CN102435934B - Random sampling analog circuit compressed sensing measurement and signal reconstruction method - Google Patents

Abstract

The invention relates to a random sampling analog circuit compressed sensing measurement and signal reconstruction method, which belongs to the field of electronic system test and fault diagnosis. Aiming at a fault signal having a sparsity distribution characteristic per se or in an orthogonal space in an output response of an analog circuit, a test node is selected according to a circuit topology structure, circuit output responses are randomly sampled under a distributed sensor test network, response signals are expressed in a sparse way on a transform domain by utilizing discrete orthonormal basis, compressed sensing measurement of the sparse signals is completed under observability matrix projection, and when the recovery rate of signal reconstruction by randomly compressed sampling points reaches more than 80 percent, the compressed measurement values of the circuit output responses are effective, can form a characteristic set and can be used for analog circuit fault diagnosis. The method solves the problems that the traditional analog signal sampling occupies a large number of hardware resources, large signal reconstruction calculated amount and the like; and the random sampling compressed sensing measurement method is utilized to improve the efficiency of electronic system testing.

Description

A kind of mimic channel compression sensing measurement and signal reconfiguring method of stochastic sampling

Technical field

The present invention relates to fields such as electronic system test and fault diagnosis, be specifically related to a kind ofly for mimic channel compression sensing measurement and response signal reconstructing method, can be applicable in military affairs, communication, electronics, aerospace field related electronic system design checking, integrated circuit testing, manufacturing and encapsulation, automatic test production line and the measuring and controlling equipment research and development.

Background technology

There are problems such as universality is poor, testing efficiency is low, test vector collection redundance height in the custom integrated circuit method of testing, allly multifactorly cause complicated LSI testing cost high, the analog circuit test technical method is conducive to improve the electronic product cost performance efficiently.But component tolerance, output respond continuously and non-linear factor causes analog circuit fault situation complexity various, and the circuit responsive state often needs to be described with the higher-dimension test data.Because the characteristic information amount that mimic channel contains is huge, the diagnosis equation modeling is difficult unusually, and traditional fault dictionary method is difficult to effectively extract fault signature; Starzyk proposes the fault dictionary method, but this method is only applicable to the diagnosis after the fault element modeling, and diagnosis large-scale circuit computing cost is big.If adopt circuit input and output response analysis method, extract time domain or frequency domain response function series nuclear as fault signature, but the on-line testing diagnosis is difficult to realize robotization and intellectuality.The newest research results of Computational intelligence technology such as neural network, wavelet analysis and genetic algorithm is used for finding the solution diagnosis equation, avoid because of computation complexity and the application that influences fault diagnosis consuming time, artificial neural network is directly learnt from observation data (training sample), be used widely as simple and effective discrimination method and heuristic technique, but the substantive test sample data causes it to lack practical value.

In sum, electronic system test and fault diagnosis key are effectively to extract the characteristic information of response signal, because the compressed sensing theoretical breakthrough traditional sampling theorem limit, it realizes Sampling for Wide-Band Signal, processing and transmission with the low rate sample mode.The present invention proposes a kind of mimic channel compression sensing measurement and signal reconfiguring method based on stochastic sampling under this background, improve the electronic system testing efficiency thereby help to construct the best features collection.

Summary of the invention

The objective of the invention is to, at fault-signal itself in the mimic channel output response or under certain transform domain, have sparse property and compressibility characteristics, provide a kind of based on the distributed testing network with compress the Analog Circuits Test Method of sensing measurement technology.Utilizing sensor stochastic sampling failure response signal to finish the mimic channel compression measures and signal reconstruction.The hardware resource that has reduced the sampling of broadband simulating signal, storage and handled has reduced electronic system testing cost and fault diagnosis difficulty.

