An equivalent circuit analysis method and system for soil resistance heating efficiency

Abstract

The application provides a soil resistance heating efficiency equivalent circuit analysis method and system, relates to the soil remediation technical field, and obtains the resistivity distribution data and the salt content distribution data of the heap space; calculates the ion conductivity according to the salt content distribution data, calculates the target conductivity of each grid unit; constructs a topology graph, and constructs a weighted adjacency matrix based on the topology graph; construct a degree matrix according to the degree of each graph node, obtain an eigenvalue sequence and a characteristic vector corresponding to each eigenvalue; extract the second smallest eigenvalue from the eigenvalue sequence as a connectivity index, and mark the mutation position as a weak connection interface; determine the blocking factor by counting the number of graph nodes located at the weak connection interface, calculate the equivalent circuit transmission efficiency representing the soil resistance heating efficiency based on the negative correlation between the connectivity index and the blocking factor, and realize accurate quantitative evaluation of the heterogeneous soil resistance heating efficiency.

Description

Technical Field

[0001] This application relates to the field of soil remediation technology, and in particular to an equivalent circuit analysis method and system for soil resistance heating efficiency. Background Technology

[0002] Soil resistance heating technology is a key means of remediating organically contaminated sites. Its heating efficiency directly determines the remediation cost and cycle. Therefore, establishing an accurate equivalent circuit analysis model is of great significance for optimizing underground energy transmission networks and reducing energy consumption.

[0003] Existing solutions typically use numerical simulation software to construct a finite element model based on average apparent resistivity data, or use simplified series-parallel equivalent circuits to calculate the total resistance between electrodes, thereby estimating the overall heat generation power density and temperature rise trend of the site.

[0004] However, existing methods rely solely on resistivity values ​​for overall assessment, neglecting the masking effect of ineffective ionic conductivity caused by uneven salt distribution within the soil on the actual skeletal heating path. They fail to identify weak interfaces and connectivity bottlenecks hindering effective current transmission at the topological level, leading to biased assessments of the heating effect on complex heterogeneous piles. Therefore, existing technologies suffer from the technical problem of accurately evaluating the effective energy transfer efficiency within heterogeneous soils. Summary of the Invention

[0005] The purpose of this application is to provide an equivalent circuit analysis method and system for soil resistance heating efficiency, so as to solve the technical problem in the prior art that it is difficult to accurately evaluate the effective energy transfer efficiency inside heterogeneous soil.

[0006] In a first aspect, this application provides an equivalent circuit analysis method for soil resistance heating efficiency, including:

[0007] Acquire resistivity distribution data and salt content distribution data of the stack space. The resistivity distribution data includes the apparent resistivity of multiple grid cells in the stack space, and the salt content distribution data includes the salt content of each grid cell.

[0008] Ionic conductivity is calculated based on salt content distribution data. The reciprocal of apparent resistivity is taken as total conductivity. The target conductivity of each grid cell is then calculated based on total conductivity and ionic conductivity.

[0009] Using grid cells as graph nodes, establishing connecting edges based on the spatial adjacency of grid cells, determining edge weights based on the target conductivity between adjacent graph nodes, constructing a topology graph, and building a weighted adjacency matrix based on the topology graph;

[0010] Construct a degree matrix based on the degree of each graph node, calculate the graph Laplacian matrix based on the degree matrix and the weighted adjacency matrix, perform eigenvalue decomposition on the graph Laplacian matrix to obtain the eigenvalue sequence and the eigenvector corresponding to each eigenvalue;

[0011] Extract the second smallest feature value from the feature value sequence as a connectivity index, extract the feature vector corresponding to the second smallest feature value, determine the abrupt change position of the positive and negative signs in the feature vector corresponding to the second smallest feature value, and mark the abrupt change position as a weak connection interface;

[0012] The barrier factor is determined by counting the number of graph nodes located at weakly connected interfaces. The equivalent circuit transmission efficiency, which represents the soil resistivity heating efficiency, is calculated based on the negative correlation between the connectivity index and the barrier factor.

[0013] Optionally, the ionic conductivity is calculated based on the salt content distribution data, the reciprocal of the apparent resistivity is used as the total conductivity, and the target conductivity of each grid cell is calculated based on the total conductivity and the ionic conductivity, including:

[0014] Substitute the preset soil porosity parameters into the Archie formula to obtain the conversion coefficient. Multiply the salt content of each grid cell in the salt content distribution data with the conversion coefficient to obtain the ionic conductivity of each grid cell.

[0015] The reciprocal of the apparent resistivity of each grid cell is taken as the total conductivity of the corresponding grid cell;

[0016] The total conductivity is corrected based on the ionic conductivity to obtain the corrected total conductivity.

[0017] If the corrected total conductivity is greater than the preset lower threshold, then the corrected total conductivity is determined as the target conductivity of the corresponding grid cell.

[0018] If the corrected total conductivity is less than or equal to the lower threshold limit, then the lower threshold limit is determined as the target conductivity of the corresponding grid cell.

[0019] Optionally, a topology graph is constructed using grid cells as graph nodes, establishing connecting edges based on the spatial adjacency of grid cells, and determining edge weights based on the target conductivity between adjacent graph nodes, including:

[0020] Each grid cell is treated as a graph node, and a node index is assigned to each graph node. The grid cells are cubic cells of equal size.

[0021] Calculate the coordinate distance between any two graph nodes. When the coordinate distance is equal to the side length of the cube element, establish a connecting edge between the two graph nodes. The graph nodes connected by the connecting edge are the first graph node and the second graph node, respectively.

[0022] The product of the target conductivity of the first graph node and the target conductivity of the second graph node is divided by the sum of the target conductivity of the first graph node and the target conductivity of the second graph node to obtain the conductivity coupling value of each connecting edge, and the conductivity coupling value is determined as the edge weight of the corresponding connecting edge.

[0023] A topological graph is constructed based on graph nodes, connecting edges, and edge weights.

[0024] Optionally, a weighted adjacency matrix is ​​constructed based on the topological graph, including:

[0025] Based on the topological graph, construct a zero matrix with the graph nodes as the dimension;

[0026] Assign the edge weights to the matrix elements in the i-th row and j-th column and the j-th row and i-th column of the zero matrix to obtain the weighted adjacency matrix, where i is the node index of the node in the first graph and j is the node index of the node in the second graph.

[0027] Optionally, a degree matrix is ​​constructed based on the degree of each graph node. The graph Laplacian matrix is ​​then calculated based on the degree matrix and the weighted adjacency matrix. Eigenvalue decomposition is performed on the graph Laplacian matrix to obtain an eigenvalue sequence and an eigenvector corresponding to each eigenvalue, including:

[0028] The degree of each graph node is obtained by summing the elements of each row in the weighted adjacency matrix to construct the degree matrix.

[0029] The difference matrix between the degree matrix and the weighted adjacency matrix is ​​calculated to obtain the graph Laplacian matrix;

[0030] The characteristic equation is constructed based on the graph Laplacian matrix, and the characteristic equation is solved iteratively to obtain multiple eigenvalues ​​and the eigenvectors corresponding to each eigenvalue. All eigenvalues ​​are arranged in ascending order to obtain the eigenvalue sequence.

