Residual life prediction method based on digital twin collaborative residual network

Abstract

The invention belongs to the technical field of life prediction, and discloses a residual life prediction method based on a digital twinning collaborative residual network, and the specific technical scheme is as follows: step 1, analyzing the working mechanism of a hollow cathode, and constructing a dynamic simulation model based on the digital twinning collaborative residual network; step 2, introducing a sub-domain adaptive mechanism, and realizing alignment of sub-domain condition distribution by minimizing the difference of fine-grained features between a simulation domain and a real domain; and step 3, constructing a ResTCN-BIGRU-Attention model for life prediction, firstly extracting local long-term dependence features in a time sequence by using a ResTCN module, introducing a multi-head attention mechanism and a feedforward network, realizing channel-level fusion of multi-sensor data, and finally realizing global modeling of key features after fusion by combining BIGRU with the attention mechanism, so as to realize life prediction. The method is good in accuracy, stability and practicability in a hollow cathode life prediction task.

Description

Technical Field

[0001] The present invention belongs to the technical field of life prediction, and specifically relates to a remaining life prediction method based on a digital twin collaborative residual network. Background Art

[0002] Because system failures often result in severe consequences and significant costs, prognostic health management (PHM) is gaining increasing attention in academia and industry. PHM aims to prevent major failures and provide more effective maintenance strategies by dynamically monitoring and assessing the health of equipment. With the widespread application of electric propulsion technology in space missions, thruster life prediction is becoming increasingly important. As the heart of the thruster, the life of the hollow cathode directly determines the life of the system. Therefore, developing advanced methods for predicting the remaining life of the hollow cathode is crucial for the efficient and safe operation of thrusters.

[0003] Remaining useful life (RUS) is the estimated length of time a system, device, or component will continue to operate normally after a certain period of use. It's based on an analysis of system conditions, usage history, and reliability data to predict how long a system will continue to operate reliably under future operating conditions and environments. Currently, research on RUS prediction can be broadly categorized into three categories: physics-based models, data-driven approaches, and hybrid model-based approaches.

[0004] The prediction method based on physical models models the degradation process of the equipment to predict the RUL of the equipment. It uses algebraic or differential equations to establish a mathematical model to simulate the degradation process of the mechanical equipment, and then calculates the predicted value of RUL based on the physical failure model and the relevant failure threshold. This method requires an advance understanding of the structure and failure mechanism of the mechanical equipment. However, due to the complex internal structure of the mechanical equipment and the high correlation between the various components, it becomes quite difficult to establish an accurate physical degradation model. This process requires a lot of prior knowledge, and it is difficult to establish an accurate degradation model for highly complex systems such as the hollow cathode of the thruster, resulting in low prediction accuracy and limitations in application.

[0005] Compared to other methods, this approach has the advantage of not requiring the collection of extensive monitoring data, and the constructed health indicators are physically meaningful. However, for complex mechanical equipment such as aircraft engines and ion thrusters, the degradation process is complex and variable, involving coupling between failure modes, making it difficult to obtain detailed failure mechanisms. Therefore, constructing physical failure models that characterize the degradation process poses significant challenges for diagnosis and prediction.

[0006] Data-driven approaches can extract key information from massive amounts of historical monitoring data and directly model it using machine learning or deep learning methods. The ultimate goal is to explore the degradation patterns of mechanical equipment and predict its remaining useful life. Compared to traditional physical failure models, data-driven approaches do not require a detailed understanding of the equipment's operating mechanism or structure beforehand. Instead, they can mine key features from large amounts of data. Consequently, data-driven RUL prediction methods have attracted considerable attention. Due to differences in modeling methods and network depth, these methods are further divided into machine learning and deep learning methods.

[0007] In machine learning, the main methods used to predict the remaining life include neural networks, Wiener process models, support vector regression models, multi-layer perceptrons, random forests, autoregressive models, etc. These typical machine learning methods have been widely used in the field of mechanical equipment life prediction. Cao et al. used genetic optimization algorithms to optimize the network structure based on BP neural networks to achieve fatigue life prediction of 304 stainless steel materials. This method has brought new progress to life prediction in the field of materials engineering. Chen et al. proposed a Wiener process model to study the bearing degradation process, which can adaptively learn the degradation trend in different bearing degradation data and effectively avoid the selection of objective functions. Wu et al. used an adaptive nonlinear Wiener process model with a closed skewed normal distribution to solve the problem of non-normal distribution of equipment changes in practice. Fu et al. adopted a local-global collaborative learning strategy and combined it with a support vector machine to establish a prediction model to accurately predict the remaining life of rolling bearings.

[0008] When using machine learning algorithms for RUL prediction, features must first be manually extracted from the raw data. This information is then used to predict the lifespan. This relies on expert prior knowledge and signal processing techniques, placing high demands on operators. Therefore, this prediction method is not particularly universal. Deep learning prediction methods, however, offer two distinct advantages over traditional machine learning: first, they use stratified sampling to automatically extract features from different samples, reducing over-reliance on relevant experience and techniques and the manual effort required by traditional methods. Second, by continuously expanding the model depth, they can better characterize the nonlinear relationship between the relevant features of the raw vibration signal and the degradation state, meeting the requirements for diverse life monitoring in the context of big data. Therefore, deep learning research in RUL prediction offers new solutions in this field.

[0009] CNNs are a well-known deep learning method due to their ability to generalize both partial and global features and their significant advantages in extracting time series features. Lei et al. proposed a convolutional neural network based on similar feature fusion for rolling bearing RUL prediction. Results showed that the feature fusion-based CNN method was superior and effective in constructing the HI and accurately predicting RUL. Liu et al. proposed an end-to-end remaining life prediction method based on a temporal convolutional neural network. Experimental results showed that this method achieved high prediction accuracy while also meeting real-time requirements. Cao Yue et al. proposed a multivariate multi-step convolutional neural network for aerospace engine RUL prediction, which was used for feature extraction and dimensionality reduction, enabling end-to-end direct RUL prediction. Li et al. proposed a RUL prediction model based on MS-DCNN. This model primarily consists of three multi-scale modules, each of which performs multidimensional convolution operations to enhance the network's ability to learn complex features. Although CNNs achieve feature extraction through multi-layer convolution, the vanishing or exploding gradient problem associated with increasing network depth has prompted residual networks to restructure the learning approach of deep networks by introducing cross-layer skip connections. To address the issue of excessive deviation in the RUL values ​​predicted by previous bearing remaining useful life prediction methods, Zhang Jianfei et al. proposed a life prediction model that combines a convolutional attention mechanism (CBAM) and a residual neural network (ResNet). Zhang et al. proposed a residual structured temporal convolutional network based on the attention mechanism to predict the remaining useful life of bearings.

