CN104007234A - Mixed gas composition identification method based on underdetermined blind source separation - Google Patents

Abstract

The invention discloses a mixed gas composition identification method based on underdetermined blind source separation, and belongs to the mixed gas composition identification problem; the problem of underdetermined blind source separation using N kinds of sensors for detecting and identifying M kinds of mixed gas components can be solved (N<M); the mixed gas composition identification method includes the following steps: step one, sampling with a gas sensor array to obtain a gas concentration signal, pretreating to obtain a observation signal matrix; step two, using a self-adaptive decomposition algorithm to construct a sparse representation blind source separation model of mixed gas signals on the basis of ensuring of the signal sparsity; step three, selecting a linearly independent vector for clustering to realize estimation of a mixed matrix in the blind source separation model; and step four, using a l1 bound norm minimizing improvement method to separate the mixed gas signals to realize identification of a mixed gas.

Description

A kind of mixed gas composition recognition methods based on owing the separation of surely blind source

Technical field

The present invention relates to gas sensor signal processing technology field, particularly a kind of mixed gas composition recognition methods based on owing the separation of surely blind source.

Background technology

Gas sensor ubiquity cross-sensitivity, same sensor may be responsive to multiple gases, when the kind of mixed gas is a lot, traditional technical scheme is to arrange more sensor array, make the number of sensor more than the kind of mixed gas, by solving overdetermined nonlinear equation, but the response more complicated of gas sensor, cause system of equations to there is nonlinearity, need certain intelligent algorithm could detect the kind of identification mixed gas, cause gas recognizer to there is very high complicacy.Therefore,, how in the situation that the kind of sensor is less, accurately the kind of fast detecting identification mixed gas, is also the hot issue research that current mixed gas detects identification.

Owing surely blind source separation theorem is that occur in recent years a kind of owing under the basic model of surely blind source separation, fully introduces sparse signal and characterizes, and utilizes the sparse property of signal to carry out estimated mixing matrix column vector.As insufficient in signal sparse, can utilize adaptive decomposition algorithm to make source signal on transform domain, well meet sparse property, thereby create conditions for estimated mixing matrix.

Summary of the invention

(1) technical matters solving

For overcoming above-mentioned the deficiencies in the prior art, the invention provides a kind of mixed gas composition recognition methods based on owing the separation of surely blind source, to solve in current gas identification, require gas sensor number to be fully greater than mixed gas kind, and storage transmission quantity is large, identify the problems such as inaccurate, reach the object with less sensor, the less accurate qualitative identification of data volume.

(2) technical scheme

To achieve the above object, the invention provides a kind of mixed gas composition recognition methods based on owing the separation of surely blind source, the method comprises, step 1: with gas sensor array sampling, obtain gas concentration signal, by pre-service, obtain observation signal matrix; Step 2: the blind source of the rarefaction representation disjunctive model that builds gas mixed signal; Step 3: estimate the hybrid matrix in the disjunctive model of blind source; Step 4: the separation of gas source signal, the identification of mixed gas; It is characterized in that, step is:

Step 1: described obtain sampled signal and pre-service, specifically comprise: mixed signal is being carried out before blind separation, we need to first carry out some pre-service.It is the average of removing signal that processing procedure mainly contains two one, and another is albefaction.

Step 2: the sparse blind source disjunctive model of setting up gas mixed signal.A kind of mixed gas composition recognition methods based on owing the separation of surely blind source according to claim 1, is characterized in that, step 2, in order to guarantee the sparse property of signal, adopts the rarefaction representation of adaptive decomposition algorithm picked up signal.The sparse of the X of a matrix can be expressed as X=C _xΦ, wherein $C_X=\left[\begin{array}{c}{c}_{x1}\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ c_{\mathrm{xp}}\end{array}\right]=[C_X\left(1\right)\&CenterDot;\&CenterDot;\&CenterDot;C_X\left(K\right)],$ By calculating the C of X=AS _xmatrix can be simplified the separation problem of this patent, so far obtains the sparse model X=AC that a universe is mixed _sΦ, wherein

