Analog circuit fault feature extraction method based on parameter random distribution neighbor embedding winner-take-all method
An analog circuit fault feature extraction method based on a parameter random distribution neighbor embedding winner-take-all method, comprising the following steps: (1) collecting a time-domain response signal of an analog circuit under test, wherein the input of the analog circuit under test is excited by using a pulse signal, a voltage signal is sampled at an output end, and the collected time-domain response signal is an output voltage signal of the analog circuit; (2) applying a discrete wavelet packet transform for the collected time-domain response signal to acquire each wavelet node signal; (3) calculating energy values and kurtosis values of the acquired wavelet node signals to form an initial fault feature data set of the analog circuit; and (4) analyzing the initial fault feature data by the parameter random distribution neighbor embedding winner-take-all method, to acquire optimum low-dimensional feature data. The invention effectively reduces redundancy and interference elements in the fault features, and greatly improves degree of separation of different fault features and degree of polymerization of samples of same fault category.
1. An analog circuit fault feature extraction method based on a parameter random distribution neighbor embedding winner-take-all method, comprising:
(1) collecting a time-domain response signal of an analog circuit under test, wherein the input of the analog circuit under test is excited by using a pulse signal, a voltage signal is sampled at an output end, and the collected time-domain response signal is an output voltage signal of the analog circuit;
(2) applying a discrete wavelet packet transform to the collected time-domain response signal to acquire each wavelet node signal;
(3) calculating energy values and kurtosis values of the acquired wavelet node signals to form an initial fault feature data set of the analog circuit;
(4) analyzing the initial fault feature data formed by the energy values and kurtosis values of each wavelet node signal with the parameter random distribution neighbor embedding winner-take-all method, to acquire optimum low-dimensional feature data; and
(5) using the optimum low-dimensional feature data to separate at least one fault categories, to improve an accuracy rate of an analog circuit fault diagnosis.
2. The analog circuit fault feature extraction method based on the parameter random distribution neighbor embedding winner-take-all method according to claim 1 , wherein, in the step (2), the discrete wavelet packet transform specifically comprises applying four-layer Coiflets 3 wavelet packet decomposition to the collected output voltage signal.
3. The analog circuit fault feature extraction method based on the parameter random distribution neighbor embedding winner-take-all method according to claim 1 , wherein, in the step (3), formulae for calculating kurtosis values and energy values are:
K
=
1
N
∑
i
=
1
N
(
x
i
-
x
_
σ
)
and
E
=
1
N
∑
i
=
1
N
(
x
i
)
2
,
wherein K is a kurtosis value, E is an energy value, N is a total number of data points in a node signal sequence, x i is the value of the data points, x is the mean value of the signal sequence, and σ is the standard deviation of the signal sequence.
4. The analog circuit fault feature extraction method based on the parameter random distribution neighbor embedding winner-take-all method according to claim 3 , wherein the specific method of the step (4) comprises:
for the high-dimensional feature data set X=[x 1 , x 2 , . . . x N ]∈R D×N formed in the step (3), wherein D is a data dimensionality before dimensionality reduction, the data after dimensionality reduction is Y=[y 1 , y 2 , . . . y N ]∈R d×N , and d is a data dimensionality after dimensionality reduction, wherein the parameter random distribution neighbor embedding winner-take-all method transforms the distance information between the data in the high dimensional space to a similarity between the data, and recovers the similarity in a low-dimensional space;
defining the similarity between the data as conditional probability p j/i for the high-dimensional feature data set before dimensionality reduction, wherein a similarity of the data x j relative to the data x i is proportional to a probability density of Gaussian distribution by taking x i as the center:
p
j
/
i
=
exp
(
-
x
i
-
x
j
2
/
2
σ
i
2
)
∑
k
≠
i
exp
(
-
x
i
-
x
k
2
/
2
σ
i
2
)
)
wherein σ i represents a variance of the Gaussian distribution by taking x i as the center;
obtaining p j/i =p i/j according to symmetry of the data, thereby acquiring:
p
ij
=
p
j
/
i
+
p
i
/
j
2
;
in order to solve the congestion problem between the data points in the low-dimensional space, using a random distribution instead of a Gaussian distribution in the low-dimensional space, wherein the similarity is defined as:
q
ij
=
(
1
+
f
(
x
i
|
W
)
-
f
(
x
j
|
W
)
2
/
α
)
-
α
+
1
2
∑
k
≠
i
(
1
+
f
(
x
k
|
W
)
-
f
(
x
i
|
W
)
2
/
α
)
-
α
+
1
2
,
wherein f represents dimensionality reduction mapping from the high-dimensional space to the low-dimensional space, that is f(x)=Y, the mapping is defined by a multi-layer forward propagation neural network taking W as weight based on a restricted Boltzmann machine, and a is a random distribution degree of freedom;
by taking the joint probability distribution between the data points in the high-dimensional space as P and the joint probability distribution between the data points in the low-dimensional space as Q, a difference between the joint probability distributions P and Q is measured by using Kullback-Leibler divergence, wherein an objective function C of the difference is shown as follows:
C
=
∑
i
KL
(
P
i
||
Q
i
)
=
∑
i
∑
j
p
ij
log
p
ij
q
ij
,
wherein the optimization procedure of the objective function C adopts a following iterative formula:
Y
(
t
)
=
Y
(
t
-
1
)
+
η
δ
C
δ
y
+
a
(
t
)
(
Y
(
t
-
1
)
-
Y
(
t
-
2
)
)
wherein in the formula, t is the iterations, η is a learning rate, and a(t) is a momentum item at the tth iterations; and
finally acquiring the optimum low-dimensional feature data Y (t) ∈R d×N subjected to dimensionality reduction according to the parameter random distribution neighbor embedding winner-take-all method, after t times of iterations.