A method for detecting invisible targets on the ground based on improved fuzzy support vector regression machine

Abstract

The present invention discloses a stealth target detection method based on an improved fuzzy support vector regression machine. During the process of detecting hidden targets with a high-sensitivity millimeter-wave radiometer, the radiometer will be affected by background noise, resulting in erroneous detection of stealth targets. The present invention incorporates the suppression of outliers and noise, and simultaneously adopts particle swarm optimization to fuse the penalty parameters and kernel parameters in Levenberg-Marquardt's fuzzy support vector regression model. The fuzzy support vector regression machine model is used to invert the measurement parameters of stealth targets in ground objects detected by the millimeter-wave radiometer. The target's emissivity is calculated based on the inverted target brightness temperature and ambient temperature, thereby realizing the detection of stealth targets in ground objects. This method reduces the influence of noise and outliers on target detection results by introducing a fuzzy membership function into the support vector regression machine, and optimizes the parameters of the fuzzy support vector regression machine using an optimization algorithm, thereby improving the accuracy of stealth target detection in ground objects.

Description

Technical Field

[0001] The present invention relates to the field of millimeter wave passive detection of stealth targets, and more specifically, it designs a method for detecting stealth targets on land objects based on an improved fuzzy support vector regression machine. Background Art

[0002] A millimeter-wave radiometer is a highly sensitive receiver that passively receives weak signals. It detects targets by exploiting differences in their radiation characteristics in the millimeter-wave band. Currently, coating a target with an absorbing material is a primary method of stealth technology, widely used in numerous military equipment. This method works by increasing the emissivity of the highly conductive material by coating the surface, thereby reducing the difference in brightness temperature between the target and the background, achieving a stealth effect.

[0003] With the rapid development of stealth technology, counter-stealth technology is becoming increasingly important. Current stealth equipment is nearly impossible to achieve complete stealth. This is because stealth targets inevitably have unobstructed areas. Once these areas are scanned by a millimeter-wave radiometer, the output waveform changes based on the brightness temperature of the measured area.

[0004] In order to accurately detect targets, the requirements for the accuracy of passive detectors are becoming increasingly higher. Current stealth target detection methods can be summarized as follows: template matching-based recognition, statistical pattern recognition-based, and neural network-based pattern recognition. These algorithms are mainly aimed at improving the accuracy of target detection algorithms, and research on target recognition algorithms has achieved certain results. However, in the process of detecting hidden targets with a high-sensitivity millimeter-wave radiometer, in addition to the brightness temperature of the stealth target itself, the radiometer will also be affected by background noise. When the target detection algorithm pays too much attention to background noise data during training, the test results will be sensitive to noise or outliers in the sample, reducing the detection effect of the target and leading to incorrect detection of stealth targets. Therefore, the present invention is based on the method of fuzzy support vector regression, using membership functions to reduce the impact of noise and outliers on the target detection algorithm during the training process, and using optimization algorithms to optimize the parameters of the fuzzy support vector regression machine to improve the accuracy of the target detection algorithm. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the deficiencies in the prior art and propose a method for detecting stealth targets based on an improved fuzzy support vector regression machine to improve the accuracy of the stealth target detection algorithm.

[0006] Existing stealth target detection algorithms are easily interfered by noise and outliers, and are prone to overfitting. In order to reduce the impact of noise and outliers and improve the accuracy of target detection, the present invention adopts a fuzzy support vector regression machine algorithm based on particle swarm optimization and Levenberg-Marquardt fusion. The algorithm uses Levenberg-Marquardt (LM) to optimize the penalty factor C and kernel parameter σ of the fuzzy support vector regression machine (FSVR), and uses particle swarm (PSO) to optimize the damping factor μ of Levenberg-Marquardt. The optimal parameters are obtained through iterative optimization, and the optimal inversion model is generated to invert the brightness temperature of the target. The technical solution adopted by the present invention is a method for detecting stealth targets on land objects based on an improved fuzzy support vector regression machine, comprising:

[0007] Step 1: Use millimeter wave radiometer measurement parameters as sample data;

[0008] Step 2: Construct a particle swarm optimization-fused Levenberg-Marquardt fuzzy support vector regression inversion model;

[0009] Step 3: Invert the millimeter wave radiometer measurement parameters based on the constructed particle swarm optimization fused with Levenberg-Marquardt fuzzy support vector regression inversion model.

[0010] Step 4: Calculate the target's emissivity based on the inversion results and ambient temperature.