The present invention has adopted following technical scheme and performing step:

A kind of mimic channel compression sensing measurement and signal reconfiguring method of stochastic sampling is characterized in that, may further comprise the steps:

1. set up the distributed testing network model of mimic channel to be measured and obtain response signal

According to circuit under test topological structure and testing requirement, select the circuit under test output node and sensor be set to obtain response signal, the distributed sensor test network of constructing analog circuit.Each sensor is measured M time same output signal node perception, sensor returns M signal of analog circuit fault response at every turn, every road simulating signal x (t) is through the discrete digital signal x that changes into of A/D stochastic sampling, N is the sampled point number for digital signal length, M＜N, x (t) ∈ R, R is real number, x ∈ R ^{1 * N}

2. the rarefaction of simulating signal x (t) is represented

Simulating signal x (t) is one dimension time domain continuous signal, and it passes through discrete orthogonal basis Ψ to the transform domain vector

Carry out projection.

Wherein,

In non-0 element be K, 0 element is N-K, degree of rarefication K is determined by the Fourier transform of simulating signal x (t).

Be discrete orthogonal basis Ψ ^HExpansion coefficient.Discrete orthogonal basis Ψ gets the white Gaussian noise matrix, Ψ ∈ R ^{N * N}, Ψ ^HBe the associate matrix of Ψ, and Ψ Ψ ^H=Ψ ^HΨ=I, I are unit matrix;

Utilize formula (1) with digital signal x by discrete orthogonal basis Ψ ^HExpansion in series and form:

$x=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\Ψ}}_n^H\widehat{y_n}={\mathrm{\Ψ}}_1^H\widehat{y_1}+\·\·\·+{\mathrm{\Ψ}}_N^H\widehat{y_N}---\left(1\right)$

Process execution is successively as follows represented in the rarefaction of digital signal x:

List of references:

[1] algebraically (Algebra (U.S.) Michael Artin), Guo Jinyun translates, China Machine Press, in January, 2009, P92-93

[2] higher algebra and how much, Pan Yanzhong, Li Hongjun, Xi'an Communications University, 1999, P256-257, P304-305

The element distribution relation is seen shown in the formula (2) in the searching process of discrete orthogonal basis Ψ and the matrix.Anglec of rotation θ ∈ [0 °, 90 °] wherein; The blank space element is 0; Diagonal line is cos θ except two elements, and the number that all the other elements are element 1 between 1, two cos θ increases to N-2 from 0; Sin θ and-sin θ is positioned on the back-diagonal of matrix, first cos θ same column that sin θ and diagonal line occur, second the cos θ that occurs with diagonal line goes together, and first cos θ that-sin θ and diagonal line occur goes together, with second cos θ same column of diagonal line appearance;

At first get θ=0 °, obtain diagonal entry and be 1 unitary matrix

(1) when formula 1 expansion satisfies K/N＜10%, shows to search out the transform domain vector with K degree of rarefication

Digital signal x is carried out rarefaction at discrete orthogonal basis Ψ represent, at this moment, fault-signal self has the sparse property of distribution and compressible characteristics in the mimic channel output response, directly forwards step 3 to and handles;

(2) when formula 1 expansion satisfies K/N＞10%, show also not search out the transform domain vector with K degree of rarefication

Digital signal x is carried out rarefaction at discrete orthogonal basis Ψ represent, fault-signal is at discrete orthogonal basis Ψ in the mimic channel output response ^HHave the sparse property characteristics of distribution.Get θ=10 °, seek a discrete orthogonal basis Ψ again, by formula 1 utilize discrete orthogonal basis Ψ again ^HSimulating signal x (t) is carried out rarefaction to be represented.Sparse property divides following two kinds of situations to judge:

1. if φ _i. satisfy K/N＜10% o'clock, forward step 3 to and handle;

