Concrete complex defect detection and imaging method based on resistance tomography signal

Abstract

The invention discloses a concrete complex defect detection and imaging method based on a resistance tomography signal. The method comprises the following steps of: 1, reconstructing an internal conductivity distribution diagram based on a boundary electric signal value by adopting an ERT image reconstruction algorithm; 2, in combination with a K-means segmentation algorithm, extracting an initial form boundary line of the internal defect in the conductivity distribution diagram obtained in the step 1, and performing super-shape function fitting on the defect form to obtain an initial parameter; and step 3, based on initial parameters obtained by fitting the super-shape function obtained in the step 2, optimizing by using a particle swarm algorithm and based on an initial defect range, and finally obtaining optimal defect position parameters and super-shape function morphological parameters, namely accurate positions and morphologies of the defects. According to the method, a mode of combining a pixel-based image imaging method and a shape-based graphic imaging method is adopted, so that the accuracy of ERT detection of the form and size of the internal defect of the concrete can be remarkably improved, and the method has the characteristics of high calculation efficiency and higher robustness.

Description

Technical Field

[0001] The present invention relates to the technical field of concrete defect detection, and in particular to a method for detecting and imaging complex concrete defects based on electrical resistance tomography signals. Background Art

[0002] As an important building material, concrete is widely used in various infrastructure projects, including bridges, tunnels, and buildings, due to its excellent mechanical properties and durability. However, over time and under the influence of the external environment, structural damage such as cracks and holes may appear within the concrete. These defects not only weaken the concrete's load-bearing capacity but also serve as pathways for the intrusion of external moisture and chemicals, further accelerating steel corrosion and concrete deterioration, ultimately affecting the service life and safety of the entire building. Therefore, timely and accurate detection and assessment of these defects can provide a scientific basis for subsequent maintenance and reinforcement work, and is of great significance in preventing potential structural damage from evolving into catastrophic accidents.

[0003] Electrical resistance tomography (ERT) technology, which measures the conductivity distribution within concrete to identify defects, has been used for concrete defect detection. However, while ERT inversion methods have shown potential for concrete defect detection, they still face numerous challenges. First, while the ERT method relies less on prior information and can accurately depict the conductivity distribution, it is prone to generating high levels of noise and artifacts during image reconstruction, which affects the accurate capture of defect size and morphology. Furthermore, ERT technology suffers from nonlinearity, underdetermination, severe ill-posedness, and high computational complexity, making it difficult to ensure imaging accuracy and stability. Although studies have proposed improved methods such as threshold correction and fast adaptive sparse reconstruction algorithms to improve imaging quality and reduce relative image error, these methods are significantly influenced by subjective factors when selecting thresholds, and finding a reasonable threshold is difficult. Therefore, while ERT technology has certain application value in concrete defect detection, it still faces many challenges in imaging complex defects. Summary of the Invention

[0004] To overcome the shortcomings of the above-mentioned prior art, the present invention aims to provide a method for detecting and imaging complex concrete defects based on electrical resistance tomography (ERT) signals. This method first employs an ERT image reconstruction algorithm to reconstruct an internal conductivity distribution map based on boundary electrical signal values. Then, in combination with a K-means segmentation algorithm, the initial morphological boundary lines of the internal defects in the conductivity distribution map are extracted and the defect morphology is fitted with a supershape function. Finally, based on the fitted initial parameters, a particle swarm algorithm is used to optimize within the initial defect range, ultimately obtaining the optimal defect location parameters and supershape function morphological parameters, i.e., the exact location and morphology of the defect. This method combines a pixel-based image imaging method with a shape-based graphic imaging method, significantly improving the accuracy of ERT detection of the size of internal concrete defects, while offering high computational efficiency and greater robustness.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for detecting and imaging complex defects in concrete based on electrical resistance tomography signals comprises the following steps:

[0007] Step 1: Use the ERT image reconstruction algorithm to obtain the internal conductivity distribution map based on the boundary electrical signal value;

[0008] Step 2: Combined with the K-means segmentation algorithm, the initial shape boundary lines of the internal defects in the conductivity distribution map obtained in step 1 are extracted and the defect shape is fitted with a super shape function to obtain the initial parameters;

[0009] Step 3: Based on the initial parameters of step 2, the particle swarm algorithm is used to search for the optimal solution based on the initial defect range, and finally the optimal defect location parameters and super shape function morphological parameters, that is, the exact location and morphology of the defect, are obtained.

[0010] The specific method of step 1 includes:

[0011] (1) Obtaining the empty field sensitivity matrix S without defects through simulation method;

[0012] The sensitivity matrix S in the empty field is obtained. Based on the actual detection equipment and its operating parameters, a circular concrete finite element ERT model without internal defects is established. n stainless steel electrodes are arranged equidistantly around the periphery. An adjacent current excitation mode is used, that is, an excitation current is passed between two adjacent electrodes. The electric field value at each sensitive point is obtained to calculate the sensitivity matrix S.

