Satellite cabin panel thermal reliability analysis method

Abstract

The application discloses a satellite cabin plate thermal reliability analysis method, comprising the following steps: converting the power of the middle component of the cabin plate into a standard random variable, constructing a sparse multi-dimensional standard orthogonal basis corresponding to each component, sampling multiple combined input data, inputting the combined input data into a component maximum temperature proxy model, calculating the maximum temperature prediction value of each component, determining the maximum temperature interval of each component according to multiple maximum temperature prediction values of each component, determining the probability interval of normal operation and the probability interval of failure of each component according to the maximum temperature interval of each component and a normal working temperature threshold, constructing a cabin plate multi-layer Bayesian network thermal reliability model according to the functions of each component, and solving the probability interval of normal operation and the probability interval of failure of the cabin plate. The application can analyze the thermal reliability of the cabin plate on the basis of considering data uncertainty, improve the accuracy of the thermal reliability analysis result, and reduce the analysis cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of satellites, and in particular to a satellite cabin plate thermal reliability analysis method. BACKGROUND

[0002] In order to reduce the mass, volume and other indicators of the aircraft, the aircraft usually adopts high-density functional integration design. Therefore, the printed circuit board (PCB) with the advantages of less wiring, low assembly error and high integration is widely used. In the development of high-performance aircraft, the high-density functional integration cabin plate based on PCB design can be used to install various subassemblies, so that the aircraft has an integrated design scheme. Although the high-density functional integration design has many advantages, it also makes temperature one of the important factors affecting the performance of the subassembly installed on the cabin plate. For example, thermal stress and thermal strain may affect the reliability of chip packaging, and temperature changes may cause corrosion, oxidation, device burst and other phenomena. In actual engineering, the power of the subassembly usually changes due to uncertain factors such as the mission environment and complexity of the aircraft, so that the heat generated by the subassembly is also different. The heat generated by the subassembly will conduct on the entire cabin plate, causing a large change in the cabin plate temperature field. When developing an aircraft, if the influence of uncertain factors on the cabin plate temperature field is ignored, the designed aircraft may not achieve the target performance, or even cause serious failure during the mission. Therefore, considering the influence of various uncertain factors on the temperature field, analyzing the thermal reliability of the cabin plate is of great significance to improve the performance of the aircraft.

[0003] The satellite high-density functional integration cabin plate usually contains multiple subassemblies, and different subassemblies have different temperature ranges suitable for normal work. In the design of the satellite cabin plate, the power of the subassembly in the cabin plate is ideally a certain value. However, due to the influence of uncertain factors such as the mission environment and complexity of the aircraft, the power of the subassembly fluctuates. In addition, the data uncertainty of the obtained cabin plate temperature field is caused by the measurement noise of the infrared camera. At present, when analyzing the thermal reliability of the satellite cabin plate, the influence of the above uncertain factors is usually ignored, and the relationship between the cabin plate and the subassembly is not used for fine thermal reliability modeling, and the accuracy of the corresponding thermal reliability analysis result is poor. SUMMARY

[0004] To solve part or all of the technical problems in the prior art, the present application provides a satellite cabin plate thermal reliability analysis method.

[0005] The technical scheme of the present application is as follows:

[0006] A satellite cabin plate thermal reliability analysis method is provided, and the method comprises:

[0007] determining sub-components in a satellite panel, converting power of the sub-components into standard random variables;

[0008] constructing a sparse multi-dimensional standard orthogonal basis corresponding to each sub-component based on the standard random variable corresponding to the sub-component;

[0009] sampling multiple quantile levels to obtain multiple combined input data, the combined input data including the standard random variable corresponding to each sub-component and a quantile level;

[0010] inputting the combined input data into a pre-constructed and trained sub-component maximum temperature proxy model to obtain adaptive expansion coefficients corresponding to each sub-component output by the sub-component maximum temperature proxy model, and calculating a maximum temperature prediction value of each sub-component according to the adaptive expansion coefficients corresponding to each sub-component and the sparse multi-dimensional standard orthogonal basis;

[0011] solving a mean value and a standard deviation of the maximum temperature prediction value of each sub-component according to multiple maximum temperature prediction values of each sub-component obtained by using multiple combined input data;

[0012] determining a maximum temperature interval of each sub-component according to the mean value and the standard deviation of the maximum temperature prediction value of each sub-component, and determining a probability interval of normal operation and a probability interval of failure of each sub-component according to the maximum temperature interval of each sub-component and a pre-set normal operating temperature threshold of each sub-component;

[0013] dividing all sub-components into multiple subsystems according to functions of the sub-components, and constructing a panel multi-layer Bayesian network thermal reliability model based on the divided subsystems, wherein root nodes, intermediate nodes and leaf nodes in the panel multi-layer Bayesian network thermal reliability model represent sub-components, subsystems and a panel, respectively;

[0014] solving a probability interval of normal operation and a probability interval of failure of the panel according to the probability interval of normal operation and the probability interval of failure of each sub-component, and using the panel multi-layer Bayesian network thermal reliability model.

