A method and system for identifying the position of layered small inclusions based on electric potential layer potential

Abstract

The present invention belongs to the technical field of object detection, and provides a method and system for identifying the position of a layered small inclusion based on the electric potential layer potential, including: obtaining the perturbation electric potential and the background electric potential of the object inclusion to be identified; respectively performing asymptotic analysis on the obtained perturbation electric potential and background electric potential considering the boundary transmission condition and the stretching transformation, considering the electric potential layer potential, obtaining the difference between the integral representation of the perturbation electric potential and the integral expression of the background electric potential, and constructing an analytical model of the electric potential field of the layered small inclusion; determining the positional relationship of the layered small inclusion according to the constructed analytical model of the electric potential field, and completing the position identification of the layered small inclusion based on the electric potential layer potential. The present invention constructs an analytical model of the electric potential field of the layered small inclusion based on the electric potential layer potential theory to achieve accurate identification of the position of the layered small inclusion without considering shape recovery.

Description

Technical Field

[0001] The present invention belongs to the technical field of object detection, and particularly relates to a method and system for identifying the position of layered small inclusions based on electric potential layer potential. Background Technique

[0002] The statements in this part only provide background technical information related to the present invention and do not necessarily constitute prior art.

[0003] In oil and gas exploration, mineral resource detection, or environmental monitoring, it is often necessary to identify small inclusions (such as ore bodies, fluid vesicles, fracture zones, etc.) embedded in underground layered media. Traditional methods mainly rely on resistivity methods, electromagnetic methods, or seismic wave techniques. However, these methods have limitations in complex layered structures (i.e., dealing with multi-parameter and multi-scale geological anomalies): The resistivity method is effective for a single horizontal layered structure, but it is difficult to distinguish the spatial distribution of multiple small inclusions. Especially when the electrical property difference between the layered medium and the inclusions is small, the resolution significantly decreases; The electromagnetic method is greatly affected by electromagnetic signal attenuation and external interference, and high-frequency signals are difficult to penetrate deep media, resulting in insufficient boundary positioning accuracy for small inclusions; The seismic wave technique relies on acoustic impedance differences and has low sensitivity to small inclusions with low impedance differences. Moreover, the equipment cost is high and the data processing is complex. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a method and system for identifying the position of layered small inclusions based on electric potential layer potential. Based on the electric potential layer potential theory, an analytical model of the electric potential field of layered small inclusions is constructed to achieve precise identification of the position of layered small inclusions without considering shape recovery.

[0005] According to some embodiments, the first solution of the present invention provides a method for identifying the position of layered small inclusions based on electric potential layer potential, adopting the following technical solution:

[0006] A method for identifying the position of layered small inclusions based on electric potential layer potential, comprising:

[0007] Obtain the perturbed electric potential and background electric potential of the object inclusion to be identified;

[0008] Considering the boundary transmission condition and stretching transformation, perform asymptotic analysis on the obtained perturbed electric potential and background electric potential respectively. Considering the electric potential layer potential, obtain the difference between the integral representation of the perturbed electric potential and the integral expression of the background electric potential, and construct an analytical model of the electric potential field of layered small inclusions;

[0009] Determine the positional relationship of the layered small inclusions according to the constructed analytical model of the electric potential field, and complete the position identification of the layered small inclusions based on the electric potential layer potential.

[0010] As a further technical limitation, the obtained perturbation potential and background potential at least satisfy the Laplace control equation ; where represents three-dimensional space, represents the divergence operator, represents the gradient operator, represents a higher-order infinitesimal quantity, is the perturbation potential, is the perturbation potential, is the eigenfunction, is the inclusion embedded in and has a smooth boundary, means that the first derivative of the function satisfies the Hörmander condition, is the background space, is the region of the closure, in the conductivity , in in , is a harmonic function in is the perturbation potential.

[0011] Furthermore, the inclusion comprises a plurality of layered inclusions ; the layered inclusions are the central regions generating the electric field, and their positions in space change with time.