[0010] When the signal has time characteristics, recurrent neural networks (RNNs) are gradually introduced into the field of life prediction. Recurrent neural networks have the function of time series memory, which can obtain a degradation trend in a continuous degradation process, and then realize RUL prediction. Traditional RNNs are prone to gradient vanishing problems during training, resulting in insufficient bearing signals and affecting the RUL prediction accuracy of bearings. Therefore, scholars have improved the structure of RNNs and optimized the structure of gated loops, so that the forgetting gate, input and output can work together, thereby solving the problem of gradient vanishing of degradation features during training and effectively improving the RUL prediction accuracy of bearings. Tang Guiji et al. proposed a rolling bearing remaining life prediction based on a Transformer-GRU parallel network with multi-domain feature fusion. Liu Sen et al. proposed a rolling bearing remaining service life prediction model that integrates three modules: deep convolutional neural network, bidirectional gated recurrent unit (BiGRU) and self-attention mechanism.

[0011] Deep learning methods have demonstrated significant advantages in the RUL field, boasting strong big data learning capabilities and high generalization performance, capable of automatically extracting features from data without human intervention. However, they also have certain limitations. First, high-quality RUL data is difficult to obtain. Data on the entire equipment lifecycle, particularly failure data, is scarce, leading to model overfitting. Second, models lack interpretability. Third, high computational complexity restricts their practical application.

[0012] To address these limitations, fusion model-based approaches have demonstrated significant advantages in improving prediction accuracy by effectively integrating physical failure models and data-driven models. However, this approach also faces some challenges. For example, the actual distribution of the data may not match the model assumptions, which may lead to decreased prediction performance. When faced with high-dimensional data, traditional machine learning methods may experience performance degradation as the data dimension increases, necessitating feature selection or data dimensionality reduction. When the relationships in the data are very complex, traditional machine learning methods may not be able to capture these complex relationships well, resulting in limited prediction performance. Summary of the Invention

[0013] In order to solve the technical problems existing in the prior art, the present invention provides a remaining life prediction method based on a digital twin collaborative residual network, which is used to accurately evaluate the remaining life of a LaB6 hollow cathode.

[0014] To achieve the above objectives, the technical solution adopted by the present invention is: a remaining life prediction method based on digital twin collaborative residual network, the specific steps are as follows:

[0015] Step 1: In-depth analysis of the working mechanism of the hollow cathode, and construction of a dynamic simulation model based on the digital twin collaborative residual network to achieve high-fidelity modeling of key operating states. By combining virtual and real methods, the problem of scarcity of real operating data is effectively solved, providing sufficient and reliable data support for model training.

[0016] Step 2: Introduce a subdomain adaptation mechanism to align the subdomain conditional distributions by minimizing the differences in fine-grained features between the simulation domain and the real domain. This strategy improves the generalization and robustness of the model under different data distributions, providing a stable data foundation for subsequent predictions.

[0017] Step 3: The ResTCN-BIGRU-Attention model was designed and applied for lifespan prediction. The ResTCN-BIGRU-Attention model integrates the channel attention mechanism and soft threshold function in the ResTCN module, allowing the network to automatically focus on key dimensional features when performing parallel local feature extraction on the data; then, a multi-head attention mechanism and a feedforward network were introduced to achieve channel-level fusion of multi-sensor data; finally, the global modeling of the fused features was achieved through BIGRU combined with the attention mechanism network, further enhancing the expression and modeling capabilities of key features.

[0018] In step 1, after the material is heated, the thermal electron emission density satisfies the Richardson-Dushman equation:

[0019]

[0020] Where, J e is the emission current density, T is the emitter temperature, is the work function of the emitter material, k is the Boltzmann constant, and A is the emitter constant;

[0021] The calculation formulas for some characteristic parameters of the hollow cathode emitter are as follows:

[0022]

[0023]

[0024] In formula (2), J e is the emission current density, is the work function of the emitter material, is the reduction in work function caused by the Schottky effect, T is the emitter temperature, A is the emitter constant, and k is the Boltzmann constant; in formula (3), V is the emitter evaporation rate, μ / h, a and b are constants, and R1 is the gas constant; in formula (4), V1 is the emitter evaporation rate, μ / (1000h), R is the outer diameter of the emitter, r is the inner diameter of the emitter, and D, B, and C are all fitted constants;

[0025] Construct a virtual device model VE = (Gv, Pv, Bv, Rv), where Gv represents the geometric model, Pv represents the physical model, Bv represents the behavioral model, and Rv represents the rule model;

[0026] Construct a data model DD = (Dp, Dv, Ds, Dk, Df), where Dp comes from PE data, Dv comes from VE data, Ds comes from Ss data, Dk represents domain knowledge, and Df represents the fusion data of Dp, Dv, Ds, and Dk;

[0027] Construct the connection model CN ​​= (CN_SD, CN_PD, CN_VD, CN_PS, CN_VS, CN_PV), where CN_SD represents the connection between Ss and DD, CN_PD represents the connection between PE and DD, CN_VD represents the connection between VE and DD, CN_PS represents the connection between PE and Ss, CN_VS represents the connection between VE and Ss, and CN_PV represents the connection between PE and VE.

[0028] In step 2, transferable features are learned by introducing inter-domain statistical moments as regularization terms in the loss function, which is expressed as follows:

[0029]

[0030] Where x s represents the sample from the source domain, x t Represents the sample from the target domain, x s and x t Following the probability distributions P and Q, E[·] represents the operation of mathematical expectation, E P [Ψ(x s )] represents the expectation of the feature value after feature mapping in the source domain sample, E Q [Ψ(x t )] represents the expectation of the eigenvalues ​​after feature mapping in the target domain sample, Ψ(·) represents the data feature mapping process, and H is the feature mapping space;

[0031] A subdomain adaptation mechanism (SAM) based on the local maximum mean difference (LMMD) metric is used to align the fine-grained features of each source domain and target domain in an independent feature space, narrowing the distribution differences between data features. LMMD characterizes the distribution differences of data in the mapping space. The LMMD value considers the distribution differences between the same subdomains in the source and target domains, and is specifically expressed as follows:

[0032]

[0033] H represents the reproducing kernel Hilbert space, P c represents the probability distribution of data category c in the simulation domain, Q c represents the probability distribution of data category c in the real domain, E[·] represents the operation of mathematical expectation, ψ(·) represents the data feature mapping process, and E c Indicates the expectation of sample features for each category c;

[0034] If each life sample belongs to category c, its weight is expressed as w c , then L H (P c ,Qc ) is expressed as:

[0035]

[0036] Among them, n s Represents the number of life samples in the source domain, n t represents the number of life samples in the target domain, ψ(·) represents the data feature mapping process, and w sc Represents the similarity of source domain samples, w tc Represents the similarity of source domain samples, and satisfies that the sum of all weights in the source domain and the target domain is 1:

[0037]

[0038] For each sample x in the source domain and the target domain i The corresponding weights are defined as:

[0039]

[0040] in, Represents the true value of the i-th sample of category c in the source domain and target domain;

[0041] If the feature extractor is represented by G f (·), SAM is defined as:

[0042]

[0043] Among them, G f (·) represents the feature extractor, k(·) represents the kernel function, C represents the similarity calculation parameter, and c represents the category.