[0015] In some optional embodiments, the standard random variable of the sub-component is obtained by using the following method:

[0016]

[0017] wherein, ξ k represents the standard random variable corresponding to the kth sub-component, P k represents the power of the kth sub-component, μ k represents the mean value of the power of the kth sub-component, σ k represents the standard deviation of the power of the kth sub-component.

[0018] In some optional embodiments, the sparse multidimensional standard orthogonal basis corresponding to each subassembly is constructed in the following manner:

[0019] According to the standard random variable of each subassembly, a set of p-order single-variable standard orthogonal bases corresponding to each subassembly is constructed by using orthogonal polynomials;

[0020] According to the set of p-order single-variable standard orthogonal bases corresponding to each subassembly, a multidimensional standard orthogonal basis is constructed;

[0021] The multidimensional standard orthogonal basis is sparsified to obtain a sparse multidimensional standard orthogonal basis corresponding to each subassembly;

[0022] wherein the multidimensional standard orthogonal basis is constructed by using the following formula:

[0023]

[0024] Φ i represents the i-th multidimensional polynomial constituting the multidimensional standard orthogonal basis {Φ1(ξ), Φ2(ξ), …, ΦM(ξ)}, M represents the number of multidimensional polynomials in the multidimensional standard orthogonal basis {Φ1(ξ), Φ2(ξ), …, ΦM(ξ)}, M = (d + p)! / (d! p!), d represents the number of subassemblies in the panel, M represents the k-th index in the multivariate index set s M represents the k-th index in the multivariate index set s represents the k-th index in the multivariate index set s i represents the standard orthogonal polynomial constituting the p-order single-variable standard orthogonal basis represents the standard orthogonal polynomial constituting the p-order single-variable standard orthogonal basis represents the standard orthogonal polynomial constituting the p-order single-variable standard orthogonal basis

[0025] In some optional embodiments, the subassembly maximum temperature proxy model is trained in the following manner:

[0026] A labeled training data set and an unlabeled training data set are obtained, the labeled training data including input data and the maximum temperature value of each subassembly corresponding to the input data, and the unlabeled training data including input data, the input data including a standard random variable corresponding to each subassembly and a quantile level;

[0027] The subassembly maximum temperature proxy model is trained based on a preset loss function and by using the labeled training data set and the unlabeled training data set.

[0028] In some optional embodiments, the subassembly maximum temperature proxy model is trained based on a preset loss function and by using the labeled training data set and the unlabeled training data set, further comprising the following steps:

[0029] Step 421, input the input data in the labeled training data in the labeled training data set and the input data in the unlabeled training data in the unlabeled training data set into the component maximum temperature proxy model in batches respectively, to obtain the adaptive expansion coefficient corresponding to each component output by the component maximum temperature proxy model;

[0030] Step 422, according to the adaptive expansion coefficient corresponding to each component output by the component maximum temperature proxy model and the sparse multidimensional standard orthogonal basis corresponding to each component, calculate the maximum temperature prediction value of each component corresponding to the input data, to obtain the maximum temperature prediction value of each component corresponding to the labeled training data, and the maximum temperature prediction value of each component corresponding to the unlabeled training data;

[0031] Step 423, according to the maximum temperature value of each component in the labeled training data, the maximum temperature prediction value of each component corresponding to the labeled training data, and the maximum temperature prediction value of each component corresponding to the unlabeled training data, calculate the loss function;

[0032] Step 424, determine whether the preset training stop condition is reached, if yes, take the current component maximum temperature proxy model as the completed training component maximum temperature proxy model, if not, update the parameters of the component maximum temperature proxy model by using the loss function, and return to step 421.

[0033] In some optional embodiments, the loss function is represented as:

[0034]

[0035] Wherein, The loss function is represented as: The supervised loss part corresponding to the kth component is represented as λ, which represents a pre-set hyperparameter, The unsupervised loss part corresponding to the kth component is represented as d, which represents the number of components in the cabin plate, and θ represents the parameters of the component maximum temperature proxy model.

[0036] In some optional embodiments, the supervised loss part corresponding to the kth component is represented as:

[0037]

[0038] Wherein, N LD The number of labeled training data input into the component maximum temperature proxy model is represented as: And ​respectively represent the standard random variable and quantile level in the input data in the l-th labeled training data, represents the highest temperature value of the k-th component in the l-th labeled training data, represents the highest temperature prediction value of the k-th component corresponding to the l-th labeled training data, represents the highest temperature prediction value and the highest temperature .

[0039] In some optional embodiments, the unsupervised loss part corresponding to the k-th component is represented as:

[0040]

[0041]

[0042] wherein, represents the first unsupervised loss, represents the second unsupervised loss, N UD represents the number of unlabeled training data input into the component highest temperature proxy model, and respectively represent the standard random variable and quantile level in the input data in the l'-th unlabeled training data, represents the highest temperature prediction value of the k-th component corresponding to the l'-th unlabeled training data, represents the mean of the highest temperature prediction values of the k-th component corresponding to N UD unlabeled training data, represents the variance of the highest temperature prediction values of the k-th component corresponding to N UD unlabeled training data, represents the first adaptive expansion coefficient of the k-th component corresponding to the l'-th unlabeled training data, represents the i-th adaptive expansion coefficient of the k-th component corresponding to the l'-th unlabeled training data, represents the mean of the first adaptive expansion coefficients of the k-th component corresponding to N UD unlabeled training data, represents the mean of the i-th adaptive expansion coefficients of the k-th component corresponding to N UD unlabeled training data, represents the number of adaptive expansion coefficients of the k-th component, and ||·||1 represents the 1-norm.