[0012] As a further technical limitation, the analytical model of the potential field of the constructed layered inclusions adopts the asymptotic behavior of the integral representation of the perturbation potential and the background potential, that is, the Laplace operator is used to perform Taylor expansion on the obtained perturbation potential, considering the conductivity of each layer in the layered inclusions, and combining the boundary transmission conditions to obtain the difference between the integral representation formula of the perturbation potential and the integral expression formula of the background potential, that is, the construction of the analytical model of the potential field of the layered inclusions is completed.

[0013] As a further technical limitation, based on the boundary measurement, the position information when the layered inclusions move is obtained, and combined with the constructed potential field analytical model, the positions of the layered inclusions are determined, and the position recognition of the layered inclusions is completed.

[0014] As a further technical limitation, in the asymptotic analysis, by combining the single-layer potential operator, double-layer potential operator and boundary integral operator of the inclusions, the jump relation of the single- and double-layer potential operators is obtained, and the obtained jump relation of the single- and double-layer potential operators is subjected to stretching transformation to obtain the integral representation formula of the perturbation potential.

[0015] According to some embodiments, the second solution of the present invention provides a layered small inclusion position recognition system based on potential layer potential, adopting the following technical solution:

[0016] A layered small inclusion position recognition system based on potential layer potential, comprising:

[0017] An acquisition module configured to acquire the perturbed potential and background potential of the object inclusion to be recognized;

[0018] A construction module configured to perform asymptotic analysis on the acquired perturbed potential and background potential respectively considering the boundary transmission condition and stretching transformation, consider the potential layer potential, obtain the difference between the integral representation of the perturbed potential and the integral expression of the background potential, and construct an analytical model of the potential field of the layered small inclusion;

[0019] An identification module configured to determine the positional relationship of the layered small inclusion according to the constructed analytical model of the potential field, and complete the position recognition of the layered small inclusion based on potential layer potential.

[0020] According to some embodiments, the third solution of the present invention provides a computer-readable storage medium, adopting the following technical solution:

[0021] A computer-readable storage medium, on which a program is stored, and when the program is executed by a processor, it implements the steps in a method for recognizing the position of a layered small inclusion based on potential layer potential as described in the first solution of the present invention.

[0022] According to some embodiments, the fourth solution of the present invention provides an electronic device, adopting the following technical solution:

[0023] An electronic device, comprising a memory, a processor, and a program stored on the memory and running on the processor, and when the processor executes the program, it implements the steps in a method for recognizing the position of a layered small inclusion based on potential layer potential as described in the first solution of the present invention.

[0024] According to some embodiments, the fifth solution of the present invention provides a computer program product, adopting the following technical solution:

[0025] A computer program product, comprising software code, and the program in the software code executes the steps in a method for recognizing the position of a layered small inclusion based on potential layer potential as described in the first solution of the present invention.

[0026] Compared with the prior art, the beneficial effects of the present invention are:

[0027] Based on the potential layer potential theory, the present invention constructs an analytical model of the potential field of the layered small inclusion to achieve accurate recognition of the position of the layered small inclusion without considering shape restoration.

[0028] The present invention establishes a mathematical theory for identifying layered anomalies using potential data. Based on the control of the Laplace system, the positions of multiple layered inclusions after change are uniquely restored. That is, a mathematical model is used to depict the non-linear relationship between the potential field and the conductive layered anomaly structure, overcoming the limitations faced by traditional methods in dealing with multi-parameter and multi-scale geological anomalies. This means that the specific positions of underground layered anomalies can be accurately deduced from the measured perturbed potential difference data, providing a solid theoretical basis and technical support for practical applications in fields such as mineral exploration, geological disaster warning, and water resource management. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The accompanying drawings forming a part of this embodiment are used to provide a further understanding of this embodiment. The schematic embodiments and descriptions thereof of this embodiment are used to explain this embodiment and do not constitute an improper limitation of this embodiment.

[0030] Figure 1 It is a flowchart of a method for identifying the positions of layered inclusions based on potential layer potential in Embodiment 1 of the present invention.

