Method of calibrating impedance measurements of a battery

Abstract

A method of calibration is described that simplifies the measurement of battery impedance conducted in-situ while determining battery state-of-health. A single shunt measurement with a known Sum of Sines (SOS) current, at the desired frequency spread and known root mean squared (RMS) current is used to create a calibration archive. A calibration selected from this archive is used to calibrate an impedance measurement made on the battery.

Claims

1. An impedance measurement apparatus, comprising: a current driver configured to generate an excitation current signal to be applied to a device; a processor communicatively coupled to a non-transitory computer readable media containing a program code, said program code executed under control of said processor to: excite said device using said excitation signal including a root mean squared current or a root mean squared voltage having a plurality of frequencies in a frequency range; record a response time record of said device excited using said excitation signal; discard said response time record of said device corresponding to a fraction of a period of lowest frequency of said plurality of frequencies in said excitation signal; apply a calibration record to said response time record of said device; and perform a single calculation of impedance of said device based on said calibration record applied to said response time record.

2. The apparatus of claim 1, wherein said computer readable code further executable to: transform said response time record of said device to a frequency domain; and normalize said response time record of said device transformed to said frequency domain.

3. The apparatus of claim 1, further comprising: excite one non-inductive shunt having one non-inductive shunt value using said excitation signal including said root mean squared current or said root mean squared voltage having said plurality of frequencies in said frequency range; record a response time record of said one non-inductive shunt; and generate said calibration record based on said response time record of said one non-inductive shunt.

4. The apparatus of claim 3, further comprising: transform each said response time record of said non-inductive shunt to said frequency domain; and normalize said response time record of said non-inductive shunt transformed to said frequency domain to said non-inductive shunt value.

5. The apparatus of claim 1, wherein said response time record includes a negative time portion corresponding to said fraction of said period of said lowest frequency of said plurality of frequencies in said excitation signal; and wherein discard of said response time record corresponds to said negative time portion of said response time record.

6. The apparatus of claim 1, wherein said computer code further executed to: determine time periods in said response time record where a voltage level exceeds a saturation level of a digitizer within a data acquisition system; discard said time periods in said response time record; discard said time periods in said calibration record; apply said calibration record having said time periods discarded to said time response record having said time periods discarded; and calculate impedance of said device.

7. A method of operating an impedance measurement apparatus, comprising: configuring a current driver to generate an excitation current signal to be applied to a device; executing a program code contained in a non-transitory computer readable media under control of a processor to actuate said current driver; exciting said device using said excitation signal including a root mean squared current or a root mean squared voltage having a plurality of frequencies in a frequency range; recording a response time record of said device excited with said excitation signal; discarding said response time record of said device corresponding to a fraction of a period of lowest frequency of said plurality of frequencies in said excitation signal; applying a calibration record to said response time record of said device; and performing a single calculation of impedance of said device based on said calibration record applied to said response time record.

8. The method of claim 7, further comprising: exciting one non-inductive shunt having one non-inductive shunt value using an excitation signal including said root mean squared current or root mean squared voltage having said plurality of frequencies in said frequency range; recording a response time record of said one non-inductive shunt; and generating said calibration record based on said response time record of said one non-inductive shunt.

9. The method of claim 8, further comprising: transforming said response time record of said one non-inductive shunt to a frequency domain; and normalizing said response time record of said one non-inductive shunt to said one non-inductive shunt value and said excitation signal including said root mean square current or said root mean squared voltage having said plurality of frequencies in said frequency range.

10. The method of claim 7, wherein said response time record includes a negative time portion corresponding to said fraction of said period of said lowest frequency of said plurality of frequencies in said excitation signal, wherein discard of said response time record corresponds to said negative time portion of said response time record.

11. The method of claim 7, further comprising: analyzing said response time record of said device; determining time periods in said response time record of said device where a voltage level exceeds a saturation level of a digitizer within a data acquisition system; discarding said time periods in said response time record of said device where said voltage level exceeds said saturation level of said digitizer; discarding said time periods in said calibration record which correspond to said time periods discarded in said response time record of said device; applying said calibration record having said time periods discarded to said time response record of said device having said time periods discarded; and calculating said impedance of said device.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) FIG. 1 shows the single shunt calibration of a test cell at 500 mA using the method of the subject invention.

(2) FIG. 2 shows the single shunt calibration of a test cell with RMS current scale 500 mA down to 250 mA using the method of the subject invention.

