CN103940388A - Method and system for detecting metal pipeline parameters - Google Patents

Abstract

The invention provides a method and system for detecting metal pipeline parameters. The method includes the steps that two detecting coils and a transmitting coil are placed in a pipeline to be detected and are coaxially arranged with the pipeline to be detected, the transmitting coil is located between the two detecting coils, and the distances between the transmitting coil and the two detecting coils are equal; a function relation formula between electromagnetic transmission impedance and the pipeline inner diameter CID and the electromagnetic property PEM is established; a function relation formula between a determined function and the CID and PEM is obtained through double parameter fitting of the CID and the PEM; Zth is obtained through simulation of the detection process, and Zex is obtained through imposing an excitation signal on the transmitting coil and actual detection; a first function value and a second function value are obtained through substituting the Zth and the Zex into the determined function; the CID and the PEM enabling the difference between the first function value and the second function value to be the smallest are solved to serve as the detection result. By means of the method and system for detecting metal pipeline parameters, the inner diameter and the electromagnetic property of the metal pipeline can be detected at the same time, and accuracy and precision of the detection result can be improved.

Description

A kind of method and system that detect metallic conduit parameter

Technical field

The present invention relates to EDDY CURRENT field, relate in particular to a kind of method and system that detect metallic conduit parameter.

Background technology

In the inversion algorithm field of metallic conduit physical attribute, modal is to utilize traditional EDDY CURRENT principle to obtain the information that comprises pipeline physical attribute, it is a complicated computation process that electromagnetic field of eddy current detects, and need to choose suitable, shortcut calculation, inverting pipeline physical parameter value.At present the measuring and calculation method of pipeline physical attribute mainly exists: parameter model complexity, the problem such as parameter mutual interference is strong, and difficulty in computation is large, and result precision is undesirable.

When prior art obtains internal diameter of the pipeline measured value, generally obtain by multiple mechanical arms or ultrasound examination, precision is high but speed is lower, and use equipment is more.There is no the report that uses electromagnetic method measuring channel internal diameter.

Summary of the invention

The technical problem to be solved in the present invention is how to detect internal diameter and the electromagnetic attributes of metallic conduit simultaneously, and improves accuracy and the precision of testing result.

In order to address the above problem, the invention provides a kind of method that detects metallic conduit parameter, described parameter comprises internal diameter of the pipeline CID and pipe electromagnetic attribute PEM; Described method comprises:

S101, two magnetic test coils and a transmitting coil are put into pipeline to be detected, described two magnetic test coils and transmitting coil all with the coaxial placement of described pipeline to be detected, described transmitting coil, between two magnetic test coils, and equates with the distance of two magnetic test coils;

S102, set up the functional relation of electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM; Obtain determining the functional relation between function and CID, PEM by CID and the two-parameter matching of PEM; Described definite function is the phase place that comprises described electromagnetic propagation impedance and the expression formula of Amplitude Ratio information;

S103, analog detection process obtain electromagnetic propagation impedance theory value Z _th, on transmitting coil, apply pumping signal the actual actual detected value Z that obtains electromagnetic propagation impedance that detects _ex; Respectively by Z _thand Z _exdescribed in substitution, determine that function obtains the first functional value and the second functional value; Solve CID and the PEM of the gap minimum that can make between first, second functional value, as testing result.

Alternatively, the step of setting up the functional relation of electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM comprises:

Described electromagnetic propagation impedance is airborne propagation impedance Z _airwith the propagation impedance Z that affected by pipeline _wsum; Wherein:

$Z_{\mathrm{air}}=\mathrm{j\ω}{\mathrm{\μ}}_0{\∫}_0^{\∞}F(x,D_T,D_R,d)\mathrm{dx};$

$Z_w=\mathrm{j\ω}{\mathrm{\μ}}_0{\∫}_0^{\∞}T(x,D_T,D_R,d)B(x,{\mathrm{\μ}}_w,{\mathrm{\μ}}_0,{\mathrm{\σ}}_w,b)\mathrm{dx};$

In formula, x represents along the integration amount of electromagnetic field transmission direction;

Function F (x, D _t, D _r, d), T (x, D _t, D _r, d) represent in air and two kinds of environmental baselines of pipeline the impedance component irrelevant with pipe parameter;

Wherein, D _tand D _rbe divided into the diameter of transmitting coil and magnetic test coil, d is the distance between transmitting coil and magnetic test coil, μ _wand σ _wbe respectively magnetic permeability and the conductivity of tube wall, μ ₀for managing the magnetic permeability of interior medium, b is CID/2, b=CID/2, the angular frequency that ω is coil excitation signals;

Described B function is: $B(x,{\mathrm{\μ}}_w,{\mathrm{\μ}}_0,{\mathrm{\σ}}_w,b)=\frac{\mathrm{\ξ}{K}_0\left(\mathrm{xb}\right)-K_1\left(\mathrm{xb}\right)}{\mathrm{\ξ}{I}_0\left(\mathrm{xb}\right)+I_1\left(\mathrm{xb}\right)};$

Wherein I _nand K (x) _n(x) be respectively the first kind and Equations of The Second Kind modified Bessel function; N is order, and value is 0,1,2;

The degree of coupling ξ that obtains pipe electromagnetic propagation impedance after simplification is:

$\mathrm{\ξ}=\frac{\sqrt{2}x}{(1+j)}\frac{1}{{\mathrm{\μ}}_0\sqrt{\mathrm{\ω}}}\mathrm{PEM},\mathrm{PEM}=\sqrt{\frac{{\mathrm{\μ}}_w}{{\mathrm{\σ}}_w}}.$

Alternatively, described definite function is:

Wherein Z is electromagnetic propagation impedance, and Re (Z) refers to the real part of Z.

Alternatively, obtain determining that by CID and the two-parameter matching of PEM the step of the functional relation between function and CID, PEM comprises:

41, with for dependent variable, ξ is carried out to matching, obtain be worth the expression formula model about ξ:

42, taking CID as independent variable, taking the value of fitting result g, h, s, t as dependent variable, find functional relation, obtain the functional relation of g about CID; Repeating step 42 is until obtain h, s, the t functional relation about CID.

