Analog circuit fault diagnosis method using single testable node

Abstract

An analog circuit fault diagnosis method using a single testable node comprises the following steps: (1) obtaining prior sample data vectors under each fault mode; (2) computing a statistical average of the prior sample data vectors under each of the fault modes; (3) decomposing a signal by an orthogonal Haar wavelet filter set; (4) extracting the feature factor of the prior sample fault modes; (5) extracting a fault-mode-to-be-tested feature factor; (6) computing a correlation coefficient matrix and correlation metric parameters between the feature factor of the prior sample fault modes and the feature factor of the fault-mode-to-be-tested; and (7) determining a fault mode according to a maximal correlation principle by comparing the correlation metric parameters. The method can convert a single signal into a plurality of signals without losing original measurement information, and extract an independent fault mode feature factor reflecting variations of a circuit structure in different fault modes, can be used to study an associated mode determination rule and successfully complete classification of circuit fault modes.

Claims

1. An analog circuit fault diagnosis method using a single testable node, comprising: (1) obtaining prior sample data vectors under each of fault modes: obtaining M groups of voltage sample vectors V.sub.ij of an analog circuit under test under each of the fault modes F.sub.i by using computer simulation software, wherein i=1, 2, . . . , N, j=1, 2, 3, . . . , M, N is a total number of the fault modes of the circuit, i represents that the circuit works under a i.sup.th fault mode, j is a j.sup.th collected sample, and V.sub.ij represents a j.sup.th voltage sample vector collected when the circuit works under a i.sup.th fault mode; (2) computing a statistical average $V_i=\underset{j=1}{\overset{M}{.Math.}}{V}_{\mathrm{ij}}/M$ of the prior sample data vectors under each of the fault modes, wherein i=1, 2, . . . , N, and V.sub.i is voltage sample statistical average vectors when the circuit works under the fault modes F.sub.i; (3) decomposing a signal by an orthogonal Haar wavelet analysis filter set: decomposing the voltage sample statistical average vectors V.sub.i under each of the fault modes into (K+1) filter output signals by a K-layer orthogonal Haar wavelet filter set; (4) extracting feature factors of prior sample fault modes: extracting (K+1) feature factors s.sub.i,d of the prior sample fault modes through processing the (K+1) filter output signals under the fault modes F.sub.i by using a blind source processing technology, wherein d represents a serial number of fault feature factors, and d=1, 2, . . . , K+1, and s.sub.i,d represents a d.sup.th feature factor of the prior sample fault modes of a voltage sample signal under the fault mode F.sub.i; (5) extracting feature factors of a fault-mode-to-be-tested: collecting M groups of voltage testable vectors of the analog circuit under the fault-mode-to-be-tested, computing a statistical average of the voltage testable vectors, decomposing by the orthogonal Haar wavelet filter set in the step (3), and obtaining (K+1) feature factors s.sub.T,h of the voltage testable vectors under the fault-mode-to-be-tested through the blind source processing technology in step (4), wherein T represents to-be-tested, which is the first letter of Test, and is intended to distinguish the fault-mode-to-be-tested and the prior sample fault modes; h represents a serial number of the feature factors, h=1, 2, . . . , K+1, and s.sub.T,h represents a h.sup.th feature factor of a voltage testable signal under the fault-mode-to-be-tested; (6) computing a correlation coefficient matrix R.sub.i and correlation metric parameters .sub.i between the feature factors of the fault-mode-to-be-tested and the feature factors of the prior sample fault modes all the fault modes F.sub.i; $R_i=\left[\begin{array}{cccc}{}_{11}& {}_{12}& \mathrm{.Math.}& {}_{1\left(K+1\right)}\\ {}_{21}& {}_{22}& \mathrm{.Math.}& {}_{2\left(K+1\right)}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ {}_{\left(K+1\right)1}& {}_{\left(K+1\right)2}& \mathrm{.Math.}& {}_{\left(K+1\right)\left(K+1\right)}\end{array}\right],{}_i=\underset{h=1}{\overset{K+1}{.Math.}}\left(\underset{d}{\mathrm{Max}}\left({}_{\mathrm{hd}}\right)\right),$ wherein .sub.hd=E((s.sub.T,hE(s.sub.T,h)).Math.(s.sub.i,dE(s.sub.i,d))), i=1, 2, . . . , N, E() represents to determine an expected value, s.sub.T,h (h=1, 2, . . . , K+1) represents the h.sup.th feature factor of the voltage testable signal under the fault-mode-to-be-tested, s.sub.i,d (h=1, 2, . . . , K+1) represents the d.sup.th feature factor of the prior sample fault modes of the voltage sample signal under the fault mode F.sub.i, the physical meaning of .sub.hd is a correlation coefficient between the h.sup.th feature factor of the voltage testable signal under the fault-mode-to-be-tested and the d.sup.th feature factor of the prior sample fault modes of the voltage sample signal under the fault mode F.sub.i; $\underset{d}{\mathrm{Max}}\left({}_{\mathrm{hd}}\right)$ represents the maximum .sub.hd when h is constant and d=1, 2, . . . , (K+1); and (7) comparing all the .sub.i and determining the fault-mode-to-be-tested of the analog circuit is a kth fault mode if $k=\mathrm{Index}\left(\underset{i}{\mathrm{Max}}\left({}_i\right)\right),$ wherein i=1, 2, . . . , N, and Index() represents to calculate an index.