(3) FIG. 3 shows the single shunt calibration of a test cell with RMS current scale 500 mA down to 125 mA using the method of the subject invention.

(4) FIG. 4 shows the single shunt calibration of a test cell with RMS current scale 500 mA down to 62.5 mA using the method of the subject invention.

(5) FIG. 5 shows a single shunt calibration with Solatron EIS of a test cell using the method of the subject invention.

(6) FIG. 6 shows a single shunt calibration with Solatron EIS of a test cell using the method of the subject invention.

(7) FIG. 7 shows a single shunt calibration with Solatron EIS of a test cell using the method of the subject invention).

(8) FIG. 8 shows a lead acid battery measured at 62.5 mA and 15 frequency SOS showing 18 to 15 frequency and 500 mA to 62.5 mA RMS current and frequency scaling.

(9) FIG. 9 shows a lead acid battery measured at 125 mA RMS SOS showing 18 to 15 frequency and 500 mA to 125 mA RMS current scaling and frequency scaling.

(10) FIG. 10 shows splining the calibration 14 frequencies in octaves downward from 1000 Hz calibrated with 15 frequencies in octaves from 0.1 Hz to 1638.4 Hz.

(11) FIG. 11A demonstrates saturation tolerance time CTC algorithm with a 12 V lead acid car battery and shows the unclipped battery time record.

(12) FIG. 11B demonstrates saturation tolerance time CTC algorithm with a 12 V lead acid car battery and shows the unclipped TCTC with baseline HCSD spectrum.

(13) FIG. 11C demonstrates saturation tolerance time CTC algorithm with a 12 V lead acid car battery and shows the clipped battery time record.

(14) FIG. 11D demonstrates saturation tolerance time CTC algorithm with a 12 V lead acid car battery and shows the clipped spectrum with baseline HCSD spectrum.

(15) FIG. 12A demonstrates saturation tolerance TCTC algorithm with a Lithium ion battery and shows the unclipped battery time record.

(16) FIG. 12B demonstrates saturation tolerance TCTC algorithm with a Lithium ion battery and shows the unclipped TCTC with baseline HCSD spectrum.

(17) FIG. 12C demonstrates saturation tolerance TCTC algorithm with a Lithium ion battery and shows the clipped battery time record.

(18) FIG. 12D demonstrates saturation tolerance TCTC algorithm with a Lithium ion battery and shows the clipped spectrum with baseline HCSD spectrum.

(19) FIG. 13 is a block flow diagram of a method for generating a measure of impedance of a test device.

DETAILED DESCRIPTIONS OF THE INVENTION

(20) The method of the subject invention is involves single shunt calibration (SSC) that applies to all generations of (Impedance Measurement Box) IMB. The subject method simplifies use of the IMB to assess battery health. The Idaho National Laboratory (INL) has described the design and construction of the IMB in numerous patent documents (see, for example, U.S. Pat. Nos. 7,688,036; 7,395,163 B1; 7,675,293 B2; 8,150,643 B1; 8,352,204 B2; 8,762,109 B2; 8,868,363 B2; and 9,244,130 B2, and U.S. Published Patent Application Nos. 2011/0270559 A1; 2014/0358462 A1; and 2017/0003354 A1). Spectrum algorithms used in the implementation are also described in the above patent documents and include, but are not limited to, harmonic compensated synchronous detection (HCSD), fast summation transformation (FST), generalized fast summation transformation (GFST), frequency cross talk compensation (FCTC), time cross talk compensation (TCTC), harmonic orthogonal synchronous transformation (HOST). Each of these spectrum algorithms are special cases of a rapid Fourier Transform that bring the measurement time record captured by the IMB measurement into the frequency domain at only the frequencies that were part of the IMB excitation signal to the test battery. The calibration in the present generation 50V IMB (U.S. Patent Application Publication No. 2014/0358462) is accomplished by a complicated measurement scheme which uses 3 different shunts to generate calibration constants that yield a very accurate measurement of the impedance spectra from a test battery (Morrison, William. H., thesis, 2012). In contrast, the claimed method requires only a single measurement with a known Sum Of Sines (SOS) current, at the desired frequency spread and known RMS current.

