Reliability Analysis Method for Satellite Frame Structure Based on Sampling Quantile Regression

Abstract

The present invention discloses a reliability analysis method for a satellite frame structure based on sampling quantile regression, including: constructing a deep neural network model for predicting the first-order frequency of the satellite frame structure; obtaining multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure based on a finite element model of the satellite frame structure to be analyzed, determining the corresponding first-order frequency for each group of input parameter values, adding random noise to the first-order frequency to obtain a corrected value of the first-order frequency, and obtaining a plurality of training data including the input parameter values and the corrected values of the first-order frequency corresponding to the input parameter values; setting a quantile, constructing a loss function using the quantile, and training the deep neural network model using the training data and the loss function; and performing reliability analysis on the satellite frame structure using the deep neural network model. The present invention can avoid the problems of long calculation time and high calculation cost existing in the analysis using a finite element model, and reduce the influence of computer noise on the prediction accuracy of the neural network model.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite structure design, and particularly relates to a method for analyzing the reliability of a satellite frame structure based on sampling quantile regression. Background Art

[0002] The design of the satellite frame structure is the central link in the overall design process of the satellite. The design of the satellite frame structure needs to consider factors such as the strength, stiffness, modal characteristics, temperature, and radiation resistance characteristics of the frame structure, and minimize the structural mass on the premise of ensuring the safe bearing of the payload. During the launch process, if the natural frequency of the satellite is close to the vibration frequency of the rocket, resonance will occur during the launch stage, which will affect the performance of the satellite payload to a lesser extent and damage the entire satellite structure to a greater extent. The natural frequency of the satellite is affected by factors such as the characteristics of the frame structure material (such as density, elastic modulus, etc.) and processing errors. Due to the high cost and high risk of satellites, in order to ensure that the satellite frame structure is not damaged during the launch process, it is necessary to perform reliability analysis on the satellite frame structure during satellite design.

[0003] In the prior art, the first-order frequency of the satellite frame structure is obtained by finite element model analysis for the reliability analysis of the satellite frame structure. However, in a single simulation analysis, it takes a long time to analyze the first-order frequency of the satellite frame structure using the finite element model. Therefore, when performing reliability analysis on the satellite frame structure, a large number of simulation experiments are required, and the calculation cost and calculation time are relatively high. Moreover, the calculation cost and calculation time will increase step by step with the complexity of the satellite frame structure. Summary of the Invention

[0004] To solve some or all of the technical problems existing in the above prior art, the present invention provides a method for analyzing the reliability of a satellite frame structure based on sampling quantile regression.

[0005] The technical solution of the present invention is as follows:

[0006] A method for analyzing the reliability of a satellite frame structure based on sampling quantile regression is provided, and the method includes:

[0007] Constructing a deep neural network model for predicting the first-order frequency of the satellite frame structure;

[0008] Obtaining multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model of the satellite frame structure to be analyzed, determining the first-order frequency corresponding to each group of input parameter values by using the finite element method, adding random noise to the first-order frequency to obtain a corrected value of the first-order frequency, and obtaining a plurality of training data including the input parameter values and the corrected values of the first-order frequency corresponding to the input parameter values;

[0009] Set the quantiles, construct a loss function using the quantiles, and train a deep neural network model with the training data and the loss function to fit the mapping relationship between the input parameter values and the first-order frequency;

[0010] Use the trained deep neural network model for reliability analysis of the satellite frame structure.

[0011] In some possible implementation manners, the deep neural network model adopts a deep feedforward neural network.

[0012] In some possible implementation manners, the obtaining of multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure to be analyzed based on a finite element model, and using the finite element method to determine the first-order frequency corresponding to each group of input parameter values includes:

[0013] According to the satellite frame structure to be analyzed, determine the input parameters for analyzing the first-order frequency of the satellite frame structure based on the finite element model and the value ranges of each input parameter, randomly sample once from the value range of each input parameter respectively to obtain a group of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model, repeat the random sampling process multiple times to obtain multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model, and use the finite element method to analyze and determine the first-order frequency corresponding to each group of input parameter values.

[0014] In some possible implementation manners, the input parameters for analyzing the first-order frequency of the satellite frame structure based on the finite element model include at least one of the aluminum alloy density, spring steel density, titanium alloy density, aluminum alloy elastic modulus, spring steel elastic modulus, and titanium alloy elastic modulus of the satellite frame structure.

