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

Abstract

The invention discloses an inverse cavity scattering inversion method and system based on an adaptive fuzzy inference system, and relates to the technical field of inverse scattering, and the method comprises the steps: employing a single point source in a cavity to emit an incident wave, receiving a scattered wave through a limited number of measurement points in the cavity, and obtaining scattering data; performing dimension reduction processing on the acquired scattering data by using a principal component analysis method; inputting the scattering data subjected to dimension reduction processing into the trained adaptive fuzzy inference system, performing inversion on shape parameters of the cavity, and reconstructing the shape of the cavity according to an output inversion result; the adaptive fuzzy inference system is a hybrid model fusing fuzzy logic and a neural network, the model is based on the fuzzy inference system, each step of the fuzzy inference process is represented through each layer in the neural network, and the model sequentially comprises a membership function layer, a rule layer, a normalization layer, a consequent layer and an output layer. According to the invention, the shape of the cavity can be efficiently and accurately inverted.

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 Art

[0002] The statements in this section merely provide background 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 a measured scattered wave, and determining its geometric shape or the distribution of physical parameters. Among them, the inversion method of obtaining the characteristics of a scatterer from a scattered field is based on the theory of electromagnetic scattering. Inverse scattering theory and methods are widely used in many fields such as nondestructive testing, radar imaging, biomedical imaging, and sonar detection. In the inverse scattering problem, it can be divided into external inverse scattering problems and internal inverse scattering problems according to the position of the incident wave. The external inverse scattering problem usually refers to the inference of the shape and other unknown features of the object by collecting scattered wave data outside the object when the object is irradiated by an external incident wave; compared with the external scattering problem, the internal scattering problem is more complicated due to the repeated reflection of the captured scattered waves in the scatterer cavity. At present, the internal inverse scattering problem has attracted a lot of attention and research due to its wide application in industry. In this internal problem, the scatterer is always described as a closed cavity, and the source and receiver are placed in the cavity. The structural integrity is tested according to the scattered waves received by the receiver, and then the possible defects or inhomogeneities are detected. This research direction has become a hot topic in current research, especially in the fields of material testing and structural monitoring.

[0004] At present, the computational methods for solving inverse scattering problems can be divided into two categories: traditional numerical methods and emerging machine learning methods. Among them, the use of traditional numerical methods to solve inverse scattering problems, although it has excellent performance in terms of accuracy, usually requires a lot of computing resources, especially when dealing with complex three-dimensional problems, the computing time and memory consumption are very high; in contrast, the use of machine learning methods can automatically learn the rules from a large amount of scattering data through data-driven, so as to predict and invert in a more efficient way. However, due to the characteristics of the inverse scattering problem itself, such as large data noise and complex nonlinear relationships, the machine learning method is not ideal when dealing with these problems, and it also exposes the problem of insufficient model interpretability. Summary of the invention

[0005] To address the deficiencies in the above-mentioned prior art, the present invention provides an inverse cavity scattering inversion method and system based on an adaptive fuzzy inference system, which reduces the dimension of the acquired scattering data through principal component analysis (PCA) to remove redundant information, improve computational efficiency and reduce the impact of noise; an adaptive fuzzy inference system (ANFIS) is proposed, which combines fuzzy inference algorithms with neural networks to accurately model nonlinear relationships in model data, more accurately extract key features in complex scattering data, enhance the robustness and prediction accuracy of the model, and efficiently and accurately invert the cavity shape, thereby solving the problems of large scattering data noise, complex nonlinear relationships and poor model interpretability existing in the existing methods.

[0006] In a 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 comprises: The incident wave is emitted by the source in the cavity, and the scattered wave is received by a limited number of measurement points in the cavity to obtain the scattering data; The principal component analysis method is used to reduce the dimension of the acquired scattering data; The scattering data after dimension reduction processing is input into the trained adaptive fuzzy inference system, the shape parameters of the cavity are inverted, and the shape of the cavity is reconstructed according to the output inversion results; The adaptive fuzzy reasoning system is a hybrid model that integrates fuzzy logic and neural network. The model is based on the fuzzy reasoning system and represents each step of the fuzzy reasoning process through each layer in the neural network. It includes a membership function layer, a rule layer, a normalization layer, a consequent layer and an output layer in sequence, wherein the membership function layer includes multiple membership functions corresponding to the input, the rule layer includes multiple fuzzy rules in the fuzzy reasoning process, the consequent layer includes consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the final cavity shape parameter inversion result.

[0008] A further technical solution is to use principal component analysis to reduce the dimension of the acquired scattering data, including: Performing data standardization processing on the acquired scattering data to obtain a standardized sample matrix of the scattering data; Calculate the covariance matrix of the standardized sample matrix; Perform eigenvalue decomposition on the covariance matrix and calculate the eigenvalues ​​and eigenvectors; According to the eigenvalues ​​and eigenvectors, several principal components are selected; The original standardized scattering data are projected into the space composed of several selected principal components to obtain the scattering data after dimension reduction.

[0009] According to a further technical solution, the fuzzy reasoning process of the fuzzy reasoning system is: The scattering data after dimension reduction is used as the input of the system. Each input corresponds to multiple membership functions, so that the input space is divided into multiple fuzzy subspaces. Each fuzzy subspace corresponds to a fuzzy rule for control. Each fuzzy rule includes multiple consequent parameters. After the input data is operated by multiple fuzzy rules, the weighted average of all rule outputs is performed to calculate the final cavity shape parameter inversion result.