(21) As an example consider application to the 50V IMB (U.S. Patent Application Publication No. 2014/0358462). With the present 50V IMB HCSD algorithm system (U.S. Patent Application Publication No. 2014/0358462), the calibration for a given SOS frequency spread (octave harmonic short 0.1 Hz to 1638.4 Hz or long 0.0125 Hz to 1638.4 Hz) and a given SOS RMS current, the measurement time record that is processed into the frequency domain is typically one period of the lowest frequency. As part of the calibration the SOS current output is pre-emphasized to mitigate the IMB system frequency response. Additionally, the 3 shunt calibration scheme computes gain and offset constants for both magnitude and phase at each frequency. Equation 1 represents the time record captured by the IMB from a measurement on a test battery.
V.sub.B(t)=I.sub.SOS(t)*A.sub.S(t)*Z.sub.B(t)  (1)

(22) Where: I.sub.SOS(t) is the SOS current time record A.sub.S(t) is the measurement system impulse response Z.sub.B(t) is the test battery impedance impulse response

(23) The * in Equation 1 is a convolution operation. Because of the calibration pre-emphasis, I.sub.SOS(t) is given by:

(24) $\begin{array}{cc}{I}_{\mathrm{SOS}}\left(t\right)=RMS\sqrt{\frac{2}{m}}\underset{i=1}{\overset{m}{.Math.}}\sin \left({\omega }_{i}t\right)& \left(2\right)\end{array}$

(25) Where: RMS is the RMS of the SOS current m is the number of frequencies in the SOS ω.sub.i is the i.sup.th radian frequency
Note that the RMS of a SOS signal is:

(26) $RMS=\sqrt{\underset{i=1}{\overset{m}{.Math.}}\left(\frac{1}{T_i}{\int }_{T_i}^{}{\left(V_P\sin \left({\omega }_{i}t\right)\right)}^2\mathrm{dt}\right)}=V_P\sqrt{\frac{m}{2}}{V}_P=RMS\sqrt{\frac{2}{m}}$
Equations 1 and 2 brought into the frequency domain via the 50V IMB HCSD algorithm (Morrison, William H., thesis, 2012) becomes:

(27) $\begin{array}{cc}{\stackrel{.Math.}{V}}_{\mathrm{Bi}}=\mathrm{RMS}\sqrt{\frac{2}{m}}\left(A_{\mathrm{Si}}{\mathrm{▯\varphi }}_{\mathrm{Si}}\right)\left(Z_{\mathrm{Bi}}{\mathrm{▯\varphi }}_{\mathrm{Bi}}\right)& \left(3\right)\end{array}$

(28) Where: A.sub.Si□ ϕ.sub.Si is the measurement system frequency response at the i.sup.th frequency Z.sub.Bi□ ϕ.sub.Bi is the desired battery impedance at the i.sup.th frequency
The effect of calibration is to multiply Equation 3 by a calibration constant given by:

(29) $\begin{array}{cc}{\mathrm{CAL}}_i={\left(\mathrm{RMS}\sqrt{\frac{2}{m}}\left(A_{\mathrm{Si}}{\mathrm{▯\varphi }}_{\mathrm{Si}}\right)\right)}^{-1}& \left(4\right)\end{array}$

(30) Clearly the calibration applied to Equation 3 results in the desired battery impedance and the 50V IMB has demonstrated this with great success via the 3 shunt magnitude calibration and the stepped phase shift calibration both yielding gain offset calibration constants that represent Equation 4 (Morrison, William H. thesis, 2012). Observe that Equation 4 is a calibration constant that is a combination of SOS current pre-emphasis and magnitude phase calibration at each frequency. The subject method does everything in a single measurement with a single shunt, single shunt calibration (SSC).

(31) For the 50V IMB system the concept is very simple. The system will perform a spectrum measurement on a known non-inductive shunt for example a 50 mOhm non-inductive calibration shunt (as shown in FIG. 13, Block B1). The SOS current is set to the high level, 500 mA RMS (as shown in FIG. 13, Block B2). The system must be configured for no pre-emphasis and no calibration (U.S. Patent Application Publication No. 2014/0358462). As the 50V IMB uses the HCSD algorithm, either 18 frequencies are selected, 0.0125 Hz to 1638.4 Hz or 15 frequencies 0.1 Hz to 1638.4 Hz both in octave steps (as shown in FIG. 13, Block B3). The measurement is performed and processed via the HCSD algorithm to convert the captured time record into the frequency domain (as shown in FIG. 13, Blocks B4 and B5 respectively). Then the complex results at each frequency are normalized to the measurement shunt value and the SOS RMS current (as shown in FIG. 13, Block B6). These results are in fact Equation 6 and are stored in a calibration file that when recalled can be used to calibrate a battery impedance measurement with the same frequency spread and different RMS current (as per Equation 9)(as shown in FIG. 13, Block B7).

