Inverse cavity scattering inversion method and system based on adaptive fuzzy inference system

Abstract

The present invention discloses an inverse cavity scattering inversion method and system based on an adaptive fuzzy inference system, which relates to the technical field of inverse scattering. The method includes: emitting an incident wave from a single point source in the cavity, receiving the scattered wave through a finite number of measurement points in the cavity, and obtaining scattering data; using the principal component analysis method to perform dimensionality reduction processing on the obtained scattering data; inputting the dimensionality reduction processed scattering data into the trained adaptive fuzzy inference system to invert the shape parameters of the cavity, and reconstructing the shape of the cavity according to the output inversion result; the adaptive fuzzy inference system is a hybrid model that combines fuzzy logic and neural networks. This model is based on the fuzzy inference system, and each layer in the neural network represents each step of the fuzzy inference process, successively including a membership function layer, a rule layer, a normalization layer, a consequent layer, and an output layer. The present invention can efficiently and accurately invert the cavity shape.

Description

Technical Field

[0001] The present invention relates to the field of inverse scattering technology, and in particular, to an inverse cavity scattering inversion method and system based on an adaptive fuzzy inference system. Background Technique

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

[0003] Inverse scattering refers to studying the characteristics of a scatterer based on a given incident wave and measured scattered wave to determine the distribution of its geometric shape or physical parameters. Among them, the inversion method of obtaining the scatterer characteristics from the scattered field is based on the electromagnetic scattering theory. The theory and method of inverse scattering have been widely applied in many fields such as nondestructive testing, radar imaging, biomedical imaging, and sonar detection. In the inverse scattering problem, according to the different positions of the incident wave, it can be divided into an external inverse scattering problem and an internal inverse scattering problem. The external inverse scattering problem usually means that when an object is irradiated by an external incident wave, the shape and other unknown characteristics of the object are inferred by collecting scattered wave data outside the object; compared with the external scattering problem, due to the repeated reflection of the captured scattered wave in the cavity of the scatterer, the internal scattering problem is more complex. Currently, due to its wide application in industry, the internal inverse scattering problem has attracted much attention and research. In this internal problem, the scatterer is always described as a closed cavity, and the source and receiver are placed in the cavity. According to the scattered wave received by the receiver, its structural integrity is tested, and then possible defects or inhomogeneities in it are detected. This research direction has become a current research hotspot, especially in the fields of material detection and structural monitoring.

[0004] Currently, the computational methods for solving the inverse scattering problem can be divided into two categories: traditional numerical methods and emerging machine learning methods. Among them, using traditional numerical methods to solve the inverse scattering problem, although it performs excellently in terms of accuracy, usually requires a large amount of computing resources. Especially when dealing with three-dimensional complex problems, the computing time and memory consumption are very high; in contrast, using machine learning methods, through data-driven, it can automatically learn the rules from a large amount of scattered data, so as to perform prediction and inversion in a more efficient way. However, due to the characteristics of the inverse scattering problem itself, such as large data noise and complex non-linear relationships, the machine learning methods are not ideal when dealing with these problems, and at the same time, the problem of insufficient model interpretability is also exposed. Summary of the Invention

[0005] To address the deficiencies of the above-mentioned existing technologies, the present invention provides an inverse cavity scattering inversion method and system based on an adaptive fuzzy inference system. The principal component analysis (PCA) is used to reduce the dimension of the acquired scattering data to remove redundant information, improve the calculation efficiency, and reduce the influence of noise. An adaptive neuro-fuzzy inference system (ANFIS) is proposed, which combines a fuzzy inference algorithm and a neural network. It can accurately model the non-linear relationships in the data, more accurately extract key features from complex scattering data, enhance the robustness and prediction accuracy of the model, and can efficiently and accurately invert the cavity shape, solving problems such as large noise in scattering data, complex non-linear relationships, and poor model interpretability in existing methods.

[0006] In the first aspect, the present invention provides an inverse cavity scattering inversion method based on an adaptive fuzzy inference system.

[0007] An inverse cavity scattering inversion method based on an adaptive fuzzy inference system includes:

[0008] Using a source inside the cavity to emit incident waves, and receiving scattered waves through a finite number of measurement points inside the cavity to obtain scattering data;

[0009] Using the principal component analysis method to perform dimensionality reduction processing on the acquired scattering data;

[0010] Inputting the scattering data after dimensionality reduction processing into the trained adaptive fuzzy inference system to invert the shape parameters of the cavity, and reconstructing the shape of the cavity according to the output inversion result;

[0011] The adaptive fuzzy inference system is a hybrid model that integrates fuzzy logic and neural networks. This model is based on a fuzzy inference system, and each layer in the neural network represents each step of the fuzzy inference process, successively including a membership function layer, a rule layer, a normalization layer, a consequent layer, and an output layer. Among them, the membership function layer includes multiple membership functions corresponding to the input, the rule layer includes multiple fuzzy rules in the fuzzy inference process, the consequent layer includes consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the final inversion result of the cavity shape parameters.

[0012] A further technical solution, using the principal component analysis method to perform dimensionality reduction processing on the acquired scattering data, includes:

[0013] Performing data standardization processing on the acquired scattering data to obtain a standardized sample matrix of the scattering data;

[0014] Calculating the covariance matrix of the standardized sample matrix;

[0015] Performing eigenvalue decomposition on the covariance matrix to calculate the eigenvalues and eigenvectors;

[0016] Select several principal components according to the eigenvalues and eigenvectors;

[0017] Project the original standardized scattering data into the space formed by the selected several principal components to obtain the dimension-reduced scattering data.

[0018] A further technical solution, the fuzzy inference process of the fuzzy inference system is as follows:

[0019] Use the dimension-reduced scattering data as the input of the system. Each input corresponds to multiple membership functions respectively, thereby dividing the input space into multiple fuzzy subspaces, and each fuzzy subspace is controlled by a fuzzy rule; wherein, each fuzzy rule includes multiple consequent parameters;

[0020] After the input data is operated by multiple fuzzy rules, perform weighted averaging on the outputs of all rules to calculate the final inversion result of the cavity shape parameters.