[0043] In some optional embodiments, the highest temperature interval of the component is determined by using the following method: ​

[0044]

[0045] in, This represents the highest temperature range of the k-th component. and These represent the highest temperature ranges. The lower and upper bounds, and Let A and B represent the mean and standard deviation of the predicted maximum temperature of the k-th component, respectively. This represents the hyperparameters that are set in advance.

[0046] In some alternative implementations, the probability range for normal operation and the probability range for failure of the component are determined using the following methods:

[0047]

[0048] in, This represents the probability interval for the k-th component to function normally. This represents the probability interval of the k-th component failing. N represents MCS The highest temperature range The conditions are met Quantity, N represents MCS The highest temperature range The conditions are met The number of items, m = 1, 2, ..., N MCS N MCS This represents the number of cabin plate operating conditions. and These represent the highest temperature ranges. The lower and upper bounds, This represents the maximum temperature range of the k-th component, determined by the mean and standard deviation of the predicted maximum temperature values ​​for the k-th component corresponding to the operating condition of the m-th compartment. This represents the pre-set normal operating temperature threshold for the kth component.

[0049] The main advantages of the technical solution of this invention are as follows:

[0050] The satellite cabin plate thermal reliability analysis method provided by the application can improve the accuracy of the cabin plate thermal reliability analysis result, significantly reduce the experimental data required for the cabin plate thermal reliability analysis, and reduce the analysis cost. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0052] Figure 1 A flow chart of a satellite cabin plate thermal reliability analysis method provided by an embodiment of the present application is shown in the figure.

[0053] Figure 2 A structure schematic diagram of a satellite cabin plate provided by an embodiment of the present application is shown in the figure.

[0054] Figure 3 A structure principle diagram of a component maximum temperature proxy model provided by an embodiment of the present application is shown in the figure.

[0055] Figure 4 A subsystem division principle schematic diagram of a cabin plate provided by an embodiment of the present application is shown in the figure.

[0056] Figure 5 A structure schematic diagram of a cabin plate multilayer Bayesian network thermal reliability model provided by an embodiment of the present application is shown in the figure. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solutions and advantages of the present application more clear, the technical solutions of the present application will be described in detail below with specific embodiments of the present application and corresponding drawings. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0058] The technical solutions provided by the embodiments of the present application will be described in detail below with reference to the drawings.

[0059] REFERENCE Figure 1The embodiment of the present application provides a satellite cabin plate thermal reliability analysis method, and the method comprises the following steps:

[0060] Step 1, determining a component assembly in the satellite cabin plate, and converting power of the component assembly into a standard random variable;

[0061] Step 2, constructing a sparse multi-dimensional standard orthogonal basis corresponding to each component assembly based on the standard random variable corresponding to the component assembly;

[0062] Step 3, sampling a plurality of quantile levels to obtain a plurality of combined input data;

[0063] In the embodiment of the present application, the combined input data comprises the standard random variable corresponding to each component assembly and a quantile level;

[0064] In the embodiment of the present application, the quantile level is sampled from a uniform distribution U(0, 1).

[0065] Step 4, inputting the combined input data into a pre-constructed and trained component assembly maximum temperature agent model to obtain adaptive expansion coefficients of each component assembly output by the component assembly maximum temperature agent model, and calculating a maximum temperature prediction value of each component assembly according to the adaptive expansion coefficients of each component assembly and the sparse multi-dimensional standard orthogonal basis;

[0066] Step 5, calculating a mean value and a standard deviation of the maximum temperature prediction value of each component assembly according to a plurality of maximum temperature prediction values of each component assembly obtained by using a plurality of combined input data;

[0067] In the embodiment of the present application, one maximum temperature prediction value of the component assembly can be obtained by using one combined input data, and a plurality of maximum temperature prediction values of the component assembly can be obtained by using a plurality of combined input data.

[0068] Step 6, determining a maximum temperature interval of each component assembly according to the mean value and the standard deviation of the maximum temperature prediction value of each component assembly, and determining a probability interval of normal operation and a probability interval of failure of each component assembly according to the maximum temperature interval of each component assembly and a pre-set normal operating temperature threshold of each component assembly;

[0069] Step 7, dividing all component assemblies into a plurality of subsystems according to functions of the component assemblies, and constructing a cabin plate multi-layer Bayesian network thermal reliability model based on the divided subsystems;

[0070] In the embodiment of the present application, the root node, the intermediate node and the leaf node in the cabin plate multi-layer Bayesian network thermal reliability model represent the component assembly, the subsystem and the cabin plate respectively;

[0071] Step 8, according to the probability interval of normal work and the probability interval of failure of each subassembly, the probability interval of normal work and the probability interval of failure of the cabin plate are solved by using the cabin plate multilayer Bayesian network thermal reliability model.

[0072] In the embodiment of the application, the probability interval of normal work of the cabin plate is solved according to the probability interval of normal work of each subassembly, and the probability interval of failure of the cabin plate is solved according to the probability interval of failure of each subassembly.

