Design method and system of phased array ground penetrating radar antenna array system for detecting tunnels

Abstract

The application belongs to the technical field of radar antenna, and aims at solving the problem of low detection efficiency of the current ground penetrating radar, and provides a phased array ground penetrating radar antenna array system design method and system for detecting a tunnel.The method comprises the following steps: constructing an eccentric function according to the beam scanning angle range of a linear phased array, combining Chebyshev inequality to form eccentric Chebyshev inequality, and then solving the antenna unit excitation weight according to the corresponding relationship between the eccentric Chebyshev inequality and the array directional pattern array factor, so as to adjust the power distribution of different antenna units and meet the requirements of the predetermined main lobe direction and the side lobe level; taking the side lobe gain level, the mutual reflection coefficient and the overall gain level of the array as the optimization target, the optimal spacing of each antenna unit is determined; and the detection strategy of the phased array ground penetrating radar antenna array system is designed, so that the underground target can be accurately and quickly positioned.

Description

Technical Field

[0001] This invention belongs to the field of radar antenna technology, and particularly relates to a design method and system for a phased array ground-penetrating radar antenna array system for detecting tunnels. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Tunnel lining inspection primarily relies on various non-destructive testing techniques to ensure the safety and durability of the tunnel structure. Among them, ground-penetrating radar (GPR) is the most widely used and efficient core technology, capable of quickly and non-invasively assessing lining thickness, internal defects, and backfill cavities. The principle of GPR is to utilize the difference in reflection of high-frequency electromagnetic waves in different media to detect the interface between the lining concrete and the surrounding rock and air, thereby determining the thickness and internal anomalies.

[0004] Existing ground-penetrating radars (GPRs) have narrow antenna bandwidths, high frequencies, and limited antenna apertures, which restricts gain and results in poor detection of deep targets. However, while lowering the frequency of a narrow-band GPR antenna can improve its ability to detect deep targets, it reduces its ability to resolve small targets. Currently, GPRs composed of single-transmitter / single-receiver antennas or array antennas have limited detection ranges and operate in a single mode, leading to low detection efficiency. Summary of the Invention

[0005] To address the technical problems mentioned above, this invention provides a design method and system for a phased array ground-penetrating radar antenna array system for detecting tunnels.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The first aspect of the present invention provides a design method for a phased array ground-penetrating radar antenna array system for detecting tunnels, comprising:

[0008] A linear phased array is formed by arranging the curved surface of the tunnel lining to obtain an array structure with a set number of antenna elements;

[0009] An eccentric function is constructed based on the beam scanning angle range of the linear phased array. An eccentric Chebyshev inequality is formed by combining the Chebyshev inequality with the array pattern factor. Then, the excitation weights of the antenna elements are solved according to the correspondence between the eccentric Chebyshev inequality and the array pattern factor, so as to adjust the power distribution of different antenna elements and meet the predetermined main lobe direction and side lobe level requirements.

[0010] The optimal spacing of each antenna element is determined by using a multi-objective optimization method with the sidelobe gain level, cross-reflection coefficient and overall array gain level as optimization objectives.

[0011] The detection strategy of the phased array ground-penetrating radar antenna array system is set as a coarse scan + fine scan working mode based on phased array beam scanning and a corresponding three-dimensional imaging strategy to achieve accurate and rapid positioning of underground targets.

[0012] As one implementation method, in the process of constructing the eccentric function, the eccentric function is defined based on the standard Chebyshev weights, and the eccentric function decays to a minimum when the maximum scanning angle is set for the linear phased array.

[0013] As one implementation method, the linear phased array adopts a micro-conformal array layout. Based on the application scenario of tunnel lining detection and referring to the design standards of tunnel lining, a micro-arc array design with the same radius of curvature is adopted. The linear phased array is arranged in an arc or broken line shape along the curved surface, and the arc contour line is perpendicular to the direction of the measurement line. While ensuring the regularity of the antenna element arrangement, the spacing and direction of the antenna elements are adjusted to keep the main lobe of the array stable and adapt to the local beam scanning requirements of the curved surface.

[0014] As one implementation method, in the process of determining the optimal spacing of each antenna element using a multi-objective optimization method, the multi-objective optimization function is determined by weighted summation of the sidelobe gain level, the mutual reflection coefficient, and the overall array gain level; the sidelobe gain level, the mutual reflection coefficient, and the overall array gain level are all functions that vary with the spacing of the antenna elements.

[0015] As one implementation method, the multi-objective optimization method employs an improved parrot algorithm, the process of which is as follows:

[0016] Random initialization sampling is performed within a defined solution space, and continuous performance surfaces are obtained using interpolation.

[0017] During the iteration process, the population is divided into a local search group and a global communication group;

[0018] The global communication group simulates the social behavior of parrots and uses the residual between the current position and the global target position to update the position. After several iterations, a three-dimensional Pareto optimal front is generated, which includes gain, sidelobe level and beam offset angle. By screening the non-dominated solution set on the Pareto front, the optimal spacing point that takes into account detection depth, beam pointing accuracy and system isolation is finally selected.

[0019] As one implementation method, in the three-dimensional imaging strategy, the imaging coordinate system is redefined using the three-dimensional parameters of depth-survey line distance-beam pointing angle, and the lateral distance of the target in the medium is determined by the tangent trigonometric function relationship between the detection depth and the real-time beam scanning angle.

[0020] As one implementation method, with the same antenna element size, the lateral detection range shows a linear expansion trend as the detection depth increases; the maximum detection range width is twice the product of the detection depth and the tangent trigonometric function of the maximum beam sweep angle.