[0031] Optionally, the second smallest eigenvalue is extracted from the eigenvalue sequence as a connectivity index, and the eigenvector corresponding to the second smallest eigenvalue is extracted. The abrupt change positions of the positive and negative signs in the eigenvector corresponding to the second smallest eigenvalue are determined, and the abrupt change positions are marked as weak connection interfaces, including:

[0032] The second feature value in the feature value sequence is used as the connectivity index;

[0033] Based on the node index of the graph node, the vector elements in the feature vector corresponding to the connectivity index are used as the node weights of the graph node.

[0034] Traverse adjacent graph node pairs with connecting edges. When the signs of the node weights of adjacent graph node pairs are opposite, determine the spatial boundary of the adjacent graph node pairs as the abrupt change position.

[0035] By combining the spatial coordinates of all mutation locations, a weakly connected interface is obtained.

[0036] Optionally, the barrier factor is determined by statistically analyzing the number of graph nodes located at weakly connected interfaces. Based on the negative correlation between the connectivity index and the barrier factor, the equivalent circuit transmission efficiency, representing the soil resistivity heating efficiency, is calculated, including:

[0037] The graph nodes connected at abrupt changes in the weakly connected interface are taken as interface nodes. The number of interface nodes and the total number of nodes in the topology graph are counted, and the ratio of the number of interface nodes to the total number of nodes is calculated to obtain the barrier factor.

[0038] The connectivity gain value is obtained by multiplying the connectivity index by the preset connectivity weight, and the barrier loss value is obtained by multiplying the barrier factor by the preset barrier weight.

[0039] The difference between the connectivity gain and the blocking loss is calculated to obtain the net transmission efficiency value, which is then determined as the equivalent circuit transmission efficiency. The equivalent circuit transmission efficiency is used to represent the soil resistance heating efficiency.

[0040] Secondly, this application provides an equivalent circuit analysis system for soil resistance heating efficiency, comprising:

[0041] The acquisition module is used to acquire resistivity distribution data and salt content distribution data of the stack space. The resistivity distribution data includes the apparent resistivity of multiple grid cells in the stack space, and the salt content distribution data includes the salt content of each grid cell.

[0042] The calculation module is used to calculate the ionic conductivity based on the salt content distribution data, take the reciprocal of the apparent resistivity as the total conductivity, and calculate the target conductivity of each grid cell based on the total conductivity and ionic conductivity.

[0043] The module is used to construct a topology graph by using grid cells as graph nodes, establishing connecting edges based on the spatial adjacency of grid cells, determining edge weights based on the target conductivity between adjacent graph nodes, and constructing a weighted adjacency matrix based on the topology graph.

[0044] The computation module is also used to construct a degree matrix based on the degree of each graph node, calculate the graph Laplacian matrix based on the degree matrix and the weighted adjacency matrix, perform eigenvalue decomposition on the graph Laplacian matrix, and obtain the eigenvalue sequence and the eigenvector corresponding to each eigenvalue.

[0045] The extraction module is used to extract the second smallest feature value from the feature value sequence as a connectivity index, extract the feature vector corresponding to the second smallest feature value, determine the abrupt change position of the positive and negative signs in the feature vector corresponding to the second smallest feature value, and mark the abrupt change position as a weak connection interface.

[0046] The calculation module is also used to determine the barrier factor by counting the number of graph nodes located at weakly connected interfaces, and to calculate the equivalent circuit transmission efficiency representing the soil resistance heating efficiency based on the negative correlation between the connectivity index and the barrier factor.

[0047] Thirdly, this application provides an electronic device, comprising:

[0048] Memory, used to store computer programs;

[0049] A processor is used to execute computer programs to implement the steps of an equivalent circuit analysis method for soil resistance heating efficiency as described in the first aspect above.

[0050] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement the steps of the equivalent circuit analysis method for soil resistance heating efficiency as described in the first aspect above.

[0051] This application provides an equivalent circuit analysis method for soil resistivity heating efficiency. By simultaneously acquiring resistivity distribution data reflecting macroscopic conductivity and salinity distribution data reflecting electrochemical characteristics, it provides a multi-source heterogeneous data foundation for distinguishing between effective conductivity of the soil skeleton and ineffective ion conductivity of pore water, solving the problem that a single data source cannot describe the complex conductivity mechanism of heterogeneous soils. It eliminates the masking effect of uneven salinity distribution on heating path evaluation, ensuring the physical authenticity of subsequent circuit model construction. It avoids the problem of excessive computation and difficulty in convergence of traditional finite element methods when dealing with large-scale heterogeneous meshes. It enables the visual identification of hidden underground barrier layers, overcoming the limitation of existing technologies in spatially locating connectivity bottlenecks. It achieves accurate quantification of the effective energy transfer efficiency within heterogeneous soils, providing a scientific basis for optimizing underground energy transfer networks and formulating targeted efficiency-enhancing measures.

[0052] Furthermore, this application introduces the Archie formula and preset soil porosity parameters to accurately convert salt content distribution data into ionic conductivity, which characterizes the conductivity of pore water electrolytes. Then, this ionic conductivity is used to correct the difference in the total conductivity calculated from the reciprocal of apparent resistivity, eliminating invalid conductive components. At the same time, a lower threshold is set to provide a catch-all constraint on the correction results, and finally, the target conductivity that reflects only the characteristics of the soil solid-liquid coupling skeleton is calculated, which improves the accuracy of evaluating the effective heating path of complex heterogeneous piles. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 A flowchart illustrating an equivalent circuit analysis method for soil resistance heating efficiency provided in this application embodiment;

[0055] Figure 2 A flowchart illustrating a method for determining a target conductivity provided in an embodiment of this application;

[0056] Figure 3 A flowchart illustrating a method for obtaining a weakly connected interface provided in an embodiment of this application;

[0057] Figure 4 A schematic diagram of the equivalent circuit analysis system for soil resistance heating efficiency provided in this application embodiment;

[0058] Figure 5 This is a schematic diagram of the hardware structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0059] Given the decisive impact of heating efficiency on remediation costs and cycles in soil resistance heating technology, and the fact that existing technologies rely solely on average apparent resistivity to construct models, ignoring the masking effect of ineffective ionic conductivity caused by uneven salt content distribution on the actual skeleton heating path, and the difficulty in identifying weak connection interfaces that hinder current transmission at the topological level, it is impossible to accurately assess the effective energy transmission efficiency of heterogeneous soils.

[0060] This application acquires resistivity distribution data and salt content distribution data simultaneously, introduces an ionic conductivity correction mechanism to remove ineffective conductive components to obtain the target conductivity that truly reflects the skeleton characteristics, then transforms the physical mesh into a weighted topology graph and constructs a graph Laplacian matrix, uses eigenvalue decomposition to locate weakly connected interfaces, and finally quantifies the equivalent circuit transmission efficiency by combining connectivity index and interface barrier factor, thereby achieving accurate evaluation and bottleneck identification of the effective heating performance of complex heterogeneous stacks.

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0062] The core of this application is to provide an equivalent circuit analysis method for soil resistance heating efficiency, and a flowchart of one specific implementation is shown below. Figure 1 As shown, the method includes:

[0063] Step 101: Obtain resistivity distribution data and salt content distribution data of the stack space. The resistivity distribution data includes the apparent resistivity of multiple grid cells in the stack space, and the salt content distribution data includes the salt content of each grid cell.

