A task performance evaluation method based on hierarchical KAN and RBF network combination
By combining hierarchical KAN and RBF networks, a high-precision and high-efficiency task performance evaluation model was achieved, solving the problems of insufficient accuracy and real-time performance of traditional methods in complex environments and improving the processing capability of multidimensional data.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING RESEARCH INSTITUTE OF MECHANICAL & ELECTRICAL TECHNOLOGY CO LTD CAM
- Filing Date
- 2026-03-23
- Publication Date
- 2026-06-02
AI Technical Summary
Traditional task performance evaluation methods lack accuracy and real-time performance in complex environments, making it difficult to handle diverse and multi-dimensional task requirements. Furthermore, RBF networks are computationally complex and inefficient when processing high-dimensional data, and KAN architectures are complex to tune.
A hierarchical KAN and RBF network approach is adopted. The KAN network is used to perform nonlinear fusion and dimensionality reduction of features from multiple categories, and the RBF network is used for further nonlinear mapping to construct a task performance evaluation model.
It improves the accuracy and efficiency of the evaluation, enhances the generalization ability of the model, can effectively handle complex multidimensional data, maintain high accuracy and efficiency, and solves the shortcomings of modeling multi-category and multi-feature variable data.
Smart Images
Figure CN122134163A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of simulation technology and relates to a task performance evaluation method based on the combination of hierarchical KAN and RBF networks. Background Technology
[0002] Mission effectiveness assessment refers to a comprehensive evaluation based on various influencing factors (such as target characteristics, perception capabilities, guidance and control) within a typical mission effectiveness index system. Currently, combat scenarios are characterized by complex environments, diverse interference, and rapidly changing mission objectives. This means that traditional assessment methods often fail to meet the accuracy and real-time requirements of complex environments. Traditional effectiveness assessment methods largely rely on experience or simplified mathematical models, lacking the ability to model complex nonlinear relationships, making them ill-suited for diverse and multi-dimensional mission requirements.
[0003] Commonly used performance evaluation methods for radial basis function (RBF) networks are applied to neural network models for nonlinear regression and classification problems. By using radial basis functions such as Gaussian kernels, they can map data in high-dimensional space to a space more suitable for classification or regression, and perform pattern matching based on the distance between the input and the center point, demonstrating excellent local feature learning capabilities. However, due to limitations in kernel function selection, a single RBF kernel function often cannot meet the requirements when the data distribution is uneven or there are strong nonlinear relationships. Furthermore, it is computationally complex and inefficient when processing high-dimensional data, and RBF is prone to overfitting, especially when the amount of data is small or the training process is insufficient, thus limiting the model's generalization ability.
[0004] Unlike traditional neural networks, Kolmogorov-Arnold Network (KAN) can perform hierarchical modeling of target features, perception capabilities, guidance and control in a multi-layered network structure. It can capture the complex relationships between different feature variables through hierarchical feature learning and nonlinear fusion, and has excellent feature dimensionality reduction and generalization capabilities. It is particularly suitable for processing complex multidimensional data. However, the KAN architecture is usually more complex than traditional deep learning, and missile models are difficult to tune and optimize. Summary of the Invention
[0005] The purpose of this invention is to at least solve one of the problems existing in the prior art.
[0006] Therefore, in order to quickly and accurately construct a performance evaluation model based on multi-dimensional features of a task, this invention provides a task performance evaluation method based on the combination of hierarchical KAN and RBF networks. The KAN network effectively integrates features from multiple categories to achieve feature dimensionality reduction, and the RBF method is used to quickly fit the performance model between input and output, thereby improving the accuracy and efficiency of the evaluation. This method can solve the shortcomings of existing technologies in modeling multi-category and multi-feature variable data, and improve the evaluation accuracy, computational efficiency and interpretability.
[0007] The technical solution of the present invention is as follows:
[0008] A task performance evaluation method based on the combination of hierarchical KAN and RBF networks is proposed. The specific steps of this method are as follows:
[0009] Step 1, determine the input data to be fed into the KAN network:
[0010] According to the task effectiveness evaluation index system, the influencing factors of task effectiveness are divided into at least three categories, namely target characteristics, perception capability, and guidance and control. Each category includes multi-dimensional feature variables x, and all feature variables x of the above different categories are used as input data.