2. The analog circuit fault diagnosis method using a single testable node according to claim 1, which characterized in, a feature of the K-layer orthogonal Haar wavelet analysis filter set in the step (3) is: each of layers of the filter set consists of a low-pass filter g(n) and a high-pass filter h(n), output portion of the high-pass filter h(n) is subjected to double downsampling to enter next layer of the wavelet filter set, and output of the low-pass filter g(n) at each layer is subjected to double downsampling and then outputted directly, the low-pass filter g(n)={1/{square root over (2)}, 1/{square root over (2)}}, and the high-pass filter h(n)={1/{square root over (2)}, 1/{square root over (2)}}.

3. The analog circuit fault diagnosis method using a single testable node according to claim 2, wherein a method of determining a layer number K of the K-layer orthogonal Haar wavelet analysis filter set in the step (3) comprises: setting an input signal of the filter set as x=V.sub.i, wherein V.sub.i is the statistical average $V_i=\underset{j=1}{\overset{M}{.Math.}}{V}_{\mathrm{ij}}/M$ of the step (2), and setting the outputs of the high-pass filter h(n) and the low-pass filter g(n) at the layer K as y.sub.K,H and y.sub.K,L respectively; (3.1) initializing: K=1, .sub.0=Th, wherein K is the layer number of filters, .sub.0 is an energy ratio threshold, and Th is a preset original value of the energy ratio threshold which can be any real number greater than 0 but less than 1; (3.2) computing the energy ratio $=\frac{.Math.y_{K,H},y_{K,H}.Math.}{.Math.x,x.Math.},$ wherein <,> represents to compute an inner product; and (3.3) if >.sub.0, then K=K+1, returning to execute the step (3.2); otherwise, outputting the layer number of filters K.