[0021] A second aspect of the present invention provides a phased array ground-penetrating radar antenna array system, which is designed using the aforementioned phased array ground-penetrating radar antenna array system design method for tunnel detection, comprising:

[0022] A linear phased array consisting of a transmitting antenna array and a receiving antenna array, wherein both the transmitting antenna array and the receiving antenna array are composed of the same number of antenna elements arranged in a uniform linear manner, and the linear phased array is a side-fire array;

[0023] Each antenna element is connected to the power divider via a time delay unit. The time delay unit applies time delay information to the corresponding channel of the antenna element, so that a group of wavefronts with different propagation times are superimposed on each other, thereby performing wideband phased array beam scanning and controlling the direction of the synthesized beam in the underground medium to point towards the target disease.

[0024] The input terminal of the power divider corresponding to the transmitting antenna array is connected to the feed source for power supply, and the output terminal of the power divider corresponding to the receiving antenna array is connected to the processor for processing the received signal. At the same time, the processor stores the time delay information of the receiving antenna array time delay unit at the same moment to calculate the beam direction at the current moment.

[0025] In one implementation, the antenna element in the linear phased array is an ultra-wideband Vivaldi pincushion antenna element, which includes a metal radiating patch, a dielectric substrate, and a feeding structure. The structure of the metal radiating patch is symmetrically arranged about the center of the antenna element to form a pincushion structure.

[0026] As one implementation method, the linear phased array adopts a micro-conformal array layout optimized for the tunnel lining detection environment; the linear phased array is arranged in an arc shape along the curved surface, so that the radiation center axis of each antenna element is perpendicular to the lining surface, and the arc contour line is perpendicular to the direction of the measurement line.

[0027] The beneficial effects of this invention are:

[0028] This invention describes a phased array ground-penetrating radar antenna array system arranged linearly on the curved surface of a tunnel lining. The power allocation of the antenna elements is determined by solving for the excitation weights of the antenna elements using the correspondence between the eccentric Chebyshev inequality and the array pattern factors. Adjusting the power allocation of different antenna elements satisfies the predetermined main lobe direction and sidelobe level requirements. For the design of the optimal spacing between each antenna element, multi-objective optimization is performed, considering the sidelobe gain level, mutual reflection coefficient, and overall array gain level as optimization targets. Finally, combining the coarse scan + fine scan working mode based on phased array beam scanning and the corresponding three-dimensional imaging strategy, accurate and rapid positioning of underground targets is achieved.

[0029] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0030] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0031] Figure 1 The comparison results of beam patterns of a four-element linear array (0°-40°) under uniform amplitude weighting and unweighting are shown in the embodiments of the present invention.

[0032] Figure 2 The beam pattern of a four-element linear array under conventional Chebyshev amplitude weighting (0°-40°) is shown.

[0033] Figure 3 This is a beam pattern (0°-40°) of an eccentric Chebyshev-weighted four-element linear array according to an embodiment of the present invention.

[0034] Figure 4 This is a schematic diagram of a phased array ground-penetrating radar antenna array system according to an embodiment of the present invention;

[0035] Figure 5 This is a schematic diagram illustrating the principle of phased array beam scanning of an antenna array in an underground medium according to an embodiment of the present invention.

[0036] Figure 6 This is a structural diagram of the antenna unit according to an embodiment of the present invention;

[0037] Figure 7 The simulation results of the operating frequency band of the antenna array in this embodiment of the invention;

[0038] Figure 8 The above are simulation results of the 0-40° beam scanning pattern of the antenna array according to an embodiment of the present invention.

[0039] Figure 9This is a curve showing the variation of the antenna array sidelobe gain level with the antenna element spacing in an embodiment of the present invention.

[0040] Figure 10 This is a curve showing the variation of the mutual reflection coefficient of the antenna array with the spacing between antenna elements in an embodiment of the present invention;

[0041] Figure 11 This is a curve showing the overall gain of the antenna array as a function of the spacing between antenna elements in an embodiment of the present invention.

[0042] Figure 12 This is a flowchart illustrating the improved MOPO algorithm for optimizing antenna element spacing in an embodiment of the present invention.

[0043] Figure 13 This is a schematic diagram of a micro-arc conformal antenna array used for detection in tunnel lining according to an embodiment of the present invention;

[0044] Figure 14 This is a schematic diagram of the three-dimensional detection and imaging range of the phased array ground-penetrating radar according to an embodiment of the present invention;

[0045] Figure 15 This is a flowchart of the "coarse detection + fine scan" working mode of the phased array ground penetrating radar in an embodiment of the present invention.

[0046] Among them, 1 is a linear phased array, 2 is a time delay unit, 3 is a power divider, 4 is a feed source, 5 is a processor, 6 is an antenna unit, 7 is time delay information, 8 is a set of wavefronts with different propagation times, 9 is the direction of the synthesized beam, 10 is the target defect, 11 is a metal radiating patch, 12 is a dielectric substrate, 13 is a feeding structure, 14 is a micro-conformal array, 15 is a tunnel lining, 16 is a survey line, 17 is the burial depth of the defect, 18 is the beam scanning angle of the defect location, and 19 is the three-dimensional imaging area of ​​the fan-shaped column. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0048] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0049] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0050] In this invention, terms such as "fixed connection," "connected," and "linked" should be interpreted broadly, indicating a fixed connection, an integral connection, or a detachable connection; a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can determine the specific meaning of these terms in this invention based on the specific circumstances, and they should not be construed as limitations on the invention.

[0051] In an embodiment of the present invention, a design method for a phased array ground-penetrating radar antenna array system for detecting tunnels includes:

[0052] Step 1: Arrange the antenna elements according to the curved surface of the tunnel lining to form a linear phased array, and obtain an array structure with a set number of antenna elements.

[0053] For example, such as Figure 4 As shown, the phased array ground-penetrating radar antenna array system of this embodiment is a 4×1 linear phased array 1, forming a four-antenna-element antenna array structure.

