A screw heat field reconstruction method for a feed system based on cross-modal fusion and hamilton with end port

Abstract

The application discloses a kind of based on cross-modal fusion and the feeding system screw heat field reconstruction method of Hamilton with end port.It comprises constructing screw heat field reconstruction dataset, constructing feeding system screw heat field reconstruction model, according to screw heat field reconstruction dataset, training is carried out to feeding system screw heat field reconstruction model, the trained feeding system screw heat field reconstruction model is deployed in actual working condition, temperature observation data and dynamics excitation data collected in actual working condition are input into the deployed feeding system screw heat field reconstruction model, and the temperature sequence after reconstruction is output;The temperature sequence after reconstruction and corresponding position sequence combination constitute the temperature observation data after reconstruction, so as to realize the reconstruction of feeding system screw heat field.The application realizes the dense space-time temperature field consistent with thermodynamic mechanism under sparse observation condition, and inhibits non-physical drift in long-term recursion.

Description

Technical Field

[0001] This invention belongs to the field of thermal error control of CNC machine tools, and specifically relates to a method for reconstructing the thermal field of a feed system lead screw based on cross-modal fusion and Hamiltonian with a port. Background Technology

[0002] In the feed chain of a gantry milling machine, the motor-driven ball screw and moving nut pair generate significant frictional heat under load. The heat source migrates spatially along the feed trajectory and couples with structural heat capacity, guide rail convection, and environmental heat transfer, resulting in a temperature field exhibiting strong spatial non-uniformity and strong transient characteristics. Engineering measurements show that thermally induced deformation accounts for a high proportion of the total machining error. Thermal error compensation relies on estimating the volumetric temperature or equivalent thermal state of key components such as the screw, bearing, and machine bed. However, due to limitations in wiring space, electromagnetic compatibility, and reliability, only a small number of discrete temperature measurement points can often be deployed on-site, making it impossible to directly obtain high-resolution volumetric temperature distribution. The emergence of digital twins and industrial intelligent scenarios further demands the continuous reconstruction of the temperature of unmeasured areas under the condition of available sparse temperature measurement and motion or control signals such as position, speed, and rotation speed output by the CNC system. The reconstruction results must be compatible with the actual thermodynamic process in terms of energy conservation, dissipation direction, and open boundary heat transfer, rather than merely fitting the measurement point readings.

[0003] In analytical and lumped parameter methods, one-dimensional lead screw thermal simplification, thermal resistance networks, or a few lumped heat capacity nodes are often used to describe the thermal state of the feed system. These methods have low computational cost and are easy to embed for compensation. However, these models make strong assumptions about geometric details, contact thermal resistance, lubricating oil film, and time-varying characteristics of convective boundaries. They are difficult to accurately characterize the changes in the intensity and width of the moving heat source caused by the reciprocating movement of the nut, and they are also insufficient in describing multi-axis coupling and the three-dimensional heat conduction path of structural components. This leads to system deviations under wide operating conditions and long-term operation. Rigorous analytical solutions are mostly limited to ideal cases such as semi-infinite bodies and constant physical property regular geometry. For feed chains containing moving heat sources, convective boundaries, and non-uniform materials, closed analytical forms are difficult to obtain, often requiring further numerical discretization, which limits the scalability of analytical routes.

[0004] Numerical discretization methods such as the finite element method and the finite volume method can solve three-dimensional transient heat conduction equations under detailed geometric and boundary conditions. Furthermore, fidelity can be improved through moving heat source subroutines, contact thermal conductivity, and convection coefficient calibration, making them important tools for offline calibration and mechanism analysis. However, in online or quasi-online applications of machine tool digital twins, the computational and storage overhead of full-mesh transient solutions is high, and mesh updates and parameter recalibration are costly during structural changes, wear, or changes in operating conditions. More importantly, forward numerical simulation solves the forward problem of deriving the temperature field from known boundaries and source terms, while the on-site task is the inverse problem of inverting the entire field using a small number of measurement points and trajectory information. Without a rapid inversion mechanism combined with measurement noise and irreversible thermodynamic constraints, simply repeatedly calling high-fidelity simulations is insufficient to meet real-time performance and closed-loop compensation delay requirements.

[0005] Regarding neural networks and data-driven methods, pure data-driven models fit the measurement points to the full field mapping using end-to-end regression or sequence prediction. While achieving low errors within the training distribution, they often fail to generalize adequately to external operating conditions, variations in measurement point layout, and long-term recursion, and struggle to guarantee physical consistency such as heat flow direction and peak temperature location. Physical information neural networks incorporate partial differential equation residuals into the loss function, and neural operators offer resolution transferability advantages in continuous field representations. However, most implementations still rely on soft-constraint penalty residuals, lacking explicit structures for attenuation, irreversible entropy production, and port energy exchange in open systems. This leads to non-physical oscillations or thermodynamic inconsistencies in the reconstructed field. Geometric methods such as port Hamiltonian networks and dissipative Hamiltonian networks can preserve energy and dissipative structures in low-dimensional lumped dynamics identification, but when dealing with high-dimensional volumetric temperature fields, the motion excitation modes and thermal response modes exhibit strong statistical and mechanistic heterogeneity. The disconnect between single-mode encoding and latent space-volume domain decoding is prominent, and the joint utilization of sparse industrial measurement points and trajectory sequences remains insufficient.

[0006] In summary, analytical and lumped models are efficient but lack sufficient mechanistic coverage, while the finite element method offers high fidelity but struggles to directly handle rapid full-field inversion under sparse measurement points. Existing neural network and operator learning methods still have significant limitations in cross-modal alignment, reversible-irreversible decomposition in the eigenvalue sense, and long-term physical residual control. Therefore, a reconstruction technique is needed that can explicitly integrate sparse temperature measurement and motion excitation, structurally characterize dissipation and port input within a Hamiltonian framework containing eigenvalue ports, and stably recursively derive high-dimensional temperature fields. Summary of the Invention

[0007] To address the problems existing in the background technology, this invention provides a method for reconstructing the thermal field of a feed system screw based on cross-modal fusion and Hamiltonian with a port. This method solves the technical problems in the prior art, such as insufficient coverage of analytical and lumped parameter models, high computational cost of finite element numerical discretization methods that are difficult to meet real-time inversion requirements, and insufficient utilization of cross-modal information and easy generation of physical illusions and thermodynamic inconsistencies in long-term recursion by existing neural networks and operator learning methods. It realizes the acquisition of a dense spatiotemporal temperature field consistent with thermodynamic mechanisms under sparse observation conditions and suppresses non-physical drift in long-term recursion.

