A method for dynamic estimation of X-ray pulsar frequency based on chaotic learning

Abstract

The present invention discloses a method for dynamic estimation of X-ray pulsar frequency based on chaotic learning, which belongs to the field of pulsar navigation technology, including: performing adaptive dimensionality reduction of the pulsar outline waterfall chart by stochastic neighbor embedding (SNE) by reconstructing a high-dimensional space sample distance model, etc. to meet the requirements of on-board industrial computer operations. A difference balance term is introduced into the cross entropy loss function, and the classification and regression performance of the model is effectively improved by enhancing the discrimination of the net activity values ​​of the positive and negative sample output layers. According to the chaotic phenomenon existing in real neurons, a loss term based on chaos enhancement is designed and added. After model screening, the most suitable X-ray pulsar frequency is obtained. The present invention has the advantages of being suitable for navigating pulsar sources, having high estimation accuracy, and strong estimation stability, and can improve the navigation performance of X-ray pulsars.

Description

Technical Field

[0001] The present invention belongs to the technical field of pulsar navigation, and in particular relates to a method for dynamic estimation of X-ray pulsar frequency based on chaos learning. Background Art

[0002] As a core technology in deep space exploration, autonomous navigation methods can improve spacecraft navigation accuracy and mission efficiency, reduce reliance on ground-based resources, and enable navigation in unknown and complex environments. X-ray pulsar navigation, as an emerging astronomical ranging navigation method, provides spacecraft with high-precision spatiotemporal references and boasts extremely long-range navigation capabilities. It holds great potential for autonomous astronomical navigation in deep space exploration. X-ray pulsar navigation often relies on ephemeris information to determine the current pulsar frequency (due to its constant frequency). Based on this frequency, the weak pulsar photons received by the detector are reconstructed to obtain a high-precision navigation measurement model. However, pulsar "failures"—unpredictable changes in the spin frequency and its derivatives—can cause the ephemeris information to no longer accurately provide the pulsar frequency, potentially rendering this navigation method ineffective. Therefore, directly using the pulsar photon information received by the detector to perform real-time dynamic estimation of the current pulsar frequency can avoid the failure of the navigation method due to pulsar "failure", thereby making X-ray pulsar navigation suitable for any time period of deep space exploration missions.

[0003] Existing methods for dynamic pulsar frequency estimation primarily rely on statistical tests. Pulsar photon profiles are folded and restored based on candidate frequencies. The resulting folded profiles are then tested for significance using various test functions. The candidate frequency with the best test results is then selected as the estimated frequency. While computationally simple, these methods are sensitive to noise. Furthermore, with the advancement of research on some pulsars, frequency estimation methods based on matching pulsar standard profiles have also been increasingly adopted. However, due to the limited number of pulsars with known standard profiles, these methods still have limitations for pulsar frequency estimation. Meanwhile, waterfall plots, an emerging pulsar profile visualization method, can also be used for dynamic pulsar frequency estimation. This method folds pulsar photons into segments, focusing not only on the significance of each folded waveform but also on the consistency of the folded waveforms to further explore photon information. While these methods can fully utilize pulsar photon information, they are computationally demanding and pose significant challenges for onboard industrial computers. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a method for dynamic estimation of X-ray pulsar frequency based on chaotic learning. It is a method for dynamic estimation of pulsar frequency with higher estimation accuracy, more stable estimation effect, and stronger computing power, so as to further improve the performance of X-ray pulsar navigation. First, by reconstructing a high-dimensional space sample distance model, the pulsar profile waterfall chart is adaptively reduced in dimension using stochastic neighbor embedding (SNE) to meet the computing requirements of onboard industrial computers. Secondly, a difference balance term is introduced into the cross-entropy loss function to effectively improve the classification and regression performance of the model by enhancing the discrimination of the net activity values ​​of the output layer of positive and negative samples. Finally, to further improve the global search capability of the model, a loss term based on chaos enhancement is designed and added based on the chaotic phenomenon existing in real neurons. After model screening, the most suitable X-ray pulsar frequency is obtained. The present invention has the advantages of being suitable for navigating pulsar sources, having high estimation accuracy and strong estimation stability, and can effectively meet the accuracy requirements of X-ray pulsar navigation solutions, thereby further improving the performance of X-ray pulsar navigation.

[0005] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0006] A method for dynamic estimation of X-ray pulsar frequency based on chaotic learning, comprising the following steps:

[0007] Step 1: Perform adaptive dimensionality reduction using SNE on the high-dimensional waterfall plot of the pulsar profile by reconstructing a high-dimensional space sample distance model. SNE stands for Stochastic Neighbor Embedding.