[0044] In step 3, based on the temporal convolution residual structure, a channel attention mechanism and a soft threshold function are introduced. One-dimensional convolution is used to extract local spatial interactions, and multi-head attention is used to capture the global correlation between sensors. The original features are added to the outputs of convolution and attention through residual connections. Then, a feedforward network is applied to further optimize the features. The combination of local convolution and global attention is adopted, and layer normalization and residual connections are used to stabilize the gradient flow.

[0045] The formula for multi-head attention is:

[0046]

[0047] Where Q represents the query vector; K represents the key vector; V represents the value vector; d k Indicates the dimension of each key vector; QK TThe query matrix is ​​multiplied by the transposed matrix of the key matrix; softmax is a normalization function. The input sequence passes through three different linear transformation layers to obtain Q, K and V matrices respectively. These three matrices are divided into multiple heads, each with different linear transformation parameters, and each head performs a scaled dot product attention operation;

[0048] The dot product of the query and key is calculated. After scaling and biasing, the softmax function is used to obtain the attention weights and used in the weighted value matrix. The weighted sum is generated as the output of each head. The outputs of all heads are concatenated together to form a long vector. The concatenated vector is finally linearly transformed to integrate the information from different heads. After the attention operation, residual connections and layer normalization are performed:

[0049] x attn =LayerNorm(x+Attention(x,x,x))(13)

[0050] x represents the input sequence, Attention(x,x,x) is the output of the self-attention mechanism, and the residual connection x + Attention(x,x,x) is normalized by LayerNorm to obtain the final output x attn ;

[0051] The feedforward neural network uses two linear layers, GELU activation function and dropout layer for regularization, and then uses residual connection and layer normalization:

[0052] FFN(x)=W2(GELU(W1x)) (14)

[0053] Output=LayerNorm(x+FFN(x)) (15)

[0054] Where x represents the input feature vector; W1 represents the weight matrix of the first linear transformation, and W2 is the weight matrix of the second linear transformation. The hidden state representation after GELU activation is remapped back to the original embedding dimension, so that the output and input are consistent in dimension. The output of FFN is added to the original input to form a residual structure x+FFN(x), and the final output result is obtained by LayerNorm normalization.

[0055] A channel attention mechanism is added on the basis of BIGRU. The formula of the BIGRU module is as follows:

[0056]

[0057] in, represents the hidden state from left to right, represents the hidden state from right to left, x trepresents the tth element in the input sequence, represents the output result of the forward propagation hidden state, represents the output result of backward propagation, GRU(·) represents the GRU unit;

[0058] The hidden states of the two directions are spliced ​​together to obtain the final hidden state h t :

[0059]

[0060] Among them, [·;·] represents the concatenation operation of vectors;

[0061] Finally, the hidden state h t Pass it to the fully connected layer to get the output y t :

[0062] y t =softmax(Wh t +b)(19)

[0063] Where W represents the weight of the hidden layer output of the forward and backward propagation of information at time t, and b represents the bias corresponding to the hidden state of the BIGRU at time t;

[0064] Construct a ResTCN-BIGRU-Attention model based on digital twin collaboration to predict the remaining life of LaB6 hollow cathode. The specific steps are as follows:

[0065] Data preprocessing, using digital twin technology to build a dynamic simulation model of the hollow cathode;

[0066] The feature extraction module feeds the hollow cathode data in parallel into the ResTCN network integrated with the channel attention mechanism to extract local temporal features. Subsequently, a multi-head attention mechanism and a feedforward network are introduced to achieve channel-level fusion of multi-sensor data. Finally, the fused features are input into the BIGRU combined with the attention mechanism network to achieve global modeling.

[0067] Residual correction: the features extracted from the simulation domain and the real domain are input into equation (11) to correct the residual between the two domains. During the iteration process, the model with the smallest training loss is selected as the final optimal model;

[0068] Model evaluation was performed using mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R 2 ) Four evaluation indicators are used to measure the model performance.

[0069] This paper proposes a new method based on digital twin collaborative ResTCN-BIGRU-Attention, which has the following specific beneficial effects:

[0070] 1. To address the problem of insufficient actual operating data on the hollow cathode of ion thrusters, the present invention designs a prediction framework that integrates digital twin technology. By constructing a twin of the hollow cathode, real-time interaction between virtual and real space is achieved, thereby generating sufficient and reliable training data, effectively alleviating the prediction difficulties caused by data scarcity.

[0071] 2. To overcome the shortcomings of traditional methods in feature extraction and modeling capabilities, this paper proposes a ResTCN-BIGRU-Attention model. This model first uses the ResTCN network with a channel attention mechanism in parallel to extract local long-term dependency features in time series; then, it introduces a multi-head attention mechanism and a feedforward network to achieve channel-level fusion of multi-sensor data; finally, it combines BIGRU and the attention mechanism to focus on key features, thereby improving the accuracy and robustness of life prediction.

[0072] 3. This paper compares the proposed model with the ResNet model, ResTCN-GRU-Atten model, ResTCN-LSTM-Atten model and ResTCN-BILSTM-Atten model. The experimental results show that the proposed model is superior in terms of mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R 2 ) The four indicators are 0.055, 0.2347, 0.1514 and 0.98738, respectively, which verifies the effectiveness and advantages of the network model in the hollow cathode life prediction task. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 Schematic diagram of the hollow cathode physical model.

[0074] Figure 2 This is a schematic diagram of the ion engine principle.

[0075] Figure 3 Schematic diagram of the five-dimensional structural model of digital twins.

[0076] Figure 4 Schematic diagram of the subdomain adaptation mechanism.

[0077] Figure 5 This is the internal structure diagram of the feature extraction part.

[0078] Figure 6 Schematic diagram of the framework for predicting the life of LaB6 hollow cathode using the digital twin collaborative ResTCN-BIGRU-Attention model.

[0079] Figure 7 This is a visualization diagram of the remaining lifetime of LaB6 emitters for each model. Figure 7 (a) is the curve diagram of the CNN model prediction results. Figure 7 (b) is the ResNet model prediction result curve. Figure 7 (c) is the LSTM model prediction result curve. Figure 7 (d) is the curve diagram of the BILSTM model prediction results. Figure 7 (e) is the curve diagram of the GRU model prediction results. Figure 7 (f) is the BIGRU model prediction result curve. Figure 7 (g) is the prediction result curve of the ResTCN-LSTM-Atten model. Figure 7 (h) is the prediction result curve of the ResTCN-BILSTM-Atten model. Figure 7 (i) is the prediction result curve of the ResTCN-GRU-Atten model, Figure 7 (j) is the curve diagram of the predicted results of the proposed model.