[0008] The technical solution adopted in this invention is:

[0009] I. A method for reconstructing the thermal field of a feed system screw based on cross-modal fusion and Hamiltonian with a tangent port:

[0010] S1. Through simulation, temperature observation data and dynamic excitation data of the feed system screw are collected over a continuous time period to construct a screw thermal field reconstruction dataset.

[0011] The temperature observation data at each moment includes a position sequence consisting of the positions of all discrete nodes along the axis of the simulated leadscrew and a temperature sequence consisting of the temperature corresponding to each position. The dynamic excitation data at each moment includes the leadscrew rotational speed, feed rate, and nut position trajectory.

[0012] S2. Construct a feed system screw thermal field reconstruction model. Train the feed system screw thermal field reconstruction model based on the screw thermal field reconstruction dataset to obtain the trained feed system screw thermal field reconstruction model.

[0013] S3. Deploy the trained feed system screw thermal field reconstruction model under actual working conditions. Input the temperature observation data and dynamic excitation data collected under actual working conditions into the deployed feed system screw thermal field reconstruction model, and output the reconstructed temperature sequence.

[0014] S4. The reconstructed temperature sequence and the corresponding position sequence are combined to form the reconstructed temperature observation data, thereby realizing the reconstruction of the hot field of the feed system screw.

[0015] Step S1 specifically involves:

[0016] S11. Through simulation, temperature observation data and dynamic excitation data of the feed system screw are collected over a continuous time period.

[0017] S12. For the temperature observation data at time t-1, mask a portion of the temperature values ​​in the temperature sequence to obtain the masked temperature sequence; combine the masked temperature sequence with the corresponding position sequence to form the masked temperature observation data at time t-1; combine the masked temperature observation data at time t-1 with the dynamic excitation data at time t-1 as the model input data.

[0018] S13. Use the temperature sequence from the temperature observation data at time t as the label data for the model output.

[0019] S14. Combine the model input data obtained in S12 with the label data obtained in step S13 to construct a single sample for model training.

[0020] S15. Repeat steps S12-S14 to construct several samples, thereby obtaining the lead screw thermal field reconstruction dataset.

[0021] The training process of the feed system lead screw thermal field reconstruction model is as follows:

[0022] D1. The masked temperature observation data and dynamic excitation data at time t-1 in a single sample are input together into the coding module of the asymmetric broadcast modulation module for processing, and the temperature branch coding features and dynamic branch coding features are obtained respectively.

[0023] D2, temperature branch coding features, and dynamics branch coding features are input together into the cross-modal fusion prediction module of the asymmetric broadcast modulation module for processing to obtain the hidden state vector.

[0024] D3. The masked temperature observation data, dynamic branch coding features, and hidden state vector are input together into the Hamiltonian propagation module with port t for processing to obtain the reconstructed temperature sequence at time t.

[0025] D4. Calculate the loss function based on the reconstructed temperature sequence at time t and the corresponding label data, and then perform backpropagation to update the model parameters based on the calculated loss function.

[0026] D5. Repeat steps D1-D4 until the training of the hot field reconstruction model of the feed system screw is completed.

[0027] The asymmetric broadcast modulation module performs the following steps:

[0028] F1. Input the masked temperature observation data and the dynamic excitation data at time t-1 into the first coding sub-network and the second coding sub-network respectively to obtain the temperature branch coding features and the dynamic branch coding features respectively.

[0029] F2. Align the temperature branch coding features and the dynamics branch coding features along the channel dimension to obtain the aligned temperature branch coding features and dynamics branch coding features.

[0030] F3. The aligned temperature branch coding features and the aligned dynamics branch coding features are fused through cross attention to obtain the fused features.

[0031] F4. After concatenating the fused features and the temperature branch coding features, flatten them into a one-dimensional vector and input them into the multilayer perceptron mapping network to obtain the hidden state vector.

[0032] The Hamiltonian propagation module containing the port is executed according to the following steps:

[0033] H1. Input the hidden state vectors into four multilayer perceptrons respectively to obtain the antisymmetric interconnection matrix, dissipative constitutive matrix, Hamiltonian and input coupling matrix respectively.

[0034] H2. The hidden state vector at time t is obtained by combining the antisymmetric interconnection matrix, dissipative composition matrix, Hamiltonian, input coupling matrix and dynamic branch coding features.

[0035] H3. The masked temperature sequence at time t-1 in the sample is mapped to a time-domain feature vector through the first embedding network, and the position sequence at time t-1 in the sample is mapped to a geometric feature matrix through the second embedding network. The hidden state vector at time t is broadcast to each spatial node and mapped to a mechanism feature matrix consistent with the number of nodes through the third embedding network.

[0036] H4. The temporal feature vector, geometric feature matrix, and mechanism feature matrix are concatenated sequentially to obtain the full feature matrix.

[0037] H5. The full feature matrix is ​​processed sequentially through the first linear layer, the attention module, and the second linear layer to output the state evolution quantity.

[0038] H6. The state evolution quantity and the masked temperature sequence at time t-1 in the sample are superimposed to obtain the reconstructed temperature sequence at time t.

[0039] The hidden state vector at time t is obtained by processing it according to the following formula:

[0040]

[0041]

[0042] Where t is the time index, and t and t-1 represent the current time and the previous time, respectively; This represents the hidden state vector at time t. This represents the hidden state vector at time t-1; Indicates the reference ambient temperature; Indicates an antisymmetric interconnect matrix; The dissipation matrix represents the structure of the matrix. Represents a positive semidefinite dissipation matrix; Represents the hidden state vector Hamiltonian at the location; Represents the Hamiltonian function In the hidden state vector gradient at; Represents the input coupling matrix; This represents the dynamic branch coding features at time t-1.