[0054] The four-antenna-element antenna array structure consists of four antenna elements 6 arranged in a uniform linear manner, forming a side-firing array. Each of the four antenna elements 6 is connected to a power divider 3 via a time delay unit 2. The time delay unit 2 applies time delay information 7 to the corresponding channels of the four antenna elements 6, causing wavefronts 8 with different propagation times to superimpose, thus performing wideband phased array beam scanning. The processor 5 controls the direction 9 of the synthesized beam in the underground medium to point towards the target defect 10. This array uses the phased array interference principle to precisely control the phase of the excitation signal of each antenna element 6, causing the emitted electromagnetic waves to coherently superimpose in the underground medium space, thereby changing the time beam direction underground. In the scenario of detecting tunnel lining 15 (such as concrete medium), this invention adjusts the feed delay of each antenna element 6 to change the distribution of the wavefront in the medium, thereby achieving energy superposition and focusing of electromagnetic waves inside the lining. This flexible beam pointing and focusing can significantly improve the detection sensitivity of deep underground defects.

[0055] Regarding signal transmission within the radar, the four antenna elements 6 in both the transmitting and receiving antenna arrays are connected to their respective power dividers 3 via independent time delay units 2. For the transmitting front end, the input of a 1-to-4 power divider is connected to a feed 4 (the feed 4 is responsible for generating an ultra-wideband excitation signal of 600MHz-2GHz). The signal is divided equally by the 1-to-4 power divider and then enters four time delay units 2 for phase compensation before finally being radiated to the underground medium by the antenna elements 6. For the receiving end, the echo signals captured by the four antenna elements 6 are first time-delayed and aligned by their respective time delay units 2, and then combined by a four-in-one power divider (combiner) to the processor 5 for filtering, amplification, and imaging processing of the received signal.

[0056] Step 2: Construct an eccentric function based on the beam scanning angle range of the linear phased array, combine it with Chebyshev's inequality to form an eccentric Chebyshev inequality, and then solve the antenna element excitation weights based on the correspondence between the eccentric Chebyshev inequality and the array pattern factor to adjust the power distribution of different antenna elements 6 to meet the predetermined main lobe direction and side lobe level requirements.

[0057] like Figure 1 As shown, when uniform amplitude weighting is used, extremely high beam grating lobes are generated under a large 40° scanning angle, severely interfering with detection; for example... Figure 2 As shown, although the traditional Chebyshev weighted average achieves isolateral sidelobe characteristics, the maximum sidelobe energy remains high at 40° scanning, which can easily cause signal distortion in underground lesions; for example... Figure 3 As shown, after introducing the eccentric function, the gain level of the maximum sidelobe is significantly suppressed when the angle approaches the limit value, thereby ensuring that the ground penetrating radar still has extremely high main lobe pointing accuracy and extremely low clutter interference when scanning at large angles.

[0058] The eccentric Chebyshev weighted method for antenna element amplitude constructs an eccentric function based on the array's beam scanning angle range and combines it with the Chebyshev inequality to form an eccentric Chebyshev inequality. Then, based on the correspondence between the inequality and the array pattern factor, the excitation weights of the antenna elements are solved to adjust the power distribution of different antenna elements, satisfying predetermined main lobe direction and side lobe level requirements. In practical implementation, the traditional Chebyshev method ensures equal sidelobe characteristics, while the introduced eccentric function further ensures that the sidelobe level is suppressed when the beam scanning angle is close to the set upper limit of the scanning angle (±40 degrees), achieving precise control of the main lobe direction.

[0059] The Chebyshev weighted method specifically expands the Chebyshev polynomial according to the specific array form, and calculates it according to a linear phased array with four antenna elements. The expanded result satisfies:

[0060] ;

[0061] ;

[0062] ;

[0063] in, to These are Chebyshev polynomials of orders 0 to 3, used to control the basic sidelobe distribution characteristics of the array pattern; Let be the independent variable of the polynomial.

[0064] For a 40° scanning angle set for linear phased array 1, an angle-related eccentricity term is constructed, and the weighting function is defined as follows: ;

[0065] in, Let θ be the mapping variable of the spatial observation angle in the cosine domain; The cosine mapping point is the maximum scanning angle. α is the eccentric attenuation control factor, which physically controls the degree to which the weighting coefficients converge towards the center of the array. The larger the value of α, the more significant the sidelobe suppression effect at the maximum scanning angle.

[0066] The improved eccentric Chebyshev polynomial is the product of the original Chebyshev polynomial expansion and the eccentric function:

[0067] ;

[0068] Where m is the order of the polynomial (m=3 in this embodiment). The sidelobe scaling factor is determined by the initial equal sidelobe level target. As the angle approaches 40 degrees, the value of the eccentricity function approaches zero, resulting in a lower weighted sidelobe target setting and the weighting converging towards the center of the array. Following the Chebyshev weighting method, the excitation weights are obtained when the (n-1)th term of the polynomial expansion (where n is the number of antenna elements) is equal to the array pattern factor. The formula for calculating the array pattern factor is:

[0069] ;

[0070] in, The array factor represents the array composite radiation pattern; N is the total number of antenna elements in the antenna array (N=4 in this embodiment). The amplitude-weighted excitation coefficients for the nth antenna element to be solved are denoted as . λ is the wave number in the medium, λ is the wavelength of the electromagnetic wave; d is the spacing between antenna elements; θ is the observation angle of the space beam.

[0071] Specifically, for a four-antenna element structure, its expression, constructed by equalizing the array factor with the expansion terms of the eccentric Chebyshev inequality, is as follows:

[0072] ;

[0073] The amplitude-weighted excitation coefficients of each antenna element are obtained by solving the above formula. Then, the power divider 3 distributes the excitation coefficients according to this amplitude weighting to each antenna element in the array, thus completing the weighted excitation.