2. if φ _i. satisfy K/N＞10% o'clock, in θ ∈ [0 °, 90 °] scope, change anglec of rotation θ (for example each rotation increases by 10 °) successively from 0 ° to 90 °, seek a new discrete orthogonal basis Ψ again, continue that digital signal x is carried out rarefaction and represent; Up to φ _i. satisfy till K/N＜10%, forward step 3 again to and handle.Otherwise, constantly repeat to seek suitable discrete orthogonal basis Ψ ^HCome rarefaction to represent digital signal x, when seeking discrete orthogonal basis Ψ repeatedly ^HRarefaction represents that the iterations of digital signal x surpasses 10 or K/N＞50%, shows when anglec of rotation θ increases to 90 ° φ _i. still can not satisfy K/N＜10%, can't find suitable discrete orthogonal basis Ψ to come rarefaction to represent digital signal x, the compressed sensing measuring process finishes;

3. be configured to the observing matrix that the response signal rarefaction is represented

Generate the observing matrix of the capable N row of M $\mathrm{\φ}=\left[\begin{array}{ccccc}{\mathrm{\φ}}_{11}& \·& \·& \·& {\mathrm{\φ}}_{1N}\\ \·& & \·& & \·\\ \·& & \·& & \·\\ \·& & \·& & \·\\ {\mathrm{\φ}}_{M1}& \·& \·& \·& {\mathrm{\φ}}_{\mathrm{MN}}\end{array}\right]\∈R^{M\×N}\text{,}$ This moment φ each the row φ _i. the once linear that is considered as a sensor is measured; Each is listed as φ. _jBe considered as simulating signal stochastic sampling compression measured value once; Observing matrix φ represents to utilize sensor to finish the measurement of M sublinear, and each linear measurement all comprises the sampled components of N simulating signal;

Attention: the observing matrix φ that constructs must satisfy following two conditions: with the discrete orthogonal basis Ψ of simulating signal x (t) ^HIrrelevant; Measure under the number condition φ Ψ certain ^HCan accurate reconstruct simulating signal.Consider that based on above factor φ is taken as white Gaussian noise and measures matrix or Bei Nuli measurement matrix.

4. the compressed sensing of digital signal x is measured

Simulating signal x (t) obtains digital signal x after handling through discretize, by obtaining compressed sensing signal y in the formula 3, has picked up the Partial Feature information of simulating signal x (t) after observing matrix φ and digital signal x multiply each other; Therefore, the discrete sampling value of representative simulation signal x (t) on corresponding observation station on the compressed sensing signal y physical significance;

$y=\mathrm{\φx}=\mathrm{\φ}{\mathrm{\Ψ}}^H\hat{y}---\left(3\right)$

5. the restoration and reconstruction of response signal

Utilize the transform domain vector of the measurement of M sublinear and observing matrix φ equivalence under reconstructed number signal x on the probability meaning or discrete orthogonal basis Ψ

Satisfying Under the constraint condition, by the protruding optimization computing of linearity optimizing objective function as shown in Equation 4:

$\min \left|\right|\hat{y}\left|\right|---\left(4\right)$

Wherein, $\left|\right|\hat{y}\left|\right|={({\left(\widehat{y_1}\right)}^2+\·\·\·+{\left(\widehat{y_N}\right)}^2)}^{1/2};$

Described simulating signal restoration and reconstruction process is when the transform domain vector

At observing matrix φ and discrete orthogonal basis Ψ ^HActing in conjunction under, the simulating signal recovery rate reaches 80% when above, these discrete orthogonal basis expansion coefficients

Can be considered the compressed sensing measured value of stochastic sampling mimic channel;

Creativeness of the present invention is mainly reflected in:

1. analog circuit fault response signal sampling mass data takies hardware resources such as a large amount of storages, transmission and processing, have distribute sparse property and compressibility characteristics when response signal self or at some orthogonal intersection space transform domains, the present invention with than low rate the mimic channel response signal is carried out that compressed sensing is measured and with high probability reconstruct it.The stochastic sampling mode is applicable to digital circuit, mimic channel and Digital Analog Hybrid Circuits test, reduces electronic system on-line testing cost, with compressed sensing measured value structure circuit feature collection, realizes the electronic system fault diagnosis.

