Icing depth migration prediction method guided by physical knowledge in small sample scene

Abstract

The invention discloses a physical knowledge-guided icing depth migration prediction method in a small sample scene, and the method comprises the steps: obtaining small sample icing data of a first region as a target domain, and obtaining large sample icing data of a second region as a source domain; constructing a physical information neural network and physical constraint loss thereof, and training the physical information neural network by using the source domain to predict the output icing thickness; a physical information neural network and self-migration learning are fused, knowledge of a source domain is effectively migrated to a target domain under guidance of physical knowledge, icing depth migration is carried out through iteration, an icing depth migration prediction model guided by the physical knowledge in a small sample scene is established, and the icing thickness of a first area is predicted. Physical knowledge is embedded into a transfer learning framework, a physical information neural network and transfer learning are fused, knowledge distillation loss based on cross entropy is used, and the physical knowledge in a teacher model is transferred into a student model, so that the student model adapting to a target domain is obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field of distribution networks, and specifically relates to a method for predicting ice depth migration guided by physical knowledge in a small sample scenario. Background Art

[0002] In recent years, with the impact of climate change, the frequency of extreme weather events has continued to increase, resulting in an increase in the frequency of icing events, and its impact on the power system has become increasingly significant. For example, freezing rain events can seriously threaten the reliability of the power system, which also highlights the urgency of predicting icing phenomena in advance.

[0003] Faced with low-frequency but high-impact icing events, the ratio of icing samples to non-icing samples is seriously unbalanced, which limits the performance of traditional prediction models. Therefore, it is urgent to develop prediction models suitable for small sample scenarios to achieve accurate prediction and evaluation of icing events.

[0004] However, the current icing prediction modeling methods, which are guided by physical knowledge and driven by data models, have poor prediction effects in small sample scenarios, fail to effectively utilize limited data resources, and ignore the complexity and diversity of icing events. Summary of the invention

[0005] The purpose of the present invention is to provide a physical knowledge-guided ice depth migration prediction method in a small sample scenario. In this scenario, advanced data mining technology is used to explore potential data correlations and regularities. It has high flexibility and robustness and can adapt to ice conditions in different regions and different climatic conditions.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] According to a first aspect of the present invention, a method for predicting ice depth migration guided by physical knowledge in a small sample scenario is provided, the method comprising:

[0008] Acquire small sample ice cover data of the first region as a target domain, and acquire large sample ice cover data of the second region as a source domain;

[0009] constructing a physical information neural network and its physical constraint loss, and training the physical information neural network using a source domain to predict output ice thickness;

[0010] The physical information neural network is integrated with self-transfer learning. Under the guidance of physical knowledge, the knowledge of the source domain is effectively transferred to the target domain. The ice depth migration is performed iteratively to establish an ice depth migration prediction model guided by physical knowledge in small sample scenarios.

[0011] The ice thickness in the first area is predicted using the ice depth migration prediction model guided by physical knowledge in a small sample scenario.

[0012] In the above scheme, the method further comprises:

[0013] The acquired ice cover data are preprocessed, including data cleaning, transformation and balancing.

[0014] In the above scheme, the ice coverage data is expressed as follows:

[0015] The ice cover data with the horizontal axis as the spatial dimension and the vertical axis as the time dimension is constructed according to the feature dimension. The specific expression is:

[0016] X∈R N×M×K

[0017] In the formula, N is the spatial dimension, representing different monitoring tower observation points; M is the feature dimension, representing the features contained in each data point; K is the time dimension, representing the ice thickness at each time point; assuming that there are N tower observation points, M feature variables, and K time points, T[n][m][t] represents the ice thickness of the nth tower, the mth feature variable, and the kth time point;

[0018] A sliding window approach is used to predict the ice thickness at each observation station in the future.

[0019] In the above scheme, the characteristic variables include meteorological data class, mechanical factor class, line data class and icing factor class; among them, the meteorological data class includes temperature, humidity and wind direction, the mechanical factor class includes tension, inclination and wind angle, the line data class includes conductor type, and the icing factor class includes icing growth rate.