[0064] In this step, the stockpile space refers to the target contaminated soil disposal site treated using ex-situ remediation technology, typically manifested as a three-dimensional geometric shape with a certain length, width, and height. Resistivity distribution data refers to a three-dimensional dataset describing the conductivity of various spatial locations within the stockpile; it can include resistivity values ​​of discrete points or continuous fields obtained through geophysical methods. Salinity distribution data refers to a three-dimensional dataset describing the concentration distribution of soluble salts at various spatial locations within the stockpile; it can be a set of values ​​calculated based on the total dissolved solids concentration or conductivity of soil pore water. A grid cell refers to the smallest volume unit obtained by discretizing the continuous stockpile space in space; it can be a cube, cuboid, or other regular geometric shape. Apparent resistivity refers to the apparent resistivity value measured by a measuring electrode system under the influence of the geoelectric field, reflecting the overall conductivity at the location of the grid cell. Salinity refers to the content of soluble salts in the soil medium within a single grid cell, which can be expressed as a mass fraction or pore water conductivity value.

[0065] In this embodiment, a three-dimensional resistivity scan of the stack space is first performed. Specifically, multiple electrode arrays can be arranged at preset positions on and inside the stack surface. By controlling the power supply and measurement combination between the electrodes, potential difference data at different depths are collected. Then, the collected potential difference data is processed using least squares inversion software to divide the stack space into... The system uses cubic grid cells of equal size. For example, a stack measuring 20 meters long, 10 meters wide, and 5 meters high can be divided into 4000 grid cells with sides of 0.5 meters each. The apparent resistivity value for each grid cell is calculated through inversion, thus constructing resistivity distribution data. This data can be represented as a set of quadruples containing coordinates and values. ,in This is the apparent resistivity.

[0066] Simultaneously, to obtain salinity distribution data, soil sampling and analysis can be conducted at a preset sampling density during the heap construction process, or soil pore water conductivity data can be simultaneously collected using an in-situ salinity sensor array. Then, geostatistical interpolation algorithms, such as Kriging interpolation, are used to map the discrete sampling point data onto a grid cell system identical to the resistivity distribution data, so that each grid cell has a corresponding salinity value, which can be represented as... ,in The salt content was then determined. Ultimately, resistivity and salt content distribution data were obtained that completely covered the heap space and corresponded to the spatial locations, providing fundamental data support for subsequent calculations of the target conductivity and the construction of the topology map.

[0067] Step 102: Calculate the ionic conductivity based on the salt content distribution data, take the reciprocal of the apparent resistivity as the total conductivity, and calculate the target conductivity of each grid cell based on the total conductivity and ionic conductivity.

[0068] In this step, ionic conductivity refers to the electrical conductivity contributed by the migration of electrolyte ions dissolved in soil pore water, and its value is related to salinity and pore structure. Total conductivity refers to the overall electrical conductivity exhibited by the grid cells macroscopically, and is numerically equal to the reciprocal of apparent resistivity. Target conductivity refers to the equivalent conductivity value used to evaluate the effective heating path of the soil skeleton after eliminating or correcting for the effects of ionic conductivity.

[0069] like Figure 2 As shown, Figure 2 This is a flowchart illustrating a method for determining a target conductivity according to an embodiment of this application.

[0070] Step 201: Substitute the preset soil porosity parameters into the Archie formula to obtain the conversion coefficient. Multiply the salt content of each grid cell in the salt content distribution data with the conversion coefficient to obtain the ionic conductivity of each grid cell.

[0071] In this step, soil porosity parameters refer to physical parameters describing the proportion of pore volume to total volume within the soil. These parameters can be values ​​determined in the laboratory or empirical constants preset based on soil texture. Archie's formula is an empirical law describing the relationship between electrical conductivity and porosity, saturation, and pore water conductivity in porous media. The conversion factor is a proportionality factor calculated based on Archie's formula and porosity parameters, used to directly map salt content values ​​to ionic conductivity.

[0072] In this embodiment, a preset soil porosity parameter is first obtained. This parameter can be selected from geotechnical engineering handbooks based on the type of soil in the pile, such as silty clay or sandy soil. Then, this porosity parameter is substituted into the Archie formula to calculate the conversion coefficient. Specifically, the conversion coefficient... The calculation formula can be shown in formula (1):

[0073] (1)

[0074] in Soil porosity describes the proportion of pore volume within the soil. It refers to saturation, which represents the degree to which pores are filled with water. It is the cementation index, which typically ranges from 1.3 to 2.5. This is the saturation index, typically with a value close to 2.0. For example, it's used to preset soil porosity. The calculated conversion coefficient is 0.4. The value is 0.05. After determining the conversion coefficient, considering that under low salinity conditions, the electrical conductivity of soil pore water and the salinity S have an approximately linear positive correlation, the salinity value of each grid cell in the salinity distribution data is read. The salinity of each grid cell is then compared with the conversion coefficient. When performing multiplication, the conversion coefficients here already include the linear mapping constant. Thus, the ionic conductivity of each grid cell contributed by dissolved salts is obtained.

[0075] For example, for a certain grid cell A, its salt content detection value is 0.8 units. It is 0.4. It is 0.8. It is version 2.0. The conversion coefficient is calculated to be 2.0. Combined with the linear proportionality constant Then calculate the ionic conductivity of grid cell A. This process converts chemical concentration data into physical conductivity parameters, quantifying the contribution of electrolytes in pore water to overall conductivity.

[0076] Step 202: Take the reciprocal of the apparent resistivity of each grid cell as the total conductivity of the corresponding grid cell.

[0077] In this step, total conductivity refers to the overall electrical conductivity exhibited by the grid cells on a macroscopic scale. Its value is equal to the reciprocal of apparent resistivity, and the unit is usually Siemens per meter.

[0078] In this embodiment, each grid cell in the resistivity distribution data is traversed, and its apparent resistivity value is read. Using the reciprocal operation, the reciprocal of the apparent resistivity is directly calculated to obtain the total conductivity of the corresponding grid cell. This total conductivity reflects the combined effect of all conductive mechanisms within the grid cell, including soil skeleton conductivity and pore water ion conductivity. For example, assuming the apparent resistivity measurement value of grid cell A is 25 ohm-meters, its reciprocal is directly calculated to obtain the total conductivity of grid cell A. .

[0079] Step 203: Correct the total conductivity based on the ionic conductivity to obtain the corrected total conductivity.

[0080] In this step, the corrected total conductivity refers to the conductivity value that reflects only the conductivity of the soil skeleton and solid-liquid interface after the ionic conductivity component has been removed through difference calculation.

[0081] In this embodiment, for each grid cell, the calculated total conductivity and ionic conductivity are obtained. The total conductivity is then corrected for the difference using the ionic conductivity; the specific calculation formula can be expressed as follows: ,in This is the corrected total conductivity. For total conductivity, This represents ionic conductivity. This subtraction operation removes the spurious high conductivity caused by high salt concentrations, resulting in a more accurate reflection of the soil's connectivity and heating potential, avoiding biases in heating pathway assessments due to salt accumulation. For example, it calculates the corrected total conductivity. .

[0082] Step 204: If the corrected total conductivity is greater than the preset lower threshold, then the corrected total conductivity is determined as the target conductivity of the corresponding grid cell.