$C_S=\left[\begin{array}{c}{c}_{s1}\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ c_{s2}\end{array}\right]=[C_S\left(1\right)\&CenterDot;\&CenterDot;\&CenterDot;C_S\left(K\right)].$

Step 3: estimate the hybrid matrix in the disjunctive model of blind source: 31: setup parameter r ₀if, || x (t) || ₂< r ₀, t=1,2 ..., N ₁, observation signal vector x (t) is removed, remember that remaining observation signal is x (t), t=1,2 ..., N ₁; 32: setup parameter M, ε ₁, ε ₂, ε ₃, make k=1; 33: find out observation signal point set x (1), x (2) ..., xN _k) in m-1 linearly independent vector, by solving equations, obtain and this group vector unit normal vector n of quadrature all _k, calculate set x (1), x (2) ..., x (N _k) meet formula observation signal number P _k; P _k< M, set x (1), x (2) ..., x (N _k) in find out again an other m-1 linearly independent vector, repeat said process, until find the vector n satisfying condition _k; 34: remove x (1), x (2) ..., x (N _k) in vector n _kmeet formula p _k< M observation signal point.The set of note after removing for x (1), x (2) ..., x (N _k+1), N _k+1> M, makes k=k+1, turns Step3, otherwise, turn step5; 35: the normal vector set { n remembering ₁, n ₂..., n _d, pass through solving equation integer solution, obtain source signal number n and size; 36: set { n ₁, n ₂..., n _din m-1 linearly independent vector be classified as a class, can gather q class altogether.In each class, by solving equations obtain with such in institute's directed quantity vectorial w of quadrature all _j, calculate set { n ₁, n ₂..., n _din with vectorial w _j, meet formula vectorial number k _jif, such is removed, j=1,2 ..., l 37: remember that remaining vector is w _j,, j=1,2 ..., l, will meet formula || w _i|-| w _j|| < ε ₃, i, j=1,2 ..., r _i, i ≠ j, vector (j=1,2 ..., l) being classified as a class, the vector of each class forms matrix W ⁱ=[w ₁, w ₂..., w _ri], j=1,2 ..., q; 38: according to formula w in compute matrix ^jr _ithe mean vector e of individual vector _i, vectorial e _ibe the estimation of the column vector of matrix A, j=1,2 ..., q.

Step 4: the separation of gas source signal, the identification of mixed gas.Specifically comprise following components: 41: obtain A's individual M * M ties up submatrix, is made as $B_k=[a_{k_l},\&CenterDot;\&CenterDot;\&CenterDot;,a_{k_M}],$ K=1, k ₁..., k _m∈ 1 ..., N}; 42: to a certain moment t, according to following formula, obtain l ₁the feasible solution of Norm minimum problem, is designated as ${\hat{s}}^{\left(k\right)}\left(t\right)={[{\hat{s}}_1^{\left(k\right)}\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\hat{s}}_N^{\left(k\right)}\left(t\right)]}^T,$ k＝1,,

43: according to following formula, obtain corresponding l ₁norm J _k, k=1,, k=1,, 44: according to following formula, determine minimum l ₁norm Solution and the estimation of (t) using it as s k=1,, l ₁norm is designated as J _min, corresponding k value is k _min; 45: setting threshold r, for differentiating the l of feasible solution ₁norm J _kwhether enough little; 46: for each k=1 ..., and k ≠ k _minif, | J _k-J _min| < rJ _min, claim for l ₁the suboptimal solution of Norm minimum problem, is designated as these suboptimal solutions c=1 ..., C, the number that C is suboptimal solution.The l that these suboptimal solutions are corresponding ₁norm is designated as J ^(c); 47: according to following formula, determine minimum l ₁

Norm Solution weighting coefficient, be designated as p _min.P _minwith J _minbe inversely proportional to. 48: according to following formula, determine suboptimal solution weighting coefficient, be designated as respectively p ^(c), c=1 ..., C.P ^(c)with J ^(c)be inversely proportional to, c=1 ..., C; 49: according to following formula by minimum l ₁norm Solution with all suboptimal solutions be weighted stack, its result replaces minimum l ₁norm Solution, as the estimation of s (t) $\hat{s}\left(t\right)=p_{\min }\&CenterDot;{\hat{s}}_{\min }\left(t\right)+\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}(p^{\left(c\right)}\&CenterDot;{\hat{s}}^{\left(c\right)}\left(t\right))$ Obtain all moment obtain the estimation of source signal.