[0010] A further technical solution is that the adaptive fuzzy inference system is based on the fuzzy inference system and represents each step of the fuzzy inference process through each layer in the neural network, which includes: A membership function layer, including a plurality of membership functions; each node in the layer corresponds to a membership function; The rule layer includes multiple fuzzy rules; each node in this layer corresponds to a fuzzy rule; Normalization layer, used to normalize the weight of each fuzzy rule; each node in this layer corresponds to the weight of the fuzzy rule; The consequent layer includes the consequent parameters corresponding to each fuzzy rule; each node in this layer outputs the inversion result after the consequent parameter operation under the corresponding fuzzy rule; The output layer is used to perform weighted summation on the inversion results under all fuzzy rules to output the final cavity shape parameter inversion results.

[0011] According to a further technical solution, the training process of the adaptive fuzzy inference system is as follows: For various types of cavities with known shape parameters, incident waves are emitted from the source in the cavity, scattered waves are received through a limited number of measurement points in the cavity, scattering data are obtained, and the principal component analysis method is used to reduce the dimension of the obtained scattering data. A data set is constructed based on the scattering data after dimension reduction and the known shape parameter data. The adaptive fuzzy inference system is trained using the data set to optimize the parameters of the membership function and the consequent parameters corresponding to the fuzzy rules, so that the error between the final output prediction result and the target result is minimized and the training is completed; wherein, the prediction result is the inversion result, and the parameters of the membership function are the antecedent parameters. After 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.

[0012] A further technical solution uses a gradient descent method to optimize the antecedent parameters, including: The 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 the parameters are iteratively updated to reduce the error through continuous iterative training. The Kalman filter algorithm is used to optimize the subsequent parameters, including: Introduce observation noise, construct the observation equation of the system prediction output, and then calculate the error between the predicted output and the target output; The Kalman gain is introduced to update the consequent parameters according to the error and the Kalman gain, and the covariance matrix of the observation noise is updated at the same time to reflect the uncertainty changes of the current consequent parameters; Through continuous iterative training, the parameters are iteratively updated to reduce the error.

[0013] In a second aspect, the present invention provides an inverse cavity scattering inversion system based on an adaptive fuzzy inference system.

[0014] An inverse cavity scattering inversion system based on an adaptive fuzzy inference system comprises: A data acquisition module, used to emit incident waves using a source in the cavity, receive scattered waves through a limited number of measurement points in the cavity, and acquire scattered data; A data preprocessing module is used to perform dimension reduction processing on the acquired scattering data using the principal component analysis method; The inverse cavity scattering inversion module is used to input the scattering data after dimension reduction processing 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 results; The adaptive fuzzy reasoning system is a hybrid model that integrates fuzzy logic and neural network. The model is based on the fuzzy reasoning system and represents each step of the fuzzy reasoning process through each layer in the neural network. It includes a membership function layer, a rule layer, a normalization layer, a consequent layer and an output layer in sequence, wherein the membership function layer includes multiple membership functions corresponding to the input, the rule layer includes multiple fuzzy rules in the fuzzy reasoning process, the consequent layer includes consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the final cavity shape parameter inversion result.

[0015] In a third aspect, the present invention further provides an electronic device, comprising: a memory for storing executable instructions; and a processor for implementing the above-mentioned inverse cavity scattering inversion method based on an adaptive fuzzy inference system when executing the executable instructions stored in the memory.

[0016] In a fourth aspect, the present invention further provides a computer-readable storage medium storing executable instructions for causing a processor to execute the executable instructions to implement the above-mentioned inverse cavity scattering inversion method based on an adaptive fuzzy inference system.

[0017] In a fifth aspect, the present invention also provides a computer program product, which includes executable instructions, and the executable instructions are stored in a computer-readable storage medium; wherein, when the processor of the 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.

[0018] One or more of the above technical solutions have the following beneficial effects: 1. Aiming at the problem of inverse acoustic scattering caused by cavities with acoustically soft boundary conditions in acoustics, the present invention proposes an inverse cavity scattering inversion method and system based on an adaptive 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 acoustically soft cavity. In the method proposed by the present invention, the near-field scattering data obtained by measurement is first reduced in dimension by principal component analysis (PCA) to remove redundant information and reduce the complexity of the near-field data; principal component analysis is used for dimensionality reduction, and high-dimensional data is projected into a new low-dimensional space using linear transformation, which retains most of the data variance, thereby reducing redundant information and noise, which not only reduces the computational burden, but also improves the efficiency and stability of the algorithm, and the dimension of the data after dimensionality reduction is reduced, avoiding the risk of overfitting and improving the generalization ability of the model; then, the fuzzy inference algorithm and the neural network are combined to propose an adaptive fuzzy inference system (ANFIS), and the scattering data after dimensionality reduction is used as the input of ANFIS, and the shape parameters of the cavity are used as ANFIS. The output of FIS uses the gradient descent method and the extended Kalman filter (EKF) algorithm to update the antecedent parameters and consequent parameters of the model, respectively, 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, implicit rules can be mined in large-scale data, and uncertainties and nonlinear mapping problems can be handled, so that the nonlinear relationship in the model data can be accurately modeled, key features can be more accurately extracted in complex scattering data, and the robustness and prediction accuracy of the model can be enhanced, thereby achieving efficient prediction and accurate inversion from scattering data to target shape parameters, achieving efficient and accurate inversion of cavity shape, and solving the problems of large scattering data noise, complex nonlinear relationships, and poor model interpretability existing in existing methods.