[0013] (2) Using the differential imaging method, based on the difference ΔU between the signal value under the real defect and the signal value under the defect-free condition, and the sensitivity matrix S obtained above, the conductivity change value Δσ is obtained by using the conjugate gradient algorithm and imaging is performed, namely ERT imaging.

[0014] The simulated signal value in the empty field is obtained by using the adjacent electrode model to obtain the surface voltage measurement signal. It is a common measurement method in electrical resistance tomography (ERT). That is, current is injected through two adjacent electrodes in sequence, and then the voltage is measured through other adjacent electrode pairs. The voltage measurement signal of the defective concrete surface is obtained by combining it with the finite element calculation method.

[0015] The specific solution method for ERT imaging is:

[0016] It is usually necessary to iteratively update the model conductivity parameter Δσ, that is, to solve the equation

[0017] SΔσ=ΔU l ,l=1,...L (1)

[0018] Here, S is the sensitivity matrix, which describes the sensitivity of conductivity to the observed data, and Δσ and ΔU l are the change values ​​of conductivity and boundary voltage signal data respectively. The sensitivity is defined as follows:

[0019]

[0020] Where S ij is the sensitivity coefficient of the jth electrode pair to the ith electrode pair, and the excitation current of the ith electrode pair and the jth electrode pair is I i , I j The field potential distribution when ; The specific solution method for obtaining the conductivity change value Δσ by the conjugate gradient algorithm is:

[0021] Directly solving the inverse problem of a large sparse matrix is ​​usually too computationally intensive. The conjugate gradient method, as an iterative solution technique, can efficiently solve large-scale sparse matrix equations. Therefore, it is very suitable for ERT inversion. Compared with the second-order method, the computational cost is low, and compared with the gradient descent method, it has better convergence characteristics. In this invention, the conjugate gradient least squares (CGLS) method is applied to the ERT inversion algorithm. The following are the iterative steps and key formulas of this method:

[0022] First, initialize the solution vector Δσ0 to a zero vector:

[0023] Δσ0=0 (3)

[0024] Calculate the initial residual vector r0 and the initial search direction d0:

[0025] r0=ΔU (4)

[0026] d0=S T ΔU (5)

[0027] Then the iterative update formula begins. In each iteration, the solution vector σ is updated j , residual r j , and search direction d j , the specific formula is as follows:

[0028] Step size α j The update formula is:

[0029]

[0030] Update of solution vector:

[0031] Δσ j+1 =Δσ j +α j d j (7)

[0032] Residual r j Update:

[0033] r j+1 =r j -α j Sd j (8)

[0034] In order to maintain the efficiency of the conjugate gradient method, the search direction needs to be updated in each iteration. The search direction correction parameter β j Calculated by the following formula:

[0035]

[0036] New search direction d j+1 Update:

[0037] d j+1 =S T r j+1 +β j d j (10)

[0038] This formula ensures that the new search direction remains conjugate with the previous search direction, thus guaranteeing the convergence of the algorithm.

[0039] The conjugate gradient method continues to update until the specified number of iterations is reached and the final solution vector is obtained.

[0040] The step 2 includes the following contents.

[0041] (1) First, convert the ERT image into a grayscale image;

[0042] The function is used to convert the color image into a grayscale image by weighted summation based on the RGB components in the image.

[0043] (2) Clustering the grayscale image obtained in (1) using the K-means algorithm to detect the defect area in the image and further extract the defect boundary;

[0044] The specific solution method is:

[0045] The K-means clustering algorithm partitions data by minimizing the squared Euclidean distance. The objective function is defined as follows:

[0046]

[0047] Where k is the number of predefined clusters, C i represents the i-th cluster, x is the data point in the cluster, μ i is the centroid of the cluster.

[0048] The iterative process of the algorithm includes the following steps:

[0049] Step 1) Randomly initialize k centroids;

[0050] Step 2) Assign data points to the nearest centroid. Assign each data point to the centroid closest to it based on the Euclidean distance, ensuring that each data point x i Assigned to the cluster S that minimizes its distance to the centroid j ; The formula is as follows:

[0051]

[0052] where d(x i , C j ) is the data point x i To cluster centroid C j Each time a data point is assigned to the nearest centroid, the distance from this data point to the centroid is ensured to be the shortest, thereby locally minimizing the distance of the data point.

[0053] Step 3) Update the position of the centroid. Once each data point is assigned to the nearest cluster, the algorithm recalculates the centroid position of each cluster. The new centroid is the average of all data points in the cluster:

[0054]

[0055] This formula represents the center of mass C j It is cluster S j The geometric center of all data points in the cluster. The geometric center has an important property: it is the point that minimizes the sum of the squared distances of the data points in the cluster to the centroid. Therefore, updating the centroid is actually minimizing the total sum of squares of the data points in the cluster by selecting the "average position" that best represents the cluster.

[0056] Step 4) Repeat steps 2) and 3) until the maximum number of iterations is reached.

[0057] (3) Perform shape analysis on these regions by fitting hypershape functions.