[0021] A further technical solution, the adaptive fuzzy inference system is based on the fuzzy inference system, and each layer in the neural network represents each step of the fuzzy inference process, successively including:

[0022] The membership function layer, including multiple membership functions; each node in this layer corresponds to a membership function;

[0023] The rule layer, including multiple fuzzy rules; each node in this layer corresponds to a fuzzy rule;

[0024] The normalization layer, used to normalize the weights of each fuzzy rule; each node in this layer corresponds to the weight of the fuzzy rule;

[0025] The consequent layer, including the consequent parameters corresponding to each fuzzy rule; each node in this layer corresponds to output the inversion result after being operated by the consequent parameters under the corresponding fuzzy rule;

[0026] The output layer, used to perform weighted summation on the inversion results under all fuzzy rules, thereby outputting the final inversion result of the cavity shape parameters.

[0027] A further technical solution, the training process of the adaptive fuzzy inference system is as follows:

[0028] For multiple types of cavities with known shape parameters, use the source in the cavity to emit incident waves, receive scattered waves through a finite number of measurement points in the cavity, obtain the scattering data, and use the principal component analysis method to perform dimension reduction processing on the obtained scattering data. According to the dimension-reduced scattering data and the known shape parameter data, construct a data set;

[0029] The adaptive fuzzy inference system is trained using a data set to optimize the parameters of the membership function and the consequent parameters corresponding to the fuzzy rules, minimizing the error between the finally output prediction result and the target result to complete the training. Among them, the prediction result is the inversion result, and the parameters of the membership function are the antecedent parameters. Through continuous iterative training, the gradient descent method is used to optimize the antecedent parameters, and the Kalman filter algorithm is used to optimize the consequent parameters.

[0030] For a further technical solution, the gradient descent method is used to optimize the antecedent parameters, including:

[0031] Training is carried out with the goal of minimizing the error function between the predicted output and the target output. During the training process, the error is propagated layer by layer, the gradient of each antecedent parameter is calculated, and through continuous iterative training, the parameters are iteratively updated to reduce the error.

[0032] The Kalman filter algorithm is used to optimize the consequent parameters, including:

[0033] Observation noise is introduced to construct an observation equation for the system's predicted output, and then the error between the predicted output and the target output is calculated.

[0034] The Kalman gain is introduced, and the consequent parameters are updated based on the error and the Kalman gain. At the same time, the covariance matrix of the observation noise is updated to reflect the uncertainty change of the current consequent parameters.

[0035] Through continuous iterative training, the parameters are iteratively updated to reduce the error.

[0036] In a second aspect, the present invention provides an inverse cavity scattering inversion system based on an adaptive fuzzy inference system.

[0037] An inverse cavity scattering inversion system based on an adaptive fuzzy inference system includes:

[0038] A data acquisition module, which is used to emit an incident wave using a source in the cavity, receive the scattered wave through a finite number of measurement points in the cavity, and acquire scattering data.

[0039] A data preprocessing module, which is used to perform dimensionality reduction processing on the acquired scattering data using the principal component analysis method.

[0040] An inverse cavity scattering inversion module, which is used to input the dimensionally reduced scattering data into the trained adaptive fuzzy inference system, invert the shape parameters of the cavity, and reconstruct the shape of the cavity according to the output inversion result.

[0041] The adaptive fuzzy inference system is a hybrid model that integrates fuzzy logic and neural networks. Based on the fuzzy inference system, each layer in the neural network represents each step of the fuzzy inference process, successively including a membership function layer, a rule layer, a normalization layer, a consequent layer, and an output layer. Among them, the membership function layer includes multiple membership functions corresponding to the inputs, the rule layer includes multiple fuzzy rules in the fuzzy inference process, the consequent layer includes consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the inversion result of the final cavity shape parameters.

[0042] In a third aspect, the present invention also provides an electronic device, including: a memory for storing executable instructions; a processor for implementing the above-mentioned inverse cavity scattering inversion method based on the adaptive fuzzy inference system when executing the executable instructions stored in the memory.

[0043] In a fourth aspect, the present invention also provides a computer-readable storage medium storing executable instructions for causing a processor to implement the above-mentioned inverse cavity scattering inversion method based on the adaptive fuzzy inference system when executing the executable instructions.

[0044] In a fifth aspect, the present invention also provides a computer program product. The computer program product includes executable instructions stored in a computer-readable storage medium; wherein, when a processor of an electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, the above-mentioned inverse cavity scattering inversion method based on the adaptive fuzzy inference system is implemented.

[0045] The above one or more technical solutions have the following beneficial effects:

[0046] 1. Aiming at the inverse acoustic scattering problem caused by a cavity with a soft acoustic boundary condition in acoustics, the present invention proposes an inverse cavity scattering inversion method and system based on an adaptive neuro-fuzzy inference system (ANFIS), which uses a single power source and a finite number of measurement points in the cavity to invert the shape of the soft acoustic cavity. In this method proposed by the present invention, first, the principal component analysis (PCA) is used to reduce the dimension of the near-field scattering data obtained by measurement to remove redundant information and reduce the complexity of the near-field data. By using the principal component analysis for dimension reduction, the high-dimensional data is projected into a new low-dimensional space through a linear transformation, retaining most of the data variance, thereby reducing redundant information and noise. This not only reduces the computational burden but also improves the efficiency and stability of the algorithm. Moreover, the dimension of the data after dimension reduction is reduced, avoiding the risk of overfitting and improving the generalization ability of the model. Then, a combination of a fuzzy inference algorithm and a neural network is used to propose an adaptive neuro-fuzzy inference system (ANFIS). The dimension-reduced scattering data is used as the input of the ANFIS, and the shape parameters of the cavity are used as the output of the ANFIS. The gradient descent method and the extended Kalman filter (EKF) algorithm are respectively used to update the antecedent parameters and consequent parameters of the model, so that the mean square error of the inverted shape parameters is minimized. By using this ANFIS, the antecedent parameters and consequent parameters can be adaptively adjusted, and the hidden rules can be mined from large-scale data, the uncertainty and non-linear mapping problems can be processed, so as to accurately model the non-linear relationship in the data, more accurately extract key features from complex scattering data, enhance the robustness and prediction accuracy of the model, and thus realize the efficient prediction and accurate inversion from scattering data to target shape parameters, achieve the efficient and accurate inversion of the cavity shape, and solve the problems of large scattering data noise, complex non-linear relationship, and poor model interpretability existing in the existing methods.

