CN105044785A - Probing method for underground pipeline with ground penetrating radar based on fuzzy clustering and Hough transform - Google Patents

Abstract

The invention discloses a probing method for an underground pipeline with a ground penetrating radar based on fuzzy clustering and Hough transform. According to the invention, an underground pipeline inverting method is provided and belongs to the field of computer digital image processing. The underground pipeline inverting method is characterized by inverting parameters, such as the position parameter of the underground pipeline and the semi-diameter parameter by a combined use of asymptote of a hyperbola, fuzzy c-mean clustering and Hough Transform. Based on a common offset ground penetrating radar, the probing method includes the following steps: obtaining radar data via B scanning, and obtaining a series of coordinates for inverting through target tracking; extracting a radar wave velocity by utilizing characteristics of variables contained in the series of coordinates; obtaining an accurate radar wave velocity in combination with the fuzzy c-mean clustering; after obtaining the radar wave velocity, obtaining a series of pipeline edge coordinates through triangle similarity, and utilizing the Hough Transform circle detection, and further accurately inverting main parameters of the pipelines. The probing method has the characteristics of accurate prediction and strong robustness.

Description

A kind of ground penetrating radar Electromagnetic Survey of Underground Pipelines method based on fuzzy clustering and Hough transform

Technical field

The invention belongs to computer digital image process field, for the feature of ground penetrating radar image, utilize hyperbolic curve asymptotic line, fuzzy C-means clustering and cluster Hough transform inverting underground utilities parameter.

Background technology

Ground penetrating radar transmitter launches ultrahigh frequency broadband short pulse electromagnetic wave to underground medium, when running into buried target and the interface of earth's surface and different medium, partial pulse ripple will be reflected back ground, received antenna receives, then data processing is carried out, when object within aerial signal scope and signal to noise ratio (S/N ratio) is suitable time, things concealed can be gone out by ground penetrating radar detection.The depth measurement of ground penetrating radar and resolution and following factor are about the electromagnetic property of antenna frequencies, emissive power, propagation medium, the shape of object and size.This patent adopts offset mode ground penetrating radar altogether, and offset mode is modal detection mode altogether, and when carrying out data acquisition, radar transmit-receive antenna moves detection with constant spacing along survey line, is called without offset mode when dual-mode antenna is spaced apart zero.Once a radar A sweep record is obtained when dual-mode antenna is simultaneously mobile, dual-mode antenna obtains a B scanning radar data record along survey line synchronizing moving, the horizontal shift of horizontal ordinate record receiving antenna, the ordinate record radar wave two-way time is poor, buried target burying depth can be estimated according to the velocity of wave in the round trip time difference and underground medium, more just can determine target location in conjunction with horizontal ordinate information.

Nineteen fifty-seven, HugoSteinhaus proposes the thought of K mean cluster first, until 1967, JamesMacQueen just achieves this algorithm.K mean cluster, the division for data is rigid, and each sample data is strictly divided into belongs to a certain class.But things does not often meet the condition of " either-or " in practical problems, that will consider there is fuzzy Problems existing, namely some things or feature are not only belong to a certain specific class, but " being this or that ", just belong to inhomogeneous degree different.Therefore fuzzy mathematics theory is introduced in cluster analysis, adopt fuzzy cluster analysis can obtain better effect.Fuzzy C-Means Cluster Algorithm, it is a kind of clustering algorithm based on fuzzy division, its thought be make to be divided into same cluster object between similarity maximum, and similarity between different bunches is minimum, determines that each data point belongs to the degree of certain cluster by degree of membership.1973, J.C.Dunn and J.C.Bezdek proposed this algorithm, and the one as early stage K means clustering method is improved.

Summary of the invention

The object of the invention is to scan by ground penetrating radar B the hyperbolic curve asymptotic line and Fuzzy C-Means Cluster Algorithm accurate inverting underground utilities parameter that obtain.This method has good adaptability, Stability and veracity.

