CN106441155A - Structural plane contour line sampling accuracy determining method - Google Patents

Abstract

A structural plane contour line sampling accuracy determining method includes following steps: (1), extracting coordinate data of each point on a structural plane contour line; (2), adopting Fourier series to approach the coordinates of each point on the structural plane contour line; (3), calculating approximate fitted values of the Fourier series at different orders; (4), calculating a mean square error of distances between each point on the structural plane contour line to a horizontal line; (5), multiplying the mean square error by a fitting coefficient to acquire a threshold value of Fourier series approaching; (6), calculating a mean square error of approximate fitted values at different orders and under same horizontal coordinates and measured coordinates of the structural plane contour line; (7), when the order n is increased to a supercritical value an En is smaller than the threshold value of Fourier series approaching, considering the order n as a lowest order; (8), acquiring a sampling interval according to a frequency expression of Fourier series and the lowest order acquired by solving; (9), solving to acquire minimum sampling accuracy. By the method, sampling accuracy of the structural plane contour line can be determined effectively.

Description

A kind of determination method of structural plane contour line sampling precision

Technical field

The invention belongs to rock mechanics engineering field, is related to a kind of determination method of structural plane contour curve sampling precision.

Background technology

Rock structural plane roughness directly affects rock mass strength, deformation and seepage flow characteristics.Chinese scholars are carried out A large amount of researchs with regard to rock structural plane roughness evaluation methodology.For realizing the quantitative evaluation of structural plane rough surface property, Scholars are typically by the coordinate data of structural plane surface profile, every geometric parameter of computational representation roughness, and then set up Their mathematical statisticss relations with structural plane roughness coefficient.However, during people's analytical structure facial contour line coordinates data, often Different sampling precisions can be adopted, this causes roughness evaluation result to differ widely.When sampling precision is compared with hour, phase on contour line Adjacent 2 points level interval is larger, and on structural plane surface profile line, asperity property cannot be embodied by coordinate data, knot Structure surface roughness evaluation index is typically small.Yu and Vayssade (1991) is 0.25mm, 0.50mm by contrasting sampling precision, During 1.00mm, the diversity of structural plane roughness result of calculation, first proposed sampling precision can be to structural plane roughness evaluation There is important impact.At present, there is larger difference in the sampling precision that structural plane roughness analysis is selected, which is mainly distributed on Between 0.05mm to 10mm.Tatone and Grasselli (2012) point out at present do not have a kind of specification being widely recognized as or Code can be used to instruct the selection of sampling precision.Obviously, a kind of method for determining sampling precision is proposed to structural plane roughness The accurate evaluation of matter is most important.

Content of the invention

In order to overcome the shortcomings of that prior art cannot determine structural plane contour line sampling precision, the invention provides a kind of knot The determination method of structure facial contour curve sampling precision, is that further structural plane roughness is studied there is provided guarantee.

The technical solution adopted for the present invention to solve the technical problems is：

A kind of determination method of structural plane contour line sampling precision, comprises the following steps：

(1) the natural structure face of analysis required for selecting, is measured using three-dimensional laser scanner process, and extracts structural plane The coordinate data of each point on contour line；

(2) using Fourier space, each point coordinates on obtained structural plane contour line is approached,

Wherein, L is that structural plane survey line length, y is the height of each point on structural plane contour line, and x is each point on contour line Horizontal coordinate, a₀、a_nWith b_nFor the coefficient of Fourier space, n is order；

(3) size of n is constantly adjusted, calculates the approximate fits value of Fourier space under the conditions of different orders

(4) in one horizontal linear of catch cropping of structural plane contour line vertical coordinate maxima and minima, the horizontal line will be tied Structure facial contour line is divided into part below above the horizon part and horizontal line, constantly adjusts horizontal position, until level The upper and lower two parts area under the curve of line is equal.On computation structure facial contour line, each point is to the mean square deviation of the horizontal distance；

(5) Fourier space is set the fitting coefficient of value and structural plane contour line is approached, for example 5%, will on contour line respectively Point is multiplied by, to the mean square deviation of horizon distance, the threshold value that fitting coefficient is approached as Fourier space；

(6) as follows, the near of Fourier space under the conditions of identical horizontal coordinate is calculated under the conditions of different orders respectively Like match valueWith actual measurement structural plane profile line coordinates Y_iMean square deviation：

Wherein, i is coordinate points numbering on structural plane contour line；M is the points on structural plane contour line.