[0073] The satellite cabin plate thermal reliability analysis method provided in the embodiment of the application can improve the accuracy of the analysis result of the thermal reliability of the cabin plate, significantly reduce the experimental data required for the thermal reliability analysis of the cabin plate, and reduce the analysis cost.

[0074] The steps and principles of the satellite cabin plate thermal reliability analysis method provided in the embodiment of the application are further described and explained below.

[0075] Reference Figure 2 , it is assumed that the cabin plate is a rectangular printed circuit board with a length of L w , a width of L h , and d subassemblies {C k |k=1,2,…,d} installed thereon, the power of the subassemblies {C k |k=1,2,…,d} is {P k |k=1,2,…,d}. In the attached Figure 2 , different geometric shapes represent different subassemblies.

[0076] In order to verify whether the current cabin plate design scheme has high thermal reliability, different working conditions can be set to simulate the satellite performing different tasks, and then temperature field data used for analyzing the thermal reliability of the cabin plate can be obtained. In the embodiment of the application, a power combination P={P k |k=1,2,…,d} of the d subassemblies corresponds to a working condition of the satellite.

[0077] In an ideal case, the power of the subassemblies in the cabin plate is {P k{ k = 1, 2, …, d} are determined design values. However, due to the influence of uncertain factors such as satellite mission execution environment and mission complexity, the power of the subassembly exists certain fluctuation. For example, when the satellite executes different tasks, the subassembly is in different working states, some subassemblies may need full load work, some subassemblies may only need half load work, and even some subassemblies remain in the shutdown state in some tasks. For the above type of subassembly, the power thereof can be modeled as a random variable subject to a uniform distribution, wherein the upper and lower bounds of the uniform distribution are the power of the subassembly in full load work and 0 (the subassembly is in the shutdown state) respectively. For other types of subassemblies, the power thereof can be modeled as a random variable subject to a certain probability distribution according to the characteristics of the working state change thereof.

[0078] Specifically, in the embodiment of the present application, the power of the kth subassembly C k is converted into a standard random variable by using the following formula:

[0079]

[0080] wherein ξ k represents the standard random variable corresponding to the kth subassembly, P k represents the power of the kth subassembly, μ k represents the mean of the power of the kth subassembly, and σ k represents the standard deviation of the power of the kth subassembly.

[0081] Further, in the embodiment of the present application, based on the standard random variable corresponding to the subassembly, the sparse multidimensional standard orthogonal basis corresponding to each subassembly is constructed by using the following method:

[0082] According to the standard random variable of each subassembly, a group of p-order monovariate standard orthogonal bases corresponding to each subassembly is constructed by using orthogonal polynomials;

[0083] According to the group of p-order monovariate standard orthogonal bases corresponding to each subassembly, a multidimensional standard orthogonal basis is constructed;

[0084] The multidimensional standard orthogonal basis is sparsified to obtain the sparse multidimensional standard orthogonal basis corresponding to each subassembly.

[0085] In the embodiment of the present application, when the standard random variable is a common probability distribution random variable listed in Table 1, the corresponding orthogonal polynomial can be directly selected to construct the monovariate standard orthogonal basis; when the standard random variable is not a common probability distribution random variable listed in Table 1, the standard random variable can be converted into a common probability distribution random variable by using Rosenblatt transformation or Nataf transformation, and then the corresponding orthogonal polynomial is directly selected to construct the monovariate standard orthogonal basis.

[0086] Table 1 Common distribution type corresponding orthogonal polynomial

[0087] Distribution type Orthogonal polynomials Random variable interval Normal distribution Hermite polynomials (-∞,+∞) Gamma distribution Laguerre polynomials [0,+∞) Beta distribution Jacobi polynomials [a, b] Uniform distribution Legendre polynomials [a, b] Exponential distribution Laguerre polynomials [0,+∞)

[0088] Further, in the embodiment of the present application, when a set of p-order single-variable standard orthogonal bases corresponding to each component assembly is obtained Then, k = 1, 2, …, d, the multi-dimensional standard orthogonal bases are constructed by using the following formula:

[0089]

[0090] Where, Φ i (ξ) represents the i-th multi-dimensional polynomial constituting the multi-dimensional standard orthogonal bases {Φ1(ξ), Φ2(ξ), …, Φ M (ξ)}, M represents the number of multi-dimensional polynomials in the multi-dimensional standard orthogonal bases {Φ1(ξ), Φ2(ξ), …, Φ M (ξ)}, M = (d + p)! / (d! p!), d represents the number of component assemblies in the cabin plate, represents the k-th index in the multi-variable index set s i represents the p-order single-variable standard orthogonal basis The k-th standard orthogonal polynomial in the p-order single-variable standard orthogonal basis.

[0091] Considering that more component assemblies are installed on the satellite high-density function integrated cabin plate, resulting in more expansion coefficients to be solved. Therefore, in the embodiment of the present application, the multi-dimensional standard orthogonal bases {Φ1(ξ), Φ2(ξ), …, Φ M (ξ)} are sparsified.

