Optimisation of triple-ring-electrodes on piezoceramic transducers using algorithmic differentiation Benjamin Jurgelucks 1 Leander Claes 2 1 Research group Mathematics and its Applications, Paderborn University 2 Measurement Engineering Group, Paderborn University 7th International Conference on Algorithmic Differentiation Oxford, United Kingdom 15.09.2016 B. Jurgelucks & L. Claes 1 / 23 AD2016
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Optimisation of triple-ring-electrodes onpiezoceramic transducers using algorithmic
differentiation
Benjamin Jurgelucks 1 Leander Claes 2
1Research group Mathematics and its Applications, Paderborn University
2Measurement Engineering Group, Paderborn University
7th International Conference on Algorithmic DifferentiationOxford, United Kingdom
15.09.2016
B. Jurgelucks & L. Claes 1 / 23 AD2016
Outline
Outline
1 Motivation2 Physical model & Sensitivity Evaluation3 Applying ADOL-C to CFS++4 Finite Differences & Algorithmic Differentiation
for Sensitivity Evaluation5 Optimisation6 Conclusion
B. Jurgelucks & L. Claes 2 / 23 AD2016
Motivation
Motivation• Piezoelectric transducers are used as hardware components
(i.e. accelerometer in smartphones), many are ceramic-based• For simulation and development of piezoceramics precise
knowledge about material parameters is indispensable• Correct material parameter data of piezoelectric ceramics can
differ up to 20% from data given by manufacturer• Existing parameter estimation methods may be inaccurate or
expensive
• Idea: formulate parameter estimation problem as inverseproblem with impedance as measurable quantity and solve(Lahmer, 2008)
• Problem: for some parameters sensitivity of impedance withrespect to material parameters is low→ Cannot solve inverse problem→ Increase sensitivity
B. Jurgelucks & L. Claes 3 / 23 AD2016
Motivation
Motivation• Piezoelectric transducers are used as hardware components
(i.e. accelerometer in smartphones), many are ceramic-based• For simulation and development of piezoceramics precise
knowledge about material parameters is indispensable• Correct material parameter data of piezoelectric ceramics can
differ up to 20% from data given by manufacturer• Existing parameter estimation methods may be inaccurate or
expensive• Idea: formulate parameter estimation problem as inverse
problem with impedance as measurable quantity and solve(Lahmer, 2008)
• Problem: for some parameters sensitivity of impedance withrespect to material parameters is low→ Cannot solve inverse problem→ Increase sensitivity
B. Jurgelucks & L. Claes 3 / 23 AD2016
Motivation
• Usually, electrode plates completely covering top and bottom ofpiezoceramic are used to excite the piezoceramic
• Studies have shown that sensitivity with respect to materialparameters can be increased by attaching triple-ring electrodes
• Sensitivity of impedance with respect to parameters of ceramicdepends on (ring) geometry
• Many configurations show low to zero sensitivity• Identify configurations with high sensitivity→ optimisation problem
• Finite differences→ a lot of locally optimal points→ investigate with AD
B. Jurgelucks & L. Claes 4 / 23 AD2016
Motivation
Triple-ring electrodes in real
B. Jurgelucks & L. Claes 5 / 23 AD2016
Applying ADOL-C to CFS++
Coupled Field Simulation in C++http://lse14.e-technik.uni-erlangen.de/forschung/
laufende-projekte/finite-element-loser-cfs/
• Mainly developed at• Vienna University of Technology• Friedrich-Alexander-Universitat Erlangen-Nurnberg• Alpen-Adria-Universitat Klagenfurt
• About 30 developers (many Ph.D. students)• Approx. 750 source files (.cc .hh), 310k lines (230k .cc & 80k .hh)• “Code-accessible” for academic purposes but not quite open source• Heavy use of templating, macros and generally use of object oriented
• Even in non-extremalcases: accuracy ofFD is unclear andcan vary for differentelectrodeconfigurations
• Goal: Eliminate FDfrom the simulationcompletely bysubstituting AD forFD
B. Jurgelucks & L. Claes 15 / 23 AD2016
Optimisation with AD
OptimisationFD optimisation using commercial tool (more details in Kulshreshthaet. al, 2015):Use derivative-free optimisation method LINCOA (Powell 2014)
• Extension to Powell’s trust-region optimiser BOBYQA• Incorporates linear constraints
Final optimisation problem:
min~r∈R4
J(~r) s.t. A~r ≤ b
with
J(~r) :=1
‖WS∇z(~r)‖2 [now J(~r) := −‖WS∇z(~r)‖2 ]
with diagonal matrices S, W ∈ R10×10 for scaling and adding weight toparameters.