[0015] In some possible implementation manners, obtain the first-order frequency correction value using the following formula;

[0016]

[0017] where y i represents the first-order frequency correction value corresponding to the i-th group of input parameter values, represents the first-order frequency corresponding to the i-th group of input parameter values determined using the finite element method, and ε represents random noise.

[0018] In some possible implementation manners, set the quantile as τ i τ i ~U(0,1), and construct the loss function as:

[0019]

[0020]

[0021] where τi Denote the quantile corresponding to the \(i\)-th training data as \(\tau\). i \(\sim U(0,1)\) represents that the quantile \(\tau\) i obeys the uniform distribution on \([0,1]\). Denote the loss function as \(L\), the first-order frequency correction value as \(y\), the first-order frequency prediction value output by the deep neural network model as \(\hat{y}\), the input parameter value for analyzing the first-order frequency of the satellite frame structure based on the finite element model as \(x\), the parameters of the deep neural network model as \(\theta\), the number of training data as \(n\), and \(x^{(i)}\) i denote the \(i\)-th group of input parameter values. Denote the \(i\)-th group of input parameter values \(x^{(i)}\) output by the deep neural network model as \(\hat{x}^{(i)}\). i The corresponding first-order frequency prediction value.

[0022] In some possible implementation manners, the reliability analysis of the satellite frame structure by using the trained deep neural network model includes:

[0023] According to the satellite frame structure to be analyzed and the input parameters for analyzing the first-order frequency of the satellite frame structure based on the finite element model, randomly sample once from the value range of each input parameter, obtain a group of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model, and repeat the random sampling process multiple times to obtain multiple groups of input parameter values \(\{x^{(j)}|j = 1,2,\cdots,M\}\); j |j = 1,2,\cdots,M\};

[0024] Given a quantile \(\tau\), input \(\{(x^{(j)},\tau)|j = 1,2,\cdots,M\}\) as input data into the trained deep neural network model to obtain the first-order frequency prediction value j corresponding to the input data, where \(\tau = 0.5\); where \(\tau = 0.5\);

[0025] Set the first-order frequency critical value of the satellite frame structure, and calculate the limit state value of the first-order frequency according to the first-order frequency prediction value and the first-order frequency critical value;

[0026] Count the number of values less than 0 among all the limit state values of the first-order frequency to determine the reliability of the satellite frame structure.

[0027] In some possible implementation manners, use the following formula to calculate the limit state value of the first-order frequency of the satellite frame structure;

[0028]

[0029] where \(\Delta\) j (x^{(j)}) represents the limit state value of the first-order frequency, and \(y_0\) j represents the first-order frequency critical value. lim represents the first-order frequency critical value.

[0030] In some possible implementation manners, the reliability of the first-order frequency of the satellite frame structure is determined by using the following formula;

[0031]

[0032] wherein, R represents the reliability score, and m represents the number of limit state values of all first-order frequencies that are less than 0.

[0033] The main advantages of the technical solution of the present invention are as follows:

[0034] The reliability analysis method of the satellite frame structure based on sampling quantile regression of the present invention realizes the prediction calculation of the first-order frequency of the satellite frame structure by using a deep neural network model, and can avoid the problems of long calculation time and high calculation cost existing in the analysis using a finite element model; meanwhile, when obtaining training data, random noise is added to the obtained first-order frequency, which can effectively overcome the influence of computer noise on the finite element simulation analysis process, reduce the deviation between the training data and the true value, and improve the prediction accuracy of the trained deep neural network model. Description of the Drawings

[0035] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0036] Figure 1 It is a flowchart of the reliability analysis method of the satellite frame structure based on sampling quantile regression according to an embodiment of the present invention. Detailed Embodiments

[0037] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions of the present invention in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0038] The following will detail the technical solutions provided by the embodiments of the present invention in conjunction with the drawings.

[0039] Refer to Figure 1 , an embodiment of the present invention provides a reliability analysis method of a satellite frame structure based on sampling quantile regression. The method includes the following steps:

[0040] S1, construct a deep neural network model for predicting the first-order frequency of the satellite frame structure;

[0041] S2, obtain multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model of the satellite frame structure to be analyzed. Use the finite element method to determine the first-order frequency corresponding to each group of input parameter values, add random noise to the first-order frequency, obtain the corrected value of the first-order frequency, and obtain multiple training data including the input parameter values and the corrected value of the first-order frequency corresponding to the input parameter values;

[0042] S3, set the quantile, construct a loss function using the quantile, and train the deep neural network model using the training data and the loss function to fit the mapping relationship between the input parameter values and the first-order frequency;

[0043] S4, perform reliability analysis of the satellite frame structure using the trained deep neural network model.