This method carries out radar wave speed prediction according to following steps:

Step (A1): radar data is detected as picture to underground utilities and has Hyperbolic Feature, and this hyperbolic curve only has half and Open Side Down, total n element on hyperbolic curve, its horizontal ordinate is horizontal level x _i, i=1,2 ..., n, ordinate is signal t two-way time _i, i=1,2 ..., n.For reducing error information impact, remove this hyperbolic curve summit (x ₀, t ₀) near data, remaining m data;

Step (A2): the slope asking this m data to form, utilizes the slope of element line on hyperbolic curve to move closer to asymptotic feature, using on this hyperbolic curve every c some line slope as asymptotic estimation slope k _j, j=1,2 ..., m-c;

Step (A3): for a series of asymptotic estimation slope k _j, j=1,2 ..., m-c, we can obtain the estimated value of a series of velocity of wave by formula v=2 λ/k, wherein for compensation coefficient;

Step (A4): utilize Fuzzy C-Means Cluster Algorithm to carry out cluster to m-c wave velocity estimation value, by Rational choice initial clustering quantity s and correction coefficient λ, using the result of class center maximum for element as actual velocity of wave

Inverting pipeline parameter concrete steps are as follows:

Step (B1): first need axial coordinate (xm, ym) in rough calculation pipeline, wherein, xm is for making t _ix when obtaining minimum value _ivalue, i.e. x ₀, or severally make t _ix when obtaining minimum value _iaverage, wherein i=1,2 ..., n, (x _f, t _f) be distance summit (x on curve ₀, t ₀) far away a bit;

Step (B2): proportional according to the similar then corresponding sides of triangle, we can obtain pipeline marginal point coordinate (x _ei, y _ei), in order to overcome the error produced when partial data extracts, here will first to hyperbolic coordinate (x _i, y _i) carry out least square fitting, draw fitting result, substitute into equation, wherein $r=\sqrt{{(x_i-\mathrm{xm})}^2+{\left(\mathrm{ym}\right)}^2}-\frac{{\hat{v}t}_i}{2},x_{\mathrm{ei}}=x_i+(\mathrm{xm}-x_i)\frac{\hat{v}{t}_i}{r+{\hat{v}t}_i},$ $y_{\mathrm{ei}}=\mathrm{ym}\×\frac{\hat{v}{t}_i}{r+\hat{v}{t}_i},i=\mathrm{1,2},......,n;$

Step (B3): pipeline marginal point coordinate (x _ei, y _ei) may on pipeline edge, also may not on pipeline edge, therefore we need the impact being got rid of error information by cluster Hough transform, and then obtain the estimated value of pipeline radius

Step (B4): pipeline radius estimated value as known, the ym that we calculate before combining again, just can obtain the new coordinate (xm, ym) of axis of pipeline, wherein xm=xm, to sum up, we just obtain the parameter of pipeline detection $\{\mathrm{xm},\mathrm{ym},\hat{r},\hat{v}\}.$

The hyperbolic curve least square fitting step adopted in the present invention is as follows:

Step (C1): by hyperbolic coordinate (x _i, t _i) obtain linear equation coordinate (X _i, T _i), wherein

Step (C2): the parameter (A, B) calculating linear equation according to the principle of least square, wherein $B=\frac{1}{m}({\mathrm{\Σ}}_1^n{Y}_i-A{\mathrm{\Σ}}_1^n{X}_i);$

Step (C3): the hyp estimated parameter of digital simulation wherein

The cluster Hough transform step adopted in the present invention is as follows:

Step (D1): pipeline marginal point coordinate (x _ei, y _ei), i=1,2 ..., n, as the input parameter of Hough transform loop truss, also will define the variation range (r of radius simultaneously _min, r _max) and each step delta r changed, also to determine the number s of the initial clustering of fuzzy C-means clustering in addition;

Step (D2): Hough transform loop truss is by pipeline marginal point coordinate (x _ei, y _ei), i=1,2 ..., n as the center of circle, any two marginal point (x _e1, y _e1), (x _e2, y _e2) intersection point (x of circle that constructs _c1, y _c1) and (x _c2, y _c2) can following formulae discovery be passed through, $x_{c1}=\frac{-b+\sqrt{b^2-4\mathrm{ac}}}{2a},x_{c1}=\frac{-b-\sqrt{b^2-4\mathrm{ac}}}{2a},$ Meanwhile, $y_{c1}=\frac{y_{e1}+y_{e2}}{2}-\left(\frac{x_{e1}-x_{e2}}{y_{e1}-y_{e2}}\right)(x_{c1}-\frac{x_{e1}+x_{e2}}{2}),$ $y_{c2}=\frac{y_{e1}+y_{e2}}{2}-\left(\frac{x_{e1}-x_{e2}}{y_{e1}-y_{e2}}\right)(x_{c2}-\frac{x_{e1}+x_{e2}}{2}),$ Wherein $c=\frac{{(x_{e1}^2+x_{e2}^2+{(y_{e1}-y_{e2})}^2)}^2-4x_{e1}^2{x}_{e2}^2}{4{(y_{e1}-y_{e2})}^2}-{(r_{\min }+\mathrm{\Δr})}^2,$ $b=(x_{e1}+x_{e2})[1+{\left(\frac{x_{e1}-x_{e2}}{y_{e1}-y_{e2}}\right)}^2],a=1+{\left(\frac{x_{e1}-x_{e2}}{y_{e1}-y_{e2}}\right)}^2,$ The intersection point of circle may have 1,2 or 0;

