Calculation method for electromagnetic wave reflection propagation in U-shaped roadway

Abstract

The invention discloses a calculation method for electromagnetic wave reflection propagation in a U-shaped roadway. The calculation method comprises the following steps: S1, constructing an electromagnetic reflection model of the U-shaped mine roadway by adopting a mirror image method; s2, according to the electromagnetic reflection model of the U-shaped mine laneway, effective reflection points are obtained through a mirror image method; s3, obtaining an effective reflection path through a mirror image method according to the effective reflection points; and S4, according to the effective reflection path, obtaining reflection field intensity distribution of each point in the path. By adopting the technical scheme of the invention, the problem that the electromagnetic wave conduction calculation becomes more complicated due to the influence of multiple reflection and diffraction on the electromagnetic wave in the U-shaped mine tunnel is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of electromagnetic wave transmission, and in particular relates to a calculation method for electromagnetic wave reflection propagation in a U-shaped tunnel. Background Art

[0002] The distribution of underground coal mine tunnels is intricate and complex. The propagation of electromagnetic waves in confined spaces is affected by various factors, and the propagation characteristics are quite different from those in the ground space. At present, the calculation of electromagnetic wave propagation in underground tunnels is mainly for straight tunnel spaces. However, in U-shaped mine tunnels, electromagnetic waves are affected by multiple reflections, diffraction, etc., and the calculation of electromagnetic wave conduction becomes more complicated. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a calculation method for the reflection and propagation of electromagnetic waves in a U-shaped tunnel.

[0004] To achieve the above object, the present invention adopts the following technical solution:

[0005] A calculation method for electromagnetic wave reflection propagation in a U-shaped tunnel, comprising:

[0006] Step S1, constructing an electromagnetic reflection model of a U-shaped mine tunnel by using a mirror image method;

[0007] Step S2, obtaining effective reflection points by using a mirror image method according to the electromagnetic reflection model of the U-shaped mine tunnel;

[0008] Step S3, obtaining a valid reflection path by using a mirror image method according to a valid reflection point;

[0009] Step S4: According to the effective reflection path, the reflection field intensity distribution of each point in the path is obtained.

[0010] Preferably, the electromagnetic reflection model of the U-shaped mine tunnel consists of three parts, namely two horizontal tunnels and one vertical tunnel, which include eight reflection surfaces and a relay node P; a reflection surface is set to coincide with the YOZ coordinate plane, denoted as m1; the plane connecting m1 is m2; the plane connecting m2 is m3; the plane closest to m1 and parallel is m4; the plane parallel to m2 is m5; the plane closest to m3 and parallel is m6; the top plane is m7; and the bottom plane is m8.

[0011] Preferably, according to the determination of the effective reflection path, the number of effective reflection lines from second to eighth times in the U-shaped lane is calculated.

[0012] Preferably, step S4 comprises:

[0013] According to the mirror method, the incident angle, reflection coefficient and effective reflection path length of each effective reflection are calculated;

[0014] According to the incident angle, reflection coefficient and effective reflection path length, the reflection field intensity distribution at each point in the path is obtained.

[0015] The present invention adopts the mirror method to construct the electromagnetic reflection model of the U-shaped mine tunnel; in order to consider the influence of path loss, the electromagnetic wave will be significantly attenuated after passing through the two corners, and may even disappear completely. At the same time, the existence of the two corners will significantly increase the number of reflection lines and the complexity of calculation. Introducing a relay node in the center of the tunnel can enhance the field strength of the electromagnetic wave at the node and reduce the complexity of the reflection line calculation. By determining the boundaries of each reflection surface, calculating the mirror point and the reflection point, and judging the validity of the mirror point, the effective reflection path is determined, and then the field strength distribution of each point in the path is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0017] Figure 1 This is a flow chart of a calculation method for electromagnetic wave reflection and propagation in a U-shaped tunnel according to an embodiment of the present invention;