[0047] 2. When facing the inverse cavity scattering inversion problem, the present invention proposes a hybrid intelligent system that combines the advantages of fuzzy logic and neural networks, namely an adaptive neuro-fuzzy inference system (ANFIS). This system can not only use the fuzzy inference system to handle the uncertainty and noise in the scattering data but also optimize the model parameters by virtue of the adaptive learning ability of the neural network, so as to more accurately predict and invert the unknown features in the inverse scattering problem. In addition, when facing a small data set, this system has strong generalization ability and computational efficiency, avoiding the overfitting problem in traditional methods. Through the above characteristics of the ANFIS, the efficient solution of the inverse scattering problem can be realized by using this system, and good interpretability can be achieved.

[0048] Advantages of additional aspects of the present invention will be partly given in the following description, partly become obvious from the following description, or be understood through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The accompanying drawings forming a part of this invention are used to provide a further understanding of the invention. The schematic embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0050] Figure 1 Schematic diagram of the inverse scattering problem inside the cavity;

[0051] Figure 2 Schematic diagram of a dual-input third-order adaptive fuzzy inference system with nine rules in an embodiment of the present invention;

[0052] Figure 3 Schematic diagram of the geometric setting of the kite cavity in Experiment 1 in an embodiment of the present invention;

[0053] Figure 4 Shape diagram of the inverted kite cavity under the measurement curves with different radii in an embodiment of the present invention;

[0054] Figure 5 Shape diagram of the inverted clover cavity under the measurement curves with different radii in an embodiment of the present invention;

[0055] Figure 6 Shape diagram of the inverted pear-shaped cavity under the measurement curves with different radii in an embodiment of the present invention;

[0056] Figure 7 Shape diagram of the inverted kite cavity under different observation apertures in an embodiment of the present invention;

[0057] Figure 8 Shape diagram of the inverted clover cavity under different observation apertures in an embodiment of the present invention;

[0058] Figure 9 Shape diagram of the inverted pear-shaped cavity under different observation apertures in an embodiment of the present invention;

[0059] Figure 10 Shape diagram of the inverted kite cavity under different Gaussian noise levels in an embodiment of the present invention;

[0060] Figure 11 Shape diagram of the inverted pear-shaped cavity under different Gaussian noise levels in an embodiment of the present invention;

[0061] Figure 12 Shape diagram of the inverted kite cavity under different uniform noise levels in an embodiment of the present invention;

[0062] Figure 13 Shape diagram of the inverted clover cavity under different uniform noise levels in an embodiment of the present invention;

[0063] Figure 14 Shape diagram of the inverted pear-shaped cavity under different uniform noise levels in an embodiment of the present invention;

[0064] Figure 15 This is a comparison chart of the inversion effects of two methods under different radius measurement curves in the embodiments of the present invention;

[0065] Figure 16 This is a comparison chart of the inversion effects of two methods under different observation apertures in the embodiments of the present invention;

[0066] Figure 17 This is a comparison chart of the inversion effects of two methods under 30% Gaussian noise and 20% uniform noise in the embodiments of the present invention. Detailed implementation manners

[0067] It should be noted that the following detailed description is exemplary only for describing the specific implementation manners, aiming to provide further illustration of the present invention and is not intended to limit the exemplary embodiments of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs. In addition, it should also be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or their combinations.

[0068] First, clarify the internal inverse scattering problem of the cavity studied by the present invention as follows:

[0069] As Figure 1 shown, assume is an impenetrable cavity, where R represents a real number, the boundary of this cavity is a bounded simply connected domain, is a cavity inside a closed smooth curve. Assume the curve is a circle centered at the origin with as the radius, that is , represents the coordinate point. Then, for the internal inverse scattering problem caused by a single point source (i.e., source) inside the impenetrable cavity, the scattered field satisfies:

[0070] (1)

[0071] (2)

[0072] In the above formula, is the incident wave, is the imaginary unit, is the wave number, represents the frequency of the time harmonic wave, is the sound speed, Indicates inside the cavity Inside, Indicates on the cavity boundary On, Is the fundamental solution of the Helmholtz equation, then there is:

[0073] (3)

[0074] In the above formula, Represents the Hankel function of the first kind of order zero, Is A point source inside, Represents the coordinate point.

[0075] The forward problem is: According to the incident wave And the wave number Determine the scattered field According to Theorem 2.1 below, the scattered field Can be represented by the combination of double-layer potentials. Among them, Theorem 2.1 is:

[0076] Use the double-layer potential to approximate the scattered field That is, Then there is:

[0077] (4)

[0078] For And Under continuous density, Is The solution of the interior Dirichlet problem in (1)-(2), that is, as long as Is the solution of the following integral equation:

[0079] (5)

[0080] Among them, Is the fundamental solution of the two-dimensional Helmholtz equation, Is the outward unit normal vector on the cavity boundary , Is the density function, Is the point on the boundary , Is the boundary The arc length element on, used for integration on the boundary.

[0081] Assume Is not The Dirichlet eigenvalue of, note that Is 0 on , The existence of the solution of this direct scattering problem is well known, and the inverse problem concerned by the present invention refers to: Through the point source Inside a scattered field is generated and determined by the measured values on the curve . Under the restrictive assumption of the cavity size, the shape of the cavity can be uniquely determined by a point source and several measured values . .

[0082] Therefore, in the above context, the present invention proposes an inverse cavity scattering inversion method and system based on an adaptive fuzzy inference system. By designing an adaptive fuzzy inference system (ANFIS), which is used as a hybrid intelligent system combining the advantages of fuzzy logic and neural networks to solve the inverse cavity scattering inversion problem. The ANFIS can not only utilize the fuzzy inference system to process the uncertainty and noise in the scattering data, but also optimize the model parameters with the help of the adaptive learning ability of the neural network, so as to more accurately predict and invert the unknown features in the inverse scattering problem, avoid the overfitting problem in the traditional method, and provide good model interpretability, realizing the efficient and accurate inversion of the cavity shape.

[0083] Embodiment 1

[0084] This embodiment provides an inverse cavity scattering inversion method based on an adaptive fuzzy inference system, which specifically includes the following steps:

[0085] Step S1: Use the source in the cavity to emit an incident wave, and receive the scattered wave through a finite number of measurement points in the cavity to obtain scattering data.

[0086] Specifically, use the source in the cavity to emit an incident wave, and receive the scattered wave through a finite number of measurement points (or observation points) in the cavity to obtain scattering data. Among them, use to represent the measured near-field data, to represent the scattered data measured at the th observation point, is the number of observation points, represents dimensional complex vector space, , is the total number of samples of the scattering data.

[0087] Step S2: Use the principal component analysis method to reduce the dimension of the obtained scattering data.

