Finite element parameter correction method, system and device based on deep neural network

Abstract

This invention discloses a finite element parameter correction method, system, and device based on a deep neural network, relating to the field of structural dynamics. The correction method includes: acquiring the geometric and material parameters of a satellite solar panel; establishing a high-order finite element model and a low-order finite element model before correction based on the geometric and material parameters of the satellite solar panel; calculating the first five natural frequencies and first mode shapes of the high-order finite element model and the low-order finite element model before correction; inputting the first five natural frequencies and first mode shapes of the high-order finite element model into a deep neural network to obtain the density, elastic modulus, and Poisson's ratio of the satellite solar panel; and, based on the density, elastic modulus, and Poisson's ratio of the satellite solar panel, dividing the finite element into orders according to a second predetermined number to obtain a low-order finite element model with corrected parameters. This invention enables the application of low-dimensional finite element models to obtain finite element parameters that are computationally fast and highly accurate.

Description

Technical Field

[0001] This invention relates to the field of structural dynamics, and in particular to a finite element parameter correction method, system, and device based on deep neural networks. Background Technology

[0002] While traditional finite element modeling methods can accurately reflect the dynamic characteristics of structures, as the mesh becomes denser, the dimension of the structure's state vector increases rapidly, the computation time becomes longer and longer, the requirements for computing equipment become more and more demanding, and the accuracy requirements for the calculated parameters become more and more demanding, which is not conducive to the design of subsequent controllers. Summary of the Invention

[0003] The purpose of this invention is to provide a finite element parameter correction method, system, and device based on deep neural networks, which can obtain finite element parameters with fast calculation and high accuracy using low-dimensional finite element models.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A finite element parameter correction method based on a deep neural network, the correction method comprising:

[0006] Obtain the geometric and material parameters of the satellite's solar panels; the material parameters include density, elastic modulus, and Poisson's ratio.

[0007] Based on the geometric and material parameters of the satellite solar panel, a high-order finite element model and a low-order finite element model before correction are established for the satellite solar panel; the high-order finite element model is a finite element model established according to a first set finite element division order; the low-order finite element model before correction is a finite element model established according to a second set finite element division order; the second set finite element division order is less than the first set finite element division order.

[0008] Calculate the first 5 natural frequencies and first mode shape of the higher-order finite element model, and the first 5 natural frequencies and first mode shape of the lower-order finite element model before correction.

[0009] The first five natural frequencies and first mode shape of the high-order finite element model are input into a deep neural network to obtain the density, elastic modulus, and Poisson's ratio of the satellite solar panel under the high-order finite element model; wherein, the deep neural network is obtained by training through a training set; the training set consists of the first five natural frequencies and first mode shape of the low-order finite element model before correction and the corresponding material parameters.

[0010] Based on the density, elastic modulus, and Poisson's ratio of the satellite solar panel under the high-order finite element model, and according to the second set finite element division order, a low-cost finite element model with parameter correction is obtained.

[0011] Optionally, the training process of the deep neural network includes:

[0012] Calculate sample material parameters as multiple set percentages of the material parameters of the satellite solar panels;

[0013] Based on the modified low-order finite element model and the sample material parameters, calculate the corresponding first 5 natural frequencies and first mode shape.

[0014] Using the corresponding first 5 natural frequencies and first mode shapes as inputs, and the sample material parameters as outputs, the deep neural network is trained using the backpropagation algorithm to obtain a trained deep neural network.

[0015] Optionally, the first five natural frequencies and the first mode shape of the higher-order finite element model are calculated, specifically including:

[0016] Based on the aforementioned high-order finite element model, determine the mass matrix and stiffness matrix;

[0017] Based on the mass matrix and the stiffness matrix, establish the equation for the undamped free vibration of the satellite solar panel;

[0018] The equation for undamped free vibration is solved to obtain the first five natural frequencies and the first mode shape.

[0019] Optionally, the equation for undamped free vibration is solved to obtain the first five natural frequencies and the first mode shape, specifically including:

[0020] Based on the undamped free vibration equation, the displacement equation of the satellite solar panel is obtained;

[0021] Find the second derivative of the displacement equation to obtain the expression for the second derivative of the displacement;

[0022] Substituting the second derivative expression into the undamped free vibration equation, we obtain the relationship between the mode shape and the natural frequency.