Accompanying drawing explanation

Clearer in order to be object of the present invention, technical scheme and beneficial effect, the invention provides following accompanying drawing and describe:

Fig. 1 is the process flow diagram of gas componant recognition methods of the present invention.

Embodiment

Below in conjunction with example, the present invention is described.

Step 1: described obtain sampled signal and pre-service, specifically comprise: mixed signal is being carried out before blind separation, we need to first carry out some pre-service.It is the average of removing signal that processing procedure mainly contains two one, and another is albefaction.

Step 2: the sparse blind source disjunctive model of setting up gas mixed signal.A kind of mixed gas composition recognition methods based on owing the separation of surely blind source according to claim 1, is characterized in that, step 2, in order to guarantee the sparse property of signal, adopts the rarefaction representation of adaptive decomposition algorithm picked up signal.The sparse of the X of a matrix can be expressed as X=C _xΦ, wherein $C_X=\left[\begin{array}{c}{c}_{x1}\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ c_{\mathrm{xp}}\end{array}\right]=[C_X\left(1\right)\&CenterDot;\&CenterDot;\&CenterDot;C_X\left(K\right)],$ By calculating the C of X=AS _xmatrix can be simplified the separation problem of this patent, so far obtains the sparse model X=AC that a universe is mixed _sΦ, wherein

$C_S=\left[\begin{array}{c}{c}_{s1}\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ c_{s2}\end{array}\right]=[C_S\left(1\right)\&CenterDot;\&CenterDot;\&CenterDot;C_S\left(K\right)].$

Step 3: estimate the hybrid matrix in the disjunctive model of blind source: 31: setup parameter r ₀if, || x (t) || ₂< r ₀, t=1,2 ..., N ₁, observation signal vector x (t) is removed, remember that remaining observation signal is x (t), t=1,2 ..., N ₁; 32: setup parameter M, ε ₁, ε ₂, ε ₃, make k=1; 33: find out observation signal point set x (1), x (2) ..., x (N _k) in m-1 linearly independent vector, by solving equations, obtain and this group vector unit normal vector n of quadrature all _k, calculate set x (1), x (2) ..., x (N _k) meet formula observation signal number P _k; P _k< M, set x (1), x (2) ..., x (N _k) in find out again an other m-1 linearly independent vector, repeat said process, until find the vector n satisfying condition _k; 34: remove x (1), x (2) ..., x (N _k) in vector n _kmeet formula p _k< M observation signal point.The set of note after removing for x (1), x (2) ..., x (N _k+1), N _k+1> M, makes k=k+1, turns Step3, otherwise, turn step5; 35: the normal vector set { n remembering ₁, n ₂..., n _d, pass through solving equation integer solution, obtain source signal number n and size; 36: set { n ₁, n ₂..., n _din m-1 linearly independent vector be classified as a class, can gather q class altogether.In each class, by solving equations obtain with such in institute's directed quantity vectorial w of quadrature all _j, calculate set { n ₁, n ₂..., n _din with vectorial w _j, meet formula vectorial number k _jif, such is removed, j=1,2 ... V, l 37: remember that remaining vector is w _j,, j=1,2 ..., l, will meet formula || w _i|-| w _j|| < ε ₃, i, j=1,2 ..., r _i, i ≠ j, vector (j=1,2 ..., l) being classified as a class, the vector of each class forms matrix W ⁱ=[w ₁, w ₂..., w _ri], j=1,2 ..., q; 38: according to formula w in compute matrix ^jr _ithe mean vector e of individual vector _i, vectorial ei is the estimation of the column vector of matrix A, j=1, and 2 ..., q.