[0019] 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 fuzzy inference system (ANFIS). The system can not only use 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; in addition, when facing small data sets, the system has strong generalization ability and computational efficiency, avoiding the overfitting problem in traditional methods; through the above-mentioned characteristics of ANFIS, the system can be used to achieve efficient solution to the inverse scattering problem and achieve good interpretability.

[0020] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0022] Figure 1 Schematic diagram of the inverse scattering problem inside the cavity; Figure 2 is a schematic diagram of a dual-input third-order adaptive fuzzy inference system with nine rules in an embodiment of the present invention; Figure 3 Schematic diagram of the geometrical arrangement of the kite cavity in Experiment 1 of the embodiment of the present invention; Figure 4 It is a shape diagram of the inversion kite cavity under the measurement curves of different radii in the embodiment of the present invention; Figure 5 It is a shape diagram of the inverted clover cavity under the measurement curves of different radii in the embodiment of the present invention; Figure 6 It is a shape diagram of the pear-shaped cavity inverted under the measurement curves of different radii in the embodiment of the present invention; Figure 7 : is a shape diagram of the inversion kite cavity under different observation apertures in an embodiment of the present invention; Figure 8 The shape diagram of the inverted clover cavity under different observation apertures in the embodiment of the present invention; Fig. 9 The shape diagram of the inverted pear-shaped cavity under different observation apertures in the embodiment of the present invention; Fig.10 : is a shape diagram of the inversion kite cavity under different Gaussian noise levels in an embodiment of the present invention; Fig.11The shape diagram of the pear-shaped cavity inverted under different Gaussian noise levels in the embodiment of the present invention; Fig.12 is a shape diagram of the inversion kite cavity under different uniform noise levels in an embodiment of the present invention; Fig.13 The shape diagram of the inverted clover cavity under different uniform noise levels in the embodiment of the present invention; Fig.14 The shape diagram of the inverted pear-shaped cavity under different uniform noise levels in the embodiment of the present invention; Fig.15 A comparison diagram of the inversion effects of the two methods under different radius measurement curves in an embodiment of the present invention; Fig.16 A comparison diagram of the inversion effects of the two methods under different observation apertures in an embodiment of the present invention; Fig.17 It is a comparison diagram of the inversion effects of the two methods under 30% Gaussian noise and 20% uniform noise in an embodiment of the present invention. DETAILED DESCRIPTION

[0023] It should be noted that the following detailed descriptions are exemplary only, are intended to describe specific embodiments, are intended to provide further explanation of the present invention, and are not intended to limit exemplary embodiments according to the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those of ordinary skill in the art 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, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0024] First, the internal backscattering problem of the cavity studied in the present invention is clarified as follows: like Figure 1 As shown, assuming is an impenetrable cavity in which R represents a real number, the boundary of the cavity is a bounded simply connected domain, It is a cavity A closed smooth curve in is a A circle with a radius of , represents the coordinate point, then for the internal inverse scattering problem caused by a single point source (i.e., source) in an impenetrable cavity, the scattered field satisfy: (1) (2) In the above formula, is the incident wave, is an imaginary unit, is the wave number, represents the frequency of the time harmonics, is the speed of sound, Indicated in the cavity internal, Indicates that at the cavity boundary superior, is the basic solution of the Helmholtz equation, then: (3) In the above formula, represents the zero-order Hankel function of the first kind, yes A point source within Indicates the coordinate point.

[0025] The forward problem is: According to the incident wave and wave number Determining the scattered field According to the following Theorem 2.1, the scattered field It can be expressed by the combination of double-layer potentials. Among them, Theorem 2.1 is: Approximating the scattered field using the double layer potential ,Right now , then: (4) for and , at continuous density, yes The solution of the internal Dirichlet problem in equations (1)-(2) is as long as is the solution to the following integral equation: (5) in, is the fundamental solution of the two-dimensional Helmholtz equation, The cavity boundary The unit normal vector pointing upwards, is the density function, It's the border The point on It's the border Arc length elements on , used for integration over the boundary.

[0026] Assumptions no The Dirichlet eigenvalue of exist The existence of the solution to this direct scattering problem is well known, and the inverse problem that the present invention is concerned with is: exist The scattered field is generated inside the The measured value is determined by The cavity can be uniquely determined from a point source and a few measurements, making restrictive assumptions about its size. shape.

[0027] Therefore, under the above background, 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), it is used as a hybrid intelligent system that combines the advantages of fuzzy logic and neural networks to solve the inverse cavity scattering inversion problem. The ANFIS can not only use 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, so as to achieve efficient and accurate inversion of the cavity shape.

[0028] Embodiment 1 This embodiment provides an inverse cavity scattering inversion method based on an adaptive fuzzy inference system, and the method specifically includes the following steps: Step S1: Use a source in the cavity to emit an incident wave, receive scattered waves through a limited number of measurement points in the cavity, and obtain scattering data.

[0029] Specifically, an incident wave is emitted from a source in the cavity, and scattered waves are received through a limited number of measurement points (or observation points) in the cavity to obtain scattered data. represents the near-field data obtained by measurement, Indicates The scattering data measured at the observation points are is the number of observation points, express dimensional complex vector space, , is the total number of samples of the scattering data.

[0030] Step S2: Perform dimension reduction processing on the acquired scattering data using principal component analysis.