[0058] The shape analysis of the initial defect area is performed by fitting the super shape function. After the defect boundary is detected, the present invention uses the super shape function to fit the shape of these areas. After obtaining the boundary parameters, they are used as initial values ​​and reference areas in the subsequent particle swarm algorithm search.

[0059] The step 3 specifically includes the following contents:

[0060] Step 1) uses a reconstruction method based on super shape function, which uses super shape function to represent the internal defect morphology. By iteratively optimizing the super shape parameters, the objective function value between the corresponding predicted voltage and the actual target measured voltage is finally minimized. The advantage of this method is that it can represent the shape of objects with smooth and sharp features through a single super shape function, thereby improving the reconstruction ability of different shapes. By adjusting the super shape function parameters, the smoothness, aspect ratio, and edge curvature of the shape can be controlled, which can be used to represent the transition between different shapes, including ellipses, rectangles and other complex shapes. The super shape function formula is as follows:

[0061]

[0062] Let n = n1 = n2 = n3, m = 4, the simplified super shape function formula is as follows:

[0063]

[0064] Here, r(q) represents the distance from point q on the boundary to the center of the supershape, q0. Parameters a and b are the semi-axes of the supershape, determining the width and height of the ellipse. n represents the shape parameter of the ellipse, adjusting the curvature. When n = 2, the equation represents a standard ellipse; when n > 2, the shape becomes more square; when n < 2, the shape becomes more pointed. q ∈ [0, 2π], and j represents the rotation angle of the supershape.

[0065] Step 2) The PSO inversion algorithm is used to minimize the error between the predicted value and the target signal value to achieve quantitative prediction of the defect location and morphology in concrete.

[0066] The method of using the PSO inversion algorithm to minimize the error between the predicted value and the target signal value to achieve quantitative prediction of the location and morphology of defects in concrete includes the following:

[0067] (1) The super shape function parameters of the defect include: the coordinate point X0, Y0 of the center coordinate q0, the rotation angle The shape parameters a, b, and n are set as the particle swarm inversion parameters.

[0068] The PSO algorithm defines the position of each particle as follows:

[0069]

[0070] Where X represents the particle position vector, i.e., the defect parameter. V represents the particle velocity, i.e., the defect parameter change rate. t represents the number of iterations, and i represents the particle number.

[0071] (2) Based on the initial parameters obtained by fitting, the initial signal U1 is obtained and the objective function value is calculated;

[0072] The objective function is defined as follows:

[0073] ε i =||U i -U t || 2 (17)

[0074] Among them, U i is the current prediction signal value, U t is the target signal value.

[0075] (3) Using particle swarm optimization to update defect parameters;

[0076] The speed update formula is as follows:

[0077]

[0078] ω=ω1-(ω1-ω2)·d / k, (19)

[0079] Among them, represents the inertia weight, which determines the ability of the particle to inherit its previous velocity. A larger inertia weight is beneficial for global search, while a smaller weight is more suitable for local search. is the initial weight, is the final weight, d represents the current iteration number, k represents the total iteration number, c1 and c2 are constants, and r1 and r2 are random numbers;

[0080] (4) After the particle swarm algorithm updates the defect parameters, the current signal U is obtained through the two-dimensional finite element ERT model of concrete containing internal defects. i , and calculate the objective function value;

[0081] (5) Iteratively calculate the particle swarm parameters (defect parameters). When the maximum number of iterations is reached, the particle that finds the global optimal objective function value is the optimal particle, that is, the optimal defect parameter is obtained.

[0082] Beneficial effects of the present invention:

[0083] 1. ERT imaging inversion methods are mostly based on pixel-based image imaging methods or shape-based graphic imaging methods. However, pixel-based image reconstruction imaging has high noise and is prone to imaging artifacts. In contrast, although shape-based image reconstruction methods can reduce noise and artifacts to a certain extent, they require a large amount of prior information related to the size, shape, position, conductivity value, etc. of the anomaly to be detected for training, resulting in high cost and limited accuracy. The present invention adopts a combination of pixel-based image imaging methods and shape-based graphic imaging to significantly improve the accuracy of ERT detection of the size of internal defects in concrete.

[0084] 2. This invention utilizes a defect reconstruction method based on a supershape function. By iteratively optimizing the supershape parameters to minimize the objective function value, the method enhances the reconstruction capability for defects of varying shapes. This method's advantage lies in its ability to represent the shapes of objects with both smooth and sharp features using a single supershape function. By adjusting the parameters of the supershape function, the smoothness, aspect ratio, and edge curvature of the shape can be controlled, enabling the description of shapes ranging from ellipses and rectangles to other complex shapes.

[0085] 3. This invention uses the K-means algorithm to process ERT images, directly obtaining preliminary information on the number and location of defects. This provides a basis for setting the initial parameters of the subsequent particle swarm optimization algorithm, thereby improving search efficiency and reducing the challenge of ill-posedness in solving such problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 This is the basic process of defect parameter inversion.

[0087] Figure 2 To obtain the ERT results and fit the super shape function of the defect using the K-means algorithm. DETAILED DESCRIPTION

[0088] The present invention will be further described in detail below with reference to the accompanying drawings.