[0083] In this step, the lower threshold refers to a pre-set minimum effective conductivity boundary value to prevent the corrected conductivity from exhibiting non-physically meaningful values, such as negative or minimum values. This lower threshold corresponds to the lowest conductivity benchmark of dry soil or rock skeletons when no pore water conducts electricity, aiming to eliminate non-physical negative values ​​caused by measurement errors or overestimation of ionic conductivity. The target conductivity refers to the effective heating conductivity after correction and threshold constraints, ultimately used for constructing the topology graph and calculating edge weights.

[0084] In this embodiment, a lower threshold is first set, which can be set to a very small positive number based on the insulation characteristics of the soil medium, for example... This value represents the typical insulating conductivity level of the dry mineral. Then, the corrected total conductivity of each grid cell is evaluated. If the corrected total conductivity is greater than the lower limit of this threshold, it indicates that the grid cell has effective framework conductivity, and the corrected total conductivity is directly determined as the target conductivity for the corresponding grid cell. For example, its corrected total conductivity is... Therefore, the target conductivity of grid cell A is determined to be... For ease of calculation later, this can be simplified to .

[0085] Step 205: If the corrected total conductivity is less than or equal to the lower threshold limit, then the lower threshold limit is determined as the target conductivity of the corresponding grid cell.

[0086] In this embodiment, the corrected total conductivity of each grid cell is determined. If the corrected total conductivity is less than or equal to the lower threshold, it indicates that there may be a measurement error or overestimation of ionic conductivity at that location, or that it is itself an insulating region. In this case, the lower threshold is forcibly set as the target conductivity of the corresponding grid cell. This step ensures that all conductivity data involved in subsequent calculations are valid positive values, guaranteeing the stability of the numerical calculation.

[0087] For example, for another grid cell B, if its corrected total conductivity calculation result is... Less than the set lower threshold Then the target conductivity of grid cell B is determined to be... Finally, through the above series of steps, the target conductivity dataset for all grid cells is obtained.

[0088] Step 103: Using grid cells as graph nodes, establish connecting edges based on the spatial adjacency of grid cells, determine edge weights based on the target conductivity between adjacent graph nodes, construct a topology graph, and construct a weighted adjacency matrix based on the topology graph.

[0089] In this step, a graph node refers to an abstract vertex representing a physical grid cell in a graph theory model. Spatial adjacency refers to the geometrical relationship between two grid cells in three-dimensional geometric space, indicating whether they share a common boundary or a common vertex. A connecting edge is a logical connection in the topology graph that links two graph nodes with spatial adjacency, representing the flow of current between these two nodes. Edge weight is a numerical attribute assigned to each connecting edge, used to quantify the smoothness of current flow or the strength of electrical coupling between adjacent nodes. A topology graph is a weighted undirected graph structure composed of all graph nodes and their connecting edges. A weighted adjacency matrix is ​​a square matrix describing the connection relationships between nodes and the edge weights in the topology graph; the values ​​of the matrix elements correspond to the edge weights of the connecting edges.

[0090] Step 301: Treat each grid cell as a graph node and assign a node index to each graph node. The grid cells are cubic cells of equal size.

[0091] In this step, the node index refers to the integer sequence number assigned to uniquely identify and access each graph node in the computer program, typically starting from 1 or 0 and incrementing. A cube element refers to a regular hexahedron with equal length, width, and height, into which the heap is divided during spatial discretization to simplify geometric calculations and ensure the uniformity of the physical model.

[0092] In this embodiment, all obtained grid cells are traversed. For each grid cell, a corresponding graph node object is created, and the spatial coordinates, target conductivity, and other attributes of the grid cell are associated with the graph node. Simultaneously, a unique integer is assigned as the node index for each graph node according to the traversal order or the spatial arrangement order of the grid cells.

[0093] For example, the first grid cell A processed in the heap is assigned a graph node index of 1; the second grid cell B is assigned an index of 2. Since the default grid cells are cubic cells of equal size, uniform side length parameters are recorded. ,For example rice.

[0094] Step 302: Calculate the coordinate distance between any two graph nodes. When the coordinate distance is equal to the side length of the cube element, establish a connecting edge between the two graph nodes. The graph nodes connected by the connecting edge are the first graph node and the second graph node, respectively.

[0095] In this step, coordinate distance refers to the Euclidean or Manhattan distance between two points in 3D space, specifically the straight-line distance between the center points of two meshes in this scenario. The first graph node and the second graph node refer to two specific graph nodes connected by connecting edges, used to distinguish the two ends of the connection relationship.

[0096] In this embodiment, a double loop traversal or a neighborhood search algorithm based on spatial indexing is used to calculate the coordinate distance between any two graph nodes. Specifically, let the center coordinates of the two graph nodes be respectively... and Calculate its Euclidean distance The calculated distance Side length of the cube unit Comparison. When equal When two graph nodes are determined to be directly adjacent in space, i.e., sharing a common surface, a connecting edge is established between them, and the two nodes are marked as the first graph node and the second graph node of the connecting edge, respectively.

[0097] For example, the center coordinates of the above grid cell A are The center coordinates of grid cell B are Calculate distance Meter, equal to the side length Therefore, a connecting edge is established between the graph nodes corresponding to A and B.

[0098] Step 303: Divide the product of the target conductivity of the first graph node and the target conductivity of the second graph node by the sum of the target conductivity of the first graph node and the target conductivity of the second graph node to obtain the conductivity coupling value of each connecting edge, and determine the conductivity coupling value as the edge weight of the corresponding connecting edge.

[0099] In this step, the conductance coupling value refers to the numerical value that quantifies the current conductance between two adjacent grid cells, reflecting the series equivalent conductance of the local micro-element circuit.

[0100] In this embodiment of the application, for each established connection edge, the target conductivity of the first graph nodes at both ends is obtained. Target conductivity of the second node The conductance coupling value is calculated using a physical model of series resistance or parallel conductance, as shown in formula (2):

[0101] (2)

[0102] in This represents the conductivity coupling value. This calculation simulates the physical process of current flowing from one grid to an adjacent grid, constrained by the conductivity of both grids, similar to the equivalent conductance calculation of two resistors in series. The calculated value is then used to determine the conductivity coupling. The value is directly assigned to the connecting edge as its edge weight.

[0103] For example, suppose the target conductivity of grid cell A is Target conductivity of grid cell B Then the conductivity coupling value of the connection side And determine 0.0225 as the edge weight of this edge.

[0104] Step 304: Construct a topology graph based on graph nodes, connecting edges, and edge weights.

[0105] In this embodiment, all generated graph nodes, all established connecting edges, and the edge weights corresponding to each edge are logically combined to construct a complete data structure object, namely a topology graph. This topology graph not only contains the spatial geometric information of the grid, but also implies the distribution characteristics of the physical field, namely electrical conductivity, through the weighted edge weights.

[0106] For example, the topology graph in the example above contains node indices 1 and 2, and an edge connecting these two nodes with a weight of 0.024.

[0107] Step 311: Based on the topology graph, construct a zero matrix with the graph nodes as the dimensions.

[0108] In this step, the zero matrix refers to a square matrix whose element values ​​are initialized to zero, and whose number of rows and columns are equal to the total number of nodes in the topology graph.