[0008] Step 2: Optimize the cross entropy loss function and introduce a difference balance term that controls the discrimination between the net activity values ​​of positive and negative samples in the output layer to improve the regression prediction performance of the MLP model. MLP stands for Multi-Layer Perceptron.

[0009] Step 3: Design and add a chaotic loss function based on a real neuron dynamics model to improve the global search capability of the MLP model and speed up the training of the MLP model;

[0010] Step 4: Execute steps 1 to 3 in all candidate periods, select the optimal SNE adaptive dimensionality reduction image through the MLP model, and obtain the corresponding high-dimensional waterfall plot based on the SNE adaptive dimensionality reduction image, and finally obtain the corresponding optimal X-ray pulsar frequency estimate.

[0011] Beneficial effects:

[0012] (1) The present invention performs SNE adaptive dimensionality reduction on the high-dimensional waterfall diagram of pulsar profiles by reconstructing a high-dimensional space sample distance model, which can significantly improve the extraction effect of waterfall diagram features, while reducing the calculation dimension and the calculation cost to meet the computing requirements of onboard industrial computers.

[0013] (2) The optimized cross-entropy loss function proposed in this paper introduces a difference balance term to control the discrimination of the net activity values ​​of positive and negative samples in the output layer, which can reduce the network training bias through manual intervention, thereby improving the model regression prediction accuracy.

[0014] (3) The present invention accelerates the convergence speed of the backpropagation algorithm by introducing a chaotic loss function based on a real neuron dynamics model, while improving the model's adaptability to disturbances and enhancing the model's stability and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a schematic diagram of the principle of a method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to the present invention;

[0016] Figure 2a , Figure 2b , Figure 2c is the contour waterfall diagram obtained by folding at different frequencies; Figure 2a To get the correct frequency-folded waterfall plot, Figure 2b is a waterfall diagram with a certain error frequency fold, Figure 2c Waterfall plot collapsed for completely wrong frequencies;

[0017] Figure 3 The following are the contour waterfall plots and SNE dimension reduction effect diagrams under different periods; from left to right, they represent the waterfall plots and SNE dimension reduction diagrams when the period is P=0.0337000000s, P=0.0336999960s, P=0.0336999920s, and P=0.0336999880s, respectively. The upper figure is the waterfall plot, and the lower figure is the SNE dimension reduction diagram;

[0018] Figure 4 Schematic diagram of the network balance optimization process based on the adjustment of the net activity value difference of the output layer;

[0019] Figure 5 Schematic diagram of the weight gradient update process;

[0020] Figure 6 Schematic diagram of the Kullback-Leibler (KL) divergence iterative process for different distances;

[0021] Figure 7The two leftmost figures represent waterfall charts under two periods of P=0.0337000000s and P=0.0336999920s, respectively. The three groups of figures on the right represent the dimensionality reduction effects of the SNE method when the perplexity is selected as 1, 40, and 200 respectively under the corresponding period P.

[0022] Figure 8 Box plot of the mean errors of the three estimation methods. DETAILED DESCRIPTION

[0023] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, exemplary embodiments of the present invention will be described in further detail below. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0024] like Figure 1 As shown, the present invention proposes a method for dynamic estimation of X-ray pulsar frequency based on chaotic learning. First, the present invention performs SNE adaptive dimensionality reduction on the pulsar profile waterfall chart by reconstructing a high-dimensional space sample distance model to meet the requirements of on-board industrial computer operations. Secondly, a difference balance term is introduced into the cross-entropy loss function. By enhancing the discrimination of the net activity values ​​of the output layer of positive and negative samples, the classification and regression performance of the model is effectively improved. Finally, in order to further improve the global search capability of the model, the present invention designs and adds a loss term based on chaos enhancement based on the chaotic phenomenon existing in real neurons; specifically, it includes the following steps:

[0025] Step 1: Use the detector to observe pulsar photons, collect data, and divide them into equal time according to the total observation time to form a pulsar profile waterfall diagram, and perform SNE (stochastic neighbor embedding) adaptive dimensionality reduction on the pulsar profile waterfall diagram (i.e. Figure 1 The SNE dimensionality reduction in the dataset meets the computational requirements of onboard industrial computers. By performing lossless dimensionality reduction on the rich waterfall chart information, the high-dimensional information is converted into a two-dimensional plane distribution. This allows the two-dimensional plane data distribution to be used as the input of the subsequent MLP model for MLP model training.