[0044] The method for reliability analysis of satellite frame structure based on sampling quantile regression provided by an embodiment of the present invention realizes the prediction calculation of the first-order frequency of the satellite frame structure by using a deep neural network model, and can avoid the problems of long calculation time and high calculation cost existing in the analysis using the finite element model; at the same time, when obtaining the training data, adding random noise to the obtained first-order frequency can effectively overcome the influence of computer noise on the finite element simulation analysis process, reduce the deviation between the training data and the true value, improve the prediction accuracy of the trained deep neural network model, and realize the fast and high-precision analysis of the reliability of the satellite frame structure.

[0045] The steps and principles of the method for reliability analysis of satellite frame structure based on sampling quantile regression provided by an embodiment of the present invention are specifically described below.

[0046] Step S1, construct a deep neural network model for predicting the first-order frequency of the satellite frame structure.

[0047] Specifically, in an embodiment of the present invention, the deep neural network model for predicting the first-order frequency of the satellite frame structure may adopt a deep feedforward neural network model. The deep feedforward neural network model includes an input layer, a hidden layer, and an output layer. The neurons in each layer receive the output of the neurons in the previous layer and generate an output to the next layer.

[0048] Among them, the number of layers of the hidden layer of the deep feedforward neural network model can be determined according to the complexity of the problem of analyzing the first-order frequency of the satellite frame structure, and the satellite frame structure is the main structure of the satellite.

[0049] Step S2: Obtain multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model. Use the finite element method to determine the first-order frequency corresponding to each group of input parameter values. Add random noise to the first-order frequency to obtain the corrected first-order frequency value, and obtain multiple training data including the input parameter values and the corrected first-order frequency values corresponding to the input parameter values.

[0050] To ensure that the deep neural network model can be used to predict the first-order frequency of the satellite frame structure, it is necessary to pre-train the deep neural network model using the training data. Since real data is difficult to obtain and usually in small quantities, in one embodiment of the present invention, the training data is obtained through simulation analysis experiments.

[0051] Specifically, obtaining multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model and using the finite element method to determine the first-order frequency corresponding to each group of input parameter values includes:

[0052] According to the satellite frame structure to be analyzed, determine the input parameters for analyzing the first-order frequency of the satellite frame structure based on the finite element model and the value range of each input parameter. Randomly sample once from the value range of each input parameter to obtain a group of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model. Repeat the random sampling process multiple times to obtain multiple groups of input parameter values {x i | i = 1, 2, …, n} for analyzing the first-order frequency of the satellite frame structure based on the finite element model, and use the finite element method to analyze and determine the first-order frequency corresponding to each group of input parameter values.

[0053] In one embodiment of the present invention, the input parameters for analyzing the first-order frequency of the satellite frame structure based on the finite element model may include at least one of the aluminum alloy density, spring steel density, titanium alloy density, aluminum alloy elastic modulus, spring steel elastic modulus, and titanium alloy elastic modulus of the satellite frame structure.

[0054] Among them, the specific value range of each input parameter can be determined according to the satellite frame structure to be analyzed.

[0055] Furthermore, considering that when obtaining training data through simulation analysis experiments using the finite element method, due to computer noise, there is a certain deviation between the first-order frequency obtained by simulation and the real value. For this reason, in one embodiment of the present invention, add random noise ε to the first-order frequency obtained by using the finite element method to obtain the corrected first-order frequency value y i , and obtain multiple training data including the input parameter values and the corrected first-order frequency values corresponding to the input parameter values {(x i , y i ) | i = 1, 2, …, n}.

[0056] Specifically, the first-order frequency correction value is obtained using the following formula;

[0057]

[0058] Among them, the random noise ε can be determined according to the specific satellite frame structure problem, and the number of training data n can be determined according to the prediction accuracy of the required deep neural network model. The more training data there are, the higher the prediction accuracy of the obtained deep neural network model, but the higher the computing time and computing cost required to obtain the training data.

[0059] In step S3, a quantile is set, a loss function is constructed using the quantile, and the deep neural network model is trained using the training data and the loss function to fit the mapping relationship between the input parameter values and the first-order frequency.