[0031] Figure 2 It is a schematic diagram of the detailed steps of a method for identifying the positions of layered inclusions based on potential layer potential in Embodiment 1 of the present invention.

[0032] Figure 3 It is a geometric schematic diagram of the layered inclusions in Embodiment 1 of the present invention.

[0033] Figure 4 It is a structural block diagram of a system for identifying the positions of layered inclusions based on potential layer potential in Embodiment 2 of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0035] It should be noted that the following detailed descriptions are all exemplary and are intended to provide a further description of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0036] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, 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.

[0037] In the present invention, terms such as "upper", "lower", "left", "right", "front", "rear", "vertical", "horizontal", "side", "bottom", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. They are only relational terms determined for the convenience of describing the structural relationships of various components or elements of the present invention, and do not specifically refer to any component or element in the present invention, and should not be construed as a limitation to the present invention.

[0038] Without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0039] Embodiment 1

[0040] Embodiment 1 of the present invention introduces a method for identifying the position of layered small inclusions based on the potential layer potential.

[0041] As Figure 1 shown, a method for identifying the position of layered small inclusions based on the potential layer potential includes:

[0042] Obtain the perturbed potential and background potential of the object inclusion to be identified;

[0043] Considering the boundary transmission conditions and stretching transformation, perform asymptotic analysis on the obtained perturbed potential and background potential respectively, consider the potential layer potential, obtain the difference between the integral representation of the perturbed potential and the integral expression of the background potential, and construct an analytical model of the potential field of the layered small inclusion;

[0044] Determine the positional relationship of the layered small inclusions according to the constructed analytical model of the potential field, and complete the position identification of the layered small inclusions based on the potential layer potential.

[0045] As Figure 2 shown, this embodiment is based on the potential layer potential theory. By establishing multiple analytical models of the potential field of layered small inclusions, the position identification of small inclusions under complex geological conditions is realized; without considering the restoration of their shapes, the influence of external interference signals is small. Establishing the analytical solutions of the potential fields of multiple layered small inclusions to achieve the decoupling of the field-source coupling effect, the positions of multiple layered small inclusions can be accurately identified. In practical applications, the wave measurement device is usually deployed at a far distance from the target; the layer potential theory, stretching transformation, asymptotic analysis and unique continuation theorem are used to prove the unique recovery of multiple layered small inclusions.

[0046] This embodiment only uses the measured potential data. Without considering the restoration of their shapes, the influence of external interference signals is small. Establishing the analytical solutions of the potential fields of multiple layered small inclusions to achieve the decoupling of the field-source coupling effect, the positions of multiple layered small inclusions can be accurately identified.

[0047] This embodiment considers the unique recovery result of the positions of multiple layered inclusions under the control of the Laplace system; specifically:

[0048] This example assumes To embed in Inclusions, and Smooth borders; is the background space, For Region The medium parameters are determined by the conductivity Decide, in middle ,exist middle . Background potential yes The harmonic function in is the disturbed potential, controlled by the Laplace system, satisfying the equation:

[0049] (1)

[0050] in, represents the characteristic function.

[0051] Assumptions is the location of the potential detection receiver, which is a bounded area and contains , The inverse problem of the conductivity problem in formula (1) is: and boundary measurements In the case of , reconstruct the inclusion position.

[0052] This example proves that the uniqueness of the positions of multiple layered small inclusions can be restored by using layer potential theory, asymptotic analysis and unique continuation theorem.

[0053] In order to solve the problem of multiple layered inclusions, this embodiment first constructs an inclusion model.

[0054] like Figure 3 As shown, assuming that the inclusion , consisting of multiple inclusions composition, The position in space changes over time. is the central region where the electric field is generated, and It is a layered structure with a conductivity of . There are non-intersecting smooth closed surfaces Will Divide Subset, satisfying , each Surround ,area Represents a uniform dielectric layer, each layer has conductivity , the conductivity satisfies:

[0055] (2)

[0056] Meet the transmission conditions:

[0057] (3)

[0058] Among them, use the symbol to represent the outward normal on, and for any function there is

[0059] (4)

[0060] Based on the description of the above multiple layered inclusions, formula (1) can be rewritten as

[0061] (5)

[0062] In this embodiment, the total perturbation electric potential is the solution of formula (2), formula (3) and formula (5), is the background electric potential.