[0026] like Figure 2a , Figure 2b , Figure 2cAs shown, profile waterfall analysis has great potential for accurately estimating pulsar frequencies. However, waterfall analysis is computationally complex and inefficient, posing a challenge to the computing power of onboard industrial computers. Stochastic Neighbor Embedding (SNE) is an effective data dimensionality reduction method and a powerful means of addressing this problem. It maps high-dimensional data points into a low-dimensional space, revealing the internal structure of the data. However, due to numerous hyperparameters and poor high-dimensional embedding performance, directly using SNE to reduce the dimensionality of waterfall plots often yields unsatisfactory results. Therefore, it is necessary to adapt the SNE method to the characteristics of pulsar profile waterfall plots to achieve better dimensionality reduction results.

[0027] Due to its intuitive simplicity and high computational efficiency, SNE often uses the Euclidean distance model as a high-dimensional sample distance model to measure the similarity of samples in the real dimension. However, since the contour waterfall plot increases the number of segmentations by reducing the number of photons in a single fold to achieve statistical analysis of dimensionality reduction data. Therefore, in a single folding process, the folding contour signal-to-noise is usually low, which leads to poor folding quality. At this time, if the Euclidean distance is still used to measure the similarity between high-dimensional samples, the measurement effect may be affected by noise and deviate from the actual situation. Based on this, the present invention introduces the cosine distance to reconstruct the high-dimensional space sample distance model. The cosine distance mainly measures the direction rather than the amplitude between each folding contour and is insensitive to amplitude noise. Secondly, the cosine distance can reduce the distance saturation effect in high-dimensional space. This makes the cosine distance more clearly reflect the similarity between contours when facing the contour waterfall plot.

[0028] (1)

[0029] in, is the spatial distance between high-dimensional samples, For the The spatial coordinates of the samples, is the sample size.

[0030] Figure 3 The high-dimensional images obtained by folding the waterfall chart under four different candidate periods P and the corresponding distribution of four two-dimensional data points after SNE dimensionality reduction are given. Figure 3 It can be found that SNE dimensionality reduction can not only retain the features of the contour waterfall plot, but also effectively reduce the data dimension, laying the foundation for the subsequent use of the folded contour phase change features for high-precision period estimation. Figure 3In the figure, from left to right, they represent the waterfall chart and SNE dimensionality reduction chart when the period is P=0.0337000000s, P=0.0336999960s, P=0.0336999920s, and P=0.0336999880s. The upper figure is the waterfall chart and the lower figure is the SNE dimensionality reduction chart.

[0031] Step 2: Introduce the difference balance term into the cross entropy loss function to obtain a balanced cross entropy loss function to increase the discrimination between positive and negative samples, thereby improving the regression prediction effect of the MLP model.

[0032] This method dynamically estimates pulsar frequencies, essentially aiming to solve the ranking problem in regression tasks using a multi-layer perceptron (MLP) model. This involves substituting candidate frequencies into the model and selecting the optimal frequency based on their probability scores. In this type of problem, data imbalance and score overlap are key factors that affect prediction performance. First, the number of positive and negative samples is balanced by undersampling "non-optimal" samples. Second, a balanced cross-entropy loss function based on the difference in net activity values ​​in the output layer is proposed to further distinguish between positive and negative samples, improving ranking accuracy.

[0033] Specifically, if Figure 4 As shown in the figure, since some "non-optimal" samples are very similar to the "optimal" sample features, it may cause the output layer net activity value of positive and negative samples to be Overlap occurs, which reverses the order of the probability values ​​after activation, directly affecting the estimation accuracy. Therefore, the cross entropy loss function is optimized by introducing a balancing term (difference balancing term) based on the difference in net activity values ​​of the output layer. This part of the loss function is the balanced cross entropy loss function. The design is as follows:

[0034] (2)

[0035] in, is the balanced cross entropy loss function obtained in this calculation, is the coefficient of the difference balance term, and it is gradually reduced using the “annealing strategy”. is the difference balance item, is the true label, Output values ​​for the model.

[0036] The main function of the difference balance term is to quantitatively consider whether there is overlap in the net activity values ​​of the positive and negative sample output layers during loss calculation and gradient update, and to further reduce the problem of poor sorting due to "score overlap" through human intervention. Specifically, it is designed to be the difference between the minimum net activity value of the positive sample output layer and the maximum net activity value of the negative sample output layer in the initial stage of network training, that is:

[0037] (3)

[0038] in, For the Layer neurons output net activity values, For the The output net activity value of the negative sample of the layer neurons, For the The net output activity value of the positive sample of the layer neurons, max represents the maximum value, and min represents the minimum value.