[0023] The relationship between the mode shape and the natural frequency is solved to obtain the first 5 natural frequencies and the first mode shape.

[0024] Optionally, the displacement equation is:

[0025] q(t)=φsin(ωt+θ)

[0026] Where q(t) is the displacement of the large satellite solar panel in simple harmonic motion at time t, φ is the mode shape, ω is the frequency of the simple harmonic motion of the solar panel, and θ is the phase angle.

[0027] Optionally, the relationship between the mode shape and the natural frequency is:

[0028] (K-ω 2 M)φ=0

[0029] Where φ is the mode shape, ω is the frequency of the simple harmonic motion of the solar panel, M is the mass matrix, and K is the stiffness matrix.

[0030] Optionally, the correction method further includes:

[0031] The vibration of the satellite solar panels was analyzed using a low-cost finite element model with the parameters corrected described above.

[0032] A finite element parameter correction system based on a deep neural network, applied to the aforementioned finite element parameter correction method based on a deep neural network, the correction system comprising:

[0033] The acquisition module is used to acquire the geometric and material parameters of the satellite's solar panels; the material parameters include density, elastic modulus, and Poisson's ratio.

[0034] The model building module is used to build a high-order finite element model and a low-order finite element model before correction of the satellite solar panel based on the geometric and material parameters of the satellite solar panel; the high-order finite element model is a finite element model built according to a first set finite element division order; the low-order finite element model before correction is a finite element model built according to a second set finite element division order; the second set finite element division order is less than the first set finite element division order.

[0035] The calculation module is used to calculate the first 5 natural frequencies and first mode shape of the higher-order finite element model and the first 5 natural frequencies and first mode shape of the lower-order finite element model before correction.

[0036] The prediction module is used to input the first five natural frequencies and first mode shape of the high-order finite element model into a deep neural network to obtain the density, elastic modulus and Poisson's ratio of the satellite solar panel under the high-order finite element model; wherein, the deep neural network is trained through a training set; the training set consists of the first five natural frequencies and first mode shape of the low-order finite element model before correction and the corresponding material parameters.

[0037] The correction module is used to obtain a low-cost finite element model with corrected parameters based on the density, elastic modulus, and Poisson's ratio of the satellite solar panels under the high-order finite element model, according to the second set finite element division order.

[0038] An apparatus, which is an electronic device, includes a memory and a processor. The memory stores a computer program, and the processor runs the computer program to enable the apparatus to perform the aforementioned finite element parameter correction method based on a deep neural network.

[0039] Optionally, the memory is a readable storage medium.

[0040] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0041] The finite element parameter correction method based on deep neural networks provided by this invention establishes a low-order finite element model and a high-order finite element model of a satellite solar panel. The first five natural frequencies and the first mode shape of the high-order finite element model are input into the deep neural network to obtain the corresponding material parameters. The corrected low-order finite element model is obtained by applying the material parameters. Thus, the low-order finite element model is corrected using deep neural networks, so that the accuracy of the corrected model is improved while maintaining low dimensionality. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 A flowchart of the finite element parameter correction method based on deep neural networks provided by the present invention;

[0044] Figure 2 This is a flowchart illustrating a specific embodiment;

[0045] Figure 3 Flowchart for modeling satellite solar panels based on the finite element method;

[0046] Figure 4 A schematic diagram showing the cumulative error variation curves of the first 15 natural frequencies of a low-order finite element model under different partitioning conditions;

[0047] Figure 5 The flowchart shows the finite element model correction algorithm based on deep neural networks.

[0048] Figure 6 A block diagram of a finite element parameter correction system based on a deep neural network provided for this invention.

[0049] Explanation of reference numerals in the attached figures:

[0050] Acquisition Module 1, Model Building Module 2, Calculation Module 3, Prediction Module 4, Correction Module 5. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] The purpose of this invention is to provide a finite element parameter correction method, system, and device based on deep neural networks, which can obtain finite element parameters with fast calculation and high accuracy using low-dimensional finite element models.

[0053] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] Example 1

[0055] like Figure 1 As shown, this invention provides a finite element parameter correction method based on a deep neural network, the correction method comprising:

[0056] Step S1: Obtain the geometric and material parameters of the satellite solar panel; the material parameters include density, elastic modulus, and Poisson's ratio. Specifically, the geometric parameters refer to the length, width, and height of the solar panel, and the material parameters refer to the material density, elastic modulus, and Poisson's ratio of the solar panel. In practical applications, these parameters are selected according to the needs of the specific project.

