A calculation method for the reflection and propagation of electromagnetic waves in a U-shaped roadway

Abstract

The present invention discloses a calculation method for the reflection and propagation of electromagnetic waves in a U-shaped roadway, including: Step S1, constructing an electromagnetic reflection model of the U-shaped mine roadway by using the mirror image method; Step S2, obtaining effective reflection points by the mirror image method according to the electromagnetic reflection model of the U-shaped mine roadway; Step S3, obtaining effective reflection paths by the mirror image method according to the effective reflection points; Step S4, obtaining the reflection field strength distribution of each point in the path according to the effective reflection paths. By adopting the technical solution of the present invention, the problem that the calculation of electromagnetic wave conduction becomes more complicated due to the multiple reflections and diffractions of electromagnetic waves in the U-shaped mine roadway is solved.

Description

Technical Field

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

[0002] The roadways in coal mines are complexly distributed. The propagation of electromagnetic waves in a confined space is affected by various factors, and there are significant differences in propagation characteristics compared to the ground space. Currently, the calculation of electromagnetic wave propagation in underground roadways mainly focuses on straight roadway spaces. However, in U-shaped mine roadways, there are problems where electromagnetic waves are affected by multiple reflections, diffractions, etc., making the calculation of electromagnetic wave conduction more complex. Summary of the Invention

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

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

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

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

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

[0008] Step S3, obtaining effective reflection paths by using the mirror image method according to the effective reflection points;

[0009] Step S4, obtaining the reflected field strength distribution of each point in the path according to the effective reflection path.

[0010] Preferably, the electromagnetic reflection model of the U-shaped mine roadway consists of three parts, namely two horizontal roadways and one vertical roadway, which includes eight reflection surfaces and one relay node P; there is a reflection surface coinciding 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.

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

[0012] Preferably, step S4 includes:

[0013] Calculating the incident angle, reflection coefficient and path length of the effective reflection for each time according to the mirror image method;

[0014] The reflection field strength distribution of each point in the path is obtained according to the incident angle, reflection coefficient, and path length of the effective reflection.

[0015] The present invention constructs an electromagnetic reflection model of a U-shaped mine roadway by using the mirror image method; in order to consider the influence of path loss, etc., the electromagnetic wave will be significantly attenuated after passing through two corners and may even disappear completely. At the same time, the existence of two corners will significantly increase the number of reflected rays and the calculation complexity. By introducing a relay node in the center of the roadway, the field strength of the electromagnetic wave at the node can be enhanced, and the calculation complexity of the reflected rays can be reduced. By determining the boundaries of each reflecting surface, calculating the mirror image points and reflection points, and judging the effectiveness of the mirror image points, the effective reflection paths are determined, and then the field strength distribution of each point in the path is obtained. Description of the Drawings

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0017] Figure 1 It is a flowchart of the calculation method for the reflection and propagation of electromagnetic waves in the U-shaped roadway in the embodiment of the present invention;

[0018] Figure 2 It is a model diagram of the U-shaped roadway;

[0019] Figure 3 It is a calculation diagram of the mirror image points;

[0020] Figure 4 It is a diagram of effective and ineffective reflected rays; among them, (a) is a diagram of effective reflected rays, (b) is a diagram of ineffective reflected rays passing through planes m4 and m5, (c) is a diagram of ineffective reflected rays passing through planes m5 and m6, and (d) is a diagram of ineffective reflected rays passing through planes m4, m5, and m6;

[0021] Figure 5 It is a two-dimensional segmentation diagram of plane m8;

[0022] Figure 6 It is a calculation diagram of the reflection points;

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

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

[0025] Figure 9 It is a two-dimensional six-time effective reflection path;

[0026] Figure 10 It is a three-dimensional primary effective reflection diagram. Specific implementation manners

[0027] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0028] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0029] Embodiment 1:

[0030] As Figure 1 shown, the embodiment of the present invention provides a calculation method for the reflection and propagation of electromagnetic waves in a U-shaped roadway, including:

[0031] Step S1: Construct an electromagnetic reflection model of a U-shaped mine roadway by using the mirror image method;

[0032] Step S2: Obtain effective reflection points by using the mirror image method according to the electromagnetic reflection model of the U-shaped mine roadway;

[0033] Step S3: Obtain effective reflection paths by using the mirror image method according to the effective reflection points;

[0034] Step S4: Obtain the reflection field strength distribution of each point in the path according to the effective reflection path.

