An uncertainty load identification method based on dimension-by-dimension method and radial basis neural network

Abstract

The application discloses an uncertainty load identification method based on a dimension-by-dimension method and a radial basis neural network, and first establishes a dynamic load identification model: under the condition of structural certainty parameters, the center and standard deviation of the hidden layer basis function, and the weight between the hidden layer and the output layer are determined to train the radial basis (RBF) neural network. Secondly, the surface formed by the superplane intercepting the structure true response on each dimension of the input parameter vector at the reference point is utilized, a polynomial approximation model based on the Legendre orthogonal polynomial is constructed, and the maximum and minimum points on the corresponding dimension are calculated. Finally, the upper and lower bounds of the dynamic load interval at any time are obtained by the dynamic load identification model at the maximum and minimum point vector, and the identification of the dynamic load interval time history is completed. The application considers the influence of the structural parameter uncertainty under the condition of small samples on the dynamic load identification result, reasonably represents the comprehensive influence of the uncertainty on the structure configuration in the load identification process, and ensures that the design itself considers safety and economy.

Description

Technical Field

[0001] This invention relates to the field of load identification for continuum structures, and particularly to an uncertain load identification method based on the dimension-by-dimensional method and radial basis neural network. This method considers the uncertainties of materials, external loads and allowable displacement values, and combines an uncertainty propagation analysis method—the dimension-by-dimensional method—to identify loads on continuum structures. Background Technology

[0002] In recent years, thanks to the tremendous advancements in computer technology, load identification technology has also developed significantly, with applications spanning numerous fields such as aerospace, machinery, civil engineering, water conservancy, and automotive. Load identification also has wide applications in the shipbuilding industry, including load monitoring, ship stability calculation, ship performance optimization, cargo tracking, and safety. Load identification refers to the process of real-time monitoring and analysis of the load on a ship using sensors and data analysis technology. This technology can help shipping companies and ship owners better manage and optimize ship loads, improving transportation efficiency and safety. Load identification is an inverse problem of structural dynamics; it calculates the dynamic loads on the structure based on the known dynamic characteristics and measured dynamic response of the structural system. Determining the dynamic load is one of the keys to structural load design. Existing load identification methods mainly include frequency domain methods and time domain methods. In recent years, time finite element method, inverse system method, neural network method, and wavelet transform method have also emerged. Among them, the basic principle of the time domain method is to use the time-series information of the signal to obtain the characteristics of load identification through time-domain analysis of the signal.

[0003] The basic idea of ​​dynamic load time-domain identification is to establish an inverse model of the structural system in the time domain using the modal parameters of the structure, and then identify the dynamic load by inputting the system's dynamic response. Existing time-domain methods are basically based on modal decomposition and Duhamel integration techniques, assuming that the external load to be identified is a step load or a piecewise linear function within a small time interval, with an initial value of zero, and using recursive chain calculation formulas for load identification. The intuitiveness and ease of engineering application of the time-domain method have made it popular in the engineering field. Its advantages lie in its ability to identify non-stationary dynamic loads. It has practical engineering value in identifying impact loads. Furthermore, the time-domain method can not only identify short sample measurement data but also potentially achieve real-time identification.