[0057] Step S2: Based on the geometric and material parameters of the satellite solar panel, establish a high-order finite element model and a low-order finite element model before correction for the satellite solar panel; the high-order finite element model is a finite element model established according to a first set finite element division order; the low-order finite element model before correction is a finite element model established according to a second set finite element division order; the second set finite element division order is less than the first set finite element division order.

[0058] Step S3: Calculate the first 5 natural frequencies and first mode shape of the higher-order finite element model, and the first 5 natural frequencies and first mode shape of the lower-order finite element model before correction. Specifically, calculating the first 5 natural frequencies and first mode shape of the higher-order finite element model includes:

[0059] Step S31: Determine the mass matrix and stiffness matrix based on the high-order finite element model.

[0060] Step S32: Based on the mass matrix and the stiffness matrix, establish the undamped free vibration equation of the satellite solar panel.

[0061] Step S33: Solve the equation for the undamped free vibration to obtain the first 5 natural frequencies and the first mode shape. S33 specifically includes:

[0062] Step S331: Based on the undamped free vibration equation, obtain the displacement equation of the satellite solar panel.

[0063] Step S332: Calculate the second derivative of the displacement equation to obtain the expression for the second derivative of the displacement.

[0064] Step S333: Substitute the second derivative expression into the undamped free vibration equation to obtain the relationship between the mode shape and the natural frequency.

[0065] Step S334: Solve the relationship between the mode shape and the natural frequency to obtain the first 5 natural frequencies and the first mode shape.

[0066] Step S4: Input the first 5 natural frequencies and first mode shape of the high-order finite element model into the deep neural network to obtain the density, elastic modulus and Poisson's ratio of the satellite solar panel under the high-order finite element model; wherein, the deep neural network is obtained by training through a training set; the training set consists of the first 5 natural frequencies and first mode shape of the low-order finite element model before correction and the corresponding material parameters.

[0067] Step S5: Based on the density, elastic modulus, and Poisson's ratio of the satellite solar panel under the high-order finite element model, the parameter-corrected low-cost finite element model is obtained according to the second set finite element division order.

[0068] The training process of the deep neural network includes:

[0069] Step 1: Calculate a sample of material parameters for multiple set percentages of the material parameters of the satellite solar panels.

[0070] Step 2: Based on the modified low-order finite element model and the sample material parameters, calculate the corresponding first 5 natural frequencies and first mode shapes.

[0071] Step 3: Using the corresponding first 5 natural frequencies and first mode shapes as inputs and the sample material parameters as outputs, train the deep neural network using the backpropagation algorithm to obtain a trained deep neural network.

[0072] Furthermore, the correction method also includes:

[0073] The vibration of the satellite solar panels was analyzed using a low-cost finite element model with the parameters corrected described above.

[0074] As a specific implementation method, such as Figure 2As shown, the application process of the finite element parameter correction method based on deep neural networks provided by this invention is as follows:

[0075] Step S001: Determine the geometric and material parameters of the large satellite solar panels.

[0076] Step S002: Model the large satellite solar panel using the finite element method to obtain its mass and stiffness matrices. Different orders of finite element methods are used to obtain mass and stiffness matrices of varying orders for the large solar panel. The mass and stiffness matrices obtained through higher-order finite element methods are called high-order finite element models, while those obtained through lower-order methods are called low-order finite element models. In practical applications, the choice between higher and lower order finite element methods is made based on the specific circumstances during the research process. The low-order finite element model is used to generate training samples for the neural network, and subsequent modifications to the low-order finite element model involve correcting its material parameters.

[0077] Step S003: Calculate the first 5 natural frequencies and first mode shape of the high-order finite element model of the large satellite solar panel. Select the first 5 natural frequencies and first mode shape of the high-order finite element model of the satellite solar panel as the input of the neural network, and output the density, elastic modulus and Poisson's ratio of the satellite solar panel.

[0078] Step S004: Set the material density, elastic modulus, and Poisson's ratio of the samples according to 95%, 90%, 85%, 80%, 70%, and 60% of the initial material density, elastic modulus, and Poisson's ratio of the large satellite solar panels determined in S001, respectively. Calculate the first 5 natural frequencies and first mode shape of the low-order finite element model of the large satellite solar panels under these parameters, obtaining a total of 216 samples, which constitute the training set.

