Measuring system repeatable bandwidth for simulation testing
First Claim
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1. A method of identifying characteristics of a physical system, the method comprising:
- applying first and second substantially identical drive ensembles to the physical system and obtaining corresponding responses from the physical system, wherein applying the first and second substantially identical drive ensembles to the physical system further comprises applying a modified drive ensemble to the physical system prior to applying the first and second substantially identical drive ensembles to the physical system, wherein the first and second substantially identical drive ensembles are substantially unmodified versions of the modified drive ensemble; and
estimating a repeatable bandwidth of the physical system as a function of the applied first and second substantially identical drive ensembles and the corresponding obtained responses.
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Abstract
A system and method for identifying characteristics of a physical system applies substantially identical drive ensembles to the physical system and obtains corresponding responses from the physical system. A repeatable bandwidth of the physical system is estimated as a function of the applied drive ensembles and the corresponding obtained responses. Instructions can be provided on a computer readable medium to perform the method.
19 Citations
24 Claims
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1. A method of identifying characteristics of a physical system, the method comprising:
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applying first and second substantially identical drive ensembles to the physical system and obtaining corresponding responses from the physical system, wherein applying the first and second substantially identical drive ensembles to the physical system further comprises applying a modified drive ensemble to the physical system prior to applying the first and second substantially identical drive ensembles to the physical system, wherein the first and second substantially identical drive ensembles are substantially unmodified versions of the modified drive ensemble; and
estimating a repeatable bandwidth of the physical system as a function of the applied first and second substantially identical drive ensembles and the corresponding obtained responses. - View Dependent Claims (2, 3, 4, 5, 6)
further comprises: - applying a first drive signal having the first drive ensemble; and
applying a second drive ensemble having the second drive ensemble.
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7. A method of identifying characteristics of a physical system, the method comprising:
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applying first and second substantially identical drive ensembles to the physical system and obtaining corresponding responses from the physical system; and
estimating a repeatable bandwidth of the physical system as a function of the applied first and second substantially identical drive ensembles and the corresponding obtained responses, wherein estimating the repeatable bandwidth of the physical system further comprises;
calculating a first cross spectral density CSD1 between the first drive ensemble and the corresponding response;
calculating a second cross spectral density CSD2 between the second drive ensemble and the corresponding response; and
calculating a variation Δ
FRF of a frequency response function FRF for the physical system as a function of the first cross spectral density CSD1 and the second cross spectral density CSD2.- View Dependent Claims (8, 9, 10, 11, 12)
where RSD is an average of the response spectral densities RSD1 and RSD2 of the responses to the first and second substantially identical drive ensembles, wherein Δ
RSD is a difference of the response spectral densities RSD1 and RSD2 of the responses to the first and second substantially identical drive ensembles, CSD′
is an average of the cross-spectral densities CSD′
1 and CSD′
2 of the responses to the first and second substantially identical drive ensembles, and Δ
CSD′
is a difference of the cross-spectral densities CSD′
1 and CSD′
2 of the responses to the first and second substantially identical drive ensembles.
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11. The method of claim 7, wherein estimating the repeatable bandwidth for the physical system further comprises comparing a singular value decomposition as a function of frequency of the variation Δ
- FRF to a singular value decomposition as a function of frequency of the frequency response function FRF.
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12. The method of claim 11, and further comprising identifying inputs to the physical system to which the physical system is insensitive as a function of frequency using the relationship:
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13. A computer readable medium including instructions readable by a computer, which when implemented, cause the computer to identify characteristics of a physical system, the instructions performing steps comprising:
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applying first and second substantially identical drive ensembles to the physical system and obtaining corresponding responses from the physical system, wherein the instructions performing step of applying the first and second substantially identical drive ensembles to the physical system further comprises applying a modified drive ensemble to the physical system prior to applying the first and second substantially identical drive ensembles to the physical system, wherein the first and second substantially identical drive ensembles are substantially unmodified versions of the modified drive ensemble; and
estimating a repeatable bandwidth of the physical system as a function of the applied drive ensembles and the corresponding obtained responses. - View Dependent Claims (14, 15, 16, 17, 18)
applying a first drive signal having the first drive ensemble; and
applying a second drive ensemble having the second drive ensemble.
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19. A computer readable medium including instructions readable by a computer, which when implemented, cause the computer to identify characteristics of a physical system, the instructions performing steps comprising:
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applying first and second substantially identical drive ensembles to the physical system and obtaining corresponding responses from the physical system; and
estimating a repeatable bandwidth of the physical system as a function of the applied first and second drive ensembles and the corresponding obtained responses, wherein the instructions performing step of estimating the repeatable bandwidth of the physical system further comprises;
calculating a first cross spectral density CSD1 between the first drive ensemble and the corresponding response;
calculating a second cross spectral density CSD2 between the second drive ensemble and the corresponding response; and
calculating a variation Δ
FRF of a frequency response function FRF for the physical system as a function of the first cross spectral density CSD1 and the second cross spectral density CSD2.- View Dependent Claims (20, 21, 22, 23, 24)
where RSD is an average of the response spectral densities RSD1 and RSD2 of the responses to the first and second substantially identical drive ensembles, wherein Δ
RSD is a difference of the response spectral densities RSD1 and RSD2 of the responses to the first and second substantially identical drive ensembles, CSD′
is an average of the cross-spectral densities CSD′
1 and CSD′
2 of the responses to the first and second substantially identical drive ensembles, and Δ
CSD′
is a difference of the cross-spectral densities CSD′
1 and CSD′
2 of the responses to the first and second substantially identical drive ensembles.
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23. The computer readable medium of claim 19, wherein the step of estimating the repeatable bandwidth for the physical system further comprises comparing a singular value decomposition as a function of frequency of the variation Δ
- FRF to a singular value decomposition as a function of frequency of the frequency response function FRF.
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24. The computer readable medium of claim 23, and further comprising an instructions performing step of identifying inputs to the physical system to which the physical system is insensitive as a function of frequency using the relationship:
Specification