[0020] In the above scheme, the physical information neural network includes a convolutional layer part and a dense layer part;

[0021] The convolution layer uses a series of convolution operations and maximum pooling operations to extract spatial information from the input data, and its output is expressed as:

[0022] N l (x) = σ(W l N l-1 (x)+b l )

[0023] Where N l (x) represents the output of the lth layer; N l-1 (x) represents the output of the (l-1)th layer; W l and b l are the weight matrix and bias vector of the lth layer respectively; σ represents the activation function;

[0024] Then the feature map is downsampled through the maximum pooling operation;

[0025] The dense layer processes and fuses features, maps the spatial features extracted by the convolutional layer to a higher dimensional space, and generates the final prediction result. The output is expressed as:

[0026] N L (x) = W L N L-1 (x)+b L

[0027] Where N L (x) represents the result of the output layer; N L-1 (x) represents the output of the (l-1)th layer; W L and b L are the weight matrix and bias vector of the output layer.

[0028] In the above scheme, the physical constraint loss of the physical information neural network It consists of two parts: regression loss and physical losses They are as follows:

[0029]

[0030] In the formula, Refers to the difference between the predicted value and the true value; It is a loss term guided by physical knowledge, using physical constraints combining angles and mechanical parameters. Include load balance constraints and moment balance constraints The specific expression is:

[0031]

[0032] Where, F is the axial tension of the insulator string; g 1 Indicates the deadweight of the insulator string and hardware; g 0 The deadweight of the conductor borne by the main tower; g i is the line ice load borne by the main tower; η is the wind deflection angle of the insulator string; θ is the deflection angle of the insulator string; l is the line span; λ is the length of the tension insulator string; β is the height difference angle; g 2 For the deadweight of the line and ice cover.

[0033] In the above scheme, the line ice load g borne by the main tower is i As shown below:

[0034]

[0035] Where ρ is the ice density; g is the gravitational acceleration constant; b is the ice thickness; d is the conductor diameter; π is the circumference; and g is the deadweight of the line and ice. 2 As shown below:

[0036] g 2 =g ice +g 0

[0037] In the formula, g ice To cover the weight of the ice.

[0038] In the above scheme, self-transfer learning is responsible for domain adaptation between the source domain and the target domain, including:

[0039] (1) Constraint is performed by minimizing the maximum mean difference MK-MMD to reduce the feature distribution difference between the source domain and the target domain;

[0040] (2) Use the kernel mapping algorithm to map the features into a high-dimensional reproducing kernel Hilbert space and calculate the distance between the embedding results;

[0041] Among them, the feature loss between the source domain and the target domain is as follows:

[0042]

[0043] In the formula, is the feature loss between the source domain and the target domain; m, n represent the sample size of the source domain dataset and the target domain dataset respectively; x, y are the source domain and target domain data respectively; i and j represent the i-th and j-th data; k(,) is defined as the convex combination distance with a semi-positive kernel;

[0044] In the domain adaptation stage, the model fine-tunes parameters to adapt to the data characteristics and distribution of the target domain;

[0045] In the target domain fine-tuning stage, the cross entropy knowledge distillation loss is used to obtain the ice depth migration prediction model guided by physical knowledge in a small sample scenario adapted to the target domain. The specific expression is:

[0046]

[0047] In the formula, The loss is calculated by comparing the output probability distributions of the teacher model and the student model; p is the softened output probability distribution of the teacher model; q is the softened output probability distribution of the student model; T is the temperature parameter that controls the smoothness of the softened output.

[0048] In the above scheme, training is performed iteratively on the source domain and the target domain, including:

[0049] Source domain training: In the source domain training phase, the physical information neural network parameters are optimized through physical constraint loss to obtain a pre-trained teacher model;

[0050] Domain Adaptation: In the domain adaptation stage, the model fine-tunes parameters to adapt to the data characteristics and distribution of the target domain. Specifically, the model fine-tunes the parameter weights of the dense layer and uses the maximum mean difference to minimize the MK-MMD loss to adapt to the characteristic distribution of the target domain.

[0051] Target domain fine-tuning: In the target domain fine-tuning stage, a student model adapted to the characteristics of the target domain is constructed through the cross entropy knowledge distillation loss function. This loss function calculates the loss by comparing the softened output probability distributions of the teacher model and the student model, guiding the student model to better learn the knowledge of the source domain and adapt to the data characteristics of the target domain;

[0052] Iterative training: By repeatedly performing the above steps, i.e. fine-tuning the model parameters and loss function, the performance and stability of the model on the target domain are improved to obtain the final student model.