[0088] Considering that scattering data is usually high-dimensional data, and high-dimensional data contains a large amount of features and information, which not only increases the computational complexity but also makes the processing more complicated. Especially when performing inversion solving, high-dimensional data may lead to a sharp increase in the computational time of the algorithm and even exceed the limit of computing resources. In addition, there are often redundant or highly correlated features in the scattering data, and these redundant information not only increases the computational burden but also may cause overfitting of the model. Therefore, in this embodiment, for the measured scattering data, principal component analysis (PCA) is first used for dimensionality reduction to effectively solve the above problems. Among them, using the principal component analysis method (PCA), the high-dimensional scattering data is projected into a new low-dimensional space through linear transformation, so as to retain most of the data variance and then reduce redundant information and noise.

[0089] In this embodiment, the principal component analysis method (PCA) is used to perform dimensionality reduction processing on the acquired scattering data, including:

[0090] (1) Data standardization, that is: perform data standardization processing on the acquired scattering data to obtain the standardized sample matrix of the scattering data.

[0091] First, according to the above problems, assume is the total number of samples of the scattering data, is the number of observation points affecting the scattering data, then the scattering field data is expressed as:

[0092] (6)

[0093] Among them, represents d-dimensional complex vector space.

[0094] Secondly, perform standardization processing on the above scattering data, that is: calculate the mean of each column in as , subtract the mean of each column from each data in , calculate each data , so that the mean of each column is zero, and finally obtain the standardized data . Through the above processing, after the sample matrix of the original scattering data is standardized, it is converted to:

[0095] (7)

[0096] (2) Calculate the covariance matrix of the standardized sample matrix. The covariance matrix is used to describe the linear relationship and correlation between each observation point, and this covariance matrix , which can be expressed as:

[0097] (8)

[0098] Among them, the element represents the covariance between the observation data of the -th observation point and the -th observation point.

[0099] (3) Perform eigenvalue decomposition on the covariance matrix to calculate the eigenvalues and eigenvectors. Specifically, perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues and eigenvectors, which can be expressed as:

[0100] (9)

[0101] Among them, is the eigenvalue, representing the variance of the -th principal component (i.e., the observation point). The larger this eigenvalue, the more information the principal component contains in the scattered data; represents the corresponding eigenvector.

[0102] (4) Select several principal components according to the eigenvalues and eigenvectors. Specifically, sort the eigenvalues from small to large, and select the first few principal components according to the magnitude of the eigenvalues. When selecting the principal components, the proportion of the explained variance can be used to determine how many principal components to retain. Usually, the first principal components are selected so that they can explain more than 98% of the total variance, which can be expressed as:

[0103] (10)

[0104] Among them, 0.98 is the preset threshold, which can be adjusted and set according to the actual situation.

[0105] (5) Construct the principal components, that is: project the original standardized scattered data into the space composed of the selected several ( k ) principal components to obtain the scattered data after dimensionality reduction, which can be expressed as:

[0106] (11)

[0107] Among them, represents the matrix composed of the first selected eigenvectors.

[0108] Through the above method, PCA can assist in combining the relevant features in the scattered data into a few principal components, which not only reduces the computational burden, but also improves the efficiency and stability of the algorithm; in addition, the dimension of the data after dimensionality reduction is reduced, avoiding the risk of overfitting, improving the generalization ability of the model, and enabling the subsequent inversion algorithm to better process and predict unknown data.

[0109] Step S3: Input the dimension-reduced scattering data into the trained adaptive neuro-fuzzy inference system (ANFIS) to invert the shape parameters of the cavity, and reconstruct the shape of the cavity according to the output inversion result. Among them, the adaptive neuro-fuzzy inference system (ANFIS) is a hybrid model that combines fuzzy logic and neural networks, and is used for non-linear system modeling and prediction of complex relationships. This model is based on the fuzzy inference system, and each layer in the neural network represents each step of the fuzzy inference process, including the membership function layer, the rule layer, the normalization layer, the consequent layer, and the output layer. Among them, the membership function layer includes multiple membership functions corresponding to the inputs, the rule layer includes multiple fuzzy rules in the fuzzy inference process, the consequent layer includes the consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the final inversion result of the cavity shape parameters.

[0110] Specifically, considering that the core problems in inverting using scattering data lie in the high dimensionality, uncertainty of the data, and the complexity of the non-linear mapping relationship, for this reason, this embodiment proposes the adaptive neuro-fuzzy inference system ANFIS. This ANFIS model is based on the Takagi-Sugeno fuzzy inference system, combines the structured expression of the fuzzy inference system with the adaptive learning ability of the neural network, and can mine hidden laws in large-scale data by adaptively adjusting the antecedent fuzzy membership function parameters and the consequent linear parameters, so as to achieve efficient prediction and accurate inversion from scattering data to target shape parameters.

[0111] Furthermore, the basic structure of the above ANFIS model is as follows: The ANFIS model is based on the Takagi-Sugeno fuzzy inference system, and its core consists of input variables, fuzzy rules, and output variables. Its basic goal is to use fuzzy rules for inference and adjust parameters through learning to make the model output close to the target value. The building process of this ANFIS model is as follows:

[0112] First, clarify the fuzzy inference process of the fuzzy inference system. Specifically, the data after the above dimension reduction processing may be two-dimensional, three-dimensional, or four-dimensional. In this embodiment, it is assumed that the dimension of the scattering data is reduced to two-dimensional according to the above PCA method, then it is expressed as: , and then the two-dimensional data obtained after the dimension reduction corresponds to two inputs. The dimension-reduced scattering data and are used as the inputs of the system, and one cavity shape parameter in is used as the output of the system. It is set that each input corresponds to multiple membership functions. In this embodiment, three membership functions are set, such as corresponding to , corresponding to , therefore, the input space can be divided into multiple fuzzy subspaces, that is, nine fuzzy subspaces. Each fuzzy subspace corresponds to a fuzzy if-then rule for control. The premise part of the rule describes a fuzzy subspace, and the result part specifies the output within that fuzzy subspace.

[0113] Furthermore, the form of each fuzzy rule can be expressed as:

[0114] : If belongs to and belongs to , then ;

[0115] wherein, and are the fuzzy sets of the input scattered data and respectively, , , are the consequent parameters, is the output of rule .

[0116] Furthermore, the total output of the system is the weighted average of the outputs of all rules, and its calculation formula is:

[0117] (12)

[0118] In the above formula, is the activation weight of rule , which is calculated by the membership function. It should be noted that the dimensionality of the scattered data input to the system and the number of membership functions are not unique and can be changed according to the actual dimensionality reduction and prediction situations.