Alternatively, described in, solving the CID of gap minimum and the step of PEM that can make between first, second functional value comprises:

Choose L-M in conjunction with Q-N algorithm, solving non-linear least square problem:

$L\left(y\right)=\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\left(v_i\left(y\right)\right)}^2$

Wherein,

V _i(y)=M _i(CID, ξ)-G _i(CID, ξ); I is residual error amount counting, and m is residual error amount, is greater than unknown quantity number; M _i(CID, ξ) is the actual value detecting, G _i(CID, ξ) is theoretical value;

After following formula meets three times continuously, be Q-N algorithm by L-M algorithmic transformation:

||L'(y)|| _∞<0.02*L(y)。

The present invention also provides a kind of system that detects metallic conduit parameter, and described parameter comprises internal diameter of the pipeline CID and pipe electromagnetic attribute PEM; Described system comprises:

Two magnetic test coils and a transmitting coil, be placed in pipeline to be detected, described two magnetic test coils and transmitting coil all with the coaxial placement of described pipeline to be detected, described transmitting coil, between two magnetic test coils, and equates with the distance of two magnetic test coils;

Detecting unit, for apply pumping signal on transmitting coil, and the actual actual detected value Z that obtains electromagnetic propagation impedance that detects _ex;

Processing unit, for setting up the functional relation of electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM; Obtain determining the functional relation between function and CID, PEM by CID and the two-parameter matching of PEM; Described definite function is the phase place that comprises described electromagnetic propagation impedance and the expression formula of Amplitude Ratio information; Analog detection process obtains electromagnetic propagation impedance theory value Z _th, respectively by Z _thand Z _exdescribed in substitution, determine that function obtains the first functional value and the second functional value; Solve CID and the PEM of the gap minimum that can make between first, second functional value, as testing result.

Alternatively, the functional relation that described processing unit is set up electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM refers to:

Described processing unit is by airborne propagation impedance Z _airwith the propagation impedance Z that affected by pipeline _wsum obtains electromagnetic propagation impedance; Wherein:

$Z_{\mathrm{air}}=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}F(x,D_T,D_R,d)\mathrm{dx};$

$Z_w=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}T(x,D_T,D_R,d)B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)\mathrm{dx};$

In formula, x represents along the integration amount of electromagnetic field transmission direction;

Function F (x, D _t, D _r, d), T (x, D _t, D _r, d) represent in air and two kinds of environmental baselines of pipeline the impedance component irrelevant with pipe parameter;

Wherein, D _tand D _rbe divided into the diameter of transmitting coil and magnetic test coil, d is the distance between transmitting coil and magnetic test coil, μ _wand σ _wbe respectively magnetic permeability and the conductivity of tube wall, μ ₀for managing the magnetic permeability of interior medium, b is CID/2, b=CID/2, the angular frequency that ω is coil excitation signals;

Described B function is: $B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)=\frac{\mathrm{\&xi;}{K}_0\left(\mathrm{xb}\right)-K_1\left(\mathrm{xb}\right)}{\mathrm{\&xi;}{I}_0\left(\mathrm{xb}\right)+I_1\left(\mathrm{xb}\right)};$

Wherein I _nand K (x) _n(x) be respectively the first kind and Equations of The Second Kind modified Bessel function; N is order, and value is 0,1,2;

The degree of coupling ξ that obtains pipe electromagnetic propagation impedance after simplification is:

$\mathrm{\&xi;}=\frac{\sqrt{2}x}{(1+j)}\frac{1}{{\mathrm{\&mu;}}_0\sqrt{\mathrm{\&omega;}}}\mathrm{PEM},\mathrm{PEM}=\sqrt{\frac{{\mathrm{\&mu;}}_w}{{\mathrm{\&sigma;}}_w}}.$

Alternatively, described definite function is:

Wherein Z is electromagnetic propagation impedance, and Re (Z) refers to the real part of Z.

Alternatively, described processing unit obtains determining that by CID and the two-parameter matching of PEM the functional relation between function and CID, PEM refers to:

The described processing unit first step first with for dependent variable, ξ is carried out to matching, obtain be worth the expression formula model about ξ:

Second step is taking CID as independent variable, taking the value of fitting result g, h, s, t as dependent variable, finds functional relation, obtains the functional relation of g about CID; Repeat second step until obtain h, s, the t functional relation about CID.

Alternatively, described processing unit solves the gap minimum that can make between first, second functional value CID and PEM refer to:

Described processing unit is chosen L-M in conjunction with Q-N algorithm, solving non-linear least square problem:

$L\left(y\right)=\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(v_i\left(y\right)\right)}^2$

Wherein,

V _i(y)=M _i(CID, ξ)-G _i(CID, ξ); I is residual error amount counting, and m is residual error amount, is greater than unknown quantity number; M _i(CID, ξ) is the actual value detecting, G _i(CID, ξ) is theoretical value;

After following formula meets three times continuously, be Q-N algorithm by L-M algorithmic transformation:

||L'(y)|| _∞<0.02*L(y)。

A kind of inversion schemes about metallic conduit parameter that technical scheme of the present invention proposes, there is extremely strong operability, it has simplified parametric function model, can utilize the instruments such as MATLAB to solve, greatly simplify and solved difficulty, improve accuracy and the precision of detected parameter, can obtain fast quality high, practical pipe parameter value.This pipe parameter detection scheme data volume is suitable, the feature of computational short cut.Be mainly reflected in complicated impedance model is simplified, obtain computable formal transformation; The fitting precision of the pipeline attribute characteristic curve obtaining by definite function of theoretical electromagnetic propagation impedance is high; The data inversion algorithm convergence of comprehensive L-M and Q-N algorithm is fast, and actual test parameter is simple and data volume is few, than existing scheme, has test data light weight, iterative computation is simplified advantage fast, improves useful in reality detects to testing the speed.