[0063] To display the position information of the inclusions, assume

[0064] (6)

[0065] Among them, , represents making a small enough parameter, is a simply connected domain centered at the origin, reflects the position information.

[0066] The inverse problem mathematical model can be described as

[0067] (7)

[0068] Among them, represents the union, represents all the small inclusions formed set.

[0069] This embodiment restores the positions of multiple layered small inclusions by monitoring the change of the electric field on the boundary ∂Ω.

[0070] This embodiment uses , and to represent the th small inclusion's The single-layer potential operator, double-layer potential operator, and boundary integral Neumann-Poincaré operator are as follows. The specific expressions are:

[0071] (8)

[0072] (9)

[0073] (10)

[0074] Among them, represents the single-layer potential operator when the density parameter of the boundary is , represents the double-layer potential operator when the density parameter of the boundary is , represents the Neumann-Poincaré operator when the density parameter of the boundary is ; is the fundamental solution of the Laplace equation, then , represents the density function of the th layer of the th small inclusion, represents the Cauchy principal value.

[0075] The jump relations of the single- and double-layer potential operators in this embodiment are

[0076] (11)

[0077] (12)

[0078] Among them, is the adjoint operator.

[0079] Let , then

[0080] (13)

[0081] (14)

[0082] Among them, represents the unit outer normal vector perpendicular to , represents the unit outer normal vector perpendicular to , is the homogeneous medium layer.

[0083] Considering , case, let , , since the distance approaches infinity, then

[0084] (15)

[0085] Consider , the case, let , , , since , then

[0086] (16)

[0087] In this embodiment, let be the solution of formula (7), the conductivity is obtained from formula (2), the transmission condition is obtained from formula (3), and there exists a unique function such that the following equation holds

[0088] (17)

[0089] where the boundary layer potential function satisfies

[0090] (18)

[0091] Since it is continuous on , it automatically satisfies the first condition in formula (3). Using the second condition in formula (3), the equation

[0092] (19)

[0093] Using the jump relation of the above single- and double-layer potential operators, the above equation can be rewritten as

[0094] (20)

[0095] where .

[0096] Introduce matrix, which is an n-order matrix-type operator, and also introduce the notation vectors and , that is

[0097] (21)

[0098] (22)

[0099] (23)

[0100] Equation (20) can be rewritten as

[0101] (24)

[0102] where the diagonal matrix .

[0103] Substituting Equation (13) and Equation (14) into Equation (24), we get

[0104] (25)

[0105] where is the identity matrix.

[0106] In this embodiment, the integral expression of

[0107] is(26)

[0108] where , .

[0109] Specifically, performing a Taylor expansion on the Laplacian fundamental solution, we obtain

[0110] is(27)

[0111] where .

[0112] Let , and let perform a variable substitution. Substituting Equation (25) into Equation (17), we get

[0113] is(28)

[0114] In this embodiment, the unique identification result after the movement of multiple layered small inclusions is derived through boundary measurement. Let and represent the small inclusions with their positions moved, and respectively replace ; respectively replace and to reflect the position information; is the solution of Equation (5).

[0115] If holds, then , ; specifically:[[]]

[0116] contains The bounded domain (which is also the position of the measurement receiver). is a harmonic function on , and combined with the principle of unique continuation, we have ; combined with formula (26), for , we then have

[0117] (29)

[0118] Let , and through direct calculation, on , we have

[0119] (30)

[0120] where , , the value of is

[0121] It should be noted that defined in formula (30) is also a harmonic function on . By using the analytic continuation of the harmonic function, we can obtain in . Define , where

[0122] (31)

[0123] By comparing the pole types, we can obtain in . If , then from , we immediately get ; from , , we can obtain .

