Impact force recognition method, device and equipment based on Fourier neural operator and readable storage medium

Abstract

The invention discloses an impact force recognition method, device and equipment based on a Fourier neural operator, and a readable storage medium, and relates to the field of structural impact monitoring, and the method comprises the steps: inputting obtained to-be-recognized system response data into a target Fourier neural operator model, the method comprises the following steps: performing linear transformation on system response data to be identified through an inverse operator module to obtain a high-dimensional input signal, performing iterative updating such as zero-filling processing on the high-dimensional input signal to obtain a target high-resolution up-sampling signal, and performing linear transformation on the target high-resolution up-sampling signal to obtain a target excitation function; and finally, pooling operation of a space dimension and a time dimension is performed on the target excitation function through a pooling module, so that a position identification result and a time history reconstruction result of the impact force can be obtained. According to the method, a high-resolution impact force positioning result can be provided under the conditions of arrangement of a small number of sensors and limited data acquisition, and instability in an inversion process is avoided, so that a stable and reliable impact force recognition result is provided.

Description

Technical Field

[0001] The present application relates to the technical field of structural impact monitoring, and in particular to an impact force identification method, apparatus, device and readable storage medium based on a Fourier neural operator. Background Art

[0002] Impact force identification is a key technology in structural design, condition assessment, and health monitoring. Impact loads, as a common external excitation source, have the potential to induce significant stress and structural damage, especially in complex environments and extreme operating conditions. For example, in wind power generation, wind turbine blades are constantly exposed to a variety of impact threats, including falling tools, debris impacts, hail, rock impacts, and bird strikes. In civil engineering, bridges and high-rise buildings may be affected by vehicle collisions, earthquake shocks, or explosive loads. In industrial equipment, heavy machinery and piping systems may be subjected to sudden loads due to operational errors or external impacts. These impact events can not only cause localized structural damage but also trigger chain reactions that significantly shorten equipment service life or even cause catastrophic failure. Therefore, accurately identifying impact loads is crucial for improving structural safety, extending equipment life, and optimizing maintenance strategies.

[0003] In related technologies, impact load identification is often achieved by inferring the impact force from the system response. This involves establishing a transfer function relationship between the input force and the structural vibration response in the time or frequency domain to invert the impact force. Ideally, the input force can be inferred from the measured data by directly inverting the transfer function matrix. However, since the transfer function matrix often suffers from pathological problems (such as excessive condition number or insufficient rank), direct inversion can lead to unstable identification results. This is especially true for large and complex structures, where the size of the transfer matrix can amplify measurement noise and errors, further exacerbating the unreliability of the inversion process.

[0004] Furthermore, with the rapid development of artificial intelligence (AI), the application of deep learning in impact force reconstruction and localization has been widely explored. However, this requires a large amount of training data. However, for impact force identification, the training data needs to cover a wide range of spatial and temporal variability. However, obtaining such a comprehensive dataset is often not feasible in practical engineering. Therefore, with limited training samples, generalization ability remains a key issue. In particular, when the test conditions exceed the range of the training samples, the model's performance may drop significantly. Summary of the Invention

[0005] The present application provides an impact force identification method, apparatus, device and readable storage medium based on a Fourier neural operator, which can provide high-resolution impact force positioning results with a small number of sensors arranged and limited data collection, and avoid instability in the inversion process to provide stable and reliable impact force identification results.

[0006] In a first aspect, an embodiment of the present application provides an impact force identification method based on a Fourier neural operator, comprising:

[0007] Obtaining response data of the system to be identified;

[0008] Inputting the response data of the system to be identified into the target Fourier neural operator model including the inverse operator module and the pooling module to output the position identification result and time history reconstruction result of the impact force;

[0009] Among them, the inverse operator module is used to perform linear transformation on the response data of the identification system to obtain a high-dimensional input signal, iteratively update the high-dimensional input signal to obtain a target high-resolution up-sampling signal, and linearly transform the target high-resolution up-sampling signal to obtain a target excitation function, and the iterative update includes zero-filling processing; the pooling module is used to perform pooling operations on the target excitation function in the spatial dimension and the time dimension respectively to obtain the position recognition result and the time history reconstruction result.

[0010] In combination with the first aspect, in one embodiment, the iterative updating of the high-dimensional input signal to obtain the target high-resolution up-sampled signal includes:

[0011] Performing Fourier transform, operator conversion, zero padding and inverse Fourier transform on the high-dimensional input signal in sequence to obtain a first high-resolution up-sampled signal;

[0012] Performing a linear transformation on the high-dimensional input signal, and superimposing the linear transformation result with the first high-resolution up-sampled signal to obtain a second high-resolution up-sampled signal;

[0013] A preset number of iterative updates are performed based on the second high-resolution up-sampled signal to obtain a target high-resolution up-sampled signal.

[0014] In combination with the first aspect, in one embodiment, the step of sequentially performing Fourier transform, operator conversion, zero padding, and inverse Fourier transform on the high-dimensional input signal to obtain the first high-resolution upsampled signal includes:

[0015] Perform Fourier transform on the high-dimensional input signal to obtain the initial frequency domain signal;

[0016] Perform operator transformation on the initial frequency domain signal to obtain the target frequency domain signal;

[0017] Performing zero-filling processing on the target frequency domain signal to obtain a zero-filled frequency domain signal;

[0018] Performing an inverse Fourier transform on the zero-padded frequency domain signal to obtain a first high-resolution up-sampled signal.

[0019] In combination with the first aspect, in one implementation, the expression of the zero-filled frequency domain signal is:

[0020]

[0021] Where, represents the zero-filled frequency domain signal, X[k] represents the target frequency domain signal, k represents the frequency domain signal sampling point, n s Indicates the number of sensors, n′ s Indicates the new length corresponding to the zero-padded signal.

[0022] In conjunction with the first aspect, in one implementation, the iterative update expression is:

[0023]

[0024] R φ =F(κ φ )

[0025] Where ξ represents the spatial position data and time data in the response data of the system to be identified, v m (ξ) represents the corresponding high-resolution up-sampled signal after the mth iteration update, σ represents the nonlinear activation function, represents the integral operator, W represents the linear transformation, F -1 represents the inverse Fourier transform, Represents the frequency domain signal obtained after Fourier transform, R φ represents the operator, κ φ Represents the kernel function.