[0004] However, engineering structural systems are rife with various uncertainties, including randomness, fuzziness, and unknown yet bounded information, and structural sample data is often scarce. Currently, commonly used uncertainty propagation analysis methods include the Monte Carlo method, the first-order Taylor expansion method, direct optimization method, vertex combination method, and interval-by-interval analysis. The first-order Taylor expansion method performs a first-order Taylor expansion at the center value of the uncertain variable, which is computationally simple, but for strongly nonlinear problems, the results obtained have relatively large errors. Some scholars have proposed a method that considers the correlation between interval parameters by performing a first-order Taylor expansion of the interval stiffness matrix at the interval parameters. The Monte Carlo method can obtain accurate results when there are enough sample points, but its computational cost is high. The interval-by-interval analysis method establishes a polynomial response surface in each dimension of the interval parameter space, and can use higher-order polynomials to capture the true response change trend in the corresponding dimension with higher accuracy. In terms of application scope, the interval-by-interval analysis method is applicable to interval analysis problems with large fluctuation radii. Furthermore, the structural finite element model participates in the interval-by-interval analysis method as a black box, without requiring modification of the simulation analysis code, making it easy to integrate with existing commercial analysis software. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides an uncertain load identification method based on the dimension-by-dimensional method and radial basis function neural networks. This invention fully considers the uncertainties prevalent in practical engineering problems, applies radial basis function (RBF) neural networks to load identification, and combines them with the dimension-by-dimensional method in uncertainty propagation analysis. The resulting design results are more consistent with reality and have stronger engineering applicability.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] An uncertainty load identification method based on the dimension-by-dimensional method and radial basis function neural network is characterized by the following steps:

[0008] Step 1: Given multiple structural parameters p1, p2, ..., p n The column vector p is formed, then the boundary is determined, and Gaussian white noise is randomly generated;

[0009] Step 2: Select various dynamic load cases as output samples for training the RBF neural network, or select distributed dynamics and calculate the corresponding Legendre distribution orthogonal polynomial coefficients. pass As the output sample for training the RBF neural network; where For t k The order coefficients at time points j1 and j2. Let H be the Legendre distribution orthogonal polynomial. H represents H different distribution dynamics;

[0010] Step 3: Calculate the dynamic response as the input sample, including: deriving the structural system response based on the selected dynamic load condition using finite element theory.

[0011] Step 4: Determine the training parameters of the RBF neural network, including the center C of the hidden layer basis functions. i The sum of the standard deviation σ and the weights ω between the hidden and output layers. ij And train the RBF neural network, including: solving the center C of the hidden layer basis functions during the unsupervised learning process. i The sum and standard deviation σ; determining the weights ω between the hidden and output layers in a supervised learning process. ij The loads to be identified are represented as a load column vector.

[0012] Step 5: Obtain the input sample point matrix based on the parameters of the Gaussian integral points;

[0013] Step Six: Replace the column vector p from Step One with the values ​​from the input sample point matrix B in Step Six. input For each column, repeat steps one through four to obtain the value of f at each sample point, and use B as the denominator. input The column-block format is stored in the output sample point matrix F output ,Right now:

[0014] F output = [F1, ..., F j F n ]

[0015] In this context, each column of F1 represents the value of f obtained by taking the same column of B1 sequentially through steps one through four. j Each column represents the value B of p in sequence. j The same column is obtained by going through steps one through four to get the value of f, F n Each column represents the value B of p in sequence. n The same column is obtained through steps one through four to get the value of f. Based on F... output And the best square approximation theory is used to establish a polynomial approximation model of the q-th component with respect to the i-th interval parameter. q is the ordinal number of the component, and i is the ordinal number of the interval parameter;

[0016] Step 7: Calculate the vector of extreme points of dynamic load in any time interval;

[0017] Step 8: Calculate the dynamic load limit for any time interval to obtain the lower bound U of the response vector. L and the upper bound U of the response vector U for:

[0018] in, This represents the minimum dynamic load over any given time interval. The first number in parentheses indicates the number of components in the response vector, and the second number indicates the degree of the interval parameter. The following... Similarly.

[0019]

[0020] Step 9: Output the dynamic load interval time history, and set p i The responses U corresponding to the maximum and minimum points are put into the RBF neural network obtained in step four, which yields the polynomial coefficients Θ of the distributed force to be identified under the uncertain system. This is the test process, written as RBFANN(U, P) = Θ.