[0043] The loss function is set according to the following formula:

[0044] ;

[0045]

[0046]

[0047] in, The loss function represents the model of the hot field reconstruction of the lead screw in the feed system; Indicates the data fitting term; Represents the gradient term weight coefficients. The gradient term representing physical consistency; The index indicates the axial position of the leadscrew. A discrete node; This represents the total number of discrete nodes along the axial direction of the leadscrew; and These are the weighting coefficients for the physical residual term and the spatial gradient matching term, respectively. , and These are the density, specific heat capacity, and thermal conductivity of the lead screw material, respectively. and These are the cross-sectional area and perimeter of the lead screw, respectively. The current moment; Indicates the first The actual temperature at each discrete node; Indicates the first The reconstructed temperature at each discrete node; Temperature after reconstruction For the current moment The first-order partial derivative; Indicates the first The spatial location of a discrete node; For true temperature Spatial location The first-order partial derivative; Temperature after reconstruction Spatial location The second-order partial derivative; and These are the convective heat transfer coefficients of the lead screw surface and the reference ambient temperature, respectively. For the first Volumetric heat generation rate at discrete nodes; The equivalent heat flux efficiency coefficient; For the current moment The instantaneous rotational speed of the lead screw; For the current moment The axial position trajectory of the nut; The parameters are heat source distribution parameters; the data fitting term uses mean square error, mean absolute error, or Huber loss.

[0048] II. A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described method.

[0049] 3. A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above method.

[0050] The beneficial effects of this invention are:

[0051] (1) The problem of cross-modal fusion between dynamic and thermal modes in the thermal field reconstruction process is solved by using an asymmetric broadcast modulation module, and the correlation information between different modes is extracted.

[0052] (2) By using the hidden state evolution of Hamiltonian theory with hidden ports and the constructed full characteristic matrix, the reversible energy exchange and irreversible dissipation in the system are explicitly decomposed, the non-thermodynamic oscillations in the reconstructed thermal field are suppressed and the physical residuals are reduced.

[0053] (3) The method of this invention achieves a deep integration of physical mechanisms and data-driven approaches by constructing a composite loss function that includes data fitting and physical consistency terms. The model can not only utilize sparse temperature measurement data, but also explicitly capture the heat generation patterns induced by dynamic trajectories, enabling it to maintain extremely low cumulative errors over long operating cycles. This high-fidelity, low-latency reconstruction capability allows the model to be directly deployed in machine tool CNC systems, supporting digital twin thermal monitoring and real-time accurate compensation for thermal errors. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0055] Figure 2This is a detailed flowchart of the method of the present invention, wherein... Figure 2 (a) in the diagram is a flowchart of the asymmetric broadcast modulation module. Figure 2 (b) is a flowchart of the Hamiltonian propagation module with port ⇲.

[0056] Figure 3 This is a schematic diagram illustrating the application scenario of thermal field reconstruction of the gantry milling machine feed system and ball screw feed chain in the embodiment. Figure 3 (a) in the figure is a subgraph of the thermal field reconstruction application at time t=250s. Figure 3 (b) in the figure is a subgraph for thermal field reconstruction at time t=500s. Figure 3 (c) in the figure is the subgraph for thermal field reconstruction at time t=750s. Figure 3 (d) in the figure represents the application subgraph for thermal field reconstruction at time t=100s. Figure 3 (e) in the figure represents the application subgraph for thermal field reconstruction at time t=1250s. Figure 3 (f) in the figure represents the application subgraph for thermal field reconstruction at time t=1500s. Figure 3 In the graph, (g) represents the application subgraph for thermal field reconstruction at time t=1750s. Figure 3 (h) in the figure represents the application subgraph for thermal field reconstruction at time t=2000s.

[0057] Figure 4 This is a qualitative comparison result of multiple models comparing the reconstructed thermal field with the thermal field gradient magnitude in the example, where... Figure 4 (a) in the figure is the X-Ham result diagram of the method of the present invention. Figure 4 (b) in the figure is the result of the Translator++ method. Figure 4 (c) in the figure is the result of the PAL-FNO method. Figure 4 (d) in the figure is the result of the PHNN method. Figure 4 (e) in the figure represents the result of the sPHNN method. Figure 4 (f) in the figure is the result of the HNN method. Figure 4 (g) in the figure represents the result of the DiffusionPDE method. Figure 4 (h) in the figure represents the result of the FNO method.

[0058] Figure 5 This is a spatial profile distribution map of the multi-timestep multi-prediction reconstructed thermal field in the embodiment, wherein... Figure 5 (a) in the diagram is a spatial profile at time t=400s. Figure 5 (b) in the diagram is a spatial profile at time t=800s. Figure 5 (c) in the diagram is a spatial profile at time t=1200s. Figure 5 (d) in the diagram is the spatial profile distribution at time t=1600s. Figure 5 (e) in the diagram is a spatial profile distribution at time t=2000s.

[0059] Figure 6 This is a time profile distribution of the reconstructed thermal field predicted at multiple time steps in the embodiment, wherein... Figure 6 (a) in the figure is a time profile distribution diagram of spatial location X=0mm. Figure 6 (b) in the figure is a time profile distribution diagram of spatial location X=250mm. Figure 6 (c) in the diagram is a time profile distribution diagram of spatial location X=500mm. Figure 6 (d) in the figure is the time profile distribution diagram of spatial location X=750mm. Figure 6 (e) in the figure is a time profile distribution diagram of spatial location X=1000mm.

[0060] Figure 7 This is a comparison chart of the reconstruction error and physical indices of the method of the present invention relative to the baseline method on the test set in the embodiment.

[0061] Figure 8 This is a comparison chart of the error accumulation and parameter quantity between the method of the present invention and other baseline methods in the embodiments, wherein... Figure 8 (a) in the figure is a comparison chart of model parameter quantities. Figure 8 (b) in the figure is a comparison of long-range stability.

[0062] Figure 9 This is a comparison chart of the global time error between the method of the present invention and other baseline methods in the embodiments.

[0063] Figure 10 This figure shows the cross-dataset test results of the method of the present invention and other baseline methods in the embodiments. Detailed Implementation

[0064] The present invention will now be described in more detail with reference to the accompanying drawings and embodiments. However, the present invention is not limited thereto. For those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

[0065] This embodiment uses the thermal field reconstruction at the discrete nodes of the ball screw axial direction in the feed system of a gantry milling machine as an example. The spatial domain is discretized into N nodes, and the time is sampled uniformly with step sizes.