[0109] In this embodiment of the application, the total number of graph nodes in the topology graph is first counted. Then, space is allocated in the computer's memory, and a... A two-dimensional array or sparse matrix object, with all its elements set to 0. The dimension of this zero matrix directly corresponds to the index space of the graph nodes, i.e., the nth dimension of the matrix. row and number The index corresponding to the column is Graph nodes.

[0110] For example, if the topology graph only contains nodes 1 and 2 as described above, then construct a... The zero matrix .

[0111] Step 312: Assign the edge weights to the matrix elements in the i-th row and j-th column and the j-th row and i-th column of the zero matrix to obtain the weighted adjacency matrix, where i is the node index of the first graph node and j is the node index of the second graph node.

[0112] In this embodiment, each connecting edge in the topology graph is traversed. For a given connecting edge, the node index of its first graph node is obtained. Node index of the second graph node and the edge weight of that edge. Weight the edge. Assigned to the first element in the zero matrix Line number Column elements Furthermore, since an undirected topological graph is being built, the connections are bidirectional, therefore the same edge weights will be applied. Assigned to the first Line number Column elements After traversing all connecting edges and completing the assignment operations, the matrix is ​​transformed into a weighted adjacency matrix, which fully records the structure and weight information of the topological graph in algebraic form.

[0113] For example, for an edge connecting node 1 and node 2 with a weight of 0.024, assign 0.024 to the first row and second column of the matrix and the second row and first column of the matrix respectively to obtain the final weighted adjacency matrix. .

[0114] Step 104: Construct a degree matrix based on the degree of each graph node, calculate the graph Laplacian matrix based on the degree matrix and the weighted adjacency matrix, perform eigenvalue decomposition on the graph Laplacian matrix to obtain the eigenvalue sequence and the eigenvector corresponding to each eigenvalue.

[0115] In this step, degree refers to the sum of the edge weights of all edges connected to a graph node. The degree matrix is ​​a diagonal square matrix whose diagonal elements are the degrees of all graph nodes, and the remaining elements are zero. The graph Laplacian matrix is ​​the difference between the degree matrix and the weighted adjacency matrix, reflecting the structural characteristics and diffusion properties of the graph. The eigenvalue sequence is the sequence of eigenvalues ​​obtained from the decomposition, sorted by their numerical values. The eigenvector is a non-zero vector corresponding to each eigenvalue, with the same dimension as the number of graph nodes.

[0116] Step 401: Accumulate the matrix elements of each row in the weighted adjacency matrix to obtain the degree of each graph node, and construct the degree matrix.

[0117] In this embodiment, each row of the weighted adjacency matrix is ​​traversed. For the first row... The row is summed by accumulating all matrix elements in that row to calculate the nth row. Degree of each graph node ,in For the weighted adjacency matrix, the first... Line number The elements of the column. After calculating the degree of all graph nodes, construct a zero matrix with the same dimensions as the weighted adjacency matrix as the initial degree matrix. Each calculated degree... Assign the first value to the diagonal of the degree matrix Line number Column elements ,Right now The final result is a diagonal matrix with non-zero values ​​only on the diagonal, i.e., the degree matrix. For example, for a weighted adjacency matrix Calculate the sum of the first row. The sum of the second row is The constructed degree matrix .

[0118] Step 402: Calculate the difference matrix between the degree matrix and the weighted adjacency matrix to obtain the graph Laplacian matrix.

[0119] In this embodiment, matrix subtraction is performed. The constructed degree matrix is ​​used... Subtract the weighted adjacency matrix The difference matrix is ​​obtained. The matrix This is the graph Laplacian matrix. Since the degree matrix is ​​a diagonal matrix and the weighted adjacency matrix is ​​a symmetric matrix, the generated graph Laplacian matrix is ​​a real symmetric matrix, and the sum of the elements in each row is zero. For example, using the above matrix... and The graph Laplacian matrix is ​​calculated. .

[0120] Step 403: Construct the characteristic equation based on the graph Laplacian matrix, and iteratively solve the characteristic equation to obtain multiple eigenvalues ​​and the eigenvectors corresponding to each eigenvalue. Sort all the eigenvalues ​​in ascending order to obtain the eigenvalue sequence.

[0121] In this step, the characteristic equation refers to the form: The algebraic equations, where For the graph Laplace matrix, For eigenvalues, The identity matrix. An eigenvalue sequence is an ordered sequence formed by arranging all the solved eigenvalues ​​in ascending order of their numerical values. An eigenvector is a non-zero vector corresponding to each eigenvalue, satisfying... ,in These are the eigenvectors.

[0122] In this embodiment, a characteristic equation is constructed based on the generated graph Laplacian matrix. For large-scale sparse matrices, the determinant is typically not directly expanded and solved; instead, iterative algorithms, such as the Lanczos algorithm or the Arnoldi algorithm, are used to approximate the solution to the characteristic equation. Through iterative calculation, the first matrix is ​​obtained. The Laplacian matrix is ​​calculated by identifying either the smallest eigenvalue or all eigenvalues, and the corresponding eigenvector for each eigenvalue. Since the Laplacian matrix is ​​positive semi-definite, its eigenvalues ​​are all non-negative real numbers, and the smallest eigenvalue is typically 0. After obtaining the calculation results, all eigenvalues ​​are sorted in ascending order to form an eigenvalue sequence. .

[0123] At the same time, the correspondence between eigenvectors and eigenvalues ​​remains unchanged, forming a corresponding sequence of eigenvectors. For example, for the matrix mentioned above... Solve the characteristic equation Solving for the eigenvalues and 5. Sort the two eigenvalues ​​in ascending order to obtain the eigenvalue sequence. .for Solve The normalized eigenvectors are obtained. ;for =0.045, solve. The normalized eigenvectors are obtained. Ultimately, the sequence of eigenvalues ​​and the corresponding eigenvectors were obtained.

[0124] Step 105: Extract the second smallest feature value from the feature value sequence as a connectivity index, extract the feature vector corresponding to the second smallest feature value, determine the mutation position of the positive and negative signs in the feature vector corresponding to the second smallest feature value, and mark the mutation position as a weak connection interface.

[0125] In this step, the connectivity index refers to the second smallest eigenvalue in the eigenvalue sequence, also known as the Fiedler value or algebraic connectivity in algebraic graph theory, used to quantify the overall connectivity of the graph. Abrupt change points are spatial interfaces where the values ​​of elements in the eigenvectors reverse sign between adjacent graph nodes, physically corresponding to regions where current transmission is obstructed. Weakly connected interfaces are planar or strip-shaped regions formed by spatially combining all identified abrupt change points.

[0126] like Figure 3 As shown, Figure 3 This is a flowchart illustrating a method for obtaining a weakly connected interface, as provided in an embodiment of this application.

[0127] Step 501: Use the second feature value in the feature value sequence as the connectivity index.

[0128] In this embodiment, the previously calculated ascending sequence of eigenvalues ​​is directly accessed. This is because the smallest eigenvalue of the Graph Laplacian matrix... Theoretically, it is always 0, corresponding to a constant eigenvector; therefore, we focus on the second element in the sequence. We directly extract the second term from the eigenvalue sequence. The value is then used as the connectivity index. For example, in a scenario connecting the two aforementioned grid cells, the feature value sequence is: Then extract As a connectivity indicator.

