Spacecraft physical field prediction model construction method based on maximum mean difference data distribution difference evaluation
Through the maximum mean difference evaluation method and transfer learning, the problem of limited training samples in spacecraft physics prediction is solved, and more efficient construction and training of physics prediction models is achieved.
Patent Information
- Application Number
- CN202510162961.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-14
- Publication Date
- 2025-06-13
AI Technical Summary
In the prediction of spacecraft physics, due to the limited training samples and the possible problems of sample imbalance and noise interference, it is difficult to support the construction and training of deep learning models.
The data distribution difference evaluation method based on maximum mean difference (MMD) is used to map the source task data and target task data to high-dimensional feature space through mapping functions, optimize the mapping function to minimize distribution differences, and use transfer learning to construct a physical field prediction model.
It effectively reduces the data distribution difference between the source task and the target task, improves the transfer learning effect, solves the problem of limited training samples, and improves the prediction accuracy of the physical prediction model.
Smart Images
Figure CN120145812A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of aerospace engineering, and particularly relates to a method for constructing a physical field prediction model of a spacecraft based on the evaluation of the maximum mean discrepancy of data distribution differences. Background Art
[0002] The prediction of the physical fields inside a spacecraft is a key technology to ensure the stable operation of the spacecraft, extend its service life, and improve the mission success rate. For example, during on-orbit operation, factors such as microgravity and radiation can affect the material properties inside the cabin. Predicting physical fields such as the stress field and vibration field inside the cabin can evaluate the mechanical stability of the structure, predict potential damage accumulation, and provide a scientific basis for designing more durable satellite structures and selecting suitable materials. In addition, the spacecraft experiences extreme temperature differences in space, and accurately predicting the temperature field distribution inside the cabin is crucial for the design of the thermal control system.
[0003] Currently, in order to ensure the accuracy of spacecraft physical field prediction and meet strict real-time requirements, deep learning methods are usually adopted to construct efficient and accurate surrogate models. The advantage of deep learning lies in its powerful data processing ability and pattern recognition ability, which can automatically extract complex non-linear features from a large amount of historical data and physical experiment data. This method can not only handle high-dimensional input-output relationships, but also be efficiently trained on large-scale datasets. Compared with traditional numerical simulation methods, it can often significantly shorten the time required for prediction, thus meeting the demand for rapid response in space missions. However, although deep learning models have powerful expressive ability and pattern recognition ability, the full play of their performance usually depends on a large amount of training samples. Space missions are costly, the experimental conditions are harsh, and the on-orbit data transmission bandwidth is limited, resulting in a relatively small size of the dataset available for training, and there may be problems such as sample imbalance and noise interference. Summary of the Invention
[0004] To solve some or all of the above-mentioned technical problems existing in the prior art, the present invention provides a method for constructing a physical field prediction model of a spacecraft based on the evaluation of the maximum mean discrepancy of data distribution differences.
[0005] The technical solution of the present invention is as follows:
[0006] A method for constructing a physical field prediction model of a spacecraft based on the evaluation of the maximum mean discrepancy of data distribution differences is provided, and the method includes:
[0007] Obtain the physical field datasets of the source task and the target task, including physical field feature data and corresponding labels;
[0008] Map the source task data and the target task data to a high-dimensional feature space through a mapping function;
[0009] Measure the distribution difference between the source task data and the target task data based on the maximum mean discrepancy (MMD).
[0010] Optimize the mapping function to minimize the distribution difference between the source task data and the target task data in the feature space.
[0011] Use the mapped source task data and target task data for transfer learning to construct a physical field prediction model.
[0012] In an embodiment of the present invention, the calculation method of the maximum mean discrepancy (MMD) includes:
[0013] Map the source task data and the target task data to the reproducing kernel Hilbert space (RKHS).
[0014] Calculate the mean difference between the source task data and the target task data in the reproducing kernel Hilbert space (RKHS) as a measure of the distribution difference.
[0015] In an embodiment of the present invention, a multi-layer perceptron is used as the mapping function to map the source task data and the target task data to the reproducing kernel Hilbert space (RKHS).
[0016] In an embodiment of the present invention, the maximum mean discrepancy (MMD) is calculated by the following formula:
[0017]
[0018] where x i is the source task data, y j is the target task data, n is the total number of source task data, m is the total number of target task data, φ(·) is the mapping function, is the reproducing kernel Hilbert space.
[0019] In an embodiment of the present invention, the projection mapping function is a multi-layer perceptron, and the distribution difference between the source task data and the target task data in the feature space is minimized by optimizing the objective function.