[0018] Figure 2 This is the U-shaped tunnel model diagram;

[0019] Figure 3 Compute graph for mirror points;

[0020] Figure 4 are effective reflection line and invalid reflection line diagrams; wherein, (a) is an effective reflection line diagram, (b) is an invalid reflection line diagram through planes m4 and m5, (c) is an invalid reflection line diagram through planes m5 and m6, and (d) is an invalid reflection line diagram through planes m4, m5 and m6;

[0021] Figure 5 is the two-dimensional segmentation map of plane m8;

[0022] Figure 6 Compute a map for the reflection points;

[0023] Figure 7 It is a two-dimensional four-times effective reflection path diagram;

[0024] Figure 8 It is a two-dimensional five-order effective reflection path diagram;

[0025] Fig. 9 It is a two-dimensional six-order effective reflection path;

[0026] Fig.10 It is a three-dimensional effective reflection map. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] Embodiment 1:

[0030] like Figure 1 As shown, an embodiment of the present invention provides a method for calculating electromagnetic wave reflection propagation in a U-shaped tunnel, comprising:

[0031] Step S1, constructing an electromagnetic reflection model of a U-shaped mine tunnel by using a mirror image method;

[0032] Step S2, obtaining effective reflection points by using a mirror image method according to the electromagnetic reflection model of the U-shaped mine tunnel;

[0033] Step S3, obtaining a valid reflection path by using a mirror image method according to a valid reflection point;

[0034] Step S4: According to the effective reflection path, the reflection field intensity distribution of each point in the path is obtained.

[0035] As an implementation method of the present invention, in step S1, the electromagnetic reflection model of the U-shaped mine tunnel is composed of three parts, namely two horizontal tunnels and one vertical tunnel, which include eight reflection surfaces and one relay node P; Figure 2 As shown, there is a reflection plane that coincides with the YOZ coordinate plane, denoted as m1; the plane connecting m1 is m2; the plane connecting m2 is m3; the plane closest to m1 and parallel is m4; the plane parallel to m2 is m5; the plane closest to m3 and parallel is m6; the top plane is m7; the bottom plane is m8. The lengths of the horizontal lanes are L1 and L3 respectively. The width is a, and the length of the vertical lane is L2, the width is c, and the height is b.

[0036] exist Figure 2 Establish a three-dimensional coordinate system in the , let the coordinates of the launch point be T(x t ,y t , z t ), the coordinates of the receiving point are R(xr ,y r , z r ), the coordinates of the mirror point are I(x i ,y i , z i ), the equation of the reflection plane m is Ax+By+Cz+D=0.

[0037] Draw a perpendicular line through the emission point T to the reflection plane m, with the foot of the perpendicular being F(x, y, z), then I is the mirror image point of the emission point T on the reflection plane m, as Figure 2 As shown. From the coordinates of the launch point T and the foot of the perpendicular point F, we can know that the straight line equation of TF is:

[0038]

[0039] Since the foot of the perpendicular point F is the midpoint of the straight line TI, the following relationship is satisfied:

[0040]

[0041] Since the foot of the perpendicular point F is on both the straight line TI and the plane m, the equation of the plane m, equation (1) and equation (2) can be combined to obtain:

[0042]

[0043] Substituting k into equation (1), we can get the coordinates of the foot of the perpendicular point F as follows:

[0044]

[0045] Finally, substitute equation (4) into equation (2) to obtain the coordinates of the mirror point I(x i ,y i , z i ).

[0046]

[0047] As an implementation method of an embodiment of the present invention, in step S2, according to the principle of the mirror method, to determine the position of the reflected line, it is necessary to connect the mirror point and the receiving point. The point where the connecting line intersects the reflecting surface is the reflection point, and the reflection point is located on the reflecting surface. When the reflection point is valid, the mirror point is also valid. The scenario applied in this article is a U-shaped tunnel, so only when the mirror points at all levels are valid can the corresponding valid reflected line be obtained. There are two corners and a relay node P between the transmitting point T and the receiving point R. Different from the propagation mode of a straight tunnel, the rays emitted by the transmitting point will be blocked by any of the planes among plane m4, plane m5 and plane m6, causing it to become an invalid reflected line, such as Figure 4 shown.