[0079] Step S005: Train the deep neural network using the training set. The specific steps are as follows:

[0080] (1) Randomly initialize the neural network parameters.

[0081] (2) Select one sample from the 216 samples determined in S4 to input into the neural network, and update the parameters of the deep neural network through the backpropagation algorithm; where each sample consists of 5 natural frequencies and 1 mode shape, selecting one sample here means inputting the 5 natural frequencies and 1 mode shape into the deep neural network. The 216 samples are 216 sets of data, each set of data consists of 5 natural frequencies and 1 mode shape, and here one set is input into the neural network.

[0082] (3) Repeat (2) until all samples in the training set have been traversed once.

[0083] (4) Repeat steps (2) and (3) until the neural network training stopping condition is met, thus completing the neural network training. The stopping condition is as follows: Before starting neural network training, two parameters are set: the maximum number of training iterations N and the neural network training error ξ. Training can stop as long as either of these parameters is reached during the training process. Specifically, if the neural network training error fails to reach ξ during training, the neural network stops training after reaching N iterations. If the neural network training error reaches ξ during training (meaning the number of training iterations has not reached N), then training stops. In this invention, the maximum number of neural network training iterations is set to 500,000, and the neural network training error is set to 0.00001.

[0084] Step S006: Using the density, elastic modulus, and Poisson's ratio output by the deep neural network, establish a modified low-order finite element model of the large satellite solar panel according to the same finite element division order as the low-order finite element model in S002.

[0085] Step S007: Apply the modified low-order finite element model of the large satellite solar panel to the vibration control of the large satellite solar panel.

[0086] The calculation process for the first 5 natural frequencies and the first mode shape of the high-order finite element model is as follows:

[0087] The mass matrix M and stiffness matrix K obtained by the high-order finite element method are used to establish the undamped free vibration equation of the large satellite solar panel as shown in Equation (1):

[0088]

[0089] Where M is the mass matrix obtained by the high-order finite element method, and K is the stiffness matrix obtained by the high-order finite element method. The second derivative of the displacement of a large satellite solar panel undergoing simple harmonic motion; The first derivative of the displacement of a large satellite's solar panel undergoing simple harmonic motion.

[0090] Assuming that the solar panels of a large satellite undergo simple harmonic motion during free vibration, the displacement q(t) is expressed as shown in formula (2):

[0091] q(t)=φsin(ωt+θ) (2)

[0092] Where q(t) is the displacement of the large satellite solar panel in simple harmonic motion at time t, φ is the shape vector of the structural displacement, called the mode shape, ω is the frequency of the simple harmonic motion of the solar panel, and θ is the phase angle.

[0093] Taking the second derivative of formula (2), we obtain formula (3):

[0094]

[0095] in, The second derivative of the displacement of a large satellite solar panel undergoing simple harmonic motion at time t, where ω is the frequency of the solar panel's simple harmonic motion, φ is the shape vector of the structural displacement, called the mode shape, and θ is the phase angle.

[0096] Substituting formulas (2) and (3) into formula (1), we obtain formula (4):

[0097] (-ω 2 M+K)φsin(ωt+θ)=0 (4)

[0098] By removing sin(ωt+θ) from both sides of formula (4), we obtain formula (5):

[0099] (K-ω 2 M)φ=0 (5)

[0100] Equation (5) is an Nth-order homogeneous linear equation system with respect to φ, which characterizes the relationship between the mode shape and the natural frequency. The necessary and sufficient condition for this equation to have a zero solution is that the determinant of the coefficient matrix is ​​equal to 0, as shown in equation (6):

[0101] |K-ω 2 M|=0 (6)

[0102] For a system with N degrees of freedom, equation (6) is about ω 2 The Nth degree equation yields formula (7):

[0103] a N (ω 2 ) N +a N-1 (ω 2 ) N-1 +…+a1ω 2 +a0=0 (7)

[0104] For a stable structural system, the corresponding frequency equation is shown in equation (7), which has N positive real roots, as shown in equation (8):

[0105]

[0106] Where, ω n(n = 1, 2, ..., N) represents the first n natural frequencies of the structure.