[0035] As an implementation manner of the embodiment of the present invention, in step S1, the electromagnetic reflection model of the U-shaped mine roadway is composed of three parts, namely two horizontal roadways and one vertical roadway, including eight reflection surfaces and one relay node P; as Figure 2 shown, there is a reflection surface coinciding 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 roadways are L1 and L3 respectively. The width is a, the length of the vertical roadway is L2, the width is c, and the height is b.

[0036] In Figure 2 a three-dimensional coordinate system is established, and the coordinates of the emission point are set as T(x t , y t , z t ), and 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 reflection plane).

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

[0051] ③ When propagating in a straight roadway, under the conditions of satisfying condition ① and condition ②, the reflection point is valid.

[0052] ④ The ray emitted from the transmitting point needs to pass through the relay node and reach the reflecting surface from the relay node. Under the conditions of satisfying condition ① and condition ②, the reflection point is valid.

[0053] For a U-shaped roadway, when the electromagnetic wave passes 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, diffraction and other phenomena are likely to occur when the electromagnetic wave passes through the boundary of this plane. Taking the reflection plane m8 as an example, it is divided into rectangular planes similar to several other reflection surfaces through the idea of segmentation, namely plane M1, plane M2, and plane M3. The boundary range is determined by verifying whether the reflection point is located within each rectangular plane. 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 image method, the mirror point is valid.

[0054] Figure 5 Figure 2D after the reflection plane m8 of the U-shaped roadway is divided into three rectangular planes M1, plane M2, and plane 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 within plane M2, it should satisfy a ≤ x h ≤ L2 - a and L1 - c < y h < L1. If it is within plane M3, it should satisfy L2 - a < x h < L2 and 0 ≤ y h < L3. Similarly, the method for judging the boundary range of several other reflection planes is the same as this method.

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

[0056] Given that the coordinates of the mirror point are 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 ). Since and have the same ratio, that is:

[0057]

[0058] Since the reflection point H is both on the line IR and in the reflection plane m, combining Equation (6) and the reflection plane equation shows that:

[0059]

[0060] Combining Equation (6) and Equation (7), the coordinates of the reflection point H(x h , y h , z h ) can be obtained.

[0061]

[0062] As an implementation manner of the 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 position of the roadway. 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 the relay nodes. According to the determination of the effective reflection path, the number of secondary to eighth effective reflection lines in the U-shaped roadway can be calculated. The following is the specific process of determining the four-, five-, and six-time effective reflection paths:

[0063] 1. Determination of the four-time effective reflection path

[0064] Figure 7 is a two-dimensional four-time effective reflection path, where the combination of the secondary reflection from point T to point P and the secondary reflection from point P to point R is taken as an example. ① Make a first-level mirror image of the transmitting point T with respect to the plane m1 to obtain the first-level mirror image point I1. Taking the point I1 as the base point, make a second-level mirror image of it in the plane m2 to obtain the second-level mirror image point I 12 . Connect the point I 12 with the point P, and the intersection point in the plane m2 is A 12 . Then connect the point A 12 with the point I1, and its intersection point in the plane m1 is the point A1. Connect T, A1, and the point A 12 in sequence to form a secondary effective reflection path. ② Make a first-level mirror image of the relay node P with respect to the plane m5 to obtain the first-level mirror image point I5, and based on this point, make a second-level mirror image in the plane m2 to obtain the second-level mirror image point I 52 . Connect the point I52 The point is connected to point R, and the intersection point on plane m2 is A 52 , and connect A 52 The point is connected to point I5, and the intersection point on plane m5 is A5. Connect P, A5, and A in sequence 52 and point R to form a secondary effective reflection path.