[0031] Considering that scattering data is usually high-dimensional data, and high-dimensional data contains a large number of features and information, this not only increases the amount of calculation, but also makes the processing more complicated. In particular, when performing inversion solutions, high-dimensional data may cause the calculation time of the algorithm to increase sharply, and may even exceed the limitation of computing resources; in addition, there are often redundant or highly correlated features in scattering data. These redundant information not only increases the calculation burden, but also may cause the model to overfit. Therefore, in this embodiment, for the scattering data obtained by measurement, principal component analysis (PCA) is first used to reduce the dimension, so as to effectively solve the above problems. Among them, using principal component analysis (PCA), high-dimensional scattering data is projected into a new low-dimensional space through linear transformation, so that most of the data variance can be retained, thereby reducing redundant information and noise.

[0032] In this embodiment, the principal component analysis (PCA) method is used to perform dimension reduction processing on the acquired scattering data, including: (1) Data standardization, that is, performing data standardization processing on the acquired scattering data to obtain a standardized sample matrix of the scattering data.

[0033] First, based on the above question, assume that is the total number of samples of scattering data, The number of observation points that affect the scattering data, the scattering field data It is expressed as: (6) in, express dimensional complex vector space.

[0034] Secondly, the above scattering data is standardized, that is, calculation The mean of each column in ,right Subtract the mean of each column from each data in the , so that the mean of each column is zero, and finally the standardized data is obtained Through the above processing, the sample matrix of the original scattering data is converted into: (7) (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. , which can be expressed as: (8) Among them, the element Indicates observation points and The covariance between the observations at each observation point.

[0035] (3) Perform eigenvalue decomposition on the covariance matrix to calculate the eigenvalues ​​and eigenvectors. Specifically, the covariance matrix Perform eigenvalue decomposition to obtain eigenvalues ​​and eigenvectors, which can be expressed as: (9) in, is the eigenvalue, indicating the The variance of the principal component (i.e., observation point). The larger the eigenvalue, the more information the principal component contains in the scattering data. represents the corresponding feature vector.

[0036] (4) Select several principal components based on the eigenvalues ​​and eigenvectors. Specifically, Sort from small to large, and select the first few principal components according to the size of the eigenvalue. When selecting the principal components, you can decide how many principal components to keep based on the proportion of variance explained. Usually, the first principal components, so that it can explain more than 98% of the total variance, which can be expressed as: (10) Among them, 0.98 is the preset threshold value, which can be adjusted and set according to actual conditions.

[0037] (5) Construct the principal components, that is, project the original standardized scattering data onto several selected ( k In the space composed of principal components, the scattering data after dimension reduction is obtained, which can be expressed as: (11) in, Indicates the selected The matrix of eigenvectors.

[0038] In the above way, PCA can help merge the relevant features in the scattering 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 is reduced after dimensionality reduction, which avoids the risk of overfitting and improves the generalization ability of the model, so that the subsequent inversion algorithm can better process and predict unknown data.

[0039] Step S3, input the scattering data after dimension reduction processing 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 results. Among them, the adaptive fuzzy inference system (ANFIS) is a hybrid model that integrates fuzzy logic and neural network, which is used to handle nonlinear system modeling and prediction of complex relationships; the model is based on the fuzzy inference system, and each layer in the neural network represents each step of the fuzzy inference process, including a membership function layer, a rule layer, a normalization layer, a consequent layer and an output layer in sequence, wherein 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 the consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the final cavity shape parameter inversion result.

[0040] Specifically, considering that the core problem of inversion using scattering data lies in the high dimensionality, uncertainty and complexity of nonlinear mapping relationships of the data, this embodiment proposes an adaptive fuzzy inference system ANFIS. The ANFIS model is based on the Takagi-Sugeno fuzzy inference system, and combines the structured expression of the fuzzy inference system with the adaptive learning ability of the neural network. By adaptively adjusting the antecedent fuzzy membership function parameters and the consequent linear parameters, it can mine implicit rules in large-scale data, thereby achieving efficient prediction and accurate inversion from scattering data to target shape parameters.

[0041] Furthermore, the basic structure of the above ANFIS model is: 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 reasoning and adjust parameters through learning to make the model output close to the target value. The construction process of this ANFIS model is: First, the fuzzy reasoning process of the fuzzy reasoning system is clarified. Specifically, the data after the above-mentioned dimensionality reduction processing may be two-dimensional, three-dimensional or four-dimensional. In this embodiment, assuming that the dimension of the scattered data is reduced to two dimensions according to the above-mentioned PCA method, it is expressed as: , and then the two-dimensional data obtained after dimensionality reduction corresponds to two inputs, and the scattered data after dimensionality reduction is and As the input of the system, A cavity shape parameter in As the output of the system, each input is set to correspond to multiple membership functions. In this embodiment, three membership functions are set, such as correspond , correspond Therefore, the input space can be divided into multiple fuzzy subspaces, that is, divided into nine fuzzy subspaces. Each fuzzy subspace corresponds to a fuzzy if-then rule control. The premise part of the rule describes a fuzzy subspace, and the result part specifies the output in the fuzzy subspace.

[0042] Furthermore, the form of each fuzzy rule can be expressed as: :like belong and belong ,but ; in, and The input scattering data are and The fuzzy set of , , is the subsequent parameter, For rules Output.

