Roadway section area measuring method based on curve fitting

Abstract

The invention belongs to the technical field of roadway measurement, and relates to a roadway section area measurement method based on curve fitting. Comprising the following steps: establishing a two-dimensional coordinate system in a roadway section; a plurality of measuring points are sequentially selected according to proper intervals in the forward extension direction of the x axis of the two-dimensional coordinate system, and coordinates of intersection points of the measuring points and the roadway section in the vertical direction are obtained; obtaining a contour characteristic curve function of the roadway section according to the plurality of intersection point coordinates, wherein the contour comprises a top plate contour and a bottom plate contour; and obtaining the area of the roadway section according to function integration. When the value change of the measurement distance is large, the distance between the measurement points is reduced, and the measurement points are increased; and when the numerical value of the measurement distance changes slightly, the distance between the measurement points is increased, and the measurement points are reduced. According to the method, the two-dimensional coordinate system is established, the multiple measurement points are selected, the coordinates of the intersection point of each measurement point and the roadway section are obtained, the irregular or seriously-deformed roadway section shape is described through the function, and the section area measurement precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of roadway measurement, and relates to a method for measuring the cross-sectional area of a roadway based on curve fitting. Background Art

[0002] With the continuous development of mine intelligent ventilation technology, the accurate determination of ventilation resistance and the effective monitoring of ventilation parameters have become key links to ensure the efficient operation of the mine ventilation system. The accurate measurement of air volume is one of the core indicators of the ventilation system, and its calculation depends on the accurate measurement of wind speed and roadway cross-sectional area. However, the current methods for measuring the roadway cross-sectional area mainly rely on empirical formula methods. This method performs well when dealing with regular roadway cross-sections, but faces many challenges in practical applications. First of all, the mine environment is complex and changeable. Due to factors such as geological conditions and mining activities, roadways often deform, resulting in irregular roadway cross-sectional shapes. In this case, there is a large deviation between the measurement results of the traditional empirical formula method and the actual situation, and the measurement error increases significantly. Secondly, the empirical formula method relies on a fixed geometric model. For irregular or severely deformed roadways, it is difficult to accurately describe their true shapes, resulting in a significant reduction in the reliability of the measurement results. In addition, the operation of the traditional method is complex, requiring manual measurement of multiple points and manual calculation of the area, which is not only time-consuming and laborious, but also prone to introducing human errors. More importantly, the accuracy of the traditional method is insufficient and difficult to meet the high-precision requirements of modern mines for ventilation resistance monitoring and ventilation safety.

[0003] With the development of intelligent technology, the demand for automated measurement in the mine ventilation system is increasing day by day, and the traditional manual measurement method can no longer meet the management needs of modern mines. Therefore, there is an urgent need for a new method for measuring the roadway cross-sectional area, which can adapt to irregular roadway cross-sections, achieve high-precision measurement, and have the ability of automated operation. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for measuring the cross-sectional area of a roadway based on curve fitting. By establishing a two-dimensional coordinate system and selecting multiple measurement points, the intersection coordinates of each measurement point and the roadway cross-section are obtained, so as to accurately describe the shape of irregular or severely deformed roadway cross-sections, fully consider the irregularity of the roadway contour, and improve the accuracy of area measurement.

[0005] To achieve the above purpose, the present invention provides a method for measuring the cross-sectional area of a roadway based on curve fitting, including the following steps:

[0006] Step S1: Establish a two-dimensional coordinate system within the roadway cross-section;

[0007] Step S2: Select multiple measurement points in sequence along the extension direction of the x-axis of the two-dimensional coordinate system, and simultaneously obtain the intersection coordinates of each measurement point and the roadway cross-section along the vertical direction;

[0008] Step S3. Obtain the contour of the roadway section based on the coordinates of multiple intersection points. The contour includes at least the roof contour and the floor contour.

[0009] Step S4. Obtain the area of the roadway section according to the contour.

[0010] Optionally, step S1 further includes:

[0011] Step S11. Obtain a reference point within the roadway section.

[0012] Step S12. Extend the reference point horizontally to obtain two intersection points with the roadway section.

[0013] Step S13. Establish a two-dimensional coordinate system based on the intersection points.

[0014] Optionally, step S13 further includes:

[0015] Step S131. Select one of the two intersection points as the origin of the two-dimensional coordinate system.