2. the present invention is by the response of distributed testing network stochastic sampling analog circuit fault, seek the signal sparse expression formula on certain orthogonal intersection space transform domain, sensor is measured M time simulating signal x (t) perception, returns M linear measurement and constitutes observing matrix φ, with discrete orthogonal basis Ψ ^HCarry out inner product operation and obtain the compressed sensing measured value.If the simulating signal recovery rate reaches more than 80%, show that the compressed sensing measured value of analog circuit fault response is effective, but the structural attitude collection is used for circuit fault diagnosis.

For convenience of description, the present invention stresses that the digital signal x after the sampling is carried out compressed sensing and measures, the method of testing that proposes is equally applicable to digital circuit, mimic channel and the test of modulus hybrid circuit and fault diagnosis etc., all should belong to scope of the present invention as long as adopt principle of the present invention to carry out the electronic system test.

Description of drawings

Fig. 1 is the synoptic diagram of the measurement of mimic channel compressed sensing and signal reconstruction process

Fig. 2 is the synoptic diagram of test case circuit

Fig. 3 is the synoptic diagram of the measurement of simulating signal compressed sensing and signal reconstruction effect

Embodiment

The invention will be further described in conjunction with the accompanying drawings and embodiments now.The present invention program's effect is described with a concrete example below.

The test case circuit as shown in Figure 2, select 7 test nodes that sensor is set respectively arbitrarily at the mimic channel output node, constructing a distributed testing network, is that example is set forth its compression measurement and signal reconstruction effect with the 7th sensor stochastic sampling failure response signal only below.

The sparse signal generative process that satisfies frequency domain K degree of rarefication is defined as follows:

1. the processing of the discretize of simulating signal x (t) and rarefaction are represented:

If the simulating signal x (t) of the 7th node output of mimic channel one dimension time domain as shown in Equation 5.

x(t)＝0.3cos(2πf ₁T _st _s)+0.6cos(2πf ₂T _st _s)+0.1cos(2πf ₃T _st _s)+0.9cos(2πf ₄T _st _s) （5）

If to response signal stochastic sampling 64 times, i.e. M=64; Sampling number is 128, i.e. N=128; Response signal is carried out the FFT computing determine degree of rarefication K=7.All the other relative parameters setting are:

f ₁=50Hz, f ₂=100Hz, f ₃=200Hz, f ₄=400Hz, f _s=800Hzt _s=1/f _s=1/800, T _sIt is 128 digital signal x that=1/N=1/128 is launched into length with simulating signal x (t), x (t) ∈ R, n=1 ... N,

Be the transform domain vector, discrete orthogonal basis Ψ value as shown in Equation 6.

Ψ ^HBe the associate matrix of Ψ, and Ψ Ψ ^H=Ψ ^HΨ=I at first makes θ=0 °, searches out a discrete orthogonal basis Ψ, more by formula 7 with x (t) with discrete orthogonal basis Ψ ^HAt the transform domain vector Last expansion:

$x=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\Ψ}}_n^H\widehat{y_n}={\mathrm{\Ψ}}_1^H\widehat{y_1}+\·\·\·+{\mathrm{\Ψ}}_N^H\widehat{y_N}\underset{\‾}{;}---\left(7\right)$

The discrete orthogonal basis Ψ of digital signal x ^HLaunch vector

In, because 7＜＜128, satisfying 5%＜10%, 7 elements of 7/128 ≈ is non-0 value, 121 elements are 0 value, so carrying out rarefaction under discrete orthogonal basis Ψ effect, digital signal x represents, at this moment,

For satisfying the transform domain vector of K degree of rarefication.

