1. A capacitance tomography image reconstruction method based on least square target correction is characterized by comprising the following steps:

step one, carrying out normalization processing on the collected capacitance values, substituting a least square function according to preset sensitive field strength, solving a target value meeting the minimum value obtained by the function, and using the target value as an iteration initial value for a subsequent step;

step two, substituting an iteration initial value into a formula according to a designed iteration formula, and solving an initial error matrix of a coefficient matrix for use in subsequent steps;

substituting the initial error matrix into a structural formula, and solving an initial value of a corrected coefficient matrix;

step four, solving a corresponding method matrix aiming at the corrected coefficient matrix, and constructing an initial value of the target matrix according to the method matrix;

step five, solving corresponding regularization parameters according to the targeting matrix by adopting an L-curve method;

step six, simultaneously adding coefficient matrix noise and random observation error vectors, and simulating a real complex noise experimental environment;

and step seven, substituting the parameters into an iteration formula to carry out iterative operation, and obtaining an experimental target estimated value after iteration is finished according to conditions.

2. The capacitance tomography image reconstruction method based on least square targeting correction of claim 1, wherein in step one, the least square function is constructed as f (g) | | SG-C | | y²G is the initial value of the iteration that satisfies the minimum of the function.

3. The method for reconstructing the electric capacitance tomography image based on the least square target correction as claimed in claim 1, wherein in step three, the structural formula is The initial value of the modified coefficient matrix is obtained.

4. The method for reconstructing the electrical capacitance tomography image based on the least square target correction as claimed in claim 1, wherein in the fourth step, based on the eigenvector corresponding to the smaller eigenvalue, the construction formula of the target matrix isG_iIs a normal matrix A^TAnd A is a feature vector corresponding to the small singular value. The method for judging the small eigenvalue can use the proportion of the sum of the standard difference components of the eigenvalue to the standard difference to reach more than 95 percent, namelyIn the formula_iIs a normal matrix A^TAnd A is the characteristic value. Matrix arrayOnly small singular values are corrected and can be called as a targeting matrix, so that unnecessary deviation is avoided while variance is reduced, and estimation is more reasonable.

5. The method for reconstructing the capacitance tomography image based on the least square target correction as claimed in claim 1, wherein in step six, random noise e is added to the normalized capacitance C and the coefficient matrix S respectively in order to verify the adaptability of the algorithm to the noise_L～N(0,σ²I_m)，σ is 0.1. The random noise is generated by Matlab.

Background

The electric capacity chromatography imaging technology is a novel multiphase flow detection technology. The principle of the method is that data are collected through an electrode array installed on the outer side of a pipeline, real-time visual measurement is conducted on dielectric constant distribution inside the pipeline, corresponding processing, collection, filtering, amplification and other operations are conducted on capacitance values between electrode pairs obtained by a sensor through a data collection unit, image reconstruction is conducted through an image reconstruction algorithm, and therefore the process of outputting images and obtaining final images is conducted. The capacitance tomography system has been gradually applied in the field of multiphase flow due to its advantages of non-invasion, fast response speed, simple structure, no radiation, wide application range, good real-time property, etc. In the whole implementation process of the capacitance tomography, an image reconstruction algorithm is the most critical step and is a critical problem which needs to be solved effectively at present, and the image reconstruction algorithm directly influences the definition and the precision of imaging.

Disclosure of Invention

The invention aims to provide a capacitance tomography image reconstruction method based on least square target correction, which can effectively reduce the influence of a complex noise environment on the accuracy of a capacitance tomography image reconstruction result.

A capacitance tomography image reconstruction method based on least square targeting correction comprises the following steps:

step one, carrying out normalization processing on the collected capacitance values, substituting a least square function according to preset sensitive field strength, solving a target value meeting the minimum value obtained by the function, and using the target value as an iteration initial value for a subsequent step;

step two, substituting an iteration initial value into a formula according to a designed iteration formula, and solving an initial error matrix of a coefficient matrix for use in subsequent steps;

substituting the initial error matrix into a structural formula, and solving an initial value of a corrected coefficient matrix;

step four, solving a corresponding method matrix aiming at the corrected coefficient matrix, and constructing an initial value of the target matrix according to the method matrix;

step five, solving corresponding regularization parameters according to the targeting matrix by adopting an L-curve method;

step six, simultaneously adding coefficient matrix noise and random observation error vectors, and simulating a real complex noise experimental environment;

and step seven, substituting the parameters into an iteration formula to carry out iterative operation, and obtaining an experimental target estimated value after iteration is finished according to conditions.