[0107] When the solar panels of a large satellite vibrate at the first-order frequency, the structure will maintain a fixed shape, which is called the first-order mode shape. Substituting the corresponding natural frequency ω1 into the characteristic equation of the equation of motion, we obtain the first-order mode shape φ1, as shown in formula (9).

[0108]

[0109] In practical applications, the first 15 natural frequencies of the corrected low-order finite element model were calculated based on a deep neural network. The 15th frequency is used as an indicator to evaluate the model correction results. The purpose of calculating the 15th frequency is to verify the model correction effect. The calculation steps are as follows: equations (1) to (8). The first 5 natural frequencies and 1st mode shape of the low-order finite element model were corrected using the first 5 natural frequencies and 1st mode shape of the high-order finite element model, improving the accuracy of the low-order finite element model while ensuring computation time. Specifically, the basic principle of neural network model correction is as follows: For a finite element model, after determining the material parameters and geometric parameters, the natural frequencies and first-order mode shapes are obtained through model analysis. That is, it is assumed that there is a mapping relationship between the model parameters and the natural frequencies and first-order mode shapes. The work of the neural network is to learn the inverse mapping of this mapping, that is, input the natural frequencies and output the model parameters. After the neural network is trained, only the natural frequencies and first-order mode shapes of the high-order model need to be input to obtain the material parameters of the corresponding low-order finite element model. After obtaining the material parameters, the parameters are input into the low-order finite element model for analysis to obtain the corresponding natural frequencies. Compared with the uncorrected low-order finite element model, the accuracy is improved.

[0110] The satellite solar panel's geometric parameters are: length 60m, width 5m, thickness 10cm. The material parameters of the solar panel are set as: density 1.8×10⁻⁶. 3 kg / m 3 With an elastic modulus of 230 GPa and a Poisson's ratio of 0.307, taking the satellite's solar panels as an example, the effectiveness of the intelligent modeling method for control proposed in this invention is demonstrated through simulation, as detailed below:

[0111] Based on the geometric and material parameters of the satellite solar panel, a finite element model of the satellite solar panel was established. First, a high-order finite element model was established, dividing the satellite solar panel into 480 segments along its length and 8 segments along its width, resulting in a total of 3840 basic elements. The specific process is as follows... Figure 3 As shown.

[0112] Table 1 shows the first 15 natural frequencies of the MATLAB high-order finite element model and the ANSYS model, as well as the errors between them. The 15th natural frequency of the ANSYS model is selected as the true value, and the first 15 natural frequencies of the MATLAB high-order finite element model are selected as approximate values ​​of the true value.

[0113] Table 1. Statistics of the first 15 natural frequencies and errors.

[0114]

[0115] When establishing a low-order finite element model in MATLAB, the impact of finite element meshing on controller design and finite element model error needs to be comprehensively considered. Dense meshing can effectively reduce the error between the finite element model and the actual structure, but it is not conducive to controller design; sparse meshing is beneficial to controller design, but the initial error of the finite element model is too large. For satellite solar panels, such as... Figure 3 As shown, the cumulative error curves of the first 15 natural frequencies of the low-order finite element model and the first 15 natural frequencies of the high-order finite element model are presented when the satellite solar panel is divided into 3 to 100 basic elements using the MATLAB finite element modeling program.

[0116] according to Figure 4 It can be seen that the cumulative error of the first 15 natural frequencies of the low-order finite element model decreases rapidly with the increase of the number of elements in the model. After the low-order finite element model is divided into 20 elements (i.e., 20 blocks), the cumulative frequency error has basically stabilized. Therefore, in order to further determine the order of the low-order finite element model, Table 2 gives the specific values ​​of the cumulative error of the first 15 natural frequencies of the low-order finite element model when divided into 3 to 20 blocks, compared with the high-order finite element model. After training the network, the finite element calculation data used for training and the results predicted by the network are shown in Table 2 below:

[0117] Table 2. Statistics of Cumulative Frequency Error

[0118]

[0119] After obtaining the high-order finite element model and the low-order finite element model, the first 15 natural frequencies of the two are calculated respectively. The calculation process is shown in formulas (1) to (8), and their errors are shown in Table 3. The first 15 natural frequencies of the MATLAB high-precision model are selected as the true values.

[0120] Table 3 shows the error statistics for the first 15 natural frequencies.

[0121]

[0122] The core of the finite element model correction method based on deep neural networks is to express the functional relationship through neural networks and directly output the target values ​​of design parameters based on the target response values. The algorithm flow is as follows: Figure 5 .