[0016] Step S132. Take the horizontal line where the origin is located as the x-axis, and take the vertical line where the origin is located as the y-axis.

[0017] Step S133. Establish a two-dimensional coordinate system according to the x-axis and the y-axis.

[0018] Optionally, step S2 further includes:

[0019] Step S21. Select a measurement point along the extension direction of the x-axis of the two-dimensional coordinate system, and record the moving distance between the measurement point and the origin.

[0020] Step S22. In the vertical direction, obtain the measurement distances between the measurement point and the roof and the floor of the roadway section.

[0021] Step S23. Obtain the two intersection point coordinates of the measurement point according to the moving distance and the measurement distances. The two intersection point coordinates include the intersection point coordinate of the vertical line where the measurement point is located and the roof of the roadway section and the intersection point coordinate of the vertical line where the measurement point is located and the floor of the roadway section.

[0022] Step S24. Repeat steps S21 - S23 to obtain multiple measurement points and multiple intersection point coordinates.

[0023] Optionally, in step S24, the distances between multiple measurement points and the origin gradually increase, and there is a measurement point that coincides with the origin.

[0024] Optionally, in step S24, when the numerical change of the measurement distance is large, reduce the spacing between the measurement points and increase the measurement points.

[0025] When the numerical change in the measured distance is small, increase the spacing between the measurement points and reduce the number of measurement points.

[0026] Optionally, step S3 further includes:

[0027] Step S31: Among the multiple intersection coordinates, take the intersection coordinates of the vertical lines where the multiple measurement points are located and the roof of the roadway section as the roof intersection coordinates;

[0028] Step S32: Fit the roof intersection coordinates to obtain the roof contour of the roadway section;

[0029] Step S33: Among the multiple intersection coordinates, take the intersection coordinates of the vertical lines where the multiple measurement points are located and the floor of the roadway section as the floor intersection coordinates;

[0030] Step S34: Fit the floor intersection coordinates to obtain the floor contour of the roadway section.

[0031] Optionally, the fitting method in step S3 includes the least squares method.

[0032] Optionally, in step S4, the area of the roadway section is obtained by function integration.

[0033] The beneficial effects of the present invention are as follows:

[0034] The present invention establishes a two-dimensional coordinate system and selects multiple measurement points to obtain the intersection coordinates of each measurement point and the roadway section, which can accurately describe the shape of an irregular or severely deformed roadway section. It fully considers the irregularity of the roadway contour and can improve the measurement accuracy. Especially for roadways with complex shapes, traditional methods are difficult to accurately measure, while this method can effectively solve this problem. In addition, compared with traditional roadway measurement methods, the measurement method proposed by the present invention can be distinguished from the empirical formula calculation method for regular sections, without considering the section type, and can also take into account the winding trend of the roadway wall in the area calculation of the section, with high area calculation accuracy and good versatility.

[0035] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be learned from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Description of the Drawings

[0036] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0037] Figure 1Flow chart of the roadway cross-sectional area measurement method provided by the present invention;

[0038] Figure 2 Schematic diagram of the coordinate system of the roadway cross-sectional area measurement method provided by the present invention. Specific implementation manners

[0039] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the drawings provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0040] Among them, the drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and cannot be understood as a limitation to the present invention; in order to better illustrate the embodiments of the present invention, some components in the drawings will be omitted, enlarged or reduced, which do not represent the dimensions of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0041] In the drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, it is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the drawings are only for illustrative purposes and cannot be understood as a limitation to the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0042] As Figure 1 , Figure 2 shown, the present invention provides a roadway cross-sectional area measurement method based on curve fitting, including the following steps:

[0043] Step S1: Establish an X-Y two-dimensional coordinate system in the roadway cross-section;

[0044] Step S2: Select a plurality of measurement points (O, O i , O i+1 ... O n ) along the positive extension direction of the x-axis of the two-dimensional coordinate system, and then obtain the intersection coordinates of each measurement point along the vertical direction with the roadway cross-section;

[0045] Step S3. Obtain the characteristic contour of the roadway section based on multiple intersection coordinates, including the roof contour and the floor contour;

[0046] Step S4. Obtain the area of the roadway section by integration according to the function extracted from the contour.