[0043] Furthermore, the total output of the system is the weighted average of all rule outputs, and its calculation formula is: (12) In the above formula, It's a rule The activation weights are calculated by the membership functions. It should be noted that the dimension of the scattering 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 situation.

[0044] Secondly, based on the fuzzy reasoning system, each layer in the neural network represents each step of the fuzzy reasoning process, thereby constructing a hierarchical network structure of ANFIS. Specifically, the ANFIS can be represented by a five-layer network structure, where each layer in the network corresponds to each step in the fuzzy reasoning process. The network structure is as follows: Figure 2 As shown, including: (1) First layer: membership function layer. The membership function layer includes multiple membership functions, and each node in the layer corresponds to a membership function.

[0045] According to the above reasoning process, assuming that the system has two input and , then each input has three membership functions associated with it, so this layer contains six adaptive nodes (each node corresponds to a membership function), and the output of the node , They are and The membership function can be any continuous and piecewise differentiable function between 0 and 1 as the membership function. In this embodiment, the Gaussian function is selected, which can be expressed as: , (13) in, , is a fuzzy set The center and width of , is a fuzzy set The center and width of the

[0046] (2) The second layer: rule layer. The rule layer includes multiple fuzzy rules, and each node in this layer corresponds to a fuzzy rule.

[0047] In this embodiment, it is assumed that the layer has nine nodes, each node corresponds to a fuzzy rule. and The activation strength of each rule (i.e., rule weight) is calculated by multiplying the membership function values ​​of (14) Furthermore, this layer outputs 9 rule weights .

[0048] (3) The third layer: normalization layer. The normalization layer is used to normalize the weight of each fuzzy rule, and each node in this layer corresponds to the weight of the fuzzy rule.

[0049] In this embodiment, the weight of each rule is normalized so that the sum of the weights of all rules is 1, indicating its relative contribution among all rules. The normalization can be expressed as: (15) 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.

[0050] (4) The fourth layer: the consequent layer. The consequent layer includes the consequent parameters corresponding to each fuzzy rule, and each node in this layer outputs the inversion result after the consequent parameter operation under the corresponding fuzzy rule.

[0051] In this embodiment, each node in the layer outputs the result of each rule, which is the product of the output value of the rule and the rule weight, which can be expressed as: (16) (5) Fifth layer: output layer. This output layer is used to perform weighted summation on the inversion results under all fuzzy rules to output the final cavity shape parameter inversion results, which can be expressed as: (17) Furthermore, based on the adaptive fuzzy inference system constructed above, the system model is trained, and the training process is as follows: First, for various types of cavities with known shape parameters, the source in the cavity is used to emit an incident wave, and the scattered wave is received by a limited number of measurement points in the cavity to obtain the scattering data. , is the total amount of data in the dataset, is the set of training cavity shapes, Indicates cavity The shape parameters, Indicated in the cavity The near-field data obtained by measurement in Indicates The scattering data measured at the observation points are is the number of observation points.

[0052] Secondly, the principal component analysis method is used to reduce the dimension of the acquired scattering data, and a data set is constructed based on the scattering data after dimension reduction and the known shape parameter data.

[0053] Afterwards, the adaptive fuzzy inference system is trained using the data set to optimize the parameters of the membership function and the consequent parameters corresponding to the fuzzy rules, so that the error between the final output prediction result and the target result is minimized and the training is completed; wherein, the prediction result is the inversion result, and the parameters of the membership function are the antecedent parameters. After 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.

[0054] 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.

[0055] (1) Use the gradient descent method to optimize the antecedent parameters.

[0056] Using the gradient descent method, for the antecedent parameter (i.e. the center of the Gaussian membership function ,width etc.) to minimize the predicted output and target output The error function between is used as the target for training. During the training process, the error is propagated layer by layer, the gradient of each antecedent parameter is calculated, and the parameters are iteratively updated to reduce the error through continuous iterative training.

[0057] Among them, the error function can be expressed as: (18) in, is the number of training samples.

[0058] In addition, the update formula of the gradient descent method is: (19) in, Represents the antecedent parameter, such as and , represents the learning rate, is the gradient of the error with respect to the parameters.

[0059] By propagating the error layer by layer, the gradient of each predecessor parameter is calculated and the parameters are iteratively updated to reduce the error.

[0060] (2) The EKF algorithm is used to optimize the subsequent parameters.

[0061] Post-parameters (such as , , The Kalman filter can be used to recursively optimize the nonlinear system parameters, which is efficient and converges quickly. Specifically, the subsequent parameters include the linear coefficients of each rule. , , , which forms the parameter vector , assuming the target output of the system is , the predicted output is , the dynamic optimization of the consequent parameters is realized through EKF, and its basic steps include state prediction and measurement update, specifically: Assume that the dynamic change of the consequent parameters satisfies the state equation: (20) in, Usually refers to the "time step" or "iteration number", that is, the number of times in the time series. The state at a moment; is process noise, which is usually assumed to satisfy zero-mean Gaussian distribution. The covariance matrix of the process noise is .

[0062] The above equation reflects the random drift characteristics of the parameters, that is, the consequent parameters may change slightly at each moment.

[0063] Introducing observation noise, constructing the observation equation representing the system prediction output is: (twenty one) in, is a weighting matrix related to input data and rule strength, is the consequent parameter vector, is the observation noise, which is also assumed to be a zero-mean Gaussian distribution. The covariance matrix of the observation noise is .