[0080] Figure 8 The comparison chart of MSE, RMSE and MAE of each model.

[0081] Figure 9 For each model R 2 Comparison picture.

[0082] Figure 10 A comparison chart of the evaluation indicators of each model. DETAILED DESCRIPTION

[0083] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below with reference to 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.

[0084] A remaining life prediction method based on digital twin collaborative residual network, the specific steps are as follows:

[0085] Step 1: In-depth analysis of the working mechanism of the hollow cathode, and construction of a dynamic simulation model based on the digital twin collaborative residual network to achieve high-fidelity modeling of key operating states. By combining virtual and real methods, the problem of scarcity of real operating data is effectively solved, providing sufficient and reliable data support for model training.

[0086] Step 2: Introduce a subdomain adaptation mechanism to align the subdomain conditional distributions by minimizing the differences in fine-grained features between the simulation domain and the real domain. This strategy improves the generalization and robustness of the model under different data distributions, providing a stable data foundation for subsequent predictions.

[0087] Step 3. Design and apply the ResTCN-BIGRU-Attention model for lifespan prediction. The ResTCN-BIGRU-Attention model integrates the channel attention mechanism and soft threshold function in the ResTCN module, so that the network can automatically focus on key dimensional features when performing parallel local feature extraction on the data. Subsequently, a multi-head attention mechanism and a feedforward network are introduced to achieve channel-level fusion of multi-sensor data. Finally, the fused features are input into the BIGRU combined with the attention mechanism network to realize global modeling, further enhancing the expression and modeling capabilities of key features.

[0088] Among them, such as Figure 1-2 As shown in the figure, the working principle and failure mechanism of the LaB6 hollow cathode are as follows: As a core component of the electric propulsion system, the hollow cathode plays the role of ignition, discharge maintenance, and ion flux neutralization, significantly affecting the performance and stability of the entire electric propulsion system. The hollow cathode operation process is as follows: When the ion engine starts, a heating current is passed through the heater to preheat the hollow cathode to an appropriate temperature, and a working gas is injected into the cathode tube to increase the pressure inside the tube. Subsequently, an ignition voltage is applied to the cathode at the holding electrode. At this time, if the gas flow rate through the cathode reaches a threshold, the gas inside the cathode will be broken down, and the holding electrode will automatically switch to the holding electrode power supply. A stable self-sustaining arc discharge is formed between the emitter and the holding electrode, generating a high-density plasma in the cathode tube. The electrons on the emitter surface acquire high energy. When the kinetic energy of the electrons perpendicular to the surface is greater than the work function of the material, they can overcome the work function limitation and escape from the material surface as hot electrons. In other words, the emitter emits hot electrons due to the field enhancement effect on the surface. At this point, voltage is applied to the ion engine's anode, causing the discharge to spread throughout the discharge chamber. With the addition of screen and accelerator grid voltages, the positive ions within the chamber are drawn out by the grid system and ejected into space, generating thrust. Simultaneously, the neutralizer (with a stable discharge between its emitter and contact electrode) injects an equal amount of electrons into the ion beam under the influence of the ion beam potential.

[0089] For LaB6 materials, electrons simply escape from the surface of the material, and there is no heavy particle diffusion inside the emitter. This is a physical process. After heating to a higher temperature, the density of thermionic emission is only related to the material temperature and the inherent work function of the material, that is, it satisfies the Richardson-Dushman equation:

[0090]

[0091] Where, J e is the emission current density, A / cm 2 ; T is the emitter temperature, unit is K; is the work function of the emitter material, eV; k is the Boltzmann constant, which is 1.38×10 -23 J / K; A is the emission constant, here we take the theoretical value (Richardson coefficient), 120A / (cm 2 ·K 2 ).

[0092] The failure of hollow cathode mainly includes emitter failure, heater failure, electrode sputtering failure, hole blockage failure, short circuit or breakdown and heater failure.

[0093] Building a digital twin model: Figure 3 As shown in Figure 1, digital twins are high-fidelity digital mirror models of devices based on the geometry, physics, behavior, and rules of real-world objects. The interactive mechanism of DT can detect interference from the environment, potential faults in the device, and defects in the model, allowing the device and digital model to continuously evolve. The DT model M of the hollow cathode is established. DT (PE,VE,Ss,DD,CN).

[0094] Constructing physical entity models: Figure 1 As shown in the figure, the traditional hollow cathode of the electric propulsion system consists of a cathode tube, a top plate, an emitter, a heater and a contact electrode. A small hole (cathode hole) is opened in the center of the cathode top plate to increase the propellant gas pressure inside the cathode tube and easily generate internal plasma discharge. The cathode aperture depends on the maximum emission current and meets the Kaufman criterion, that is, the ratio of emission current to aperture is less than 12A / mm, so as to control the sputtering corrosion of the cathode hole at a low level.

[0095] The following are calculation formulas for some characteristic parameters of hollow cathode emitters, which can provide a basis for studying the life of hollow cathodes:

[0096]

[0097] For LaB6 emitter, in formula (2), J e is the emission current density, in A / cm 2 ; is the work function of the emitter material, which is taken as 2.66 eV; is the reduction of work function caused by the Schottky effect, which is taken as 0.05 eV; T is the emitter temperature, in K; A is the emitter constant, which is taken as 90 A / (cm 2 k 2 ); k is the Boltzmann constant, which is 1.38×10 -23In formula (3), V is the evaporation rate of the emitter, in μ / h; a and b are both constants and are taken as 4×10 14 μ / h, 570×10 3 J / mol; R1 is the gas constant, which is 8.314 [J / (molk)]; in formula (4), V1 is the evaporation rate of the emitter, in μ / (1000)h; R and r are the outer and inner diameters of the emitter, respectively; D, B, and C are fitting constants, which are 66.26 μm / (kh), 0.02477 cm / (kh), and 0.02477 cm / (kh), respectively. 2 / A, -88.66μm / (kh).

[0098] Constructing a virtual equipment model (VE): The virtual environment integrates the multiple variables, scales, and capabilities of physical entities, constructing their geometry, physical properties, behaviors, and rules within the virtual world. VE modeling is VE = (Gv, Pv, Bv, Rv), where Gv, Pv, Bv, and Rv represent the geometric model, physical model, behavioral model, and rule model, respectively.

[0099] Gv is constructed as a 2D solid model, while Pv simulates the physical properties of the PE. Transformations in emitter size, temperature distribution, and the work function of the emitter material can be simulated using ANSYS finite element simulation software. Bv describes the behavior of the PE, which is controlled by driving factors (such as heating the emitter to the rated ignition temperature and maintaining a stable operating current emission at an appropriate operating voltage) or interference factors (such as human interference with the material embedded in the hollow cathode and the exposed environment). Rv includes constraints, associations, and inference rules, enabling the virtual model to make judgments, assessments, optimizations, and / or predictions. The constructed VE, Gv, Pv, Bv, and Rv are functionally and structurally coupled to form a complete mirror image of the PE.