(32) For the single shunt calibration (SSC), we assume that single shunt used is constant and independent of frequency over the frequency range of the IMB. Additionally, all measurements are made without any pre-emphasis. Thus as a function of time the IMB measurement of that shunt V.sub.SHUNT(RMS,iΔt) is given by Equation 5.
V.sub.SHUNT(RMS,iΔt)=V.sub.SOS(RMS,iΔt)*H.sub.OUT(t)*R.sub.SHUNT*H.sub.IN(iΔt)  (5)
Where *: indicates the convolution operation V.sub.SOS(RMS,iΔt): is the computer generated signal to IMB current drivers H.sub.OUT(t): is the current driver system response in time iΔt: is the computer discrete time R.sub.SHUNT: is the calibration shunt, ohms H.sub.IN(iΔt): is the IMB system input response in discrete time
Also as a function of time the IMB measurement of a test battery is given by Equation 6.
V.sub.Meas(RMS,iΔt)=V.sub.SOS(RMS,iΔt)*H.sub.OUT(t)*Z.sub.BAT(t)*H.sub.IN(iΔt)  (6)

(33) Where: Z.sub.BAT(t) is the impedance impulse response of the battery as a function of time.

(34) For the SSC the time record of the shunt (Equation 5) is processed by the HCSD algorithm of the IMB, normalized by R.sub.SHUNT and stored as calibration. Equation 7 illustrated the shunt time record brought into the frequency domain at one of the SOS frequencies ω.sub.i.
V.sub.SHUNT(ω.sub.i)=V.sub.SOS(RMS,ω.sub.i)H.sub.OUT(ω.sub.i)R.sub.SHUNTH.sub.IN(ω.sub.i)  (7)

(35) Where: ω.sub.i is radians/sec

(36) Note that the convolution operation in Equation 5 goes to multiplication in Equation 7. The time record of the battery given by Equation 6 when brought into the frequency domain at one of the SOS frequencies ω.sub.i is given by Equation 8.
V.sub.Meas(ω.sub.i)=V.sub.SOS(RMS,ω.sub.i)H.sub.OUT(ω.sub.i)Z.sub.BAT(ω.sub.i)H.sub.IN(ω.sub.i)  (8)

(37) Performing division in the frequency domain the essence of calibration is given by Equation 9.

(38) $\begin{array}{cc}{Z}_{\mathrm{BAT}}\left({\omega }_i\right)=R_{\mathrm{SHUNT}}\frac{V_{\mathrm{SOS}}\left(\mathrm{RMS},{\omega }_i\right)H_{\mathrm{OUT}}\left({\omega }_i\right)Z_{\mathrm{BAT}}\left({\omega }_i\right)H_{\mathrm{IN}}\left({\omega }_i\right)}{V_{\mathrm{SOS}}\left(\mathrm{RMS},{\omega }_i\right)H_{\mathrm{OUT}}\left({\omega }_i\right)R_{\mathrm{SHUNT}}{H}_{\mathrm{IN}}\left(\mathrm{i\Delta t}\right)}& \left(9\right)\end{array}$
Thus the SSC is a collection of measurements of R.sub.SHUNT at standardized RMS currents and SOS frequency spreads brought into the frequency domain by the HCSD algorithm. For the IMB there are 2 standardized frequency ranges and 4 standardized RMS currents. To calibrate for this, results in 8 measurements with the single shunt for SSC which are performed fully automated with a single shunt hook-up. A vast improvement over the original manual 3 shunt calibration process.

(39) Observe Equation 7, if in addition to being normalized to the shunt if it were normalized also to the calibration RMS current it can be used as a calibration for any battery measurement RMS current by scaling it to that measurement RMS current.