[0011] The sample data in step 1 includes the radiometer output parameters and environmental parameters of the millimeter wave radiometer at each moment during a period of time when the millimeter wave radiometer measures the ground object and the metal plate covered with the coating; the radiometer output parameter is the output voltage of the radiometer; and the environmental parameters include the ambient temperature, the radiometer feeder temperature, and the radiometer antenna temperature;

[0012] The step 2 includes:

[0013] Step 2.1: Normalize the sample data;

[0014] Step 2.2: Shuffle the normalized sample data, randomly select four-fifths of the normalized sample data as the training set, and use the remaining one-fifth as the test set;

[0015] Step 2.3: Build the fuzzy support vector regression model;

[0016] Step 2.4: Construct an algorithm model for the Levenberg-Marquardt optimization of the penalty factor C and kernel parameter σ of the fuzzy support vector regression machine;

[0017] Step 2.5: Construct an algorithm model for the damping factor μ of the particle swarm optimization Levenberg-Marquardt algorithm, and finally obtain the optimized particle swarm optimization fused with Levenberg-Marquardt fuzzy support vector regression machine inversion model;

[0018] The step 4 comprises:

[0019] Step 4.1: Denormalize the target brightness temperature obtained after inversion;

[0020] Step 4.2: Calculate the target's emissivity according to the formula:

[0021] T B =T0×ε

[0022] Where, T B is the brightness temperature of the target, T0 is the physical temperature of the target, and ε is the emissivity of the target.

[0023] Step 4.3: Compare the target emissivity with the ground object emissivity to detect the stealth target in the ground object.

[0024] The step 2.3 includes:

[0025] Step 2.3.1: Given a training dataset where x k ∈R m is the M-dimensional input data, y∈R is the output data, N is the amount of data in the training set, in the main space R m The quadratic programming problem is formulated as:

[0026]

[0027] Where L is the loss function, w∈R m Represents the weight vector of the original weight space, b∈R m represents the offset, C represents the penalty factor, u k ∈R m represents the fuzzy membership, ξ k ∈R m represents the error amount of each sample, Represents a nonlinear mapping function;

[0028] Among them, the membership function adopts the membership function based on the hyperplane distance metric, which can be expressed as:

[0029]

[0030] Where, d k Represents the distance from the sample to the class center hyperplane, δ is the adjustment u k The size parameter has no practical meaning;

[0031] Step 2.3.2: Convert the established quadratic programming problem into a dual programming problem:

[0032]

[0033] Among them, the optimal solution of this dual programming problem can be expressed as:

[0034]

[0035] The final regression model obtained can be expressed as:

[0036]

[0037] The Gaussian radial basis function (RBF) is selected as the kernel function of the fuzzy support vector regression machine:

[0038]

[0039] Where, σ represents the distance from the RBF kernel function to the center;

[0040] The step 2.4 includes:

[0041] Step 2.4.1: Initialize the parameters and number of iterations of the Levenberg-Marquardt algorithm, and set the initial value range of the penalty factor and kernel parameter;

[0042] Step 2.4.2: Use Levenberg-Marquardt to train the fuzzy support vector regression model, let:

[0043]

[0044] Where e(x) is the neural network mean square error column vector, is the gradient of the error indicator function L, J(x) is the Jacobian matrix;

[0045] The weight correction formula of the Levenberg-Marquardt algorithm is:

[0046] x p+1 =x p -[J T (x)J(x)+μI] -1 J(x)e(x)

[0047] Where x p represents the vector of weights of the neural network in the pth iteration, I represents the identity matrix, and μ represents the damping factor;

[0048] Step 2.4.3: Adjust the kernel parameters and penalty factors of the Levenberg-Marquardt optimized fuzzy support vector regression model through iterative updating before reaching the set iteration threshold. During the iterative adjustment process, calculate the difference between the current mean square error and the target mean square error, adjust the weights according to the weight adjustment formula, and then update the kernel parameters and penalty factors. Then, enter the next iteration and recalculate the mean square error. When the maximum number of iterations is reached, stop training. If the difference between the current mean square error and the target mean square error is close to 0, indicating that the global optimal solution has been retrieved, output the final kernel parameters and penalty factors as the parameters of the fuzzy support vector regression machine, and establish the corresponding regression model.