[0060] Specifically, the quantile is set to τ i , τ i ~U(0,1), and the loss function is constructed as:

[0061]

[0062]

[0063] Among them, τ i represents the quantile corresponding to the i-th training data, τ i ~U(0,1) indicates that the quantile τ i follows a uniform distribution on [0,1], represents the loss function, y represents the first-order frequency correction value, represents the predicted value of the first-order frequency output by the deep neural network model, x represents the input parameter value for analyzing the first-order frequency of the satellite frame structure based on the finite element model, θ represents the parameters of the deep neural network model, n represents the number of training data, x i represents the i-th set of input parameter values, y i represents the first-order frequency correction value corresponding to the i-th set of input parameter values x i , represents the predicted value of the first-order frequency corresponding to the i-th set of input parameter values x i output by the deep neural network model.

[0064] According to the above constructed loss function, the training data for training the deep neural network model is actually {[(x i , τ i ), y i |i = 1, 2, …, n}.

[0065] Further, based on the obtained training data and the constructed loss function, and using deep learning technology, the deep neural network model is trained by minimizing the loss function to update the parameters of the deep neural network model, so as to obtain a deep neural network model that can be used to predict the first-order frequency of the satellite frame structure.

[0066] Specifically, the parameters of the updated deep neural network model obtained by training can be expressed as:

[0067]

[0068] Among them, represents the parameters of the updated deep neural network model.

[0069] By using the obtained training data and the constructed loss function to train the deep neural network model, the deep neural network model can learn the physical laws in the training data, so as to obtain a neural network with strong generalization ability, which can realize fast and high-precision prediction of the first-order frequency of the satellite frame structure. Essentially, the deep neural network is an agent model.

[0070] Step S4: Use the trained deep neural network model to perform reliability analysis on the satellite frame structure.

[0071] Specifically, after the training of the deep neural network model is completed, when the first-order frequency of the satellite frame structure needs to be predicted, according to the satellite frame structure to be predicted, the input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model are given, and a specific quantile is given. The determined input parameter values and the quantile are input into the trained deep neural network model to obtain the output of the deep neural network model, that is, the predicted value of the first-order frequency. Among them, the given quantile can be 0.5.

[0072] Further, in an embodiment of the present invention, using the trained deep neural network model to perform reliability analysis on the satellite frame structure includes:

[0073] According to the satellite frame structure to be analyzed and the input parameters for analyzing the first-order frequency of the satellite frame structure based on the finite element model, a random sample is taken once from the value range of each input parameter to obtain a set of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model. The random sampling process is repeated multiple times to obtain multiple sets of input parameter values {x j |j = 1, 2, …, M};

[0074] Given a quantile τ, then {(x j, τ)| j = 1, 2, …, M} as input data into the trained deep neural network model to obtain the first-order frequency prediction value corresponding to the input data where τ = 0.5;

[0075] Set the critical value of the first-order frequency of the satellite frame structure, and calculate the limit state value of the first-order frequency according to the first-order frequency prediction value and the critical value of the first-order frequency;

[0076] Count the number of values less than 0 among all the limit state values of the first-order frequency to determine the reliability of the satellite frame structure.

[0077] Specifically, when performing the reliability analysis of the satellite frame structure, the following formula can be used to calculate the limit state value of the first-order frequency of the satellite frame structure;

[0078]

[0079] where Δ j (x j ) represents the limit state value of the first-order frequency, y lim represents the critical value of the first-order frequency. The critical value of the first-order frequency can be determined according to the vibration frequency of the launch vehicle when the satellite to be analyzed is launched. When the limit state value Δ j (x j ) is less than 0, it indicates that the satellite frame structure resonates and the structure fails.

[0080] Specifically, when performing the reliability analysis of the satellite frame structure, the following formula can be used to calculate and determine the reliability of the satellite frame structure;

[0081]

[0082] where R represents the reliability score, m represents the number of values less than 0 among all the limit state values of the first-order frequency. The closer the value of R is to 1, the higher the reliability of the satellite frame structure.