[0089] The present invention discloses a method for detecting and imaging complex defects in concrete based on electrical resistance tomography signals. Figure 2 As shown, the present invention respectively adopts the detection of multiple defects with the same shape but different positions and the detection of multiple defects with different shapes and different positions to carry out two case studies.

[0090] like Figure 1 As shown, the detection method of the present invention includes the following contents:

[0091] Step 1: Use the ERT image reconstruction algorithm to reconstruct the internal conductivity distribution based on the boundary electrical signal value to obtain the initial information of the internal defects.

[0092] Step 2: Combined with the K-means segmentation algorithm, the initial morphological boundary lines of the internal defects in the conductivity distribution map obtained in step 1 are extracted and the defect morphology is fitted with a super shape function.

[0093] Step 3: Based on the initial parameters obtained by fitting in step 2, the particle swarm algorithm is used to search for the optimal solution within the initial defect range, and finally the optimal defect position parameters and super shape function morphological parameters, that is, the accurate position and morphology of the defect, are obtained.

[0094] Step 1 uses ERT technology to perform preliminary conductivity imaging of defects in concrete to obtain the number and approximate location of defects. Obtaining ERT images facilitates determining the number and initial shape of defects and facilitates setting defect parameters. The specific method includes:

[0095] This application first uses ERT technology to perform preliminary conductivity imaging of defects in concrete. This method can determine the number and approximate location of defects, laying the foundation for further determination of their precise location and morphology. ERT uses a differential imaging method, first obtaining the sensitivity matrix S in the empty field through simulation. Then, combining the difference between the measured signal value and the simulated signal value in the empty field, a conjugate gradient algorithm is used to solve and image the conductivity distribution within the concrete.

[0096] Using ERT technology to perform preliminary imaging of defects in concrete can obtain the number and approximate location of defects. The specific methods include:

[0097] (1) Using ERT technology to perform preliminary imaging of defects in concrete can obtain the number and approximate location of defects, laying the foundation for further determination of the precise location and morphology of defects.

[0098] The ERT image reconstruction algorithm is used to reconstruct the internal conductivity distribution based on the boundary electrical signal value to obtain the number and initial shape of internal defects.

[0099] (2) Secondly, the differential imaging method is used to obtain the sensitivity matrix S in the empty field through simulation method;

[0100] The sensitivity matrix S in the empty field is obtained by simulation method, such as Figure 2 As shown in the figure, a two-dimensional finite element ERT model of concrete with a diameter of 50 mm and internal defects was established, with 16 stainless steel electrodes arranged equidistantly around it for simulation and solution.

[0101] Using the differential imaging method, the sensitivity matrix S in the empty field is obtained by simulation method. The specific method is as follows;

[0102] Under the condition that the excitation current and measurement voltage are known, the conductivity distribution is reconstructed. Using the differential imaging method, the sensitivity matrix S in the empty field is first obtained through simulation. Then, the difference between the measured signal value and the simulated signal value in the empty field is combined with the conjugate gradient algorithm to solve and image the conductivity distribution inside the concrete. The specific solution method is as follows:

[0103] It is usually necessary to iteratively update the model conductivity parameter Δσ, that is, to solve the equation

[0104] SΔσ=ΔU l ,l=1,...L (1)

[0105] Here, S is the sensitivity matrix, which describes the sensitivity of conductivity to the observed data, and Δσ and ΔU l are the change values ​​of conductivity and boundary voltage signal data respectively. The sensitivity is defined as follows:

[0106]

[0107] Where S ij is the sensitivity coefficient of the jth electrode pair to the ith electrode pair, and the excitation current of the ith electrode pair and the jth electrode pair is I i , I j The field potential distribution at .

[0108] (3) Combining the difference between the measured signal value and the simulated signal value in the empty field, the conjugate gradient algorithm is used to solve and image the internal conductivity distribution of the concrete. The simulated signal value in the empty field is obtained by using the adjacent electrode model to obtain the surface voltage measurement signal. It is a common measurement method in electrical resistance tomography (ERT), that is, injecting current through two adjacent electrodes in sequence, and then measuring the voltage through other adjacent electrode pairs, and finally obtaining 16*13=208 voltage measurement values. The voltage measurement signal of the surface of the defective concrete is obtained by combining the finite element calculation method. The specific solution method is as follows:

[0109] Directly solving the inverse problem of a large sparse matrix is ​​usually too computationally intensive. The conjugate gradient method, as an iterative solution technique, can efficiently solve large-scale sparse matrix equations. Therefore, it is very suitable for ERT inversion. Compared with the second-order method, the computational cost is low, and compared with the gradient descent method, it has better convergence characteristics. In this invention, the conjugate gradient least squares (CGLS) method is applied to the ERT inversion algorithm. The following are the iterative steps and key formulas of this method:

[0110] First, initialize the solution vector Δσ0 to a zero vector:

[0111] Δσ0=0 (3)