[0066] like Figure 1 and Figure 2 As shown, the feed system lead screw thermal field reconstruction method of this embodiment is implemented according to the following steps:

[0067] S1. Through simulation, dense temperature observation data and dynamic excitation data of the feed system screw are collected over a continuous time period to construct a screw thermal field reconstruction dataset.

[0068] Temperature observation data at each moment includes a position sequence consisting of the positions of all discrete nodes along the axis of the lead screw in the discrete space and a temperature sequence consisting of the temperature corresponding to each position; dynamic excitation data at each moment includes lead screw rotation speed, feed rate, and nut position trajectory, etc.

[0069] S11. Through simulation, dense temperature observation data and dynamic excitation data of the feed system screw are collected over a continuous time period.

[0070] In the simulation process of this implementation, the temperature at the discrete node locations of the one-dimensional lead screw simulation can be governed by the heat conduction equation containing convection and volumetric heat, denoted as:

[0071]

[0072] in, , and These are the density, specific heat capacity, and thermal conductivity of the lead screw material, respectively. The spatial position of the discrete node along the axis of the lead screw; For time; This represents the actual temperature at the corresponding discrete node location; and Let be the cross-sectional area and perimeter of the lead screw; The convective heat transfer coefficient; For reference ambient temperature; The volumetric heat generation rate.

[0073] The frictional heat generated by the moving nut can be approximated by a Gaussian heat source that migrates with position. The heat conduction expression of its Gaussian thermal field can be written as:

[0074]

[0075] in For a moment The axial position of the nut Instantaneous rotational speed The equivalent heat flux efficiency coefficient. This is the parameter for the width of the heat source space.

[0076] Furthermore, the temperature observation data and dynamic excitation data at the same time are aligned on the time axis. After alignment, they are normalized to the interval [-1,1] or zero mean unit variance to facilitate training stability and preserve temperature direction information.

[0077] Specifically, the location sequence of the collected temperature observation data consists of the positions of N nodes, and the temperature sequence consists of the temperatures corresponding to the N node positions. The masked temperature sequence only contains the temperature values ​​corresponding to the n node positions, and the temperature values ​​corresponding to the (Nn) points are masked. Here, n is much smaller than N.

[0078] In this implementation, the location sequence of the collected temperature observation data consists of the locations of 100 nodes, and the temperature sequence consists of the temperatures corresponding to the locations of those 100 nodes. The masked temperature sequence only contains the temperature values ​​corresponding to the locations of 5 nodes; the temperature values ​​corresponding to the 95th node are masked.

[0079] S12. For the dense temperature observation data at time t-1, mask some temperature values ​​in the temperature sequence to obtain the masked temperature sequence; combine the sparse masked temperature sequence with the corresponding position sequence to form the sparse masked temperature observation data at time t-1; combine the sparse masked temperature observation data at time t-1 with the dynamic excitation data at time t-1 as sparse model input data.

[0080] S13. Use the temperature sequence from the dense temperature observation data at time t as the label data for the model output.

[0081] S14. Combine the model input data obtained in S12 with the label data obtained in step S13 to construct a single sample for model training.

[0082] S15. Repeat steps S12-S14 to construct several samples, thereby obtaining the lead screw thermal field reconstruction dataset.

[0083] Specifically, the temperature observation data acquired through simulation is dense. For example, temperature observation data at one hundred points are collected in the simulation of the feed system's lead screw. After masking, the resulting masked temperature sequence only contains data from a subset of points (sparse data). By using sparse data as input and dense data as labels, the model learns the relationships between them, enabling it to reconstruct a dense temperature field even when sparse data is acquired under actual operating conditions.

[0084] S2. Construct a feed system screw thermal field reconstruction model. Train the feed system screw thermal field reconstruction model based on the screw thermal field reconstruction dataset to obtain the trained feed system screw thermal field reconstruction model.

[0085] The training process of the feed system leadscrew thermal field reconstruction model is as follows:

[0086] D1. The masked temperature observation data and the dynamic excitation data at time t-1 in a single sample are input together into the coding module of the asymmetric broadcast modulation module for processing, so as to obtain the temperature branch coding features and the dynamic branch coding features at time t-1 respectively.

[0087] D2, the temperature branch coding feature, and the dynamics branch coding feature are input together into the cross-modal fusion prediction module of the asymmetric broadcast modulation module for processing to obtain the hidden state vector at time t-1.

[0088] like Figure 2 As shown in (a), the asymmetric broadcast modulation module performs the following steps:

[0089] The specific processing steps of the encoding module are as follows:

[0090] F1. The masked temperature observation data and the dynamic excitation data at time t-1 are input into the first coding sub-network and the second coding sub-network, respectively, to obtain the temperature branch coding features and dynamic branch coding features that can be aligned in the channel dimension.

[0091] Specifically, the method of the present invention does not impose a unique limitation on the first coding sub-network and the second coding sub-network.

[0092] In this embodiment, the first encoding sub-network specifically adopts a structure consisting of a first Conv2d, a first ReLU, a first MaxPool2d, a second Conv2d, a second ReLU, a second MaxPool2d, a third Conv2d, and a third ReLU connected in series. The second encoding sub-network specifically adopts a structure consisting of a first Conv1d, a fourth ReLU, a first MaxPool1d, a second Conv1d, a fifth ReLU, a second MaxPool1d, a third Conv1d, a sixth ReLU, and an AvgPool1d connected in series.

[0093] F2. Align the temperature branch coding features and the dynamics branch coding features along the channel dimension to obtain the aligned temperature branch coding features and dynamics branch coding features.

[0094] The specific processing steps of the cross-modal fusion prediction module are as follows:

[0095] F3. The aligned temperature branch coding features and the aligned dynamics branch coding features are fused using cross-attention to obtain the fused features.

[0096] F4. After concatenating the fused features and the temperature branch coding features, flatten them into a one-dimensional vector and input them into the multilayer perceptron mapping network to obtain the hidden state vector at time t-1 containing the port Hamiltonian dynamics.

[0097] D3. The masked temperature observation data at time t-1, the dynamic branch coding features at time t-1, and the hidden state vector at time t-1 are input together into the Hamiltonian propagation module with port t for processing to obtain the reconstructed temperature sequence at time t.