[0049] The step 2.5 includes:

[0050] Step 2.5.1: Initialize the parameters and number of iterations of the particle swarm algorithm, set the initial value range of the damping factor in the Levenberg-Marquardt algorithm, and set L as the individual optimal solution and the global optimal solution of the particle swarm; Step 2.5.2: Use the particle swarm algorithm to train the initial value of the damping factor in Levenberg-Marquardt. The particle update speed can be expressed as:

[0051] v i+1 =ω×v i +c1×rand()×(gbest i -x i )+c2×rand()×(zbest i -x i )

[0052] Where, v i Indicates the particle speed in the i-th iteration, rand() is a random number between (0,1); gbest i It is a sequence of N-dimensional individual optimal solutions; zbest i is a sequence of N-dimensional global optimal solutions; c1 and c2 are learning factors that determine the effect of the two extreme values ​​in the speed update process; ω is the inertia factor, with a value between (0,1);

[0053] The solution update of the particle sequence can be expressed as:

[0054] x i+1 =x i +v i

[0055] Step 2.5.3: Calculate the fitness function of the current solution sequence. If the fitness value of the current solution sequence is higher than the individual optimal solution of the corresponding particle, then update the individual optimal solution to the current solution of the corresponding particle. If the set of solutions with the highest fitness value in the current solution sequence is higher than the global optimal solution, then update the global optimal solution to the set of solutions with the highest fitness value in the current solution sequence.

[0056] Step 2.5.4: Adjust the damping factor of the particle swarm optimization fusion Levenberg-Marquardt fuzzy support vector regression model through iterative updating before reaching the set iteration number threshold. During the iterative adjustment process, calculate the difference between the current mean square error and the target mean square error, adjust the weights according to the weight adjustment formula, and then update the damping factor and enter the next iteration to recalculate the mean square error. When the maximum number of iterations is reached, stop training and output the global optimal solution sequence as the Levenberg-Marquardt damping factor.

[0057] Step 2.5.5: Stop training when the maximum number of iterations is reached, obtain the optimal damping factor of Levenberg-Marquardt, and output the final kernel parameters and penalty factors based on the damping factor as the parameters of the fuzzy support vector regression machine. Finally, the optimized particle swarm optimization is integrated with the Levenberg-Marquardt fuzzy support vector regression machine inversion model, and the model is tested using the test set. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Flowchart of the method for detecting invisible targets based on the improved fuzzy support vector regression machine in the present invention;

[0059] Figure 2 This is a comparison curve of the MSE indicators of different algorithms in the present invention;

[0060] Figure 3 This is a graph showing the brightness temperature inversion curve of the ground stealth target under different numbers of auxiliary samples in the present invention. DETAILED DESCRIPTION

[0061] 1. The invention is further described below with reference to the accompanying drawings and specific implementation examples. The method of the present invention uses a millimeter-wave radiometer to measure the radiation characteristics of stealth targets within ground features. Levenberg-Marquardt optimization is used to optimize the penalty factor and kernel parameters of a fuzzy support vector regression machine. Particle swarm optimization is also used to optimize the Levenberg-Marquardt damping factor. Through iterative optimization, the optimal parameters are obtained, generating an optimal inversion model to invert the target's brightness temperature. The target's emissivity is then calculated based on the ambient temperature and the target's brightness temperature, enabling detection of stealth targets within ground features.

[0062] 2. A method for detecting invisible targets on land objects based on an improved fuzzy support vector regression machine. The method first uses millimeter-wave radiometer measurement parameters as sample data; then constructs a particle swarm optimization-fused Levenberg-Marquardt fuzzy support vector regression machine inversion model; and then inverts the millimeter-wave radiometer measurement parameters based on the constructed particle swarm optimization-fused Levenberg-Marquardt fuzzy support vector regression machine inversion model. The method includes:

[0063] Step 1: Using millimeter wave radiometer measurement parameters as sample data; the sample data includes the millimeter wave radiometer output parameters and environmental parameters at each moment during a period of time when measuring the ground object and the metal plate covered with the coating; the radiometer output parameter is the output voltage of the radiometer; the environmental parameters include the ambient temperature, the radiometer feeder temperature, and the radiometer antenna temperature;

[0064] Step 2: Construct a particle swarm optimization-integrated Levenberg-Marquardt fuzzy support vector regression inversion model; including:

[0065] Step 2.1: Normalize the sample data;

[0066] Step 2.2: Shuffle the normalized sample data, randomly select four-fifths of the normalized sample data as the training set, and use the remaining one-fifth as the test set;