[0021] The advantages of this invention compared to the prior art are as follows:

[0022] This invention provides a novel approach to uncertain load identification based on the dimension-by-dimensional method and radial basis function neural networks, overcoming and improving upon the limitations of traditional model-driven load identification design methods under uncertainty. The combination of the constructed data-driven load identification model and uncertainty propagation analysis, on the one hand, learns the relationships between variables through repeated exposure to these variables, thereby characterizing the complexity of the structure. On the other hand, it effectively accounts for and quantifies the impact of uncertainty on load identification. When identifying loads on continuum structures under finite sample conditions with uncertainties in parameters such as load, material properties, and design allowable values, the load identification variation law under uncertainty can be fully considered. Combined with the interval dimension-by-dimensional analysis method, which exhibits good performance in both computational efficiency and accuracy, the design cycle and economic costs are reduced. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of an uncertain load identification method based on the dimension-by-dimensional method and radial basis neural network;

[0024] Figure 2 This is a flowchart of an uncertainty load identification method based on the dimension-by-dimensional method and radial basis neural network;

[0025] Figure 3 This is a schematic diagram of the rectangular steel plate used in the embodiment;

[0026] Figure 4 This is a graph of the input displacement response signal;

[0027] Figure 5 This is a diagram showing the identification results of the time history of the dynamic load interval in the embodiment. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0029] This invention discloses an uncertain load identification method based on a dimension-by-dimensional method and a radial basis function neural network, wherein the principle is as follows: Figure 1 As shown, the specific process is as follows: Figure 2 As shown, it includes the following steps:

[0030] Step 1: Given multiple structural parameters p1, p2, ..., p n The column vector p is formed, and then the boundary is determined. Gaussian white noise is generated randomly.

[0031] Step 2: Select various dynamic load cases as output samples for training the RBF neural network, or select distributed dynamics and calculate the corresponding Legendre distribution orthogonal polynomial coefficients. pass As the output sample for training the RBF neural network; where For t k The order coefficients at time points j1 and j2. Let H be the Legendre distribution orthogonal polynomial. H represents H different distribution dynamics.

[0032] Step 3: Calculate the dynamic response as the input sample, including: deriving the structural system response based on the selected dynamic load condition using finite element theory. Alternatively, experimental methods can be used to discretely measure the structural displacement response, structural velocity response, and structural acceleration response using sensors.

[0033] Step 4: Adjust the polynomial coefficients Θ * and structural system response U * Perform normalization. Determine the training parameters of the RBF neural network. Determine the center C of the hidden layer basis functions. i The sum of the standard deviation σ and the weights ω between the hidden and output layers. ij And train the RBF neural network, specifically as follows:

[0034] The central C of solving the hidden layer basis functions in the unsupervised learning process i The sum and standard deviation σ; determining the weights ω between the hidden and output layers in a supervised learning process. ij The logical centers of the RBF (Redundant Baseline Flow) are found using the K-means clustering algorithm, which divides the data into several categories. The similar characteristics of the same category ensure that the selected cluster centers are more representative. Let there be I cluster centers, and let the i-th cluster center in the nth iteration be denoted as... The process of selecting cluster centers includes:

[0035] Step (1) Initialization. From the structural system response U′ * I1 distinct samples were randomly selected as the initial cluster centers.

[0036] Step (2) Input sample. From the structural system response U′ * Randomly select training sample vector X′ k As input.

[0037] Step (3) Matching. Calculate the closest sample vector X′. k Find the cluster center, locate the corresponding i, and then set X′ k It is classified into the i-th category. That is:

[0038] findi(X′ k ), i = 1, 2, ..., I

[0039]

[0040] Here, findi(·) means to search, and ||·|| represents the norm.

[0041] Step (4) Update the cluster center. Because of the new sample X′ k With the addition of [a variable], the i-th cluster center will change. The new cluster center can be defined as:

[0042]

[0043] Where μ∈[0,1] is the learning step size. In each iteration, only one cluster center will be updated, while the other centers remain in their original state.

[0044] Step (5) Judgment. Set a small threshold. If the change in cluster centers is less than this threshold, for example, 10... -6 If the condition is met, the algorithm converges. Otherwise, jump to step (2) until the convergence condition is met.