[0098] like Figure 2 As shown in (b), the Hamiltonian propagation module with port ☐ performs the following steps:

[0099] H1, the hidden state vector at time t-1 The inputs are fed into four multilayer perceptrons respectively, yielding antisymmetric interconnection matrices. Dissipation constitutes a matrix Hamiltonian and the input coupling matrix .

[0100] Specifically, a high-dimensional hidden state vector is achieved through one of the multilayer perceptrons. Hamiltonian mapped to scalar .

[0101] H2, antisymmetric interconnection matrix Dissipation constitutes a matrix Hamiltonian Input coupling matrix Dynamic branch coding features at time t-1 The hidden state vector at time t is obtained by matrix combination. .

[0102] Specifically, the method of this invention is based on Hamiltonian mechanics and symplectic geometry. In generalized coordinates... With generalized momentum The Hamiltonian equation can be written as follows:

[0103]

[0104] in, and These represent the derivatives of the displacement and momentum of the feed system, respectively.

[0105] In the hidden state vector In the embedded representation, the invertible partial evolution equation of the feed system can be written as:

[0106]

[0107] in, For an antisymmetric interconnection matrix and satisfying When there are only reversible internal exchanges and open dissipation is neglected, the Hamiltonian is conserved along the trajectory, i.e.:

[0108]

[0109] The method of this invention uses the relative velocity (∂ / ∂t) to the reference environment as the Hamiltonian potential. Under this condition, the Hamiltonian can be written as:

[0110]

[0111] in , and These represent energy, entropy, and generalized matter or mass-related quantities, respectively. It is a constant. and Here, denoted by the reference ambient temperature and the reference chemical potential, respectively. For an open and dissipative feed system, when using the tandem Hamiltonian form, its hidden state evolution satisfies:

[0112]

[0113]

[0114] in, The dissipation matrix is ​​constructed; It is a positive semidefinite dissipation matrix; The input coupling matrix; For external dynamic excitation (dynamic branch encoding characteristics at time t-1); a positive semidefinite dissipation matrix is ​​introduced. Subsequently, the irreversible part of the feed system will correspond to dissipation and non-equilibrium entropy production, which will be used to constrain the thermodynamic reliability of the reconstructed trajectory.

[0115] Therefore, the hidden state vector at time t satisfies the following formula:

[0116]

[0117]

[0118] Where t is the time index, and t and t-1 represent the current time and the previous time, respectively; This represents the hidden state vector at time t. This represents the hidden state vector at time t-1; Indicates the reference ambient temperature; Represents the hidden state vector at time t-1. The antisymmetric interconnect matrix below; Represents the hidden state vector at time t-1. The dissipation under these conditions forms a matrix; Represents the hidden state vector at time t-1. The positive semidefinite dissipation matrix under the given conditions; Represents the hidden state vector Hamiltonian (scalar) at the location; Represents the Hamiltonian function In the hidden state vector The gradient (vector) at that point; Represents the hidden state vector at time t-1. The input coupling matrix below; This represents the dynamic branch coding features at time t-1.

[0119] Specifically, antisymmetric interconnection matrix A matrix whose transpose equals its negative is used to characterize reversible internal energy exchange. (Positive semi-definite dissipation matrix) Compared with reference ambient temperature The reciprocals work together to characterize irreversible dissipation. Input coupling matrix. Dynamic branch coding features at time t-1 The multiplication forms a port input term, which is used to inject the excitation of heat generation by the feed motion into the latent state dynamics.

[0120] Construction of the full feature matrix: Construct the temporal feature vector, geometric feature matrix, and mechanism feature matrix respectively, and then concatenate them to obtain the full feature matrix. The specific steps are steps H3 and H4.

[0121] H3. The masked temperature sequence at time t-1 in the sample is mapped to a time-domain feature vector through the first embedding network, and the position sequence at time t-1 in the sample (normalized spatial coordinates of each discrete node) is mapped to a geometric feature matrix through the second embedding network. The hidden state vector at time t is broadcast to each spatial node and mapped to a mechanism feature matrix consistent with the number of nodes through the third embedding network.

[0122] In this embodiment, both the first and second embedded networks are multilayer perceptrons. The third embedded network is a linear layer or a small multilayer perceptron.

[0123] H4. The temporal feature vector, geometric feature matrix and mechanism feature matrix are concatenated sequentially to obtain the full feature matrix; the full feature matrix forms a local representation of the fusion thermal state, geometric position and Hamiltonian dynamic mechanism containing the port at each node.

[0124] Dense field update: Perform eigenvalue transformation on the full feature matrix to generate state evolution variables; use the state evolution variables as the dense temperature field increment, and superimpose them onto the dense temperature field at the current time step to obtain the dense temperature field at the next time step. The specific steps are steps H5 and H6.

[0125] EPHS Guiding Module: H5 processes the full feature matrix sequentially through the first linear layer, the attention module, and the second linear layer to output the state evolution at time t-1.

[0126] In this embodiment, the attention module specifically adopts eidetic attention from Transolver++. Eidetic attention is the attention method disclosed in the paper "Transolver++: An Accurate Neural Solver for PDEson Million-Scale Geometries".

[0127] H6. The state evolution at time t-1 is superimposed with the masked temperature sequence at time t-1 in the sample to obtain the reconstructed temperature sequence at time t.

[0128] D4. Calculate the loss function based on the reconstructed temperature sequence at time t and the corresponding label data (temperature sequence at time t in the sample), and update the model parameters by backpropagation based on the calculated loss function.

[0129] D5. Repeat steps D1-D4 until the training of the hot field reconstruction model of the feed system screw is completed.