In the first step, a least square function is specifically constructed as f (g) | | SG-C | | non-calculation²G is the initial value of the iteration that satisfies the minimum of the function.

Further, in the third step, the structural formula is The initial value of the modified coefficient matrix is obtained.

Further, in the fourth step, based on the eigenvector corresponding to the smaller eigenvalue, the structural formula of the targeting matrix is as followsGi is the eigenvector corresponding to the small singular value of the Fa matrix ATA. The method for judging the small eigenvalue can use the proportion of the sum of the standard difference components of the eigenvalue to the standard difference to reach more than 95 percent, namelyIn the formula_iIs a normal matrix A^TAnd A is the characteristic value. Matrix arrayOnly small singular values are corrected and can be called as a targeting matrix, so that unnecessary deviation is avoided while variance is reduced, and estimation is more reasonable.

Further, in the sixth step, in order to verify the adaptability of the algorithm to noise, random noise e is added to the normalized capacitor C and the coefficient matrix S respectively_L～N(0，σ²I_m)，σ＝0.1。

The main advantages of the invention are: the invention firstly uses least square to calculate iterative estimation, converts the ill-conditioned problem into the nonlinear unconstrained minimization problem, avoids the matrix inversion problem, continuously mutates the coefficient matrix in the iterative process, also presents the ill-conditioned problem in the solving process, and aims at solving the final estimation accuracy problem brought by the problem, the invention combines the capacitance tomography image reconstruction working principle, the coefficient matrix is corrected in a targeted way in the overall least square iterative process, a new coefficient matrix is firstly solved, then a regularization matrix corrected by self-adaptive targeted singular values is obtained, thereby reducing the ill-conditioned problem, introducing the mathematical model of EIV, aiming at the problem that the measured data and the coefficient matrix have errors of different degrees, the total least square iteration method is further subjected to targeted correction, the problem of influence of external noise interference on measurement data is solved, and finally the optimal estimated value of imaging is calculated in an iterative mode. Experimental results show that the method can effectively solve the problem that the image reconstruction effect is not ideal enough in precision in a complex noise environment.

Drawings

FIG. 1 is a flowchart of a least square targeting correction-based capacitance tomography image reconstruction method according to the present invention;

FIG. 2 is a core flow pattern processing effect diagram, wherein FIG. 2(a) is a core flow original flow pattern diagram, and FIG. 2(b) is an image reconstructed by the method;

FIG. 3 is a view of the effect of laminar flow pattern processing, wherein FIG. 3(a) is a view of the original laminar flow pattern, and FIG. 3(b) is a reconstructed image by the method;

fig. 4 is a processing effect diagram of a circulation flow pattern, wherein fig. 4(a) is a circulation original flow pattern diagram, and fig. 4(b) is an image reconstructed by the method.

Detailed Description

The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

As shown in fig. 1 to 4, an example of a capacitance tomography image reconstruction method based on least square target correction according to the present embodiment includes the following steps:

step one, carrying out normalization processing on the collected capacitance values, substituting a least square function according to preset sensitive field strength, solving a target value meeting the minimum value obtained by the function, and using the target value as an iteration initial value for a subsequent step;

f(G)＝||SG-C||²＝min

f (G) is a least square function, and G is an iteration initial value which satisfies the minimum value of the function.

Step two, substituting an iteration initial value into a formula according to a designed iteration formula, and solving an initial error matrix of a coefficient matrix for use in subsequent steps;

wherein R is a regularization matrix and α is a regularization parameter greater than zero.

Substituting the initial error matrix into a structural formula, and solving an initial value of a corrected coefficient matrix;

wherein the content of the first and second substances,is a matrix of coefficients.