[0020] In an embodiment of the present invention, the source task data set includes data of other spacecraft physical field tasks, the target task data set is data of the current physical field prediction task, and the source task data set is used to assist the model training of the target task data.
[0021] In an embodiment of the present invention, the transfer learning adopts a model construction method based on deep learning, and uses the prior knowledge of the source task data to improve the prediction accuracy of the target task data. The deep learning model includes, but is not limited to, a convolutional neural network (CNN), a recurrent neural network (RNN), a Transformer, or a graph neural network.
[0022] In an embodiment of the present invention, the physical field characteristics include multi-dimensional physical parameters, including but not limited to stress fields, vibration fields, or temperature fields, for predicting the physical fields inside spacecraft cabins.
[0023] The main advantages of the technical solution of the present invention are as follows:
[0024] The method for constructing a spacecraft physical field prediction model based on maximum mean discrepancy data distribution difference evaluation of the present invention proposes a data distribution difference evaluation method based on maximum mean discrepancy. By measuring the data distribution differences between different physical field prediction problems, it supports the design of an effective projection mapping function to reduce the data distribution differences between the source task and the target task, solves the problem that the limited training samples of the spacecraft physical field are difficult to support the construction of the physical field prediction deep learning model, and improves the transfer learning effect. Description of the Drawings
[0025] 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, without creative efforts, other drawings can also be obtained based on these drawings.
[0026] Figure 1 It is a flowchart of the method for constructing a spacecraft physical field prediction model based on maximum mean discrepancy data distribution difference evaluation according to an embodiment of the present invention. Detailed Embodiments
[0027] 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 and corresponding drawings of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.
[0028] The following will detail the technical solutions provided by the embodiments of the present invention with reference to the drawings.
[0029] The embodiment of the present invention provides a method for constructing a spacecraft physical field prediction model based on maximum mean discrepancy data distribution difference evaluation. As shown in the attached Figure 1 figure, it includes:
[0030] S1, obtaining the physical field data sets of the source task and the target task, including physical field feature data and corresponding labels.
[0031] The source task data is physical field data in other spacecraft or similar environments, including physical field characteristic data and corresponding labels. For example, the source task data can be sensor data such as temperature, stress, or vibration during the on-orbit operation of a certain type of spacecraft, and the corresponding label is the temperature classification of the temperature field, stress field, or vibration field constructed based on the sensor data.
[0032] The target task data is the physical field data inside the spacecraft to be predicted currently, including physical field characteristic data and corresponding labels. For example, the target task data can be the temperature field distribution data inside the current spacecraft cabin.
[0033] The physical field characteristic data can be multi-dimensional physical parameters (such as temperature, stress, vibration, etc.), and the label data can be the specific distribution values or classification results of the physical field.
[0034] S2, Map the source task data and the target task data to a high-dimensional feature space through a mapping function.
[0035] By designing a mapping function (such as a multi-layer perceptron MLP), map the source task data and the target task data from the original space to a high-dimensional feature space to facilitate measuring the distribution difference between the source task data and the target task data in the high-dimensional feature space.
[0036] S3, Based on the maximum mean discrepancy MMD, measure the distribution difference between the source task data and the target task data.
[0037] MMD maps the data to a high-dimensional feature space and calculates the mean difference between the two distributions in this space. Through the MMD metric, quantify the distribution difference between the source task data and the target task data, providing a basis for subsequent mapping and optimization.
[0038] S4, Optimize the mapping function to minimize the distribution difference between the source task data and the target task data in the feature space.
[0039] By optimizing the mapping function, minimize the distribution difference between the source task data and the target task data in the mapped feature space. Specifically, the optimization goal is to minimize the MMD value.
[0040] S5, Use the mapped source task data and target task data for transfer learning to construct a physical field prediction model.
[0041] During the transfer learning process, the mapped source task data and target task data are used to train the physical field prediction model. The source task data provides prior knowledge, and the target task data is used to fine-tune the model. Based on the mapped data, a physical field prediction model is constructed using machine learning or deep learning methods. For example, a neural network model can be used to predict the temperature field, stress field, or vibration field distribution inside a spacecraft cabin. The output of the physical field prediction model can be the specific distribution values of the physical field (such as a temperature field distribution map) or classification results (such as the stability classification of the vibration field).
[0042] In summary, the method for constructing a spacecraft physical field prediction model based on the evaluation of the maximum mean discrepancy data distribution difference provided by the embodiments of the present invention proposes a method for evaluating the data distribution difference based on the maximum mean discrepancy. By measuring the data distribution difference between different physical field prediction problems, it supports the design of an effective projection mapping function to reduce the data distribution difference between the source task and the target task, solves the problem that the limited training samples of the spacecraft physical field are difficult to support the construction of the physical field prediction deep learning model, and improves the transfer learning effect.