[0092] Specifically, taking the k-th component assembly C k as an example, based on the obtained multi-dimensional standard orthogonal bases {Φ1(ξ), Φ2(ξ), …, Φ M (ξ)}, the orthogonal matching pursuit algorithm is used to obtain the sparse multi-dimensional standard orthogonal bases corresponding to the k-th component assembly C k

[0093] Referring to Figure 3 Further, in the embodiment of the present application, the input of the component assembly maximum temperature proxy model is the standard random variable corresponding to each component assembly and a quantile level, and the output is the adaptive expansion coefficient corresponding to each component assembly.

[0094] In the embodiment of the present application, the component assembly maximum temperature proxy model is trained in the following manner:

[0095] ​​​Step 41, obtaining a labeled training data set and an unlabeled training data set, the labeled training data comprising input data and a highest temperature value of each component corresponding to the input data, and the unlabeled training data comprising input data, the input data comprising a standard random variable corresponding to each component and a quantile level;

[0096] Step 42, training a component highest temperature proxy model based on a preset loss function and using the labeled training data set and the unlabeled training data set.

[0097] In the embodiment of the present application, the training data can be simulation test data or existing real data.

[0098] In the embodiment of the present application, the quantile level is sampled from a uniform distribution U(0, 1).

[0099] In the embodiment of the present application, the component highest temperature proxy model adopts a deep neural network model (DNN).

[0100] Further, in the embodiment of the present application, the training of the component highest temperature proxy model based on the preset loss function and using the labeled training data set and the unlabeled training data set further comprises steps 421-424:

[0101] Step 421, inputting the input data in the labeled training data in the labeled training data set and the input data in the unlabeled training data in the unlabeled training data set into the component highest temperature proxy model in batches respectively to obtain an adaptive expansion coefficient of each component output by the component highest temperature proxy model;

[0102] Step 422, calculating a highest temperature prediction value of each component corresponding to the input data according to the adaptive expansion coefficient of each component output by the component highest temperature proxy model and a sparse multidimensional standard orthogonal basis corresponding to each component, to obtain a highest temperature prediction value of each component corresponding to the labeled training data and a highest temperature prediction value of each component corresponding to the unlabeled training data;

[0103] Step 423, calculating a loss function according to the highest temperature value of each component in the labeled training data, the highest temperature prediction value of each component corresponding to the labeled training data, and the highest temperature prediction value of each component corresponding to the unlabeled training data;

[0104] Step 424, determining whether a preset training stop condition is reached, if yes, taking the current component highest temperature proxy model as a completed component highest temperature proxy model, and if no, updating parameters of the component highest temperature proxy model using the loss function and returning to step 421.

[0105] In the embodiment of the present application, the parameters of the subcomponent maximum temperature proxy model are initialization parameters, and the parameters of the subcomponent maximum temperature proxy model can be continuously updated and learned in the training process of the subcomponent maximum temperature proxy model.

[0106] In the embodiment of the present application, the loss function for training the subcomponent maximum temperature proxy model is represented as:

[0107]

[0108] wherein, represents the loss function, represents the supervised loss part corresponding to the kth subcomponent, and λ represents a pre-set hyperparameter, represents the unsupervised loss part corresponding to the kth subcomponent, d represents the number of subcomponents in the panel, and θ represents the parameters of the subcomponent maximum temperature proxy model.

[0109] Further, the supervised loss part corresponding to the kth subcomponent is represented as:

[0110]

[0111] wherein, N LD represents the number of labeled training data input into the subcomponent maximum temperature proxy model, and respectively represent the standard random variable and the quantile level in the input data in the lth labeled training data, represents the maximum temperature value of the kth subcomponent in the lth labeled training data, represents the maximum temperature prediction value of the kth subcomponent corresponding to the lth labeled training data, represents the deviation between the maximum temperature prediction value and the maximum temperature .

[0112] Further, the unsupervised loss part corresponding to the kth subcomponent is represented as:

[0113]

[0114] wherein, represents the first unsupervised loss, specifically the L1 norm of the deviation between the mean and the first adaptive unfolding coefficient mean , represents the second unsupervised loss, specifically the variance and the mean of the second to last adaptive unfolding coefficient​​ The L1 norm of the deviation between the sums of squares, N UD This indicates the amount of unlabeled training data for the proxy model with the highest temperature in the input component. and Let represent the standard random variable and quantile level in the input data of the l′-th unlabeled training data, respectively. This represents the predicted highest temperature value of the k-th component corresponding to the l′-th unlabeled training data. N represents UD The mean of the highest temperature prediction values ​​of the k-th component corresponding to each unlabeled training data point. N represents UD The variance of the predicted maximum temperature of the k-th component corresponding to each unlabeled training data point. This represents the first adaptive expansion coefficient of the k-th component corresponding to the l′-th unlabeled training data. This represents the i-th adaptive expansion coefficient of the k-th component corresponding to the l′-th unlabeled training data. N represents UD The mean of the first adaptive unfolding coefficient of the k-th component corresponding to each unlabeled training data point. N represents UD The mean of the i-th adaptive unfolding coefficients of the k-th component corresponding to each unlabeled training data point. represents the number of adaptive expansion coefficients of the k-th component, and ‖·‖1 represents the 1-norm.