[0011] Step 2: Preprocess the input data using a standardization method, and output the preprocessed feature variables x. z ;
[0012] Step 3: Construct multiple KAN networks that correspond one-to-one with target features, perception capabilities, and guidance and control. Each KAN network is used to process multidimensional feature variables x of the same category. z Perform hierarchical nonlinear transformations and fusions to output feature variables x with reduced dimensionality. z ', i.e., low-dimensional feature variable x z ';
[0013] Step 4: Construct the RBF network and convert the low-dimensional feature variables x output by each KAN network in Step 3 into a single network. z The input is fed into the RBF network, which then processes all the low-dimensional feature variables x. z As input, a nonlinear mapping is performed, and the task performance evaluation results are output; finally, the transformation from the task performance evaluation index system to the task performance evaluation results is completed.
[0014] Furthermore, in step 1, the target characteristics include: target RCS characteristics, target radiation intensity, and signal-to-noise ratio; the sensing capabilities include: identification error and tracking error; and the guidance and control include: maximum overload and maximum speed.
[0015] Furthermore, in step 2, the preprocessing involves converting the data into a distribution with zero mean and unit variance, as shown in the following formula:
[0016]
[0017] Where x is the original data, μ is the mean of the data, and σ is the standard deviation of the data. z This represents the standardized value.
[0018] Furthermore, in step 3, each KAN network performs a nonlinear transformation of its hidden layers on the multidimensional feature variables x of the same category. z Nonlinear transformation and fusion of similar feature variables in the model are performed to output a low-dimensional feature variable x. z ', and retain relevant information between feature variables.
[0019] Furthermore, the output dimension of each KAN network is designed as a low-dimensional continuous vector.
[0020] Furthermore, the output dimension of each KAN network is 3-dimensional.
[0021] Furthermore, in step 4, the RBF network uses radial basis functions to perform nonlinear mapping on the data.
[0022] Furthermore, after step 4, MSE, MAE, and R are used. 2 The verification metrics are compared to assess the predictive performance of the constructed model, thus verifying the accuracy of the task performance model construction.
[0023] By applying the above technical solution, the present invention has the following beneficial effects:
[0024] (1) This invention combines the KAN network and the RBF network to leverage their respective advantages. The KAN network performs nonlinear feature fusion and dimensionality reduction on the feature variables of each category, and the fused feature variables are input into the RBF network for further mapping. That is, based on the low-dimensional features output by the KAN network, the RBF network further completes the accurate mapping of task performance. This combination method can maintain high accuracy and efficiency when dealing with complex and high-dimensional data, effectively reducing the dimensionality of the input data, reducing the amount of computation, and retaining the key information of the data. This greatly improves the training and prediction efficiency of the evaluation model, and enhances the accuracy and generalization of performance evaluation.
[0025] (2) This invention proposes a feature fusion and nonlinear modeling based on a hierarchical structure of KAN network, which solves the shortcomings of existing technologies in modeling multi-class variables and can more effectively capture the complex interaction relationships and nonlinear dependencies between variables. At the same time, it significantly improves the computational efficiency, especially the scheme for efficient evaluation under high-dimensional data.
[0026] (3) This invention employs a KAN network to effectively fuse and reduce the dimensionality of multidimensional features, and then inputs the output features into an RBF network to achieve a precise mapping from the evaluation index system to mission effectiveness. The RBF network maintains high computational speed and provides accurate operational effectiveness assessment during further feature processing. Attached Figure Description
[0027] The accompanying drawings, which form part of this specification, are provided to further illustrate embodiments of the invention and, together with the textual description, explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.
[0028] Figure 1 Flowchart of a task performance evaluation method based on hierarchical KAN and RBF;
[0029] Figure 2 This is a schematic diagram of a task performance evaluation method based on hierarchical KAN and RBF.
[0030] Figure 3 The graph shows the changes in training loss and validation loss for a standard KAN network.
[0031] Figure 4 The graph shows the changes in training loss and validation loss for Example 1. Detailed Implementation
[0032] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0033] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0034] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.