[0043] In some optional embodiments of the present invention, the calculation method of the maximum mean discrepancy MMD includes:
[0044] Map the source task data and the target task data to the reproducing kernel Hilbert space RKHS. RKHS is a high-dimensional feature space that can map data to an infinite dimension through a kernel function.
[0045] Calculate the mean difference between the source task data and the target task data in the reproducing kernel Hilbert space RKHS as a measure of the distribution difference. Specifically, calculate the difference between the mean vector of the source task data in RKHS and the mean vector of the target task data in RKHS. Take the mean difference as a measure of the distribution difference between the source task data and the target task data. The smaller the difference, the closer the two data distributions are.
[0046] Through MMD calculation, the distribution difference between the source task data and the target task data can be accurately quantified, providing a basis for subsequent mapping and optimization.
[0047] In some optional embodiments of the present invention, a multi-layer perceptron is used as the mapping function to map the source task data and the target task data to the reproducing kernel Hilbert space RKHS. In the prior art, implicit kernel functions (linear kernel functions, polynomial kernel functions, or Gaussian kernel functions) are generally selected for data mapping. In the embodiments of the present invention, according to the characteristics of the physical field task, a new MMD method is constructed by using a multi-layer perceptron MLP as the mapping function, overcoming problems such as high data dimensions, large redundancy between data, and small data volume in physical field prediction problems.
[0048] In some alternative embodiments of the present invention, the calculation method of the maximum mean discrepancy (MMD) is as follows:
[0049]
[0050] where x i is the source task data, y j is the target task data, n is the total number of source task data, m is the total number of target task data, φ(·) is the mapping function, is the reproducing kernel Hilbert space.
[0051] As can be seen from the above, by calculating the mean discrepancy between the source task data and the target task data in the RKHS, the difference between the two data distributions can be quantified.
[0052] In some alternative implementation manners of the present invention, the projection mapping function is a multi-layer perceptron (MLP). By optimizing the objective function, the distribution difference between the source task data and the target task data in the feature space is minimized. The MLP is a feed-forward neural network that includes an input layer, a hidden layer, and an output layer. By adjusting the parameters of the MLP, the data can be mapped into a high-dimensional feature space. Optimizing the parameters of the MLP to minimize the distribution difference between the source task data and the target task data in the mapped feature space, that is, the optimization objective is to minimize the MMD value.
[0053] The MLP can map the data into a high-dimensional feature space and capture the complex non-linear relationships in the data. And taking the minimization of the MMD value as the optimization objective of the MLP can effectively reduce the distribution difference between the source task data and the target task data and improve the effect of transfer learning.
[0054] In some alternative embodiments of the present invention, the source task data set includes data of other spacecraft physical field tasks, the target task data set is data of the current physical field prediction task, and the source task data set is used to assist in the model training of the target task data.
[0055] With such a design, by using the physical field data of other spacecraft to assist in the model training of the current task, the problem of insufficient training samples is solved. The source task data provides rich prior knowledge and can improve the generalization ability of the target task model.
[0056] In some alternative embodiments of the present invention, transfer learning adopts a model construction method based on deep learning, and uses the prior knowledge of the source task data to improve the prediction accuracy of the target task data. The deep learning model includes but is not limited to a convolutional neural network (CNN), a recurrent neural network (RNN), a Transformer, or a graph neural network.
[0057] Deep learning models can extract complex features from source task data and apply them to target tasks. Selecting a suitable deep learning model according to the characteristics of the target prediction task has strong flexibility and can match different task requirements.
[0058] In some optional embodiments of the present invention, the physical field features include multi-dimensional physical parameters, including but not limited to stress fields, vibration fields, or temperature fields, for predicting the physical fields inside the spacecraft cabin. That is to say, the physical field prediction models provided by the embodiments of the present invention can be used to construct stress field prediction models, vibration field prediction models, temperature field prediction models, etc., with strong applicability.
[0059] The following will detail each step and the involved principles in the method for constructing a spacecraft physical field prediction model based on the evaluation of the maximum mean discrepancy data distribution difference provided by the embodiments of the present invention.
[0060] The embodiments of the present invention propose a method for constructing a spacecraft physical field prediction model based on the evaluation of the maximum mean discrepancy data distribution difference. The technical points involved include the maximum mean discrepancy, reproducing kernel Hilbert space, the maximum mean discrepancy in the reproducing kernel Hilbert space, and the physical field prediction adaptive transfer learning method.