[0064] During the EKF update process, the current prediction output is first calculated With target output The error is: (twenty two) Then, the Kalman gain is introduced To adjust the parameters, the calculation formula of the Kalman gain is: (twenty three) in, is the covariance matrix of the posterior parameters, which is used to measure the uncertainty of the current parameter estimate.

[0065] Afterwards, the subsequent parameters are updated according to the error and Kalman gain, which is: (twenty four) At the same time, the covariance matrix of the observation noise is updated to reflect the uncertainty changes of the current parameters. The update formula is: (25) Through the above process, EKF can use the recursive formula to adjust the subsequent parameters in real time. After continuous iterative training, the parameters are iteratively updated to reduce the error, making the predicted output As close to the target output as possible Compared with the traditional least squares method, EKF has dynamic adaptability and can converge to the optimal solution more quickly, and is particularly suitable for processing non-stationary or dynamically changing data scenarios.

[0066] Furthermore, the scattering data after the dimension reduction process 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 results.

[0067] The effectiveness of the method proposed in this embodiment is demonstrated through the following examples, and it is verified that selecting appropriate measurement curves and aperture ranges will lead to better inversion effects. It is also found that the method has a certain robustness to noise in scattered field measurements. Finally, the effects of the adaptive fuzzy inference system and the traditional feedforward neural network on cavity inversion are compared to further verify the effectiveness of the method proposed in this embodiment.

[0068] For simplicity, let the curve is a circle, that is , is a constant that places a single point source at the origin (0,0). The synthetic scattering data on is obtained by linear combination approximation of the double-layer potential using equations (4) and (5). The scattering data after dimensionality reduction using PCA is recorded as , the shape parameter is recorded as , the data set is , 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: Kite shape: , (26) Clover shape: , (27) Pear Shape: , (28) In all the following experiments, according to the complexity of the shapes and experimental demonstration, the total amount of data selected during the experiment for the three different shapes of kite, clover and pear is , , ; Nine receivers are placed equidistantly on the curve The number of observation points on the measured curve is 9; the parameter values ​​of ANFIS are shown in Table 1, where 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 settings of the inverted shape, unless otherwise specified, the blue solid line represents the precise cavity shape boundary, and the red dotted line represents the inverted cavity shape boundary.

[0069] Table 1: ANFIS parameter settings

[0070] Experiment 1: Measuring curves with different radii In this experiment, the wave number , the finite aperture is set to , and set the radii of the three measurement curves to , there is no noise in the near-field data. Taking the kite as an example, the geometric setting is as follows Figure 3 As shown, the black dashed line has a radius of r=0.2, the green dashed line has a radius of r=0.3, the red dashed line has a radius of r=0.4, and the blue solid line represents the precise shape boundary of the kite cavity.

[0071] like Figure 4 , Figure 5 and Figure 6As shown in the figure, the kite-shaped, clover-shaped and pear-shaped cavities are obtained by inverting the measured curves with different radii. The measured radii are , , . It can be seen that, when the total amount of data set and the number of training times remain unchanged, the larger the radius of the measurement curve, the closer the measurement points on the curve are to the cavity boundary, and the less the near-field data obtained will be affected 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 drawn 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.

[0072] Experiment 2: The influence of different observation apertures on the cavity inversion effect. In this experiment, the wave number , the radius of the three shape measurement curves is set to , there is no noise in the near-field data. Consider when the observation aperture is set to , , The inversion results of ANFIS are as follows: Figure 7 , Figure 8 and Fig. 9 shown.

[0073] According to Experiment 1, when the curve measures the radius The cavity inversion effect is the best when the total amount of data set, the number of training times and the curve measurement radius are unchanged. Under the conditions of Figure 7 , Figure 8 , Fig. 9 It can be seen that when the observation aperture When the inversion effect of the three cavities is the best, it can be observed that as the observation aperture range gradually decreases, the inversion effect also decreases. This is because as the observation aperture decreases, the similarity between the near-field data increases, resulting in a gradual decrease in the available cavity information, which pushes up the inversion error of the shape parameters and thus affects the inversion accuracy. Further observation shows that within a certain observation aperture range, ANFIS can still invert the shape information of the cavity more accurately.

[0074] Experiment 3: The influence of different noise levels on the cavity inversion effect. In this experiment, the wave number , the radius of the measured curve is set to , the observation aperture is set to , Gaussian white noise with noise levels of 0%, 10%, and 30% and uniform noise with noise levels of 0%, 10%, and 20% are added to the near-field data respectively.

[0075] In practical applications, near-field data is usually interfered by noise. Therefore, this experiment is used to explore the impact of different noise levels on the inversion effect of the ANFIS model. In order to verify the robustness of the ANFIS model to noise, based on the conclusions of Experiments 1 and 2, this experiment is carried out with the total amount of data set unchanged, the number of training times unchanged, and the curve measurement radius of and the observation aperture is set to Under the conditions of Fig.10 , Fig.11 It can be seen that when the Gaussian white noise level is 0%, 10%, and 30%, the mean square error of the inversion is basically unchanged, and the inverted cavity shape boundary is also very consistent with the real shape boundary. It can be seen that the ANFIS model has good robustness to Gaussian white noise. In addition, the third experiment also explored the influence of different levels of uniform noise on the inversion effect. Fig.12 , Fig.13 and Fig.14 It can be seen that when the uniform noise level is below 10%, the noise has little effect on the inversion effect of the ANFIS model; as the noise level increases, the mean square error of the inversion parameters will also increase, and the inversion effect will become worse and worse; when the noise level is 20%, for slightly complex cavities such as clover-shaped and pear-shaped cavities, there will be a gap between the shape boundary inverted by ANFIS and the real shape boundary, but in general, when the uniform noise level is relatively small, the ANFIS model has a certain robustness to uniform noise.