[0026] In combination with the first aspect, in one embodiment, the method for constructing the target Fourier neural operator model is:

[0027] Acquiring training data, the training data including historical system response data, the historical system response data including historical spatial position data and historical time data corresponding to the impact force, the historical spatial position data being spatial position data obtained by modeling based on a truncated Gaussian distribution function;

[0028] The initial Fourier neural operator model is trained based on the training data to obtain a target Fourier neural operator model.

[0029] In a second aspect, an embodiment of the present application provides an impact force recognition device based on a Fourier neural operator, comprising:

[0030] A data acquisition unit, which is used to acquire response data of the system to be identified;

[0031] An impact force identification unit is used to input the response data of the system to be identified into a target Fourier neural operator model including an inverse operator module and a pooling module to output the position identification result and time history reconstruction result of the impact force; wherein, the inverse operator module is used to perform a linear transformation on the response data of the system to be identified to obtain a high-dimensional input signal, iteratively update the high-dimensional input signal to obtain a target high-resolution up-sampling signal, and linearly transform the target high-resolution up-sampling signal to obtain a target excitation function, and the iterative update includes zero-filling processing; the pooling module is used to perform pooling operations on the target excitation function in the spatial dimension and the time dimension respectively to obtain the position identification result and the time history reconstruction result.

[0032] In conjunction with the second aspect, in one implementation, the inverse operator module is specifically configured to:

[0033] Performing Fourier transform, operator conversion, zero padding and inverse Fourier transform on the high-dimensional input signal in sequence to obtain a first high-resolution up-sampled signal;

[0034] Performing a linear transformation on the high-dimensional input signal, and superimposing the linear transformation result with the first high-resolution up-sampled signal to obtain a second high-resolution up-sampled signal;

[0035] A preset number of iterative updates are performed based on the second high-resolution up-sampled signal to obtain a target high-resolution up-sampled signal.

[0036] In conjunction with the second aspect, in one implementation, the inverse operator module is further configured to:

[0037] Perform Fourier transform on the high-dimensional input signal to obtain the initial frequency domain signal;

[0038] Perform operator transformation on the initial frequency domain signal to obtain the target frequency domain signal;

[0039] Performing zero-filling processing on the target frequency domain signal to obtain a zero-filled frequency domain signal;

[0040] Performing an inverse Fourier transform on the zero-padded frequency domain signal to obtain a first high-resolution up-sampled signal.

[0041] In conjunction with the second aspect, in one implementation, the expression of the zero-filled frequency domain signal is:

[0042]

[0043] Where, represents the zero-filled frequency domain signal, X[k] represents the target frequency domain signal, k represents the frequency domain signal sampling point, n s Indicates the number of sensors, n′ s Indicates the new length corresponding to the zero-padded signal.

[0044] In conjunction with the second aspect, in one implementation, the iterative update expression is:

[0045]

[0046] R φ =F(κ φ )

[0047] Where ξ represents the spatial position data and time data in the response data of the system to be identified, v m (ξ) represents the corresponding high-resolution up-sampled signal after the mth iteration update, σ represents the nonlinear activation function, represents the integral operator, W represents the linear transformation, F -1 represents the inverse Fourier transform, Represents the frequency domain signal obtained after Fourier transform, R φ represents the operator, κ φ Represents the kernel function.

[0048] In conjunction with the second aspect, in one embodiment, the method for constructing the target Fourier neural operator model is:

[0049] Acquiring training data, the training data including historical system response data, the historical system response data including historical spatial position data and historical time data corresponding to the impact force, the historical spatial position data being spatial position data obtained by modeling based on a truncated Gaussian distribution function;

[0050] The initial Fourier neural operator model is trained based on the training data to obtain a target Fourier neural operator model.

[0051] In a third aspect, an embodiment of the present application provides an impact force identification device based on a Fourier neural operator, wherein the impact force identification device based on a Fourier neural operator includes a processor, a memory, and an impact force identification program based on a Fourier neural operator stored in the memory and executable by the processor, wherein when the impact force identification program based on a Fourier neural operator is executed by the processor, the steps of the impact force identification method based on a Fourier neural operator as described above are implemented.

[0052] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, on which is stored an impact force recognition program based on a Fourier neural operator. When the impact force recognition program based on a Fourier neural operator is executed by a processor, the steps of the aforementioned impact force recognition method based on a Fourier neural operator are implemented.

[0053] The beneficial effects of the technical solutions provided in the embodiments of the present application include:

[0054] The inverse operator module in the target Fourier neural operator model performs a linear transformation on the response data of the system to be identified to obtain a high-dimensional input signal, and iteratively updates the high-dimensional input signal including zero-padding processing to obtain a target high-resolution up-sampled signal, and then linearly transforms the target high-resolution up-sampled signal to obtain a target excitation function; then, the target excitation function is pooled in the spatial dimension and the temporal dimension respectively, so as to obtain the impact force position identification result and the time history reconstruction result. It can be seen that the present application uses the Fourier neural operator model to perform load inversion identification, that is, directly fitting the inverse operator corresponding to the physical operator to complete the mapping of the system response function to the excitation function without the need for matrix inversion to avoid the instability caused by the inversion, and at the same time, combined with the zero-padding processing, provides stable and reliable impact force identification results for complex structures; in addition, the Fourier operator model fits the mapping relationship between functions, so it does not require a large amount of training data, and it uses Fourier transform to convert the input function to the frequency domain, so that the operator learns from the global frequency representation rather than the local details, so as to improve the generalization ability under the condition of a small number of sensor arrangements and limited data collection, thereby providing high-resolution impact force positioning results. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a flow chart of an embodiment of the impact force recognition method based on Fourier neural operator of this application;

[0056] Figure 2 This is a schematic diagram of an experimental scenario involving an experimental steel beam as an experimental object in the embodiment of the present application;

[0057] Figure 3 This is a schematic diagram of positioning results using a test steel beam as an experimental object involved in the embodiment of the present application;

[0058] Figure 4 This is a schematic diagram of the reconstruction results of the experimental steel beam involved in the embodiment of the present application;

[0059] Figure 5 Schematic diagram of an experimental scenario involving a scaled carbon fiber wind turbine blade as an experimental object in an embodiment of the present application;

[0060] Figure 6 A schematic diagram of the position between the fixed end and the accelerometer on the scaled carbon fiber wind turbine blade involved in the embodiment of the present application;

[0061] Figure 7 This is a schematic diagram of positioning results of a scaled carbon fiber wind turbine blade used as an experimental object in an embodiment of the present application;

[0062] Figure 8 This is a schematic diagram of the reconstruction results of a scaled carbon fiber wind turbine blade used as an experimental object in the embodiment of the present application;

[0063] Figure 9 This is a schematic diagram of the hardware structure of the impact force recognition device based on Fourier neural operator involved in the embodiment of the present application. DETAILED DESCRIPTION

[0064] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0065] In order to make the objectives, technical solutions and advantages of this application clearer, the implementation methods of this application will be further described in detail below with reference to the accompanying drawings.