[0048] For U-shaped lanes, effective reflection points must meet the following conditions:

[0049] ① The reflection point should be located on the line connecting the mirror point and the receiving point, and have an intersection with the reflecting surface (except the boundary of the reflecting plane).

[0050] ② The lines connecting the reflection point and the transmitting point, the reflection point, the relay node and the receiving point cannot be blocked by plane m4, plane m5 and plane m6.

[0051] ③ When propagating in a straight channel, the reflection point is valid if conditions ① and ② are met.

[0052] ④ The rays emitted from the emission point need to pass through the relay node and reach the reflection surface. If conditions ① and ② are met, the reflection point is valid.

[0053] For U-shaped lanes, when electromagnetic waves pass through the boundary of the reflection plane, diffraction and other phenomena may occur. To determine whether the reflection point exists in the reflection plane, the boundary range of the reflection plane must be determined. Since the reflection planes m7 and m8 are U-shaped, electromagnetic waves are prone to diffraction and other phenomena when passing through the boundary of the plane. Taking the reflection plane m8 as an example, it is divided into rectangular planes similar to the other reflection planes through the idea of ​​segmentation, namely plane M1, plane M2 and plane M3. For each rectangular plane, it is verified whether the reflection point is located in the plane to determine the boundary range. If the reflection point is within the range of any of its planes, the reflection point is valid. According to the principle of the mirror method, it can be known that the mirror point is valid.

[0054] Figure 5 The two-dimensional schematic diagram of the U-shaped tunnel after the reflection plane m8 is divided into three rectangular planes M1, M2 and M3. Let the coordinates of the reflection point be H(x h ,y h , z h ), when point H is within the rectangular plane M1, it should satisfy 0<x h <a and 0≤y h <L1. If it is in plane M2, it should satisfy a≤x h ≤L2-a and L1-c<y h <L1. If it is in plane M3, it should satisfy L2-a<x h <L2 and 0≤y h <L3. Similarly, the boundary range judgment methods of several other reflection planes are consistent with this method.

[0055] By calculating the mirror point, the receiving point R is connected to intersect any reflection surface m at point H. At this time, point H is the reflection point, such as Figure 6 shown.

[0056] The coordinates of the mirror point are known to be I(x i ,y i , zi ), the coordinates of the receiving point are R(x r ,y r , z r ), find the coordinates of the reflection point H(x h ,y h , z h ),because and The ratio is the same, that is:

[0057]

[0058] Since the reflection point H is both on the straight line IR and in the reflection plane m, the simultaneous equation (6) and the reflection surface equation yields:

[0059]

[0060] Combining equations (6) and (7), we can get the coordinates of the reflection point H(x h ,y h , z h ).

[0061]

[0062] As an implementation method of an embodiment of the present invention, in step S3, taking the maximum number of reflections of eight times as an example, the relay node is set at the center of the lane. This position ensures that the relay node can cover the electromagnetic waves on both sides to the greatest extent and maintain the stable transmission of electromagnetic waves between relay nodes. According to the determination of the effective reflection path, the number of effective reflection lines from two to eight times in the U-shaped lane can be calculated. The following is the specific process of determining the four, five and six effective reflection paths:

[0063] 1. Determination of the four effective reflection paths

[0064] Figure 7 is a two-dimensional four-time effective reflection path, in which the combination of point T to point P as a secondary reflection and point P to point R as a secondary reflection is taken as an example. ① Make a primary mirror image of the emission point T relative to plane m1 to obtain the primary mirror image point I1. Take point I1 as the base point and make a secondary mirror image on plane m2 to obtain the secondary mirror image point I 12 . Will I 12 Point is connected to point P, and the intersection point on plane m2 is A 12 , and then A 12 Connect point T with point I1, and their intersection on plane m1 is point A1. Connect T, A1 and A in sequence. 12 ② Make a first-level mirror image of the relay node P relative to plane m5 to obtain the first-level mirror image point I5. Based on this point, make a second-level mirror image on plane m2 to obtain the second-level mirror image point I 52 . Will I52 Connect point A with point R, and the intersection point on plane m2 is A 52 , A 52 Connect point P, A5, and A in turn. 52 and point R, forming a secondary effective reflection path.