[0061] I. Maximum Mean Discrepancy
[0062] Considering the complex physical processes and multi-scale characteristics existing in the data physical processes of the physical field-level twin calculation problem, the present invention proposes a data distribution evaluation method based on the maximum mean discrepancy (MMD).
[0063] For two probability distributions P and q, assume p = q, and then according to different two-sample detection methods, it can be decided whether to accept or reject this hypothesis. Its basic idea is:
[0064] If the arbitrary-order moments of two random variables are equal, it can be determined that these two probability distributions are the same;
[0065] If there are differences between the two distributions, a specific order moment that maximizes the difference between the two distributions should be selected as the standard for measuring the difference between these two distributions.
[0066] The basic definition of MMD is shown in the following formula:
[0067]
[0068] In the formula, sup represents seeking the upper bound, that is, the maximum value; E p(·) is used to represent the expected value; f(·) represents the mapping function that maps data from the original space to a high-dimensional feature space; F represents the function domain, that is, the set of all possible mapping functions. x and y respectively represent data samples in two probability distributions p and q, and f(x), f(y) are the values of these samples after being processed by the mapping function f(·). The core of this formula is to find a mapping function f(·) that can effectively map the sample variables to a high-dimensional space. Subsequently, the difference between the expected values of the two distributions in the mapped space is calculated. This difference is defined as the mean difference between the two distributions. The ultimate goal is to determine the upper bound of this mean difference, that is, MMD, by solving for the mapping function f(·) in the function domain F that maximizes the expected difference.
[0069] MMD demonstrates its unique advantages in the field of statistical metrics: it can measure the distance between samples of different datasets without introducing additional parameters, thereby effectively evaluating the data distribution. This technology can further solve problems such as high data dimensions in physical field prediction problems by introducing a multi-layer perceptron as the mapping function. This method is achieved by mapping the data distribution to the RKHS and calculating the mean difference after mapping. Next, this method will be introduced in detail.
[0070] II. Reproducing Kernel Hilbert Space
[0071] A Hilbert space is a complete inner product vector space, and its concept extends the traditional Euclidean space. This space uses the techniques of vector algebra and calculus to generalize from two-dimensional and three-dimensional Euclidean spaces to arbitrary dimensions that may include infinite dimensions. This generalization allows the definition of a Hilbert space not to be limited to the real number or finite-dimensional cases and maintains the completeness of the space. An inner product space that can define a norm based on its inner product, thereby forming a normed space, and this space is complete, such an inner product space is called a Hilbert space.
[0072] RKHS is a Hilbert space defined by a kernel function, and its core property is the reproducing property. In RKHS, the mapping defined by the kernel function can map random variables to infinite dimensions. Here, the kernel function plays a key role. It evaluates and generates the elements in the space, that is, the basis vectors. The reproducing property of the kernel function ensures that the evaluation of any function f in RKHS can be achieved through the inner product of this function and the kernel function. In RKHS, the mapping function φ(·) corresponding to the kernel function can map the random variable x to infinite dimensions (φ(x)), and f(x) represents the dot product of the basis vector f and the vector φ(x) in RKHS, that is
[0073]
[0074] In the formula: represents RKHS.
[0075] After a random variable is mapped to the RKHS, its expectation can be expressed by the following formula:
[0076]
[0077] where: μ p represents the average embedding of the probability distribution p in the RKHS. The kernel function can map the random variable x to an infinite-dimensional space, in which the kernel function enables the expectation value of each dimension of the random variable to be obtained.
[0078] III. Maximum Mean Discrepancy in Reproducing Kernel Hilbert Space
[0079] When calculating the MMD, a function space F needs to be constructed, and each function f in this space is regarded as a point. In this framework, F can be understood as a subset in this space. Intuitively, if it has sufficient "richness", then MMD[F, p, q] will only approach zero when p = q. However, if F is too rich, for most finite samples X, Y, this statistic will often deviate significantly from zero.
[0080] Consider an extreme case. If F contains all real-valued functions defined on the set X, and X and Y are disjoint, then it is easy to construct an arbitrarily large MMD[F, X, Y]. For example, a function f can be selected such that it takes large values on X and zero values on Y. In this case, although the MMD value is extremely large, this extreme function selection actually leads to overfitting, that is, the generalization ability of MMD for finite samples is poor.
[0081] To avoid this overfitting phenomenon, it is necessary to set appropriate restrictions on the function space F. These restrictions should not prevent the MMD from playing a role when there are actual differences between the probability distributions p and q. In the context of RKHS, defining F as the unit ball in the RKHS forms an effective balance.