4. The analog circuit fault diagnosis method using a single testable node according to claim 1, wherein a method of extracting the feature factor by using the blind source processing technology in the step (4) is: setting a signal matrix needing to be processed by the blind source technology as Y.sub.i, wherein an extracted feature factor matrix is S.sub.i=[s.sub.i,1 s.sub.i,2 . . . s.sub.i,d . . . s.sub.i,(K+1)], represents the d.sup.th feature factor of the prior sample fault mode under the fault mode F.sub.i, and the dimensionalities of Y.sub.i and S.sub.i are equal; (4.1) initializing a feature extracting matrix W.sub.0 and an update step-length , and letting W.sub.1W.sub.0, wherein represents to assign the value of W.sub.0 to W.sub.1, W.sub.0 is any unit matrix, and is a real number between (0, 0.3); (4.2) computing: S.sub.i=W.sub.0Y.sub.i; (4.3) updating W.sub.1: W.sub.1W.sub.0+[If[S.sub.i]]g.sup.T[S.sub.i], wherein forms of functions f() and g() herein are respectively f[S.sub.i]=S.sub.i and g[S.sub.i]=S.sub.i.sup.3, g.sup.T() represents matrix transposition; and I represents a standard unit matrix; (4.4) standardizing W.sub.1: $W_1\frac{W_1}{.Math.W_1.Math.},$ wherein represents a matrix norm, $\frac{W_1}{.Math.W_1.Math.}$ represents to standardize W.sub.1, and represents to standardize W.sub.1 and then assign a value to W.sub.1; and (4.5) determining convergence: determining whether W.sub.1W.sub.1.sup.T.fwdarw.I, i.e., determining whether a product of W.sub.1W.sub.1.sup.T is infinitely approaching to I, .fwdarw. represents infinitely approaching; if yes, then outputting S.sub.i; otherwise, W.sub.0W.sub.1, wherein represents assigning, and returning to the step (4.2); and I represents a standard unit matrix.

5. The analog circuit fault diagnosis method using a single testable node according to claim 1, wherein a method of determining a layer number K of the K-layer orthogonal Haar wavelet analysis filter set in the step (3) comprises: setting an input signal of the filter set as x=V.sub.i, wherein V.sub.i is the statistical average $V_i=\underset{j=1}{\overset{M}{.Math.}}{V}_{\mathrm{ij}}/M$ of the step (2), and setting the outputs of the high-pass filter h(n) and the low-pass filter g(n) at the layer K as y.sub.K,H and y.sub.K,L respectively; (3.1) initializing: K=1, .sub.0=Th, wherein K is the layer number of filters, .sub.0 is an energy ratio threshold, and Th is a preset original value of the energy ratio threshold which can be any real number greater than 0 but less than 1; (3.2) computing the energy ratio $=\frac{.Math.y_{K,H},y_{K,H}.Math.}{.Math.x,x.Math.},$ wherein <,> represents to compute an inner product; and (3.3) if >.sub.0, then K=K+1, returning to execute the step (3.2); otherwise, outputting the layer number of filters K.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A and FIG. 1B are block diagrams of an analog circuit fault diagnosis method using a single testable node.

(2) FIG. 2 is a structural diagram of a wavelet filter set.

(3) FIG. 3 is a flow of determining a layer number of the filter set.

(4) FIG. 4 is a flow of extracting a feature factor using a single testable node.

DETAILED DESCRIPTION

(5) The invention is explained in details hereinafter with reference to the drawings.

(6) Referring to FIG. 1A and FIG. 1B, an analog circuit fault diagnosis method using a single testable node comprises the following steps:

(7) (1) obtaining prior sample data vectors under each fault mode: obtaining M groups of voltage sample vectors V.sub.ij of an analog circuit under test under each of fault modes F.sub.i by using computer simulation software, wherein i=1, 2, . . . , N, j=1, 2, 3, . . . , M, N is a total number of the fault modes of the circuit, i represents that the circuit works under a i.sup.th fault mode, j is a j.sup.th collected samples, and V.sub.ij represents a j.sup.th voltage sample vector collected when the circuit works under the i.sup.th fault mode; in FIG. 1A and FIG. 1B, it is expressed as: collecting M groups of the voltage sample vectors under the first type fault mode, collecting M groups of the voltage sample vectors under the second type fault mode, . . . , and collecting M groups of the voltage sample vectors under the N.sup.th type fault mode;