[0053] According to a second aspect of the present invention, a physical knowledge-guided ice depth migration prediction system in a small sample scenario is provided for implementing any one of the above-mentioned physical knowledge-guided ice depth migration prediction methods in a small sample scenario, the system comprising:

[0054] An acquisition module, used to acquire small sample ice cover data of a first region as a target domain, and acquire large sample ice cover data of a second region as a source domain;

[0055] A training module, for constructing a physical information neural network and its physical constraint loss, and training the physical information neural network using a source domain to predict an output ice thickness;

[0056] The migration module is used to integrate the physical information neural network with self-transfer learning, effectively migrate the knowledge of the source domain to the target domain under the guidance of physical knowledge, perform ice depth migration through iteration, and establish an ice depth migration prediction model guided by physical knowledge in small sample scenarios;

[0057] The prediction module is used to predict the ice thickness of the first area by using an ice depth migration prediction model guided by physical knowledge in a small sample scenario.

[0058] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0059] The present invention provides a physical knowledge-guided ice depth migration prediction method and system in a small sample scenario. The proposed strategy embeds physical knowledge into the transfer learning framework, integrates physical information neural network (PINN) and transfer learning (STL), and uses cross-entropy-based knowledge distillation loss to transfer the physical knowledge in the teacher model to the student model to obtain a student model adapted to the target domain.

[0060] In addition, in view of the particularity of ice prediction, the present invention comprehensively considers regression loss and physical loss to ensure that the constructed physical information neural network PINN model can fully conform to the physical knowledge of ice. The construction of the physical constraint part needs to be combined with the characteristics of the ice phenomenon, including the relationship between ice thickness and time and space, and the correlation between ice thickness and other meteorological factors. By reasonably designing the physical constraint part, the accuracy and stability of the model can be effectively improved, thereby better predicting the ice situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is an overall flow chart of the ice depth migration prediction method guided by physical knowledge in a small sample scenario of an embodiment of the present invention;

[0062] Figure 2 is a physical constraint circuit model diagram of an embodiment of the present invention; wherein, Figure 2 (a) is a schematic diagram of load balance constraint. Figure 2 (b) is a schematic diagram of moment balance constraint;

[0063] Figure 3 This is a pseudocode diagram of the iterative training process of the model. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain 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 can be combined with each other as long as they do not conflict with each other.

[0065] The present invention provides a method for predicting ice depth migration in small sample scenarios. First, in the data preprocessing stage, the data is divided into source domain and target domain through key links such as cleaning, transformation and balancing, and the corresponding three-dimensional tensor representation is constructed. Then, in the model construction stage, the physical information neural network (PINN) is integrated with the self-transfer learning (STL) to realize the migration of knowledge. Specifically, the source domain branch is responsible for training the teacher model PINN to ensure that it conforms to the physical knowledge of ice coverage, and combines the physical constraint part to perform effective ice coverage prediction; the self-migration branch reduces the feature distribution difference between the source domain and the target domain through the multi-core maximum mean difference (MK-MMD) constraint; the target domain branch uses the knowledge distillation loss of cross entropy to transfer the physical knowledge in the teacher model to the student model, and obtain a student model adapted to the target domain. Finally, the historical ice coverage data of multiple transmission lines in a certain section are used for example simulation, and compared with the traditional data model-driven algorithm, the effectiveness and advancement of this method in small sample scenarios are verified.

[0066] The present invention provides a method for predicting ice depth migration guided by physical knowledge in a small sample scenario. Figure 1 As shown, the specific steps are as follows:

[0067] Step 1: Divide into source domain and target domain and construct a three-dimensional tensor.

[0068] The present invention obtains small sample ice cover data of the first area as the target domain, and obtains large sample ice cover data of the second area as the source domain. The source domain data is used to support the pre-training or initial learning stage of the model, helping the model to identify and extract feature patterns, and providing a large amount of sample data. In contrast, the target domain is usually a part with a small amount of data, and the data characteristics or distribution are somewhat different from the source domain. Due to the small amount of data, the target domain is mainly used for adaptive training and testing on the pre-trained model, and the model needs to transfer the knowledge learned from the source domain to the target domain.

[0069] The first region is the region where ice thickness prediction is desired, but the first region is a small sample region, i.e., the amount of ice data is small. The amount of ice data in the second region is large, but may have certain differences in data characteristics or distribution from the first region. Therefore, the present invention uses the large sample ice data of the second region as the source domain to support the pre-training or initial learning stage of the model.

[0070] The division in step 1 is into source domain and target domain, and the three-dimensional tensor is constructed as follows:

[0071] Step 1.1: Simplify the data preprocessing steps, including key links such as data cleaning, transformation and balancing.

[0072] Step 1.2: To effectively process and analyze ice cover data, the dataset is divided into a source domain and a target domain, where the small sample ice cover data in the first region is used as the target domain and the large sample ice cover data in the second region is used as the source domain.