[0074] During beam scanning, the principle of beam focusing in underground phased arrays follows the law of spherical wave interference, and the pattern array factor of its synthesized electric field is... It can be represented as:

[0075] ;

[0076] in, The number of antenna elements (e.g.) ), For antenna element amplitude weighting, The wave number in the medium. The spacing between antenna elements. For scanning angle, For the first Additional phase of each antenna element.

[0077] To balance detection depth and resolution, the linear phased array 1 operates over an ultra-wide bandwidth of 600MHz to 2000MHz. Within this wide frequency range, traditional narrowband phase shifters face significant limitations. This is because the phase shift provided by the phase shifter… It typically remains constant as the operating frequency changes, while the beam points to the required phase difference. With frequency Proportional relationship:

[0078] ;

[0079] in, The speed at which electromagnetic waves propagate in the lining medium. This is the predetermined beam scanning angle. If a fixed phase shifter is used, the beam pointing angle... The beam will shift with frequency changes, resulting in a beam squint phenomenon.

[0080] ;

[0081] Frequency-dependent pointing deviations can cause energy defocusing and image distortion in ultra-wideband signals during scanning and detection. To address this issue, this embodiment of the invention replaces the traditional phase shifter with a time delay unit (TDU) for each channel corresponding to antenna element 6. The time delay unit 2 provides a constant true delay. The resulting phase shift is in strict linear proportion to the frequency:

[0082] ;

[0083] The corresponding formula for calculating beam scanning delay difference is:

[0084] ;

[0085] because With frequency Regardless of the frequency, the phased array ground-penetrating radar antenna array system for tunnel detection can achieve stable beam pointing control in the full frequency band from 600MHz to 2000MHz, eliminating beam squint effect. This enables the antenna array to perform precise energy focusing and beam pointing switching in complex underground media, thereby achieving accurate positioning of underground cavities, voids and other defects.

[0086] During the detection process, processor 5 is responsible for signal processing and simultaneously stores the time delay information 7 of the receiving time delay unit 2 at each sampling moment in real time. This time delay information 7 has a one-to-one functional relationship with the beam deflection angle θ at the current moment, providing basic data support for the subsequent establishment of the depth-angle coordinate system and three-dimensional imaging.

[0087] like Figure 5 As shown, the beam scanning angle range of the antenna array in the underground medium is set at... The range is derived by comprehensively considering the electromagnetic wave attenuation law in the lining concrete medium and its corresponding effective detection range. This aims to ensure the effectiveness of the detection scanning area while preventing high sidelobe interference caused by large-angle scanning during the detection process. For example... Figure 6 As shown, antenna element 6 is an ultra-wideband Vivaldi heel antenna element, including a metal radiating patch 11, a dielectric substrate 12 and a feeding structure 13. The structure of the metal radiating patch 11 is symmetrically arranged about the center of antenna element 6 to form a heel-type structure, and its inner edge adopts an exponentially gradient groove line to meet the wideband impedance matching performance.

[0088] In the design of antenna arrays with phased array beam scanning capabilities, the commonly used weighting method is the Chebyshev weighting method, which ensures that the energy amplitude of each sidelobe is equal. However, the ground-penetrating radar phased array antenna array in this invention is limited by the size of the ground-penetrating radar, with only 4 antenna elements per array. The number of sidelobes is small and the energy is relatively high. If the traditional Chebyshev weighting method is used for weighting, when the scanning angle reaches the set limit (40° / -40°), although the equal sidelobe characteristics are still maintained, the energy of the sidelobes is not much different from that of the main lobe. This will result in distortion of the target signal or inaccurate position information in the detection results of the ground-penetrating radar. Therefore, in the process of obtaining the Chebyshev weighting coefficients, an eccentricity factor is introduced into the Chebyshev polynomial. The closer the array scanning angle is to ±40°, the smaller the weighting coefficient obtained by the antenna element 6 at the edge of the array is, thus ensuring the accuracy of the detection results when the array scanning angle is large.

[0089] Step 3: Using the sidelobe gain level, mutual reflection coefficient and overall array gain level as optimization objectives, determine the optimal spacing of each antenna element using a multi-objective optimization method.

[0090] In this embodiment, the spacing between the antenna elements of the antenna array is precisely set to 132 mm. The determination of this key parameter comprehensively considers the constraints of multiple performance indicators, such as the array's sidelobe level, antenna gain, and port isolation (represented by S23). Due to the dual requirements of resolution and depth for ground-penetrating radar in tunnel lining detection, optimizing a single target often leads to a drastic deterioration of other performance aspects. Therefore, this invention constructs a multi-objective optimization objective function for the optimal antenna spacing of the array and introduces an improved Parrot multi-objective optimization algorithm to find the optimal antenna spacing solution corresponding to the Pareto front within the complex multi-objective solution space, thereby achieving global optimization of the array's overall performance.

[0091] First, three key objective functions were obtained through numerical simulation to guide the selection of upper and lower limits for antenna element spacing. The first objective function is the sidelobe gain level (SLL) as a function of the antenna element spacing. In a phased array ground-penetrating radar antenna array system for tunnel detection, when the antenna element spacing is too large, due to phase interference effects, high-energy beam gratings pointing at different directions than the main lobe beam will appear in the radiation pattern. This directly leads to the generation of false targets and seriously interferes with the accuracy of the beam pointing angle corresponding to the target position. The sidelobe gain level is used to quantify the size of these beam gratings. The above beam lobe suppression requirements determine the physical upper limit of the antenna element spacing, that is, the sidelobe gain level determines the physical upper limit of the antenna element spacing. By setting the maximum scanning angle of the antenna array ( By performing a fixed-angle scan and extracting the curves of the maximum sidelobe gain of the radiation pattern with frequency under different spacings, the spacing range can be determined, which can effectively prevent the appearance of grid lobes during the scanning process.