[0066] In a first aspect, an embodiment of the present application provides an impact force recognition method based on a Fourier neural operator.

[0067] In one embodiment, referring to Figure 1 , Figure 1 This is a flow chart of an embodiment of the impact force identification method based on Fourier neural operator in this application. Figure 1 As shown in FIG, the impact force recognition method based on Fourier neural operator includes:

[0068] Step S10: Obtain response data of the system to be identified.

[0069] Exemplarily, in this embodiment, the system response data to be identified refers to the system response data corresponding to the target structure that needs to perform impact force identification, that is, by performing impact force identification on the system response data to be identified, the position identification result and time reconstruction result of the impact force of the target structure can be determined; it should be noted that the system response data to be identified includes but is not limited to acceleration, strain or displacement in different spatial and temporal dimensions; wherein u(x, t) can be used to represent the system response data to be identified, x represents the spatial dimension, and t represents the temporal dimension.

[0070] Step S20: Input the response data of the system to be identified into the target Fourier neural operator model including the inverse operator module and the pooling module to output the position recognition result and the time history reconstruction result of the impact force; wherein, the inverse operator module is used to perform linear transformation on the response data of the system to be identified to obtain a high-dimensional input signal, iteratively update the high-dimensional input signal to obtain the target high-resolution up-sampling signal, linearly transform the target high-resolution up-sampling signal to obtain the target excitation function, and the iterative update includes zero-filling processing; the pooling module is used to perform pooling operations on the target excitation function in the spatial dimension and the time dimension respectively to obtain the position recognition result and the time history reconstruction result.

[0071] For example, it should be understood that the current direct measurement of impact loads through force sensors faces many challenges in engineering practice: on the one hand, impact events are often instantaneous and random, making it difficult to pre-arrange sensors; on the other hand, force sensors are usually expensive, and their installation locations are limited by structural design, making them unsuitable for high-temperature, high-pressure, and other scenarios. Therefore, engineering more often uses methods to infer impact forces from system responses, that is, to indirectly identify the characteristics of impact loads by measuring the dynamic response of the structure (such as acceleration, strain, or displacement); among these, traditional methods are mainly based on modal analysis, frequency domain analysis, or time domain analysis techniques, which estimate the position, magnitude, and time history of the impact force by establishing a dynamic model of the structure and using an inversion algorithm, but they suffer from the problem of unstable identification results. In addition, in recent years, with the rapid development of artificial intelligence technology, intelligent methods based on machine learning and deep learning have gradually become a research hotspot. These methods can train models through large amounts of data, automatically extract impact features and achieve high-precision impact force identification, especially when dealing with complex structures and multi-source impact scenarios. They show significant advantages; however, they rely on a large amount of training data, and for the impact force identification task, obtaining such a comprehensive data set is often not feasible in actual engineering. Therefore, when training samples are limited, its generalization ability remains a key issue.

[0072] Based on this, this embodiment will use the Fourier Neural Operator model (FNO) to construct an inverse operator By using the inverse operator To complete the inversion of the excitation function, it is possible to provide high-resolution impact force positioning results with a small number of sensors and limited data collection, and avoid instability in the inversion process to provide stable and reliable impact force identification results.

[0073] Among them, it can be understood that for a physical operator For example, given any activation function f(x,t), through this physical operator The dynamic system response u(x,t) can be obtained; naturally, there will be an inverse operator The inversion from the dynamic system response to the excitation function can be completed, that is, However, load inversion identification based on physical system models usually involves inverting the transfer function matrix between the load and the system response. However, the transfer function matrix often has ill-posed problems, and direct inversion will lead to unstable identification results. In particular, when using a small number of system response sensors to invert load identification results with high spatial resolution, the instability will be aggravated.

[0074] Therefore, this embodiment will use the FNO model to construct an inverse operator Make it as close as possible to the inverse operator Right now So that when the FNO model is fully trained to obtain the target Fourier neural operator model (i.e., the target FNO model), the inverse operator it constructs The dynamic system response u(x,t) is used as the input function to output the excitation function This completes the inversion of the activation function, namely It can be seen that in this embodiment, there is no matrix inversion in the process of load inversion identification using FNO, which avoids the instability caused by inversion, and it directly fits the inverse operator. To complete the mapping of the system response function to the excitation function, thereby further avoiding the instability of the inversion process.

[0075] Specifically, the target Fourier neural operator model in this embodiment includes but is not limited to the inverse operator module And pooling module M; Among them, the inverse operator module It mainly consists of three parts, namely, lifting, iterative updating and projection. For the sake of clarity, this embodiment will use the symbol ξ to uniformly represent the spatial variable x and the time variable t, that is, use u(ξ) to represent the response data u(x, t) of the system to be identified. Therefore, when the response data u(ξ) of the system to be identified is input into the target Fourier neural operator model, u(ξ) will first be linearly transformed P to lift the input to a higher-dimensional representation, that is, to obtain a high-dimensional input signal v0, that is, v0 = P(u(ξ)); then, this representation is iteratively updated from v0 to v1,…,v m , that is, the target high-resolution up-sampled signal v is obtained m ; Then upsample the target high resolution signal v m A linear transformation Q is performed to project the lifted representation back into the output space, yielding the function f(ξ)=Q(v m (ξ)), which is the target activation function to be identified.