Brief description of the drawings

Fig. 1 is longitudinal profile schematic diagram and the parameter instruction of pipeline and transmitting coil, magnetic test coil;

Fig. 2 is the impedance Z under complex coordinates;

Fig. 3 is ANSYS software simulation detection model;

Fig. 4 is definite function theoretical under different tube diameters value curve;

Fig. 5 is theoretical determining about the three-dimensional plot of ID and ξ.

Embodiment

Below in conjunction with drawings and Examples, technical scheme of the present invention is described in detail.

It should be noted that, if do not conflicted, each feature in the embodiment of the present invention and embodiment can mutually combine, all within protection scope of the present invention.In addition, although there is shown logical order in flow process, in some cases, can carry out shown or described step with the order being different from herein.Pay particular attention to, in the following description, in the time that detected pipeline is different, conclusion can be different, and in the time that perhaps the detailed description of known function and design can desalinate main contents of the present invention, these are described in here and will be left in the basket.

Embodiment mono-, a kind of method that detects metallic conduit parameter, described parameter comprises internal diameter of the pipeline CID and pipe electromagnetic attribute PEM; Described method comprises the steps S101～S103.

S101, two magnetic test coils and a transmitting coil are put into pipeline to be detected, described two magnetic test coils and transmitting coil all with the coaxial placement of described pipeline to be detected, described transmitting coil, between two magnetic test coils, and equates with the distance of two magnetic test coils;

S102, set up the functional relation of electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM; Obtain determining the functional relation between function and CID, PEM by CID and the two-parameter matching of PEM; Described definite function is the phase place that comprises described electromagnetic propagation impedance and the expression formula of Amplitude Ratio information;

S103, analog detection process obtain electromagnetic propagation impedance theory value Z _th, on transmitting coil, apply pumping signal the actual actual detected value Z that obtains electromagnetic propagation impedance that detects _ex; Respectively by Z _thand Z _exdescribed in substitution, determine that function obtains the first functional value and the second functional value; Solve CID and the PEM of the gap minimum that can make between first, second functional value, as testing result.

The present embodiment based on high-frequency vortex detect principle, in near-field detection place inverting pipeline physical attribute (CID, PEM); Can utilize data inversion method, and computational tool (being such as but not limited to ANSYS, MATLAB and nonlinear least square method etc.), obtain the value of metallic conduit near field place's physics or electromagnetic parameter.

In an embodiment of the present embodiment, the step of the described functional relation of setting up electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM specifically can comprise:

Described electromagnetic propagation impedance is airborne propagation impedance Z _airwith the propagation impedance Z that affected by pipeline _wsum; Wherein:

$Z_{\mathrm{air}}=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}F(x,D_T,D_R,d)\mathrm{dx};---\left(1\right)$

$Z_w=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}T(x,D_T,D_R,d)B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)\mathrm{dx};---\left(2\right)$

In formula, x represents along the integration amount of electromagnetic field transmission direction;

Function F (x, D _t, D _r, d), T (x, D _t, D _r, d) represent in air and two kinds of environmental baselines of pipeline the impedance component irrelevant with pipe parameter;

Wherein, D _tand D _rbe divided into the diameter of transmitting coil and magnetic test coil, d is the distance between transmitting coil and magnetic test coil, μ _wand σ _wbe respectively magnetic permeability and the conductivity of tube wall, μ ₀for managing the magnetic permeability of interior medium, b is CID/2, b=CID/2, the angular frequency that ω is coil excitation signals;

Described B function is: $B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)=\frac{\mathrm{\&xi;}{K}_0\left(\mathrm{xb}\right)-K_1\left(\mathrm{xb}\right)}{\mathrm{\&xi;}{I}_0\left(\mathrm{xb}\right)+I_1\left(\mathrm{xb}\right)};$

Wherein I _nand K (x) _n(x) be respectively the first kind and Equations of The Second Kind modified Bessel function; N is order, and value is 0,1,2;

The degree of coupling ξ that obtains pipe electromagnetic propagation impedance after simplification is:

$\mathrm{\&xi;}=\frac{\sqrt{2}x}{(1+j)}\frac{1}{{\mathrm{\&mu;}}_0\sqrt{\mathrm{\&omega;}}}\mathrm{PEM},\mathrm{PEM}=\sqrt{\frac{{\mathrm{\&mu;}}_w}{{\mathrm{\&sigma;}}_w}}.$

In present embodiment, according to traditional EDDY CURRENT ultimate principle, simplify boundary condition, derive the electromagnetic propagation impedance of required pipeline and the functional relation of internal diameter of the pipeline CID and electromagnetic attributes PEM.Traditional EDDY CURRENT principle is based on Faraday's electromagnetic induction law, magnetic field energy is converted into electric signal and calculates the ratio of the electric current on induced voltage and the transmitting coil on magnetic test coil, calculate electromagnetic propagation impedance Z, the electromagnetic attributes of pipeline and the information of mean inside diameter have stronger dependence to electromagnetic propagation impedance Z.

In present embodiment, the detection model geometric parameter of described pipe parameter as shown in Figure 1.Wherein D _tand D _rbe divided into the diameter of transmitting coil 11 and magnetic test coil 12, l _tand l _rbe respectively the axial length of transmitting coil 11 and magnetic test coil 12, d is the distance between transmitting coil 11 and magnetic test coil 12, and C is the wall thickness of pipeline 10, and CID is internal diameter of the pipeline, μ _wand σ _wbe respectively magnetic permeability and the conductivity of tube wall, μ ₀for managing the magnetic permeability of interior medium, the angular frequency that ω is coil excitation signals.In geometric parameter, two magnetic test coils 12 are placed about transmitting coil 11 is symmetrical.