[0092] The second objective function is the mutual reflection coefficient as a function of the antenna element spacing. This index directly reflects the mutual coupling level between antenna elements and determines the physical lower limit of the antenna element spacing. For the 4×1 linear phased array 1 used in the phased array ground-penetrating radar antenna array system for tunnel detection, there are six unequal mutual reflection coefficients (S12, S13, S14, S24, and S23) between the antenna elements. In the design process of this invention, the four antenna elements are denoted as antenna element 1, antenna element 2, antenna element 3, and antenna element 4. The mutual reflection coefficient S23 between antenna elements 2 and 3, located in the middle of the array, is selected as the final objective function index. This is because in the four-antenna element linear array, antenna elements 2 and 3 are located at the core of the array and are affected by the symmetrical mutual coupling of the antenna elements on both sides. As adjacent elements, they are most affected by the mutual coupling from each other. Therefore, S23 is the largest mutual reflection coefficient in the array, and minimizing it can ensure that the array maintains a high degree of isolation even with a compact layout.

[0093] The third objective function is the overall gain of the array as a function of the antenna element spacing. In ground-penetrating radar (GPR) applications, detection depth is a core indicator of the quality of a phased array GPR antenna array system capable of detecting tunnels, and detection depth physically depends primarily on the overall gain of the antenna array. Array gain is also affected by element spacing; too small a spacing reduces the effective aperture of the antenna array, thus lowering the gain and consequently reducing the detection depth. Therefore, the overall array gain level also determines the lower limit of the antenna element spacing. By extracting the curve of the maximum directional gain at a specified frequency as a function of element spacing, the spacing range that guarantees the maximum detection depth can be determined.

[0094] Array-type ground-penetrating radars typically employ MIMO (Multiple-Transmit, Multiple-Receive) antennas or multi-polarized antennas. The former aims to acquire three-dimensional geological information covering a wide range of areas through multiple transmit and receive channels formed by the antenna array, while the latter can acquire geological information containing various target information sensitive to different polarization modes. However, neither of these array-type ground-penetrating radars can effectively extend the lateral detection range. This invention designs a phased array antenna array, enabling the antenna array to have lateral beam scanning capability perpendicular to the survey line direction, thereby extending the lateral detection range of the ground-penetrating radar.

[0095] To achieve a balance among multiple objectives, this invention applies weighting coefficients to the three objective functions mentioned above. Considering the importance of detection depth in tunnel lining detection environments, the highest weighting coefficient for the overall array gain is assigned, set to 0.5. Addressing the accuracy requirements for beam pointing in complex tunnel environments, the second highest weighting coefficient for sidelobe gain is assigned, set to 0.3. Considering hardware system stability, the third highest weighting coefficient for the mutual reflection coefficient S23 is assigned, set to 0.2. The unified objective function constructed based on this weighting scheme is:

[0096] ;

[0097] in, The objective function value is denoted as d; d represents the spacing between antenna elements. The normalized overall array gain level under spacing d; This represents the normalized sidelobe gain level. This is the normalized mutual reflection coefficient between antenna elements 2 and 3.

[0098] In the above formula, each component is a normalized function. The weighting coefficients (0.5, 0.3, 0.2) represent the priority of each performance indicator in the design of the phased array ground-penetrating radar antenna array system for tunnel detection. These weighting coefficients can be set to other values ​​according to different actual detection scenarios. The setting principle is as follows: if the application scenario (such as deep geological exploration) has extremely high requirements for the detection depth of the ground-penetrating radar, then the weighting coefficient with the largest overall array gain should be assigned; if the application scenario (such as shallow complex pipeline detection) requires extremely high beam pointing accuracy to avoid false targets, then the weighting ratio of the sidelobe gain level (SLL) can be appropriately increased. This embodiment takes into account both the detection depth of the tunnel lining and the accuracy of defect location, so a relatively balanced distribution of weighting coefficients of 0.5, 0.3, and 0.2 is selected.

[0099] Figure 7 Simulation results for the operating frequency band of the antenna array; such as Figure 8 As shown in the figure, the lines of different shades correspond to the beam scanning range of antenna elements one through four in the set range of -40° to 40°. It can be seen from the figure that the antenna array designed in this embodiment of the invention has precise pointing and low sidelobe level in the set beam scanning range of -40° to 40°, so that it can achieve accurate detection with wide-area coverage over a large angle by means of time delay control without moving the physical antenna.

[0100] The phased array ground-penetrating radar antenna array system for tunnel detection uses the improved Parrot Algorithm (MOPO algorithm) for iterative solution. The traditional Paretosearch algorithm usually relies on interpolation to obtain a continuous objective function curve and obtains the Pareto front through local search. When dealing with the irregular, nonlinear electromagnetic optimization problem of the phased array ground-penetrating radar antenna array system for tunnel detection, this approach is prone to getting trapped in local optima and cannot comprehensively search the complex solution space.

[0101] In this embodiment, the improved Parrot algorithm (MOPO algorithm) is used to solve the multi-objective problem. The improved Parrot algorithm (MOPO algorithm) is an improvement on the Parrot Optimization algorithm for multi-objective scenarios. Figure 12 The array element in the text refers to the antenna element; combined with Figure 12 First, random initialization sampling is performed within the solution space ranging from 20mm to 200mm, and a continuous performance surface is obtained using interpolation. During the iteration process, the population is divided into a local search group and a global communication group. The global communication group simulates the social behavior of parrots, updating its position using the residual between its current position and the global target position. The update formula is as follows:

[0102] ;

[0103] in, The spatial location of the new individual generated after global communication (i.e., the new candidate solution for antenna element spacing). Represents the current spatial location of an individual (i.e., the current antenna element spacing). represents the position of the globally optimal individual in the population during this iteration (i.e., the currently found optimal antenna element spacing); r is a random learning factor that takes values ​​in the range [0,1] and is used to control the step size for updating the target position.