[0100] Service Model (Ss): Ss includes PE and VE services, which ensures the high fidelity of the virtual environment by calibrating and optimizing the virtual environment parameters during the operation of the virtual environment, thereby ensuring the performance of the virtual environment.

[0101] Build a data model (DD): It contains five parts: DD = (Dp, Dv, Ds, Dk, Df); among them, Dp comes from PE data, Dv comes from VE data, Ds comes from Ss data, Dk represents domain knowledge, and Df represents the fusion data of Dp, Dv, Ds and Dk. DD includes both physical and virtual data and the fusion between them, which greatly enriches the data.

[0102] Build a connection model (CN): CN consists of 6 parts:

[0103] CN=(CN_SD, CN_PD, CN_VD, CN_PS, CN_VS, CN_PV); among them, CN_SD, CN_PD, CN_VD, CN_PS, CN_VS and CN_PV represent the connections between Ss and DD, PE and DD, VE and DD, PE and Ss, VE and Ss, and PE and VE respectively.

[0104] Transfer learning is generally applicable to life prediction for multiple operating conditions or multiple devices. It narrows the feature distribution gap between source and target domain data, thereby leveraging empirical knowledge from the source domain to improve feature learning in the target domain. Among these, mapping-based metrics, as a classic transfer learning strategy, have received widespread attention. By introducing inter-domain statistical moments as regularization terms in the loss function, transferable features are learned. The core idea is expressed as follows:

[0105]

[0106] Where x s represents the sample from the source domain, x t Represents the sample from the target domain, x s and x t Following the probability distributions P and Q, E[·] represents the operation of mathematical expectation, E P [Ψ(x s )] represents the expectation of the feature value after feature mapping in the source domain sample, E Q [Ψ(x t )] represents the expectation of the eigenvalues ​​after feature mapping in the target domain sample, Ψ(·) represents the data feature mapping process, and H is the feature mapping space;

[0107] like Figure 4 As shown in the figure, to reduce the distribution discrepancy between the data in the digital twin simulation domain and the real-world target domain, the feature transfer method based on the mean maximum discrepancy (MMD) ignores the granularity of the alignment between the two domains. To improve the accuracy of life prediction, a subdomain adaptation mechanism (SAM) based on the local maximum mean discrepancy (LMMD) is adopted to perform fine-grained feature alignment of each degradation stage of the source and target domains in an independent feature space, thus reducing the distribution discrepancy between the data features.

[0108] Similar to MMD, LMMD also characterizes the distribution differences of data in the mapping space, but the difference is that the LMMD value considers the distribution differences between the same sub-domains in the source domain and the target domain. LMMD is expressed as follows:

[0109]

[0110] H represents the reproducing kernel Hilbert space, P crepresents the probability distribution of data category c in the simulation domain, Q c represents the probability distribution of data category c in the real domain, E[·] represents the operation of mathematical expectation, ψ(·) represents the data feature mapping process, and E c It represents the expected feature of each sample of category c. If each life sample belongs to category c, its weight is expressed as w c , then L H (P c ,Q c ) is expressed as:

[0111]

[0112] Among them, n s Represents the number of life samples in the source domain, n t represents the number of life samples in the target domain, w sc and w tc Represent the similarity of source domain and target domain samples respectively, and satisfy the sum of all weights in the source domain and target domain is 1:

[0113]

[0114] For each sample x in the source domain and the target domain i The corresponding weights are defined as:

[0115]

[0116] in, Represents the true value of the i-th sample of category c in the source domain and target domain;

[0117] If the feature extractor is represented by G f (·), SAM is defined as:

[0118]

[0119] Among them, G f (·) represents the feature extractor, k(·) represents the kernel function, C represents the similarity calculation parameter, and c represents the category.

[0120] Constructing a LaB6 hollow cathode remaining life prediction framework: Constructing a time convolution residual network residual module. By introducing nonlinear mapping into the dilated causal convolution network, cross-layer jump connections are achieved, which effectively alleviates the gradient vanishing and explosion problems, reduces the training difficulty, and also supports the construction of deeper networks. Based on the original time convolution residual structure, a channel attention mechanism and a soft threshold function are introduced. The soft threshold of each feature channel in the attention mechanism is used to replace the traditional nonlinear layer, so that the network can automatically focus on key features, thereby improving the feature learning ability of the time convolution residual model on time series data, and ultimately obtaining a better model, such as Figure 5 As shown in the ResTCN section.

[0121] This part is used for feature fusion between multiple sensors, integrating features from different sensor modalities, such as Figure 5 The feature fusion part of the proposed method. First, one-dimensional convolution is used to extract local spatial interactions. Second, multi-head attention is used to capture global correlations between sensors. The original features are added to the outputs of the convolution and attention via residual connections. A feedforward network is then applied to further refine the features. By combining local convolution and global attention, and using layer normalization and residual connections to stabilize the gradient flow, the method effectively addresses the complex interactions between different sensors.

[0122] The formula for multi-head attention is:

[0123]

[0124] Among them, Q, K, V represent query vector, key vector and value vector respectively; d k Indicates the dimension of each key vector; QK T is the transposed matrix multiplication of the query matrix and the key matrix; softmax is the normalization function. The input sequence passes through three different linear transformation layers to obtain the Q, K and V matrices respectively. These three matrices are divided into multiple heads, each with different linear transformation parameters, and each head performs a scaled dot product attention operation. Specifically, the dot product of the query and the key is calculated, and after scaling and biasing, the softmax function is used to obtain the attention weight, which is used to weight the value matrix to generate the weighted sum as the output of each head. The outputs of all heads are spliced ​​together to form a long vector. The spliced ​​vector is then subjected to a final linear transformation to integrate the information from different heads. After the attention operation, it is normalized through residual connections and layers:

[0125] x attn =LayerNorm(x+Attention(x,x,x))(13)

[0126] x represents the input sequence; Attention(x,x,x) is the output of the self-attention mechanism; the residual connection x + Attention(x,x,x) is normalized by LayerNorm to obtain the final output x attn This ensures the effective capture of global information and the stable transfer of gradients.

[0127] The feedforward neural network uses two linear layers, GELU activation function and dropout layer for regularization, and then uses residual connection and layer normalization:

[0128] FFN(x)=W2(GELU(W1x)) (14)

[0129] Output=LayerNorm(x+FFN(x)) (15)

[0130] Among them, x represents the input feature vector; W1 represents the weight matrix of the first linear transformation, which projects the input features from the original embedding dimension to a higher hidden dimension, expanding the feature space; W2 is the weight matrix of the second linear transformation, which remaps the hidden state representation after GELU activation back to the original embedding dimension, so that the output and input are consistent in dimension; the output of FFN is added to the original input x+FFN(x) to form a residual structure, and the final output result is obtained by LayerNorm normalization, which enhances the expressiveness and nonlinear modeling capabilities of the model.