[0045] In conclusion, the final It is the final cluster center.

[0046] After selecting cluster centers, the standard deviation of the Gaussian function can be expressed as: Where d max It is the maximum distance between the cluster centers. Therefore, the basis function can be further refined as:

[0047] Among them, C i X′ is the final cluster center selected. k This represents the closest sample vector obtained during the cluster center selection process. The standard deviation of the Gaussian function can be expressed as: Where d max It is the maximum distance between the cluster centers.

[0048] Define the cost function as follows Among them, E j Let e ​​represent the error of the j-th output layer node. jk Let K represent the error between the result of the k-th training sample of the j-th output layer node and the expected result. There exists 1 ≤ k ≤ K, where K is the maximum or minimum value of the training sample result.

[0049] Let the polynomial coefficients Θ * =[a jk ] J×KH e represents the expected output of the input sample. jk It can be defined as: The weights ω between the hidden layer and the output layer are analyzed by minimizing the cost function. ij The error of the j-th output layer node, i.e., the cost function E. j For weight w jk Take the partial derivative of and then make it equal to 0.

[0050] The process of force reconstruction using an RBF neural network is called the training process, which can be simply summarized as RBFANN(U * ,p)=Θ * RBFANN represents the input structural system response U of the distributed force. * With output polynomial coefficients Θ * The complex relationship between them. Figure 2 The training process based on sample data is shown. Changing certain parameters of p in the structural system allows for the training of different RBF neural networks, yielding different training results; this is the distributed dynamic force reconstruction RBF neural network. The loads to be identified are represented by the load column vector f. * Represented as

[0051] Step 5: Obtain the input sample point matrix based on the parameters of the Gaussian integral points.

[0052] In step five, the load column vector Based on the structural parameter column vector p, the experimental data based on p are modeled with interval numbers for each component of p, resulting in an interval number column vector. in This indicates the fluctuation range of the first parameter. It is the lower bound of the first parameter. It is the upper bound of the first parameter. This indicates the fluctuation range of the second parameter. This indicates the lower bound of the second parameter. It is the upper bound of the second parameter. This represents the fluctuation range of the nth parameter. It is the lower bound of the nth parameter. It is the upper bound of the nth parameter, p IThe upper bound column vector is represented as The lower bound column vector is represented as p I The midpoint column vector p C for:

[0053]

[0054] Where, p U p represents the upper bound of the parameter. L p represents the lower bound of the parameter. U This represents the column vector of the midpoint. This represents the midpoint value of the first parameter. This represents the midpoint value of the second parameter. This represents the midpoint value of the nth parameter. The radius column vector p r for:

[0055]

[0056] in, This represents the radius of the first parameter. This represents the radius of the second parameter. Let X represent the radius of the nth parameter, given the Gaussian integration point X. G The dimension s is used to characterize the degree of nonlinearity of the curve. The true function has an m1-th order nonlinearity, where n1 is the order of the best square approximation polynomial, satisfying... Indicates no more than The largest integer. Obtain the column vector X of Gaussian integral points G for Using X G Sampling of structural parameters and storage of sample points in a block-form input sample point matrix B input ,Right now:

[0057]

[0058] Among them, B input There are μ column vectors in total, 1 ≤ j ≤ μ. B j B represents the j-th column vector of the sample point matrix. μ This represents the highest-dimensional column vector of the sample point matrix.