[0104] Through this information exchange mechanism, the algorithm can escape local extrema and achieve "selection of the best among the best" across the entire domain. Finally, after several iterations, the algorithm generates a result including gain, sidelobe level, and beam offset angle. The three-dimensional Pareto optimal front, including [missing information], was determined. By screening the non-dominated solution set on the Pareto front, this invention ultimately selected the optimal spacing point that simultaneously considers detection depth, beam pointing accuracy, and system isolation. Results show that a spacing of 132 mm can minimize mutual coupling interference while maintaining ultra-wideband characteristics and ensuring [missing information] throughout [missing information]. It maintains excellent performance with high gain and low sidelobe throughout the scanning range.

[0105] For phased array ground-penetrating radar (GPR) antenna array systems used for tunnel detection, the spacing between antenna elements is a crucial factor affecting the overall array gain, beam pointing accuracy, and beamwidth. In traditional array antennas, the spacing is typically selected based on an empirical value of λ / 2 (half the wavelength). This empirical spacing primarily ensures low coupling levels, thus preventing the array gain from being affected. However, in phased array GPR antenna array systems used for tunnel detection, the spacing also affects the beamwidth and beam scanning accuracy, directly determining the accuracy of detection results using beam scanning. Furthermore, the antenna array operates on an ultra-wideband 600MHz-GHz band, with a half-wavelength range of 75mm-200mm, making it difficult to directly use an empirical value of half the wavelength as the array spacing. This invention constructs a function of the array spacing based on the array's sidelobe level (SLL), half-power beamwidth (BW), antenna gain, and port isolation (S23), and performs multi-target optimization to obtain the optimal spacing that simultaneously ensures array gain while improving beam scanning accuracy.

[0106] Figure 9 This demonstrates that as the spacing between antenna elements increases, the sidelobe energy in the array pattern shows an upward trend, which provides data support for the physical upper limit of spacing optimization. At the same time, this curve is the objective function characterizing the sidelobe gain level in multi-objective spacing optimization (improved parrot algorithm).

[0107] Figure 10This demonstrates that within a certain size range, as the spacing between antenna elements decreases, the electromagnetic coupling between adjacent antenna elements increases sharply. This provides data support for the physical lower limit of spacing optimization. At the same time, this curve is the objective function characterizing the mutual reflection coefficient (S23) in multi-objective spacing optimization (improved parrot algorithm).

[0108] Figure 11 This demonstrates that as the spacing between antenna elements increases, the overall radiation gain of the antenna array tends to rise, providing data support for the physical lower limit of spacing optimization. At the same time, this curve is the objective function characterizing the overall gain level of the array in multi-objective spacing optimization (improved parrot algorithm).

[0109] Step 4: Set the detection strategy of the phased array ground penetrating radar antenna array system to a coarse scan + fine scan working mode based on phased array beam scanning and the corresponding three-dimensional imaging strategy to achieve accurate and rapid positioning of underground targets.

[0110] Traditional 3D ground-penetrating radar typically consists of multiple antenna arrays arranged side-by-side. The resulting 3D data volume is composed of "depth (time axis) - survey line travel distance (longitudinal axis) - physical channel spacing between antenna elements (lateral axis)". In this traditional mode, the radar's lateral detection range perpendicular to the survey line is strictly limited by the physical width of the antenna array. To increase the detection width, the number of antenna elements and the system size must be increased without limit, resulting in redundant and bulky equipment.

[0111] In this embodiment, the imaging coordinate system is redefined using the three-dimensional parameters of depth-survey distance-beam pointing angle in the three-dimensional imaging strategy. The lateral distance of the target in the medium is determined by the tangent trigonometric function relationship between the detection depth and the real-time beam scanning angle.

[0112] At each sampling point along the survey line, the beam is controlled by time delay to achieve [the desired effect]. Continuous deflection within the range. As the beam sweeps, the detection trajectory is no longer a vertically downward thin line, but forms an unfolding fan-shaped area in a transverse plane perpendicular to the measurement line. At this point, the target's transverse distance (distance perpendicular to the measurement line) W in the medium is no longer determined by the physical position of the antenna element, but by the detection depth D and the real-time beam scanning angle. The trigonometric relationships are determined as follows: .

[0113] With the same antenna element size, the lateral detection range shows a linear expansion trend as the detection depth increases; the maximum detection range width is twice the product of the detection depth and the tangent trigonometric function of the maximum beam sweep angle.

[0114] Based on this physical model, the three-dimensional detection data volume formed by this invention presents as a "fan-shaped cylindrical region." With the same antenna element size, its lateral detection range exhibits a linear expansion trend with increasing detection depth. Its maximum detection range width... Determined by the following formula:

[0115] ;

[0116] At a depth of In this case, the present invention can cover approximately [area missing] in a single survey line walk. The wide lateral area far exceeds that of a traditional four-antenna linear array. The physical width. This imaging method enables the system to have a wider detection coverage capability, that is, by using a compact miniaturized array structure, a lateral detection coverage area larger than the physical size of the array is achieved.

[0117] In one or more embodiments, such as Figure 13 As shown, the linear phased array 1 adopts a micro-conformal array 14 layout. Based on the application scenario of tunnel lining detection and referring to the design standard of tunnel lining 15, a corresponding micro-arc array design with the same radius of curvature is adopted. The linear phased array 1 is arranged in an arc or broken line shape along the curved surface, and the arc contour line is perpendicular to the direction of the measuring line 16. While ensuring the regularity of the antenna element arrangement, the spacing and direction of the antenna elements are adjusted to maintain the stability of the array main lobe and adapt to the local beam scanning requirements of the curved surface.