(7) E is analyzed_nWith the Changing Pattern that order n increases, the magnitude relationship of the threshold value that Fourier space is approached is judged.When When order n increases to a certain value, E_nLess than the threshold value that Fourier space is approached, now approached by Fourier space will for order n The minimum order that asks.

(8) according to Shannon's sampling theorem, only when sample frequency is more than the highest frequency of more than 2 times figures, image Essential information just accurately can be expressed.According to the minimum order that the frequency expression of Fourier space is obtained with solution, obtain The expression formula of sampling interval：

(9) minimum sampling precision is solved.

Beneficial effects of the present invention are mainly manifested in：Effectively determine structural plane contour line sampling precision.

Description of the drawings

Fig. 1 is actual measurement structural plane topography curve chart.

Fig. 2 is mean square deviation E_nGraph of relation with order n.

Specific embodiment

The invention will be further described below in conjunction with the accompanying drawings.

See figures.1.and.2, a kind of determination method of structural plane contour line sampling precision, comprise the following steps：

(1) the natural structure face of analysis required for selecting, is measured using high-precision three-dimensional laser scanner process, and extracts The coordinate data of each point on structural plane contour line；

(2) using Fourier space, each point coordinates on obtained structural plane contour line is approached,

Wherein, L is that structural plane survey line length, y is the height of each point on structural plane contour line, and x is each point on contour line Horizontal coordinate, a₀、a_nWith b_nFor the coefficient of Fourier space, n is order；

(3) size of n is constantly adjusted, calculates the approximate fits value of Fourier space under the conditions of different orders

(4) in one horizontal linear of catch cropping of structural plane contour line vertical coordinate maxima and minima, the horizontal line will be tied Structure facial contour line is divided into part below above the horizon part and horizontal line, constantly adjusts horizontal position, until level The upper and lower two parts area under the curve of line is equal.On computation structure facial contour line, each point is to the mean square deviation of the horizontal distance；

(5) Fourier space is set the fitting coefficient of value and structural plane contour line is approached, for example 5%, will on contour line respectively Point is multiplied by, to the mean square deviation of horizon distance, the threshold value that fitting coefficient is approached as Fourier space；

(6) as follows, the near of Fourier space under the conditions of identical horizontal coordinate is calculated under the conditions of different orders respectively Like match valueWith actual measurement structural plane profile line coordinates Y_iMean square deviation：

Wherein, i is coordinate points numbering on structural plane contour line；M is the points on structural plane contour line.

(7) E is analyzed_nWith the Changing Pattern that order n increases, the magnitude relationship of the threshold value that Fourier space is approached is judged.When When order n increases to a certain value, E_nLess than the threshold value that Fourier space is approached, now approached by Fourier space will for order n The minimum order that asks.

(8) according to Shannon's sampling theorem, only when sample frequency is more than the highest frequency of more than 2 times figures, image Essential information just accurately can be expressed.According to the minimum order that the frequency expression of Fourier space is obtained with solution, obtain The expression formula of sampling interval：

(9) minimum sampling precision is solved.