[0065] Since there are six reflection planes from the transmitting point T to the relay node P, each plane theoretically has a first-level mirror point, for a total of six first-level mirror points, and each first-level mirror point has five second-level mirror points excluding its own reflection plane, so there are theoretically 30 second-level mirror points from the transmitting point T to the relay node P, that is, 30 reflection lines, and there are theoretically 30 second-level mirror points from the relay node P to the receiving point R, that is, 30 reflection lines, so this combination theoretically has a total of 60 mirror points and 900 reflection lines. Similarly, when there is a combination of one reflection from the transmitting point T to the relay node P and three reflections from the relay node P to the receiving point R, and a combination of three reflections from the transmitting point T to the relay node P and one reflection from the relay node P to the receiving point R, there are theoretically 156 mirror points and 900 reflection lines. Therefore, all combinations of four-reflection paths theoretically have a total of 372 mirror points and 2700 reflection lines.

[0066] 2. Determination of five effective reflection paths

[0067] Figure 8 is a two-dimensional five-time effective reflection path, in which the combination of T point to P point is a second reflection and P point to R point is a third reflection. ① Make a primary mirror image of the emission point T relative to plane m1 to obtain the primary mirror image point I1. Take I1 as the base point and make a secondary mirror image on plane m2 to obtain the secondary mirror image point I 12 . Will I 12 Point is connected to point P, and the intersection point on plane m2 is B 12 , and then B 12 Point 1 is connected to point I1, and the intersection point on plane m1 is B1. Connect T, B1 and B in sequence 12 ② Make a primary mirror image of the relay node P relative to plane m5 to obtain the primary mirror image point I5. Taking I5 as the base point, make a secondary mirror image on plane m2 to obtain the secondary mirror image point I 52 . Then I 52 As the base point, make a three-level mirror image on plane m3 to obtain the three-level mirror point I 523 , will I 523 Connect point 1 with point R, and the intersection point on plane m3 is B 523 , and then B 523 Dot and I 52 The points are connected, and the intersection point on plane m2 is B 52 , and finally B 52Point P is connected to point I5, and the intersection point on plane m5 is B5. 52 Point, B 523 Points 1 and 2 form a three-fold effective reflection path.

[0068] From the above, it can be seen that there are theoretically 30 secondary mirror points from the transmitting point T to the relay node P, that is, 30 reflection lines, and there are theoretically 150 tertiary mirror points from the relay node P to the receiving point R, that is, 150 reflection lines. This combination theoretically has 180 mirror points and 4500 reflection lines. Similarly, when the transmitting point T to the relay node P is a combination of three reflections and the relay node P to the receiving point R is a combination of two reflections, there are theoretically 180 mirror points and 4500 reflection lines. When the transmitting point T to the relay node P is a combination of one reflection and the relay node P to the receiving point R is a combination of four reflections and the transmitting point T to the relay node P is a combination of four reflections and the relay node P to the receiving point R is a combination of one reflection, there are theoretically 756 mirror points and 4500 reflection lines. Therefore, all combinations of the five-reflection path theoretically have a total of 1872 mirror points and 18,000 reflection lines.