[0076] Furthermore, it should be noted that in the FNO model, the continuous Fourier transform (F) is approximated by the discrete Fourier transform (DFT), which requires uniformly spaced sample data in the spatial and temporal domains. Furthermore, the number and location of the sampling points remain unchanged before and after the Fourier transform. Therefore, for the impact force identification task, the identified impact force location is confined to the sampling grid, and unsampled locations are not identified. This constraint means that the spatial resolution of the force identification task is limited by the number of available sensors. To address this issue, this embodiment implements zero padding in the frequency domain (zero padding refers to adding high-frequency components with zero values ​​to expand the frequency domain signal). Specifically, this embodiment incorporates zero padding as part of the iterative update process to zero-pad the frequency domain signal during the iterative update, thereby expanding the frequency domain signal by adding high-frequency components with zero values ​​in the spatial dimension. This process does not introduce new spectral content, but produces an upsampled version of the original domain when performing the inverse DFT (i.e., IDFT), thereby freeing the identified excitation locations from being restricted to the deployed sensor locations.

[0077] After upsampling the target excitation function f(ξ), this embodiment defines two additional pooling layers M for the recognition of the excitation of impact force. l (·) and M t (·), that is, the pooling module includes the pooling layer M l (·) and pooling layer M t (·), to be used as output f(ξ) to the predicted position (i.e., the position recognition result ) and the reconstruction time history (i.e., the reconstruction results of the time course) ), which can provide the impact force positioning and recognition results, that is,

[0078]

[0079] and

[0080] It is worth noting that other neural network models fit point-to-point mappings between data, and a small number of point-to-point mappings are difficult to cover a wide range of spatial and temporal variability, so a large amount of training data is required; however, compared with other neural network models, the FNO model in this embodiment fits the mapping relationship between functions, so it does not require a large amount of training data; secondly, the FNO model in this embodiment completes operator learning in the Fourier domain, that is, FNO uses Fourier transform to convert the input function into the frequency domain, so that the operator learns from the global frequency representation rather than the local details, and this global representation in the frequency domain is particularly advantageous in the case of a small amount of data, because it makes FNO less sensitive to the local features or discretization degree of the input data, that is, it makes the model more generalizable to the data. Therefore, this embodiment can improve the generalization ability with a small number of sensor arrangements and limited data collection, thereby providing high-resolution impact force positioning results.

[0081] Furthermore, in one embodiment, the iterative updating of the high-dimensional input signal to obtain the target high-resolution up-sampled signal includes:

[0082] Performing Fourier transform, operator conversion, zero padding and inverse Fourier transform on the high-dimensional input signal in sequence to obtain a first high-resolution up-sampled signal;

[0083] Performing a linear transformation on the high-dimensional input signal, and superimposing the linear transformation result with the first high-resolution up-sampled signal to obtain a second high-resolution up-sampled signal;

[0084] A preset number of iterative updates are performed based on the second high-resolution up-sampled signal to obtain a target high-resolution up-sampled signal.

[0085] Exemplarily, in this embodiment, the input signal represented in a high dimension (i.e., a high-dimensional input signal) is sequentially subjected to Fourier transform, operator conversion, zero-filling processing, and inverse Fourier transform to achieve high-dimensional and high-resolution conversion, thereby obtaining a first high-resolution up-sampled signal; the high-dimensional input signal is then linearly transformed W and superimposed with the obtained signal with a higher spatial resolution (i.e., the first high-resolution up-sampled signal) to obtain a second high-resolution up-sampled signal; the above process is repeated based on the second high-resolution up-sampled signal, and after m iterative updates, the operator learning is completed to obtain the target high-resolution up-sampled signal.

[0086] Furthermore, in one embodiment, the step of sequentially performing Fourier transform, operator conversion, zero padding, and inverse Fourier transform on the high-dimensional input signal to obtain the first high-resolution upsampled signal includes:

[0087] Perform Fourier transform on the high-dimensional input signal to obtain the initial frequency domain signal;

[0088] Perform operator transformation on the initial frequency domain signal to obtain the target frequency domain signal;

[0089] Performing zero-filling processing on the target frequency domain signal to obtain a zero-filled frequency domain signal;

[0090] Performing an inverse Fourier transform on the zero-padded frequency domain signal to obtain a first high-resolution up-sampled signal.

[0091] Exemplarily, in this embodiment, the high-dimensional input signal is first Fourier transformed to obtain a frequency domain signal representation (i.e., the initial frequency domain signal); and an operator R is established in the frequency domain to use the operator R to perform an operator transformation on the initial frequency domain signal; thereafter, the converted signal (i.e., the target frequency domain signal) is zero-filled to obtain a spatially upsampled signal (i.e., the zero-filled frequency domain signal); finally, the spatially upsampled signal is inverse Fourier transformed to obtain a signal with a higher spatial resolution (i.e., the first high-resolution upsampled signal).

[0092] Furthermore, in one embodiment, the expression for iterative update is:

[0093]

[0094] R φ =F(κ φ )

[0095] Where ξ represents the spatial position data and time data in the response data of the system to be identified, v m (ξ) represents the corresponding high-resolution up-sampled signal after the mth iteration update, σ represents the nonlinear activation function, represents the integral operator, W represents the linear transformation, F -1 represents the inverse Fourier transform, Represents the frequency domain signal obtained after Fourier transform, R φ represents the operator, κ φ Represents the kernel function.

[0096] Exemplarily, in this embodiment, each iterative update in the target Fourier neural operator model is performed by combining the integral operator It is realized by linear transformation W and nonlinear activation function σ. The specific expression is:

[0097]

[0098] It should be noted that the number of iterative updates, that is, the size of m, can be determined according to the complexity of the data and is not limited here; It represents the result of performing the integral operator operation on the high-resolution up-sampled signal obtained by iterative update with ξ as input. Defined as:

[0099]

[0100] It should be understood that the kernel function κ in this embodiment φ It is modeled as a neural network with φ as a parameter, where the parameter φ can be learned through the training data set, D represents the function domain of ξ, and y represents the empty variable; this embodiment will be implemented by applying κ φ (ξ,y)=κ φ (ξ-y) and assuming translation invariance, the above equation (2) can be simplified to a convolution operation, which can be efficiently calculated in Fourier space using the convolution theorem. Specifically, suppose F represents the Fourier transform, F -1 represents the inverse function of Fourier transform, then equation (2) can be converted to:

[0101]

[0102] In this way, the kernel function κ can be parameterized directly in Fourier space φ , that is, let R φ is the kernel function κ φ Fourier transform and expressed as a neural network with φ as parameter, that is, R φ =F(κ φ ), then formula (3) is converted to:

[0103]

[0104] Furthermore, in one embodiment, the expression of the zero-filled frequency domain signal is:

[0105]

[0106] Where, represents the zero-filled frequency domain signal, X[k] represents the target frequency domain signal, k represents the frequency domain signal sampling point, n s Indicates the number of sensors, n′ s Indicates the new length corresponding to the zero-padded signal.

