US 8,150,643 B1 · Method of detecting system function by measuring frequency response

Abstract

Real-time battery impedance spectrum is acquired using a one-time record. Fast Summation Transformation (FST) is a parallel method of acquiring a real-time battery impedance spectrum using a one-time record that enables battery diagnostics. An excitation current to a battery is a sum of equal amplitude sine waves of frequencies that are octave harmonics spread over a range of interest. A sample frequency is also octave and harmonically related to all frequencies in the sum. The time profile of this signal has a duration that is a few periods of the lowest frequency. The voltage response of the battery, average deleted, is the impedance of the battery in the time domain. Since the excitation frequencies are known and octave and harmonically related, a simple algorithm, FST, processes the time record by rectifying relative to the sine and cosine of each frequency. Another algorithm yields real and imaginary components for each frequency.

A method for detecting function of a unit under test by measuring frequency response the method comprising;

the acts of:
setting measurement conditions comprising choosing a Root Mean Square (RMS) level of current, identifying a start frequency, and choosing a period of a lowest frequency,
selecting a number of octave harmonic frequencies relative to the start frequency over which the function of the unit under test will be tested, wherein the number of octave harmonic frequencies is one or more;
assembling an excitation time record including a sum of sinusoids of the number of octave harmonic frequencies and a duration of the period of the lowest frequency;
conditioning the excitation time record to be compatible with the measurement conditions;
exciting the unit under test with the excitation time record and simultaneously capturing a resulting response time record with a data acquisition system having a sample frequency that is octave related and harmonically related to the frequencies within the sum of sinusoids and at least four times the highest frequency in the sum of sinusoids;
rectifying the response time record relative to a sine at each frequency of the octave harmonic frequencies with a first sine rectification sum m11, comprising:
m
11
=
sum
=
∑
n
=
0
N
1
2
-
1
⁢
⁢
T
⁢
⁢
R
⁡
(
n
⁢
⁢
Δ
⁢
⁢
t
)
-
∑
n
=
N
1
2
N
1
-
1
⁢
⁢
T
⁢
⁢
R
⁡
(
n
⁢
⁢
Δ
⁢
⁢
t
)
Where:
TR is a captured response time record with discrete time index n and duration of one period of a first frequency f1
Ni is a number of sample points for a period of the first frequency f1 wherein for each sum of sinusoid frequencies fi, Ni is constrained as log2 (Ni) and is an integer greater than 1 and wherein the frequency of interest is given as:
f
i
=
1
N
i
⁢
Δ
⁢
⁢
t
wherein Δt is a sample period
summing the sine rectification sum for each frequency of interest of the octave harmonic frequencies to create a sine-rectified response time record sum, normalizing the sine-rectified response time record sum to a number of periods known to be within the sine-rectified response time record sum for each frequency, and storing a normalized sine sum result, m1,i, where i is an ith frequency of interest;
rectifying the response time record relative to a cosine at each frequency of the octave harmonic frequencies with a first cosine rectification sum m21, comprising:
m
21
=
sum
=
∑
n
=
0
N
1
4
-
1
⁢
⁢
T
⁢
⁢
R
⁢
(
n
⁢
⁢
Δ
⁢
⁢
t
)
-
∑
n
=
N
1
4
3
⁢
N
1
4
-
1
⁢
⁢
T
⁢
⁢
R
⁡
(
n
⁢
⁢
Δ
⁢
⁢
t
)
+
∑
n
=
3
⁢
N
1
4
N
1
-
1
⁢
⁢
T
⁢
⁢
R
⁡
(
n
⁢
⁢
Δ
⁢
⁢
t
)
summing the cosine rectification sum for each frequency of interest of the octave harmonic frequencies to create a cosine-rectified response time record sum, normalizing the cosine-rectified response time record sum to the number of periods known to be within the cosine-rectified response time record sum for each frequency, and storing a normalized cosine sum result, m2,i, where i is the ith frequency of interest;
determining a real and an imaginary form of a magnitude and a phase of each of the octave harmonic frequencies:
[
V
i
⁢
cos
⁢
⁢
ϕ
i
V
i
⁢
sin
⁢
⁢
ϕ
i
]
=
[
K
4
K
1
⁢
K
4
-
K
2
⁢
K
3
,
K
2
K
2
⁢
K
3
-
K
1
⁢
K
4
K
3
K
2
⁢
K
3
-
K
1
⁢
K
4
,
K
1
K
1
⁢
K
4
-
K
2
⁢
K
3
]
⁡
[
m
1
,
i
m
2
,
i
]
Where:
Vi is a magnitude of the voltage for the frequency fi
φi is a phase of the voltage for the frequency fi
m1,i, m2,i are rectification sums for the frequency fi
K
1
=
∑
n
=
0
N
i
2
-
1
⁢
(
sin
⁡
(
2
⁢
π
N
i
⁢
n
)
)
-
∑
n
=
N
i
2
N
i
-
1
⁢
(
sin
⁡
(
2
⁢
π
N
i
⁢
n
)
)
K
2
=
∑
n
=
0
N
i
2
-
1
⁢
(
cos
⁡
(
2
⁢
π
N
i
⁢
n
)
)
-
∑
n
=
N
i
2
N
i
-
1
⁢
(
cos
⁡
(
2
⁢
π
N
i
⁢
n
)
)
K
3
=
∑
n
=
0
N
i
4
-
1
⁢
(
sin
⁡
(
2
⁢
π
N
i
⁢
n
)
)
-
∑
n
=
N
i
4
3
⁢
N
i
4
-
1
⁢
(
sin
⁡
(
2
⁢
π
N
i
⁢
n
)
)
+
∑
n
=
3
⁢
N
i
4
N
i
-
1
⁢
(
sin
⁡
(
2
⁢
π
N
i
⁢
n
)
)
K
4
=
∑
n
=
0
N
i
4
-
1
⁢
(
cos
⁡
(
2
⁢
π
N
i
⁢
n
)
)
-
∑
n
=
N
i
4
3
⁢
N
i
4
-
1
⁢
(
cos
⁡
(
2
⁢
π
N
i
⁢
n
)
)
+
∑
n
=
3
⁢
N
i
4
N
i
-
1
⁢
(
cos
⁡
(
2
⁢
π
N
i
⁢
n
)
)
and, obtaining the magnitude and the phase via a standard rectangular to polar conversion:
Let:
⁢
⁢
V
i
⁢
sin
⁢
⁢
ϕ
i
=
C
1
V
i
⁢
cos
⁢
⁢
ϕ
i
=
C
2
,
then:
⁢
⁢
V
i
=
C
1
2
+
C
2
2
ϕ
i
=
tan
-
1
⁡
(
C
1
C
2
)
⁢
assembling the magnitude and the phase at each of the octave harmonic frequencies to determine the frequency response.

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Method of detecting system function by measuring frequency response

Life of this patent

Method of detecting system function by measuring frequency response

Life of this patent

Abstract

Claims12