[0112] Calculate the initial residual vector r0 and the initial search direction d0:

[0113] r0=ΔU (4)

[0114] d0=S T ΔU (5)

[0115] Then the iterative update formula begins. In each iteration, the solution vector σ is updated j , residual r j , and search direction d j , the specific formula is as follows:

[0116] Step size α j The update formula is:

[0117]

[0118] Update of solution vector:

[0119] Δσ j+1 =Δσ j +α j d j (7)

[0120] Residual r j Update:

[0121] r j+1 =r j -α j Sd j (8)

[0122] In order to maintain the efficiency of the conjugate gradient method, the search direction needs to be updated in each iteration. The search direction correction parameter β j Calculated by the following formula:

[0123]

[0124] New search direction d j+1 Update:

[0125] d j+1 =S T r j+1 +β j d j (10)

[0126] This formula ensures that the new search direction remains conjugate with the previous search direction, thus ensuring the convergence of the algorithm. The conjugate gradient method continues to iterate until the specified number of iterations is reached and the final solution vector is obtained.

[0127] Step 2, combined with the K-means segmentation algorithm, extracts the initial morphological boundaries of internal defects in the conductivity distribution map and performs super-shape function fitting on the defect morphology, including the following. Processing the ERT image with the K-means segmentation algorithm can obtain the initial defect shape and range, facilitating subsequent fitting to obtain initial shape parameters and perform particle swarm optimization.

[0128] (1) First, convert the ERT image into a grayscale image;

[0129] (2) Clustering the image using the K-means algorithm to detect defect areas in the image and further extract defect boundaries;

[0130] The specific solution method is:

[0131] The K-means clustering algorithm partitions data by minimizing the squared Euclidean distance. The objective function is defined as follows:

[0132]

[0133] Where k is the number of predefined clusters, C i represents the i-th cluster, x is the data point in the cluster, μ i is the centroid of the cluster.

[0134] The iterative process of the algorithm includes the following steps:

[0135] Step 1) Randomly initialize k centroids.

[0136] Step 2) Assign data points to the nearest centroid. Assign each data point to the centroid closest to it based on the Euclidean distance, ensuring that each data point x i Assigned to the cluster S that minimizes its distance to the centroid j The formula is as follows:

[0137]

[0138] where d(x i , C j ) is the data point x i To cluster centroid C j Each time a data point is assigned to the nearest centroid, it ensures that the distance from this data point to the centroid is the shortest, thereby locally minimizing the distance of the data point.

[0139] Step 3) Update the centroid position. Once each data point has been assigned to the closest cluster, the algorithm recalculates the centroid position for each cluster. The new centroid is the average of all data points in that cluster:

[0140]

[0141] This formula represents the center of mass C j It is cluster S j The geometric center of all data points in the cluster. The geometric center has an important property: it is the point that minimizes the sum of the squared distances of the data points within the cluster to the centroid. Therefore, updating the centroid is actually minimizing the total sum of squares of the data points within the cluster by selecting the "average position" that best represents the cluster.

[0142] 4) Repeat steps 2) and 3) until the maximum number of iterations is reached.

[0143] (3) Finally, shape analysis is performed on these regions by fitting supershape functions.

[0144] The shape analysis of these areas is performed by fitting the super shape function. After detecting the defect boundary, the present invention uses the super shape function to fit the shape of these areas. After obtaining the boundary parameters, it is used as the initial value and reference area for the subsequent particle swarm algorithm search. The ERT method is used to perform initial imaging of the defect. Then, the image result is converted into a grayscale image using the K-means clustering algorithm and segmented to obtain the initial boundary of the defect. Then, the least squares method is used to fit the super function graph of the defect boundary to obtain the super shape parameters. The results of the two examples are shown as follows: Figure 2 shown.

[0145] In step 3, based on the initial parameters obtained by fitting, the particle swarm algorithm is used to search for the optimal solution within the initial defect range, ultimately obtaining the optimal defect location parameters and super shape function morphological parameters. That is, the exact location and morphology of the defect include the following. Using the fitted parameters as the initial values ​​and performing particle swarm optimization on the exact defect parameters within the defect range improves the search efficiency of the particle swarm algorithm and ultimately obtains more accurate defect parameter information.

[0146] (1) A reconstruction method based on super shape function is used. The super shape function is used to represent the internal defect morphology. By iteratively optimizing the super shape parameters, the objective function value between the corresponding predicted voltage and the actual target measured voltage is finally minimized. The advantage of this method is that it can represent the shape of objects with smooth and sharp features through a single super shape function, thereby improving the reconstruction ability of different shapes. By adjusting the super shape function parameters, the smoothness, aspect ratio, and edge curvature of the shape can be controlled, and it can be used to represent the transition between different shapes, including ellipses, rectangles and other complex shapes. The super shape function formula is as follows:

[0147]

[0148] In this paper, let n = n1 = n2 = n3, m = 4, and the simplified super shape function formula is as follows:

[0149]

[0150] Here, r(q) represents the distance from point q on the boundary to the center of the supershape, q0. Parameters a and b are the semi-axes of the supershape, determining the width and height of the ellipse. n represents the shape parameter of the ellipse, which adjusts the curvature. When n = 2, the equation represents a standard ellipse; when n > 2, the shape becomes more square; when n < 2, the shape becomes more pointed. q ∈ [0, 2π], and j represents the rotation angle of the supershape.