[0059] Step Six: Replace the column vector p from Step One with the values ​​from the input sample point matrix B in Step Six. input For each column, repeat steps one through four to obtain the value of f at each sample point, and use B as the denominator. input The column-block format is stored in the output sample point matrix F output,Right now:

[0060] F output = [F1, ..., F j F n ]

[0061] In this context, each column of F1 represents the value of f obtained by taking the same column of B1 sequentially through steps one through four. j Each column represents the value B of p in sequence. j The same column is obtained by going through steps one through four to get the value of f, F n Each column represents the value B of p in sequence. n The same column is obtained by proceeding through steps one through four to get the value of f. n is F output The dimension. According to F output And the best square approximation theory is used to establish a polynomial approximation model of the q-th component with respect to the j-th interval parameter. It can be represented as:

[0062]

[0063] The approximate polynomial model represented by this formula is a continuous function within the standard interval [-1, 1]. Describe the k1th Legendre polynomial in x j The value at that location. F represents j The element in the first column. q is the ordinal number of the component, and j is the ordinal number of the interval parameter.

[0064] Step 7: Calculate the vector of the extreme points of the dynamic load in any time interval.

[0065] According to step six Find the zeros of the first derivative. According to the theorem for the extreme values ​​of continuous functions, the extreme points of this function can be obtained by finding the zeros of its derivative and the endpoints of the independent variable. The zero of the derivative function can be calculated using the following formula:

[0066]

[0067] have:

[0068]

[0069] Where, x root This represents the set of extreme points of the q-th component of the structural response vector with respect to the i-th interval parameter. Of course, according to the polynomial approximation model... Given the range of the independent variable, the above formula needs to be further modified as follows:

[0070]

[0071] Where r represents the number of extreme points. This represents the r-th extreme point of the q-th component of the structural response vector with respect to the i-th interval parameter. Let represent the uncertain value of the j-th component with respect to the i-th interval parameter as the independent variable changes. Im(·) and Re(·) represent the imaginary and real parts of the corresponding variable, respectively.

[0072] Furthermore, the minimum and maximum points of the q-th component of the structural response vector with respect to the i-th interval parameter are calculated as follows:

[0073]

[0074]

[0075] Where q = 1, 2, ..., N, and N is the dimension of the structural response vector. The minimum point obtained by calculation, The maximum value point is calculated. The minimum and maximum values ​​of each component of the structural response vector with respect to all interval parameters are calculated using the method described in step seven. Finally, the minimum and maximum values ​​of the q-th component of the structural response vector within the standard interval [-1, 1] can be obtained, i.e.:

[0076]

[0077]

[0078] Step 8: Calculate the dynamic load limits for any time interval. Obtain the lower bound U of the structural response vector. L The upper bound U of the structural response vector U for:

[0079]

[0080] in, This represents the minimum dynamic load over any given time interval. The first number in parentheses indicates the number of components in the response vector, and the second number indicates the degree of the interval parameter. The following... Similarly.

[0081]

[0082] Step 9: Output the time history of the dynamic load interval. (Put p) i The responses U corresponding to the maximum and minimum points are fed into the RBF neural network obtained in step four to obtain the polynomial coefficients Θ of the distributed force to be identified under the uncertain system. This process can be described as a testing process and can be written as RBFANN(U, P) = Θ.

[0083] In summary, by reconstructing the force based on Legendre polynomials, the lower bound fi can ultimately be obtained. L and the upper boundary f U Finally, the dynamic load interval vector is obtained as f. I =[f L f U [This completes the identification of the time history of the dynamic load interval.]

[0084] Example:

[0085] To gain a fuller understanding of the features of this invention and its applicability to practical engineering, this invention addresses, for example... Figure 3 The rectangular steel plate shown is subjected to topology optimization design. The design area is a rectangular region of 100mm × 50mm with a thickness of 0.001m, divided into 20 × 10 elements. The material's elastic modulus E = 210MPa and density ρ = 7800kg / m³. 3 (Ideal value). One side of the rectangular region is fixed, while the other side is free. A load is applied at the Gaussian integration point, and the response of the input sample is obtained based on the load. The specific signal is as follows: Figure 4 As shown, the effect of gravity is neglected. Assume that the elastic modulus E and density ρ both fluctuate by 5% relative to their nominal values, i.e., E = [199.5, 220.5] MPa, ρ = [7410, 8190] kg / m³. 3 Finally, the time history of the load interval was identified as follows: Figure 5 As shown.

