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inverse method

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i want to estimate the temperature derivative of elastic stiffness of quartz by an inverse method
(levenberg, nelder mead ....)
the aim is to fit accuratly with my experimental frequency temperature curves
i use comsol with matlab
i would like to know if anybody has dealt with this kind of probleme and could help me

3 Replies Last Post 2009年10月9日 GMT+2 15:28
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 2009年10月5日 GMT+2 14:16
Hi

from my understanding that is typicallywhat the optimising toolbox does, check "fitting" on teh modelling documentation, and read through the optimisation documentations, this should give you some good clues,
there is also someting similar in the smeug, and memsmodlib documents
Good luck
Ivar

Hi from my understanding that is typicallywhat the optimising toolbox does, check "fitting" on teh modelling documentation, and read through the optimisation documentations, this should give you some good clues, there is also someting similar in the smeug, and memsmodlib documents Good luck Ivar

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 2009年10月6日 GMT+2 07:35
Hi again

one more thing, the eigenfrequency scales as sqrt(E/rho) since the temperature dependence of SiO2 is small and "rho" would not change really, you can always make a developpment f+df=C*sqrt((E+dE)).

Once you have set up your model and fixed a good starting point you can do a simple sensitivity analysis with COMSOL and then resolve the rest in Matalb (I do not really dear to propose EXCEL but even that should work).

Now if you are dealing with SiO2-Si-SiO2 MEMS layers (and not bulk amorphe or crystalline quartz), you should take into account the distances from the neutral fiber, COMSOL does not have specific elements for layer-structured material, but finally the formulas are given in many books and its rather straightforward.

Finally if its the temperature sensitivity of SiO2 in thin films you are studying, do not forget that these resonators are also used as material mass deposit sensor, and often the humidity response is greater than the thermal response. The experimantal metrology requires carefull monitoring of RH and T, from the moment the wafer comes out of the oven to they are being measured,

Good luck
Ivar
Hi again one more thing, the eigenfrequency scales as sqrt(E/rho) since the temperature dependence of SiO2 is small and "rho" would not change really, you can always make a developpment f+df=C*sqrt((E+dE)). Once you have set up your model and fixed a good starting point you can do a simple sensitivity analysis with COMSOL and then resolve the rest in Matalb (I do not really dear to propose EXCEL but even that should work). Now if you are dealing with SiO2-Si-SiO2 MEMS layers (and not bulk amorphe or crystalline quartz), you should take into account the distances from the neutral fiber, COMSOL does not have specific elements for layer-structured material, but finally the formulas are given in many books and its rather straightforward. Finally if its the temperature sensitivity of SiO2 in thin films you are studying, do not forget that these resonators are also used as material mass deposit sensor, and often the humidity response is greater than the thermal response. The experimantal metrology requires carefull monitoring of RH and T, from the moment the wafer comes out of the oven to they are being measured, Good luck Ivar

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Posted: 1 decade ago 2009年10月9日 GMT+2 15:28
i have succesfully implement the levenberg marquardt algo into comsol and with it , my new set of temperature derivative fit well with the experiment.
Nevertheless, it takes time to evaluate the sensivity matrix (18 parameter)
Does the nelder mead algo make the job faster?
i have succesfully implement the levenberg marquardt algo into comsol and with it , my new set of temperature derivative fit well with the experiment. Nevertheless, it takes time to evaluate the sensivity matrix (18 parameter) Does the nelder mead algo make the job faster?

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