[0083] It should be noted that in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "including", "comprising" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. In addition, "front", "rear", "left", "right", "up" and "down" in this article are all referenced to the placement state shown in the drawings.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A reliability analysis method for satellite frame structures based on sampling quantile regression, characterized in that, Including: Constructing a deep neural network model for predicting the first-order frequency of a satellite frame structure; Obtaining multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure based on a finite element model, determining the first-order frequency corresponding to each group of input parameter values by using the finite element method, adding random noise to the first-order frequency, obtaining a corrected value of the first-order frequency, and obtaining multiple training data including the input parameter values and the corrected values of the first-order frequency corresponding to the input parameter values; Setting a quantile, constructing a loss function by using the quantile, and training the deep neural network model by using the training data and the loss function to fit the mapping relationship between the input parameter values and the first-order frequency; Performing reliability analysis of the satellite frame structure by using the trained deep neural network model; The obtaining of multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure based on a finite element model and determining the first-order frequency corresponding to each group of input parameter values by using the finite element method includes: According to the satellite frame structure to be analyzed, determining the input parameters for analyzing the first-order frequency of the satellite frame structure based on a finite element model and the value ranges of each input parameter, randomly sampling once from the value range of each input parameter to obtain a group of input parameter values for analyzing the first-order frequency of the satellite frame structure based on a finite element model, repeating the random sampling process multiple times to obtain multiple groups of input parameter values for analyzing the first-order frequency of the satellite frame structure based on a finite element model, and analyzing and determining the first-order frequency corresponding to each group of input parameter values by using the finite element method; Obtaining the corrected value of the first-order frequency by using the following formula; Among them, y i represents the first-order frequency correction value corresponding to the i-th group of input parameter values, represents the first-order frequency corresponding to the i-th group of input parameter values determined by the finite element method, and ε represents random noise; Set the quantile as τ i , τ i ~U(0,1), and construct the loss function as follows: Among them, τ i represents the quantile corresponding to the i-th training data, and τ i ~U(0,1) indicates that the quantile τ i obeys the uniform distribution on [0,1]. represents the loss function, y represents the first-order frequency correction value, represents the first-order frequency prediction value output by the deep neural network model, x represents the input parameter value for analyzing the first-order frequency of the satellite frame structure based on the finite element model, θ represents the deep neural network model parameters, n represents the number of training data, and x i represents the i-th group of input parameter values, represents the first-order frequency prediction value corresponding to the i-th group of input parameter values x i output by the deep neural network model.

2. The reliability analysis method of the satellite frame structure based on sampling quantile regression according to claim 1, characterized in that The deep neural network model adopts a deep feedforward neural network.

3. The reliability analysis method of the satellite frame structure based on sampling quantile regression according to claim 1, characterized in that, The input parameters for analyzing the first-order frequency of the satellite frame structure based on a finite element model include at least one of the aluminum alloy density, spring steel density, titanium alloy density, aluminum alloy elastic modulus, spring steel elastic modulus, and titanium alloy elastic modulus of the satellite frame structure.

4. The reliability analysis method of the satellite frame structure based on sampling quantile regression according to claim 1, characterized in that, The performing of reliability analysis of the satellite frame structure by using the trained deep neural network model includes: According to the satellite frame structure to be analyzed and the input parameters for analyzing the first-order frequency of the satellite frame structure based on the finite element model, randomly sample once from the value range of each input parameter to obtain a set of input parameter values for analyzing the first-order frequency of the satellite frame structure based on the finite element model. Repeat the random sampling process multiple times to obtain multiple sets of input parameter values {x j | j = 1, 2, …, M}; Given a quantile τ, input the set {(x j , τ)| j = 1, 2, …, M} as input data into the trained deep neural network model to obtain the first-order frequency prediction value corresponding to the input data where τ = 0.5; Setting a critical value of the first-order frequency of the satellite frame structure, and calculating the limit state value of the first-order frequency according to the predicted value of the first-order frequency and the critical value of the first-order frequency; Counting the number of values less than 0 among all the limit state values of the first-order frequency, and determining the reliability of the satellite frame structure.

5. The reliability analysis method of the satellite frame structure based on sampling quantile regression according to claim 4, wherein Calculating the limit state value of the first-order frequency of the satellite frame structure by using the following formula; Among them, Δ j (x j ) represents the limit state value of the first-order frequency, and y lim represents the critical value of the first-order frequency.

6. The reliability analysis method of the satellite frame structure based on sampling quantile regression according to claim 5, characterized in that, Determining the reliability of the first-order frequency of the satellite frame structure by using the following formula; Wherein, R represents the reliability score, and m represents the number of values less than 0 among all the limit state values of the first-order frequency.

Images