[0151] The super shape parameters used for the defect shapes in the two sets of examples are: for Example 1, the super shape parameters of the three defects are (8, 10, 4, 2, 2, -60), (-10, 0, 4, 2, 2, -60), and (8, -8, 4, 2, 2, -60). For Example 2, the super shape parameters of the three defects are (8, 10, 4, 2, 6, 10), (-10, 2, 4, 2, 2, -60), and (3, -10, 4, 1.5, 6, -60).

[0152] (2) The PSO inversion algorithm is used to minimize the error between the predicted value and the target signal value to achieve quantitative prediction of the defect location and morphology in concrete.

[0153] The PSO inversion algorithm is used to minimize the error between the predicted value and the target signal value to achieve quantitative prediction of the location and morphology of defects in concrete. The following are included:

[0154] Step 1) The super shape function parameters of the defect in the present invention include: coordinate points X0, Y0 of the center coordinate q0, rotation angle The shape parameters a, b, and n are set as the particle swarm inversion parameters.

[0155] The PSO algorithm defines the position of each particle as follows:

[0156]

[0157] Where X represents the particle position vector, i.e., the defect parameter. V represents the particle velocity, i.e., the defect parameter change rate. t represents the number of iterations, and i represents the particle number.

[0158] Step 2) Use the defect parameters obtained in step 2 as the initial values ​​of the particle swarm optimization algorithm and perform optimization within this range. Based on the initial parameters obtained by fitting, obtain the initial signal U1 and calculate the objective function value;

[0159] The objective function is defined as follows:

[0160] ε i =||U i -Ut || 2 (17)

[0161] Among them, U i is the current prediction signal value, U t is the target signal value.

[0162] Step 3) Using particle swarm optimization to update defect parameters;

[0163] The speed update formula is as follows:

[0164]

[0165] ω=ω1-(ω1-ω2)·d / k, (19)

[0166] where represents the inertia weight, which determines the particle's ability to inherit its previous velocity. A larger inertia weight favors global search, while a smaller weight is more suitable for local search. is the initial weight, is the final weight, d represents the current iteration number, and k represents the total number of iterations. c1 and c2 are constants, typically set to numbers in the interval [0, 2]. r1 and r2 are random numbers in the interval [0, 1]. When the maximum number of iterations is reached, the particle that finds the global optimal objective function value is considered the optimal particle, and the corresponding position is the optimal parameter.

[0167] In a defective model, the electrical signal values ​​after the particle swarm optimization algorithm updates the defect parameters need to be processed by the ERT image reconstruction algorithm to reconstruct the internal conductivity distribution based on the boundary electrical signal values ​​and obtain the number and initial shape of internal defects.

[0168] Step 4) Get the current signal U i And calculate the objective function value;

[0169] Step 5) Perform iterative calculation to obtain the optimal defect parameters.

[0170] like Figure 2 As shown in the figure, the final results show that for concrete with multiple defects, the defect parameter information can be obtained more accurately and quickly through the multi-step inversion algorithm.

[0171] like Figure 2 As shown in the figure, two case studies were conducted using the same shape, different position multiple defect detection and different shape, different position multiple defect detection. Figure 2 The defect shape is represented by the super shape function, and the defect schematic diagram is shown as follows: Figure 2 First, the conductivity of the cross section is reconstructed using the ERT technique for each case. The results are shown in Figure 2b. Then the result image is converted into a grayscale image, and the K-means clustering algorithm is used to obtain the initial boundary of the internal defect as shown in Figure 2 c, and then the three initial defects are fitted with super shape functions using the least squares method for each case. The results are shown in Figure 2 d. Afterwards, the particle swarm algorithm is used to accurately search for multiple defect parameters. The number of particle swarms is set to 150 and the number of iterations is set to 50.

[0172] For the first case (containing three defects of the same shape but different positions), the supershape parameters of the three defects are (8, 10, 4, 2, 2, -60), (-10, 0, 4, 2, 2, -60), and (8, -8, 4, 2, 2, -60). Using the defect parameters obtained from the above fitting as the initial values ​​of the particle swarm optimization algorithm and referencing the initial defect range for optimization can improve the optimization efficiency of the particles. After 50 iterations, the optimal parameters obtained by the particle swarm optimization algorithm are (9.934, 8.056, 3.751, 1.801, -59.549), (-9.908, -0.100, 3.844, 1.823, 2.494, -60.654), and (8.273, -7.769, 3.774, 1.772, 1.978, -59.943). It can be seen that the parameters of each defect are close to the true value.