[0115] Furthermore, in this embodiment of the invention, based on the adaptive expansion coefficients of the component corresponding to the component output by the component's highest temperature proxy model and the sparse multidimensional orthogonal basis of the component corresponding to the component, the predicted value of the highest temperature of the component corresponding to the input data is calculated using the following formula:

[0116]

[0117] in, This represents the predicted maximum temperature value of the k-th component. Represents the adaptive expansion coefficient corresponding to the k-th component. The number of terms in Represents the adaptive expansion coefficient corresponding to the k-th component. The first in item, Represents the sparse multidimensional orthonormal basis corresponding to the k-th component. The first in A multidimensional polynomial.

[0118] In the embodiments of the present application, the training stop condition is specifically set according to actual conditions, for example, the training iteration number reaches a set iteration number or the optimization index reaches a set threshold. The loss function can be used as the optimization index.

[0119] Further, in the embodiments of the present application, the random gradient descent method is used to update the parameters of the highest temperature proxy model of the component assembly.

[0120] Specifically, the parameters of the highest temperature proxy model of the component assembly can be updated by using the following formula:

[0121]

[0122] wherein θ t+1 represents the parameters of the highest temperature proxy model of the component assembly at the t+1th iteration, θ t represents the parameters of the highest temperature proxy model of the component assembly at the tth iteration, Δ[·] represents the optimizer, η represents the learning rate, represents the loss function, and θ represents the parameters of the highest temperature proxy model of the component assembly. The optimizer is, for example, Adam, SGD, etc., and the learning rate is set in advance to control the speed of parameter update.

[0123] Further, in the embodiments of the present application, when the highest temperature of the cabin plate component assembly is predicted, the working conditions P pre of the satellite cabin plate determined based on the highest temperature proxy model of the component assembly are converted into standard random variables ξ d . T pre d T N pre quantile levels of the uniform distribution U(0, 1) are constructed. N pre combination input data are constructed. The highest temperature prediction value of each component assembly is obtained by using the trained highest temperature proxy model of the component assembly and the above set calculation formula of the highest temperature prediction value. Further, in the embodiments of the present application, taking N pre combination input data as an example, the mean and standard deviation of the highest temperature prediction value of the component assembly are calculated by using the following formula:

[0124]

[0125]

[0126] ​​​​​​a mean value of the highest temperature prediction value of the kth component, a highest temperature prediction value of the kth component corresponding to the kth combination of input data, a highest temperature prediction value of the kth component corresponding to the kth combination of input data, a standard deviation of the highest temperature prediction value of the kth component.

[0127] In the embodiments of the present application, the standard deviation of the highest temperature prediction value of the component is taken as the data uncertainty of the highest temperature prediction value of the component.

[0128] Further, in the embodiments of the present application, considering the influence of data noise on the highest temperature prediction result of the component, based on the mean value and the data uncertainty of the highest temperature prediction value of the component obtained under the current working condition, the highest temperature interval of the component under the current working condition of the cabin plate is constructed.

[0129] Specifically, taking the kth component C k as an example, the highest temperature interval of the component is determined in the following manner:

[0130]

[0131]

[0132] wherein, represents the highest temperature interval of the kth component, and represent the lower bound and the upper bound of the highest temperature interval, respectively, and represent the mean value and the standard deviation of the highest temperature prediction value of the kth component, and ω represents a pre-set hyperparameter.

[0133] Further, assuming that C k = 0 and C k = 1 represent that the kth component C k fails and works normally, respectively, the condition that the kth component C k is in the above two working states can be represented as:

[0134]

[0135] wherein, represents the normal working temperature threshold of the kth component, which is pre-set.

[0136] Further, given N MCS kinds of satellite cabin plate working conditions , the trained highest temperature proxy model of the component and the above-mentioned set calculation processing manner are used to calculate N MCSN MCS MCS N MCS MCS N MCS

[0137] Based on the above setting and calculation results, the lower bound set and the upper bound set of the maximum temperature of the kth component can be represented as:

[0138]

[0139] wherein, and represent the lower bound and the upper bound of the maximum temperature interval , respectively.

[0140] Define a set and the set satisfies two conditions: and

[0141] Further define three parameters and represent the number of N MCS maximum temperature intervals that satisfy the condition , represent the number of N MCS maximum temperature intervals that satisfy the condition , represent the number of N MCS maximum temperature intervals that satisfy the condition , m = 1, 2, …, N MCS .

[0142] Based on the above definitions, the parameters and satisfy the following inequalities:

[0143]

[0144] The three normal working probabilities of the kth component C k can be represented as:

[0145] ​​​​​​

[0146] The three normal working probabilities satisfy the following inequalities:

[0147]

[0148] According to the above analysis, the kth part component C k The probability interval of normal working and the probability interval of failure can be respectively expressed as:

[0149]

[0150] Wherein, represents the probability interval of the kth part component working normally, represents the probability interval of the kth part component failing.

[0151] Referring to Figure 4 , further, in the embodiment of the present application, according to the function of the part component on the satellite cabin plate, the part component can be divided into subsystems

[0152] In the attached Figure 4 , Su represents the satellite cabin plate, represents the part component, represents the subsystem, and Su represents the structure function between the satellite cabin plate and subsystems, represents the structure function between the subsystem and its part components.