[0073] Step 1.3: Take the ice cover data with the horizontal axis as the spatial dimension and the vertical axis as the time dimension, and construct a three-dimensional tensor according to the feature dimension. The specific expression is:

[0074] X∈R N×M×K

[0075] In the formula, N is the spatial dimension, representing different monitoring tower observation points; M is the feature dimension, representing the features contained in each data point; K is the time dimension, representing the ice thickness at each time point. Specifically, assuming that there are N tower observation points, M feature variables, and K time points, T[n][m][t] represents the ice thickness at the kth time point for the nth tower and the mth feature variable. The types of each feature variable are shown in Table 1.

[0076] Table 1 Source domain and target domain variable table

[0077]

[0078]

[0079] In this embodiment, the ice coverage data of the first area and the second area are constructed into three-dimensional tensors according to the characteristic dimensions, and the ice coverage data include each characteristic variable and its corresponding response variable (ice coverage thickness).

[0080] Step 2: Integrate the Physics-Informed Neural Network (PINN) with Self-Transfer Learning (STL), effectively transfer the knowledge of the source domain to the target domain under the guidance of physical knowledge, perform ice depth migration through iteration, and establish an ice depth migration prediction model guided by physical knowledge in small sample scenarios.

[0081] The physical knowledge-guided ice depth migration prediction model in step 2 is as follows:

[0082] Step 2.1: The first part of the model is the source domain branch, which focuses on training the teacher model PINN model to ensure that the construction of the physical information neural network PINN conforms to the icing physics knowledge. The basic structure of the physical information neural network PINN includes the neural network part and the physical constraint part. The network structure table is shown in Table 2:

[0083] (1) The PINN convolutional layer uses a series of convolution operations and maximum pooling operations to extract spatial information from the input data. Its output can be expressed as:

[0084] N l (x) = σ(W l N l-1 (x)+b l )

[0085] Where N l (x) represents the output of the lth layer; N l-1 (x) represents the output of the (l-1)th layer; W l and b l are the weight matrix and bias vector of the lth layer respectively; σ represents the activation function.

[0086] Next, the feature map is downsampled through a maximum pooling operation while retaining key information.

[0087] (2) The dense layer processes and fuses features, mapping the spatial features extracted by the convolutional layer to a higher-dimensional space to generate the final prediction result. The output can be expressed as:

[0088] N L (x) = W L N L-1 (x)+b L

[0089] Where N L (x) represents the result of the output layer; N L-1 (x) represents the output of the (l-1)th layer; W L and b L are the weight matrix and bias vector of the output layer.

[0090] Table 2 PINN structure table

[0091]

[0092] (3) PINN physical constraint loss It consists of two parts: regression loss and physical losses

[0093]

[0094] In the formula, Refers to the difference between the model regression prediction value and the true value. It is a loss term guided by physical knowledge, which comprehensively utilizes the online monitoring data collected by tension sensors and angle sensors, and adopts physical constraints that combine angles with mechanical parameters. Include load balance constraints and moment balance constraints The specific expression is:

[0095]

[0096] Where, F is the axial tension of the insulator string; g 1 represents the deadweight of the insulator string and hardware, which is a known quantity; g 0 The deadweight of the conductor borne by the main tower; g i is the line ice load borne by the main tower; g is the gravity acceleration constant, b is the ice thickness; d is the conductor diameter; η is the wind deflection angle of the insulator string; θ is the deflection angle of the insulator string; θ′ is the angle between the insulator string and the vertical direction.

[0097] Among them, the load balance constraint ensures the horizontal force balance of the wire suspension point and the relationship between the wire tension and the comprehensive load, such as Figure 2 As shown in (a) in the vertical direction of the vertical plane, ignoring the wind load and ice load of the insulator string, the static equilibrium equation of the axial tension of the insulator string is as follows:

[0098] F v =g 1 +g 0 +g i

[0099] In the formula, F v g is the vertical component of the axial tension F of the insulator string; 1 represents the deadweight of the insulator string and hardware, which is a known quantity; g 0 The deadweight of the conductor borne by the main tower; g i The line ice load borne by the main tower is as follows:

[0100]

[0101] Where ρ is the ice density; g is the gravity acceleration constant, b is the ice thickness; and d is the conductor diameter. The relationship between the insulator string wind deflection angle η, the insulator string deflection angle θ, and the angle θ′ between the insulator string and the vertical direction, so the comprehensive load of the insulator string in the vertical direction is as follows.