Further, based on the G-M model, the adjustment model and the least square adjustment criterion are:

wherein, A is an mxn coefficient matrix, L is an mx1 observation vector, and X is an nx1 unknown parameterVector, σ₀ ²Is the unit weight variance, and e is an n × 1 random error vector. The least squares estimation and the estimated covariance are as follows:

the least squares estimation belongs to an unbiased estimation, and the variance can be represented by the trace of the covariance matrix:

wherein, Λ_iAre the singular values of the coefficient matrix a.

In consideration of the possibility of error of the coefficient matrix A, an EIV observation model is introduced, and due to the existence of complex diversity of measurement data, TLS adjustment in the EIV model is relatively appropriate. The EIV model is as follows:

L＝(A+E_A)X+e

the above formula can be expressed as

Wherein E is_AIs an error matrix of the coefficient matrix a,is the product of Kronecker, vec (-) is the straightening transform, I_nIs a unit array.

The adjustment criterion is:

the lagrange objective function is constructed as:

the formula obtained by the arrangement is as follows:

order toAn iterative equation can be derived:

the parameters are solved by an iterative method, least square estimation can be adopted as an iterative initial value, and the method can be used for solving the parameters in the iterative methodThen the iteration terminates (k is the number of iterations and epsilon is the iteration threshold).

When the coefficient matrix is ill-conditioned, its method matrix A^TThe inversion process of a becomes very unstable, and the mean square error is used as the reference for estimation, and it can be seen from the above formula that when Λ i is close to 0, the variance will be very large, resulting in that the obtained parameter estimation has no reference.

Under an EIV adjustment model, the regularization method is to add a stable functional to the TLS adjustment criterion:

f(E_A，e)＝vec(E_A)^Tvec(E_A)+e^Te+αX^TRX＝min

in the formula, R is a regularization matrix, and alpha is a regularization parameter greater than zero. The parameters are according to:

performing regularized iterative operation according to the above formulaThe iteration terminates. The conclusion can be obtained from the formula, and the corresponding matrix is added in the methodAfter the functional is stabilized, the inversion becomes stable, and the obtained parameter estimation value is reliable.

Step four, solving a corresponding method matrix aiming at the corrected coefficient matrix, and constructing an initial value of the target matrix according to the method matrix;

wherein Gi is a normal matrix A^TAnd A is a feature vector corresponding to the small singular value. The small characteristic value judging method can use the characteristic value standard difference component sum to account for more than 95% of the standard difference proportion.

In the formula_iIs a normal matrix A^TAnd A is the characteristic value. Matrix arrayOnly small singular values are corrected and can be called as a targeting matrix, so that unnecessary deviation is avoided while variance is reduced, and estimation is more reasonable.

Step five, solving corresponding regularization parameters according to the targeting matrix by adopting an L-curve method;

and step six, simultaneously adding coefficient matrix noise and random observation error vectors to simulate a real complex noise experimental environment. In order to verify the adaptability of the algorithm to noise, random noise e is respectively added into the normalized capacitance C and the coefficient matrix S_L～N(0，σ²I_m)，σ＝0.1：

And step seven, substituting the parameters into an iteration formula to carry out iterative operation, and obtaining an experimental target estimated value after iteration is finished according to conditions.

Further, the adjustment criterion f (E) is determined according to EIV model L ═ A + EA) X + E and pathological TLS_A，e)＝vec(E_A)^Tvec(E_A)+e^Te+αX^TRX is min, and a Lagrange objective function is constructed

And (5) solving a first-order partial derivative:

from the above formula, e ═ λ and EA ═ λ X can be obtained^TAnd substituting the parameters into an EIV model:

the following is obtained according to the formula:

the following formula can be obtained:

the coefficient matrix is reconstructed from the EA

Then solving parameters by using a regularization method

Performing iterative computation according to the formula:

the iterative operation is carried out according to the above formula,and then, finishing iteration to obtain an experimental target estimated value. Wherein, the smaller epsilon represents the smaller error between the reconstructed image and the original image, and the longer the iterative computation process in the experiment follows.

In summary, the preferred embodiments of the present invention are described above, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the scope of the present invention, and equivalents and modifications of the technical solutions and concepts of the present invention should be included in the scope of the present invention.