[0130] The loss function of the feed system leadscrew thermal field reconstruction model is set according to the following formula:

[0131]

[0132]

[0133]

[0134] in, The loss function represents the model of the hot field reconstruction of the lead screw in the feed system; Indicates the data fitting term; Represents the gradient term weight coefficients. The gradient term representing physical consistency; The index indicates the axial position of the leadscrew. A discrete node; This represents the total number of discrete nodes along the axial direction of the feed system's leadscrew in the discrete space. and These are the weighting coefficients for the physical residual term and the spatial gradient matching term, respectively. , and These are the density, specific heat capacity, and thermal conductivity of the lead screw material, respectively. and These are the cross-sectional area and perimeter of the lead screw, respectively. The current moment; Indicates the first The actual temperature at each discrete node; Indicates the first The reconstructed temperature at each discrete node; For the first Reconstructed temperature at each discrete node For the previous moment The first-order partial derivative is used to characterize the transient thermal evolution rate; Indicates the first The spatial location of a discrete node; For the first The true temperature at each discrete node Spatial location The first-order partial derivative; For the first Reconstructed temperature at each discrete node Spatial location The second-order partial derivative is used to characterize the intensity of thermal diffusion; and These are the convective heat transfer coefficients of the lead screw surface and the reference ambient temperature, respectively. For the first Volumetric heat generation rate at discrete nodes; The equivalent heat flux efficiency coefficient; For the current moment The instantaneous rotational speed of the lead screw; For the current moment The axial position trajectory of the nut; The heat source distribution parameters define the width of the heat source space; It is a constant; It is an exponential function with the natural constant e as its base.

[0135] Specifically, the total number of discrete nodes Weighting coefficients of physical residual terms Weight coefficients of spatial gradient matching term ,density Specific heat capacity thermal conductivity Cross-sectional area ,perimeter Real temperature convective heat transfer coefficient Reference ambient temperature Equivalent heat flux efficiency coefficient Instantaneous speed of the lead screw Nut axial position trajectory Heat source distribution parameters All parameters are preset, known, or readily acquireable. Reconstructed temperature. The data is obtained from the reconstructed temperature sequence. In this embodiment, the mean squared error is used for the data fitting term.

[0136] The loss function in this invention employs a physically consistent gradient term, explicitly introducing the partial differential equation of heat conduction and time smoothness constraints into the model optimization process. This allows the neural network to follow the thermodynamic physical evolution manifold under extremely sparse perception conditions. Its core value lies in reducing the physical illusion of purely data-driven models together with the Hamiltonian module containing the tangent port, effectively suppressing non-physical oscillations and cumulative drift in long-range recursion processes. While ensuring high accuracy of full-field heat flow reconstruction, it also improves the mechanistic credibility and long-term operational stability of the machine tool digital twin system under complex and variable operating conditions.

[0137] S3. Deploy the trained feed system screw thermal field reconstruction model under actual working conditions. Input the temperature observation data and dynamic excitation data collected under actual working conditions into the deployed feed system screw thermal field reconstruction model, and output the reconstructed dense temperature sequence.

[0138] In this embodiment, the temperature sequence in the temperature observation data collected under actual operating conditions only has temperature values ​​corresponding to 5 node positions. The reconstructed dense temperature sequence has temperature values ​​corresponding to 100 node positions.

[0139] In actual working conditions, only a few sensors are arranged on the feed system screw, forming a small number of discrete stages. Therefore, the collected temperature observation data is sparse. The sparse temperature observation data and dynamic excitation data are input together into the feed system screw thermal field reconstruction model to reconstruct a dense temperature sequence.

[0140] S4. The reconstructed dense temperature sequence and the corresponding position sequence are combined to form the reconstructed dense temperature observation data, thereby realizing the reconstruction of the hot field of the feed system screw.

[0141] This embodiment provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the method of the present invention.

[0142] This embodiment also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method of the present invention.

[0143] To verify the beneficial effects of this invention, a benchmark lead screw thermal field reconstruction dataset was generated using a thermal simulation engine calibrated experimentally or validated by an analytical model. The generalization performance of the model was tested by randomizing the training and testing conditions on parameters such as boundary convection coefficient, friction factor, ambient temperature, and maximum feed rate. Simultaneously, the number of sparse measurement points under available operating conditions was limited to less than five percent of the total number of discrete nodes to simulate the situation of limited sensing resources in industrial settings.

[0144] like Figure 3 The diagram shows a schematic of the application scenario of thermal field reconstruction for the feed system and ball screw feed chain of a gantry milling machine. Figure 3 (a) in the figure is a subgraph of the thermal field reconstruction application at time t=250s. Figure 3 (b) in the figure is a subgraph for thermal field reconstruction at time t=500s. Figure 3 (c) in the figure is the subgraph for thermal field reconstruction at time t=750s. Figure 3 (d) in the figure represents the application subgraph for thermal field reconstruction at time t=100s. Figure 3 (e) in the figure represents the application subgraph for thermal field reconstruction at time t=1250s. Figure 3 (f) in the figure represents the application subgraph for thermal field reconstruction at time t=1500s. Figure 3 In the graph, (g) represents the application subgraph for thermal field reconstruction at time t=1750s. Figure 3 (h) in the figure represents the application subgraph for thermal field reconstruction at time t=2000s.

[0145] Fourier Neural Operator (FNO), Physically Enhanced Neural Operator (PAL-FNO), DiffusionPDE, Transolver++, and Ported Hamiltonian Neural Networks (PHNN, sPHNN) were selected as baselines for comparison under the same hidden dimension and training budget. Image metrics such as root mean square error, coefficient of determination, structural similarity, and edge structure similarity are reported, along with physical consistency metrics such as peak temperature error, root mean square error of gradient, root mean square error of Laplacian, temporal smoothness, and physical residuals of the heat conduction equation. In qualitative comparisons, the temperature field and spatial temperature gradient amplitude are simultaneously displayed to verify whether the heat flow direction and high gradient regions are correctly reconstructed. In temporal comparisons, multiple spatial nodes can be extracted to plot temperature-time curves to verify long-term recursive stability and noise suppression capabilities. Comparison results with each network are as follows: Figures 4-10 As shown.

[0146] in, Figure 4 A qualitative comparison result diagram of multiple models for comparing the reconstructed thermal field with the thermal field gradient magnitude. Figure 4 (a) in the figure is the X-Ham result diagram of the method of the present invention. Figure 4 (b) in the figure is the result of the Translator++ method. Figure 4 (c) in the figure is the result of the PAL-FNO method. Figure 4 (d) in the figure is the result of the PHNN method. Figure 4 (e) in the figure represents the result of the sPHNN method. Figure 4 (f) in the figure is the result of the HNN method. Figure 4 (g) in the figure represents the result of the DiffusionPDE method. Figure 4 (h) in the figure represents the result of the FNO method.