[0118] The antenna array employs a micro-conformal array layout optimized for the detection environment of tunnel lining 15. Due to the curvature of the tunnel lining surface, traditional planar array ground-penetrating radars (GPRs) create uneven air coupling gaps between the antenna elements and the lining surface during close-fitting detection. These gaps not only lead to impedance mismatch but also cause significant electromagnetic wave reflection and refraction losses due to the large difference in dielectric constant between air (refractive index approximately 1) and concrete (refractive index between 2.5 and 3). This invention primarily references the lining design standards for urban subway tunnels, with a curvature radius of approximately ten meters. Based on this condition, the antenna array is arranged in an arc shape along the curved surface, ensuring that the radiation center axis of each antenna element is as perpendicular as possible to the lining surface, while the arc contour line is perpendicular to the measurement line direction. This micro-conformal design minimizes the air coupling effect, guaranteeing the effective detection depth of the GPR within the lining medium.

[0119] In the detection method of this invention, the tunnel lining is detected by using the current survey line travel distance, the depth of the defect burial (obtained by the two-way travel of radar waves), and the beam scanning angle of the previous defect location to perform three-dimensional detection of the tunnel lining, forming a fan-shaped columnar three-dimensional imaging area. This method makes full use of the angle and frequency band redundancy information provided by multi-channel data, effectively improving the imaging resolution and signal-to-noise ratio.

[0120] Traditional 3D ground-penetrating radar uses a multi-transmitter, multi-receiver antenna configuration to simultaneously acquire multiple sets of data along the lateral (perpendicular to the survey line) distance and spatially overlay them, forming a 3D cubic imaging area representing the survey line travel distance, disease burial depth, and lateral distance. While the detection results contain rich geological information, the lateral coverage is equivalent to the antenna array's coverage area. Improving the lateral detection range relies on large-scale antenna arrays, which limits its practical application. For example... Figure 14 As shown, the antenna array in this invention has a beam scanning function, and the beam scanning angle information is recorded in real time, forming a fan-shaped cylindrical three-dimensional imaging area 19 of the current survey line 16 travel distance - disease burial depth 17 - current disease location beam scanning angle 18. This allows for the coverage of a larger lateral detection range with a smaller antenna array size. This embodiment of the invention provides a multi-mode integrated detection strategy that balances operational efficiency and detection accuracy. Through a progressive detection scheme of coarse detection + fine scanning, it solves the contradiction between the slow survey speed and insufficient local identification accuracy of traditional ground-penetrating radar in long-distance tunnel detection.

[0121] like Figure 15 As shown, during the initial travel phase of the tunnel lining survey, the phased array ground-penetrating radar antenna array system operates in "coarse exploration" mode. At this time, the beam direction of the phased array antenna array is fixed perpendicular to the detection plane. Direction. Since electromagnetic waves propagate through concrete media with the shortest path and minimal interface reflection loss when incident perpendicularly, maximum vertical penetration depth can be guaranteed. In this mode, large-scale surveys can be conducted along the survey line at a relatively fast operating speed. The backend processor 5 monitors abnormal fluctuations in the echo signal in real time. Once areas potentially exhibiting defects such as voids, delamination, or abnormal thinning are identified, the spatial coordinates of the current traveling mechanism are automatically collected and marked, recorded, and stored as key areas of focus.

[0122] In the second walking phase after marking, the phased array ground-penetrating radar antenna array system for tunnel detection switches to "fine scan" detection mode. In this mode, the location information of key defect areas stored in the previous phase is automatically loaded. When the radar array approaches the marked area, it automatically reduces its walking speed and simultaneously activates the phased array beam scan. At this time, the antenna array rapidly performs scanning at each sampling point... arrive The system employs a full-angle scanning detection method. This fixed-point, decelerated scanning approach allows electromagnetic waves to cover the diseased target multiple times from multiple angles, thereby acquiring rich geological information about the diseased area. This enhanced detection targeting key areas greatly improves the system's ability to characterize the fine structural features of the disease and provides core data support for the subsequent generation of high-resolution 3D imaging results of the fan-shaped columnar area.

[0123] In one or more embodiments, a phased array ground-penetrating radar antenna array system, designed using the aforementioned phased array ground-penetrating radar antenna array system design method for tunnel detection, includes:

[0124] A linear phased array 1 consisting of a transmitting antenna array and a receiving antenna array, wherein both the transmitting antenna array and the receiving antenna array are composed of the same number of antenna elements 6 arranged in a uniform linear manner, and the linear phased array 1 is a side-fire array;

[0125] Each antenna element 6 is connected to the power divider 3 through a time delay unit 2. Time delay information 7 is applied to the corresponding channel of the antenna element 6 through the time delay unit 2, so that a group of wavefronts 8 with different propagation times are superimposed on each other, thereby performing wideband phased array beam scanning and controlling the direction 9 of the synthetic beam in the underground medium to point to the target lesion 10.

[0126] The input terminal of the power divider 3 corresponding to the transmitting antenna array is connected to the feed source 4 for power feeding, and the output terminal of the power divider 3 corresponding to the receiving antenna array is connected to the processor for processing the received signal. At the same time, the processor stores the time delay information 7 of the receiving antenna array time delay unit at the same moment to calculate the beam direction at the current moment.

[0127] Among them, the antenna element 6 in the linear phased array 1 is an ultra-wideband Vivaldi pincushion antenna element, which includes a metal radiating patch 11, a dielectric substrate 12 and a feeding structure 13. The structure of the metal radiating patch 11 is symmetrical about the center of the antenna element to form a pincushion structure.

[0128] In this embodiment, the linear phased array 1 adopts a micro-conformal array 14 layout optimized for the detection environment of the tunnel lining 15; the linear phased array 1 is arranged in an arc shape along the curved surface, so that the radiation center axis of each antenna element 6 is perpendicular to the lining surface, and the arc contour line is perpendicular to the direction of the measuring line 16.