[0039] When performing weight and bias backpropagation, the gradients of the two can be expressed as:

[0040] (4)

[0041] (5)

[0042] in, For the The weights of the neurons in the layer, For the The error term of the neurons in the layer, For the The activity value of the neurons in the layer, For the The bias term of the layer neurons, the superscript T represents the transpose of the matrix. For the The number of neurons in the layer.

[0043] Combined with formula (2), the error term of the output layer neuron of the MLP model of the present invention can be expressed as:

[0044] (6)

[0045] in, For the The gradient of back propagation of neurons in the layer, For the Tier The output activity value of a neuron, is the coefficient of the difference balance term, is the difference balance item, is the true label, Output values ​​for the model.

[0046] As can be seen from formula (6), the difference balance term proposed in the present invention directly participates in the gradient update process of the model weights and biases, that is, by introducing the difference in the net activity value of the output layer of positive and negative samples, the model parameter training process is affected, so that the model pays more attention to the network training deviation caused by the "score overlap" problem during training, and adjusts the network parameters as much as possible to increase the discrimination between positive and negative samples, thereby further improving the model regression prediction effect.

[0047] Step 3: Design and add a new loss term based on chaos enhancement to enhance global exploration capabilities and accelerate the convergence process;

[0048] The above-mentioned balanced optimization of the cross-entropy loss function significantly improves model prediction accuracy. However, some positive and negative samples with very similar characteristics still lead to weak gradient signals and stagnant weight updates, further exacerbating the slow convergence of the backpropagation algorithm. This may be because the model training process ignores a key characteristic of neuronal dynamics in the brain: chaos.

[0049] Chaos is a deterministic dynamic behavior characterized by aperiodicity and nonlinearity, making it extremely sensitive to initial values. Traditional gradient descent methods often involve local optimization and are prone to falling into local minima. Introducing chaotic behavior can enhance the exploratory nature of the search space, helping to more comprehensively uncover underlying patterns in the data and prevent the network from falling into overfitting or low-quality solutions. Furthermore, chaotic behavior can improve the network's adaptability to external perturbations, thereby enhancing the model's stability and reliability.

[0050] Based on this, chaotic behavior is introduced into gradient dynamics, and a chaotic loss function with a high degree of state variable dependence is designed and proposed. :

[0051] (7)

[0052] in, is the number of neuron layers in the MLP model, For the The number of neurons in the layer, To control the chaotic strength coefficient of weight update, For the Tier The activity value of a neuron.

[0053] Combining formula (2) and formula (7), the dynamic model of weight gradient update can be obtained as follows:

[0054] (8)

[0055] in, is the weight after the neuron gradient is updated, is the learning rate, For the Tier The error term of each neuron, is the cross entropy loss function The activity value of the layer, is the first chaotic loss function Tier The activity value of a neuron, is the first chaotic loss function Tier The net activity of neurons, It can be reflected as the chaotic strength coefficient that controls the weight update. The superscript T represents the transpose of the matrix.

[0056] The update process of weight gradient is as follows Figure 5 As shown in Figure 2, the neural network consists of an input layer, a hidden layer, and an output layer. Figure 5 In the equation (8), k represents the kth neuron in this layer, and j represents the jth neuron in the previous layer. Formula (8) shows that the model weight update process is affected by the traditional gradient term and the chaotic term introduced in step 3, which has a clear biological meaning. First, the introduction of the chaotic term simulates the phenomenon that neurons in the brain use chaotic dynamics to avoid falling into local optimal solutions from gradient dynamics when learning. Secondly, the above-mentioned gradient update model has a more consistent form with the neuron biological model proposed by Nagumo-Sato, and can more realistically approximate the neuron learning process. At the same time, the model simulates the critical state behavior of the brain. Specifically, the present invention has a strong chaotic coefficient. Adopt annealing strategy. In the early stage of network training, adopt strong chaotic behavior to enhance global exploration ability and accelerate the convergence process. As the network training deepens, the chaotic phenomenon is gradually reduced, and the training effect is stabilized by traditional gradient update method, realizing the mutual switching between traditional gradient learning and chaotic learning. In addition, the chaotic loss function The second-order state variable feedback is adopted, which can well reflect the high dependence of neuron state variables.

