Multispectral impedance determination under dynamic load conditions

1. A method of measuring impedance, comprising:

exciting a device under test with a multispectral excitation signal for an excitation time period while the device under test is under a load condition from a load operably coupled to the device under test;

sampling a response of the device under test over a sample time period, wherein the excitation time period is within the sample time period such that the sample time period includes an in-band interval during the excitation time period, and one or more out-of-band intervals outside of the in-band interval;

estimating a load response of the device under test to the load condition during the in-band interval by analyzing samples of the response from the one or more out-of-band intervals;

computing adjusted samples by subtracting the estimated load response during the in-band interval from the samples from the in-band interval; and

estimating an impedance of the device under test by analyzing the adjusted samples.

2. The method of claim 1 , wherein the excitation time period includes two excitation time periods and the one or more out-of-band intervals include an interval between the two excitation time periods.

3. The method of claim 2 , wherein the one or more out-of-band intervals include at least one of a pre-band interval before the two excitation time periods and a post-band interval after the two excitation time periods.

4. The method of claim 1 , wherein the excitation time period is within the sample time period such that the sample time period includes a pre-band interval immediately before the excitation time period, the in-band interval during the excitation time period, and a post-band interval immediately after the excitation time period.

5. The method of claim 4 , further comprising determining a change in the load condition from a first load condition to a second load condition during the excitation time period, and wherein:

estimating the load response comprises:

fitting a first mathematical expression to samples of the response from the pre-band interval; and

fitting a second mathematical expression to samples of the response from the post-band interval;

computing the adjusted samples comprises:

analyzing the first mathematical expression at time points corresponding to the samples from the in-band interval before the change in the load condition to determine first adjusted samples; and

analyzing the second mathematical expression at time points corresponding to the samples from the in-band interval after the change in the load condition to determine second adjusted samples; and

analyzing the adjusted samples comprises analyzing the first adjusted samples and the second adjusted samples.

6. The method of claim 1 , wherein:

estimating the load response comprises fitting a mathematical expression to samples of the response from the one or more out-of-band intervals; and

computing the adjusted samples comprises analyzing the mathematical expression at time points corresponding to the samples from the in-band interval.

7. The method of claim 6 , wherein fitting the mathematical expression comprises fitting an exponential expression.

8. The method of claim 6 , wherein fitting the mathematical expression comprises using linear regression to perform curve fitting.

9. The method of claim 6 , wherein the mathematical expression includes an adjustment factor for at least one element of the mathematical expression, the method further comprising:

performing an optimization process by varying the adjustment factor to optimize the fit of the mathematical expression to samples from the one or more out-of-band intervals; and

using the optimized mathematical expression for the process of analyzing the mathematical expression.

10. The method of claim 9 , wherein the optimization process comprises minimizing a mean-square-error of samples from the one or more out-of-band intervals relative to the mathematical expression.

11. The method of claim 1 , further comprising using a potentiostatic mode wherein: exciting the device under test comprises applying a voltage signal; and

sampling the response of the device under test comprises sampling a current response.

12. The method of claim 1 , further comprising using a galvanostatic mode wherein: exciting the device under test comprises applying a current signal; and

sampling the response of the device under test comprises sampling a voltage response.

13. The method of claim 1 , wherein sampling the response of the device under test comprises sampling the response of a battery while the battery is under a charging load condition.

14. The method of claim 1 , wherein sampling the response of the device under test comprises sampling the response of a battery while the battery is under a discharging load condition.

15. The method of claim 1 , wherein:

exciting the device under test with the multispectral excitation signal comprises applying a sum-of-sines signal to a battery; and

analyzing the adjusted samples comprises analyzing the adjusted samples with a sum-of-sines analysis.

16. An impedance measurement system, comprising:

a signal conditioner configured for generating a multispectral excitation signal from a composed multispectral signal and applying the multispectral excitation signal to a device under test for an excitation time period;

a data acquisition system configured for sampling a response of the device under test to generate measurements over a sample time period while the device under test is under a load condition from a load operably coupled to the device under test; and

a computing system configured for:

generating the composed multispectral signal;

generating one or more timing indicators to create the sample time period, wherein the excitation time period is within the sample time period such that the sample time period includes an in-band interval during the excitation time period, and one or more out-of-band intervals outside of the excitation time period;

fitting a mathematical expression to the measurements during the one or more out-of-band intervals;

analyzing the mathematical expression at time points corresponding to time points of the response during the in-band interval to estimate in-band corruption correlated to a corruption of the response by the load condition;

computing adjusted samples by subtracting the estimated in-band corruption during the in-band interval from the measurements from the in-band interval; and

analyzing the adjusted samples to estimate an impedance of the device under test.

17. The impedance measurement system of claim 16 , wherein the computing system is further configured for generating the one or more timing indicators such that the sample time period includes a pre-band interval immediately before the excitation time period, the in-band interval during the excitation time period, and a post-band interval immediately after the excitation time period.

18. The impedance measurement system of claim 16 , wherein the computing system is further configured for generating the one or more timing indicators responsive to a condition selected from the group consisting of a pre-determined time, an event within the impedance measurement system, an event related to the device under test, detected anomalous behavior of the device under test, and a detected change in the load condition.