[0119] Secondly, based on the fuzzy inference system, each step of the fuzzy inference process is represented by each layer in the neural network, thereby constructing a hierarchical network structure of ANFIS. Specifically, the ANFIS can be represented by a five-layer network structure. Each layer in the network corresponds to each step in the fuzzy inference process. This network structure is as Figure 2 shown, including:

[0120] (1) The first layer: the membership function layer. This membership function layer includes multiple membership functions, and each node in this layer corresponds to a membership function respectively.

[0121] According to the above inference process, assume that the system has two inputs and , each input is associated with three membership functions, so this layer contains six adaptive nodes (each node corresponds to a membership function), and the output of the node , are respectively and 's membership functions. Specifically, any continuous and piecewise differentiable function between 0 and 1 can be selected as the membership function. In this embodiment, a Gaussian function is selected and can be expressed as:

[0122] , (13)

[0123] where , are the center and width of the fuzzy set , , are the center and width of the fuzzy set .

[0124] (2) The second layer: the rule layer. This rule layer includes multiple fuzzy rules, and each node in this layer corresponds to a fuzzy rule.

[0125] In this embodiment, it is assumed that there are nine nodes in this layer, and each node corresponds to a fuzzy rule. By multiplying the membership function values of and , the activation strength (i.e., the rule weight) of each rule is calculated as:

[0126] (14)

[0127] Furthermore, this layer outputs 9 rule weights .

[0128] (3) The third layer: the normalization layer. This normalization layer is used to normalize the weights of each fuzzy rule, and each node in this layer corresponds to the weight of the fuzzy rule.

[0129] In this embodiment, the weights of each rule are normalized so that the sum of all rule weights is 1, indicating their relative contributions among all rules. This normalization can be expressed as:

[0130] (15)

[0131] The number and type of nodes in the normalization layer designed above are the same as those in the previous layer, and the output of each node is a normalized weight.

[0132] (4) The fourth layer: the consequent layer. This consequent layer includes the consequent parameters corresponding to each fuzzy rule, and each node in this layer corresponds to output the inversion result after the operation of the consequent parameters under the corresponding fuzzy rule.

[0133] In this embodiment, each node in this layer corresponds to outputting the result of each rule, and the result is the product of the output value of the rule and the rule weight, which can be expressed as:

[0134] (16)

[0135] (5) The fifth layer: the output layer. This output layer is used to perform weighted summation on the inversion results under all fuzzy rules, so as to output the final inversion result of the cavity shape parameters, which can be expressed as:

[0136] (17)

[0137] Furthermore, based on the above constructed adaptive fuzzy inference system, the system model is trained, and the training process is as follows:

[0138] First, for multiple types of cavities with known shape parameters, an incident wave is emitted by a source in the cavity, and the scattered wave is received through a finite number of measurement points in the cavity to obtain scattering data. Among them, the data set is defined as , is the total amount of data in the data set, is the set of training cavity shapes, represents the cavity 's shape parameters, represents the near-field data measured in the cavity , represents the th observation point's measured scattering data, is the number of observation points.

[0139] Secondly, the obtained scattering data is processed by the principal component analysis method for dimensionality reduction, and a data set is constructed according to the dimensionality-reduced scattering data and the known shape parameter data.

[0140] After that, the data set is used to train the adaptive fuzzy inference system to optimize the parameters of the membership function and the consequent parameters corresponding to the fuzzy rules, so that the error between the finally output prediction result and the target result is minimized, and the training is completed; among them, the prediction result is the inversion result, the parameters of the membership function are the antecedent parameters, and through continuous cyclic iterative training, the gradient descent method is used to optimize the antecedent parameters, and the Kalman filter algorithm is used to optimize the consequent parameters.

[0141] In the above process, the core of training the ANFIS model is to optimize the parameters of the membership function (i.e., the antecedent parameters) and the linear parameters of the rule consequent (i.e., the consequent parameters), so as to minimize the error between the system output and the target output. This optimization can be divided into two steps: antecedent parameter optimization and consequent parameter optimization.

[0142] (1) The gradient descent method is used to optimize the antecedent parameters.

[0143] Using the gradient descent method, the antecedent parameters (i.e., the centers of the Gaussian membership functions , widths , etc.) are optimized as follows: training is carried out with the goal of minimizing the error function between the predicted output and the target output . During the training process, by propagating the error layer by layer, the gradient of each antecedent parameter is calculated, and through continuous iterative training, the parameters are iteratively updated to reduce the error.

[0144] Among them, the error function can be expressed as:

[0145] (18)

[0146] Among them, is the number of training samples.

[0147] In addition, the update formula of the gradient descent method is:

[0148] (19)

[0149] Among them, represents the antecedent parameters, such as and , represents the learning rate, is the gradient of the error with respect to the parameter.

[0150] By propagating the error layer by layer, the gradient of each antecedent parameter is calculated, and the parameters are iteratively updated to reduce the error.

[0151] (2) The extended Kalman filter (EKF) algorithm is used to optimize the consequent parameters.

[0152] The consequent parameters (such as , , , etc.) can be updated through the extended Kalman filter algorithm. Using the Kalman filter to recursively optimize the parameters of the nonlinear system has the characteristics of high efficiency and fast convergence. Specifically, the consequent parameters include the linear coefficients , , of each rule, which constitute the parameter vector . Let the target output of the system be , and the predicted output be . Then, the dynamic optimization of the consequent parameters is achieved through EKF. Its basic steps include state prediction and measurement update, specifically:

[0153] Assume that the dynamic change of the consequent parameters satisfies the state equation:

[0154] (20)

[0155] Among them, usually represents the "time step" or "iteration number", that is, the state at the th moment in the time series; is the process noise, usually assumed to satisfy a zero-mean Gaussian distribution, and the covariance matrix of this process noise is .

[0156] The above equation reflects the stochastic drift characteristics of the parameters, that is, the consequent parameters may change slightly at each moment.

[0157] Introduce the observation noise and construct the observation equation representing the predicted output of the system, which is:

[0158] (21)

[0159] Among them, is the weighted matrix related to the input data and the rule strength, is the consequent parameter vector, is the observation noise, also assumed to be a zero-mean Gaussian distribution, and the covariance matrix of this observation noise is .