Step (D3): utilize Fuzzy C-Means Cluster Algorithm to the set (x of the intersection point of circle _ck, y _ck), k=1,2 ..., n (n-1)/2 carries out cluster, due to usual x _ckerror is less, therefore main to y _ckcarry out cluster, we are using the estimated value of class center maximum for element as pipeline axis y coordinate recycling obtain the estimated value of caliber

The present invention just has following advantage:

1, radar wave speed prediction accurately, can meet the needs that pipeline parameter calculates.

2, there is stronger robustness, be applicable to the process of multiple Coherent Noise in GPR Record.

3, memory requirements is lower, avoids the situation of low memory.

Accompanying drawing explanation

Fig. 1 the present invention predicts radar wave speed process flow diagram

Fig. 2 inverting pipeline of the present invention parameter process flow diagram

Fig. 3 cluster Hough transform of the present invention process flow diagram

Fig. 4 brief flowchart of the present invention

Embodiment

The present invention adopts common offset mode ground penetrating radar, utilizes B to scan the radar data obtained, in conjunction with hyperbolic curve asymptotic line and fuzzy C-means clustering prediction radar wave speed.Utilize velocity of wave tentatively to determine pipeline axle center coordinate, obtain pipeline edge coordinate by the similar corresponding sides of triangle are proportional, then determine pipeline axle center further by cluster Hough transform loop truss, thus be finally inversed by underground utilities parameter.

Prediction radar wave speed flow process is as follows:

(1) as shown in Figure 1, scanning by extracting B the radar data obtained, obtaining a series of coordinate (x _i, t _i).This series of coordinate has Hyperbolic Feature, finds apex coordinate (x in coordinate ₀, t ₀), remove data near apex coordinate.

(2) remaining data (x is utilized _i, t _i) estimate slope k _j, and obtain a series of radar wave speed v further by calculating _j.Fuzzy C-means clustering is adopted to calculate radar wave speed v _jestimated value

Inverting pipeline parameter flow process is as follows:

(1) as shown in Figure 2, a series of coordinate (x is first utilized _i, t _i) and the estimated value of radar wave speed axial coordinate (xm, ym) in rough calculation pipeline, and then further fetch pipeline marginal point coordinate (x _ei, y _ei).

(2) to pipeline marginal point coordinate (x _ei, y _ei) do cluster Hough transform, obtain axial coordinate (xm, ym) in pipeline comparatively accurately.Thus determine the estimated value of pipeline radius further so just obtain the parameter of pipeline inverting

Cluster Hough transform flow process is as follows:

(1) by pipeline marginal point coordinate (x _ei, y _ei) as the center of circle, calculate its intersection point set (x _ck, y _ck).

(2) Fuzzy C-Means Cluster Algorithm antinode y is utilized _ckcluster, thus the estimated value obtaining pipeline axis y coordinate recycling obtain further

Claims (4)

1. the ground penetrating radar Electromagnetic Survey of Underground Pipelines method based on fuzzy clustering and Hough transform, the method is based upon radar data and is detected as in the theoretical foundation of picture to underground utilities, it is characterized in that, contrast with the hyperbolic curve figure of theory deduction, adopt asymptote slope as the basis of radar wave speed, rectification parameter and Fuzzy C-Means Cluster Algorithm is utilized to obtain radar wave speed accurately, in calculating radar wave speed process, successively containing following steps:

Step (A1): radar data is detected as picture to underground utilities and has Hyperbolic Feature, and this hyperbolic curve only has half and Open Side Down, total n element on hyperbolic curve, its horizontal ordinate is horizontal level x _i, i=1,2 ..., n, ordinate is signal t two-way time _i, i=1,2 ..., n.For reducing error information impact, remove this hyperbolic curve summit (x ₀, t ₀) near data, remaining m data;

Step (A2): the slope asking this m data to form, utilizes the slope of element line on hyperbolic curve to move closer to asymptotic feature, using on this hyperbolic curve every c some line slope as asymptotic estimation slope k _j, j=1,2 ..., m-c;

Step (A3): for a series of asymptotic estimation slope k _j, j=1,2 ..., m-c, we can obtain the estimated value of a series of velocity of wave by formula v=2 λ/k, wherein λ is compensation coefficient;

Step (A4): utilize Fuzzy C-Means Cluster Algorithm to carry out cluster to m-c wave velocity estimation value, by Rational choice initial clustering quantity s and correction coefficient λ, using the result of class center maximum for element as actual velocity of wave

2. method as claimed in claim 1, is characterized in that, obtains pipeline edge coordinate according to triangle is similar, and recycling cluster Hough transform loop truss determines the middle axial coordinate of pipeline further, thus obtains pipeline radius in interior series of parameters, and step is as follows:

Step (B1): first need axial coordinate (xm, ym) in rough calculation pipeline, wherein, xm is for making t _ix when obtaining minimum value _ivalue, i.e. x ₀, or severally make t _ix when obtaining minimum value _iaverage, wherein i=1,2 ..., n, (x _f, t _f) be distance summit (x on curve ₀, t ₀) far away a bit;

Step (B2): proportional according to the similar then corresponding sides of triangle, we can obtain pipeline marginal point coordinate (x _ei, y _ei), in order to overcome the error produced when partial data extracts, here will first to hyperbolic coordinate (x _i, y _i) carry out least square fitting, draw fitting result, substitute into equation, wherein

Step (B3): pipeline marginal point coordinate (x _ei, y _ei) may on pipeline edge, also may not on pipeline edge, therefore we need the impact being got rid of error information by cluster Hough transform, and then obtain the estimated value of pipeline radius

Step (B4): pipeline radius estimated value as known, the ym that we calculate before combining again, just can obtain the new coordinate of axis of pipeline wherein to sum up, we just obtain the parameter of pipeline detection

3. for the hyperbolic curve mentioned in method described in claim 2 calculate least square fitting, we by the method for dimensionality reduction, will realize least square fitting to linear function, then draw hyp estimated parameter concrete steps are as follows:

Step (C1): by hyperbolic coordinate (x _i, t _i) obtain linear equation coordinate (X _i, T _i), wherein

Step (C2): the parameter (A, B) calculating linear equation according to the principle of least square, wherein

Step (C3): the hyp estimated parameter of digital simulation wherein

4. for the cluster Hough transform mentioned in method described in claim 2, it is characterized in that, fuzzy C-means clustering is utilized to carry out cluster to the intersection point of Hough transform, the classification that wherein element is maximum regards the most concentrated region of space intersection as, this class center is as the estimated position of actual intersection point, and this, with regard to the clustering problem making the statistical problem of parameter space be converted to space intersection, exchanges space for the time, drastically reduce the area the memory consumption of calculating, concrete steps are as follows:

Step (D1): pipeline marginal point coordinate (x _ei, y _ei), i=1,2 ..., n, as the input parameter of Hough transform loop truss, also will define the variation range (r of radius simultaneously _min, r _max) and each step delta r changed, also to determine the number s of the initial clustering of fuzzy C-means clustering in addition;

Step (D2): Hough transform loop truss is by pipeline marginal point coordinate (x _ei, y _ei), i=1,2 ..., n as the center of circle, any two marginal point (x _e1, y _e1), (x _e2, y _e2) intersection point (x of circle that constructs _c1, y _c1) and (x _c2, y _c2) can following formulae discovery be passed through, meanwhile, wherein the intersection point of circle may have 1,2 or 0;

Step (D3): utilize Fuzzy C-Means Cluster Algorithm to the set (x of the intersection point of circle _ck, y _ck), k=1,2 ..., n (n-1)/2 carries out cluster, due to usual x _ckerror is less, therefore main to y _ckcarry out cluster, we are using the estimated value of class center maximum for element as pipeline axis y coordinate recycling obtain the estimated value of caliber