[0102]

[0103] The moment balance constraint describes the relationship between the horizontal force at the conductor suspension point and the insulator string tension, comprehensive load, span and other parameters, such as Figure 2 As shown in (b) in the figure. Taking the moment at the suspension point A, the horizontal moment equilibrium condition of the given conductor suspension point can be obtained as follows.

[0104]

[0105] Where V a F a Upward component; H a F a The horizontal component; h is the height difference of the suspension point; l is the line span; λ is the length of the tension insulator string; β is the height difference angle; where V a , H a , g 2 The calculation formula is as follows.

[0106] V a =Fsinθ

[0107] H a =Fcosθ

[0108] g 2 =g ice +g 0

[0109] In the formula, g 2 is the weight of the line and ice, g ice To cover the weight of the ice.

[0110] (4) For the ice cover prediction problem, the PINN training steps are as follows:

[0111] First of all, for the ice cover prediction problem, the first task is to construct a three-dimensional tensor that retains the correlation between time and space. The three-dimensional tensor contains three dimensions: space, feature, and time. The spatial dimension represents the data of different observation sites; the feature dimension includes the parameters that affect ice cover at each site, such as temperature, humidity, etc.; the time dimension records the measurement data of each site at multiple consecutive time steps. Simply put, the data of each site can be regarded as a layer containing multiple features that are observed over a continuous period of time. By using convolutional layers, the network is able to extract three-dimensional data in space. Most deep learning frameworks require the input tensor to have a specific shape, which adjusts the tensor to the form of (depth, height, width). Here, depth corresponds to the time dimension, and height and width can correspond to the two dimensions of spatial features respectively.

[0112] In this process, the concept of time window is used to predict the ice cover conditions at each observation station in the future by using a sliding window method. To achieve the prediction of time series, the sliding window method is used to process time dimension data. The sliding window selects a fixed-size time step (such as 5 consecutive hours of data) from the three-dimensional tensor as the input of the neural network. The network is trained and predicted through the data in the window to obtain the predicted value of ice thickness for the next time step. After the prediction is completed, the window will slide forward one time step (for example, from 1-5 hours to 2-6 hours), and the process will be repeated to continuously predict the future ice cover conditions.

[0113] Secondly, constructing the physical constraint part is a key step in the PINN training process. Taking into account the particularity of ice cover prediction, it is necessary to comprehensively consider regression loss and physical loss to ensure that the constructed PINN model can fully conform to the physical knowledge of ice cover. The construction of the physical constraint part needs to be combined with the characteristics of the ice cover phenomenon, including the relationship between ice cover thickness and time and space, as well as the correlation between ice cover thickness and other meteorological factors. By reasonably designing the physical constraint part, the accuracy and stability of the model can be effectively improved, thereby better predicting the ice cover.

[0114] Finally, reverse weight adjustment is one of the key steps in the PINN training process. During the training process, back propagation and weight update are performed by minimizing the loss function to adjust the network parameters and obtain a pre-trained PINN teacher model. In the process of reverse weight adjustment, it is necessary to combine the three-dimensional tensor and physical constraint parts constructed in the first two steps, as well as the real observation data, and continuously optimize the model's fitting ability and generalization ability through the optimization algorithm. Through reverse weight adjustment, the performance of the model in ice cover prediction can be effectively improved, thereby more accurately predicting future ice cover conditions.

[0115] In the PINN training process, the above three steps are intertwined and interact with each other to jointly build a physical knowledge-guided ice prediction model. This model can not only make full use of physical knowledge to guide the model construction and training process, but also accurately predict the ice situation in a small sample scenario, providing strong support for the safe and stable operation of the power system.

[0116] Step 2.2: The second part of the model is the self-migration branch, which is responsible for domain adaptation between the source domain and the target domain, such as Figure 3 As shown:

[0117] (1) MK-MMD is used to constrain and reduce the difference in feature distribution between the source domain and the target domain.

[0118] (2) Use the kernel mapping algorithm to map the features into a high-dimensional reproducing kernel Hilbert space and calculate the distance between the embedding results.

[0119] (3) Feature loss between source domain and target domain As shown below, the upper layer parameters of the network are constrained by MK-MMD to reduce the feature distribution difference between the source domain and the target domain. In the domain adaptation stage, the model fine-tunes parameters to adapt to the data characteristics and distribution of the target domain. In particular, for the fine-tuning of the dense layer parameter weights, MK-MMD loss is used to adapt to the feature distribution of the target domain.