[0147] according to Figure 4 As can be seen, the method of this invention can accurately reconstruct a temperature distribution that is highly consistent with the real field, especially in capturing the drastic gradient changes caused by moving heat sources. In contrast, other baseline methods exhibit significant random noise and ringing artifacts in the gradient plot, resulting in poor physical consistency.

[0148] in, Figure 5 To provide a spatial profile of the reconstructed thermal field over multiple time steps and predictions. Figure 5 (a) in the diagram is a spatial profile at time t=400s. Figure 5 (b) in the diagram is a spatial profile at time t=800s. Figure 5 (c) in the diagram is a spatial profile at time t=1200s. Figure 5 (d) in the diagram is the spatial profile distribution at time t=1600s. Figure 5 (e) in the diagram is a spatial profile distribution at time t=2000s.

[0149] according to Figure 5 It can be seen that the spatial profile reconstruction results of the method of the present invention can closely fit the real curve at multiple typical time steps. Even in the later stage of operation when the cumulative error usually reaches the peak, it can still accurately restore the peak temperature and heat flow edge, which proves the model's ability to capture the evolution law of volume heat distribution.

[0150] in, Figure 6 This is a time profile distribution of the reconstructed thermal field predicted over multiple time steps. Figure 6 (a) in the figure is a time profile distribution diagram of spatial location X=0mm. Figure 6 (b) in the figure is a time profile distribution diagram of spatial location X=250mm. Figure 6 (c) in the diagram is a time profile distribution diagram of spatial location X=500mm. Figure 6 (d) in the figure is the time profile distribution diagram of spatial location X=750mm. Figure 6 (e) in the figure is a time profile distribution diagram of spatial location X=1000mm.

[0151] according to Figure 6It can be seen that at the five selected representative spatial nodes, the method of the present invention exhibits good tracking stability over the entire time trajectory. Even at the node position where the thermal gradient fluctuation is most severe, it can effectively suppress non-physical jitter, indicating that the Hamiltonian propagation module with port 1 plays a role in maintaining physical consistency.

[0152] in, Figure 7 This is a comparison graph showing the reconstruction error and physical indices of the method of the present invention relative to the baseline method on the test set.

[0153] according to Figure 7 It can be seen that the method of the present invention is effective in RMSE, MAE, and R 2 It outperforms all baseline models in all standard metrics, as well as multiple physical consistency metrics such as PTE and PR.

[0154] in, Figure 8 This is a comparison chart of the cumulative error and parameter count between the method of this invention and other baseline methods. Figure 8 (a) in the figure is a comparison chart of model parameter quantities. Figure 8 (b) in the figure is a comparison of long-range stability.

[0155] according to Figure 8 As can be seen, the method of this invention has extremely high parameter efficiency, achieving optimal accuracy with only 0.37M parameters. Furthermore, in long-range stability comparisons, the method of this invention can maintain the prediction error at a stable low level, avoiding the cumulative drift common in traditional operator learning models.

[0156] in, Figure 9 This is a comparison chart of the global time error of the method of this invention with other baseline methods.

[0157] according to Figure 9 It can be seen that the instantaneous RMSE curve of the method of the present invention is always at the bottom of all the comparative models and fluctuates very little in the complete test sequence.

[0158] in, Figure 10 This figure shows the results of cross-dataset testing comparing the method of this invention with other baseline methods.

[0159] according to Figure 10 It can be seen that the method of the present invention exhibits strong robustness under different boundary conditions and dynamic working conditions, and all error indicators remain at a consistently low level, proving that the model learns the underlying physical control law rather than simply the features of the training set.

[0160] Furthermore, the quantitative results of the comparative tests of the method of the present invention with other typical baseline models on the test set on some basic metrics in deep learning are shown in Table 1 below:

[0161] Table 1:

[0162]

[0163] As can be seen from the quantitative data in Table 1, this invention has achieved optimal levels in core accuracy indicators such as RMSE, MAE, and SSIM. Among these, the root mean square error and mean absolute error are both percentage errors between the predicted and actual values. The coefficient of determination, structural similarity, and marginal structure similarity are all dimensionless indicators.

[0164] To ensure the method of this invention has good industrial significance and physical authenticity, this invention further compared several models, including the model of this invention, on some physical and industrial indicators. The specific comparison results are shown in Table 2.

[0165] Table 2:

[0166]

[0167] The unit of the peak error index is degrees Celsius. The unit of the root mean square error index is ( ), The unit of the Laplace root mean square error index is The unit of the time smoothness index is The unit of the physical residual index is As shown in Table 2, the method of the present invention achieves order-of-magnitude precision optimization compared with traditional neural operators, especially in terms of peak temperature error reflecting industrial safety and physical residual reflecting physical reality, where it has superior performance.

[0168] The numerical results of this embodiment fully demonstrate the potential advantages of the present invention over the baseline in terms of accuracy and physical consistency. Not only are the number of model parameters small, but there are also significant improvements in various performance indicators.

[0169] Furthermore, this invention explicitly embeds a physical framework with Hamiltonian antisymmetric and dissipative structures into the neural network, mathematically ensuring that the field reconstruction process strictly adheres to the laws of energy conservation and thermal decay. This deep mechanistic embedding not only significantly enhances the model's spatial interpolation capability under extremely sparse sensor conditions but also endows the model with excellent noise suppression and long-range extrapolation potential, laying a solid physical foundation for realizing high-fidelity machine tool digital twins and real-time accurate thermal error compensation.