[0131] The Gated Recurrent Unit (GRU) is a commonly used variant of the Recurrent Neural Network (RNN). Compared to traditional RNNs and LSTMs, it is simpler and has fewer parameters. By introducing update gates, reset gates, and candidate hidden states, the GRU can better capture long-distance dependencies and enhance modeling capabilities. The BIGRU introduces a bidirectional structure based on the GRU to better capture the bidirectional dependencies of sequence data. The current hidden layer state is determined by the forward and backward propagation hidden layer outputs and the current input. Figure 5 As shown in the BIGRU+Atten section, this section adds a channel attention mechanism on the basis of BIGRU, allowing it to better focus on the modeling of key information. The formula of the BIGRU module is as follows:

[0132]

[0133] in, represents the hidden state from left to right, represents the hidden state from right to left, x t represents the tth element in the input sequence, represents the output result of the forward propagation hidden state, represents the output result of backward propagation, GRU(·) represents the GRU unit;

[0134] The hidden states of the two directions are spliced ​​together to obtain the final hidden state h t :

[0135]

[0136] Among them, [·;·] represents the concatenation operation of vectors;

[0137] Finally, the hidden state h t Pass it to the fully connected layer to get the output y t :

[0138] y t =softmax(Wh t +b)(19)

[0139] Where W represents the weight of the hidden layer output of the forward and backward propagation of information at time t, and b represents the bias corresponding to the hidden state of the BIGRU at time t;

[0140] By integrating the proposed method details, this paper proposes a new framework for predicting the remaining life of LaB6 hollow cathode based on the digital twin collaborative ResTCN-BIGRU-Attention model. Figure 6 The specific steps are as follows:

[0141] (1) Data preprocessing: Since it is difficult to obtain a large amount of operating data of hollow cathodes in the physical world, the research on their remaining life prediction is greatly limited. Therefore, digital twin technology is used to construct a dynamic simulation model of the hollow cathode to generate rich simulation data. The obtained data is normalized to the maximum and minimum values, laying a good foundation for model training.

[0142] (2) Feature extraction module: The data of the hollow cathode is input in parallel into the ResTCN network integrated with the channel attention mechanism to extract local temporal features; a multi-head attention mechanism and a feedforward network are introduced to realize channel-level fusion of multi-sensor data; the fused features are input into the BIGRU combined with the attention mechanism network to realize global modeling, further enhance the expression ability of key features, and improve the discriminability of the model.

[0143] (3) Residual correction: The features extracted from the simulation domain and the real domain are input into equation (11) to correct the residual between the two domains. When the residual loss function reaches a minimum value, it indicates that the model prediction result has a high degree of credibility; otherwise, feature extraction and residual correction need to be performed again. During the iterative process, the model with the smallest training loss is selected as the final optimal model.

[0144] (4) Model evaluation: Mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R 2 ) Four evaluation indicators are used to measure the model performance, and a comparative analysis is conducted with other prediction models to verify the effectiveness and superiority of the proposed model in the hollow cathode life prediction task.

[0145] Experimental verification and result analysis:

[0146] Dataset description: Assuming that the emitter lifetime is the primary factor limiting the hollow cathode lifetime, eight input parameters are considered. The uncertain influence of T, R, r, B, C, and D and the calculation based on equations (3), (4), (5), and (6) show that the parameter that has the greatest impact on the life of the hollow cathode emitter is the emitter work function. Work function Data collection and generation for the five parameters (temperature T, emitter outer diameter R, and inner diameter r) within their uncertainty ranges constitute the hollow cathode data set. Table 1 shows the uncertainty ranges for these parameters.

[0147] The five parameters with the greatest impact are considered to be data collected by five different types of sensors. To eliminate the dimensionality impact between different types of sensors and improve the model training speed, the max-min normalization method is used to normalize the data. The mathematical expression of the max-min normalization method is:

[0148]

[0149] The core of this method is to map the value of each feature to the range of [0, 1] according to formula (20), where x represents the original feature value and x represents the original feature value. min and x max are the minimum and maximum values ​​of the feature, respectively.

[0150] Table 1 Input parameters in the life model

[0151]

[0152] The mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R 2 ) Four commonly used indicators are used to evaluate the accuracy of the prediction results of the proposed model. The smaller the values ​​of MSE, RMSE and MAE, the higher the R 2 The closer the value is to 1, the better the model is. The mathematical expressions are as follows:

[0153]

[0154] Where m represents the number of samples; y iIndicates the true value of RUL; Represents the RUL predicted value at each time step.

[0155] Experimental results analysis: RUL prediction results and analysis The comparison results between the RUL prediction value and the true value of the ResTCN-BIGRU-Attention model on the hollow cathode test dataset are as follows Figure 7 The results of the test set are divided into 55 cycles, and the average of the results is taken as the RUL of each cycle. In order to verify that the proposed ResTCN-BIGRU-Atten model can better predict the remaining lifetime of hollow cathode emitters, CNN, ResNet, LSTM, BILSTM, GRU, BIGRU, ResTCN-LSTM-Atten, ResTCN-BILSTM-Atten, and ResTCN-GRU-Atten models were selected and compared with different models. The prediction results of (a) CNN, (c) LSTM, (d) BILSTM, (e) GRU, and (f) BIGRU models show that the traditional convolutional time series model has the problems of insufficient capture of multivariate features and lack of modeling ability, resulting in a large deviation from the true decay trend in the early or middle stages of the cycle; as an improvement of the traditional CNN, (b) ResNet significantly improves the effect in fitting the RUL prediction curve; the RUL prediction curves obtained by combining ResNet with LSTM, BILSTM and GRU models plus attention mechanism are shown in (g), (h), and (i). The prediction results are all good, but due to the large amount of computation, the gradient instability affects the long-term dependency modeling effect. As can be seen from Figure (j), the proposed model can well predict the RUL of the hollow cathode, especially in the area where the true RUL value is small, the gap between the predicted RUL value and the true value is small; the predicted curve is more in line with the actual degradation trend; the fluctuation of the predicted value is small, especially in the accelerated degradation stage, the performance is robust.