The metallic conduit of the present embodiment indication can be considered as a columniform conductor, can describe electromagnetic propagation impedance Z with Bessel's function.If pipeline be endless, evenly, linear, isotropic, when transmitting coil 11 and magnetic test coil 12 are during with the coaxial placement of pipeline 10, the electromagnetic propagation impedance Z between magnetic test coil 12 and transmitting coil 11 is defined as: airborne propagation impedance Z _airwith the propagation impedance Z that affected by pipeline 10 _wsum.Be Z=Z _air+ Z _w.

Wherein, $F(x,D_T,D_R,d)=\left\{\begin{array}{c}\frac{D_R{D}_T}{2}{K}_1\left(\frac{x{D}_T}{2}\right)I_1\left(\frac{x{D}_R}{2}\right)\cos \left(\mathrm{xd}\right),D_R<D_T\\ \frac{D_R{D}_T}{2}{I}_1\left(\frac{x{D}_T}{2}\right)K_1\left(\frac{x{D}_R}{2}\right)\cos \left(\mathrm{xd}\right),D_T<D_R\end{array}\right.---\left(3\right)$

$T(x,D_T,D_R,d)=\frac{D_R{D}_T}{2}{I}_1\left(\frac{x{D}_T}{2}\right)I_1\left(\frac{x{D}_R}{2}\right)\cos \left(\mathrm{xd}\right)---\left(4\right)$

T function in F function in formula (1) and formula (2) physical dimension of coil that places one's entire reliance upon, and do not comprise pipe parameter information.

The computing formula of skin depth δ is as follows:

$\mathrm{\&delta;}=\sqrt{\frac{2}{{\mathrm{\&sigma;}}_w{\mathrm{\&mu;}}_w\mathrm{\&omega;}}}---\left(5\right)$

From formula (5), skin depth δ reduces along with the increase of the frequency of pumping signal.

In the time that the frequency of pumping signal is tending towards high frequency, skin depth δ is much smaller than the thickness C of tube wall 10.B function in this up-to-date style (2) can be expressed as:

$B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)=\frac{\mathrm{\&xi;}{K}_0\left(\mathrm{xb}\right)-K_1\left(\mathrm{xb}\right)}{\mathrm{\&xi;}{I}_0\left(\mathrm{xb}\right)+I_1\left(\mathrm{xb}\right)}---\left(6\right)$

Wherein I _nand K (x) _n(x) be respectively the first kind and Equations of The Second Kind modified Bessel function (n is exponent number, and the value is here 0,1,2), ξ dimensionless, and can be expressed as following formula:

$\mathrm{\&xi;}=\frac{{\mathrm{\&mu;}}_w}{{\mathrm{\&mu;}}_0}\frac{x}{\sqrt{x^2+\mathrm{j\&omega;}{\mathrm{\&mu;}}_w{\mathrm{\&sigma;}}_w}}\frac{K_1\left(\sqrt{x^2+\mathrm{j\&omega;}{\mathrm{\&mu;}}_w{\mathrm{\&sigma;}}_w}b\right)}{K_0\left(\sqrt{x^2+\mathrm{j\&omega;}{\mathrm{\&mu;}}_w{\mathrm{\&sigma;}}_w}b\right)}---\left(7\right)$

In the time that pumping signal is high-frequency signal, modified Bessel function convergence is consistent, and ξ is done to further simplification, and defines the degree of coupling that characteristic ξ is pipe electromagnetic propagation impedance:

$\mathrm{\&xi;}=\frac{\sqrt{2}x}{(1+j)}\frac{1}{{\mathrm{\&mu;}}_0\sqrt{\mathrm{\&omega;}}}\sqrt{\frac{{\mathrm{\&mu;}}_w}{{\mathrm{\&sigma;}}_w}}=\frac{\sqrt{2}x}{(1+j)}\frac{\mathrm{PEM}}{{\mathrm{\&mu;}}_0\sqrt{\mathrm{\&omega;}}}---\left(8\right)$

Therefore, the ξ that the electromagnetic attributes PEM of pipeline 10 also can simplify in electromagnetic propagation impedance model expresses, and avoids the solution procedure of complicated impedance, under the certain condition of frequency, ξ in propagation impedance model is only relevant with the electromagnetic attributes PEM of pipeline 10, irrelevant with the physical size of pipeline 10.

In present embodiment, described definite function can be, but not limited to into:

Wherein Z is electromagnetic propagation impedance, and Re (Z) refers to the real part of Z.

In present embodiment, the CID and the PEM that solve the gap minimum that can make between first, second functional value namely solve following formula:

Wherein, Z _exfor the actual detected value of electromagnetic propagation impedance, refer to and can make minimum PEM and CID.

In present embodiment, can utilize simulation software to replace complex mathematical computations to obtain theoretical definite function greatly simplify the funtcional relationship of parameters C ID and PEM.Such as utilizing finite element emulation software to replace complex mathematical computations, obtain definite function of theoretical electromagnetic propagation impedance can be, but not limited to utilize software ANSYS software set up the detection model of pipe parameter and electromagnetic eddy testing process is simulated; Can be, but not limited to utilize MATLAB software to carry out matching.

First, if electromagnetic propagation impedance Z is expressed as in detecting:

$Z=\frac{V_{\mathrm{receiver}}}{I_{\mathrm{transmitter}}}---\left(10\right)$

Wherein V _receiverthe voltage of magnetic test coil 12, I _transmitterfor the electric current of transmitting coil 11.

Electromagnetic propagation impedance is a plural number, and in eddy current detection method, phase place and Amplitude Ratio packet have contained the whole specified datas to electromagnetic attributes, can, by a definite function that comprises phase place and Amplitude Ratio information, obtain the physical attribute PEM of pipeline and the information of CID.See Fig. 2, function is determined in definition:

Set up detection model at finite element analysis software ANSYS environment, in order to simplify realistic model, improve simulation efficiency, three-dimensional model is equivalent to two dimensional model, and in realistic model, the induced voltage of magnetic test coil calculates according to following formula:

V _receiver=-jωB _ySN； （11）

Wherein B _yfor axial magnetic induction, S is the cross-sectional area of magnetic test coil 12, and N is the number of turn of magnetic test coil 12.When the simulation parameter of transmitting coil 11 is during as table 1 in example hereinafter, one-sided 2D realistic model as shown in Figure 3.