[0035] This embodiment provides a task performance evaluation method based on the combination of hierarchical KAN (Kolmogorov-Arnold Network) and RBF network. See appendix. Figures 1-2 The specific steps of this method are as follows:
[0036] Step 1, determine the input data to be fed into the KAN network:
[0037] Based on the task performance evaluation index system (understanding within the task performance domain), the influencing factors of task performance are divided into at least three categories. This embodiment adopts three categories: target characteristics, perception capabilities, and guidance and control. Each category includes multi-dimensional feature variables x. Specifically, target characteristics include: target RCS characteristics, target radiation intensity, signal-to-noise ratio, etc.; perception capabilities include: recognition error, tracking error, etc.; guidance and control include: maximum overload, maximum speed, etc. All feature variables x of the above different categories are used as input data.
[0038] Step 2: Preprocess the input data using a standardization method to ensure the uniformity and usability of all feature variables when input into the KAN network;
[0039] Standardization (Z-score standardization): Transforms data into a distribution with zero mean and unit variance, as shown in the following formula:
[0040]
[0041] Where x is the original data, μ is the mean of the data, and σ is the standard deviation of the data. z This represents the standardized value;
[0042] Step 3: Construct multiple KAN networks that correspond one-to-one with the target features, perception capabilities, and guidance and control. The number of KAN networks is the same as the number of input data categories. Each KAN network is specifically used to process the feature variables of the same category, i.e., for the multidimensional feature variables x of the same category. z Hierarchical nonlinear feature fusion is performed, which reduces the dimensionality of the input data and improves the evaluation accuracy.
[0043] Each KAN network applies a nonlinear transformation of its hidden layers to the multidimensional feature variables x of the same category. z Nonlinear transformation and fusion of similar feature variables in the data, that is, multidimensional feature variables x of the same category. z Mapping to a lower-dimensional space, the output feature variable x has a reduced dimension. z ', that is, outputting low-dimensional feature variables x z This approach preserves relevant information between feature variables. Therefore, by using a classification KAN network structure (i.e., the number of KAN networks is the same as the number of input data categories), the dimensionality of the input data can be effectively reduced, excessive redundant information can be avoided, model complexity can be reduced, and computational efficiency can be improved.
[0044] The output dimension of each KAN network is designed as a low-dimensional continuous vector, preferably 3-dimensional. On the one hand, this can preserve the performance representation capabilities of multiple angles and mechanisms within a single KAN network, avoiding information loss caused by excessive compression. On the other hand, it can effectively control the overall feature dimension, so that the RBF input vector formed by splicing the outputs of various KAN networks is in the working range of 6-12 dimensions, thereby ensuring the stability of the Gaussian function center distribution and computational efficiency.
[0045] Step 4: Construct the RBF network and convert the low-dimensional feature variables x output by each KAN network in Step 3 into a single network. z The input is fed into the RBF network, which then processes all the low-dimensional feature variables x. z As input, a nonlinear mapping is performed, and the task performance evaluation results are output; finally, the transformation from the task performance evaluation index system to the task performance evaluation results is completed.
[0046] The RBF network uses radial basis functions (such as Gaussian kernel functions) to perform nonlinear mapping on the data, ensuring that the low-dimensional feature variables x output by the KAN network can be represented. z To convert the results into task performance evaluation, during training, the maximum number of neurons and the width of the Gaussian kernel function are set (usually set to 1 or 2) to constrain the network size and avoid overfitting, and to control the response range and smoothness characteristics of each hidden neuron to the input space.
[0047] Step 5, use MSE (mean squared error), MAE (mean squared absolute error), and R... 2(Correlation coefficient) Validation indicators compare the predictive performance of the constructed model and verify the accuracy of the task performance model construction:
[0048] Generally, the smaller the MSE (mean squared error) and MAE (mean squared absolute error) values, the closer the constructed model is to the actual model; R 2 The closer the correlation coefficient value is to 1, the closer the constructed model is to the actual model.
[0049] Example 2:
[0050] Based on Example 1, this embodiment uses both the traditional KAN network and the method proposed in Example 1 to perform regression fitting tasks for the 19 feature variables x input to the KAN network and the 1 variable output after fusion. The 19 input variables are divided into 3 categories, with each category having an index dimension of 6, 6, and 7.
[0051] (1) Construct a traditional KAN network with an input dimension of 9 and an output dimension of 1. The first layer contains 19 x 8 nodes, the second layer contains 8 x 3 nodes, and the third layer contains 3 x 1 nodes.