(8) (2) computing a statistical average

(9) $V_i=\underset{j=1}{\overset{M}{.Math.}}{V}_{\mathrm{ij}}/M$
of the prior sample data vectors under each of the fault modes, wherein i=1, 2, . . . , N, and V.sub.i is voltage sample statistical average vectors of the voltage sample when the circuit works under the fault modes F.sub.i;

(10) (3) decomposing a signal by an orthogonal Haar wavelet analysis filter set: decomposing the voltage sample statistical average vector V.sub.i (i=1, 2, . . . , N) under each of the fault modes into (K+1) filter output signals by a K-layer orthogonal Haar wavelet filter set;

(11) (4) extracting feature factors of prior sample fault modes: extracting (K+1) feature factors s.sub.i,d of the prior sample fault modes through processing the (K+1) filter output signals under the fault modes Fi by using the blind source processing technology under the fault mode F.sub.i, wherein d represents a serial number of fault feature factors, and d=1, 2, . . . , K+1, and s.sub.i,d represents a d.sup.th feature factor of the prior sample fault modes of a voltage sample signal under the fault mode F.sub.i;

(12) (5) extracting feature factors of a fault-mode-to-be-tested: collecting M groups of voltage testable vectors under the fault-mode-to-be-tested, computing a statistical average of the voltage testable vectors, decomposing by the orthogonal Haar wavelet filter set in the step (3), and obtaining (K+1) feature factors s.sub.T,h of the voltage testable vectors under the fault-mode-to-be-tested through the blind source processing technology in step (4), wherein T represents to-be-tested, which is the first letter of Test, and is intended to distinguish the fault-mode-to-be-tested and the prior fault modes; h represents a serial number of the feature factors, h=1, 2, . . . , K+1, and s.sub.T,h represents a h.sup.th feature factor of a voltage testable signal under the fault-mode-to-be-tested;

(13) (6) computing a correlation coefficient matrix R.sub.i and correlation metric parameters .sub.i between the feature factor of the fault-mode-to-be-tested and the feature factor of the prior sample fault modes of all the fault modes F.sub.i (i=1, 2, . . . , N);

(14) $R_i=\left[\begin{array}{cccc}{}_{11}& {}_{12}& \mathrm{.Math.}& {}_{1\left(K+1\right)}\\ {}_{21}& {}_{22}& \mathrm{.Math.}& {}_{2\left(K+1\right)}\\ \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}& \mathrm{.Math.}\\ {}_{\left(K+1\right)1}& {}_{\left(K+1\right)2}& \mathrm{.Math.}& {}_{\left(K+1\right)\left(K+1\right)}\end{array}\right],{}_i=\underset{h=1}{\overset{K+1}{.Math.}}\left(\underset{d}{\mathrm{Max}}\left({}_{\mathrm{hd}}\right)\right)$
wherein .sub.hd=E((s.sub.T,hE(s.sub.T,h)).Math.(s.sub.i,dE(s.sub.i,d))), i=1, 2, . . . , N, E() represents to determine an expected value, s.sub.T,h (h=1, 2, . . . , K+1) represents the h.sup.th feature factor of the voltage testable signal under the fault-mode-to-be-tested, s.sub.i,d (d=1, 2, . . . , K+1) represents the d.sup.th feature factor of the prior sample fault modes of the voltage sample signal under the fault mode F.sub.i, the physical meaning of .sub.hd is a correlation coefficient between the h.sup.th feature factor of the voltage testable signal under the fault-mode-to-be-tested and the d.sup.th feature factor of the prior sample fault modes of the voltage sample signal under the prior fault mode F.sub.i,

(15) 0$\underset{d}{\mathrm{Max}}\left({}_{\mathrm{hd}}\right)$
represents the maximum .sub.hd when h is constant and d=1, 2, . . . , (K+1); and

(16) (7) comparing all the .sub.i, and determining a k.sup.th fault mode if

(17) $k=\mathrm{Index}\left(\underset{i}{\mathrm{Max}}\left({}_i\right)\right),$
wherein i=1, 2, . . . , N, and Index() represents to calculate an index.