In a kind of alternatives of present embodiment, obtain determining that by CID and the two-parameter matching of PEM the step of the functional relation between function and CID, PEM specifically can comprise:

41, with for dependent variable, ξ is carried out to matching, obtain be worth the expression formula model about ξ:

42, taking CID as independent variable, taking the value of fitting result g, h, s, t as dependent variable, find functional relation, obtain the functional relation of g about CID; Repeating step 42 is until obtain h, s, the t functional relation about CID.

In this alternatives, first calculate the above-mentioned ξ under different excitation frequencies according to formula (8), calculate the theory under different excitation frequencies, different tube diameters according to formula (9), (10), (11) value (table), and draw curve, as shown in Figure 4; Independent variable taking CID and ξ value as binary function, with for dependent variable, drawing three-dimensional image, as shown in Figure 5.

For obtaining theoretical parametric line relational expression, utilize MATLAB couple here matching that curve carries out two-parameter (CID, ξ), the definite function that obtains theoretical electromagnetic propagation impedance is suc as formula (12):

Using this function curve as theoretical parametric function curved line relation formula, be designated as function G (CID, ξ), it has described theoretical definite function and the relation of electromagnetic attributes.

In a kind of alternatives of present embodiment, it is described that to solve the CID of gap minimum and the step of PEM that can make between first, second functional value be the refutation process of internal diameter of the pipeline CID and electromagnetic attributes PEM, can, by the application process of comprehensive L-M (Levenberg-Marquardt) algorithm and Q-N (Quasi-Newton) algorithm, solve non-linear least square problem in the problem of inverting; This step specifically can comprise:

Choose L-M in conjunction with Q-N algorithm, solving non-linear least square problem:

$L\left(y\right)=\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(v_i\left(y\right)\right)}^2$

Wherein,

V _i(y)=M _i(CID, ξ)-G _i(CID, ξ); I is residual error amount counting, and m is residual error amount, is greater than unknown quantity number; M _i(CID, ξ) is the actual definite functional value detecting the definite functional value calculating according to measured value and formula (9), (10) and (11); G _i(CID, ξ) is theoretical definite functional value, and the algorithm of choosing is for obtaining y ⁺=argmin _y{ L (y) } condition meets;

After following formula meets three times continuously, be Q-N algorithm by L-M algorithmic transformation:

||L'(y)|| _∞<0.02*L(y)。

In present embodiment, choose the algorithm of most suitable least square method, can improve by accuracy, the precision of estimated parameter CID and PEM calculating, and add the speed of convergence of fast process.Its calculating still can utilize MATLAB to carry out quick, easy calculating.

In present embodiment, utilize L-M(Levenberg-Marquardt) algorithm solution parameters C ID and PEM iterative problem in the early stage, until CID and PEM approach optimum value, because algorithm exists the not enough problem of certain linear convergence, choose again Q-N(Quasi-Newton) algorithm approaches CID and PEM, until acquisition y ⁺=argmin _y{ L (y) } condition meets.

With a concrete example explanation the present embodiment, the simulation parameter of ANSYS simulated experiment process is: the material of coil is copper, relative permeability μ below ₁=1, conductivityσ ₁=5.8 × 10 ⁶s/m; The relative permeability μ of ferromagnetic pipeline _w/ μ ₀=80, conductivity is σ ₂=5.95 × 10 ⁶s/m, bore is 0.06～0.105m (stepping 0.005m), 0.11～0.22m (stepping 0.01m), pipe thickness is 0.02m, duct length is 1m.Exciting current is set as 0.015A, the alternating signal that initial phase is 0.Transmitting coil 11 is placed in the pipeline 10 0.5m place on axially.The parameter of transmitting coil 11 used is as shown in table 1.

Table 1, transmitting coil parameter

Detecting step in this example specifically can comprise step a and step b.

Step a,

Set up realistic model as shown in Figure 3, for the magnetic induction data analysis at range transmission coil 0.08m place, obtain parametric function formula (13)～(14) based on Faraday's electromagnetic induction law:

$\mathrm{\&xi;}=\frac{1}{{\mathrm{\&mu;}}_0\sqrt{\mathrm{\&omega;}}}\sqrt{\frac{{\mathrm{\&mu;}}_w}{{\mathrm{\&sigma;}}_w}}=\frac{\mathrm{PEM}}{{\mathrm{\&mu;}}_0\sqrt{\mathrm{\&omega;}}}---\left(13\right)$

Step b,

Acquisition theoretical simulation curve, as shown in Figure 4.

Two-parameter matching curve, model of fit is as follows:

Matching step is divided into two steps:

The first step, with for dependent variable, ξ is carried out to matching, obtain be worth the expression formula about ξ, during as CID=0.06m, function expression is:

Coefficient g, h, s, t that different CID is corresponding are as shown in table 2.

The value of coefficient g, h, s, t under different CID in table 2, two-parameter matching

CID(m)	g	h	s	t
					0.06	0.818832	-18.0725	-1.02838	-372.19
0.065	0.745727	-17.0534	-O.90601	-325.441
					0.07	0.680384	-16.0912	-0.80144	-287.522
0.075	0.621888	-15.1918	-0.7145	-256.852
					0.08	0.569484	-14.3543	-0.64073	-231.443
0.085	0.522333	-13.5716	-0.57775	-210.28
					0.09	0.480166	-12.862	-0.52311	-192.057
0.095	0.442036	-12.2016	-0.4757	-176.613
					0.1	0.407325	-11.5768	-0.43412	-163.505
0.105	0.376197	-11.0201	-0.39739	-151.858
					0.11	0.347855	-10.5009	-0.36477	-141.749
0.12	0.298388	-9.56383	-0.30943	-125.142
					0.13	0.257245	-8.76412	-0.26458	-111.986
0.14	0.222593	-8.0569	-0.22762	-101.508
					0.15	0.193595	-7.45387	-0.197	-92.7701
0.16	0.169017	-6.9289	-0.17146	-85.6275
					0.17	0.14813	-6.45945	-0.14986	-79.5542
0.18	0.130228	-6.02453	-0.13144	-74.3709
					0.19	0.114756	-5.60036	-0.11556	-69.8938
0.2	0.091076	-3.46309	-0.09321	-74.7728
					0.2l	0.077625	-2.51534	-0.07989	-74.3987
0.22	0.066225	-1.56902	-0.06859	-74.4998

Second step, taking CID as independent variable, taking the value of fitting result g, the h of the first step, s, t as dependent variable, finds functional relation, obtains g, h, s, the t functional relation about CID, if g is about the function of CID:

g=2.27e ^-17.512*CID+0.00087e ^21.348*CID (17)

Repeat second step until obtain h, s, the t functional relation about CID.