[0069] 3. Determination of the six effective reflection paths

[0070] Fig. 9 It is a two-dimensional six-time effective reflection path, in which the combination of T point to P point is a second reflection and P point to R point is a fourth reflection. ① Make a first-level mirror image of the emission point T relative to plane m1 to obtain the first-level mirror image point I1. With I1 as the base point, make a second-level mirror image on plane m2 to obtain the second-level mirror image point I 12 . Will I 12 Point is connected to point P, and the intersection point on plane m2 is C 12 , and then C 12 Point T is connected to point I1, and the intersection point on plane m1 is C1. Connect points T, C1 and C 12 ② Make a first-level mirror image of the relay node P relative to plane m5 to obtain the first-level mirror image point I5. Taking I5 as the base point, make a second-level mirror image on plane m2 to obtain the second-level mirror image point I 52 . Then I 52 As the base point, make a three-level mirror image of its plane m3 to obtain the three-level mirror point I 523 , and finally I 523 As the base point, make a four-level mirror image on plane m6 to obtain the four-level mirror point I 5236 . Will I 5236 Connect point C with point R, and the intersection point on plane m6 is C 5236 , and then C 5236 Dot and I 523 The points are connected, and the intersection point on plane m3 is C 523 Then C523 Dot and I 52 The points are connected, and the intersection point on plane m2 is C 52 Finally, C 52 Point P is connected to point I5, and the intersection point on plane m5 is C5. Connect points P, C5, C 52 Point, C 523 Point, C 5236 Points 1 and 2 form a four-time effective reflection path.

[0071] From the above, it can be seen that there are theoretically 30 secondary mirror points from the transmission point T to the relay node P, that is, 30 reflection lines, and there are theoretically 750 fourth-level mirror points from the relay node P to the receiving point R, that is, 750 reflection lines. In theory, this combination has 780 mirror points and 22,500 reflection lines. Similarly, when the transmission point T to the relay node P is a combination of four reflections and the relay node P to the receiving point R is a combination of two reflections, there are theoretically 780 mirror points and 22,500 reflection lines. When the transmission point T to the relay node P is a combination of one reflection and the relay node P to the receiving point R is a combination of five reflections and the transmission point T to the relay node P is a combination of five reflections and the relay node P to the receiving point R is a combination of one reflection, there are theoretically 3756 mirror points and 22,500 reflection lines. When the transmission point T to the relay node P is a combination of three reflections and the relay node P to the receiving point R is a combination of three reflections, there are theoretically 300 mirror points and 22,500 reflection lines. Therefore, all combinations of six reflection paths theoretically have a total of 9372 mirror points and 112500 reflection lines.

[0072] As an implementation method of an embodiment of the present invention, in step S4, in order to simplify the model calculation, a relay node is set at the center of the lane. The node is usually equipped with an amplifier, which can receive weaker electromagnetic waves and amplify them to close to the original strength through enhancement processing, so that it can be regarded as the antenna re-transmitting electromagnetic waves at the relay node. From the above theory, it can be seen that the maximum number of reflections from the relay node to the receiving point is seven times. It includes:

[0073] Step 41: Calculate the incident angle, reflection coefficient and path length of each effective reflection according to the mirror method.

[0074] According to the mirror method, the incident angle, reflection coefficient and path length of each effective reflection are calculated, and the effective reflection field intensity is synthesized at the receiving point. Taking the reflection surfaces m2 and m3 as an example, the ray emitted from point P reaches point R after one effective reflection.

[0075] Depend on Fig.10 It can be seen that the ray emitted by the relay node P is reflected once by the reflection surface m2 and reaches the receiving point R, then the vector and the normal vector of the reflecting surface m2 The acute angle between them is the incident angle θ i , that is, the cosine value is:

[0076]

[0077] The path length L of an effective reflection is the sum of the distance between the relay node P and the reflection point H and the distance between the reflection point H and the receiving point R. According to the distance formula between two points:

[0078]

[0079] L=PH+HR (12)

[0080] When a uniform plane wave is incident on the interface, the electric field vector of the incident wave in any direction should be divided into a component parallel to the incident plane and a component perpendicular to the incident plane. According to the Fresnel reflection law, the reflection coefficient R of the horizontally polarized wave is calculated respectively. ‖ and the reflection coefficient R of the vertically polarized wave ⊥ , whose expression is:

[0081]

[0082] Step 42: Obtain the reflected field intensity distribution at each point in the path according to the incident angle, reflection coefficient and effective reflection path length.