(18) Referring to FIG. 2, a feature of the K-layer orthogonal Haar wavelet analysis filter set in the step (3) is that each of the layers of the filter set consists of a low-pass filter g(n) and a high-pass filter h(n), output portion of the high-pass filter h(n) is subjected to double downsampling to enter next layer of wavelet filter set, and the output of the low-pass filter g(n) at each layer is subjected to double downsampling and then outputted directly, the low-pass filter g(n)={1/{square root over (2)}, 1/{square root over (2)}}, and the high-pass filter h(n)={1/{square root over (2)}, 1/{square root over (2)}}. In FIG. 2, y.sub.cL (c=1, 2, . . . , K) represents the output of a low pass filter at a c.sup.th layer of the filter set, subscript c represents the serial number of the filter layer of the filter, L represents low-pass; y.sub.KH represents output of a high-pass filter at a k.sup.th layer of the filter set, subscript K represents the serial number of the filter layer of the filter, and H represents high-pass.

(19) Referring to FIG. 3, a method of determining a layer number K of the K-layer orthogonal Haar wavelet analysis filter set in the step (3) is: setting an input signal of the filter set as x, and the outputs of the high-pass filter h(n) and the low-pass filter g(n) at the layer K as y.sub.K,H and y.sub.K,L respectively, then steps of determining the K value are as follows:

(20) (3.1) initializing: K=1, .sub.0=Th, wherein K is the layer number of filters, .sub.0 is an energy ratio threshold, and Th is a preset original value of the energy ratio threshold which can be any real number greater than 0 but less than 1;

(21) (3.2) computing the energy ratio

(22) $=\frac{.Math.y_{K,H},y_{K,H}.Math.}{.Math.x,x.Math.},$
wherein <,> represents to compute an inner product; and

(23) (3.3) if >.sub.0, then K=K+1, returning to execute the step (3.2); otherwise, outputting the layer number of filters K.

(24) Referring to FIG. 4, a method of extracting the feature factor using a blind source processing technology in the step (4) is: setting a signal matrix needing to be processed by the blind source technology as Y.sub.i, wherein an extracted feature factor matrix is S.sub.i=[s.sub.i,1 s.sub.i,2 . . . s.sub.i,d . . . s.sub.i,(K+1)], s.sub.i,d represents the d.sup.th feature factor of the prior sample fault of the voltage sample signal under the fault mode F.sub.i; and the dimensionalities of Y.sub.i and S.sub.i are equal;

(25) (4.1) initializing a feature extracting matrix W.sub.0 and an update step-length , and letting W.sub.1W.sub.0, wherein represents to assign the value of W.sub.0 to W.sub.1, W.sub.0 is any unit matrix, and is a real number between (0, 0.3);

(26) (4.2) computing: S.sub.i=W.sub.0Y.sub.i;

(27) (4.3) updating W.sub.1: W.sub.1W.sub.0+[If[S.sub.i]]g.sup.T[S.sub.i], wherein forms of functions f() and g() herein are respectively f[S.sub.i]=S.sub.i and g[S.sub.i]=S.sub.i.sup.3, g.sup.T() represents matrix transposition; and I represents a standard unit matrix;

(28) (4.4) standardizing W.sub.1:

(29) $W_1\frac{W_1}{.Math.W_1.Math.},$
wherein represents a matrix norm

(30) $\frac{W_1}{.Math.W_1.Math.}$
represents to standardize W.sub.1, and represents to standardize W.sub.1 and then assign a value to W.sub.1; and

(31) (4.5) determining convergence: determining whether W.sub.1W.sub.1.sup.T.fwdarw.I, i.e., determining whether a product of W.sub.1W.sub.1.sup.T is infinitely approaching to I, .fwdarw. represents infinitely approaching; if yes, then outputting S.sub.i; otherwise, W.sub.0W.sub.1, wherein represents assigning, and returning to the step (4.2); and I represents a standard unit matrix.