[0173] Next, we analyzed the second case (three defects of different shapes and locations). The supershape parameters of the three defects were (8, 10, 4, 2, 6, -10), (-10, 2, 4, 2, 2, -60), and (3, -10, 4, 1.5, 6, -60). After 50 iterations, the particle swarm optimization algorithm (PSO) optimized the three defects to find the following optimal parameters: (7.966, 10.034, 4.142, 2.068, 5.604, -10.075), (-10.074, 2.297, 3.784, 1.821, 2.133, -58.709), and (2.954, -9.804, 4.238, 1.645, 5.887, -59.856). The predicted results were consistent with the actual results.

[0174] The above results show that for concrete containing multiple defects, the detection and imaging method proposed in the present invention can still obtain defect parameter information relatively accurately and quickly.

[0175] This invention combines pixel-based image formation with shape-based graph formation. First, a conjugate gradient algorithm is used to image the cross section. K-means is then used for image segmentation to obtain initial defect information. A supershape function is then used to represent the defect boundary shape. A particle swarm optimization algorithm is used to optimize the function parameters. Finally, a shape-based graph formation method is used to accurately capture the defect's location, size, and morphology. Compared to existing technologies, this method significantly improves the accuracy of ERT detection of internal concrete defect morphology and size by combining pixel-based image formation with shape-based graph formation. Furthermore, this method offers higher computational efficiency and greater robustness.

Claims

1. A method for complex concrete defect detection and imaging based on electrical resistance tomography signals, characterized in that: The steps include: Step 1: Using the ERT image reconstruction algorithm, obtain the internal conductivity distribution map based on the boundary electrical signal value; Step 2: Combined with the K-means segmentation algorithm, the initial shape boundary line of the internal defect in the conductivity distribution map obtained in step 1 is extracted and the defect shape is fitted with a super shape function to obtain the initial parameters; Step 3: Based on the initial parameters of step 2, the particle swarm algorithm is used to optimize based on the initial defect range, and finally the optimal defect location parameters and super shape function morphological parameters, that is, the exact location and morphology of the defect, are obtained.

2. The method for complex concrete defect detection and imaging based on electrical resistance tomography signals according to claim 1 is characterized in that: The specific method of step 1 includes: (1) Obtaining the empty field sensitivity matrix S without defects by simulation method; The sensitivity matrix S in the empty field is obtained, and a two-dimensional finite element ERT model of concrete without internal defects is established. Stainless steel electrodes are arranged equidistantly around the periphery. The adjacent current excitation mode is adopted, that is, the excitation current is passed between two adjacent electrodes, and the electric field value at each sensitive point is obtained and the empty field sensitivity matrix S is calculated by the formula; the sensitivity is defined as follows: In the formula, S ij is the sensitivity coefficient of the jth electrode pair to the ith electrode pair, and the excitation current of the ith electrode pair and the jth electrode pair is I i , I j Field potential distribution at time ; (2) Using the differential imaging method, based on the difference ΔU between the signal value under the real defect and the signal value under the defect-free condition, and the sensitivity matrix S obtained above, the conductivity change value Δσ is calculated by using the conjugate gradient algorithm and imaged, namely ERT imaging.

3. The method for complex concrete defect detection and imaging based on electrical resistance tomography signals according to claim 2 is characterized in that: The simulated signal value in the empty field is obtained, and the surface voltage measurement signal is obtained by using the adjacent electrode model, that is, the current is injected through two adjacent electrodes in turn, and then the voltage is measured through other adjacent electrode pairs, and finally the voltage measurement value is obtained. The voltage measurement signal of the defective concrete surface is obtained by combining the finite element calculation method.

4. The method for complex concrete defect detection and imaging based on electrical resistance tomography signals according to claim 2 is characterized in that: The specific solution method for ERT imaging is: Iteratively update the model conductivity parameter Δσ, that is, solve the equation SΔσ=ΔU l ,l=1,...L (1) S is the sensitivity matrix, describing the sensitivity of conductivity to the observed data, Δσ and ΔU l They are the change values ​​of conductivity and boundary voltage signal data respectively; The specific solution method for obtaining the conductivity change value Δσ using the conjugate gradient algorithm is: First, initialize the solution vector Δσ0 to a zero vector: Δσ0=0 (3) Calculate the initial residual vector r0 and the initial search direction d0: r0=ΔU (4) d0=S T ΔU (5) Then the iterative update formula begins. In each iteration, the solution vector σ is updated j , residual r j , and search direction d j , the specific formula is as follows: Step size α j The update formula is: Update of solution vector: Board j+1 =Ds j +a j d j (7) Residual r j Update: r j+1 =r j -α j Sd j (8) Search direction correction parameter β j Calculated by the following formula: New search direction d j+1 Update: d j+1 =S T r j+1 +b j d j (10) The iterations of the conjugate gradient method will continue to update until the specified number of iterations is reached and the final solution vector is obtained.