[0153] In combination with the actual demand, in the embodiment of the present application, the structure function existing in the satellite cabin plate is mainly considered as series or parallel, and the corresponding subsystem may be a series block or a parallel block block to form the satellite cabin plate Su through series or parallel.

[0154] Referring to Figure 5 , further, in the embodiment of the present application, based on the divided subsystem, a cabin plate multilayer Bayesian network thermal reliability model is constructed, and then based on the constructed cabin plate multilayer Bayesian network thermal reliability model, according to the probability interval of normal working and the probability interval of failure of each part component, the probability interval of normal working and the probability interval of failure of the cabin plate are solved.

[0155] In the embodiment of the present application, the root node in the cabin plate multilayer Bayesian network thermal reliability model is the part component, the intermediate node is the subsystem, and the leaf node is the satellite cabin plate.

[0156] In the embodiment of the present application, the probability interval of the root node is obtained by using the above-mentioned obtaining method of the probability interval of the component, the probability interval (NPT) of the intermediate node is determined according to the logical relationship between the child node and the intermediate node, and the probability interval of the system (i.e., the satellite cabin plate) is determined based on the determined probability interval of the intermediate node.

[0157] In the embodiment of the present application, the subsystems are divided according to the functions of the components, and therefore the logical relationship is a functional relationship.

[0158] Further, in the embodiment of the present application, the probability interval of the first subsystem is set as the probability interval of the first intermediate node, and the probability interval of the second subsystem is set as the probability interval of the second intermediate node. The probability interval of the first subsystem is set as the probability interval of the first intermediate node, and the probability interval of the second subsystem is set as the probability interval of the second intermediate node. The probability interval of the satellite cabin plate Su is The probability interval of the satellite cabin plate Su is The probability interval of the satellite cabin plate Su is

[0159]

[0160] Wherein, P(Su|NPT1, NPT2) represents the conditional probability of Su given NPT1 and NPT2.

[0161] It should be noted that the relational terms herein such as "first" and "second" are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. Moreover, the terms "include", "contain" or any other variants thereof are 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 explicitly listed or inherent to such process, method, article or device. In addition, "front", "back", "left", "right", "up", "down" in this paper are referred to the placement state shown in the drawings.

[0162] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.​​

Claims

1. A method for satellite panel thermal reliability analysis, characterized in that, The method comprises the following steps: determining subassemblies in a satellite cabin panel, converting the power of the subassemblies into standard random variables; constructing a sparse multidimensional standard orthogonal basis corresponding to each subassembly based on the standard random variable corresponding to the subassembly; sampling multiple quantile levels to obtain multiple combined input data, the combined input data comprising the standard random variable corresponding to each subassembly and a quantile level; inputting the combined input data into a pre-constructed and trained subassembly maximum temperature proxy model to obtain the adaptive expansion coefficient corresponding to each subassembly output by the subassembly maximum temperature proxy model, and calculating the maximum temperature prediction value of each subassembly according to the adaptive expansion coefficient corresponding to each subassembly and the sparse multidimensional standard orthogonal basis; solving the mean and standard deviation of the maximum temperature prediction value of each subassembly according to the multiple maximum temperature prediction values of each subassembly obtained by using multiple combined input data; determining the maximum temperature interval of each subassembly according to the mean and standard deviation of the maximum temperature prediction value of each subassembly, and determining the probability interval of normal operation and the probability interval of failure of each subassembly according to the maximum temperature interval of each subassembly and the pre-set normal operating temperature threshold of each subassembly; dividing all subassemblies into multiple subsystems according to the functions of the subassemblies, constructing a cabin panel multi-layer Bayesian network thermal reliability model based on the divided subsystems, and the root node, intermediate node and leaf node in the cabin panel multi-layer Bayesian network thermal reliability model representing the subassembly, subsystem and cabin panel, respectively; solving the probability interval of normal operation and the probability interval of failure of the cabin panel according to the probability interval of normal operation and the probability interval of failure of each subassembly, and using the cabin panel multi-layer Bayesian network thermal reliability model.

2. The method of claim 1, wherein, The standard random variable of the subassembly is obtained by the following method: wherein, ξ k represents the standard random variable corresponding to the kth component assembly, P k represents the power of the kth component assembly, μ k represents the mean of the power of the kth component assembly, σ k represents the standard deviation of the power of the kth component assembly.