[0107] In this embodiment, a novel spatial upsampling method is provided to achieve signal upsampling, so that the identifiable excitation location is no longer limited to the deployed sensor location. The following explanation will be based on a one-dimensional signal as an example, but it can certainly be expanded to multi-dimensional signals.

[0108] Specifically, consider the time domain discrete signal x[n] sampled at a given sensor position, whose DFT is:

[0109]

[0110] Where X[k] is the frequency domain representation of x[n], k is the frequency domain signal sampling point, n is the time domain signal sampling point, and n s is the preset number of sensors; i represents an imaginary unit.

[0111] Zero padding refers to adding high-frequency components with zero values ​​to expand the frequency domain signal. The process is mathematically expressed as:

[0112]

[0113] Where, is the zero-filled frequency domain signal, n′ s The new length of the zero-padded signal.

[0114] Zero-fill signal The IDFT is given by:

[0115]

[0116] Where, is the upsampled signal, whose length is n′ s (n′ s >n s ). It should be noted that for traditional spatial upsampling, after IDFT, The resolution is still determined by n s Control, in addition, if not upsampled to n′ s , then its identifiable excitation locations will be limited to the deployed sensor locations.

[0117] This embodiment incorporates the above-mentioned spatial upsampling mechanism into the FNO framework, that is, in the iterative update, the frequency signal (i.e., the target frequency domain signal) Zero padding is performed to expand the frequency domain signal q by adding high-frequency components with zero values ​​in the spatial dimension; then the inverse Fourier transform F is applied -1 When the force is detected, an upsampled signal is generated in the spatial dimension. The length of the upsampled signal can be adjusted according to the spatial recognition resolution required by the recognition task, so that the identifiable stimulus location is no longer limited to the deployed sensor location. It should be noted that the spatial upsampling in this embodiment can be performed across multiple iterative updates, and the spatial resolution of the force recognition solution can be improved through the above-mentioned spatial upsampling method, thereby providing stimulus recognition results for more spatial locations.

[0118] Furthermore, in one embodiment, the method for constructing the target Fourier neural operator model is:

[0119] Acquiring training data, the training data including historical system response data, the historical system response data including historical spatial position data and historical time data corresponding to the impact force, the historical spatial position data being spatial position data obtained by modeling based on a truncated Gaussian distribution function;

[0120] The initial Fourier neural operator model is trained based on the training data to obtain a target Fourier neural operator model.

[0121] For example, in this embodiment, the initial Fourier neural operator model is trained by a training data set containing system response and excitation to generate an approximate The inverse operator The target Fourier neural operator model of ; when the new system response data is input, as long as it is in the same function space as the training data, the inverse operator It can output accurate excitation function to complete the identification of excitation.

[0122] It should be noted that the excitation of impact force is usually represented in a very sparse form in space (that is, it only appears at a single position among all possible excitation positions), and this extremely sparse form of data is usually not conducive to the training of neural networks. To address this problem, this embodiment will use a truncated Gaussian distribution function to model the force position, that is, it converts discrete numerical data (desired position μ) into a continuous function representation. This provides a continuous form of data as training data for the FNO model to address the adverse effects of the extremely sparse form of impact force data. Here is an example of a one-dimensional problem (which can be expanded to multi-dimensional problems):

[0123]

[0124] Where μ is the mean, σ is the predefined standard deviation, and Φ is the cumulative distribution function of the standard normal distribution. a and b are defined as the cutoff limits, which correspond to the physical boundaries of the structure. That is, the specific values ​​of a and b can be determined by the physical boundaries of the structure.

[0125] Based on this, when constructing historical spatial position data corresponding to the impact force and historical system response data corresponding to the historical time data as training data, this embodiment will use a truncated Gaussian distribution function to model the historical spatial position data; then the FNO model is trained using the training data to generate a target FNO model, so that the target FNO model can accurately locate the impact force by determining the maximum value position of the output distribution.

[0126] In general, this embodiment uses a truncated Gaussian distribution function to model the force position, so that a continuous function representation of the force position can be provided regardless of the spatial resolution; this operation converts the sparse form positioning result into a distribution function form positioning result, thereby avoiding the instability problem that may be caused by the sparse solution of the operator model.

[0127] In summary, the Fourier neural operator-based impact force identification method provided in this embodiment is a data-driven method. It utilizes local structural acceleration and other responses as model inputs, uses FNO learning to map from the system response function space to the spatiotemporal source function space, and combines it with the proposed spatial upsampling method to accurately reconstruct and locate the impact force applied to the structure. In addition, this embodiment uses a continuous distribution to represent single-point impact forces, overcoming the training difficulties of data-driven models for highly sparse data. Compared with existing technologies, this embodiment can provide positioning results with high spatial resolution while maintaining high robustness even with limited sensors and training data.

[0128] The following content shows Algorithm 1 of this embodiment for implementing impact force localization and reconstruction using FNO and spatial upsampling:

[0129]

[0130]

[0131] It should be noted that the model parameter θ refers to all parameters involved in the FNO model, such as linear transformation W, linear transformation P, linear transformation Q, etc.; η represents the learning rate, Represents the gradient in back propagation.

[0132] Specifically, the principle of realizing impact force location and reconstruction through Fourier neural operator and spatial upsampling is explained in combination with the above algorithm 1: First, the system response data arranged on the structure is collected, the model parameters are initialized and the number of iterative updates is determined, and the total number of samples N of the system response signal in space and time is counted. x ,N t ; Then the model training begins. The first step is to enhance the input system response signal to a higher dimensional representation (i.e., the first line of Algorithm 1). The number of dimensions can be determined according to the complexity of the structure, and the spatial resolution of the signal does not change in this step. The second step is iteration, which is to perform Fourier transform on the input signal represented in the high dimensional representation to obtain the frequency domain signal representation, and establish the operator R in the frequency domain. d , to use the operator R d Perform operator transformation on the frequency domain signal; then, perform zero padding on the transformed signal to obtain the spatial upsampled signal It is understandable that the spatially upsampled signal will obtain a signal with higher spatial resolution when the inverse Fourier transform is performed; in addition, the input signal represented by the high dimension is linearly transformed W d And superimpose it with the obtained higher spatial resolution signal. After m iterations, the operator learning is completed (i.e., lines 3-6 of Algorithm 1). The third step is projection, which is to project the high spatial resolution signal after the operator learning back to the output space to generate the impact force signal to be identified. And through two pooling layers M l ,M t The position and time history of the impact force signal are output separately (i.e., lines 7-8 of Algorithm 1). Next, a loss function is constructed based on the difference between the actual impact force signal used for training and the model-predicted impact force signal. The position difference is calculated using the mean squared error, and the time history difference is calculated using the mean absolute error. The model parameters are then updated based on the backpropagation of the loss function (i.e., lines 9-10 of Algorithm 1). When convergence conditions are reached, the model can use the system response signal as input and accurately output the position and time history of the impact force signal.