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

[0066] 2. Determination of the five - order effective reflection path

[0067] Figure 8 Take the combination of two reflections from point T to point P and three reflections from point P to point R as an example for the two - dimensional five - order effective reflection path. ① Make a first - order mirror image of the transmitting point T with respect to plane m1 to obtain the first - order mirror point I1. Taking I1 as the base point, make a second - order mirror image of it in plane m2 to obtain the second - order mirror point I 12 . Connect the point I 12 to point P, and the intersection point on plane m2 is B 12 , then connect the point B 12 to point I1, and the intersection point on plane m1 is B1. Connect T, B1, and B 12 in sequence to form a secondary effective reflection path. ② Make a first - order mirror image of the relay node P with respect to plane m5 to obtain the first - order mirror point I5. Taking I5 as the base point, make a second - order mirror image of it in plane m2 to obtain the second - order mirror point I 52 . Then, taking I 52 as the base point, make a third - order mirror image of it in plane m3 to obtain the third - order mirror point I 523 . Connect the point I 523 to point R, and the intersection point on plane m3 is B 523 , then connect the point B 523 to point I 52 , and the intersection point on plane m2 is B 52 . Finally, connect the point B 52The point is connected to point I5, and the intersection point in plane m5 is B5. Connect point P, point B5, point B 52 point, point B 523 point and point R in sequence to form a three - time effective reflection path.

[0068] As can be seen from the above, 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. Then, this combination theoretically has a total of 180 mirror points and 4500 reflection lines. Similarly, when the combination is that there are three - time reflections from the transmitting point T to the relay node P and two - time reflections from the relay node P to the receiving point R, there are theoretically 180 mirror points and 4500 reflection lines. When the combination is that there is one - time reflection from the transmitting point T to the relay node P and four - time reflections from the relay node P to the receiving point R, and when the combination is that there are four - time reflections from the transmitting point T to the relay node P and one - time reflections from the relay node P to the receiving point R, there are theoretically 756 mirror points and 4500 reflection lines. Therefore, all combinations of five - time reflection paths theoretically have a total of 1872 mirror points and 18000 reflection lines.

[0069] 3. Determination of six - time effective reflection path

[0070] Figure 9 Take the combination of two - time reflections from point T to point P and four - time reflections from point P to point R as an example for the two - dimensional six - time effective reflection path. ① Make a first - level mirror image of the transmitting point T with respect to plane m1 to obtain the first - level mirror point I1. Taking I1 as the base point, make a second - level mirror image of it in plane m2 to obtain the second - level mirror point I 12 . Connect point I 12 to point P, and the intersection point in plane m2 is C 12 . Then connect point C 12 to point I1, and the intersection point in plane m1 is C1. Connect point T, point C1 and point C 12 in sequence to form a two - time effective reflection path. ② Make a first - level mirror image of the relay node P with respect to plane m5 to obtain the first - level mirror point I5. Taking I5 as the base point, make a second - level mirror image of it in plane m2 to obtain the second - level mirror point I 52 . Then taking I 52 as the base point, make a third - level mirror image of it in plane m3 to obtain the third - level mirror point I 523 . Finally, taking I 523 as the base point, make a fourth - level mirror image of it in plane m6 to obtain the fourth - level mirror point I 5236 . Connect point I 5236 to point R, and the intersection point in plane m6 is C 5236 . Then connect point C 5236 to point I 523 , and the intersection point in plane m3 is C 523 . Then connect point C523 The point is connected to I 52 The points are connected, and the intersection point in the plane m2 is C 52 Finally, connect point C 52 to point I5, and the intersection point in the plane m5 is C5. Connect point P, point C5, C 52 point, C 523 point, C 5236 point and point R in sequence to form a four - time effective reflection path.