[0160] In the update process of the EKF, first calculate the current predicted output and the error with the target output , which is:

[0161] (22)

[0162] Then, introduce the Kalman gain to adjust the parameters, and the calculation formula of this Kalman gain is:

[0163] (23)

[0164] Among them, is the covariance matrix of the consequent parameters, which is used to measure the uncertainty of the current parameter estimation.

[0165] After that, update the consequent parameters according to the error and the Kalman gain, which is:

[0166] (24)

[0167] At the same time, update the covariance matrix of the observation noise to reflect the change of the current parameter uncertainty, and the update formula is:

[0168] (25)

[0169] Through the above process, the EKF can adjust the consequent parameters in real time using the recursive formula. After continuous cyclic iterative training, the parameters are iteratively updated to reduce the error, making the predicted output as close as possible to the target output . Compared with the traditional least squares method, the EKF has dynamic adaptability and can converge to the optimal solution more quickly, especially suitable for dealing with non-stationary or dynamically changing data scenarios.

[0170] Furthermore, the dimension-reduced scattering data is input into the above-mentioned trained adaptive fuzzy inference system to invert the shape parameters of the cavity, and the shape of the cavity can be reconstructed according to the output inversion result.

[0171] The effectiveness of the method proposed in this embodiment is demonstrated by the following examples, verifying that selecting appropriate measurement curves and aperture ranges will make the inversion have better effects, and obtaining that this method has a certain robustness to the noise in the scattering field measurement. Finally, the inversion effects of the adaptive fuzzy inference system and the traditional feedforward neural network on the cavity are compared to further verify the effectiveness of the method proposed in this embodiment.

[0172] For simplicity, assume that the curve is a circle, that is , is a constant, and a single point source is placed at the origin (0, 0). The synthetic scattering data on the curve is approximated by the linear combination of double-layer potentials through equations (4) and (5). The scattering data after PCA dimension reduction is denoted as , the shape parameter is denoted as , the data set is , and the data set is equally divided into 8:2, that is, 80% is the training set and 20% is the test set. In addition, the boundary parameter equations of several scatterers involved are:

[0173] Kite-shaped: , (26)

[0174] Clover-shaped: , (27)

[0175] Pear-shaped: , (28)

[0176] In all the following experiments, according to the complexity of the shape and experimental demonstration, for three different shapes of kite-shaped, clover-shaped and pear-shaped, the total amount of data selected during the experiment is respectively , , ; Nine receivers are placed equidistantly on the curve , that is, the number of observation points on the measurement curve is 9; The parameter values of ANFIS are shown in Table 1 below. The value of mf can be adjusted according to the input, and the values of other parameters are obtained through multiple experiments. In addition, in the graphic geometry setting of the inverse shape, unless otherwise specified, the blue solid line represents the exact cavity shape boundary, and the red dashed line represents the inversed cavity shape boundary.

[0177] Table 1: ANFIS Parameter Settings

[0178]

[0179] Experiment 1: Influence of measurement curves with different radii on the cavity inversion effect. In this experiment, let the wave number , the finite aperture is set to , and the radii of the three measurement curves are set to respectively. There is no noise in the near-field data, and the geometric setting with a kite as an example is as Figure 3 shown, where the black dashed line has a radius r = 0.2, the green dashed line has a radius r = 0.3, the red dashed line has a radius r = 0.4, and the blue solid line represents the exact kite cavity shape boundary.

[0180] As Figure 4 , Figure 5 and Figure 6 shown, the kite-shaped, clover-shaped, and pear-shaped cavities inversed by using measurement curves with different radii are respectively shown. The measurement radii are , , respectively. It can be seen from this that, under the condition that the total amount of the data set and the number of training times remain unchanged, the larger the radius of the measurement curve, the closer the measurement points distributed on the curve are to the cavity boundary, and the smaller the influence of the near-field data by other media in the cavity, thus making the inversion effect of the cavity shape better. At the same time, this conclusion can also be obtained by observing the mean square error of the inversion parameters, that is, as the radius of the measurement curve increases, the mean square error becomes smaller and smaller.

[0181] Experiment 2: Influence of different observation apertures on the cavity inversion effect. In this experiment, let the wave number , the radii of the three shape measurement curves are set to , and there is no noise in the near-field data. Considering the inversion situation of ANFIS when the observation aperture is set to , , , the inversion effects are respectively shown as Figure 7 , Figure 8 and Figure 9 shown.

[0182] According to Experiment 1, when the radius of the curve measurement is used, the inversion effect of the cavity is the best. Therefore, Experiment 2 is carried out under the conditions that the total amount of the dataset, the number of training times remain unchanged, and the radius of the curve measurement remains the same. From Figure 7 , Figure 8 , Figure 9 , it can be seen that when the observation aperture is used, the inversion effects of the three cavities are the best. It can be observed that as the range of the observation aperture gradually decreases, the inversion effect also decreases. This is because as the observation aperture shrinks, the similarity between the near-field data increases, resulting in a gradual reduction in the available cavity information, which raises the inversion error of the shape parameters and thus affects the inversion accuracy. Further observation shows that within a certain range of the observation aperture, ANFIS can still accurately invert the shape information of the cavity.

[0183] Experiment 3: The influence of different noise levels on the cavity inversion effect. In this experiment, the wavenumber is set as , the radius of the measurement curve is set as , the observation aperture is set as , and Gaussian white noise with noise levels of 0%, 10%, 30% and uniform noise with noise levels of 0%, 10%, 20% are respectively added to the near-field data.

[0184] In practical applications, near-field data is usually interfered by noise. Therefore, Experiment 3 is used to explore the influence of different noise levels on the inversion effect of the ANFIS model. In order to verify the robustness of the ANFIS model to noise, according to the conclusions obtained from Experiment 1 and Experiment 2, Experiment 3 is carried out under the conditions that the total amount of the dataset remains unchanged, the number of training times remains unchanged, the radius of the curve measurement is and the observation aperture is set as . From Figure 10 , Figure 11 , it can be seen that when the Gaussian white noise levels are 0%, 10%, 30% respectively, the mean square error of the inversion basically remains unchanged, and the boundary of the inverted cavity shape is also very close to the true shape boundary. It can be seen that the ANFIS model has good robustness to Gaussian white noise. In addition, Experiment 3 also explores the influence of different levels of uniform noise on the inversion effect. From Figure 12 , Figure 13 and Figure 14It can be seen that when the uniform noise level is below 10%, the impact of noise on the inversion effect of the ANFIS model is small. As the noise level increases, the mean square error of the inversion parameters also increases, and the inversion effect becomes worse and worse. When the noise level is 20%, for slightly more complex cavities such as clover-shaped and pear-shaped cavities, there will be a gap between the shape boundaries inverted by ANFIS and the true shape boundaries. Generally speaking, when the uniform noise level is relatively small, the ANFIS model has a certain robustness to uniform noise.