B. Jurgelucks & L. Claes 16 / 23 AD2016
Results
Initial configurationsUse barely feasable configurations as initial points:
−5 0 5−2
0
2
−5 0 5−2
0
2
−5 0 5−2
0
2
B. Jurgelucks & L. Claes 17 / 23 AD2016
Results
Initial configurationsparam. gain ratio case1 gain ratio case2 gain ratio case3c11 1.2434 0.9293 1.1830c33 1.4205 0.8531 2.3508c44 5.3202 1.1749 4.3539c12 1.0125 0.5684 2.6384c13 1.0978 0.8933 1.3414ε33 1.3629 0.6659 2.5290e31 1.1556 1.0677 1.2714e33 1.8522 0.9212 2.4383ε11 2.8385 1.2864 2.0128e15 3.2481 1.4586 1.8070• Initial and optimised sensitivities are still relatively small• every optimisation converges to a different end configuration→ many locally optimal points
B. Jurgelucks & L. Claes 17 / 23 AD2016
Results
Optimisation using CFS++ with AD:Points evaluated
Consider optimisation fmincon with only one material parameter:
0 1 2 3 4 5 6
r(1)
-10
0
10
r(2
)
0 1 2 3 4 5 6
r(3)
-10
0
10
r(4
)
0 1 2 3 4 5 6
r(1)
-10
0
10
r(2
)
0 1 2 3 4 5 6
r(3)
-10
0
10
r(4
)
⇒ Different starting points (blue) now run into the same end points (red)
B. Jurgelucks & L. Claes 18 / 23 AD2016
Results
Optimisation using CFS++ with AD:Function iterations
1 1.5 2 2.5 3
Iteration number
-160
-140
-120
-100
-80
-60
Fu
ncti
on
valu
e
Iterations of optimisation procedure
1 2 3 4
Iteration number
-170
-160
-150
-140
-130
-120
-110
-100
-90
Functi
on v
alu
e
Iterations of optimisation procedure
Note: Optimisation configured to stop at ∆~r ≤ 10−5
B. Jurgelucks & L. Claes 19 / 23 AD2016
Results
Optimisation using CFS++ with FD:Points evaluated
r(1)
0 1 2 3 4 5 6
r(2
)
-2
0
2
4
6
8
r(3)
0 1 2 3 4 5 6
r(4
)
-2
0
2
4
6
8
0 1 2 3 4 5 6
r(1)
-10
0
10
r(2
)
0 1 2 3 4 5 6
r(3)
-10
0
10
r(4
)
⇒ Different starting points (blue) do not run into the same end points (red)
B. Jurgelucks & L. Claes 20 / 23 AD2016
Results
Optimisation using CFS++ with FD:Function iterations
1 1.5 2 2.5 3
Iteration number
-85
-80
-75
-70
-65
-60
Functi
on v
alu
e
Iterations of optimisation procedure
1 1.5 2 2.5 3
Iteration number
-94.2
-94
-93.8
-93.6
-93.4
-93.2
-93
-92.8
Functi
on v
alu
e
Iterations of optimisation procedure
Note: Optimisation configured to stop at ∆~r ≤ 10−5
B. Jurgelucks & L. Claes 21 / 23 AD2016
Conclusion
Conclusions:• Optimisation with FD feasable, many locally optimal points• Cost function using AD is easier to optimise• Finally possible optimisation of triple-ring case with AD
Challenges:• Computationally expensive simulation• Find globally optimal point if possible• Further fine tuning of weights is necessary→ Pareto optimality?
Ongoing work:• Optimisation for all material parameters• Eliminate FD from simulation and optimisation• ADOL-C’s traceless higher order vector mode make
derivative-based optimisation possible. Final implementationongoing
B. Jurgelucks & L. Claes 22 / 23 AD2016
Bibliography
Bibliography
Kulshreshtha, K., Jurgelucks, B.,Bause, F., Rautenberg, J. and Unverzagt, C.: Increasing thesensitivity of electrical impedance to piezoelectric material parameters with non-uniformelectrical excitation. In: Journal of Sensors and Sensor Systems, Vol. 4, No. 1, pp. 217-227,2015
Lahmer, T.: Forward and inverse problems in piezoelectricity, PhD thesis, University ofErlangen-Nuremberg, 2008
Unverzagt, C., Rautenberg, J. and Henning, B.: Sensitivitatssteigerung bei der inversenMaterialparameterbestimmung fur Piezokeramiken. In: tm - Technisches Messen, 82(2), pp.102-109, from doi:10.1515/teme-2014-0008, 2015