[0071] As can be seen from the above, there are theoretically 30 secondary mirror points from the emission point T to the relay node P, that is, 30 reflection lines. There are theoretically 750 quaternary mirror points from the relay node P to the receiving point R, that is, 750 reflection lines. Then, this combination theoretically has a total of 780 mirror points and 22500 reflection lines. Similarly, when the combination is such that there are four - time reflections from the emission point T to the relay node P and two - time reflections from the relay node P to the receiving point R, there are theoretically 780 mirror points and 22500 reflection lines. When the combination is such that there is one - time reflection from the emission point T to the relay node P and five - time reflections from the relay node P to the receiving point R, and when the combination is such that there are five - time reflections from the emission point T to the relay node P and one - time reflections from the relay node P to the receiving point R, there are theoretically 3756 mirror points and 22500 reflection lines. When the combination is such that there are three - time reflections from the emission point T to the relay node P and three - time reflections from the relay node P to the receiving point R, there are theoretically 300 mirror points and 22500 reflection lines. Therefore, all combinations of six - time reflection paths theoretically have a total of 9372 mirror points and 112500 reflection lines.

[0072] As an implementation manner 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 roadway. An amplifier is usually equipped at this node, which can receive weak electromagnetic waves and amplify them to be close to the original intensity through enhancement processing, so that it can be regarded as the antenna re - emitting electromagnetic waves at the relay node. As can be known from the above theory, the maximum number of reflections from the relay node to the receiving point is seven times. It includes:

[0073] Step 41: According to the mirror image method, calculate the incident angle, reflection coefficient, and path length of each effective reflection

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

[0075] From Figure 10 it can be known that the ray emitted by the relay node P reaches the receiving point R after one - time reflection from the reflecting surface m2, then the vector and the normal vector of the reflecting surface m2 The acute angle between them is the angle of incidence θ i , that is, the cosine value is:

[0076]

[0077] The path length L of a single 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, it can be known that:

[0078]

[0079] L = PH + HR (12)

[0080] When a uniform plane wave is incident on the interface, for the incident wave electric field vector in any direction, it 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 ⊥ , and its expression is:

[0081]

[0082] Step 42: Obtain the reflected field strength distribution of each point in the path according to the angle of incidence, the reflection coefficient, and the path length of the effective reflection

[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 angle of incidence.

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

[0087]

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

[0089]

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

[0091]

[0092]

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

[0094]

[0095] In Equation (21), R 1⊥ and R 1‖ are the reflection coefficients of the vertically and horizontally polarized waves of the single reflection respectively, and are the unit vectors of the horizontal and vertical polarizations before the single reflection respectively, and are the unit vectors of the horizontal and vertical polarizations after the single reflection respectively, 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 single reflection lines, the total field strength generated by them is:

[0097]

[0098] The calculation method of the reflection field strength of the reflection lines from the second to the seventh time is the same as the above. According to the superposition theorem, the direct field strength is vectorially superposed with the reflection field strengths from the first to the seventh time, which is the field strength at the receiving point and its expression is:

[0099]

[0100] When converting the unit of the field strength to dB, first calculate the modulus of the field strength at the receiving point, as shown in Equation (25), and then divide it by the modulus of the field strength when the distance of the receiving point is 0m, denoted as to obtain the reflection field strength at the receiving point in dB, as shown in Equation (26).

[0101]

[0102] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A calculation method for the reflection and propagation of electromagnetic waves in a U-shaped roadway, characterized in that, Including: Step S1: Construct an electromagnetic reflection model of the U-shaped mine roadway using the mirror image method; Step S2: Obtain effective reflection points through the mirror image method according to the electromagnetic reflection model of the U-shaped mine roadway; Step S3: Obtain effective reflection paths through the mirror image method according to the effective reflection points; Step S4: Obtain the reflected field strength distribution of each point in the path according to the effective reflection path; The electromagnetic reflection model of the U-shaped mine roadway consists of three parts, namely two horizontal roadways and one vertical roadway, which includes eight reflection surfaces and one relay node P; there is a reflection surface coinciding 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.

2. The calculation method of electromagnetic wave reflection and propagation in a U-shaped roadway according to claim 1, wherein According to the determination of the effective reflection path, the number of secondary to octal effective reflection lines in the U-shaped roadway is calculated.

3. The calculation method of electromagnetic wave reflection and propagation in a U-shaped roadway according to claim 2, characterized in that, Step S4 includes: According to the mirror image method, calculate the incident angle, reflection coefficient and path length of each effective reflection; Obtain the reflected field strength distribution of each point in the path according to the incident angle, reflection coefficient and path length of the effective reflection.

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