Step 4: the separation of gas source signal, the identification of mixed gas.Specifically comprise following components: 41: obtain A's individual M * M ties up submatrix, is made as $B_k=[a_{k_l},\&CenterDot;\&CenterDot;\&CenterDot;,a_{k_M}],$ K=1,, k ₁..., k _m∈ 1 ..., N}; 42: to a certain moment t, according to following formula, obtain l ₁the feasible solution of Norm minimum problem, is designated as ${\hat{s}}^{\left(k\right)}\left(t\right)={[{\hat{s}}_1^{\left(k\right)}\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\hat{s}}_N^{\left(k\right)}\left(t\right)]}^T,$ K=1,, 43: according to following formula, obtain corresponding l ₁norm J _k, k=1,, k=1,, 44: according to following formula, determine minimum l ₁norm Solution and the estimation of (t) using it as s k=1,, l ₁norm is designated as J _min, corresponding k value is k _min; 45: setting threshold r, for differentiating the l of feasible solution ₁norm J _kwhether enough little; 46: for each k=1,, and k ≠ k _minif, | J _k-J _min| < rJ _min, claim for l ₁the suboptimal solution of Norm minimum problem, is designated as these suboptimal solutions , c=1 ..., C, the number that C is suboptimal solution.The l that these suboptimal solutions are corresponding ₁norm is designated as J ^(c); 47: according to following formula, determine minimum l ₁norm Solution weighting coefficient, be designated as p _min.P _minwith J _minbe inversely proportional to. 48: according to following formula, determine suboptimal solution weighting coefficient, be designated as respectively p ^(c), c=1 ..., C.P ^(c)with J ^(c)be inversely proportional to, c=1 ..., C; 49: according to following formula by minimum l ₁norm Solution with all suboptimal solutions be weighted stack, its result replaces minimum l ₁norm Solution, as the estimation of s (t) $\hat{s}\left(t\right)=p_{\min }\&CenterDot;{\hat{s}}_{\min }\left(t\right)+\underset{c=1}{\overset{C}{\mathrm{\&Sigma;}}}(p^{\left(c\right)}\&CenterDot;{\hat{s}}^{\left(c\right)}\left(t\right))$ Obtain all moment obtain the estimation of source signal.

Claims (5)

1. the mixed gas composition recognition methods based on owing the separation of surely blind source, detects people by sensor and can obtain the data that contain information, by processing these data acquisition information, and these information is processed the ability of acquire knowledge and nature remodeling; In the more situation of the composition of mixed gas, how to utilize the less sensor of kind, accurately fast detecting identifies each composition and the kind in mixed gas, this patent adopts owes to determine blind source separation method based on rarefaction representation, the method is well isolated various compositions for original signal the unknown and the unknown combination gas physical efficiency of hybrid mode, it is characterized in that:

Key step comprises as follows:

Step 1: obtain gas concentration signal with gas sensor array sampling, obtain observation signal matrix by pre-service;

Step 2: by adaptive decomposition algorithm, guarantee, on the basis of the sparse property of signal, to build the blind source of the rarefaction representation disjunctive model of mixed gas signal;

Step 3: carry out cluster by choosing linearly independent vector, realize the hybrid matrix of estimating in the disjunctive model of blind source;

Step 4: utilize and improve l1 Norm minimum method, mixed gas signal is carried out to separation, realize the identification of mixed gas.

2. a kind of mixed gas composition recognition methods based on owing the separation of surely blind source according to claim 1, it is characterized in that, step 1 is exactly that this each composition of unknown mixed gas is considered as to blind source, by sensor array, obtain the mixed signal in blind source, and the pre-service of going average and albefaction.