Finally obtain one group of embodiment of theory function, as follows:

$\begin{array}{c}f(\mathrm{CID},\mathrm{\&xi;})=({2.27e}^{-17.512*\mathrm{CID}}+0.00087e^{21.348*\mathrm{CD}})e^{(-33.191e^{-11.0633*\mathrm{CID}}-0.003e^{35.765*\mathrm{CID}})*\mathrm{\&xi;}}\\ +(-47.0599e^{68.389*\mathrm{CID}}-1.261e^{11.907*\mathrm{CID}})e^{(8800.197e^{63.253*\mathrm{CID}}+{449.018e}^{-10.506*\mathrm{CID}})*\mathrm{\&xi;}}\end{array}$

Step c,

To detected value, choose L-M in conjunction with Q-N algorithm, utilize MATLAB instrument solving non-linear least square problem:

$L\left(y\right)=\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(v_i\left(y\right)\right)}^2---\left(18\right)$

Wherein,

v _i(y)=M _i(ID，ξ)-G _i(ID，ξ) (19)

M _i(CID, ξ) is the actual definite functional value detecting, G _i(CID, ξ) is theoretical definite functional value, calculated value, and have

[G ₁,G ₂,...,G _n]=[G(CID,ξ ₁),G(CID,ξ ₂),...,G(CID,ξ _n)] （20）

Be that following formula meets three times continuously to the conversion condition of Q-N algorithm by L-M algorithm:

||L'(y)|| _∞<0.02*L(y) （21）

The result of the present embodiment gained is as shown in table 3.

The CID of table 3, inverting and μ _w/ μ ₀value and true value

CID inversion result (m)	μ w/μ 0Inversion result	CID true value (m)	μ w/μ 0True value
				0.060097001	84.10846381	0.06	80
0.06506881	82.3758832	0.065	80
				0.070049029	80.82209658	0.07	80
0.075007104	79.59935751	0.075	80
				0.079938129	78.73706558	0.08	80
0.084852156	78.25144858	0.085	80
				0.089764362	78.09583852	0.09	80
0.094685605	78.23395696	0.095	80
				0.099630289	78.59909023	0.10	80
0.104606974	79.14840102	0.105	80
				0.109622213	79.8212487	0.11	80
0.119779529	81.31400279	0.12	80
				0.130094539	82.70540908	0.13	80
0.140519589	83.66820109	0.14	80
				0.150974923	84.03271862	0.15	80
0.161365963	83.71631349	0.16	80
				0.171607505	82.73898215	0.17	80
0.181624977	81.20837166	0.18	80
				0.19136922	79.26224302	0.19	80
0.200813784	77.0326483	0.20	80
				0.209944707	74.62840193	0.21	80
0.218764736	72.14600579	0.22	80

The present embodiment utilizes ANSYS to set up realistic model and gross data, utilize MATLAB to carry out two-parameter matching, greatly simplify parametric function, accelerate computing velocity, finally solving in the problem of nonlinear least square method, choose the algorithm of L-M in conjunction with Q-N, improved the degree of accuracy of parameter value, and convergence speedup process.

Embodiment bis-, a kind of system that detects metallic conduit parameter, described parameter comprises internal diameter of the pipeline CID and pipe electromagnetic attribute PEM; Described system comprises:

Two magnetic test coils and a transmitting coil, be placed in pipeline to be detected, described two magnetic test coils and transmitting coil all with the coaxial placement of described pipeline to be detected, described transmitting coil, between two magnetic test coils, and equates with the distance of two magnetic test coils;

Detecting unit, for apply pumping signal on transmitting coil, and the actual actual detected value Zex that obtains electromagnetic propagation impedance that detects;

Processing unit, for setting up the functional relation of electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM; Obtain determining the functional relation between function and CID, PEM by CID and the two-parameter matching of PEM; Described definite function is the phase place that comprises described electromagnetic propagation impedance and the expression formula of Amplitude Ratio information; Analog detection process obtains electromagnetic propagation impedance theory value Z _th, respectively by Z _thand Z _exdescribed in substitution, determine that function obtains the first functional value and the second functional value; Solve CID and the PEM of the gap minimum that can make between first, second functional value, as testing result.

In an embodiment of the present embodiment, the functional relation that described processing unit is set up electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM specifically can refer to:

Described processing unit is by airborne propagation impedance Z _airwith the propagation impedance Z that affected by pipeline _wsum obtains electromagnetic propagation impedance; Wherein:

$Z_{\mathrm{air}}=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}F(x,D_T,D_R,d)\mathrm{dx};$

$Z_w=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}T(x,D_T,D_R,d)B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)\mathrm{dx};$

In formula, x represents along the integration amount of electromagnetic field transmission direction;

Function F (x, D _t, D _r, d), T (x, D _t, D _r, d) represent in air and two kinds of environmental baselines of pipeline the impedance component irrelevant with pipe parameter;

Wherein, D _tand D _rbe divided into the diameter of transmitting coil and magnetic test coil, d is the distance between transmitting coil and magnetic test coil, μ _wand σ _wbe respectively magnetic permeability and the conductivity of tube wall, μ ₀for managing the magnetic permeability of interior medium, b is CID/2, b=CID/2, the angular frequency that ω is coil excitation signals;