3. The method of claim 2, wherein, The sparse multidimensional standard orthogonal basis corresponding to each subassembly is constructed by the following method: constructing a set of p-order single-variable standard orthogonal bases corresponding to each subassembly by using orthogonal polynomials according to the standard random variable of each subassembly; constructing a multidimensional standard orthogonal basis according to the set of p-order single-variable standard orthogonal bases corresponding to each subassembly; sparsifying the multidimensional standard orthogonal basis to obtain the sparse multidimensional standard orthogonal basis corresponding to each subassembly; The multidimensional standard orthogonal basis is constructed by the following formula: Φ i (ξ) represents the i-th multidimensional polynomial constituting the multidimensional orthonormal basis {Φ1(ξ), Φ2(ξ), …, Φ M (ξ)}, M represents the number of multidimensional polynomials in the multidimensional orthonormal basis {Φ1(ξ), Φ2(ξ), …, Φ M (ξ)}, M = (d + p)! / (d! p!), d represents the number of subassemblies in the panel, represents the k-th index in the set of multivariate indices s i represents the orthonormal polynomials constituting the p-th order univariate orthonormal basis .​ 4. The method of claim 1 or 3, wherein, The subassembly maximum temperature proxy model is trained by the following method: obtaining a labeled training data set and an unlabeled training data set, the labeled training data comprising input data and the maximum temperature value of each subassembly corresponding to the input data, and the unlabeled training data comprising input data, the input data comprising the standard random variable corresponding to each subassembly and a quantile level; training the subassembly maximum temperature proxy model based on the preset loss function and using the labeled training data set and the unlabeled training data set.

5. The method of claim 4, wherein, The training of the subassembly maximum temperature proxy model based on the preset loss function and using the labeled training data set and the unlabeled training data set further comprises the following steps: Step 421, input the input data in the labeled training data in the labeled training data set and the input data in the unlabeled training data in the unlabeled training data set into the component maximum temperature proxy model in batches respectively, to obtain the adaptive expansion coefficients corresponding to each component output by the component maximum temperature proxy model; Step 422, according to the adaptive expansion coefficients corresponding to each component output by the component maximum temperature proxy model and the sparse multidimensional standard orthogonal basis corresponding to each component corresponding to the input data, calculate the maximum temperature prediction value of each component corresponding to the input data, to obtain the maximum temperature prediction value of each component corresponding to the labeled training data, and the maximum temperature prediction value of each component corresponding to the unlabeled training data; Step 423, according to the maximum temperature value of each component in the labeled training data, the maximum temperature prediction value of each component corresponding to the labeled training data, and the maximum temperature prediction value of each component corresponding to the unlabeled training data, calculate the loss function; Step 424, determine whether the preset training stop condition is reached, if yes, take the current component maximum temperature proxy model as the completed training component maximum temperature proxy model, if not, update the parameters of the component maximum temperature proxy model by using the loss function, and return to step 421.

6. The method of claim 5, wherein, The loss function is expressed as: wherein, represents a loss function, represents a supervised loss part corresponding to the kth subassembly, and λ represents a pre-set hyperparameter, represents an unsupervised loss part corresponding to the kth subassembly, d represents the number of subassemblies in the panel, and θ represents the parameters of the subassembly maximum temperature proxy model.

7. The method of claim 6, wherein, the kth part assembly corresponds to a supervised loss part is represented as: where N LD denotes the number of labeled training data input to the component maximum temperature proxy model, and denote the standard random variable and quantile level in the input data in the l-th labeled training data, respectively, denotes the maximum temperature value of the k-th component in the l-th labeled training data, denotes the maximum temperature prediction value of the k-th component corresponding to the l-th labeled training data, denotes the maximum temperature prediction value and the maximum temperature deviation between.

8. The method of claim 6, wherein, The kth part assembly corresponds to an unsupervised loss part Is expressed as: wherein, represents the first unsupervised loss, represents the second unsupervised loss, N UD represents the number of unlabeled training data inputted into the highest temperature proxy model of the subassembly, and respectively represent a standard random variable and a quantile level in the input data in the l'th unlabeled training data, represents the highest temperature prediction value of the k'th subassembly corresponding to the l'th unlabeled training data, represents the mean of the highest temperature prediction values of the k'th subassembly corresponding to N UD unlabeled training data, represents the variance of the highest temperature prediction values of the k'th subassembly corresponding to N UD unlabeled training data, represents the 1st adaptive unfolding coefficient of the k'th subassembly corresponding to the l'th unlabeled training data, represents the i'th adaptive unfolding coefficient of the k'th subassembly corresponding to the l'th unlabeled training data, represents the mean of the 1st adaptive unfolding coefficient of the k'th subassembly corresponding to N UD unlabeled training data, represents the mean of the i'th adaptive unfolding coefficient of the k'th subassembly corresponding to N UD unlabeled training data, represents the number of adaptive unfolding coefficients of the k'th subassembly, ||·||1 represents the 1-norm.

9. The method of claim 1, wherein, The maximum temperature interval of the component is determined by the following method: wherein, represents the upper bound of the highest temperature interval of the kth component, and respectively represent the lower bound and the upper bound of the highest temperature interval , and respectively represent the mean and the standard deviation of the highest temperature prediction value of the kth component, represents a pre-set hyperparameter.

10. The method of claim 9, wherein, The probability interval of the normal operation of the component and the probability interval of the failure are determined by the following method: wherein, represents the probability interval of the kth component working normally, represents the probability interval of the kth component failing, represents the number of the N MCS highest temperature intervals that satisfy the condition , represents the number of the N MCS highest temperature intervals that satisfy the condition , m = 1, 2, …, N MCS , N MCS represents the given number of panel working conditions, and respectively represent the lower bound and the upper bound of the highest temperature interval , represents the highest temperature interval of the kth component determined according to the mean and the standard deviation of the highest temperature prediction value of the kth component corresponding to the mth panel working condition, represents the pre-set normal working temperature threshold of the kth component.

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