[0047] Furthermore, step S1 further includes:

[0048] Step S11. Obtain a reference point within the roadway section;

[0049] Step S12. Extend the reference point horizontally to obtain two intersections with the roadway section;

[0050] Step S13. Establish a two-dimensional coordinate system based on the intersections.

[0051] Furthermore, step S13 further includes:

[0052] Step S131. Select one of the two intersections as the origin O of the two-dimensional coordinate system;

[0053] Step S132. Take the horizontal line where the origin is located as the x-axis, and take the vertical line where the origin is located as the y-axis;

[0054] Step S133. Establish a two-dimensional coordinate system according to the x-axis and the y-axis.

[0055] Furthermore, step S2 further includes:

[0056] Step S21. Sequentially select measurement points along the extension direction of the x-axis of the two-dimensional coordinate system, and record the distance d between the measurement point and the previous measurement point i ;

[0057] Step S22. Vertically, obtain the measurement distances between the measurement point and the roof and the floor of the roadway section. The distance between the measurement point and the roof of the roadway section is l 01 ,..., l i1 , l i+11 ,..., l n1 , and the distance between the measurement point and the floor of the roadway section is l 02 ,..., l i2 , l i+12 ,..., l n2 ;

[0058] Step S23. Extend along the two vertical directions of the measurement point to obtain two intersections with the roadway contour. The two intersection coordinates include the intersection coordinates of the vertical line where the measurement point is located and the roof of the roadway section and the intersection coordinates of the vertical line where the measurement point is located and the floor of the roadway section;

[0059] Step S24. Repeat steps S21 - S23 to obtain multiple measurement points and multiple intersection coordinates; the intersection coordinates of the vertical line where the measurement point is located and the roof of the roadway section are: A0(0, l 01 ), A i (d i , l i1 ), A i+1 (d i+1 , l i+11 )... A n (d n , l n1 ); the intersection coordinates of the vertical line where the measurement point is located and the floor of the roadway section are B0(0, l 02 ), B i (d i , l i2 ), B i+1 (d i+1 , l i+12 )... B n (d n , l n2 ).

[0060] Further, in step S24, the distances between the multiple measurement points and the origin gradually increase, and there is a measurement point that coincides with the origin.

[0061] Further, in step S24, when the numerical change of the measured distance is large, it indicates that the contour curvature changes greatly here. Reduce the spacing between measurement points and increase the measurement points to improve the measurement density; when the numerical change of the measured distance is small, it indicates that the contour curvature changes little here. Increase the spacing between measurement points and reduce the measurement points to improve the measurement efficiency.

[0062] Further, step S3 further includes:

[0063] Step S31. Among the multiple intersection coordinates, take the multiple intersection coordinates of the vertical lines where the multiple measurement points are located and the roof of the roadway section as the roof intersection coordinates;

[0064] Step S32. Fit the roof intersection coordinates to obtain the roof contour feature curve function of the roadway section, denoted as f1(x);

[0065] Step S33. Among the multiple intersection coordinates, take the multiple intersection coordinates of the vertical lines where the multiple measurement points are located and the floor of the roadway section as the floor intersection coordinates;

[0066] Step S34. Fit the floor intersection coordinates to obtain the floor contour feature curve function of the roadway section, denoted as f2(x).

[0067] Further, the fitting method in step S3 includes the least squares method, and the commonly used functions for the fitting curve are as follows:

[0068] (1) Linear model y = a1x + a2;

[0069] (2) Polynomial model y = a1x m + a2x m-1 + … + a m x + a m+1 (Generally, m is taken within 3 and should not be too high);

[0070] For the distribution of point coordinates that does not conform to linear or polynomial, non - linear fitting can be tried, such as exponential, logarithmic, power, etc.

[0071] Further, in step S4, the area of the roadway section is obtained by function integration, and the specific calculation formula is:

[0072]

[0073] In the formula: d is the sum of the moving distances of the measuring points, d = d1 + d2 + … + d n .

[0074] When implementing the roadway section area measurement method based on curve fitting provided by the present invention, tracks can be arranged horizontally in the roadway, a laser rangefinder is installed on the tracks, the laser rangefinder moves on the tracks, and measures distances upward and downward at the selected measurement points, so as to obtain the intersection coordinates of the vertical line where the measurement points are located and the roof contour and the floor contour. After the laser rangefinder has completed distance measurement at all measurement points, curve fitting is respectively performed on the coordinates related to the roof contour and the coordinates related to the floor contour, and finally a two - dimensional closed figure is obtained, which is the shape of the roadway section.