[0123] The first 15 natural frequencies of the corrected low-order finite element model were calculated based on the structural parameters output by the neural network, and compared with those of the high-order finite element model. The results are shown in Table 4.

[0124] Table 4. Statistics of the first 15 natural frequencies of the corrected low-order finite element model.

[0125]

[0126]

[0127] As shown in Table 4, using the first 15 frequencies as the evaluation index for model accuracy verifies that the accuracy of the corrected low-order finite element model has been improved.

[0128] In practical applications, the modified low-order finite element model of large satellite solar panels is used for vibration control of these panels. Specifically, this includes:

[0129] Still considering a solar panel 60m long, 5m wide, and 10cm thick, before model modification, the panel was divided into 3840 basic units. The unmodified model was directly used for vibration control. Since each basic unit has four nodes and each node has three degrees of freedom, there are a total of 11367 degrees of freedom. Using MATLAB for simulation, the LQR algorithm was applied to this model for vibration control. The control law was calculated in MATLAB, requiring 47.2 seconds of computation time. For the modified solar panel model, which has only 6 basic units, each with four nodes and three degrees of freedom, there are a total of 72 degrees of freedom. Using MATLAB for simulation, the LQR algorithm was also applied to the modified model for vibration control. The control law was calculated in MATLAB, requiring only 0.72 seconds of computation time. It can be seen that applying the method proposed in this invention to actual vibration control can greatly reduce the computational power required to calculate the control law. Considering the precious computing power in space, the method proposed in this invention is very meaningful.

[0130] Example 2

[0131] To implement the method corresponding to Embodiment 1 above and achieve the corresponding functions and technical effects, a finite element parameter correction system based on a deep neural network is provided below, such as... Figure 6 As shown, the system includes:

[0132] Acquisition module 1 is used to acquire the geometric parameters and material parameters of the satellite solar panels; the material parameters include density, elastic modulus and Poisson's ratio.

[0133] Model building module 2 is used to build a high-order finite element model and a low-order finite element model before correction of the satellite solar panel based on the geometric and material parameters of the satellite solar panel; the high-order finite element model is a finite element model built according to a first set finite element division order; the low-order finite element model before correction is a finite element model built according to a second set finite element division order; the second set finite element division order is less than the first set finite element division order.

[0134] Calculation module 3 is used to calculate the first 5 natural frequencies and first mode shape of the higher-order finite element model and the first 5 natural frequencies and first mode shape of the lower-order finite element model before correction.

[0135] Prediction module 4 is used to input the first 5 natural frequencies and first mode shape of the high-order finite element model into a deep neural network to obtain the density, elastic modulus and Poisson's ratio of the satellite solar panel under the high-order finite element model; wherein, the deep neural network is trained through a training set; the training set consists of the first 5 natural frequencies and first mode shape of the low-order finite element model before correction and the corresponding material parameters.

[0136] The correction module 5 is used to obtain a low-cost finite element model with corrected parameters based on the density, elastic modulus, and Poisson's ratio of the satellite solar panel under the high-order finite element model, according to the second set finite element division order.

[0137] Example 3

[0138] This invention provides a device including a memory and a processor. The memory stores a computer program, and the processor runs the computer program to enable the device to perform the security monitoring video privacy protection method of Embodiment 1.

[0139] Alternatively, the aforementioned device may be a server.

[0140] In addition, embodiments of the present invention also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for protecting the privacy of security monitoring videos as described in Embodiment 1.

[0141] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0142] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A finite element parameter correction method based on deep neural networks, characterized in that, The correction method includes: Obtain the geometric and material parameters of the satellite's solar panels; the material parameters include density, elastic modulus, and Poisson's ratio. Based on the geometric and material parameters of the satellite solar panel, a high-order finite element model and a low-order finite element model before correction are established for the satellite solar panel; the high-order finite element model is a finite element model established according to a first set finite element division order; the low-order finite element model before correction is a finite element model established according to a second set finite element division order; the second set finite element division order is less than the first set finite element division order. Calculate the first 5 natural frequencies and first mode shape of the higher-order finite element model, and the first 5 natural frequencies and first mode shape of the lower-order finite element model before correction. The first five natural frequencies and first mode shape of the high-order finite element model are input into a deep neural network to obtain the density, elastic modulus, and Poisson's ratio of the satellite solar panel under the high-order finite element model; wherein, the deep neural network is obtained by training through a training set; the training set consists of the first five natural frequencies and first mode shape of the low-order finite element model before correction and the corresponding material parameters. Based on the density, elastic modulus, and Poisson's ratio of the satellite solar panel in the high-order finite element model, and according to the second set finite element division order, a low-order finite element model with corrected parameters is obtained.