[0076] Experiment 4: Comparison of the inversion effects of feedforward neural network (FNN) and adaptive fuzzy inference system. The first method is to use a feedforward neural network to directly use the measured scattering data for shape inversion, and the second method is to use the PCA method to reduce the dimension of the obtained scattering data and use ANFIS to perform shape inversion on the reduced-dimensional data. The experiment is as follows: (1) Under the premise that the near-field data is noise-free, the radius of the measurement curve is set to , observe the inversion effect of the kite cavity using two methods.

[0077] (2) Under the premise that the near-field data is noise-free, the observation apertures are set to , , , observe the inversion effect of the kite cavity using two methods.

[0078] (3) In the measurement curve , observation aperture Under the condition of , 30% Gaussian noise and 20% uniform noise are added to the near-field data respectively, and the inversion effects of the two methods are observed.

[0079] In the fourth experiment, under the premise of the same total amount of data set and the same number of training times, different radius measurement curves, measurement apertures and noises are set to compare the effects of the traditional feedforward neural network and the adaptive fuzzy inference system proposed in this embodiment on cavity inversion. Fig.15 and Fig.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 FNN, and the inverted shape boundary is closer to the real boundary, and when , When , ANFIS inversion effect is the best. Fig.17 It can be seen that when 30% Gaussian noise and 20% uniform noise are added to the near-field data, the kite cavity boundary inverted by FNN (feedforward neural network) is very different from the real boundary, indicating that this method is sensitive to noise. When inverted by ANFIS, it can be seen that ANFIS has a certain robustness to both Gaussian and uniform noise. Therefore, the inversion of cavity shape by ANFIS is better than that by traditional FNN inversion.

[0080] In summary, the inverse cavity scattering inversion method based on the adaptive fuzzy inference system proposed in this embodiment reduces the dimension of the obtained scattering data through the PCA method, and designs the adaptive fuzzy inference system ANFIS, which is used to invert the shape parameters of the cavity, and then reconstruct the shape of the cavity. The above experiments have proved 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 a suitable measurement curve and aperture range makes the inversion have a better effect, and verifies that the method has a certain robustness to Gaussian noise and uniform noise, and compares the effect of the adaptive fuzzy inference system and the traditional feedforward neural network inversion cavity, which can also further highlight the comprehensive advantages of ANFIS in complex problems, such as better interpretability, robustness and training efficiency.

[0081] Embodiment 2 This embodiment provides an inverse cavity scattering inversion system based on an adaptive fuzzy inference system, comprising: A data acquisition module, used to emit incident waves using a source in the cavity, receive scattered waves through a limited number of measurement points in the cavity, and acquire scattered data; A data preprocessing module is used to perform dimension reduction processing on the acquired scattering data using the principal component analysis method; The inverse cavity scattering inversion module is used to input the scattering data after dimension reduction processing 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 results; The adaptive fuzzy reasoning system is a hybrid model that integrates fuzzy logic and neural network. The model is based on the fuzzy reasoning system and represents each step of the fuzzy reasoning process through each layer in the neural network. It includes a membership function layer, a rule layer, a normalization layer, a consequent layer and an output layer in sequence, wherein the membership function layer includes multiple membership functions corresponding to the input, the rule layer includes multiple fuzzy rules in the fuzzy reasoning process, the consequent layer includes consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the final cavity shape parameter inversion result.

[0082] Embodiment 3 This embodiment provides an electronic device, including: a memory, used to store executable instructions; and a processor, used to implement the above method provided in this embodiment when executing the executable instructions stored in the memory.

[0083] Embodiment 4 This embodiment also provides a computer-readable storage medium storing executable instructions. When the executable instructions are executed by a processor, the processor will be caused to execute the above method provided in this embodiment.

[0084] Embodiment 5 This embodiment provides a computer program product, which includes an executable instruction, which is a computer instruction; the executable instruction is stored in a computer-readable storage medium. When a processor of an electronic device reads the executable instruction from the computer-readable storage medium and the processor executes the executable instruction, the electronic device executes the above method provided in this embodiment.

[0085] The steps involved in the above embodiments 2 to 5 correspond to the method embodiment 1. For the specific implementation, please refer to the relevant description part of embodiment 1. The term "computer-readable storage medium" should be understood as 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 enable the processor to execute any method in the present invention.

[0086] Those skilled in the art should understand that the modules or steps of the present invention described above can be implemented by a general-purpose computer device, or alternatively, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0087] The above description is only a preferred embodiment of the present invention. Although the specific implementation mode of the present invention is described in conjunction with the accompanying drawings, it is not a limitation of the protection scope of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative work are still within the protection scope of the present invention.