[0083] The transmitting antenna used is a half-wave dipole antenna, and the calculation formula for its electric field is:

[0084]

[0085] In formula (15), d is the distance from the reflection point to the relay node, I m is the maximum current in the antenna, k is the propagation constant, and θ is the incident angle.

[0086] Then the electric field vector of the incident wave is:

[0087]

[0088] According to Fresnel's reflection law, the electric field vector of the reflected wave is:

[0089]

[0090] In formula (17), α is the angle between the incident wave and the horizontal polarization wave, β is the angle between the incident wave and the vertical polarization wave, and are the unit vectors of horizontal and vertical polarization before reflection, and are the unit vectors of horizontal and vertical polarization after reflection, is the vector of the incident wave, which satisfies the following expression:

[0091]

[0092]

[0093] For a single reflection, the field strength of each single reflection is:

[0094]

[0095] In formula (21), R 1⊥ and R 1‖ are the reflection coefficients of vertical and horizontal polarized waves of the first reflection, and are the unit vectors of horizontal and vertical polarization before one reflection, and are the unit vectors of horizontal and vertical polarization after one reflection, q is the distance from the relay node to the reflection point, and q' is the distance from the reflection point to the receiving point.

[0096] Therefore, for p1 primary reflected rays, the total field strength generated is for:

[0097]

[0098] The calculation method for the reflected field intensity of the second to seventh order reflected rays is the same as above. According to the superposition theorem, the direct field intensity The field strength at the receiving point is superimposed with the first to seventh reflected field strength vectors. Its expression is:

[0099]

[0100] When converting the field strength unit to dB, first calculate the field strength at the receiving point The modulus of the field strength is shown in equation (25), and then divided by the modulus of the field strength when the distance from the receiving point is 0m, which is expressed as The reflected field strength at the receiving point in dB is obtained, as shown in formula (26).

[0101]

[0102] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for calculating electromagnetic wave reflection propagation in a U-shaped tunnel, characterized in that: include: Step S1, constructing an electromagnetic reflection model of a U-shaped mine tunnel by using a mirror image method; Step S2, obtaining effective reflection points by using a mirror image method according to the electromagnetic reflection model of the U-shaped mine tunnel; Step S3, obtaining a valid reflection path by using a mirror image method according to a valid reflection point; Step S4: According to the effective reflection path, the reflection field intensity distribution of each point in the path is obtained.

2. The method for calculating the reflection and propagation of electromagnetic waves in a U-shaped tunnel according to claim 1, characterized in that: The electromagnetic reflection model of the U-shaped mine tunnel consists of three parts, namely two horizontal tunnels and one vertical tunnel, which contain eight reflection surfaces and a relay node P; there is a reflection surface that coincides with the YOZ coordinate plane, denoted as m1; the plane connecting m1 is m2; the plane connecting m2 is m3; the plane closest to m1 and parallel is m4; the plane parallel to m2 is m5; the plane closest to m3 and parallel is m6; the top plane is m7; and the bottom plane is m8.

3. The method for calculating the reflection and propagation of electromagnetic waves in a U-shaped tunnel according to claim 1, characterized in that: According to the determination of the effective reflection path, the number of effective reflection lines from the second to the eighth order in the U-shaped lane is calculated.

4. The method for calculating the reflection and propagation of electromagnetic waves in a U-shaped tunnel as claimed in claim 3, characterized in that: Step S4 includes: According to the mirror method, the incident angle, reflection coefficient and effective reflection path length of each effective reflection are calculated; According to the incident angle, reflection coefficient and effective reflection path length, the reflection field intensity distribution at each point in the path is obtained.

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