[0156] Table 2 Figure 8 、 Figure 9is the comparison result of the evaluation indicators of each model. It can be seen from the table that on the hollow cathode data set, the RUL prediction accuracy of the ResTCN-BIGRU-Attention model is better than that of the other compared models. The MSE of the model is 0.05509, which is about 16 times lower than the second-best model ResTCN-BILSTM-Atten (0.9356), indicating that the overall deviation between its predicted value and the true value is extremely small, and the sum of squared errors is the smallest; the RMSE of the proposed model is 0.23471, which is much lower than ResNet (0.7505) and LSTM (1.1596), indicating that the average absolute deviation between its predicted value and the true value is the smallest and the model stability is the highest; the MAE value is as low as 0.15141, which is about 1 / 4 of the second-best model BIGRU (0.65), indicating that the absolute value of its prediction error is extremely small, and the estimation of RUL is closer to the true value; R 2 It is as high as 0.98738, close to 1, indicating that it can explain about 98.7% of the variance in the data, and its goodness of fit is significantly better than other models (0.9241 for ResNet and 0.8898 for BIGRU). Compared with ResTCN-BILSTM-Atten, the RMSE of the proposed model is reduced by about 51.6%, and the MAE is reduced by 77%, proving that after the introduction of bidirectional GRU and Attention mechanism, the model's ability to capture long-term dependencies and key degradation stages is greatly improved. Compared with CNN and ResNet, the MSE of the proposed model is only about 3% of that of CNN (1.6692), indicating that the pure CNN model has a significantly increased error due to its lack of time series modeling capabilities, while ResTCN's multi-scale feature extraction makes up for this shortcoming. Compared with BIGRU and LSTM, the R 2 This is 10.8% higher than the BIGRU (0.8898), demonstrating that the Attention mechanism significantly improves the model's adaptability to complex degradation patterns by dynamically focusing on key degradation stages (such as the period of rapid RUL decline at the end). The proposed model minimizes error and maximizes model interpretability in the hollow cathode RUL prediction task.

[0157] Table 2 Comparison of prediction performance of different models

[0158]

[0159] Ablation test results and analysis: In order to verify the contribution of each core component in the model proposed in this invention, the hollow cathode LaB6 dataset was used to perform an ablation experiment on the ResTCN-BIGRU-Attention model with an iteration cycle of 500. The baseline model was ResNet18, and the comparison models were ResNet18-BIGRU (to verify the timing modeling capability of BIGRU), ResNet18-Atten (to verify the focusing capability of Attention), ResNet18-BIGRU-Atten, ResTCN (to verify multi-scale timing feature extraction), ResTCN-BIGRU, and ResTCN-Atten (to verify the dynamic weight allocation of Attention). The ablation test results are shown in Table 3.

[0160] From Table 3 and Figure 10 It can be seen that the MSE of ResTCN (0.1274) is 84% ​​lower than that of ResNet18 (1.1083), indicating that its multi-scale convolution structure is more suitable for temporal feature extraction. The proposed model ResTCN captures features of different time granularities through parallel multi-scale convolution and combined channel attention mechanism, which is more suitable for the complex temporal pattern of hollow cathode emitters; the MSE of ResNet18-BIGRU (0.8798) is 20% higher than that of ResNet18, proving that BIGRU can effectively model temporal dependencies, while BIGRU alone fails to do so well. To realize its potential, it needs to be combined with ResTCN to form the ResTCN-BIGRU model with an MSE of 0.1206. The performance of ResNet18-Atten (MSE = 0.9581) may be due to the lack of temporal dependencies when using the attention mechanism alone. In the proposed model, after the attention mechanism is combined with BIGRU, the MSE is further reduced to 0.1167. The multi-head attention mechanism gives dynamic weights to the temporal features extracted by BIGRU, highlighting key features. BIGRU handles long-range dependencies, and Attention optimizes local feature focus. The proposed model ResTCN-BIGRU-Attention improves by 9% compared to ResTCN (MSE = 0.1274), proving that BIGRU+Attention makes up for the shortcomings of ResTCN in dynamic temporal adjustment. Compared with ResNet18, the overall MSE value of this model is reduced by 89%. 2 It reaches 0.9848, which is close to perfect fit.

[0161] Table 3 Ablation experiment results on the hollow cathode emitter dataset

[0162]

[0163] In order to accurately estimate the remaining life of hollow cathodes, a new digital twin collaborative ResTCN-BIGRU-Attention method is proposed, and the following conclusions are obtained:

[0164] To address the lack of actual operational data for the hollow cathode of an ion thruster, a prediction framework incorporating digital twin technology was designed. By constructing a twin of the hollow cathode, real-time interaction between virtual and real space is achieved, generating sufficient and reliable training data, effectively alleviating the prediction difficulties caused by data scarcity.

[0165] To overcome the shortcomings of traditional methods in feature extraction and modeling capabilities, a ResTCN-BIGRU-Attention model is proposed. This model first uses a parallel ResTCN network integrated with a channel attention mechanism to extract local long-term dependency features in time series; then, a multi-head attention mechanism and a feedforward network are introduced to achieve channel-level fusion of multi-sensor data; finally, BIGRU and the attention mechanism are combined to focus on key features for global modeling, thereby improving the accuracy and robustness of life prediction.

[0166] The proposed model is compared with ResNet, ResTCN-GRU-Atten, ResTCN-LSTM-Atten and ResTCN-BILSTM-Atten models. The experimental results show that the proposed model is superior in terms of mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R 2 ) The four indicators are 0.055, 0.2347, 0.1514 and 0.98738, respectively, which verifies the effectiveness and advantages of the network model in the hollow cathode life prediction task.

[0167] The above description is only a preferred embodiment of the present invention and is 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 scope of the present invention.

Claims

1. A method for predicting remaining life based on digital twin collaborative residual network, characterized in that: The specific steps are as follows: Step 1: Analyze the working mechanism of the hollow cathode and build a dynamic simulation model based on the digital twin collaborative residual network; Step 2: Introduce a subdomain adaptation mechanism to achieve alignment of subdomain conditional distributions by minimizing the difference in fine-grained features between the simulation domain and the real domain; Step 3. Construct the ResTCN-BIGRU-Attention model for lifespan prediction. This model integrates the channel attention mechanism and soft threshold function in the ResTCN module, automatically focuses on key dimensional features when performing local feature extraction, introduces a multi-head attention mechanism and a feedforward network to achieve channel-level fusion of multi-sensor data, and realizes global modeling of long time series through the BIGRU network. Multi-head attention and channel attention mechanisms are introduced in the ResTCN-BIGRU-Attention model.