[0120] MK-MMD is an extended form of MMD. It uses the kernel mapping algorithm to map features into a high-dimensional reproducing kernel Hilbert space and calculates the distance between the embedding results. The feature loss between the source domain and the target domain is shown as follows:

[0121]

[0122] In the formula, is the feature loss between the source domain and the target domain; m and n represent the sample sizes of the source domain dataset and the target domain dataset, respectively; x and y are the source domain and target domain data, respectively; k(,) is defined as the convex combination distance with a semi-positive kernel.

[0123] Step 2.3: The third part of the model is the target domain branch. The knowledge distillation loss of cross entropy is used to obtain the student model adapted to the target domain. The specific expression is:

[0124]

[0125] In the formula, The loss is calculated by comparing the output probability distribution of the teacher model and the student model; p is the softened output probability distribution of the teacher model; q is the softened output probability distribution of the student model; T is the temperature parameter, which controls the smoothness of the softened output. The smaller the value of the cross entropy loss function, the closer the prediction result is to the true value.

[0126] In the target domain fine-tuning phase, a student model adapted to the target domain characteristics is constructed through the cross entropy knowledge distillation loss function. The loss is calculated by comparing the softened output probability distributions of the teacher model and the student model. Different temperature parameters are set to find a compromise between the accuracy and generalization of the balanced model.

[0127] Step 2.4: In ice cover prediction, the data distribution of the source domain and the target domain may be different. Directly applying the source domain training model to the target domain may result in performance degradation. Therefore, iterative training is performed on the source domain and the target domain.

[0128] Source domain training: In the source domain training phase, first, the input layer of the PINN neural network is designed to receive a three-dimensional tensor to preserve the correlation of space, features, and time. Then, the physical constraint part is introduced to improve the generalization ability of the model, and the model parameters are updated on the source domain to adapt to the physical laws and prediction performance. In this process, the parameters are optimized by minimizing the regression loss and the physical constraint loss to obtain the pre-trained teacher model.

[0129] Domain Adaptation: In the domain adaptation stage, the model needs to fine-tune parameters to adapt to the data characteristics and distribution of the target domain. Specifically, special attention needs to be paid to the fine-tuning of the dense layer parameter weights, and the maximum mean difference minimization (MK-MMD) loss is used to adapt to the characteristic distribution of the target domain. By adjusting the parameter weights, the model can better adapt to the data characteristics of the target domain, thereby improving the generalization ability of the model.

[0130] Target domain fine-tuning: In the target domain fine-tuning stage, a student model adapted to the characteristics of the target domain is constructed through the cross entropy knowledge distillation loss function. This loss function calculates the loss by comparing the softened output probability distributions of the teacher model and the student model, thereby guiding the student model to better learn the knowledge of the source domain and adapt to the data characteristics of the target domain. In this process, by setting different temperature parameters, a balance can be found between the accuracy and generalization of the model.

[0131] Iterative training: Finally, by repeatedly executing steps 2 and 3 above, i.e. fine-tuning the model parameters and loss function, the performance and stability of the model on the target domain are improved to obtain the final student model. During the iterative training process, the model continuously learns from the data in the source and target domains, and gradually optimizes its own structure and parameters to achieve accurate prediction of ice cover.

[0132] Step 3: Based on the physical knowledge-guided ice depth migration prediction model in the small sample scenario established in Step 2, a case simulation was performed using the historical ice data of multiple transmission lines in a certain section to verify its effectiveness and advancement in small sample scenarios.

[0133] The specific steps of performing a simulation on the model established in step 2 described in step 3 are as follows:

[0134] Step 3.1: In data preparation, the dataset is divided into two parts: the source domain and the target domain. A three-dimensional tensor construction method is introduced to integrate multi-dimensional data into a unified representation framework. The sliding window method is used to predict the data in a specific window, and then the window moves one time step and uses the new data for the next round of prediction.

[0135] Step 3.2: The case analysis is compared with the traditional data model drive, and a significance analysis is performed to verify the effectiveness and advancement of this method in a small sample scenario. The performance of machine learning and deep learning models and PINN in ice cover prediction in the data model drive is compared. The evaluation indicators before and after the self-migration of the model proposed in this invention are shown in Table 3.

[0136] Table 3 Comparison between data model driven and PINN

[0137]

[0138]

[0139] Based on the above-mentioned method for predicting ice depth migration guided by physical knowledge in a small sample scenario, the present application embodiment further provides a system for predicting ice depth migration guided by physical knowledge in a small sample scenario, including:

[0140] An acquisition module, used to acquire small sample ice cover data of a first region as a target domain, and acquire large sample ice cover data of a second region as a source domain;

[0141] A training module, for constructing a physical information neural network and its physical constraint loss, and training the physical information neural network using a source domain to predict an output ice thickness;

[0142] The migration module is used to integrate the physical information neural network with self-transfer learning, effectively migrate the knowledge of the source domain to the target domain under the guidance of physical knowledge, perform ice depth migration through iteration, and establish an ice depth migration prediction model guided by physical knowledge in small sample scenarios;

[0143] The prediction module is used to predict the ice thickness of the first area by using an ice depth migration prediction model guided by physical knowledge in a small sample scenario.