[0082] Given that μ p and μ q represent the expectations E p (φ(x)) and E q (φ(y)) respectively, and substituting μ p and μ q with the means for calculation, the calculation formula for the MMD metric of the RKHS can be derived as the following formula:
[0083]
[0084] Assuming that there are n samples for x and m samples for y, the following formula can be obtained:
[0085]
[0086] Using the kernel function, there is no need to explicitly represent the mapping function φ(·). Solving the inner product of two vectors mapped to a high-dimensional space can be directly transformed into calculating K(x, y). Therefore, taking the square of both sides of the above formula, simplifying to obtain the inner product and expressing it with the kernel function, the following formula is obtained
[0087]
[0088] where: x i and y i The inner product in the RKHS is equal to the result calculated by the kernel function in the original sample space. Since the RKHS is often a high-dimensional or even infinite-dimensional space, the corresponding kernel generally selects the Gaussian kernel representing infinite dimensions, and the following can be obtained:
[0089]
[0090] where σ is the width of the kernel function.
[0091] IV. Adaptive Transfer Learning for Physical Field Prediction
[0092] Combined with the maximum mean discrepancy evaluation method introduced above, the adaptive transfer learning method for physical field prediction first uses a multi-layer perceptron as the mapping function φ(·), and then takes minimizing Equation (4) as the optimization objective function to learn the mapping function φ(·). Then, based on the mapping function φ(·), the physical field features are mapped to the feature space, and then the projected source domain / target domain samples are used as training data for transfer learning, and the physical field prediction model of the spacecraft can be obtained.
[0093] 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 such actual relationship or order between these entities or operations. Moreover, the terms "including", "comprising" or any other variant 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 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 based on the placement state shown in the drawings.
[0094] 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 described in the foregoing embodiments, or perform equivalent replacements for 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 embodiments of the present invention.
Claims
1. A method for constructing a spacecraft physical field prediction model based on maximum mean difference data distribution difference evaluation, characterized in that: include: Obtain the physical field datasets of the source task and the target task, including physical field feature data and corresponding labels; Map the source task data and the target task data to a high-dimensional feature space through a mapping function; The distribution difference between the source task data and the target task data is measured based on the maximum mean difference (MMD). Optimizing the mapping function to minimize the distribution difference between the source task data and the target task data in the feature space; The mapped source task data and target task data are used for transfer learning to build a physical field prediction model.
2. The method for constructing a spacecraft physical field prediction model based on maximum mean difference data distribution difference evaluation according to claim 1, characterized in that: The calculation method of the maximum mean difference MMD includes: Mapping the source task data and the target task data to the reproducing kernel Hilbert space RKHS; The mean difference between the source task data and the target task data is calculated in the reproducing kernel Hilbert space RKHS as a measure of the distribution difference.
3. The method for constructing a spacecraft physical field prediction model based on maximum mean difference data distribution difference evaluation according to claim 2, characterized in that: A multilayer perceptron is used as the mapping function to map the source task data and the target task data to the reproducing kernel Hilbert space RKHS.
4. The method for constructing a spacecraft physical field prediction model based on maximum mean difference data distribution difference evaluation according to claim 3, characterized in that: The maximum mean difference MMD is calculated by the following formula: Among them, x i is the source task data, y j is the target task data, n is the total number of source task data, m is the total number of target task data, φ(·) is the mapping function, is the reproducing kernel Hilbert space.
5. The method for constructing a spacecraft physical field prediction model based on maximum mean difference data distribution difference evaluation according to claim 1, characterized in that: The projection mapping function is a multi-layer perceptron, which minimizes the distribution difference between the source task data and the target task data in the feature space by optimizing the objective function.
6. The method for constructing a spacecraft physical field prediction model based on maximum mean difference data distribution difference evaluation according to claim 1, characterized in that: The source mission data set includes data of other spacecraft physical field missions, the target mission data set is data of the current physical field prediction mission, and the source mission data set is used to assist model training of the target mission data.
7. The method for constructing a spacecraft physical field prediction model based on maximum mean difference data distribution difference evaluation according to claim 1, characterized in that: The transfer learning adopts a model building method based on deep learning, using the prior knowledge of source task data to improve the prediction accuracy of target task data. The deep learning model includes but is not limited to convolutional neural network CNN, recurrent neural network RNN, Transformer or graph neural network.
8. The method for constructing a spacecraft physical field prediction model based on maximum mean difference data distribution difference evaluation according to claim 1, characterized in that: The physical field characteristics include multi-dimensional physical parameters, including but not limited to stress field, vibration field or temperature field, which are used to predict the physical field in the spacecraft cabin.