[0057] Step 4: Execute steps 1-3 within all candidate periods, select the optimal SNE adaptive dimensionality reduction image through the MLP model, and obtain the corresponding waterfall plot based on the period P corresponding to the SNE adaptive dimensionality reduction image. Further reverse deduction is performed to obtain the pulsar folding profile corresponding to the waterfall plot, and finally obtain the corresponding optimal X-ray pulsar frequency estimate.

[0058] Example:

[0059] This paper selects the pulsar PSR B0531+21 for frequency dynamic estimation. Due to the limited real data set, this paper uses a simulated data set (4200 sets of positive and negative sample data) for model training and experimental analysis.

[0060] Table 1 shows the KL divergence iterative convergence values ​​under different numbers of divisions. As the number of photon event divisions increases, the quality of the single folding profile begins to decline. At this time, the cosine distance is significantly better than the Euclidean distance. At the same time, Figure 6 The specific KL iterative change process of the two distance representation methods when the number of photon event divisions is 200 is also given.

[0061] Table 1 KL convergence values ​​of two distance representations under different numbers of partitions

[0062]

[0063] It can be seen that when using cosine distance to measure the similarity between high-dimensional samples, the KL divergence iterative convergence value is smaller, which means that the present invention uses cosine distance to obtain a low-dimensional representation that is closer to the distribution characteristics of high-dimensional samples, and can achieve better dimensionality reduction effect.

[0064] In addition, perplexity is the most important hyperparameter in the SNE method. It is a parameter that measures the local structure of the data and essentially controls the size of the local neighborhood. It is usually described as an approximation of the number of neighbors perceived by each data point in a high-dimensional data sample. The SNE dimensionality reduction effect of different perplexities is as follows: Figure 7 As shown in the figure, the two figures on the far left represent waterfall charts under two periods of P=0.0337000000s and P=0.0336999920s respectively, and the three groups of figures on the right represent the dimensionality reduction effect of the SNE method when the perplexity is selected as 1, 40, and 200 respectively under the corresponding period P.

[0065] It can be seen that when the perplexity value is appropriate, the dimensionality reduction effect is not greatly affected by interference and can reflect the changes of subtle cycles in a timely manner. Therefore, the perplexity is set to 40 in the present invention.

[0066] Finally, the training effect of the model is analyzed. First, the model finally formed by the present invention is compared and analyzed with other machine learning methods.

[0067] Table 2 Overall performance of parameter indicators of each model in 10-fold cross validation

[0068]

[0069] As shown in Table 2, the above-mentioned model was used to perform 10-fold cross validation on the generated data set. Among them, the support vector machine model has a low precision and a high recall rate. This shows that the model has over-learned the positive samples, resulting in the model may have overfitting. The traditional MLP model also has an imbalance between precision and recall, but the recall rate is low. This shows that the model has not learned the features sufficiently, which may be due to the loss function problem mentioned above. The random forest model overcomes the shortcomings of the first two models and is more effective in learning data. However, the overall performance is still not as good as the MLP model of the present invention. The MLP model of the present invention is the best in overall performance and has the highest accuracy. It not only prevents overfitting, but also achieves sufficient learning of features through optimization of the loss function. Table 3 shows the specific performance of the MLP model of the present invention in 10-fold cross validation.

[0070] Table 3 Specific performance of the parameter indicators of the MLP model proposed in this invention in 10-fold cross validation

[0071]

[0072] In order to more intuitively demonstrate the performance of the model of the present invention, the model of the present invention is compared with the traditional one based on the frequency estimation accuracy. Test function and The frequency estimation method of the test function is compared. According to the property that the estimated frequency and the estimated period are reciprocal to each other, the present invention uses the estimated period as the quantitative evaluation index when conducting quantitative analysis. The observation time is set to 1000s and the detector area is set to 1m 2 , the search range is [0.0336999950s, 0.0337000050s], and the search step is 10 -10 s. At the same time, in order to ensure a more stable estimation effect, multiple sub-MLP models based on under-sampling negative samples are used to comprehensively estimate the optimal frequency. Hundreds of Monte Carlo experiments were conducted on the above three methods, and the period estimation error and root mean square error (RMSE) were obtained as shown in Table 4 below. The box plot of the mean error of the three estimation methods is as follows Figure 8 shown.