2. The finite element parameter correction method based on deep neural networks according to claim 1, characterized in that, The training process of the deep neural network includes: Calculate sample material parameters as multiple set percentages of the material parameters of the satellite solar panels; Based on the modified low-order finite element model and the sample material parameters, calculate the corresponding first 5 natural frequencies and first mode shape. Using the corresponding first 5 natural frequencies and first mode shapes as inputs, and the sample material parameters as outputs, the deep neural network is trained using the backpropagation algorithm to obtain a trained deep neural network.

3. The finite element parameter correction method based on deep neural networks according to claim 1, characterized in that, The calculation of the first five natural frequencies and first mode shape of the higher-order finite element model includes: Based on the aforementioned high-order finite element model, determine the mass matrix and stiffness matrix; Based on the mass matrix and the stiffness matrix, establish the equation for the undamped free vibration of the satellite solar panel; The equation for undamped free vibration is solved to obtain the first five natural frequencies and the first mode shape.

4. The finite element parameter correction method based on deep neural networks according to claim 3, characterized in that, Solving the equation for undamped free vibration yields the first five natural frequencies and the first mode shape, specifically including: Based on the undamped free vibration equation, the displacement equation of the satellite solar panel is obtained; Find the second derivative of the displacement equation to obtain the expression for the second derivative of the displacement; Substituting the second derivative expression into the undamped free vibration equation, we obtain the relationship between the mode shape and the natural frequency. The relationship between the mode shape and the natural frequency is solved to obtain the first 5 natural frequencies and the first mode shape.

5. The finite element parameter correction method based on deep neural networks according to claim 4, characterized in that, The displacement equation is: ； in, Performing simple harmonic motion for large satellite solar panels t Displacement at any moment For vibration modes, ω The frequency of the simple harmonic vibration of the solar panel. θ This is the phase angle.

6. The finite element parameter correction method based on deep neural networks according to claim 4, characterized in that, The relationship between the mode shape and the natural frequency is as follows: ； in, For vibration modes, ω The frequency of the simple harmonic vibration of the solar panel. M For the quality matrix, K Here is the stiffness matrix.

7. The finite element parameter correction method based on deep neural networks according to claim 1, characterized in that, The correction method further includes: The vibration of the satellite solar panels was analyzed using a low-order finite element model modified with the aforementioned parameters.

8. A finite element parameter correction system based on a deep neural network, characterized in that, The correction system includes: The acquisition module is used to acquire the geometric and material parameters of the satellite's solar panels; the material parameters include density, elastic modulus, and Poisson's ratio. The model building module is used to build a high-order finite element model and a low-order finite element model before correction of the satellite solar panel based on the geometric and material parameters of the satellite solar panel; the high-order finite element model is a finite element model built according to a first set finite element division order; the low-order finite element model before correction is a finite element model built according to a second set finite element division order; the second set finite element division order is less than the first set finite element division order. The calculation module is used to calculate the first 5 natural frequencies and first mode shape of the higher-order finite element model and the first 5 natural frequencies and first mode shape of the lower-order finite element model before correction. The prediction module is used to input the first five natural frequencies and first mode shape of the high-order finite element model into a deep neural network to obtain the density, elastic modulus and Poisson's ratio of the satellite solar panel under the high-order finite element model; wherein, the deep neural network is trained through a training set; the training set consists of the first five natural frequencies and first mode shape of the low-order finite element model before correction and the corresponding material parameters. The correction module is used to obtain a low-order finite element model with corrected parameters based on the density, elastic modulus, and Poisson's ratio of the satellite solar panel under the high-order finite element model, according to the second set finite element division order.

9. A device, characterized in that, The device is an electronic device, including a memory and a processor. The memory is used to store a computer program, and the processor runs the computer program to enable the device to perform the finite element parameter correction method based on a deep neural network according to any one of claims 1 to 7.

10. The device according to claim 9, characterized in that, The memory is a readable storage medium.

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