US 11,486,925 B2 · Method for diagnosing analog circuit fault based on vector-valued regularized kernel function approximation

Abstract

A method for diagnosing analog circuit fault based on vector-valued regularized kernel function approximation, includes steps of: step (1) acquiring a fault response voltage signal of an analog circuit; step (2) carrying out wavelet packet transform on the collected signal, and calculating a wavelet packet coefficient energy value as a characteristic parameter; step (3) utilizing a quantum particle swarm optimization algorithm to optimize a regularization parameter and kernel parameter of vector-valued regularized kernel function approximation, and training a fault diagnosis model; and step (4) utilizing the trained diagnosis model to recognize circuit faults.

A method for diagnosing an analog circuit fault based on vector-valued regularized kernel function approximation, comprising steps of:

step (1):
collecting output signals comprising:
extracting time domain response voltage signals of all nodes of an analog circuit under test;
step (2):
carrying out wavelet packet decomposition on the output signals collected, calculating energy of all nodes as original sample characteristic data, and equally dividing the original sample characteristic data into a training sample set and a test sample set;
step (3):
utilizing a quantum particle swarm optimization (QPSO) algorithm to optimize a regularization parameter and kernel parameter of vector-valued regularized kernel function approximation (VVRKFA) on the basis of the training sample set, and constructing a VVRKFA-based fault diagnosis model;
step (4):
inputting the test sample set to the constructed VVRKFA-based fault diagnosis model to recognize circuit fault classes;
wherein in step (3), the process of constructing the VVRKFA-based fault diagnosis model comprises steps of:
(3.a) determining a type of a kernel function:
adopting a Gaussian kernel function K(xi,xj)=exp(σ∥xi−xj) is as the kernel function of VVRKFA to establish a mathematic model of VVRKFA, wherein σ is a width factor of the Gaussian kernel function;
wherein a mathematic model of VVRKFA is:
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wherein, Θ∈RN×m is a regression coefficient matrix for mapping a characteristic inner product space to a label space;
N is an amount of fault classes;
m is a dimensionality of training samples in the training sample set;
m is a dimensionality of samples in a dimensionality-reduced sample data set obtained after the dimensionality of the training sample set is reduced;
b∈N×1 is a base vector;
C is the regularization parameter;
ξi∈N×1 is a slack variable;
matrix B∈m×n is the dimensionality-reduced sample data set (m≤m) obtained after the dimensionality of the training sample set is reduced;
n is an amount of all the training samples in the training sample set;
K(.,.) is the kernel function;
xi is the training samples in the training sample set;
Yi is a category label vector of the training sample xi;
T is a matrix transpose symbol;
J is a target function name;
[Θ b]=YPT[CI+PPT]−1, wherein P=[k(A,BT)e]T∈(m+1)×m is the training sample set;
I is a unit matrix, and Y∈N×m is a matrix comprising m category label vectors of the training samples;
(3.b) by utilizing the quantum particle swarm optimization algorithm to optimize the mathematic model of VVRKFA, obtaining an optimum regularization parameter and an optimum kernel parameter of the mathematic model of VVRKFA;
(3.c) taking the training samples xi in the training sample set as input data, constructing a vector value mapping function (2) for the optimum regularization parameter and the optimum kernel parameter obtained in step (3.b);
p(xi)=ΘK(xiT,BT)T+b (2)
wherein, Θ∈N×m is the regression coefficient matrix;
B∈m×n is the dimensionality-reduced sample data set obtained after the dimensionality of the training sample set is reduced;
K(.,.) is the kernel function, and in formula (2), the kernel function refers to the optimum kernel function obtained in step (3.b);
C is the regularization parameter, and in formula (2), the regularization parameter C is the optimum kernel parameter obtained in step (3.b);
b∈N×1 is the base vector, N is the number of fault classes;
m is the dimensionality of training samples in the training sample set;
m is the dimensionality of the samples in the dimensionality-reduced sample data set obtained after the dimensionality of the training sample set is reduced;
n is the amount of all the training samples in the training sample set;
(3.d) by utilizing the mapping function constructed in step (3.c), establishing a decision function of VVRKFA, wherein the decision function of VVRKFA is expressed as:
Class(x)=argmin1≤j≤NdM({circumflex over (p)}(xt),p(j)|Σ) (3)
wherein, xt is test samples in the test sample set;
p(j)=(1/nj)Σi=1nj{circumflex over (p)}(xi) is the center point of all training samples corresponding to the jth fault class in the training sample set, dM is the Mahalanobis distance, xi is the training samples in the training sample set, {circumflex over (Σ)}=Σj=1N(nj−1){circumflex over (Σ)}(j)/(n−N) is an intra-class covariance matrix, and n is the amount of all the training samples in the training sample set;
N is the number of fault classes;
nj is the amount of training samples corresponding to the jth fault class in the training sample set;
{circumflex over (p)}(xi) is a mapping projection of the training samples xi in a characteristic sub-space;
{circumflex over (p)}(xt) is a mapping projection of the test samples xt in the characteristic sub-space.
wherein when the decision function is established, constructing the VVRKFA-based fault diagnosis model is accomplished.

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Method for diagnosing analog circuit fault based on vector-valued regularized kernel function approximation

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Method for diagnosing analog circuit fault based on vector-valued regularized kernel function approximation

Life of this patent

Abstract

Claims3