[0124] Combined with formula (30), we can obtain ; if , then we also have established.

[0125] In this embodiment, a mathematical theory for identifying layered anomalies using potential data is established. Based on the Laplace system control, the positions of multiple layered inclusions after change are uniquely restored. That is, a mathematical model is used to describe the non-linear relationship between the potential field and the conductive layered anomaly structure, overcoming the limitations faced by traditional methods in dealing with multi-parameter and multi-scale geological anomalies. This means that the measured perturbed potential difference data can accurately invert the specific positions of the underground layered anomalies, providing a solid theoretical basis and technical support for practical applications in fields such as mineral exploration, geological disaster warning, and water resource management.

[0126] Embodiment 2

[0127] Embodiment 2 of the present invention introduces a system for identifying the positions of layered inclusions based on potential layer potential.

[0128] As Figure 4 shown, a system for identifying the positions of layered inclusions based on potential layer potential includes:

[0129] An acquisition module configured to acquire the perturbed potential and background potential of the object inclusion to be identified;

[0130] A construction module configured to perform asymptotic analysis on the acquired perturbed potential and background potential respectively considering the boundary transmission conditions and stretching transformation, consider the potential layer potential, obtain the difference between the integral representation of the perturbed potential and the integral expression of the background potential, and construct an analytical model of the potential field of the layered inclusions;

[0131] An identification module configured to determine the positional relationship of the layered inclusions according to the constructed analytical model of the potential field, and complete the identification of the positions of the layered inclusions based on potential layer potential.

[0132] The detailed steps are the same as those of a method for identifying the positions of layered inclusions based on potential layer potential provided in Embodiment 1, and will not be elaborated here.

[0133] Embodiment 3

[0134] Embodiment 3 of the present invention provides a computer-readable storage medium.

[0135] A computer-readable storage medium, on which a program is stored, and when the program is executed by a processor, it implements the steps in a method for identifying the positions of layered inclusions based on potential layer potential as described in Embodiment 1 of the present invention.

[0136] The detailed steps are the same as those of a method for identifying the positions of layered inclusions based on potential layer potential provided in Embodiment 1, and will not be elaborated here.

[0137] Embodiment 4

[0138] Embodiment 4 of the present invention provides an electronic device.

[0139] An electronic device includes a memory, a processor, and a program stored on the memory and running on the processor. When the processor executes the program, it implements the steps in a method for identifying the position of a layered small inclusion based on potential layer potential as described in Embodiment 1 of the present invention.

[0140] The detailed steps are the same as those in the method for identifying the position of a layered small inclusion based on potential layer potential provided in Embodiment 1, and will not be elaborated here.

[0141] Embodiment 5

[0142] Embodiment 5 of the present invention provides a computer program product.

[0143] A computer program product includes software code, and the program in the software code implements the steps in a method for identifying the position of a layered small inclusion based on potential layer potential as described in Embodiment 1 of the present invention.

[0144] The detailed steps are the same as those in the method for identifying the position of a layered small inclusion based on potential layer potential provided in Embodiment 1, and will not be elaborated here.

[0145] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented in various computer languages, for example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript.

[0146] The present invention is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0147] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction means that implements the functions specified in one or more of the processes Figure 1 one or more of the processes and / or Figure 1 boxes specified in one or more of the boxes.

[0148] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, such that a series of operational steps are performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one or more of the processes Figure 1 one or more of the processes and / or Figure 1 boxes specified in one or more of the boxes.

[0149] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made by those skilled in the art once they learn of the basic inventive concept. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications that fall within the scope of the present invention.

[0150] It is obvious that those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

[0151] The above are only the preferred embodiments of this example and are not used to limit this example. For those skilled in the art, this example can have various changes and variations. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of this example shall be included within the protection scope of this example.