[0075] The present invention establishes a two - dimensional coordinate system and selects multiple measurement points to obtain the intersection coordinates of each measurement point and the roadway section, which can accurately describe the shape of the irregular or severely deformed roadway section, fully consider the irregularity of the roadway contour, and can improve the measurement accuracy. Especially for roadways with complex shapes, it is difficult to accurately measure with traditional methods, while this method can effectively solve this problem. In addition, compared with traditional roadway measurement methods, the measurement method proposed by the present invention can be distinguished from the empirical formula calculation method for regular sections, without considering the section type, and can also take into account the winding trend of the roadway wall in the area calculation of the section, with high area calculation accuracy and good versatility.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for measuring the cross-sectional area of a roadway based on curve fitting, characterized in that, It includes the following steps: Step S1: Establish a two-dimensional coordinate system within the roadway section; Step S2: Sequentially select multiple measurement points along the extension direction of the x-axis of the two-dimensional coordinate system, and obtain the intersection coordinates of each measurement point with the roadway section in the vertical direction; Step S3: Obtain the contour of the roadway section according to the multiple intersection coordinates, and the contour at least includes the roof contour and the floor contour; Step S4: Obtain the area of the roadway section according to the contour.

2. The roadway cross-sectional area measurement method according to claim 1, characterized in that: The step S1 further includes: Step S11: Obtain a reference point within the roadway section; Step S12: Extend the reference point horizontally to obtain two intersection points with the roadway section; Step S13: Establish the two-dimensional coordinate system according to the intersection points.

3. The roadway cross-sectional area measurement method according to claim 2, wherein: The step S13 further includes: Step S131: Select one of the two intersection points as the origin of the two-dimensional coordinate system; Step S132: Take the horizontal line where the origin is located as the x-axis, and take the vertical line where the origin is located as the y-axis; Step S133: Establish the two-dimensional coordinate system according to the x-axis and the y-axis.

4. The roadway cross-sectional area measurement method according to claim 3, wherein: The step S2 further includes: Step S21: Select a measurement point along the extension direction of the x-axis of the two-dimensional coordinate system, and obtain the moving distance between the measurement point and the origin; Step S22: In the vertical direction, obtain the measurement distances between the measurement point and the roof and the floor of the roadway section; Step S23: Obtain the two intersection coordinates of the measurement point according to the moving distance and the measurement distances, and the two intersection coordinates include the intersection coordinate of the vertical line where the measurement point is located with the roof of the roadway section and the intersection coordinate of the vertical line where the measurement point is located with the floor of the roadway section; Step S24: Repeat steps S21 - S23 to obtain multiple measurement points and multiple intersection coordinates.

5. The roadway cross-sectional area measurement method according to claim 4, wherein: In step S24, the distances between multiple measurement points and the origin gradually increase, and there is a measurement point that coincides with the origin.

6. The roadway cross-sectional area measurement method according to claim 4, characterized in that: In step S24, when the numerical change of the measurement distance is large, reduce the spacing between the measurement points and increase the measurement points; When the numerical change of the measurement distance is small, increase the spacing between the measurement points and reduce the measurement points.

7. The roadway cross-sectional area measurement method according to claim 4, wherein: The step S3 further includes: Step S31: Among the multiple intersection coordinates, take the multiple intersection coordinates of the vertical lines where the multiple measurement points are located with the roof of the roadway section as the roof intersection coordinates; Step S32: Fit the roof intersection coordinates to obtain the roof contour characteristic curve function of the roadway section; Step S33: Among the multiple intersection coordinates, take the multiple intersection coordinates of the vertical lines where the multiple measurement points are located with the floor of the roadway section as the floor intersection coordinates; Step S34: Fit the floor intersection coordinates to obtain the floor contour characteristic curve function of the roadway section.

8. The roadway cross-sectional area measurement method according to claim 7, wherein: The fitting method in step S3 includes the least squares method.

9. The roadway cross-sectional area measuring method according to claim 7, wherein: In step S4, the area of the roadway section is obtained by function integration.

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