[0144] In summary, the present invention provides a method and system for predicting ice depth migration guided by physical knowledge in a small sample scenario. The proposed strategy embeds physical knowledge into the migration learning framework, integrates physical information neural network (PINN) and migration learning (STL), and uses knowledge distillation loss based on cross entropy to migrate the physical knowledge in the teacher model to the student model to obtain a student model adapted to the target domain. In addition, the historical ice data of multiple transmission lines in a certain section are used for example simulation, and compared with the traditional data model-driven algorithm, the effectiveness and advancement of this method in a small sample scenario are verified.

[0145] In addition, in view of the particularity of ice prediction, the present invention comprehensively considers regression loss and physical loss to ensure that the constructed physical information neural network PINN model can fully conform to the physical knowledge of ice. The construction of the physical constraint part needs to be combined with the characteristics of the ice phenomenon, including the relationship between ice thickness and time and space, and the correlation between ice thickness and other meteorological factors. By reasonably designing the physical constraint part, the accuracy and stability of the model can be effectively improved, thereby better predicting the ice situation.

[0146] It should be noted that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0147] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, and two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0148] It will be easily understood by those skilled in the art that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A physical knowledge-guided ice depth migration prediction method in a small sample scenario, characterized in that: The method includes: Acquire small sample ice cover data of the first region as a target domain, and acquire large sample ice cover data of the second region as a source domain; constructing a physical information neural network and its physical constraint loss, and training the physical information neural network using a source domain to predict output ice thickness; The physical information neural network is integrated with self-transfer learning to effectively transfer the knowledge of the source domain to the target domain under the guidance of physical knowledge. The ice depth migration is performed iteratively to establish an ice depth migration prediction model guided by physical knowledge in small sample scenarios. The ice thickness in the first area is predicted using the ice depth migration prediction model guided by physical knowledge in a small sample scenario.

2. The method for predicting ice depth migration guided by physical knowledge in a small sample scenario according to claim 1 is characterized in that: The method further includes: The acquired ice cover data are preprocessed, including data cleaning, transformation and balancing.

3. The method for predicting ice depth migration guided by physical knowledge in a small sample scenario according to claim 1 is characterized in that: Ice cover data is shown as follows: The ice cover data with the horizontal axis as the spatial dimension and the vertical axis as the time dimension is constructed according to the feature dimension. The specific expression is: X∈R N×M×K In the formula, N is the spatial dimension, representing different monitoring tower observation points; M is the feature dimension, representing the features contained in each data point; K is the time dimension, representing the ice thickness at each time point; assuming that there are N tower observation points, M feature variables, and K time points, T[n][m][t] represents the ice thickness of the nth tower, the mth feature variable, and the kth time point; A sliding window approach is used to predict the ice thickness at each observation station in the future.

4. The method for predicting ice depth migration guided by physical knowledge in a small sample scenario according to claim 3 is characterized in that: The characteristic variables include meteorological data class, mechanical factor class, line data class and icing factor class; among them, the meteorological data class includes temperature, humidity and wind direction, the mechanical factor class includes tension, inclination and wind angle, the line data class includes conductor type, and the icing factor class includes icing growth rate.

5. The method for predicting ice depth migration guided by physical knowledge in a small sample scenario according to claim 1 is characterized in that: The physical information neural network includes a convolutional layer part and a dense layer part; The convolution layer uses a series of convolution operations and maximum pooling operations to extract spatial information from the input data, and its output is expressed as: N l (x)=σ(W l N l-1 (x)+b l ) Where N l (x) represents the output of the lth layer; N l-1 (x) represents the output of the (l-1)th layer; W l and b l are the weight matrix and bias vector of the lth layer respectively; σ represents the activation function; Then the feature map is downsampled through the maximum pooling operation; The dense layer processes and fuses features, maps the spatial features extracted by the convolutional layer to a higher dimensional space, and generates the final prediction result. The output is expressed as: N L (x)=W L N L-1 (x)+b L Where N L (x) represents the result of the output layer; N L-1 (x) represents the output of the (l-1)th layer; W L and b L are the weight matrix and bias vector of the output layer.