[0133] In summary, this embodiment can provide high-resolution positioning results while avoiding instability in the inversion process. It can also achieve high-precision impact force identification with a small number of sensors and limited data collection, overcoming the problem of data-driven methods relying on large-scale training data. In addition, by combining spatial upsampling, it can provide stable and reliable impact force identification results for complex structures, thus providing a new solution for impact force monitoring and evaluation in engineering practice.

[0134] Among them, compared with the existing impact force identification method based on the U-Net model, this embodiment can reduce the absolute error of the impact force positioning result by up to 81%, and the relative error of the impact force reconstruction result by up to 32%, and the peak error by up to 61% (it should be noted that there are differences in the error results of different experimental structures).

[0135] To better demonstrate the advantages of the target FNO model provided by this embodiment, a test steel beam and a scaled carbon fiber wind turbine blade were used as experimental subjects, respectively. Three accelerometers and a data acquisition instrument were used to collect system response data in both tests, and a hammer was used to conduct impact force tests. It should be noted that the U-Net model (a fully convolutional neural network architecture, commonly used for accurate and efficient image processing and optimization, and suitable for processing multidimensional signals) was used as the baseline model for comparative research. Furthermore, while the results of a one-dimensional positioning experiment are presented in this section, a two-dimensional positioning experiment was also conducted on the test steel beam (the results are not presented). These experimental results demonstrate that the target FNO model provided by this embodiment can still achieve highly accurate positioning and reconstruction results.

[0136] Example 1:

[0137] It should be noted that the experimental scenario of Example 1 is as follows Figure 2 As shown in the figure, the experimental object is a test steel beam, and a hammer is used to perform a knock test on the test steel beam. The digital signal processing system collects the system response data generated by the knock on the test steel beam, and the impact force is identified by the model in the computer. Figure 3 As shown in the figure, the accelerometer signals (indicated by "×") from three sensors (at both ends and the midpoint of the structure) are recorded, and only the measurement data of these three sensors are used as the input for model training. There are a total of 19 impact force locations, of which 7 are selected as training impact force locations (indicated by unfilled circles) at 60mm intervals, and the remaining 12 are designated as test impact force locations (indicated by filled black circles); it should be understood that Figure 3 in It indicates that the accelerometer overlaps with the training impact force location. It is worth noting that the training impact force locations in this embodiment are very sparse, and the test location is not included in the training.

[0138] Based on this, the impact force positioning can be performed using the target FNO model and the U-Net benchmark model of this embodiment as follows: Figure 3 The dark gray squares are the impact force positioning results of the target FNO model provided in this embodiment, and the light gray triangles are the impact force positioning results of the U-Net benchmark model. It can be seen that the positioning result of the target FNO model is better than that of the U-Net benchmark model, and the average positioning error is 5.80 mm, which is much lower than the interval value of the training impact force position (i.e., 60 mm).

[0139] In addition, the target FNO model and the U-Net benchmark model of this embodiment are used to reconstruct the impact force of the test point 12, and the following can be obtained: Figure 4 The black solid line is the true value of the impact force, the blue dotted line is the impact force reconstruction result of the target FNO model, and the red dotted line is the impact force reconstruction result of the U-Net benchmark model. The figure shows two randomly selected impact force reconstruction results. It can be seen that the reconstruction result of the target FNO model is better than that of the U-Net benchmark model, especially in the performance of peak reconstruction. The relative reconstruction error is 9.45%, and the peak reconstruction error is only 3.14%.

[0140] Example 2:

[0141] It should be noted that the experimental scenario of Example 2 is as follows Figure 5 and 6As shown in the figure, the experimental object is a scaled carbon fiber fan blade, and the scaled carbon fiber fan blade is hit by a hammer, and the system response data generated by the hitting of the scaled carbon fiber fan blade is collected by a digital signal processing system, and then the impact force of the system response data is identified by the model in the computer; the purpose of this experiment is to apply the target FNO model to a more complex and realistic structure for testing. Similarly, Figure 6 As shown in the figure, the measurement data of three acceleration sensors (at both ends and the midpoint of the structure) are used as the input for model training; there are a total of 28 impact force locations, 10 of which are selected as training impact force locations at 90 mm intervals (indicated by unfilled circles), and the remaining 18 are designated as test impact force locations (indicated by filled black circles).

[0142] Based on this, the impact force positioning can be performed using the target FNO model and the U-Net benchmark model of this embodiment as follows: Figure 7 The dark gray squares are the impact force positioning results of the target FNO model provided in this embodiment, and the light gray triangles are the impact force positioning results of the U-Net benchmark model. It can be seen that the positioning result of the target FNO model is better than that of the U-Net benchmark model, and the average positioning error is 9.03 mm, which is much lower than the interval value of the training impact force position (i.e., 90 mm).

[0143] In addition, the target FNO model and the U-Net benchmark model of this embodiment are used to reconstruct the impact force of the test point 10, and the following can be obtained: Figure 8 The black solid line is the true value of the impact force, the blue dotted line is the impact force reconstruction result of the target FNO model, and the red dotted line is the impact force reconstruction result of the U-Net benchmark model. The figure shows two randomly selected impact force reconstruction results. It can be seen that the reconstruction result of the target FNO model is better than that of the U-Net benchmark model, especially in the performance of peak reconstruction. The relative reconstruction error is 12.69%, and the peak reconstruction error is only 3.80%.

[0144] As can be seen, this embodiment proposes a data-driven method that can achieve high spatial resolution and accurately identify impact forces. It does not require systematic structural modeling or a large amount of training data to ensure recognition accuracy. It can simultaneously localize and reconstruct impact forces and has been validated on multiple experimental structures, outperforming baseline models. In addition, to address the model training challenges posed by the highly sparse form of impact force data, a method using a truncated Gaussian distribution to represent single-point impact forces is proposed, effectively addressing training challenges while ensuring accurate positioning.