Example 1—Validation Using 50V IMB and RMS Current Scaling

(40) The 50V IMB at Montana Tech of the University of Montana (Butte, Mont.) was used for initial testing. A long run frequency (0.0125 Hz to 1638.4 Hz) domain calibration file was generated (via HCSD) with-out any calibration or pre-emphasis at an SOS current of 500 mA and a 50 mOhm shunt (as shown in FIG. 13, Blocks B1-B7). It was normalized to the 50 mOhm shunt and the RMS current. Time records of measurements (long runs, 0.0125 Hz to 1638.4 Hz) were made and captured for Test Cell (TC) #3 (Morrison, William H., thesis, 2012) at RMS currents of 500 mA, 250 mA, 125 mA and 62.5 mA again without any pre-emphasis (as shown in FIG. 13, Blocks B8 and B9). All those Test Cell time records were post processed into the frequency domain with the HCSD algorithm ((as shown in FIG. 13, Block B10). The frequency domain calibration was scaled to each measurement current RMS ((as shown in FIG. 13, Block B11). Test cell measurements were made at all the different currents (of 62.5 mA, 125 mA, 250 mA and 500 mA) and calibrated per Equation 9. The results are shown in FIGS. 1-4. The detected TC #3 spectra are plotted with Electro-chemical impedance spectroscopy (EIS) (Solartron Analytical, 2012) data by INL on TC #3. The validity of the subject method is realized by the degree of coincidence of the two plots. Like results were achieved when the subject method was applied to Test Cells #3, #5, and #7. Results demonstrating SSC with these test cells are plotted and shown in FIGS. 5-7.

(41) These results show that 500 mA shunt data can reach all the way down the 62.5 mA to capture the spectra of TC #3 and the results match closely with INL EIS (Solartron Analytical, 2012) data for TC #3 (as shown in FIG. 13, Block B12). This means that for calibration all that is needed is frequency domain files of known shunt, known frequencies and that file will work on measurements with the same frequencies and different known current with good results. This is a significant enhancement to the existing 50V IMB.

(42) As stated previously, with the single shunt calibration, with standard RMS currents and standard frequency ranges, a calibration is fully automated with as few as 8 measurements. Never the less, that can be reduced to a single calibration measurement with frequency scaling and RMS current scaling. In examining Equation 5 for calibration it would be normalized to the calibration RMS current and the shunt value. Then for a calibration it would be scaled by the measurement RMS. Consider the RMS of an SOS:

(43) $\begin{array}{cc}RMS\left(SOS\right)=\sqrt{\left(\underset{M}{.Math.}\frac{V_P^2}{2}\right)}=V_P\sqrt{\frac{M}{2}}& \text{(10)}\end{array}$

(44) Where: M is the number of frequencies V.sub.P is the peak voltage of the sine waves in the SOS
Thus given that a measurement frequency range is an octave harmonic subset of a calibration frequency range the frequency domain the subset of real and imaginary constants are selected out and scaled per:

(45) $\begin{array}{cc}\left(\mathrm{Calibration}\right)\times \sqrt{\frac{M_{CAL}}{M_{\mathrm{MEAS}}}}\times \frac{RM{S}_{\mathrm{MEAS}}}{RM{S}_{\mathrm{CAL}}}& \left(11\right)\end{array}$

Example 2—Validation Test of Frequency and RMS Calibration Scaling

(46) Small lead acid battery measured by IMB with 62.5 mA and 15 frequency SOS. IMB spectrum obtained with normal IMB calibration. Uncalibrated time record post processed to the frequency domain and calibrated by an 18 frequency 500 mA shunt time record brought to the frequency domain and scaled to 15 frequency and 62.5 mA RMS. Both spectra are given in FIG. 8. FIG. 9 shows the battery measured by IMB at 125 mA RMS SOS (as shown in FIG. 13, Block B13). These results support frequency and RMS current scaling for SSC.

Example 3—Negative Time to Reinforce the Assumption of Steady State

(47) The fundamental assumption of all IMB data processing algorithms is that the system being measured is in steady state relative to all excitation frequencies. Clearly this is in contradiction to the requirement of performing a rapid measurement. The IMB measurement technique is to excite the test article with a sum of sinusoids with an excitation time record of no more than one period of the lowest frequency. Some researchers using the IMB measurement concept (Waligo, A., 2016) have resorted to using multiple periods of the lowest frequency in order to re-inforce this assumption. A better solution is “Negative Time” (NT), whereby the sum of sinusoids starting at time zero would all be zero but if one goes backwards in time for a fraction of the period of the lowest frequency, then start the excitation there, this has been shown to work very well to establish the steady state approximation (10% is typical) (as shown in FIG. 13, Block B14). This NT portion is either ignored or discarded from the captured voltage response (as shown in FIG. 13, Block B15). Additionally, NT is also needed for shunt calibration as smoothing filter in the IMB will need to be brought to steady state.