[0067] Step 2.3: Construct a fuzzy support vector regression model; including:

[0068] Step 2.3.1: Given a training dataset where x k ∈R m is the M-dimensional input data, y∈R is the output data, N is the amount of data in the training set, in the main space R m The quadratic programming problem is formulated as:

[0069]

[0070] Where L is the loss function, w∈R m Represents the weight vector of the original weight space, b∈R m represents the offset, C represents the penalty factor, u k ∈R m represents the fuzzy membership, ξ k ∈R m represents the error amount of each sample, Represents a nonlinear mapping function;

[0071] Among them, the membership function adopts the membership function based on the hyperplane distance metric, which can be expressed as:

[0072]

[0073] Where, d k Represents the distance from the sample to the class center hyperplane, δ is the adjustment u k The size parameter has no practical meaning;

[0074] Step 2.3.2: Convert the established quadratic programming problem into a dual programming problem:

[0075]

[0076] Among them, the optimal solution of this dual programming problem can be expressed as:

[0077]

[0078] The final regression model obtained can be expressed as:

[0079]

[0080] The Gaussian radial basis function (RBF) is selected as the kernel function of the fuzzy support vector regression machine:

[0081]

[0082] Where, σ represents the distance from the RBF kernel function to the center;

[0083] Step 2.4: Construct an algorithm model for the Levenberg-Marquardt optimization of the penalty factor C and kernel parameter σ of the fuzzy support vector regression machine; including:

[0084] Step 2.4.1: Initialize the parameters and number of iterations of the Levenberg-Marquardt algorithm according to Table 1, and set the initial value range of the penalty factor and kernel parameter;

[0085] Step 2.4.2: Use Levenberg-Marquardt to train the fuzzy support vector regression model, let:

[0086]

[0087] Where e(x) is the neural network mean square error column vector, is the gradient of the error indicator function L, J(x) is the Jacobian matrix;

[0088] The weight correction formula of the Levenberg-Marquardt algorithm is:

[0089] x p+1 =x p -[J T (x)J(x)+μI] -1 J(x)e(x)

[0090] Where x p represents the vector of weights of the neural network in the pth iteration, I represents the identity matrix, and μ represents the damping factor;

[0091] Step 2.4.3: Adjust the kernel parameters and penalty factors of the Levenberg-Marquardt optimized fuzzy support vector regression model through iterative updating before reaching the set iteration threshold. During the iterative adjustment process, calculate the difference between the current mean square error and the target mean square error, adjust the weights according to the weight adjustment formula, and then update the kernel parameters and penalty factors. Then, enter the next iteration and recalculate the mean square error. When the maximum number of iterations is reached, stop training. If the difference between the current mean square error and the target mean square error is close to 0, indicating that the global optimal solution has been retrieved, output the final kernel parameters and penalty factors as the parameters of the fuzzy support vector regression machine, and establish the corresponding regression model.

[0092] Step 2.5: Construct an algorithm model for the damping factor μ of the particle swarm optimization Levenberg-Marquardt algorithm, and finally obtain the optimized particle swarm optimization fused with Levenberg-Marquardt fuzzy support vector regression machine inversion model; including:

[0093] Step 2.5.1: Initialize the parameters and number of iterations of the particle swarm algorithm according to Table 1, set the initial value range of the damping factor in the Levenberg-Marquardt algorithm, and set L as the individual optimal solution and the global optimal solution of the particle swarm;

[0094] Step 2.5.2: Use the particle swarm algorithm to train the initial value of the damping factor in Levenberg-Marquardt. The particle update speed can be expressed as:

[0095] v i+1 =ω×v i +c1×rand()×(gbest i -x i )+c2×rand()×(zbest i -x i )

[0096] Where, v i Indicates the particle speed in the i-th iteration, rand() is a random number between (0,1); gbest iIt is a sequence of N-dimensional individual optimal solutions; zbest i is a sequence of N-dimensional global optimal solutions; c1 and c2 are learning factors that determine the effect of the two extreme values ​​in the speed update process; ω is the inertia factor, with a value between (0,1);

[0097] The solution update of the particle sequence can be expressed as:

[0098] x i+1 =x i +v i

[0099] Step 2.5.3: Calculate the fitness function of the current solution sequence. If the fitness value of the current solution sequence is higher than the individual optimal solution of the corresponding particle, then update the individual optimal solution to the current solution of the corresponding particle. If the set of solutions with the highest fitness value in the current solution sequence is higher than the global optimal solution, then update the global optimal solution to the set of solutions with the highest fitness value in the current solution sequence.