Described B function is: $B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)=\frac{\mathrm{\&xi;}{K}_0\left(\mathrm{xb}\right)-K_1\left(\mathrm{xb}\right)}{\mathrm{\&xi;}{I}_0\left(\mathrm{xb}\right)+I_1\left(\mathrm{xb}\right)};$

Wherein I _nand K (x) _n(x) be respectively the first kind and Equations of The Second Kind modified Bessel function; N is order, and value is 0,1,2;

The degree of coupling ξ that obtains pipe electromagnetic propagation impedance after simplification is:

$\mathrm{\&xi;}=\frac{\sqrt{2}x}{(1+j)}\frac{1}{{\mathrm{\&mu;}}_0\sqrt{\mathrm{\&omega;}}}\mathrm{PEM},\mathrm{PEM}=\sqrt{\frac{{\mathrm{\&mu;}}_w}{{\mathrm{\&sigma;}}_w}}.$

In present embodiment, described definite function can be, but not limited to into:

Wherein Z is electromagnetic propagation impedance, and Re (Z) refers to the real part of Z.

In a kind of alternatives of present embodiment, described processing unit obtains determining that by CID and the two-parameter matching of PEM the functional relation between function and CID, PEM specifically can refer to:

The described processing unit first step first with for dependent variable, ξ is carried out to matching, obtain be worth the expression formula model about ξ:

Second taking CID as independent variable, taking the value of fitting result g, h, s, t as dependent variable, finds functional relation, obtains the functional relation of g about CID; Repeat second step until obtain h, s, the t functional relation about CID.

In a kind of alternatives of present embodiment, CID and PEM that described processing unit solves the gap minimum that can make between first, second functional value specifically can refer to:

Described processing unit is chosen L-M in conjunction with Q-N algorithm, solving non-linear least square problem:

$L\left(y\right)=\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(v_i\left(y\right)\right)}^2$

Wherein,

V _i(y)=M _i(CID, ξ)-G _i(CID, ξ); I is residual error amount counting, and m is residual error amount, is greater than unknown quantity number; M _i(CID, ξ) is the actual value detecting, G _i(CID, ξ) is theoretical value;

After following formula meets three times continuously, be Q-N algorithm by L-M algorithmic transformation:

||L'(y)|| _∞<0.02*L(y)。

Although above the illustrative embodiment of the present invention is described; so that those skilled in the art understand the present invention; but should be clear; the present invention is at the concrete practical range of measuring channel loss; to those skilled in the art; as long as various variations appended claim limit and the of the present invention spiritual scope determined in, these variations are apparent, all utilize innovation and creation that the present invention conceives all at the row of protection.

Claims (10)

1. detect a method for metallic conduit parameter, described parameter comprises internal diameter of the pipeline CID and pipe electromagnetic attribute PEM; Described method comprises:

S101, two magnetic test coils and a transmitting coil are put into pipeline to be detected, described two magnetic test coils and transmitting coil all with the coaxial placement of described pipeline to be detected, described transmitting coil, between two magnetic test coils, and equates with the distance of two magnetic test coils;

S102, set up the functional relation of electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM; Obtain determining the functional relation between function and CID, PEM by CID and the two-parameter matching of PEM; Described definite function is the phase place that comprises described electromagnetic propagation impedance and the expression formula of Amplitude Ratio information;

S103, analog detection process obtain electromagnetic propagation impedance theory value Z _th, on transmitting coil, apply pumping signal the actual actual detected value Z that obtains electromagnetic propagation impedance that detects _ex; Respectively by Z _thand Z _exdescribed in substitution, determine that function obtains the first functional value and the second functional value; Solve CID and the PEM of the gap minimum that can make between first, second functional value, as testing result.

2. the method for claim 1, is characterized in that, the step of setting up the functional relation of electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM comprises:

Described electromagnetic propagation impedance is airborne propagation impedance Z _airwith the propagation impedance Z that affected by pipeline _wsum; Wherein:

$Z_{\mathrm{air}}=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}F(x,D_T,D_R,d)\mathrm{dx};$

$Z_w=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}T(x,D_T,D_R,d)B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)\mathrm{dx};$

In formula, x represents along the integration amount of electromagnetic field transmission direction;

Function F (x, D _t, D _r, d), T (x, D _t, D _r, d) represent in air and two kinds of environmental baselines of pipeline the impedance component irrelevant with pipe parameter;

Wherein, D _tand D _rbe divided into the diameter of transmitting coil and magnetic test coil, d is the distance between transmitting coil and magnetic test coil, μ _wand σ _wbe respectively magnetic permeability and the conductivity of tube wall, μ ₀for managing the magnetic permeability of interior medium, b is CID/2, b=CID/2, the angular frequency that ω is coil excitation signals;

Described B function is: $B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)=\frac{\mathrm{\&xi;}{K}_0\left(\mathrm{xb}\right)-K_1\left(\mathrm{xb}\right)}{\mathrm{\&xi;}{I}_0\left(\mathrm{xb}\right)+I_1\left(\mathrm{xb}\right)};$

Wherein I _nand K (x) _n(x) be respectively the first kind and Equations of The Second Kind modified Bessel function; N is order, and value is 0,1,2;

The degree of coupling ξ that obtains pipe electromagnetic propagation impedance after simplification is:

$\mathrm{\&xi;}=\frac{\sqrt{2}x}{(1+j)}\frac{1}{{\mathrm{\&mu;}}_0\sqrt{\mathrm{\&omega;}}}\mathrm{PEM},\mathrm{PEM}=\sqrt{\frac{{\mathrm{\&mu;}}_w}{{\mathrm{\&sigma;}}_w}}.$

3. method as claimed in claim 2, is characterized in that, described definite function is:

Wherein Z is electromagnetic propagation impedance, and Re (Z) refers to the real part of Z.