Example：A kind of determination method of structural plane contour line sampling precision, comprises the following steps：

(1) the 10cm natural structure face of analysis required for selecting, using handheld structure facial contour line measuring instrument record Structural plane contour line, by 0.5mm level point away from extract structural plane contour line on each point coordinate data, as shown in Figure 1；

(2) using Fourier space, each point coordinates on obtained structural plane contour line is approached, constantly adjusts n's Size, calculates the approximate fits value of Fourier space under the conditions of different orders

(3) in one horizontal linear of catch cropping of the structural plane contour line vertical coordinate maxima and minima, water is constantly adjusted The position of horizontal line, until the upper and lower two parts area under the curve of horizontal line is equal.On computation structure facial contour line, each point is to the horizontal line Distance mean square deviation be equal to 0.132mm；The mean square deviation of each point on contour line to horizon distance is multiplied by fitting coefficient 5% obtain To threshold value 0.0064mm that Fourier space is approached；

(4) the approximate fits value of Fourier space under the conditions of identical horizontal coordinate under the conditions of different orders is calculatedWith reality Geodesic structure facial contour line coordinates Y_iMean square deviation E_n, which is as shown in Figure 2 with the relation of order Changing Pattern.

(5) when order n increases to 37, E_nEqual to threshold value 0.0064mm that Fourier space is approached, now order 37 is Fourier space approaches required minimum order.

(6) minimum sampling precision or maximum sampling interval are calculated：

Therefore, the recommendation sampling precision of the structural plane contour curve should be less than 0.901mm.

Claims (1)

1. a kind of determination method of structural plane contour line sampling precision, it is characterised in that：The determination method is comprised the following steps：

(1) the natural structure face of analysis required for selecting, is measured using three-dimensional laser scanner process, and extracts structure facial contour The coordinate data of each point on line；

(2) using Fourier space, each point coordinates on obtained structural plane contour line is approached,

$y\left(x\right)=a_0+\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\[a_{n}cos\left(\frac{2n\mathrm{\π}}{L}x\right)+b_{n}sin\left(\frac{2n\mathrm{\π}}{L}x\right)\]$

Wherein, L is that structural plane survey line length, y is the height of each point on structural plane contour line, and x is the level of each point on contour line Coordinate, a₀、a_nWith b_nFor the coefficient of Fourier space, n is order；

(3) size of n is constantly adjusted, calculates the approximate fits value of Fourier space under the conditions of different orders

(4) in one horizontal linear of catch cropping of structural plane contour line vertical coordinate maxima and minima, the horizontal line is by structural plane Contour line is divided into part below above the horizon part and horizontal line, constantly adjusts horizontal position, until on horizontal line Lower two parts area under the curve is equal, and on computation structure facial contour line, each point is to the mean square deviation of the horizontal distance；

(5) Fourier space is set and approaches the fitting coefficient of value and structural plane contour line, by each point on contour line to horizontal line away from From mean square deviation be multiplied by the threshold value that fitting coefficient is approached as Fourier space；

(6) as follows, the approximate plan of Fourier space under the conditions of identical horizontal coordinate under the conditions of different orders is calculated respectively Conjunction valueWith actual measurement structural plane profile line coordinates Y_iMean square deviation：

$E_n=\sqrt{\frac{1}{m}\underset{i=1}{\overset{m}{\Σ}}{({\left({\hat{Y}}_i\right)}_n-{\left(Y_i\right)}_n)}^2}$

Wherein, i is coordinate points numbering on structural plane contour line；M is the coordinate points sum on structural plane contour line；

(7) E is analyzed_nWith the Changing Pattern that order n increases, the magnitude relationship of the threshold value that Fourier space is approached is judged, as order n When increasing to marginal value, E_nLess than the threshold value that Fourier space is approached, now, order n approaches required for Fourier space Minimum order；

(8) according to Shannon's sampling theorem, only when sample frequency is more than the highest frequency of more than 2 times figures, image basic Information just accurately can be expressed, and according to the minimum order that the frequency expression of Fourier space is obtained with solution, be adopted The expression formula of sample spacing：

${\mathrm{SI}}_{max}=\frac{L}{3n}$

(9) minimum sampling precision is solved.