[0100] Step 2.5.4: Adjust the damping factor of the particle swarm optimization fusion Levenberg-Marquardt fuzzy support vector regression model through iterative updating before reaching the set iteration number threshold. During the iterative adjustment process, calculate the difference between the current mean square error and the target mean square error, adjust the weights according to the weight adjustment formula, and then update the damping factor and enter the next iteration to recalculate the mean square error. When the maximum number of iterations is reached, stop training and output the global optimal solution sequence as the Levenberg-Marquardt damping factor.

[0101] Step 2.5.5: Stop training when the maximum number of iterations is reached. Obtain the optimal Levenberg-Marquardt damping factor. Based on this damping factor, output the final kernel parameters and penalty factor as the parameters of the fuzzy support vector regression machine. Finally, the optimized particle swarm optimization fusion Levenberg-Marquardt fuzzy support vector regression machine inversion model is tested using the test set.

[0102] Step 3: Invert the millimeter wave radiometer measurement parameters based on the constructed particle swarm optimization fused with Levenberg-Marquardt fuzzy support vector regression inversion model.

[0103] Step 4: Calculate the target's emissivity based on the inversion results and ambient temperature, including:

[0104] Step 4.1: Denormalize the target brightness temperature obtained after inversion;

[0105] Step 4.2: Calculate the target's emissivity according to the formula:

[0106] T B =T0×ε

[0107] Where, T B is the brightness temperature of the target, T0 is the physical temperature of the target, and ε is the emissivity of the target.

[0108] Step 4.3: Compare the target emissivity with the ground object emissivity to detect the stealth target in the ground object.

[0109] Table 1 Initial values ​​of key parameters

[0110]

Claims

1. A method for detecting invisible ground objects based on an improved fuzzy support vector regression machine, characterized in that: include: Step 1: Use millimeter wave radiometer measurement parameters as sample data; Step 2: Construct a particle swarm optimization-fused Levenberg-Marquardt fuzzy support vector regression inversion model; The step 2 includes: Step 2.1: Normalize the sample data; Step 2.2: Shuffle the normalized sample data, randomly select four-fifths of the normalized sample data as the training set, and use the remaining one-fifth as the test set; Step 2.3: Build the fuzzy support vector regression model; Step 2.4: Construct an algorithm model for the Levenberg-Marquardt optimization of the penalty factor C and kernel parameter σ of the fuzzy support vector regression machine; Step 2.5: Construct an algorithm model for the damping factor μ of the particle swarm optimization Levenberg-Marquardt algorithm, and finally obtain the optimized particle swarm optimization fused with Levenberg-Marquardt fuzzy support vector regression machine inversion model; Step 3: Invert the millimeter wave radiometer measurement parameters based on the constructed particle swarm optimization fused with Levenberg-Marquardt fuzzy support vector regression inversion model; Step 4: Calculate the target's emissivity based on the inversion results and ambient temperature.

2. The method for detecting invisible targets based on an improved fuzzy support vector regression machine according to claim 1, characterized in that: The sample data in step 1 includes the radiometer output parameters and environmental parameters of the millimeter wave radiometer measuring the ground object and the metal plate covered with the coating at each moment within a period of time; the radiometer output parameter is the output voltage of the radiometer; and the environmental parameters include the ambient temperature, the radiometer feeder temperature, and the radiometer antenna temperature.

3. The method for detecting invisible targets based on an improved fuzzy support vector regression machine according to claim 1, characterized in that: The step 4 comprises: Step 4.1: Denormalize the target brightness temperature obtained after inversion; Step 4.2: Calculate the target's emissivity according to the formula: T B =T0×ε Where, T B is the brightness temperature of the target, T0 is the physical temperature of the target, and ε is the emissivity of the target; Step 4.3: Compare the target emissivity with the ground object emissivity to detect the stealth target in the ground object.