4. method as claimed in claim 3, is characterized in that, obtains determining that by CID and the two-parameter matching of PEM the step of the functional relation between function and CID, PEM comprises:

41, with for dependent variable, ξ is carried out to matching, obtain be worth the expression formula model about ξ:

42, taking CID as independent variable, taking the value of fitting result g, h, s, t as dependent variable, find functional relation, obtain the functional relation of g about CID; Repeating step 42 is until obtain h, s, the t functional relation about CID.

5. method as claimed in claim 3, is characterized in that, described in solve the CID of gap minimum and the step of PEM that can make between first, second functional value and comprise:

Choose L-M in conjunction with Q-N algorithm, solving non-linear least square problem:

$L\left(y\right)=\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(v_i\left(y\right)\right)}^2$

Wherein,

V _i(y)=M _i(CID, ξ)-G _i(CID, ξ); I is residual error amount counting, and m is residual error amount, is greater than unknown quantity number; M _i(CID, ξ) is the actual value detecting, G _i(CID, ξ) is theoretical value;

After following formula meets three times continuously, be Q-N algorithm by L-M algorithmic transformation:

||L'(y)|| _∞<0.02*L(y)。

6. detect a system for metallic conduit parameter, described parameter comprises internal diameter of the pipeline CID and pipe electromagnetic attribute PEM; It is characterized in that, described system comprises:

Two magnetic test coils and a transmitting coil, be placed in pipeline to be detected, described two magnetic test coils and transmitting coil all with the coaxial placement of described pipeline to be detected, described transmitting coil, between two magnetic test coils, and equates with the distance of two magnetic test coils;

Detecting unit, for apply pumping signal on transmitting coil, and the actual actual detected value Z that obtains electromagnetic propagation impedance that detects _ex;

Processing unit, for setting up the functional relation of electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM; Obtain determining the functional relation between function and CID, PEM by CID and the two-parameter matching of PEM; Described definite function is the phase place that comprises described electromagnetic propagation impedance and the expression formula of Amplitude Ratio information; Analog detection process obtains electromagnetic propagation impedance theory value Z _th, respectively by Z _thand Z _exdescribed in substitution, determine that function obtains the first functional value and the second functional value; Solve CID and the PEM of the gap minimum that can make between first, second functional value, as testing result.

7. system as claimed in claim 6, is characterized in that, the functional relation that described processing unit is set up electromagnetic propagation impedance and internal diameter of the pipeline CID and electromagnetic attributes PEM refers to:

Described processing unit is by airborne propagation impedance Z _airwith the propagation impedance Z that affected by pipeline _wsum obtains electromagnetic propagation impedance; Wherein:

$Z_{\mathrm{air}}=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}F(x,D_T,D_R,d)\mathrm{dx};$

$Z_w=\mathrm{j\&omega;}{\mathrm{\&mu;}}_0{\&Integral;}_0^{\&infin;}T(x,D_T,D_R,d)B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)\mathrm{dx};$

In formula, x represents along the integration amount of electromagnetic field transmission direction;

Function F (x, D _t, D _r, d), T (x, D _t, D _r, d) represent in air and two kinds of environmental baselines of pipeline the impedance component irrelevant with pipe parameter;

Wherein, D _tand D _rbe divided into the diameter of transmitting coil and magnetic test coil, d is the distance between transmitting coil and magnetic test coil, μ _wand σ _wbe respectively magnetic permeability and the conductivity of tube wall, μ ₀for managing the magnetic permeability of interior medium, b is CID/2, b=CID/2, the angular frequency that ω is coil excitation signals;

Described B function is: $B(x,{\mathrm{\&mu;}}_w,{\mathrm{\&mu;}}_0,{\mathrm{\&sigma;}}_w,b)=\frac{\mathrm{\&xi;}{K}_0\left(\mathrm{xb}\right)-K_1\left(\mathrm{xb}\right)}{\mathrm{\&xi;}{I}_0\left(\mathrm{xb}\right)+I_1\left(\mathrm{xb}\right)};$

Wherein I _nand K (x) _n(x) be respectively the first kind and Equations of The Second Kind modified Bessel function; N is order, and value is 0,1,2;

The degree of coupling ξ that obtains pipe electromagnetic propagation impedance after simplification is:

$\mathrm{\&xi;}=\frac{\sqrt{2}x}{(1+j)}\frac{1}{{\mathrm{\&mu;}}_0\sqrt{\mathrm{\&omega;}}}\mathrm{PEM},\mathrm{PEM}=\sqrt{\frac{{\mathrm{\&mu;}}_w}{{\mathrm{\&sigma;}}_w}}.$

8. system as claimed in claim 7, is characterized in that, described definite function is:

Wherein Z is electromagnetic propagation impedance, and Re (Z) refers to the real part of Z.

9. system as claimed in claim 8, is characterized in that, described processing unit obtains determining that by CID and the two-parameter matching of PEM the functional relation between function and CID, PEM refers to:

The described processing unit first step first with for dependent variable, ξ is carried out to matching, obtain be worth the expression formula model about ξ:

Second step is taking CID as independent variable, taking the value of fitting result g, h, s, t as dependent variable, finds functional relation, obtains the functional relation of g about CID; Repeat second step until obtain h, s, the t functional relation about CID.

10. system as claimed in claim 8, is characterized in that, CID and PEM that described processing unit solves the gap minimum that can make between first, second functional value refer to:

Described processing unit is chosen L-M in conjunction with Q-N algorithm, solving non-linear least square problem:

$L\left(y\right)=\frac{1}{2}\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left(v_i\left(y\right)\right)}^2$

Wherein,

V _i(y)=M _i(CID, ξ)-G _i(CID, ξ); I is residual error amount counting, and m is residual error amount, is greater than unknown quantity number; M _i(CID, ξ) is the actual value detecting, G _i(CID, ξ) is theoretical value;

After following formula meets three times continuously, be Q-N algorithm by L-M algorithmic transformation:

||L'(y)|| _∞<0.02*L(y)。