[0145] In a second aspect, an embodiment of the present application also provides an impact force recognition device based on a Fourier neural operator.

[0146] In one embodiment, the impact force recognition device based on the Fourier neural operator includes:

[0147] A data acquisition unit, which is used to acquire response data of the system to be identified;

[0148] An impact force identification unit is used to input the response data of the system to be identified into a target Fourier neural operator model including an inverse operator module and a pooling module to output the position identification result and time history reconstruction result of the impact force; wherein, the inverse operator module is used to perform a linear transformation on the response data of the system to be identified to obtain a high-dimensional input signal, iteratively update the high-dimensional input signal to obtain a target high-resolution up-sampling signal, and linearly transform the target high-resolution up-sampling signal to obtain a target excitation function, and the iterative update includes zero-filling processing; the pooling module is used to perform pooling operations on the target excitation function in the spatial dimension and the time dimension respectively to obtain the position identification result and the time history reconstruction result.

[0149] Furthermore, in one embodiment, the inverse operator module is specifically configured to:

[0150] Performing Fourier transform, operator conversion, zero padding and inverse Fourier transform on the high-dimensional input signal in sequence to obtain a first high-resolution up-sampled signal;

[0151] Performing a linear transformation on the high-dimensional input signal, and superimposing the linear transformation result with the first high-resolution up-sampled signal to obtain a second high-resolution up-sampled signal;

[0152] A preset number of iterative updates are performed based on the second high-resolution up-sampled signal to obtain a target high-resolution up-sampled signal.

[0153] Furthermore, in one embodiment, the inverse operator module is further configured to:

[0154] Perform Fourier transform on the high-dimensional input signal to obtain the initial frequency domain signal;

[0155] Perform operator transformation on the initial frequency domain signal to obtain the target frequency domain signal;

[0156] Performing zero-filling processing on the target frequency domain signal to obtain a zero-filled frequency domain signal;

[0157] Performing an inverse Fourier transform on the zero-padded frequency domain signal to obtain a first high-resolution up-sampled signal.

[0158] Furthermore, in one embodiment, the expression of the zero-filled frequency domain signal is:

[0159]

[0160] Where, represents the zero-filled frequency domain signal, X[k] represents the target frequency domain signal, k represents the frequency domain signal sampling point, n s Indicates the number of sensors, n′ s Indicates the new length corresponding to the zero-padded signal.

[0161] Furthermore, in one embodiment, the expression for iterative update is:

[0162]

[0163] R φ =F(k φ )

[0164] Where ξ represents the spatial position data and time data in the response data of the system to be identified, v m (ξ) represents the corresponding high-resolution up-sampled signal after the mth iteration update, σ represents the nonlinear activation function, represents the integral operator, W represents the linear transformation, F -1 represents the inverse Fourier transform, Represents the frequency domain signal obtained after Fourier transform, R φ represents the operator, k φ Represents the kernel function.

[0165] Furthermore, in one embodiment, the method for constructing the target Fourier neural operator model is:

[0166] Acquiring training data, the training data including historical system response data, the historical system response data including historical spatial position data and historical time data corresponding to the impact force, the historical spatial position data being spatial position data obtained by modeling based on a truncated Gaussian distribution function;

[0167] The initial Fourier neural operator model is trained based on the training data to obtain a target Fourier neural operator model.

[0168] Among them, the functional implementation of each unit in the above-mentioned impact force identification device based on Fourier neural operator corresponds to the various steps in the above-mentioned impact force identification method embodiment based on Fourier neural operator, and its functions and implementation processes will not be repeated here one by one.

[0169] In a third aspect, an embodiment of the present application provides an impact force recognition device based on a Fourier neural operator. The impact force recognition device based on a Fourier neural operator can be a personal computer (PC), a laptop computer, a server, or other device with data processing capabilities.

[0170] Reference Figure 9 , Figure 9 Schematic diagram of the hardware structure of the impact force recognition device based on Fourier neural operator involved in the embodiment of the present application. In the embodiment of the present application, the impact force recognition device based on Fourier neural operator may include a processor, a memory, a communication interface and a communication bus.

[0171] The communication bus may be of any type and is used to interconnect the processor, memory, and communication interface.

[0172] Communication interfaces include input / output (I / O) interfaces, physical interfaces, and logical interfaces, used to interconnect components within the Fourier neural network-based impact force recognition device, as well as interfaces used to interconnect the Fourier neural network-based impact force recognition device with other devices (e.g., other computing devices or user devices). Physical interfaces can include Ethernet interfaces, fiber optic interfaces, ATM interfaces, etc.; user devices can include displays, keyboards, etc.

[0173] The memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0174] The processor may be a general-purpose processor that can call an impact force recognition program based on a Fourier neural operator stored in a memory and execute the impact force recognition method based on a Fourier neural operator provided in the embodiments of the present application. For example, the general-purpose processor may be a central processing unit (CPU). The method executed when the impact force recognition program based on a Fourier neural operator is called may refer to the various embodiments of the impact force recognition method based on a Fourier neural operator of the present application, and will not be repeated here.

[0175] Those skilled in the art will understand that Figure 9 The hardware structure shown in the figure does not constitute a limitation to the present application and may include more or fewer components than shown in the figure, or a combination of certain components, or a different arrangement of components.

[0176] In a fourth aspect, an embodiment of the present application also provides a computer-readable storage medium.

[0177] The readable storage medium of the present application stores an impact force recognition program based on a Fourier neural operator, wherein when the impact force recognition program based on a Fourier neural operator is executed by a processor, the steps of the impact force recognition method based on a Fourier neural operator as described above are implemented.

[0178] Among them, the method implemented when the impact force recognition program based on the Fourier neural operator is executed can refer to the various embodiments of the impact force recognition method based on the Fourier neural operator in this application, and will not be repeated here.

[0179] It should be noted that the serial numbers of the above-mentioned embodiments of the present application are for description only and do not represent the advantages or disadvantages of the embodiments.

[0180] The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices. The terms "first", "second" and "third" are used to distinguish different objects, etc., and do not represent a sequence, nor do they limit the "first", "second" and "third" to different types.