(48) When a calibration is scaled the objective is to make V.sub.P of a measurement and calibration the same thus the frequency range could be kept standardized as subsets of the calibration frequency range. Never the less, for non-standard subsets, even non-octave harmonic subsets processed via time or frequency CTC (U.S. Pat. No. 8,762,109) the technique of “cubic spline” (U.S. Pat. No. 8,868,363) will select out the calibration constants and they will scale exactly as the above relationship (as shown in FIG. 13, Block B16). FIG. 10 shows splining the calibration of 14 frequencies in octaves downward from 1000 Hz calibrated with 15 frequencies in octaves from 0.1 Hz to 1638.4 Hz (as shown in FIG. 13, Block B17).

Example 4—Application to Saturation Tolerant Time and Frequency CTC

(49) A critical feature of the concept for a High Resolution Impedance Measurement Box (HRIMB) is its ability to digitize signals where the voltage level of the signal is near and occasionally beyond the saturation level of the digitizer within the Data Acquisition system (DAQ). This capability of the HRIMB is realized by replacing the data processing algorithm (HCSD Morrison, W. H., thesis, 2012)) with a variation of time or frequency CTC (U.S. Pat. No. 8,762,109) (TCTC, FCTC). This feature for these 2 algorithms is achieved by examining the captured voltage time record for saturation points (as shown in FIG. 13, Block B18), noting the exact times of saturation, deleting those points from the voltage time record (as shown in FIG. 13, Block B19), and computing the algorithm correction matrices at only the times for non-saturation. This technique works for both TCTC and FCTC. These algorithms will bring the time domain voltage measurements (with occasional saturation) into the frequency domain but they must be calibrated to become impedance. This is achieved by retrieving an archived time record of a single shunt measurement that has the exact frequencies of the “to be calibrated voltage” measurement, has been normalized to the measurement shunt and its RMS current. That time record is scaled to the RMS current of the “to be calibrated voltage” and the exact points of the saturation in “to be calibrated voltage” time record are deleted from this time record (as shown in FIG. 13, Block B20). It is then processed with the same correction matrices used with the “to be calibrated voltage” time record (as shown in FIG. 13, Block B21). The impedance at each frequency is the ratio of the “to be calibrated voltage” phasor to the calibration phasor. Note that if decimation was used on the time records in the application of TCTC or FCTC the same decimation must be applied to the calibration time record. Decimation is a technique of uniformly discarding data points from time records to speed up data processing for TCTC or FCTC. Depending on the type of battery being tested it should be kept below X16 and should be applied prior to deletion of saturated data points.

(50) Demonstration of saturation tolerance Time CTC algorithm with a 12V lead acid car battery, 500 mA RMS SOS current, 15 frequencies (0.1 Hz to 1638.4 Hz) plotted with the IMB HCSD measurement response is shown in FIG. 11. Simulated clipping was done by discarding all points in the time record of the response above or below 0.17V. The algorithm was calibrated by a time record of 15 frequencies and 500 mA RMS applied to a shunt. FIG. 11A is the battery voltage time record. FIG. 11B is the spectrum plotted without clipping plotted with the IMB HCSD spectrum. FIG. 11C shows the clipped at +/−0.17V battery voltage time record. FIG. 11D shows the Time CTC clipped spectrum plotted with the baseline HCSD spectrum.

(51) FIG. 12 shows a similar demonstration of time CTC clipping Li Ion battery. An 18 frequency (0.0125 Hz to 1638.4 Hz) 500 mA RMS SOS measurement was made on an Li Ion battery and a 50.27 mOhm shunt. Clipping tolerance was demonstrated by the battery voltage response at +/−0.2V. The Time CTC results are plotted with the baseline HCSD IMB spectrum. FIG. 12A gives the unclipped battery voltage time record. FIG. 12B gives the time CTC processing of FIG. 12A calibrated with the shunt time record plotted with the HCSD baseline spectrum. FIG. 12C gives the +/−0.2V clipped battery voltage time record plotted with the clipping adjusted shunt time record. FIG. 12D gives the time CTC clipped spectrum plotted with the baseline HCSD spectrum. All time CTC processing was done with a X16 decimation.

(52) It is understood that the foregoing examples are merely illustrative of the present invention. Certain modifications of the articles and/or methods may be made and still achieve the objectives of the invention. Such modifications are contemplated as within the scope of the claimed invention.