[0086] In summary, this invention proposes an uncertainty load identification method based on the dimension-by-dimensional method and radial basis function neural network. This method first establishes a dynamic load identification model: under deterministic structural parameter conditions, it normalizes different dynamic load conditions and dynamic responses to determine the center C of the hidden layer basis functions. i The sum of the standard deviation σ and the weights ω between the hidden and output layers. ij The RBF neural network is trained first. Then, the hyperplane at each dimension of the input parameter vector at the reference point is used to extract the surface formed by the actual structural response, and a polynomial approximation model of the extracted curve is constructed to calculate the maximum and minimum points in the corresponding dimensions. Finally, at the vector of the maximum and minimum points, the upper and lower bounds of the dynamic load interval at any time are obtained using a dynamic load identification model, ultimately completing the identification of the dynamic load interval time history. This invention considers the uncertainty effects of parameters such as load, material properties, and design allowable values ​​under finite sample conditions. During the load identification process, it reasonably characterizes the comprehensive influence of uncertainty on the structural configuration, and can improve the identification accuracy, ensuring that the design itself takes into account both safety and economy.

[0087] The above are merely specific steps of the present invention and do not constitute any limitation on the scope of protection of the present invention; it can be extended to the field of uncertain load identification, and all technical solutions formed by equivalent transformation or equivalent substitution fall within the scope of protection of the present invention.

[0088] The parts of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A method for identifying uncertain loads based on the dimension-by-dimensional method and radial basis function neural networks, characterized in that, Includes the following steps: Step 1: Given multiple structural parameters , , ..., The column vector formed Then, the boundary is determined, and Gaussian white noise is generated randomly. Step 2: Select various dynamic load cases as output samples for training the RBF neural network, or select distributed dynamics and calculate the corresponding Legendre distribution orthogonal polynomial coefficients. ,pass As the output samples for training the RBF neural network, for The order coefficient j at time step 1, j2 order coefficients, Let H be the Legendre distribution orthogonal polynomial, and H represent H different distribution dynamics; Step 3: Calculate the dynamic response as the input sample, including: deriving the structural system response based on the selected dynamic load condition using finite element theory. ; Step 4: Determine the training parameters of the RBF neural network, including the center of the hidden layer basis functions. and standard deviation and the weights between the hidden layer and the output layer. And train the RBF neural network, including: solving for the center of the hidden layer basis functions during the unsupervised learning process. and standard deviation Determine the weights between the hidden layer and the output layer during the supervised learning process. The loads to be identified are represented as a load column vector. ; Step 5: Obtain the input sample point matrix based on the parameters of the Gaussian integral points; Step Six: Convert the column vector from Step One The values ​​are sequentially taken from the input sample point matrix in step six. Repeat steps one through four for each column to obtain the load. The value at each sample point, and in The column-block format is stored in the output sample point matrix. ,Right now: ； in, Each column represents Take values ​​in sequence The same column is obtained through steps one through four. The value, Each column represents Take values ​​in sequence The same column is obtained through steps one through four. The value, Each column represents Take values ​​in sequence The same column is obtained through steps one through four. The value; according to And establish a polynomial approximation model based on the best square approximation theory Where q is the ordinal number of the component and j is the ordinal number of the interval parameter; Step 7: Calculate the vector of extreme points of dynamic load in any time interval; Step 8: Calculate the dynamic load limit for any time interval to obtain the lower bound of the load vector. and the upper bound of the load vector for: in, This represents the minimum value of the dynamic load at any given time interval. The first number in parentheses indicates the number of components in the response vector, and the second number indicates the degree of the interval parameter. ； in, This represents the maximum value of the dynamic load at any given time interval. The first number in parentheses indicates the number of components in the response vector, and the second number indicates the degree of the interval parameter. Step 9: Output the time history of the dynamic load interval. The responses corresponding to the maximum and minimum points By feeding these coefficients into the RBF neural network obtained in step four, the polynomial coefficients of the distributed forces to be identified in the uncertain system can be obtained. The test process is written as follows: .