[0129] Step 502: Based on the node index of the graph node, use the vector elements in the feature vector corresponding to the connectivity index as the node weight of the graph node.

[0130] In this step, the eigenvector element values ​​refer to the specific values ​​of each component in the Fiedler eigenvector. These values ​​play a role similar to coordinates in spectral clustering analysis, used to map graph nodes to a one-dimensional spectral space.

[0131] In this embodiment of the application, the connectivity index is first located. corresponding feature vector This refers to the Fiedler vector. The length of this vector is equal to the total number of graph nodes. Using the node indices of graph nodes as mapping bridges, vectors are... The first in element Extract it and assign it directly to the index. The graph nodes are used as the numerical values ​​of the feature vector elements of those nodes. This process realizes the attribute mapping from the abstract algebraic vector space to the concrete physical grid space.

[0132] For example, the corresponding feature vector is According to the index, Assign the value to node 1 as the element value of its feature vector. The value is assigned to node 2 as the element value of its feature vector.

[0133] Step 503: Traverse adjacent graph node pairs with connecting edges. When the signs of the node weights corresponding to adjacent graph node pairs are opposite, determine the spatial boundary of the adjacent graph node pairs as the abrupt change position.

[0134] In this step, an adjacent graph node pair refers to two graph nodes that are directly connected in the topology graph by a connecting edge.

[0135] In this embodiment, each connecting edge in the topology graph is traversed. For a given connecting edge, the feature vector element values ​​of its two endpoints, i.e., adjacent graph node pairs, are obtained. The signs of these two values ​​are determined to be opposite, i.e., their product is checked to see if it is less than zero. If one is positive and the other is negative, it indicates that there is a zero crossing between these two nodes. In this case, the common boundary of these two mesh cells in physical space, such as the contact surface of two cubic meshes, is marked as abrupt change location.

[0136] For example, examining the edge connecting node 1 and node 2 reveals that node 1 has a positive value of +0.707, while node 2 has a negative value of -0.707, with opposite signs. Therefore, the contact surface between node 1 and node 2 is determined. The plane at that point represents a sudden change location.

[0137] Step 504: Combine the spatial coordinates of all mutation locations to obtain the weakly connected interface.

[0138] In this embodiment, all abrupt change locations identified in the previous step are collected. The spatial geometric information corresponding to these abrupt change locations is obtained, such as the center coordinates of the interface, the normal vector, or the coordinates of the mesh boundary where it is located. All these spatial coordinate data are aggregated to form a spatial coordinate set. This set geometrically constitutes one or more continuous or discontinuous surfaces, which are defined as weakly connected interfaces.

[0139] For example, obtaining the spatial coordinate information of the contact surface, such as the center point. This is then added to the set, resulting in a weakly connected interface formed by the contact surface. This result intuitively reveals that in this two-node system, the main bottleneck of current transmission is located at the interface between the two nodes. Essentially, it utilizes the principle of spectral clustering to perform graph segmentation on the current transmission network, thereby identifying the connectivity bottleneck.

[0140] Step 106: Determine the barrier factor by counting the number of graph nodes located at weakly connected interfaces, and calculate the equivalent circuit transmission efficiency representing the soil resistance heating efficiency based on the negative correlation between the connectivity index and the barrier factor.

[0141] In this step, the barrier factor is a numerical indicator that quantifies the degree to which weakly connected interfaces impede overall current transmission; it can be expressed as the proportion of node size involved in the interface. The equivalent circuit transmission efficiency is the final evaluation index used to represent the soil resistance heating efficiency, taking into account both overall connectivity and local barrier properties.

[0142] Step 601: Take the graph nodes connected at the mutation positions in the weakly connected interfaces as interface nodes, count the number of interface nodes and the total number of nodes in all graph nodes in the topology graph, and calculate the ratio of the number of interface nodes to the total number of nodes to obtain the barrier factor.

[0143] In this step, an interface node refers to a graph node that is physically adjacent to a weakly connected interface, meaning its corresponding mesh cell boundary forms abrupt change points. The number of interface nodes refers to the total number of all interface nodes counted. The total number of nodes refers to the total number of graph nodes contained in the topology graph.

[0144] In this embodiment, firstly, based on the identified weakly connected interfaces, all mutation locations forming the interface are traced. For each mutation location, its two adjacent graph nodes (i.e., the first graph node and the second graph node) are found, and these two nodes are marked as interface nodes. This operation is performed on all mutation locations, and duplicates are removed. The final number of interface nodes is then counted. At the same time, count the total number of nodes in all graph nodes of the topology graph. The ratio separation factor was calculated. .

[0145] For example, in a scenario that connects the two aforementioned grid units, the mutation point connects node 1 and node 2, therefore the number of interface nodes... Total number of nodes Calculate the barrier factor This indicates that all nodes are on the barrier interface, representing an extremely blocked situation. It should be noted that the two node examples above are for illustrative purposes, demonstrating an extreme simplification of the computational logic. In real-world complex heterogeneous stacks containing thousands of grid cells, the barrier factor... The value of is usually in The value reflects the proportion of nodes involved in the underground concealed barrier layer to the total; the larger the value, the more severe the interruption of the effective current path.

[0146] Step 602: Calculate the product of the connectivity index and the preset connectivity weight to obtain the connectivity gain value, and calculate the product of the barrier factor and the preset barrier weight to obtain the barrier loss value.

[0147] In this step, the preset connectivity weight refers to a positive coefficient set based on engineering experience to measure the contribution of connectivity to the final efficiency. The preset barrier weight refers to a coefficient used to measure the negative impact of barrier factors on the final efficiency. The connectivity gain value refers to the weighted positive efficiency component. The barrier loss value refers to the weighted negative efficiency component.

[0148] In this embodiment of the application, a preset connectivity weight is obtained. and blocking weight These weights are not randomly assigned, but rather empirical coefficients obtained through multiple linear regression fitting based on historical heating efficiency data of restoration sites in actual engineering projects. Among them, the connectivity weights... Used to amplify the contribution of connectivity to transmission, its value typically ranges from [value range missing]. Blocking weights Used to correct energy loss caused by local obstruction, the value typically ranges from [value range missing]. Connectivity metrics With connection weight Multiply to obtain the connectivity gain value. The blocking factor With blocking weight Multiply to obtain the blocking loss value. .

[0149] For example, let the preset connectivity weights be set. Preset blocking weight Known connectivity index Then calculate the connectivity gain value. Known barrier factor Then calculate the blocking loss value. .

[0150] Step 603: Calculate the difference between the connectivity gain and the blocking loss to obtain the net transmission efficiency value, and determine the net transmission efficiency value as the equivalent circuit transmission efficiency. The equivalent circuit transmission efficiency is used to represent the soil resistance heating efficiency.

[0151] In this step, the net transmission efficiency value refers to the calculation result that takes into account both positive connectivity gain and negative blocking loss.

[0152] In this embodiment of the application, the connectivity gain value is used. Subtract barrier loss value The net transmission efficiency value is obtained. The net transmission performance value The final equivalent circuit transmission efficiency is determined. This metric uses a mathematical model to transform topological characteristics into a single efficiency score, facilitating rapid evaluation by engineers. In the example above, the net transmission efficiency value is calculated. The value of 0.38 represents the equivalent resistance heating efficiency of the soil mound under a given electrode arrangement. If the mound is humidified, increasing the target conductivity, it may... Increase this, thereby improving the final efficiency score.