5. The method for complex concrete defect detection and imaging based on electrical resistance tomography signals according to claim 4 is characterized in that: The step 2 includes the following contents. (1) First, convert the ERT image into a grayscale image; Use the function to convert the color image into a grayscale image by weighted summation based on the RGB components in the image; Y=0.2989×R+0.5870×G+0.1140×B Where R, G, B are the pixel values ​​of the red, green and blue channels respectively, and Y is the grayscale value; (2) Clustering the obtained grayscale image using the K-means algorithm to detect the defect area in the image and further extract the defect boundary; The specific solution method is: The K-means clustering algorithm partitions data by minimizing the squared Euclidean distance. The objective function is defined as follows: Where k is the number of predefined clusters, C i represents the i-th cluster, x is the data point in the cluster, μ i is the centroid of the cluster.

6. The method for complex concrete defect detection and imaging based on electrical resistance tomography signals according to claim 5 is characterized in that: The iterative process of the K-means clustering algorithm includes the following steps: Step 1) Randomly initialize k centroids; Step 2) Assign data points to the nearest centroid. Assign each data point to the centroid closest to it based on the Euclidean distance, ensuring that each data point x i Assigned to the cluster S that minimizes its distance to the centroid j ; The formula is as follows: Where d(x i , C j ) is the data point x i To cluster centroid C j The Euclidean distance of , each time a data point is assigned to the nearest centroid, ensure that the distance from this data point to the centroid is the shortest, thereby locally minimizing the distance of the data point; Step 3) Update the position of the centroid. Once each data point is assigned to the nearest cluster, the algorithm recalculates the centroid position of each cluster. The new centroid is the average of all data points in the cluster: The formula represents the centroid C j It is cluster S j The geometric center of all data points in the cluster; updating the centroid actually minimizes the total sum of squares of data points in the cluster by selecting the "average position" that best represents the cluster; Step 4) Repeat steps 2) and 3) until the maximum number of iterations is reached; (3) shape analysis of these regions by fitting supershape functions; After detecting the defect boundaries, the shapes of these areas are fitted using the hypershape function. After obtaining the boundary parameters, they are used as initial values ​​and reference areas in the subsequent particle swarm algorithm search.

7. The method for complex concrete defect detection and imaging based on electrical resistance tomography signals according to claim 4 is characterized in that: The step 3 specifically includes the following contents: Step 1) Using a reconstruction method based on a super shape function, a super shape function is used to represent the internal defect morphology, and the super shape parameters are iteratively optimized to ultimately minimize the objective function value between the corresponding predicted voltage and the actual target measured voltage; by adjusting the super shape function parameters to control the smoothness, aspect ratio, and edge curvature of the shape, it is used to represent the transition between different shapes, including ellipses, rectangles, and other complex shapes. The super shape function formula is as follows: Let n = n1 = n2 = n3, m = 4, the simplified super shape function formula is as follows: Here, r(θ) represents the distance from point q on the boundary to the center point q0 of the supershape. Parameters a and b are the semi-axes of the supershape, which determine the width and height of the ellipse. n represents the shape parameter of the ellipse, which adjusts the curvature. When n=2, the equation represents a standard ellipse. When n>2, the shape becomes more square. When n<2, the shape becomes sharper, θ∈[0, 2π], Indicates the rotation angle of the super shape graphic; Step 2) The PSO inversion algorithm is used to minimize the error between the predicted value and the target signal value to achieve quantitative prediction of the defect location and morphology in concrete.

8. The method for complex concrete defect detection and imaging based on electrical resistance tomography signals according to claim 7 is characterized in that: The method of using the PSO inversion algorithm to minimize the error between the predicted value and the target signal value to achieve quantitative prediction of the defect location and morphology in concrete includes the following contents: (1) The super shape function parameters of the defect include: the coordinate point X0, Y0 of the center coordinate q0, the rotation angle The shape parameters a, b, and n are set as the particle swarm inversion parameters; The PSO algorithm defines the position of each particle as follows: Where X represents the particle position vector, i.e. the defect parameter. V represents the particle velocity, i.e. the defect parameter change velocity. t represents the number of iterations. i represents the particle number. (2) Based on the initial parameters obtained by fitting, the initial signal U1 is obtained and the objective function value is calculated; The objective function is defined as follows: ε i =||U i -IN t || 2 (17) Among them, U i is the current prediction signal value, U t is the target signal value; (3) Using particle swarm algorithm to update defect parameters; The speed update formula is as follows: ω=ω1-(ω1-ω2)·d / k, (19) Where ω represents the inertia weight, which determines the ability of the particle to inherit its previous velocity. A larger inertia weight is conducive to global search, while a smaller weight is more suitable for local search. ω1 is the initial weight, ω2 is the final weight, d represents the current number of iterations, k represents the total number of iterations, c1 and c2 are constants, usually set to numbers in the interval [0, 2], and r1 and r2 are random numbers in the interval [0, 1]. (4) After the particle swarm algorithm updates the defect parameters, the current signal U is obtained through the two-dimensional finite element ERT model of concrete containing internal defects. i , and calculate the objective function value; (5) Iteratively calculate the particle swarm parameters. When the maximum number of iterations is reached, the particle that finds the global optimal objective function value is the optimal particle, that is, the optimal defect parameters are obtained.

Images