6. The method for predicting ice depth migration guided by physical knowledge in a small sample scenario according to claim 1 is characterized in that: Physically Constrained Loss for Physically Informed Neural Networks It consists of two parts: regression loss and physical losses They are as follows: In the formula, Refers to the difference between the predicted value and the true value; It is a loss term guided by physical knowledge, using physical constraints combining angles and mechanical parameters. Include load balance constraints and moment balance constraints The specific expression is: Where, F is the axial tension of the insulator string; g1 represents the deadweight of the insulator string and hardware; g0 is the deadweight of the conductor borne by the main tower; g i is the line ice load borne by the main tower; η is the wind deflection angle of the insulator string; θ is the deflection angle of the insulator string; l is the line span; λ is the length of the tension insulator string; β is the height difference angle; g2 is the deadweight of the line and ice.

7. The method for predicting ice depth migration guided by physical knowledge in a small sample scenario according to claim 6 is characterized in that: Line ice load on the main tower g i As shown below: Where ρ is the ice density; g is the gravitational acceleration constant; b is the ice thickness; d is the wire diameter; π is the circumference of a circle; The deadweight g2 of the line and ice cover is as follows: g2=g ice +g0 In the formula, g ice To cover the weight of the ice.

8. The method for predicting ice depth migration guided by physical knowledge in a small sample scenario according to claim 1 is characterized in that: Self-transfer learning is responsible for domain adaptation between the source domain and the target domain, including: (1) Constraint is performed by minimizing the maximum mean difference MK-MMD to reduce the feature distribution difference between the source domain and the target domain; (2) Use the kernel mapping algorithm to map the features into a high-dimensional reproducing kernel Hilbert space and calculate the distance between the embedding results; Among them, the feature loss between the source domain and the target domain is as follows: In the formula, is the feature loss between the source domain and the target domain; m, n represent the sample size of the source domain dataset and the target domain dataset respectively; x, y are the source domain and target domain data respectively; i and j represent the i-th and j-th data; k(,) is defined as the convex combination distance with a semi-positive kernel; In the domain adaptation stage, the model fine-tunes parameters to adapt to the data characteristics and distribution of the target domain; In the target domain fine-tuning stage, the cross entropy knowledge distillation loss is used to obtain the ice depth migration prediction model guided by physical knowledge in a small sample scenario adapted to the target domain. The specific expression is: In the formula, The loss is calculated by comparing the output probability distributions of the teacher model and the student model; p is the softened output probability distribution of the teacher model; q is the softened output probability distribution of the student model; T is the temperature parameter that controls the smoothness of the softened output.

9. The method for predicting ice depth migration guided by physical knowledge in a small sample scenario according to claim 8 is characterized in that: Iterative training on the source domain and the target domain includes: Source domain training: In the source domain training phase, the physical information neural network parameters are optimized through physical constraint loss to obtain a pre-trained teacher model; Domain Adaptation: In the domain adaptation stage, the model fine-tunes parameters to adapt to the data characteristics and distribution of the target domain. Specifically, the model fine-tunes the weights of dense layer parameters and uses the maximum mean difference to minimize the MK-MMD loss to adapt to the characteristic distribution of the target domain. Target domain fine-tuning: In the target domain fine-tuning stage, a student model adapted to the characteristics of the target domain is constructed through the cross entropy knowledge distillation loss function. This loss function calculates the loss by comparing the softened output probability distributions of the teacher model and the student model, guiding the student model to better learn the knowledge of the source domain and adapt to the data characteristics of the target domain; Iterative training: By repeatedly performing the above steps, i.e. fine-tuning the model parameters and loss function, the performance and stability of the model on the target domain are improved to obtain the final student model.

10. A physical knowledge-guided ice depth migration prediction system under small sample scenarios for implementing the physical knowledge-guided ice depth migration prediction method under small sample scenarios as described in any one of claims 1 to 9, characterized in that: The system includes: An acquisition module, used to acquire small sample ice cover data of a first region as a target domain, and acquire large sample ice cover data of a second region as a source domain; A training module, for constructing a physical information neural network and its physical constraint loss, and training the physical information neural network using a source domain to predict an output ice thickness; The migration module is used to integrate the physical information neural network with self-transfer learning, effectively migrate the knowledge of the source domain to the target domain under the guidance of physical knowledge, perform ice depth migration through iteration, and establish an ice depth migration prediction model guided by physical knowledge in small sample scenarios; The prediction module is used to predict the ice thickness of the first area by using an ice depth migration prediction model guided by physical knowledge in a small sample scenario.

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