Claims

1. A method for identifying the position of layered small inclusions based on the electric potential layer potential, characterized in that, Including: Obtain the perturbation potential and the background potential of the object inclusion to be recognized; Considering the boundary transmission conditions and the stretching transformation, perform asymptotic analysis on the obtained perturbation potential and background potential respectively, consider the potential layer potential, obtain the difference between the integral representation of the perturbation potential and the integral expression of the background potential, and construct an analytical model of the potential field of the layered small inclusion; Determine the positional relationship of the layered small inclusion according to the constructed analytical model of the potential field, and complete the position recognition of the layered small inclusion based on the potential layer potential; The constructed analytical model of the potential field of the layered small inclusion adopts the asymptotic behavior of the integral representation of the perturbation potential and the background potential, that is, perform Taylor expansion on the obtained perturbation potential using the Laplace operator, consider the conductivity of each layer in the layered small inclusion, and combine the boundary transmission conditions to obtain the difference between the integral representation of the perturbation potential and the integral expression of the background potential, that is, complete the construction of the analytical model of the potential field of the layered small inclusion; Based on the boundary measurement, obtain the position information when the layered small inclusion moves, and combine the constructed analytical model of the potential field to determine the position of the layered small inclusion, and complete the position recognition of the layered small inclusion; Inclusion including a plurality of layered small inclusions , the layered small inclusions are the central regions generating an electric field, and their positions in space change with time; Among them, , represents a parameter that makes sufficiently small, is a simply connected domain centered at the origin, reflecting position information; wherein, represents the unit outer normal vector perpendicular to ; represents the unit outer normal vector perpendicular to ; is a homogeneous medium layer; represents the Neumann-Poincaré operator when the density function of the boundary is ; represents the density function of the -th layer of the -th small inclusion; is the adjoint operator of; represented as a diagonal matrix, specifically: Denotes an n - order matrix - type operator, specifically: Among them, is the total disturbance electric potential, is the background electric potential, represents the th layer density function of the 2. The method for identifying the position of a layered small inclusion based on the potential layer potential according to claim 1, wherein , the obtained perturbation electric potential and background electric potential at least satisfy the Laplace control equation ; where represents three-dimensional space, represents the divergence operator, represents the gradient operator, represents a higher-order infinitesimal, is the eigenfunction, is the inclusion embedded in , and there is with a smooth boundary, represents that the first-order derivative of the function satisfies the Hölder condition, is the background space, is the region 's closure. In , the conductivity , and in .

3. A method for identifying the position of a layered small inclusion based on the electric potential layer potential as described in claim 1, characterized in that In the asymptotic analysis, combine the single-layer potential operator, the double-layer potential operator and the boundary integral operator of the small inclusion to obtain the jump relationship of the single- and double-layer potential operators, and perform stretching transformation on the obtained jump relationship of the single- and double-layer potential operators to obtain the integral representation of the perturbation potential.

4. A layered small inclusion position recognition system based on electric potential layer potential, which adopts a layered small inclusion position recognition method according to any one of claims 1-3, characterized in that, Including: An acquisition module configured to obtain the perturbation potential and the background potential of the object inclusion to be recognized; A construction module configured to perform asymptotic analysis on the obtained perturbation potential and background potential respectively considering the boundary transmission conditions and the stretching transformation, consider the potential layer potential, obtain the difference between the integral representation of the perturbation potential and the integral expression of the background potential, and construct an analytical model of the potential field of the layered small inclusion; An identification module configured to determine the positional relationship of the layered small inclusion according to the constructed analytical model of the potential field, and complete the position recognition of the layered small inclusion based on the potential layer potential.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, the steps of a method for recognizing the position of a layered small inclusion based on potential layer potential as described in any one of claims 1-3 are implemented.

6. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and running on the processor, wherein, When the processor executes the program, the steps of a method for recognizing the position of a layered small inclusion based on potential layer potential as described in any one of claims 1-3 are implemented.

7. A computer program product, comprising software code, characterized in that, The program in the software code executes the steps of a method for recognizing the position of a layered small inclusion based on potential layer potential as described in any one of claims 1-3.

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