3. a kind of mixed gas composition recognition methods based on owing the separation of surely blind source according to claim 1, it is characterized in that, step 2, in order to guarantee the sparse property of signal, adopts the rarefaction representation of adaptive decomposition algorithm picked up signal, and the sparse of the X of a matrix can be expressed as X=C _xΦ, by calculating the C of X=AS _xmatrix can be simplified the separation problem of this patent, so far obtains the sparse model X=AC that a universe is mixed _sΦ, wherein

4. a kind of mixed gas composition recognition methods based on owing the separation of surely blind source according to claim 1, is characterized in that, step 3 is taked following mode: 41: setup parameter r ₀if, || x (t) || ₂< r ₀, t=1,2 ..., N ₁, observation signal vector x (t) is removed, remember that remaining observation signal is x (t), t=1,2 ..., N ₁; 42: setup parameter M, ε ₁, ε ₂, ε ₃, make k=1; 43: find out observation signal point set x (1), x (2) ..., x (N _k) in m-1 linearly independent vector, by solving equations, obtain and this group vector unit normal vector n of quadrature all _k, calculate set x (1), x (2) ..., x (N _k) meet formula observation signal number P _k; If P _k< M set x (1), x (2) ..., x (N _k) in find out again an other m-1 linearly independent vector, repeat said process, until find the vector n satisfying condition _k; 44: remove x (1), x (2) ..., x (N _k) in vector n _kmeet formula p _k< M observation signal point.The set of note after removing for x (1), x (2) ..., x (N _k+1), if N _k+1> M, k=k+1 turns step3, otherwise, turn step5; 45: the normal vector set of remembering is { n ₁, n ₂..., n _dpass through solving equation integer solution, obtain source signal number n and size; 46: set { n ₁, n ₂..., n _din m-1 linearly independent vector be classified as a class, can gather q class altogether.In each class, by solving equations obtain with such in institute's directed quantity vectorial w of quadrature all _j, calculate set { n ₁, n ₂..., n _din with vectorial w _jmeet formula vectorial number k _jif, , such is removed, j=1,2 ..., l; 47: remember that remaining vector is w _j, j=1,2 ..., l will meet formula || w _i|-| w _j|| < ε ₃, i, j=1,2 ..., ri, the vectorial w of i ≠ j _j, j=1,2 ..., l will be classified as a class, and the vector of each class forms square W ⁱ=[w ₁, w ₂..., w _ri] j=1,2 ..., q; 48: according to formula w in compute matrix ^jr _ithe mean vector e of individual vector _i, vectorial e _ibe the column vector a of matrix A _jestimation, j=1,2 ..., q.

5. a kind of mixed gas composition recognition methods based on owing the separation of surely blind source according to claim 1, is characterized in that, step 4 is taked following mode: 51: obtain A's individual M * M ties up submatrix, is made as k=1 ..., k ₁..., k _m∈ 1 ..., N}; 52: to a certain moment t, according to following formula, obtain l ₁the feasible solution of Norm minimum problem, is designated as k=1 ..., 53: according to following formula, obtain corresponding l ₁norm J _k, k=1 ..., 54: according to following formula, determine minimum l ₁norm Solution and the estimation of (t) using it as s l ₁norm is designated as J _min, corresponding k value is k _min; 55: setting threshold r, for differentiating the l of feasible solution ₁norm J _kwhether enough little; 56: for each k=1 ..., and k ≠ k _minif, | J _k-J _min| < rJ _min, claim (t) be l ₁the suboptimal solution of Norm minimum problem, is designated as these suboptimal solutions c=1 ..., C, the number that C is suboptimal solution.The l that these suboptimal solutions are corresponding ₁norm is designated as J ^(c); 57: according to following formula, determine minimum l ₁norm Solution weighting coefficient, be designated as p _min, p _minwith J _minbe inversely proportional to 58: according to following formula, determine suboptimal solution (t) weighting coefficient, is designated as respectively p ^(c), c=1 ..., C _.p ^(c)with J ^(c)be inversely proportional to, c=1 ..., C; 59: according to following formula by minimum l ₁norm Solution with all suboptimal solutions be weighted stack, its result replaces minimum l ₁norm Solution, as the estimation of s (t) obtain all moment obtain the blending constituent of each gas.