19. The impedance measurement system of claim 16 , wherein the computing system is further configured for applying the multispectral excitation signal at a predetermined time and for a set duration relative to the one or more timing indicators responsive to at least one of a type of multispectral excitation signal used, an expected load condition type, an expected load condition duration, and a desired sampling rate.

20. The impedance measurement system of claim 16 , wherein the computing system is further configured for fitting the mathematical expression as an exponential expression.

21. The impedance measurement system of claim 16 , wherein the mathematical expression includes an adjustment factor for at least one element of the mathematical expression, and the computing system is further configured for:

performing an optimization process by varying the adjustment factor to optimize the fit of the mathematical expression to measurements from the one or more out-of-band intervals; and

using the optimized mathematical expression for the process of analyzing the mathematical expression.

22. The impedance measurement system of claim 21 , wherein the computing system is further configured such that the optimization process comprises minimizing a mean-square-error of the measurements from the one or more out-of-band intervals applied to the mathematical expression.

23. The impedance measurement system of claim 16 , wherein the multispectral excitation signal comprises at least one of a Harmonic Compensated Synchronous Detection (HCSD) signal, a Harmonic Orthogonal Synchronous Transform (HOST) signal, a Fast Summation Transformation (FST) signal, a Time CrossTalk Compensation (TCTC) signal, and a triads-based Generalized Fast Summation Transformation (GFST) signal.

24. The impedance measurement system of claim 16 , wherein the computing system comprises a local computing system and a remote computing system, and wherein the processes performed by the computing system are allocated between the local computing system and the remote computing system.

25. The impedance measurement system of claim 16 , wherein the device under test comprises one or more batteries.

26. The impedance measurement system of claim 25 , further comprising a vehicle including the one or more batteries and the load.

27. A method of measuring impedance, comprising:

applying a multispectral excitation signal over an excitation time period to a device under test while the device under test is under a load condition from a load operably coupled to the device under test;

measuring an electrical signal from the device under test during a sampling window to capture a sample time record of the electrical signal, wherein the excitation time period is within the sampling window such that the sample time record includes in-band samples during the excitation time period, and out-of-band samples outside of the excitation time period;

fitting a mathematical expression to the out-of-band samples;

estimating in-band corruption correlated to a corruption of the electrical signal by the load condition by analyzing the mathematical expression at time points corresponding to the in-band samples to determine in-band corruption elements;

adjusting the in-band samples by removing the in-band corruption elements from the in-band samples to develop a measurement time record;

converting the measurement time record to a frequency domain representation; and

analyzing the frequency domain representation to estimate an impedance of the device under test.

28. The method of claim 27 , wherein applying the multispectral excitation signal comprises applying a sum-of-sines signal.

29. The method of claim 28 , further comprising determining that the load condition is a charge pulse and inverting the sum-of-sines signal before applying the sum-of-sines signal.

30. The method of claim 28 , wherein applying the sum-of-sines signal further comprises applying a Time CrossTalk Compensation (TCTC) signal, and the method further comprises:

determining a change between the load condition and a no-load condition during the excitation time period; and

disregarding a portion of the in-band samples from the measurement time record to remove samples corrupted by the load condition.

31. The method of claim 30 , wherein:

determining the change in the load condition between the load condition and the no-load condition comprises a change from the load condition to the no-load condition; and

disregarding a portion of the in-band samples from the measurement time record comprises truncating a portion of the in-band samples at a beginning portion of the in-band samples.

32. The method of claim 27 , wherein fitting the mathematical expression comprises fitting an exponential expression.

33. The method of claim 27 , wherein the mathematical expression includes an adjustment factor for at least one element of the mathematical expression, the method further comprising:

performing an optimization process by varying the adjustment factor to optimize the fit of the mathematical expression to the out-of-band samples; and

using the optimized exponential expression for the process of analyzing the mathematical expression.

34. The method of claim 33 , wherein the optimization process comprises minimizing a mean-square-error of the out-of-band samples applied to the mathematical expression.

35. The method of claim 27 , wherein the excitation time period includes two excitation time periods and the out-of-band samples include samples in an interval between the two excitation time periods.

36. The method of claim 35 , wherein the out-of-band samples include at least one of samples in a pre-band interval before the two excitation time periods and samples in a post-band interval after the two excitation time periods.

37. The method of claim 27 , wherein:

the excitation time period is within the sample window such that the sample time record includes the in-band samples, pre-band samples from before the excitation time period, and post-band samples from after the excitation time period;

fitting the mathematical expression comprises fitting a first mathematical expression to the pre-band samples and fitting a second mathematical expression to the post-band samples; and

estimating the in-band corruption comprises analyzing the first mathematical expression at time points corresponding to a first portion of the in-band samples and analyzing the second mathematical expression at time points corresponding to a second portion of the in-band samples.

38. The method of claim 27 , wherein the load condition is a no-load condition, and the method further comprises:

analyzing at least some of the out-of-band samples to determine if they can be represented as an exponential expression;

communicating the exponential expression as a possibility of internal leakage of the device under test.

39. The method of claim 27 , wherein:

the load condition is a no-load condition, and

estimating the impedance of the device under test indicates corruption that is not due to a load; and

the method further comprises:

analyzing the impedance spectrum for an indication of possible internal leakage of the device under test; and

communicating the indication as a possibility of internal leakage of the device under test.