2. the compressed sensing measuring process of simulating signal x (t):

Because observing matrix φ ∈ R herein ^{64 * 128}Be the white Gaussian noise matrix, with function wgn (64,128,1) generation observing matrix be ${\mathrm{\φ}}_{64\×128}=\left[\begin{array}{ccccc}-0.4853& \·& \·& \·& 0.3563\\ \·& & \·& & \·\\ \·& & \·& & \·\\ \·& & \·& & \·\\ -2.1027& \·& \·& \·& -1.4182\end{array}\right],$ Digital signal x is carried out rarefaction represent to measure with compressed sensing, obtain 64 groups of linear measurements respectively, every group of vector comprises 128 sampled data points.Utilize formula 3 that digital signal x is passed through observing matrix φ _{64 * 128}Project on the transform domain, the position of maximal projection coefficient is followed successively by [65,33,97,17,113,9,121,125,5,112,18,61,69,4] on the record coordinate, reconstruct spectral domain vector Β _{1 * 128}In, except above 14 for nonzero element is other is neutral element, rarefaction is represented effectively based on claim 2 judgement digital signal x.

Checking compressed sensing measured value is to the restoration and reconstruction effect of simulating signal x (t) below.Digital signal x is at observing matrix φ _{64 * 128}Effect obtains reconstruction signal y to its restoration and reconstruction down.At this moment, restructuring procedure is equivalent to observing matrix φ _{64 * 128}With discrete orthogonal basis Ψ ^HTo the transform domain vector

The acting in conjunction result.

Satisfy equation

Under the constraint, to the orthogonal transform domain vector Delivery,

The optimizing objective function

The one group of sparse coefficient vector that makes the mould minimum is the sparse transform domain vector of simulating signal x (t).The restoration and reconstruction effect of digital signal x as shown in Figure 3, stochastic sampling to the precision of compression sensing measurement value reconstruction signal reach 95%, show that the compressed sensing of analog circuit fault response signal is measured effectively.

Claims (1)

1. the mimic channel of stochastic sampling compression sensing measurement and signal reconfiguring method is characterized in that, may further comprise the steps:

1) structure mimic channel to be measured the distributed testing network and obtain response signal

Select the test node of mimic channel to be measured and sensor is set to obtain response signal, each sensor is measured M time the output signal perception of same node, and sensor returns M response signal of mimic channel at every turn; Simulating signal x (t) turns to digital signal x through the A/D stochastic sampling is discrete, and N is that the digital signal x after the discretize is the sampled point number, M＜N, and x (t) ∈ R, R is real number, x ∈ R ^{1 * N}

2) rarefaction of simulating signal x (t) is represented

Simulating signal x (t) is one dimension time domain continuous signal, and it passes through discrete orthogonal basis Ψ to the transform domain vector

Carry out projection;

, wherein,

In non-0 element be K, 0 element is N-K, degree of rarefication K is determined by the Fourier transform of simulating signal x (t);

Be discrete orthogonal basis expansion coefficient; Discrete orthogonal basis Ψ gets the white Gaussian noise matrix, Ψ ∈ R ^{N * N}, Ψ ^HBe the associate matrix of Ψ, and Ψ Ψ ^H=Ψ ^HΨ=I, I are unit matrix;

Utilize formula (1) with digital signal x by discrete orthogonal basis Ψ ^HExpansion in series and form:

$x=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\Ψ}}_n^H\widehat{y_n}={\mathrm{\Ψ}}_1^H\widehat{y_1}+\·\·\·+{\mathrm{\Ψ}}_N^H\widehat{y_N}---\left(1\right)$

Process execution is successively as follows represented in the rarefaction of digital signal x:

The element distribution relation is seen shown in the formula (2) in the searching process of discrete orthogonal basis Ψ and the matrix; Anglec of rotation θ ∈ [0 °, 90 °] wherein; The blank space element is 0; Diagonal line is cos θ except two elements, and the number that all the other elements are element 1 between 1, two cos θ increases to N-2 from 0; Sin θ and-sin θ is positioned on the back-diagonal of matrix, first cos θ same column that sin θ and diagonal line occur, second the cos θ that occurs with diagonal line goes together, and first cos θ that-sin θ and diagonal line occur goes together, with second cos θ same column of diagonal line appearance;

