Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 41. Effect of the Regularization Parameter (1) Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 42. Effect of the Regularization Parameter (2) Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 43. Effect of the Regularization Parameter (3) Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 44. Effect of Using PSO Variants Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 45.
  • 46. PSO Is Stable for Small Time Steps Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 47. Test Case III: 3D Steady Problem Background > Classical Methods > Particle Swarm Optimization > Test Cases and Results > Efficiency > Effectiveness > Conclusion
  • 48.
  • 49.
  • 50.
  • 51.
  • 52.

Editor's Notes

  1. James Kennedy (social psychologist) / Eberhart: Professor of Electrical and Computer Engineering / Survival
  2. Performance w/ GA
  3. Make these two one!
  4. Maybe skip this one
  5. Performance w/ GA