[0181] In the description of the embodiments of this application, the words "exemplary," "for example," or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary," "for example," or "for example" in the embodiments of this application should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary," "for example," or "for example" is intended to present the relevant concepts in a concrete manner.

[0182] In the description of the embodiments of the present application, unless otherwise specified, “ / ” means or, for example, A / B can mean A or B; “and / or” in the text is merely a description of the association relationship of associated objects, indicating that three relationships may exist, for example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, in the description of the embodiments of the present application, “multiple” refers to two or more than two.

[0183] In some processes described in the embodiments of the present application, multiple operations or steps are included that appear in a specific order. However, it should be understood that these operations or steps may not be performed in the order in which they appear in the embodiments of the present application or may be performed in parallel. The sequence numbers of the operations are only used to distinguish between different operations, and the sequence numbers themselves do not represent any order of execution. In addition, these processes may include more or fewer operations, and these operations or steps may be performed in sequence or in parallel, and these operations or steps may be combined.

[0184] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the necessary general hardware platform, of course, it can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes a number of instructions for enabling a terminal device to execute the methods described in each embodiment of the present application.

[0185] The above are only preferred embodiments of the present application and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A method for identifying impact force based on Fourier neural operator, characterized in that: include: Obtaining response data of the system to be identified; Inputting the response data of the system to be identified into the target Fourier neural operator model including the inverse operator module and the pooling module to output the position identification result and time history reconstruction result of the impact force; Among them, the inverse operator module is used to perform linear transformation on the response data of the identification system to obtain a high-dimensional input signal, iteratively update the high-dimensional input signal to obtain a target high-resolution up-sampling signal, and linearly transform the target high-resolution up-sampling signal to obtain a target excitation function, and the iterative update includes zero-filling processing; the pooling module is used to perform pooling operations on the target excitation function in the spatial dimension and the time dimension respectively to obtain the position recognition result and the time history reconstruction result.

2. The impact force identification method based on Fourier neural operator according to claim 1, characterized in that: The iterative updating of the high-dimensional input signal to obtain a target high-resolution up-sampled signal includes: Performing Fourier transform, operator conversion, zero padding and inverse Fourier transform on the high-dimensional input signal in sequence to obtain a first high-resolution up-sampled signal; Performing a linear transformation on the high-dimensional input signal, and superimposing the linear transformation result with the first high-resolution up-sampled signal to obtain a second high-resolution up-sampled signal; A preset number of iterative updates are performed based on the second high-resolution up-sampled signal to obtain a target high-resolution up-sampled signal.

3. The impact force identification method based on Fourier neural operator according to claim 2, characterized in that: The step of sequentially performing Fourier transform, operator conversion, zero padding, and inverse Fourier transform on the high-dimensional input signal to obtain a first high-resolution up-sampled signal includes: Perform Fourier transform on the high-dimensional input signal to obtain the initial frequency domain signal; Perform operator transformation on the initial frequency domain signal to obtain the target frequency domain signal; Performing zero-filling processing on the target frequency domain signal to obtain a zero-filled frequency domain signal; Performing an inverse Fourier transform on the zero-padded frequency domain signal to obtain a first high-resolution up-sampled signal.

4. The impact force identification method based on Fourier neural operator according to claim 3, characterized in that: The expression of the zero-filled frequency domain signal is: Where, represents the zero-filled frequency domain signal, X[k] represents the target frequency domain signal, k represents the frequency domain signal sampling point, n s Indicates the number of sensors, n s Indicates the new length corresponding to the zero-padded signal.

5. The impact force identification method based on Fourier neural operator according to claim 1, characterized in that: The expression of the iterative update is: R φ =F(k φ ) Where ξ represents the spatial position data and time data in the response data of the system to be identified, v m (ξ) represents the corresponding high-resolution up-sampled signal after the mth iteration update, σ represents the nonlinear activation function, represents the integral operator, W represents the linear transformation, F -1 represents the inverse Fourier transform, Represents the frequency domain signal obtained after Fourier transform, R φ represents the operator, κ φ Represents the kernel function.

6. The impact force identification method based on Fourier neural operator according to claim 1, characterized in that: The target Fourier neural operator model is constructed as follows: Acquiring training data, the training data including historical system response data, the historical system response data including historical spatial position data and historical time data corresponding to the impact force, the historical spatial position data being spatial position data obtained by modeling based on a truncated Gaussian distribution function; The initial Fourier neural operator model is trained based on the training data to obtain a target Fourier neural operator model.

7. An impact force recognition device based on Fourier neural operator, characterized in that: include: A data acquisition unit, which is used to acquire response data of the system to be identified; An impact force identification unit is used to input the response data of the system to be identified into a target Fourier neural operator model including an inverse operator module and a pooling module to output the position identification result and time history reconstruction result of the impact force; wherein, the inverse operator module is used to perform a linear transformation on the response data of the system to be identified to obtain a high-dimensional input signal, iteratively update the high-dimensional input signal to obtain a target high-resolution up-sampling signal, and linearly transform the target high-resolution up-sampling signal to obtain a target excitation function, and the iterative update includes zero-filling processing; the pooling module is used to perform pooling operations on the target excitation function in the spatial dimension and the time dimension respectively to obtain the position identification result and the time history reconstruction result.

8. The impact force identification device based on Fourier neural operator according to claim 7, characterized in that: The inverse operator module is specifically used for: Performing Fourier transform, operator conversion, zero padding and inverse Fourier transform on the high-dimensional input signal in sequence to obtain a first high-resolution up-sampled signal; Performing a linear transformation on the high-dimensional input signal, and superimposing the linear transformation result with the first high-resolution up-sampled signal to obtain a second high-resolution up-sampled signal; A preset number of iterative updates are performed based on the second high-resolution up-sampled signal to obtain a target high-resolution up-sampled signal.

9. An impact force recognition device based on Fourier neural operator, characterized in that: The impact force identification device based on the Fourier neural operator includes a processor, a memory, and an impact force identification program based on the Fourier neural operator stored in the memory and executable by the processor. When the impact force identification program based on the Fourier neural operator is executed by the processor, the steps of the impact force identification method based on the Fourier neural operator as described in any one of claims 1 to 6 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores an impact force recognition program based on a Fourier neural operator, wherein when the impact force recognition program based on a Fourier neural operator is executed by a processor, the steps of the impact force recognition method based on a Fourier neural operator as described in any one of claims 1 to 6 are implemented.

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