[0153] This application provides a multi-source heterogeneous data foundation for distinguishing between effective conductivity of the soil skeleton and ineffective ion conductivity of pore water by simultaneously acquiring resistivity distribution data reflecting macroscopic conductivity and salinity distribution data reflecting electrochemical properties. This solves the problem that a single data source cannot describe the complex conductivity mechanism of heterogeneous soils. It eliminates the masking effect of uneven salinity distribution on heating path evaluation, ensuring the physical realism of subsequent circuit model construction. It avoids the problem of excessive computation and difficulty in convergence of traditional finite element methods when dealing with large-scale heterogeneous meshes. It enables the visual identification of hidden underground barrier layers, overcoming the limitation of existing technologies in spatially locating connectivity bottlenecks. It achieves accurate quantification of the effective energy transfer efficiency within heterogeneous soils, providing a scientific basis for optimizing underground energy transfer networks and formulating targeted efficiency-enhancing measures.

[0154] Figure 4 This is a schematic diagram of a specific embodiment of an equivalent circuit analysis system for soil resistance heating efficiency provided in this application, with reference to... Figure 4 The system may include:

[0155] The acquisition module 21 is used to acquire resistivity distribution data and salt content distribution data of the stack space. The resistivity distribution data includes the apparent resistivity of multiple grid cells in the stack space, and the salt content distribution data includes the salt content of each grid cell.

[0156] The calculation module 22 is used to calculate the ionic conductivity based on the salt content distribution data, take the reciprocal of the apparent resistivity as the total conductivity, and calculate the target conductivity of each grid cell based on the total conductivity and ionic conductivity.

[0157] Module 23 is used to construct a topology graph by using grid cells as graph nodes, establishing connecting edges based on the spatial adjacency of grid cells, determining edge weights based on the target conductivity between adjacent graph nodes, and constructing a weighted adjacency matrix based on the topology graph.

[0158] The calculation module 22 is also used to construct a degree matrix based on the degree of each graph node, calculate the graph Laplacian matrix based on the degree matrix and the weighted adjacency matrix, perform eigenvalue decomposition on the graph Laplacian matrix, and obtain the eigenvalue sequence and the eigenvector corresponding to each eigenvalue.

[0159] Extraction module 24 is used to extract the second smallest feature value from the feature value sequence as a connectivity index, extract the feature vector corresponding to the second smallest feature value, determine the abrupt change position of the positive and negative signs in the feature vector corresponding to the second smallest feature value, and mark the abrupt change position as a weak connection interface.

[0160] The calculation module 22 is also used to determine the barrier factor by statistically analyzing the number of graph nodes located at weakly connected interfaces, and to calculate the equivalent circuit transmission efficiency representing the soil resistance heating efficiency based on the negative correlation between the connectivity index and the barrier factor.

[0161] An equivalent circuit analysis system for soil resistance heating efficiency according to an embodiment of this application is used to implement the aforementioned equivalent circuit analysis method for soil resistance heating efficiency. Therefore, the specific implementation of the equivalent circuit analysis system for soil resistance heating efficiency can be found in the embodiment section of the equivalent circuit analysis method for soil resistance heating efficiency mentioned above. The specific implementation can be referred to the description of the corresponding embodiments, which will not be repeated here.

[0162] Figure 5 A schematic diagram of the hardware structure of the electronic device provided in an embodiment of this application is shown.

[0163] This application also provides an electronic device, comprising: a memory for storing a computer program; and a processor for executing the computer program to implement the steps of the equivalent circuit analysis method for soil resistance heating efficiency described above.

[0164] The electronic device may include a processor 510 and a memory 520 storing computer program instructions.

[0165] Specifically, the processor 510 may include a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits that can be configured to implement the embodiments of this application.

[0166] Memory 520 may include mass storage for data or instructions. For example, and not limitingly, memory 520 may include a hard disk drive (HDD), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, or Universal Serial Bus (USB) drive, or a combination of two or more of these. Where appropriate, memory 520 may include removable or non-removable (or fixed) media. Where appropriate, memory 520 may be internal or external to the integrated gateway disaster recovery device. In a particular embodiment, memory 520 is non-volatile solid-state memory.

[0167] Memory may include read-only memory (ROM), random access memory (RAM), disk storage media devices, optical storage media devices, flash memory devices, and electrical, optical, or other physical / tangible memory storage devices. Therefore, typically, memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), it is operable to perform the operations described with reference to the method according to the first aspect of this disclosure.

[0168] The processor 510 reads and executes computer program instructions stored in the memory 520 to implement any of the equivalent circuit analysis methods for soil resistance heating efficiency in the above embodiments.

[0169] In one example, the electronic device may also include a communication interface 530 and a bus 540. Wherein, such as Figure 5 As shown, the processor 510, memory 520, and communication interface 530 are connected through bus 540 and complete communication with each other.

[0170] The communication interface 530 is mainly used to realize communication between various modules, devices, units and / or equipment in the embodiments of this application.

[0171] Bus 540 includes hardware, software, or both, that couples components of an online data traffic metering device together. For example, and not limitingly, the bus may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a Front Side Bus (FSB), HyperTransport (HT) interconnect, an Industry Standard Architecture (ISA) bus, an Infinite Bandwidth Interconnect, a Low Pin Count (LPC) bus, a memory bus, a Microchannel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a Serial Advanced Technology Attachment (SATA) bus, a Video Electronics Standards Association Local (VLB) bus, or other suitable buses, or combinations of two or more of these. Where appropriate, bus 540 may include one or more buses. Although specific buses are described and illustrated in embodiments of this application, this application contemplates any suitable bus or interconnect.

[0172] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the above-described methods for analyzing the equivalent circuit of soil resistance heating efficiency.

[0173] In one exemplary embodiment, the aforementioned computer-readable storage medium may include, but is not limited to, various media capable of storing computer programs, such as USB flash drives, read-only memory, random access memory, portable hard drives, magnetic disks, or optical disks.

[0174] Embodiments of the present invention also provide a computer program product, which includes a computer program that, when executed by a processor, implements the steps in any of the above embodiments of the equivalent circuit analysis method for soil resistance heating efficiency.

[0175] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0176] The equivalent circuit analysis method and system for soil resistance heating efficiency provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the embodiments above are only for the purpose of helping to understand the method and its core ideas. It should be noted that those skilled in the art can make several improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. An equivalent circuit analysis method for soil resistance heating efficiency, characterized in that, include: Acquire resistivity distribution data and salt content distribution data of the stack space. The resistivity distribution data includes the apparent resistivity of multiple grid cells within the stack space, and the salt content distribution data includes the salt content of each grid cell. The ionic conductivity is calculated based on the salt content distribution data, the reciprocal of the apparent resistivity is taken as the total conductivity, and the target conductivity of each grid cell is calculated based on the total conductivity and the ionic conductivity. Using the grid cells as graph nodes, establishing connecting edges based on the spatial adjacency of the grid cells, determining edge weights based on the target conductivity between adjacent graph nodes, constructing a topology graph, and constructing a weighted adjacency matrix based on the topology graph; Construct a degree matrix based on the degree of each graph node, calculate the graph Laplacian matrix based on the degree matrix and the weighted adjacency matrix, and perform eigenvalue decomposition on the graph Laplacian matrix to obtain an eigenvalue sequence and an eigenvector corresponding to each eigenvalue. Extract the second smallest feature value from the feature value sequence as a connectivity index, extract the feature vector corresponding to the second smallest feature value, determine the mutation position of the positive and negative signs in the feature vector corresponding to the second smallest feature value, and mark the mutation position as a weak connection interface; The barrier factor is determined by counting the number of graph nodes located at the weak connection interface, and the equivalent circuit transmission efficiency, which represents the soil resistivity heating efficiency, is calculated based on the negative correlation between the connectivity index and the barrier factor.