At first get θ=0 °, obtain diagonal entry and be 1 unitary matrix (1) when formula (1) expansion satisfies K/N＜10%, shows to search out the transform domain vector with K degree of rarefication Digital signal x is carried out rarefaction at discrete orthogonal basis Ψ represent, at this moment, fault-signal self has the sparse property of distribution and compressible characteristics in the mimic channel output response, directly forwards step 3) to and handles; (2) satisfy K/N when formula (1) expansion〉10% the time, show also not search out the transform domain vector with K degree of rarefication

Digital signal x is carried out rarefaction at discrete orthogonal basis Ψ represent, the analog circuit fault response signal is at discrete orthogonal basis Ψ ^HHave the sparse property characteristics of distribution; Get θ=10 °, seek a discrete orthogonal basis Ψ again, more by formula (1) utilizes discrete orthogonal basis Ψ ^HSimulating signal x (t) is converted to sparse signal; Divide following two kinds of situations to judge:

1. if φ _ISatisfy K/N＜10% o'clock, forward step 3) to and handle;

2. if φ _ISatisfy K/N〉10% o'clock, in θ ∈ [0 °, 90 °] scope, change anglec of rotation θ successively from 0 ° to 90 °, seek a new discrete orthogonal basis Ψ again, continue that digital signal x is carried out rarefaction and represent; Up to φ _ISatisfy till K/N＜10%, forward step 3) again to and handle; Otherwise, constantly repeat to seek suitable discrete orthogonal basis Ψ ^HCome rarefaction to represent digital signal x, when seeking discrete orthogonal basis Ψ repeatedly ^HRarefaction represent the iterations of digital signal x surpass 10 or K/N 50%, show when anglec of rotation θ increases to 90 ° φ _IStill can not satisfy K/N＜10%, can't find suitable discrete orthogonal basis Ψ to come rarefaction to represent digital signal x, the compressed sensing measuring process finishes;

3) be configured to the observing matrix that the response signal rarefaction is represented

Generate the observing matrix of the capable N row of M

, this observing matrix is that white Gaussian noise is measured matrix or Bei Nuli measures matrix; This moment φ each the row φ _IThe once linear that is considered as a sensor is measured; Each is listed as φ _JBe considered as response signal stochastic sampling compression measured value once; Observing matrix φ represents to utilize sensor to finish the measurement of M sublinear, and each linear measurement all comprises the sampled components of N response signal;

4) compressed sensing of digital signal x is measured

Simulating signal x (t) obtains digital signal x after handling through discretize, obtains perception compressed signal y by formula (3), has picked up the Partial Feature information of simulating signal x (t) after matrix φ and digital signal x multiply each other; The discrete sampling value of perception compressed signal y representative simulation signal x (t) on corresponding observation station;

$y=\mathrm{\φx}={\mathrm{\φ\Ψ}}^H\hat{y}---\left(3\right)$

Carry out the method for signal reconstruction, step is as follows:

Utilize the transform domain vector of the measurement of M sublinear and observing matrix φ equivalence under reconstructed number signal x on the probability meaning or discrete orthogonal basis Ψ

, satisfying

Under the constraint condition, by the protruding optimization computing of linearity optimizing objective function as shown in Equation (4):

$\min \left|\right|\hat{y}\left|\right|---\left(4\right)$

Wherein, $\left|\right|\hat{y}\left|\right|={({\left(\widehat{y_1}\right)}^2+\·\·\·+{\left(\widehat{y_N}\right)}^2)}^{1/2};$

Described simulating signal restoration and reconstruction process is when the transform domain vector

At observing matrix φ and discrete orthogonal basis Ψ ^HUnder the acting in conjunction, the simulating signal recovery rate reaches 80% when above, these discrete orthogonal basis expansion coefficients

Can be considered the compressed sensing measured value of stochastic sampling mimic channel.

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