[0052] (2) The input variables are divided into 3 categories, and 3 KAN networks are constructed. For the indicators with a dimension of 6, the first layer of the KAN network contains 6X8 nodes, the second layer contains 8X3 nodes, and the output dimension is 3. For the indicators with a dimension of 7, the first layer of the KAN network contains 7X8 nodes, the second layer contains 7X3 nodes, and the output dimension is 3.
[0053] (3) The input of the RBF neural network is the output of each class of KAN network. The input dimension is 3X3. The maximum number of neurons in the RBF neural network is set to 600, and the spread factor is 1.
[0054] (4) The experimental dataset consisted of 5028 sets, of which 500 sets were used for testing, and the remaining data were used for training and validation. The relevant training results are as follows: Figure 3 and Figure 4 As shown in the figure, Training Loss represents the training loss, and Val Loss represents the validation loss. Compared with the traditional KAN network, Example 1 achieves faster training convergence and higher accuracy. MSE (mean squared error), MAE (mean squared absolute error), and R0 are used. 2 The correlation coefficient is used to verify the fitting results, as shown in Table 1.
[0055] Table 1 Comparison of Fitting Results
[0056]
[0057] As can be seen from Table 1, the method in Example 1 has smaller errors in MSE and MAE compared to the traditional KAN network method, and R... 2 The result is closer to 1 than the traditional KAN method, indicating that Example 1 has higher accuracy.
[0058] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.
[0059] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.
[0060] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A task performance evaluation method based on a combination of hierarchical KAN and RBF networks, characterized in that, The specific steps of this method are as follows: Step 1, determine the input data to be fed into the KAN network: According to the task effectiveness evaluation index system, the influencing factors of task effectiveness are divided into at least three categories, namely target characteristics, perception capability, and guidance and control. Each category includes multi-dimensional feature variables x, and all feature variables x of the above different categories are used as input data. Step 2: Preprocess the input data using a standardization method, and output the preprocessed feature variable χ. z ; Step 3: Construct multiple KAN networks that correspond one-to-one with target features, perception capabilities, and guidance and control. Each KAN network is used to process the multidimensional feature variable χ of the same category. z Perform hierarchical nonlinear transformations and fusions to output feature variables x with reduced dimensionality. z ', i.e., low-dimensional feature variable χ z '; Step 4: Construct the RBF network and convert the low-dimensional feature variables x output by each KAN network in Step 3 into a single network. z The input is fed into the RBF network, which then processes all the low-dimensional feature variables χ. z As input, a nonlinear mapping is performed, and the task performance evaluation results are output; finally, the transformation from the task performance evaluation index system to the task performance evaluation results is completed.
2. The task performance evaluation method based on the combination of hierarchical KAN and RBF networks as described in claim 1, characterized in that, In step 1, target characteristics include: target RCS characteristics, target radiation intensity, and signal-to-noise ratio; sensing capabilities include: identification error and tracking error; guidance and control include: maximum overload and maximum speed.
3. The task performance evaluation method based on the combination of hierarchical KAN and RBF networks as described in claim 1, characterized in that, In step 2, the preprocessing involves converting the data into a distribution with zero mean and unit variance, as shown in the following formula: Where x is the original data, μ is the mean of the data, and σ is the standard deviation of the data. z This represents the standardized value.
4. The task performance evaluation method based on the combination of hierarchical KAN and RBF networks as described in claim 1, characterized in that, In step 3, each KAN network performs a nonlinear transformation of its hidden layers on the multidimensional feature variables χ of the same category. z Nonlinear transformation and fusion of similar feature variables in the model are performed to output a low-dimensional feature variable χ. z ', and retain relevant information between feature variables.
5. The task performance evaluation method based on the combination of hierarchical KAN and RBF networks as described in claim 4, characterized in that, The output dimension of each KAN network is designed to be in the form of a low-dimensional continuous vector.
6. The task performance evaluation method based on the combination of hierarchical KAN and RBF networks as described in claim 5, characterized in that, Each KAN network has a 3-dimensional output.
7. The task performance evaluation method based on the combination of hierarchical KAN and RBF networks as described in claim 1, characterized in that, In step 4, the RBF network uses radial basis functions to perform nonlinear mapping on the data.
8. The task performance evaluation method based on the combination of hierarchical KAN and RBF networks as described in claim 1, characterized in that, After step 4, MSE, MAE, and R are used. 2 The verification metrics are compared to assess the predictive performance of the constructed model, thus verifying the accuracy of the task performance model construction.