2. The method according to claim 1, characterized in that, The ionic conductivity is calculated based on the salt content distribution data. The reciprocal of the apparent resistivity is taken as the total conductivity. The target conductivity of each grid cell is calculated based on the total conductivity and the ionic conductivity, including: Substitute the preset soil porosity parameters into the Archie formula to obtain the conversion coefficient. Multiply the salt content of each grid cell in the salt content distribution data with the conversion coefficient to obtain the ionic conductivity of each grid cell. The reciprocal of the apparent resistivity of each grid cell is taken as the total conductivity of the corresponding grid cell; The total conductivity is corrected based on the ionic conductivity to obtain the corrected total conductivity; If the corrected total conductivity is greater than the preset lower threshold, then the corrected total conductivity is determined as the target conductivity of the corresponding grid cell. If the corrected total conductivity is less than or equal to the lower threshold limit, then the lower threshold limit is determined as the target conductivity of the corresponding grid cell.

3. The method according to claim 1, characterized in that, Using the grid cells as graph nodes, establishing connecting edges based on the spatial adjacency of the grid cells, and determining edge weights based on the target conductivity between adjacent graph nodes, a topology graph is constructed, including: Each grid cell is treated as a graph node, and a node index is assigned to each graph node. The grid cells are cubic cells of equal size. Calculate the coordinate distance between any two graph nodes. When the coordinate distance is equal to the side length of the cube element, establish a connecting edge between the two graph nodes. The graph nodes connected by the connecting edge are the first graph node and the second graph node, respectively. The product of the target conductivity of the first graph node and the target conductivity of the second graph node is divided by the sum of the target conductivity of the first graph node and the target conductivity of the second graph node to obtain the conductivity coupling value of each connecting edge, and the conductivity coupling value is determined as the edge weight of the corresponding connecting edge. A topology graph is constructed based on the graph nodes, the connecting edges, and the edge weights.

4. The method according to claim 3, characterized in that, Constructing a weighted adjacency matrix based on the aforementioned topology graph includes: Based on the topology graph, construct a zero matrix with the graph nodes as its dimensions; The edge weights are assigned to the matrix elements in the i-th row and j-th column and the j-th row and i-th column of the zero matrix to obtain a weighted adjacency matrix, where i is the node index of the first graph node and j is the node index of the second graph node.

5. The method according to claim 1, characterized in that, Construct a degree matrix based on the degree of each graph node, calculate the graph Laplacian matrix based on the degree matrix and the weighted adjacency matrix, and perform eigenvalue decomposition on the graph Laplacian matrix to obtain an eigenvalue sequence and an eigenvector corresponding to each eigenvalue, including: The degree of each graph node is obtained by summing the matrix elements of each row in the weighted adjacency matrix to construct the degree matrix. Calculate the difference matrix between the degree matrix and the weighted adjacency matrix to obtain the graph Laplacian matrix; Based on the graph Laplacian matrix, a characteristic equation is constructed, and the characteristic equation is solved iteratively to obtain multiple eigenvalues ​​and eigenvectors corresponding to each eigenvalue. All eigenvalues ​​are then arranged in ascending order to obtain an eigenvalue sequence.

6. The method according to claim 1, characterized in that, Extract the second smallest feature value from the feature value sequence as a connectivity index, extract the feature vector corresponding to the second smallest feature value, determine the abrupt change position of the positive and negative signs in the feature vector corresponding to the second smallest feature value, and mark the abrupt change position as a weak connection interface, including: The second feature value in the feature value sequence is used as the connectivity index; Based on the node index of the graph node, the vector elements in the feature vector corresponding to the connectivity index are used as the node weights of the graph node. Traverse adjacent graph node pairs that have the connecting edge. When the signs of the node weights corresponding to the adjacent graph node pairs are opposite, determine the spatial boundary of the adjacent graph node pairs as a mutation position. By combining the spatial coordinates of all mutation locations, a weakly connected interface is obtained.

7. The method according to claim 1, characterized in that, The barrier factor is determined by statistically analyzing the number of graph nodes located at the weakly connected interfaces. Based on the negative correlation between the connectivity index and the barrier factor, the equivalent circuit transmission efficiency, representing the soil resistivity heating efficiency, is calculated, including: The graph nodes connected at the mutation positions in the weakly connected interface are taken as interface nodes. The number of interface nodes and the total number of nodes in the topology graph are counted, and the ratio of the number of interface nodes to the total number of nodes is calculated to obtain the barrier factor. The connectivity gain value is obtained by multiplying the connectivity index by the preset connectivity weight, and the barrier loss value is obtained by multiplying the barrier factor by the preset barrier weight. The difference between the connectivity gain and the blocking loss is calculated to obtain the net transmission efficiency value, and the net transmission efficiency value is determined as the equivalent circuit transmission efficiency, which is used to represent the soil resistance heating efficiency.

8. An equivalent circuit analysis system for soil resistance heating efficiency, characterized in that, include: The acquisition module is used to acquire resistivity distribution data and salt content distribution data of the stack space. The resistivity distribution data includes the apparent resistivity of multiple grid cells in the stack space, and the salt content distribution data includes the salt content of each grid cell. The calculation module is used to calculate the ionic conductivity based on the salt content distribution data, take the reciprocal of the apparent resistivity as the total conductivity, and calculate the target conductivity of each grid cell based on the total conductivity and the ionic conductivity. The construction module is used to construct a topology graph by using the grid cells as graph nodes, establishing connecting edges based on the spatial adjacency of the grid cells, determining edge weights based on the target conductivity between adjacent graph nodes, and constructing a weighted adjacency matrix based on the topology graph. The calculation module is also used to construct a degree matrix based on the degree of each graph node, calculate the graph Laplacian matrix based on the degree matrix and the weighted adjacency matrix, and perform eigenvalue decomposition on the graph Laplacian matrix to obtain an eigenvalue sequence and an eigenvector corresponding to each eigenvalue. The extraction module is used to extract the second smallest feature value from the feature value sequence as a connectivity index, extract the feature vector corresponding to the second smallest feature value, determine the mutation position of the positive and negative signs in the feature vector corresponding to the second smallest feature value, and mark the mutation position as a weak connection interface. The calculation module is also used to determine the barrier factor by statistically analyzing the number of graph nodes located at the weak connection interface, and to calculate the equivalent circuit transmission efficiency representing the soil resistance heating efficiency based on the negative correlation between the connectivity index and the barrier factor.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor, configured to execute the computer program to implement the steps of the equivalent circuit analysis method for soil resistance heating efficiency as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, enables an equivalent circuit analysis method for soil resistance heating efficiency as described in any one of claims 1 to 7.

Images