2. The remaining life prediction method based on digital twin collaborative residual network according to claim 1 is characterized in that: In step 1, after the material is heated, the thermal electron emission density satisfies the Richardson-Dushman equation: Where, J e is the emission current density, T is the emitter temperature, is the work function of the emitter material, k is the Boltzmann constant, and A is the emitter constant; The calculation formulas for some characteristic parameters of the hollow cathode emitter are as follows: In formula (2), J e is the emission current density, is the work function of the emitter material, is the reduction in work function caused by the Schottky effect, T is the emitter temperature, A is the emitter constant, and k is the Boltzmann constant; in formula (3), V is the emitter evaporation rate, a and b are constants, and R1 is the gas constant; in formula (4), V1 is the emitter evaporation rate, R is the outer diameter of the emitter, r is the inner diameter of the emitter, and D, B, and C are all fitted constants; Construct a virtual device model VE = (Gv, Pv, Bv, Rv), where Gv represents the geometric model, Pv represents the physical model, Bv represents the behavioral model, and Rv represents the rule model; Construct a data model DD = (Dp, Dv, Ds, Dk, Df), where Dp comes from PE data, Dv comes from VE data, Ds comes from Ss data, Dk represents domain knowledge, and Df represents the fusion data of Dp, Dv, Ds, and Dk; Construct the connection model CN ​​= (CN_SD, CN_PD, CN_VD, CN_PS, CN_VS, CN_PV), where CN_SD represents the connection between Ss and DD, CN_PD represents the connection between PE and DD, CN_VD represents the connection between VE and DD, CN_PS represents the connection between PE and Ss, CN_VS represents the connection between VE and Ss, and CN_PV represents the connection between PE and VE.

3. The remaining life prediction method based on digital twin collaborative residual network according to claim 2 is characterized in that: In step 2, transferable features are learned by introducing inter-domain statistical moments as regularization terms in the loss function, which is expressed as follows: Where x s represents the sample from the source domain, x t Represents the sample from the target domain, x s and x t Following the probability distributions P and Q, E[·] represents the operation of mathematical expectation, E P [Ψ(x s )] represents the expectation of the feature value after feature mapping in the source domain sample, E Q [Ψ(x t )] represents the expectation of the eigenvalues ​​after feature mapping in the target domain sample, Ψ(·) represents the data feature mapping process, and H represents the feature mapping space; A subdomain adaptation mechanism (SAM) based on the local maximum mean difference (LMMD) metric is used to align the fine-grained features of each source domain and target domain in an independent feature space, narrowing the distribution differences between data features. LMMD characterizes the distribution differences of data in the mapping space. The LMMD value considers the distribution differences between the same subdomains in the source and target domains, and is specifically expressed as follows: H represents the reproducing kernel Hilbert space, P c represents the probability distribution of data category c in the simulation domain, Q c represents the probability distribution of data category c in the real domain, E[·] represents the operation of mathematical expectation, ψ(·) represents the data feature mapping process, and E c Indicates the expectation of sample features for each category c; If each life sample belongs to category c, its weight is expressed as w c , then L H (P c ,Q c ) is expressed as: Among them, n s Represents the number of life samples in the source domain, n t represents the number of life samples in the target domain, ψ(·) represents the data feature mapping process, and w sc represents the similarity of source domain samples, w tc Represents the similarity of the target domain sample, and satisfies that the sum of all weights in the source domain and the target domain is 1: For each sample x in the source domain and the target domain i The corresponding weights are defined as: in, Represents the true value of the i-th sample of category c in the source domain and target domain; If the feature extractor is represented by G f (·), SAM is defined as: Among them, G f (·) represents the feature extractor, k(·) represents the kernel function, C represents the similarity calculation parameter, and c represents the category.

4. The remaining life prediction method based on digital twin collaborative residual network according to claim 3 is characterized in that: In step 3, based on the temporal convolution residual structure, a channel attention mechanism and a soft threshold function are introduced. One-dimensional convolution is used to extract local spatial interactions, and multi-head attention is used to capture the global correlation between sensors. The original features are added to the outputs of convolution and attention through residual connections. Then, a feedforward network is applied to further optimize the features. The combination of local convolution and global attention is adopted, and layer normalization and residual connections are used to stabilize the gradient flow. The formula for multi-head attention is: Where Q represents the query vector; K represents the key vector; V represents the value vector; d k Indicates the dimension of each key vector; QK T The query matrix is ​​multiplied by the transposed matrix of the key matrix; softmax is a normalization function. The input sequence passes through three different linear transformation layers to obtain Q, K and V matrices respectively. These three matrices are divided into multiple heads, each with different linear transformation parameters, and each head performs a scaled dot product attention operation; The dot product of the query and key is calculated. After scaling and biasing, the softmax function is used to obtain the attention weights and used in the weighted value matrix. The weighted sum is generated as the output of each head. The outputs of all heads are concatenated to form a long vector. The concatenated vector is finally linearly transformed to integrate the information from different heads. After the attention operation, residual connections and layer normalization are performed: x attn =LayerNorm(x+Attention(x,x,x)) (13) x represents the input sequence, Attention(x,x,x) is the output of the self-attention mechanism, and the residual connection x + Attention(x,x,x) is normalized by LayerNorm to obtain the final output x attn ; The feedforward neural network uses two linear layers, GELU activation function and dropout layer for regularization, and then uses residual connection and layer normalization: FFN(x)=W2(GELU(W1x)) (14) Output=LayerNorm(x+FFN(x)) (15) Where x represents the input feature vector; W1 represents the weight matrix of the first linear transformation, and W2 is the weight matrix of the second linear transformation. The hidden state representation after GELU activation is remapped back to the original embedding dimension, so that the output and input are consistent in dimension. The output of FFN is added to the original input to form a residual structure x+FFN(x), and the final output result is obtained by LayerNorm normalization. A channel attention mechanism is added on the basis of BIGRU. The formula of the BIGRU module is as follows: in, represents the hidden state from left to right, represents the hidden state from right to left, x t represents the tth element in the input sequence, represents the output result of the forward propagation hidden state, represents the output result of backward propagation, GRU(·) represents the GRU unit; The hidden states of the two directions are spliced ​​together to obtain the final hidden state h t : Among them, [·;·] represents the concatenation operation of vectors; Finally, the hidden state h t Pass it to the fully connected layer to get the output y t : y t =softmax(Wh t +b) (19) Where W represents the weight of the hidden layer output of the forward and backward propagation of information at time t, and b represents the bias corresponding to the hidden state of the BIGRU at time t; Construct a ResTCN-BIGRU-Attention model based on digital twin collaboration to predict the remaining life of LaB6 hollow cathode. The specific steps are as follows: Data preprocessing, using digital twin technology to build a dynamic simulation model of the hollow cathode; The feature extraction module inputs the hollow cathode data in parallel into the ResTCN network integrated with the channel attention mechanism. After extracting the local temporal features, it introduces a multi-head attention mechanism and a feedforward network to achieve channel-level fusion of multi-sensor data. The fused features are then input into the BIGRU combined with the attention mechanism network to achieve global modeling. Residual correction: The features extracted from the simulation domain and the real domain are input into equation (11) to correct the residual between the two domains. During the iteration process, the model with the smallest training loss is selected as the final optimal model; model evaluation: four evaluation indicators, namely mean square error, root mean square error, mean absolute error and determination coefficient, are used to measure the model performance.

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