4. The method for detecting invisible targets based on an improved fuzzy support vector regression machine according to claim 1, characterized in that: The step 2.3 includes: Step 2.3.1: Given a training dataset k=1,2,……,N, where x k ∈R m is the M-dimensional input data, y∈R is the output data, N is the amount of data in the training set, in the main space R m The quadratic programming problem is formulated as: Where L is the loss function, w∈R m Represents the weight vector of the original weight space, b∈R m represents the offset, C represents the penalty factor, u k ∈R m represents the fuzzy membership, ξk∈R m represents the error amount of each sample, Represents a nonlinear mapping function; Among them, the membership function adopts the membership function based on the hyperplane distance metric, which can be expressed as: Where, d k Represents the distance from the sample to the class center hyperplane, δ is the adjustment u k The size parameter has no practical meaning; Step 2.3.2: Convert the established quadratic programming problem into a dual programming problem: Among them, the optimal solution of this dual programming problem can be expressed as: The final regression model obtained can be expressed as: The Gaussian radial basis function (RBF) is selected as the kernel function of the fuzzy support vector regression machine: Where σ represents the distance from the RBF kernel function to the center.

5. The method for detecting invisible targets based on an improved fuzzy support vector regression machine according to claim 1, characterized in that: The step 2.4 includes: Step 2.4.1: Initialize the parameters and number of iterations of the Levenberg-Marquardt algorithm, and set the initial value range of the penalty factor and kernel parameter; Step 2.4.2: Use Levenberg-Marquardt to train the fuzzy support vector regression model, let: Where e(x) is the neural network mean square error column vector, is the gradient of the error indicator function L, J(x) is the Jacobian matrix; The weight correction formula of the Levenberg-Marquardt algorithm is: x p+1 =x p -[J T (x)J(x))+μI] -1 J(x)e(x) Where x p represents the vector of weights of the neural network in the pth iteration, I represents the identity matrix, and μ represents the damping factor; Step 2.4.3: Adjust the kernel parameters and penalty factors of the Levenberg-Marquardt optimized fuzzy support vector regression model through iterative updating before reaching the set iteration number threshold; calculate the difference between the current mean square error and the target mean square error during the iterative adjustment process, adjust the weights according to the weight adjustment formula, and then update the kernel parameters and penalty factors and enter the next iteration round to recalculate the mean square error; stop training when the maximum number of iterations is reached, and the difference between the current mean square error and the target mean square error is close to 0, that is, the global optimal solution has been retrieved, output the final kernel parameters and penalty factors as the parameters of the fuzzy support vector regression machine, and establish the corresponding regression model.

6. The method for detecting invisible targets based on an improved fuzzy support vector regression machine according to claim 1, characterized in that: The step 2.5 includes: Step 2.5.1: Initialize the parameters and number of iterations of the particle swarm algorithm, set the initial value range of the damping factor in the Levenberg-Marquardt algorithm, and set L as the individual optimal solution and the global optimal solution of the particle swarm; Step 2.5.2: Use the particle swarm algorithm to train the initial value of the damping factor in Levenberg-Marquardt. The update speed of the particles can be expressed as: v i+1 =ω×v i +c1×rand()×(gbest i -x i )+c2×rand()×(zbest i -x i ) Where, v i Indicates the particle speed in the i-th iteration, rand() is a random number between (0,1); gbest i It is a sequence of N-dimensional individual optimal solutions; zbest i is a sequence of N-dimensional global optimal solutions; c1 and c2 are learning factors that determine the effect of the two extreme values ​​in the speed update process; ω is the inertia factor, with a value between (0,1); The solution update of the particle sequence can be expressed as: x i+1 =x i +v i Step 2.5.3: Calculate the fitness function of the current solution sequence. If the fitness value of the current solution sequence is higher than the individual optimal solution of the corresponding particle, then update the individual optimal solution to the current solution of the corresponding particle. If the set of solutions with the highest fitness value in the current solution sequence is higher than the global optimal solution, then update the global optimal solution to the set of solutions with the highest fitness value in the current solution sequence. Step 2.5.4: Adjust the damping factor of the particle swarm optimization fusion Levenberg-Marquardt fuzzy support vector regression model through iterative updating before reaching the set iteration number threshold. During the iterative adjustment process, calculate the difference between the current mean square error and the target mean square error, adjust the weights according to the weight adjustment formula, and then update the damping factor and enter the next iteration to recalculate the mean square error. When the maximum number of iterations is reached, stop training and output the global optimal solution sequence as the Levenberg-Marquardt damping factor. Step 2.5.5: Stop training when the maximum number of iterations is reached, obtain the optimal damping factor of Levenberg-Marquardt, and output the final kernel parameters and penalty factors based on the damping factor as the parameters of the fuzzy support vector regression machine. Finally, the optimized particle swarm optimization is integrated with the Levenberg-Marquardt fuzzy support vector regression machine inversion model, and the model is tested using the test set.

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