[0129] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A design method for a phased array ground-penetrating radar antenna array system for detecting tunnels, characterized in that, include: A linear phased array is formed by arranging the curved surface of the tunnel lining to obtain an array structure with a set number of antenna elements; An eccentricity function is constructed based on the beam scanning angle range of the linear phased array, specifically: For a linear phased array with a set scanning angle of 40°, an angle-related eccentricity term is constructed, and the weighting function is defined as follows: ; in, Let θ be the mapping variable of the spatial observation angle in the cosine domain; α is the cosine mapping point of the maximum scanning angle; α is the eccentric attenuation control factor, which physically controls the degree to which the weighting coefficients converge toward the center of the array. By combining Chebyshev polynomials, an eccentric Chebyshev polynomial is formed. The eccentric Chebyshev polynomial is the product of the expansion of the original Chebyshev polynomial and the eccentric function. Then, the excitation weights of the antenna elements are solved according to the correspondence between the eccentric Chebyshev polynomial and the array pattern factors, so as to adjust the power distribution of different antenna elements and meet the predetermined main lobe direction and side lobe level requirements. The optimal spacing of each antenna element is determined by using a multi-objective optimization method with the sidelobe gain level, cross-reflection coefficient and overall array gain level as optimization objectives. The detection strategy of the phased array ground-penetrating radar antenna array system is set as a coarse scan + fine scan working mode based on phased array beam scanning and a corresponding three-dimensional imaging strategy to achieve accurate and rapid positioning of underground targets.

2. The design method for a phased array ground-penetrating radar antenna array system for detecting tunnels as described in claim 1, characterized in that, In the process of constructing the eccentric function, the eccentric function is defined based on the standard Chebyshev weights. When the maximum scanning angle of the linear phased array is set, the eccentric function decays to a minimum.

3. The design method for a phased array ground-penetrating radar antenna array system for tunnel detection as described in claim 1, characterized in that, The linear phased array adopts a micro-conformal array layout. Based on the application scenario of tunnel lining detection and referring to the design standards of tunnel lining, a micro-arc array design with the same radius of curvature is adopted. The linear phased array is arranged along the curved surface into an arc or broken line shape, and the arc contour line is perpendicular to the direction of the measuring line. While ensuring the regularity of the antenna element arrangement, the spacing and direction of the antenna elements are adjusted to maintain the stability of the array main lobe and adapt to the local beam scanning requirements of curved surfaces.

4. The design method for a phased array ground-penetrating radar antenna array system for detecting tunnels as described in claim 1, characterized in that, In determining the optimal spacing between antenna elements using a multi-objective optimization method, the multi-objective optimization function is determined by weighted summation of the sidelobe gain level, mutual reflection coefficient, and overall array gain level; the sidelobe gain level, mutual reflection coefficient, and overall array gain level are all functions that vary with the spacing between antenna elements.

5. The design method for a phased array ground-penetrating radar antenna array system for detecting tunnels as described in claim 1, characterized in that, The multi-objective optimization method employs an improved parrot algorithm, the process of which is as follows: Random initialization sampling is performed within a defined solution space, and continuous performance surfaces are obtained using interpolation. During the iteration process, the population is divided into a local search group and a global communication group; The global communication group simulates the social behavior of parrots and uses the residual between the current position and the global target position to update the position. After several iterations, a three-dimensional Pareto optimal front is generated, which includes gain, sidelobe level and beam offset angle. By screening the non-dominated solution set on the Pareto front, the optimal spacing point that takes into account detection depth, beam pointing accuracy and system isolation is finally selected.

6. The design method for a phased array ground-penetrating radar antenna array system for detecting tunnels as described in claim 1, characterized in that, In the three-dimensional imaging strategy, the imaging coordinate system is redefined using the three-dimensional parameters of depth-survey line distance-beam pointing angle. The lateral distance of the target in the medium is determined by the tangent trigonometric function relationship between the detection depth and the real-time beam scanning angle.

7. The design method for a phased array ground-penetrating radar antenna array system for detecting tunnels as described in claim 1, characterized in that, With the same antenna element size, the lateral detection range shows a linear expansion trend as the detection depth increases; the maximum detection range width is twice the product of the detection depth and the tangent trigonometric function of the maximum beam sweep angle.

8. A phased array ground-penetrating radar antenna array system, characterized in that, Designed using the phased array ground-penetrating radar antenna array system design method for tunnel detection as described in any one of claims 1-7, comprising: A linear phased array consisting of a transmitting antenna array and a receiving antenna array, wherein both the transmitting antenna array and the receiving antenna array are composed of the same number of antenna elements arranged in a uniform linear manner, and the linear phased array is a side-fire array; Each antenna element is connected to the power divider via a time delay unit. The time delay unit applies time delay information to the corresponding channel of the antenna element, so that a group of wavefronts with different propagation times are superimposed on each other, thereby performing wideband phased array beam scanning and controlling the direction of the synthesized beam in the underground medium to point towards the target disease. The input terminal of the power divider corresponding to the transmitting antenna array is connected to the feed source for power supply, and the output terminal of the power divider corresponding to the receiving antenna array is connected to the processor for processing the received signal. At the same time, the processor stores the time delay information of the receiving antenna array time delay unit at the same moment to calculate the beam direction at the current moment.

9. The phased array ground-penetrating radar antenna array system as described in claim 8, characterized in that, The antenna element in the linear phased array is an ultra-wideband Vivaldi pincushion antenna element, which includes a metal radiating patch, a dielectric substrate and a feeding structure. The structure of the metal radiating patch is symmetrical about the center of the antenna element to form a pincushion structure.

10. The phased array ground-penetrating radar antenna array system as described in claim 8, characterized in that, The linear phased array adopts a micro-conformal array layout optimized for the tunnel lining detection environment; the linear phased array is arranged in an arc shape along the curved surface, so that the radiation center axis of each antenna element is perpendicular to the lining surface, and the arc contour line is perpendicular to the direction of the measurement line.

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