[0185] Experiment 4: Comparison of the inversion effects between the feedforward neural network (FNN) and the adaptive fuzzy inference system. In this experiment, let the wave number , the first method is to directly use the measured scattering data for shape inversion by the feedforward neural network, and the second method is to reduce the dimension of the obtained scattering data by the PCA method and use ANFIS to perform shape inversion on the dimension-reduced data. The experiment is as follows:

[0186] (1) On the premise that the near-field data is noise-free, the radii of the measurement curves are set to respectively, and observe the inversion effects of the two methods on the kite cavity.

[0187] (2) On the premise that the near-field data is noise-free, the observation apertures are set to , , respectively, and observe the inversion effects of the two methods on the kite cavity.

[0188] (3) Under the conditions of the measurement curve and the observation aperture , add 30% Gaussian noise and 20% uniform noise to the near-field data respectively, and observe the inversion effects of the two methods.

[0189] In this Experiment 4, on the premise that the total amount of the data set and the number of training times remain unchanged, by setting different radius measurement curves, measurement apertures and noises, compare the inversion effects of the traditional feedforward neural network and the adaptive fuzzy inference system proposed in this embodiment on the cavity. From Figure 15 and Figure 16 it can be seen that under the conditions of different radius measurement curves and different measurement apertures, the inversion effect of ANFIS on the kite cavity is better than that of using FNN for inversion, and the inverted shape boundary is closer to the true boundary. And when , , the inversion effect of ANFIS is the best. From Figure 17It can be seen that when 30% Gaussian noise and 20% uniform noise are respectively added to the near-field data, the kite cavity boundary inverted by the FNN (feedforward neural network) has a large deviation from the true boundary, indicating that this method is sensitive to noise. When using ANFIS for inversion, it can be seen that ANFIS has a certain robustness to both Gaussian and uniform noise. Therefore, using ANFIS to invert the cavity shape has a better effect than using the traditional FNN inversion.

[0190] In summary, an inverse cavity scattering inversion method based on an adaptive fuzzy inference system proposed in this embodiment reduces the dimension of the obtained scattering data by the PCA method, designs an adaptive fuzzy inference system ANFIS, uses this ANFIS to invert the shape parameters of the cavity, and then reconstructs the shape of the cavity. It can be seen from the above experimental verification that for the inverse cavity scattering problem using a single point source and a finite number of measurement points, this method can successfully invert the shape of the cavity; in addition, selecting appropriate measurement curves and aperture ranges makes the inversion have a better effect, and it is verified that this method has a certain robustness to Gaussian noise and uniform noise. Moreover, by comparing the effects of the adaptive fuzzy inference system and the traditional feedforward neural network in inverting the cavity, the comprehensive advantages of ANFIS in terms of better interpretability, robustness, and training efficiency in complex problems can be further highlighted.

[0191] Embodiment 2

[0192] This embodiment provides an inverse cavity scattering inversion system based on an adaptive fuzzy inference system, including:

[0193] A data acquisition module, configured to use a source in the cavity to emit an incident wave, receive the scattered wave through a finite number of measurement points in the cavity, and obtain scattering data;

[0194] A data preprocessing module, configured to perform dimensionality reduction processing on the obtained scattering data by using the principal component analysis method;

[0195] An inverse cavity scattering inversion module, configured to input the dimensionally reduced scattering data into the trained adaptive fuzzy inference system, invert the shape parameters of the cavity, and reconstruct the shape of the cavity according to the output inversion result;

[0196] The adaptive fuzzy inference system is a hybrid model that combines fuzzy logic and neural networks. This model is based on a fuzzy inference system, and each layer in the neural network represents each step of the fuzzy inference process, successively including a membership function layer, a rule layer, a normalization layer, a consequent layer, and an output layer. Among them, the membership function layer includes multiple membership functions corresponding to the input, the rule layer includes multiple fuzzy rules in the fuzzy inference process, the consequent layer includes consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the final inversion result of the cavity shape parameters.

[0197] Embodiment 3

[0198] This embodiment provides an electronic device, including: a memory for storing executable instructions; a processor for implementing the above method provided in this embodiment when executing the executable instructions stored in the memory.

[0199] Embodiment 4

[0200] This embodiment also provides a computer-readable storage medium storing executable instructions, which, when executed by a processor, will cause the processor to execute the above method provided in this embodiment.

[0201] Embodiment 5

[0202] This embodiment provides a computer program product, which includes executable instructions. The executable instructions are a kind of computer instructions; the executable instructions are stored in a computer-readable storage medium. When the processor of an electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, the electronic device is caused to execute the above method provided in this embodiment.

[0203] The steps involved in Embodiments 2 to 5 above correspond to those in Method Embodiment 1. For specific implementation manners, reference may be made to the relevant description part of Embodiment 1. The term "computer-readable storage medium" should be understood to include a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and cause the processor to execute any method in the present invention.

