01.11.2010  Industrial Application  Ausgabe 5/2010 Open Access
Optimization of forging processes using Finite Element simulations
A comparison of Sequential Approximate Optimization and other algorithms
 Zeitschrift:
 Structural and Multidisciplinary Optimization > Ausgabe 5/2010
1 Introduction
2 Sequential Approximate Optimization algorithm
2.1 Modelling
2.2 Design Of Experiments (DOE)
2.3 Running the FEM simulations and fitting the metamodels

linear

linear + interaction

pure quadratic or elliptic

(full) quadratic

Kriging with a zeroth order trend function

Kriging with a first order trend function

Kriging with a second order trend function
2.4 Metamodel validation, optimization and accuracy evaluation
2.5 Sequential improvement

adding new DOE points in a spacefilling way (SAOSF),

adding new DOE points by Minimising a Merit Function (SAOMMF),

adding new DOE points by Maximising Expected Improvement (SAOMEI).
2.6 Other algorithms
3 A comparison between the optimization algorithms by application to forging
3.1 Spindle
N_{opt}/N_{tot}  μ_{1} (mm)  μ_{2} (mm)  μ_{3} (mm)  Φ_{fold}
 OK?  

Initial  –  0  0  0  10.49  No 
BFGS  3/12  7.02  2.92  6.55  10.25  No 
SCPIP  10/10  −4.25  −6.01  −3.07  9.17  Yes 
MAES  30/48  −7.26  −3.84  −10  8.35  Yes 
SAOSF  36/50  −1.69  −5.95  8.33  9.20  No 
SAOMMF  38/48  −10  −6.50  −9.82  8.06  Yes 
SAOMEI  22/50  −8.52  −6.40  −10  7.97  Yes 
3.2 Gear
N_{opt}/N_{tot}  μ_{1} (mm)  μ_{2} (mm)  μ_{3} (mm)  Φ_{ene}
 Φ_{fold}
 Φ_{tot}
 

Initial  –  44.60  21.65  32.33  100%  100%  1.19 
BFGS  3/7  40.91  18.00  30.11  N/A  N/A  1.157 
SCPIP  3/21  45.80  19.80  30.00  N/A  N/A  1.123 
MAES  42/49  45.67  18.36  30.25  −9.7%  −7.6%  1.079 
SAOSF  51/51  45.25  18.00  30.58  −8.7%  −6.6%  1.091 
SAOMMF  31/49  45.25  18.18  30.65  −8.2%  −9.8%  1.076 
SAOMEI  49/54  45.35  18.00  30.41  −9.4%  −9.8%  1.068 