Claims

1. A method for inverse cavity scattering inversion based on an adaptive fuzzy inference system, characterized in that: include: The incident wave is emitted by the source in the cavity, and the scattered wave is received by a limited number of measurement points in the cavity to obtain the scattering data; The principal component analysis method is used to reduce the dimension of the acquired scattering data; The scattering data after dimension reduction processing is input into the trained adaptive fuzzy inference system, the shape parameters of the cavity are inverted, and the shape of the cavity is reconstructed according to the output inversion results; The adaptive fuzzy reasoning system is a hybrid model that integrates fuzzy logic and neural network. The model is based on the fuzzy reasoning system and represents each step of the fuzzy reasoning process through each layer in the neural network. It includes a membership function layer, a rule layer, a normalization layer, a consequent layer and an output layer in sequence, wherein the membership function layer includes multiple membership functions corresponding to the input, the rule layer includes multiple fuzzy rules in the fuzzy reasoning process, the consequent layer includes consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the final cavity shape parameter inversion result.

2. The inverse cavity scattering inversion method based on an adaptive fuzzy inference system according to claim 1, characterized in that: The principal component analysis method is used to reduce the dimension of the acquired scattering data, including: Performing data standardization processing on the acquired scattering data to obtain a standardized sample matrix of the scattering data; Calculate the covariance matrix of the standardized sample matrix; Perform eigenvalue decomposition on the covariance matrix and calculate the eigenvalues ​​and eigenvectors; According to the eigenvalues ​​and eigenvectors, several principal components are selected; The original standardized scattering data are projected into the space composed of several selected principal components to obtain the scattering data after dimension reduction.

3. The inverse cavity scattering inversion method based on an adaptive fuzzy inference system according to claim 1, characterized in that: The fuzzy reasoning process of the fuzzy reasoning system is: The scattering data after dimension reduction is used as the input of the system. Each input corresponds to multiple membership functions, so that the input space is divided into multiple fuzzy subspaces. Each fuzzy subspace corresponds to a fuzzy rule for control. Each fuzzy rule includes multiple consequent parameters. After the input data is operated by multiple fuzzy rules, the weighted average of all rule outputs is performed to calculate the final cavity shape parameter inversion result.

4. 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 represents each step of the fuzzy inference process through each layer in the neural network, which includes: A membership function layer, including a plurality of membership functions; each node in the layer corresponds to a membership function; The rule layer includes multiple fuzzy rules; each node in this layer corresponds to a fuzzy rule; Normalization layer, used to normalize the weight of each fuzzy rule; each node in this layer corresponds to the weight of the fuzzy rule; The consequent layer includes the consequent parameters corresponding to each fuzzy rule; each node in this layer outputs the inversion result after the consequent parameter operation under the corresponding fuzzy rule; The output layer is used to perform weighted summation on the inversion results under all fuzzy rules to output the final cavity shape parameter inversion results.

5. 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: For various types of cavities with known shape parameters, incident waves are emitted from the source in the cavity, scattered waves are received through a limited number of measurement points in the cavity, scattering data are obtained, and the principal component analysis method is used to reduce the dimension of the obtained scattering data. A data set is constructed based on the scattering data after dimension reduction and the known shape parameter data. The adaptive fuzzy inference system is trained using the data set to optimize the parameters of the membership function and the consequent parameters corresponding to the fuzzy rules, so that the error between the final output prediction result and the target result is minimized and the training is completed; wherein, the prediction result is the inversion result, and the parameters of the membership function are the antecedent parameters. After 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.

6. The inverse cavity scattering inversion method based on an adaptive fuzzy inference system as claimed in claim 5, characterized in that: The gradient descent method is used to optimize the antecedent parameters, including: The 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 the parameters are iteratively updated to reduce the error through continuous iterative training. The Kalman filter algorithm is used to optimize the subsequent parameters, including: Introduce observation noise, construct the observation equation of the system prediction output, and then calculate the error between the predicted output and the target output; The Kalman gain is introduced to update the consequent parameters according to the error and the Kalman gain, and the covariance matrix of the observation noise is updated at the same time to reflect the uncertainty changes of the current consequent parameters; Through continuous iterative training, the parameters are iteratively updated to reduce the error.

7. An inverse cavity scattering inversion system based on an adaptive fuzzy inference system, characterized in that: include: A data acquisition module, used to emit incident waves using a source in the cavity, receive scattered waves through a limited number of measurement points in the cavity, and acquire scattered data; A data preprocessing module is used to perform dimension reduction processing on the acquired scattering data using the principal component analysis method; The inverse cavity scattering inversion module is used to input the scattering data after dimension reduction processing 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 results; The adaptive fuzzy reasoning system is a hybrid model that integrates fuzzy logic and neural network. The model is based on the fuzzy reasoning system and represents each step of the fuzzy reasoning process through each layer in the neural network. It includes a membership function layer, a rule layer, a normalization layer, a consequent layer and an output layer in sequence, wherein the membership function layer includes multiple membership functions corresponding to the input, the rule layer includes multiple fuzzy rules in the fuzzy reasoning process, the consequent layer includes consequent parameters corresponding to each fuzzy rule, and the output layer is used to output the final cavity shape parameter inversion result.

8. An electronic device, characterized in that: include: A memory for storing executable instructions; A processor, used to implement the inverse cavity scattering inversion method based on an adaptive fuzzy inference system as described in any one of claims 1 to 6 when executing the executable instructions stored in the memory.

9. A computer-readable storage medium, characterized in that: Executable instructions are stored, which are used to cause the processor to execute the executable instructions to implement the inverse cavity scattering inversion method based on an adaptive fuzzy inference system as described in any one of claims 1 to 6.

10. A computer program product, characterized in that The computer program product includes executable instructions 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, the inverse cavity scattering inversion method based on an adaptive fuzzy inference system as described in any one of claims 1 to 6 is implemented.

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