[0204] Those skilled in the art should understand that the above-mentioned modules or steps of the present invention can be implemented by a general-purpose computer device. Optionally, they can be implemented by program codes executable by a computing device, so that they can be stored in a storage device for execution by the computing device, or they can be separately fabricated into individual integrated circuit modules, or multiple modules or steps among them can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0205] The above are only the preferred embodiments of the present invention. Although the specific implementation manners of the present invention have been described in conjunction with the accompanying drawings, it is not a limitation on the protection scope of the present invention. Those skilled in the art should understand that various modifications or deformations that can be made without creative efforts on the basis of the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. An inverse cavity scattering inversion method based on an adaptive fuzzy inference system, characterized in that Including: Using a point source in the cavity In the cavity An incident wave is emitted inside to generate a scattering field. Through a Closed smooth curve in the cavity Scattered waves are received at a finite number of measurement points on it to obtain scattering data; Using the principal component analysis method to perform dimensionality reduction processing on the acquired scattering data, including: performing data standardization processing on the acquired scattering data to obtain a standardized sample matrix of the scattering data; calculating the covariance matrix of the standardized sample matrix; performing eigenvalue decomposition on the covariance matrix to calculate the eigenvalues and eigenvectors; selecting several principal components according to the eigenvalues and eigenvectors; projecting the original standardized scattering data into the space composed of the selected several principal components to obtain the dimensionality-reduced scattering data; Inputting the dimensionality-reduced scattering data into the trained adaptive fuzzy inference system. Each input corresponds to multiple membership functions, and the input space is divided into multiple fuzzy subspaces according to fuzzy rules. Each fuzzy subspace is controlled by a corresponding fuzzy rule; Among them, each fuzzy rule is represented in the form of: If belongs to and belongs to , then ; Among them, and are the fuzzy sets of the input scattering data and respectively, , , are the consequent parameters, is the output of the rule . Each fuzzy rule includes multiple consequent parameters; after the input data is operated by multiple fuzzy rules, the outputs of all rules are weighted and averaged to calculate the final inversion result of the cavity shape parameters, and the shape of the cavity is reconstructed according to the output inversion result; The training of the adaptive fuzzy inference system includes using the gradient descent method to optimize the antecedent parameters and using the Kalman filter algorithm to optimize the consequent parameters; among them, the optimization of the consequent parameters is as follows: Introducing observation noise, constructing an observation equation for the system predicted output, and then calculating the error between the predicted output and the target output; Introducing the Kalman gain, updating the consequent parameters according to the error and the Kalman gain, and at the same time updating the covariance matrix of the observation noise to reflect the uncertainty change of the current consequent parameters; Through continuous cyclic iterative training, iteratively updating the parameters to reduce the error.

2. The inverse cavity scattering inversion method based on an adaptive fuzzy inference system according to claim 1, characterized in that, The adaptive fuzzy inference system is based on the fuzzy inference system, and each layer in the neural network represents each step of the fuzzy inference process, successively including: The membership function layer, including multiple membership functions; each node in this layer corresponds to a membership function; The rule layer, including multiple fuzzy rules; each node in this layer corresponds to a fuzzy rule; The normalization layer, used to normalize the weights of each fuzzy rule; each node in this layer corresponds to the weight of the fuzzy rule; The consequent layer, including the consequent parameters corresponding to each fuzzy rule; each node in this layer corresponds to outputting the inversion result after the operation of the consequent parameters under the corresponding fuzzy rule; The output layer, used to perform weighted summation on the inversion results under all fuzzy rules to output the final inversion result of the cavity shape parameters.

3. The inverse cavity scattering inversion method based on an adaptive fuzzy inference system according to claim 1, characterized in that The training process of the adaptive fuzzy inference system is as follows: For multiple types of cavities with known shape parameters, using a source in the cavity to emit incident waves, receiving scattered waves through a finite number of measurement points in the cavity to obtain scattering data, and using the principal component analysis method to perform dimensionality reduction processing on the acquired scattering data, and constructing a data set according to the dimensionality-reduced scattering data and the known shape parameter data; The adaptive fuzzy inference system is trained using a data set to optimize the parameters of the membership function and the consequent parameters corresponding to the fuzzy rules, minimizing the error between the finally output prediction result and the target result to complete the training; where the prediction result is the inversion result, and the parameters of the membership function are the antecedent parameters. Through continuous iterative training, the gradient descent method is used to optimize the antecedent parameters, and the Kalman filter algorithm is used to optimize the consequent parameters.

4. The inverse cavity scattering inversion method based on an adaptive fuzzy inference system according to claim 1, characterized in that Using the gradient descent method to optimize the antecedent parameters includes: Training with the goal of minimizing the error function between the predicted output and the target output. During the training process, the error is propagated layer by layer to calculate the gradient of each antecedent parameter. Through continuous iterative training, the parameters are iteratively updated to reduce the error.

5. An inverse cavity scattering inversion system based on an adaptive fuzzy inference system, characterized in that, Including: A data acquisition module, which is used to utilize a point source in the cavity to emit an incident wave inside the cavity to generate a scattered field, and receive scattered waves at a finite number of measurement points on a closed smooth curve inside the cavity, so as to obtain scattered data; A data preprocessing module for dimensionality reduction of the acquired scattering data using the principal component analysis method, including: performing data standardization processing on the acquired scattering data to obtain the standardized sample matrix of the scattering data; calculating the covariance matrix of the standardized sample matrix; performing eigenvalue decomposition on the covariance matrix to calculate the eigenvalues and eigenvectors; selecting several principal components according to the eigenvalues and eigenvectors; projecting the original standardized scattering data into the space formed by the selected several principal components to obtain the dimensionality-reduced scattering data; An inverse cavity scattering inversion module for inputting the dimensionality-reduced scattering data into the trained adaptive fuzzy inference system. Each input corresponds to multiple membership functions, and the input space is divided into multiple fuzzy subspaces according to the fuzzy rules, and each fuzzy subspace is controlled by a corresponding fuzzy rule; Among them, each fuzzy rule is expressed in the form of: If belongs to and belongs to , then ; wherein, and are respectively the fuzzy sets of the input scattered data and , , , are the consequent parameters, is the output of the rule . Each fuzzy rule includes multiple consequent parameters; after the input data is operated by multiple fuzzy rules, the outputs of all rules are weighted and averaged to calculate the final inversion result of the cavity shape parameters, and the shape of the cavity is reconstructed according to the output inversion result; The training of the adaptive fuzzy inference system includes using the gradient descent method to optimize the antecedent parameters and using the Kalman filter algorithm to optimize the consequent parameters; where the optimization of the consequent parameters is: Introducing observation noise to construct the observation equation of the system predicted output, and then calculating the error between the predicted output and the target output; Introducing the Kalman gain, updating the consequent parameters according to the error and the Kalman gain, and at the same time updating the covariance matrix of the observation noise to reflect the uncertainty change of the current consequent parameters; Through continuous iterative training, the parameters are iteratively updated to reduce the error.

6. An electronic device, characterized in that, Including: A memory for storing executable instructions; A processor for implementing an inverse cavity scattering inversion method according to any one of claims 1-4 when executing the executable instructions stored in the memory.

7. A computer-readable storage medium, characterized in that, Stored with executable instructions for causing the processor to implement an inverse cavity scattering inversion method according to any one of claims 1-4 when executing the executable instructions.

8. A computer program product, characterized in that, The computer program product includes executable instructions, and the executable instructions are stored in a computer-readable storage medium; When the processor of the electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, an inverse cavity scattering inversion method based on an adaptive fuzzy inference system according to any one of claims 1-4 is implemented.

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