[0073] Table 4 Mean error and RMSE of three estimation methods

[0074]

[0075] As shown in Table 4, under the same observation conditions, the proposed method is significantly better than the traditional estimation method in terms of mean error and RMSE, especially compared with the more suitable X-ray band frequency search. The test method shows that the mean error and RMSE of our method are reduced by nearly half. This shows that the method of the present invention has significant advantages in estimation accuracy and estimation stability. Figure 8 The box plots of the three estimation methods can further verify that the method of the present invention has the smallest error distribution and interquartile range, and has the highest estimation accuracy and the most reliable estimation results among the three methods, which shows that the method of the present invention is more suitable for deep space exploration missions with complex and changeable detection conditions.

[0076] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for dynamic estimation of X-ray pulsar frequency based on chaotic learning, characterized in that: The following steps are involved: Step 1: Adaptively perform SNE dimensionality reduction on the high-dimensional waterfall plot of the pulsar profile by reconstructing a high-dimensional spatial sample distance model. SNE stands for Stochastic Neighbor Embedding. Observe pulsar photons using a detector, collect data, and perform equal-time segmentation based on the total observation time to form a high-dimensional waterfall plot of the pulsar profile. Step 2: Optimize the cross entropy loss function and introduce a difference balance term that controls the discrimination between the net activity values ​​of positive and negative samples in the output layer to improve the regression prediction performance of the MLP model. MLP stands for Multi-Layer Perceptron. Step 3: Design and add a chaotic loss function based on a real neuron dynamics model to improve the global search capability of the MLP model and speed up the training of the MLP model; Step 4: Execute steps 1-3 for all candidate periods. Use the MLP model to select the optimal SNE adaptive dimensionality reduction image. Based on the period corresponding to the SNE adaptive dimensionality reduction image, obtain the corresponding high-dimensional waterfall plot. Further reverse analysis is performed to obtain the pulsar folding profile corresponding to the high-dimensional waterfall plot, and finally obtain the corresponding optimal X-ray pulsar frequency estimate.

2. The method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to claim 1, characterized in that: The step 1 comprises: The cosine distance is introduced to reconstruct the high-dimensional space sample distance model, so that the SNE dimensionality reduction can retain the contour waterfall plot features and effectively reduce the data dimension.

3. The method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to claim 2, characterized in that: The high-dimensional space sample distance model in step 1 is: (1) in, is the spatial distance between high-dimensional samples, For the The spatial coordinates of the samples, is the sample size.

4. The method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to claim 1, characterized in that: The step 2 includes: First, the number of positive and negative samples is balanced by undersampling non-optimal samples; then a balanced cross-entropy loss function based on the difference in net activity values ​​of the output layer is proposed to further distinguish positive and negative samples and improve sorting accuracy.

5. The method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to claim 4, characterized in that: The step 2 includes: Balanced cross entropy loss function based on the difference in net activity values ​​of the output layer for: (2) in, is the coefficient of the difference balance term, is the difference balance item, is the true label, Output values ​​for the model.

6. The method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to claim 5, characterized in that: The step 2 includes: The introduction of a difference balance term that controls the discrimination between the net activity values ​​of positive and negative samples in the output layer affects the training process of the model parameters. This allows the MLP model to consider the training bias caused by the score overlap problem during training, and adjust the network parameters to increase the discrimination between positive and negative samples, further improving the regression prediction effect of the MLP model.

7. The method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to claim 6, characterized in that: In step 2, the error term of the neurons in the output layer of the MLP model is expressed as: (6) in, For the The gradient of back propagation of neurons in the layer, For the Tier The output activity value of a neuron, For the The number of neurons in the layer, Indicates the symbol for partial derivative.

8. The method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to claim 5, characterized in that: The step 3 comprises: Introducing chaotic behavior into gradient dynamics to obtain chaotic loss function for: (7) in, is the number of neuron layers in the MLP model, For the The number of neurons in the layer, To control the chaotic strength coefficient of weight update, For the Tier The activity value of a neuron.

9. The method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to claim 8, characterized in that: The step 3 includes designing a dynamic model for weight gradient update, which is expressed as: (8) in, is the weight after the neuron gradient is updated, is the learning rate, For the Tier The error term of each neuron, is the cross entropy loss function The activity value of the layer, is the first chaotic loss function Tier The activity value of a neuron, is the first chaotic loss function Tier The net activity of neurons, It is reflected as the chaotic strength coefficient that controls the weight update; the superscript T represents the transpose of the matrix.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method for dynamic estimation of X-ray pulsar frequency based on chaotic learning according to any one of claims 1 to 9 are implemented.

Images