2. The uncertainty load identification method based on the dimension-by-dimensional method and radial basis function neural network according to claim 1, characterized in that: The load identification in steps one through four uses an RBF neural network.

3. The uncertainty load identification method based on the dimension-by-dimensional method and radial basis neural network according to claim 1, characterized in that: In step five, the load column vector Dependent on structural parameter column vectors ,based on The experimental data are presented in interval pairs. Model each component to obtain an interval sequence vector. ,in This indicates the fluctuation range of the first parameter. It is the lower bound of the first parameter. It is the upper bound of the first parameter. This indicates the fluctuation range of the second parameter. This indicates the lower bound of the second parameter. It is the upper bound of the second parameter. This represents the fluctuation range of the nth parameter. It is the lower bound of the nth parameter. It is the upper bound of the nth parameter. The upper bound column vector is represented as , The lower bound column vector is represented as , midpoint column vector for: ； in, Indicates the upper bound of the parameter. Indicates the lower bound of the parameter; This represents the midpoint value of the first parameter. This represents the midpoint value of the second parameter. This represents the midpoint value of the nth parameter. radius column vector for: ； in, This represents the radius of the first parameter. This represents the radius of the second parameter. Let the radius of the nth parameter be given the Gaussian integration point. The dimension s is used to characterize the degree of nonlinearity of the curve. The true function has an m1-th order nonlinearity, where n1 is the order of the best square approximation polynomial, satisfying... , Indicates no more than The largest integer; by Obtain the column vector of Gaussian integration points for ,use Sampling is performed on the structural parameters, and the sample points are stored in a block-form input sample point matrix. ,Right now: ； in, There are μ column vectors, 1≤j≤μ. This represents the j-th column vector of the sample point matrix. This represents the highest-dimensional column vector of the sample point matrix.

4. The uncertainty load identification method based on the dimension-by-dimensional method and radial basis function neural network according to claim 1, characterized in that: The polynomial approximation model of the q-th component of the structural response vector in step six with respect to the j-th interval parameter. The calculation formula is: ； The approximate polynomial model represented by this formula is over a standard interval. Internally continuous functions; where Indicates the first Legendre polynomial in The value at that location, express The elements in the first column are q, which is the ordinal number of the component, and j, which is the ordinal number of the interval parameter.

5. The uncertainty load identification method based on the dimension-by-dimensional method and radial basis neural network according to claim 1, characterized in that: The hidden layer basis functions in step four are further refined as follows: , in, It is the final cluster center selected; The standard deviation of the Gaussian function is the closest sample vector obtained during the selection of cluster centers. Represented as: ,in It is the maximum distance between the cluster centers, and exp() represents the exponential function. 2 Let I represent the 2-norm, and I be the total number of cluster centers.

6. The uncertainty load identification method based on the dimension-by-dimensional method and radial basis function neural network according to claim 1, characterized in that: Step six considers the uncertainties in the material's elastic modulus, load, and allowable displacement values, and represents them in the form of interval vectors.

7. The uncertainty load identification method based on the dimension-by-dimensional method and radial basis function neural network according to claim 1, characterized in that: Step seven includes: according to step six We can find the zeros of the first derivative; according to the theorem for the extreme values ​​of continuous functions, the extreme points of a function are generated through the zeros of its derivative and the endpoints of its independent variable. The zero of the derivative function is calculated by the following formula: ； get ; in, Let represent the set of extreme points of the q-th component of the structural response vector with respect to the j-th interval parameter; then calculate the minimum and maximum points of the q-th component of the structural response vector with respect to the j-th interval parameter; calculate the minimum and maximum points of each component of the response vector with respect to all interval parameters in the same way, and finally obtain the q-th component of the structural response vector in the standard interval. The minimum and maximum points within.

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