[0170] The above embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for reconstructing the thermal field of a feed system screw based on cross-modal fusion and Hamiltonian with a tangent port, characterized in that, Includes the following steps: S1. Through simulation, temperature observation data and dynamic excitation data of the feed system screw are collected over a continuous time period to construct a screw thermal field reconstruction dataset. The temperature observation data at each moment includes a position sequence composed of the positions of all discrete nodes along the axis of the simulated lead screw and a temperature sequence composed of the temperature corresponding to each position; the dynamic excitation data at each moment includes the lead screw rotation speed, feed rate and nut position trajectory. S2. Construct a feed system screw thermal field reconstruction model. Train the feed system screw thermal field reconstruction model based on the screw thermal field reconstruction dataset to obtain the trained feed system screw thermal field reconstruction model. The training process of the feed system lead screw thermal field reconstruction model is as follows: D1. The masked temperature observation data and dynamic excitation data at time t-1 in a single sample are input together into the coding module of the asymmetric broadcast modulation module for processing, and the temperature branch coding features and dynamic branch coding features are obtained respectively. D2, temperature branch coding features and dynamics branch coding features are input together into the cross-modal fusion prediction module of the asymmetric broadcast modulation module for processing to obtain the hidden state vector; D3. Input the masked temperature observation data, dynamic branch coding features and hidden state vector into the Hamiltonian propagation module with port t for processing to obtain the reconstructed temperature sequence at time t. D4. Calculate the loss function based on the reconstructed temperature sequence at time t and the corresponding label data, and then perform backpropagation to update the model parameters based on the calculated loss function. D5. Repeat steps D1-D4 until the training of the feed system screw thermal field reconstruction model is completed. S3. Deploy the trained feed system screw thermal field reconstruction model under actual working conditions, input the temperature observation data and dynamic excitation data collected under actual working conditions into the deployed feed system screw thermal field reconstruction model, and output the reconstructed temperature sequence. S4. The reconstructed temperature sequence and the corresponding position sequence are combined to form the reconstructed temperature observation data, thereby realizing the reconstruction of the hot field of the feed system screw.

2. The method for reconstructing the thermal field of a feed system screw based on cross-modal fusion and Hamiltonian with a port, as described in claim 1, is characterized in that... Step S1 specifically involves: S11. Through simulation, collect temperature observation data and dynamic excitation data of the feed system screw over a continuous time period; S12. For the temperature observation data at time t-1, mask a portion of the temperature values ​​in the temperature sequence to obtain the masked temperature sequence; combine the masked temperature sequence with the corresponding position sequence to form the masked temperature observation data at time t-1; combine the masked temperature observation data at time t-1 with the dynamic excitation data at time t-1 as the model input data. S13. Use the temperature sequence in the temperature observation data at time t as the label data for the model output; S14. Combine the model input data obtained in S12 and the label data obtained in step S13 to construct a single sample for model training. S15. Repeat steps S12-S14 to construct several samples, thereby obtaining the lead screw thermal field reconstruction dataset.

3. The method for reconstructing the thermal field of a feed system screw based on cross-modal fusion and Hamiltonian with a port, as described in claim 1, is characterized in that... The asymmetric broadcast modulation module performs the following steps: F1. Input the masked temperature observation data and the dynamic excitation data at time t-1 into the first coding sub-network and the second coding sub-network respectively to obtain the temperature branch coding features and the dynamic branch coding features respectively. F2. Align the temperature branch coding features and the dynamics branch coding features along the channel dimension to obtain the aligned temperature branch coding features and dynamics branch coding features. F3. The aligned temperature branch coding features and the aligned dynamics branch coding features are fused through cross attention to obtain the fused features; F4. After concatenating the fused features and the temperature branch coding features, flatten them into a one-dimensional vector and input them into the multilayer perceptron mapping network to obtain the hidden state vector.

4. The method for reconstructing the thermal field of a feed system screw based on cross-modal fusion and Hamiltonian with a port, as described in claim 1, is characterized in that... The Hamiltonian propagation module containing the port is executed according to the following steps: H1. Input the hidden state vectors into four multilayer perceptrons respectively to obtain the antisymmetric interconnection matrix, dissipative composition matrix, Hamiltonian and input coupling matrix respectively. H2. The hidden state vector at time t is obtained by combining the antisymmetric interconnection matrix, dissipative composition matrix, Hamiltonian, input coupling matrix and dynamic branch coding features. H3. The masked temperature sequence in the sample at time t-1 is mapped into a time-domain feature vector through the first embedding network, and the position sequence in the sample at time t-1 is mapped into a geometric feature matrix through the second embedding network. The hidden state vector at time t is broadcast to each spatial node and mapped to a mechanism feature matrix consistent with the number of nodes via a third embedding network; H4. The temporal feature vector, geometric feature matrix, and mechanism feature matrix are concatenated sequentially to obtain the full feature matrix; H5. The full feature matrix is ​​processed sequentially through the first linear layer, the attention module, and the second linear layer to output the state evolution quantity. H6. The state evolution quantity and the masked temperature sequence at time t-1 in the sample are superimposed to obtain the reconstructed temperature sequence at time t.

5. The method for reconstructing the thermal field of a feed system screw based on cross-modal fusion and Hamiltonian with a port, as described in claim 4, is characterized in that: The hidden state vector at time t is obtained by processing it according to the following formula: ； ； Where t is the time index, and t-1 represents the current time and the previous time, respectively; This represents the hidden state vector at time t. This represents the hidden state vector at time t-1; Indicates the reference ambient temperature; Indicates an antisymmetric interconnect matrix; The dissipation matrix represents the structure of the matrix. Represents a positive semidefinite dissipation matrix; Represents the hidden state vector Hamiltonian at the location; Represents the Hamiltonian function In the hidden state vector gradient at; Represents the input coupling matrix; This represents the dynamic branch coding features at time t-1.

6. The method for reconstructing the thermal field of a feed system screw based on cross-modal fusion and Hamiltonian with a tangent port, as described in claim 1, is characterized in that: The loss function is set according to the following formula: ； ； ； in, Represents the loss function; Indicates the data fitting term; Represents the gradient term weight coefficients. Represents the gradient term; The index indicates the axial position of the leadscrew. A discrete node; This represents the total number of discrete nodes; and All are weighting coefficients; , and These are the density, specific heat capacity, and thermal conductivity of the lead screw, respectively. and These are the cross-sectional area and perimeter of the lead screw, respectively. The current moment; Indicates the actual temperature; Indicates the temperature after reconstruction; Temperature after reconstruction For the current moment The first-order partial derivative; Indicates spatial location; For true temperature Spatial location The first-order partial derivative; Temperature after reconstruction Spatial location The second-order partial derivative; and These are the convective heat transfer coefficient and the reference ambient temperature, respectively. The heat generation rate by volume; The equivalent heat flux efficiency coefficient; The instantaneous rotational speed of the leadscrew; This represents the axial position trajectory of the nut. The parameters are heat source distribution parameters; the data fitting term uses mean square error, mean absolute error, or Huber loss.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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