A laser soldering temperature field real-time prediction and parameter inversion method and system

Abstract

The present application belongs to the field of microelectronic intelligent manufacturing and digital twin technology, and specifically relates to a laser soft soldering temperature field real-time prediction and parameter inversion method and system. The method comprises: obtaining the geometric and physical parameters of the measured solder paste, and simultaneously obtaining the laser power time sequence data of the laser processing process; constructing a geometric feature coding neural network based on a deep residual architecture, combining the geometric and physical parameters to obtain local physical parameters; constructing a spherical cap geometry model, combining the geometric and physical parameters to obtain an equivalent density; based on the geometric and physical parameters and the equivalent density, constructing a variable cross-section one-dimensional heat conduction finite element grid model with mass conservation constraint; based on the variable cross-section one-dimensional heat conduction finite element grid model, combining the laser power time sequence data, the local physical parameters and the equivalent density, using the lumped mass format and the implicit time integration algorithm, obtaining the predicted temperature field data and the inverted thermal physical parameters.

Description

Technical Field

[0001] This invention belongs to the field of microelectronic intelligent manufacturing and digital twin technology, specifically relating to a method and system for real-time prediction of laser soldering temperature field and parameter inversion. Background Technology

[0002] As electronic packaging evolves towards higher density and miniaturization, laser soldering, with its advantages of non-contact and localized heating, has become a core process for interconnecting microelectronic devices. During soldering, the temperature field evolution at the solder joint directly determines the growth of intermetallic compounds and the reliability of the connection. However, existing modeling and monitoring technologies face a dual bottleneck: traditional finite element methods are computationally intensive and have rigid parameter settings, making it difficult to adaptively handle disturbances caused by phase transitions in solder paste due to temperature changes, as well as significant differences in boundary thermal conductivity under complex conditions such as grounded and ungrounded environments, leading to a substantial decrease in model prediction accuracy under varying environments; while purely data-driven neural network models, although inferring rapidly, often result in predictions that violate the laws of mass or energy conservation due to a lack of physical constraints, and cannot invert contact thermal resistance or absorptivity parameters with clear physical meaning. Therefore, this invention proposes a modeling and parameter inversion method that deeply integrates physical control equations with deep learning, satisfying both real-time performance and geometric generalization capabilities while strictly adhering to physical conservation laws. Summary of the Invention

[0003] To overcome the problems of low computational efficiency and difficulty in handling phase transitions in traditional finite element methods, as well as the lack of physical constraints and difficulty in inverting real thermal property parameters in pure data-driven models, this invention provides a method and system for real-time prediction of temperature field and parameter inversion in laser soldering. It aims to adaptively handle the disturbances caused by phase transitions in solder paste due to temperature changes, and effectively solve the problems of high-precision mechanism modeling and real-time parameter identification under complex working conditions of variable cross-section geometry and grounded / ungrounded conditions.

[0004] To achieve the above objectives, the present invention provides the following solution: A method for real-time prediction of temperature field and parameter inversion in laser soldering, the method comprising: The geometric and physical parameters of the solder paste to be tested are obtained, and the laser power timing data of the laser processing process are also obtained. A geometric feature encoding neural network based on a deep residual architecture is constructed, and local physical parameters are obtained by combining the geometric physical parameters. Construct a spherical cap geometric model and, in conjunction with the aforementioned geometric and physical parameters, obtain the equivalent density; Based on the aforementioned geometric and physical parameters and the equivalent density, a one-dimensional thermal conduction finite element mesh model with mass conservation constraints is constructed. Based on a variable cross-section one-dimensional thermal conduction finite element mesh model, combined with the laser power time series data, the local physical parameters, and the equivalent density, the predicted temperature field data and the inverted thermal property parameters are obtained using a lumped mass scheme and implicit time integration algorithm.

[0005] Preferably, the geometric feature encoding neural network includes: a geometric feature encoding module; The geometric feature encoding module first performs dimensionless processing on the input geometric physical parameters and the height-to-diameter ratio calculated therefrom, then adaptively extracts nonlinear geometric features that are strongly correlated with the physical parameters, and finally maps and outputs local physical parameters.

[0006] Preferably, the method for constructing a spherical cap geometric model and obtaining the equivalent density by combining the geometric and physical parameters includes: ; in, For equivalent density, The measured physical quality of the solder paste. The geometric volume of the finite element mesh. The number of elements in the finite element mesh. The average cross-sectional area, For the first The axial height of each unit.

[0007] Preferably, the method for constructing a one-dimensional thermal conduction finite element mesh model with mass conservation constraints based on the geometric physical parameters and the equivalent density includes: Substituting the equivalent density and cross-sectional area into the one-dimensional variable cross-section unsteady heat conduction control equation: ; in, This represents the dynamic specific heat capacity that varies with temperature and heating rate. As the axial height z The changing cross-sectional area function, For temperature, For time, Thermal conductivity as a function of temperature; The formula for calculating laser heat flux density is: ; in, For laser absorption rate, For laser power, The equivalent projected area of ​​the laser spot at the top of the spherical cap; Coupled top boundary conditions: ; in, For dot painting height, This refers to the heat loss on the upper surface of the solder paste. By using the equivalent density in the one-dimensional variable cross-section unsteady heat conduction control equation This ensures that the variable cross-section one-dimensional heat conduction finite element mesh model satisfies the energy conservation constraint.

[0008] Preferably, the one-dimensional variable cross-section unsteady-state heat conduction control equation adopts a dynamic physical parameter model that evolves with the phase change state, including: Dynamic laser absorptivity model: ; in, The initial laser absorption rate, This is the attenuation coefficient, used to simulate the light absorption attenuation caused by the melting and brightening of solder paste. The liquid phase fraction at the top of the solder paste; Non-equilibrium specific heat capacity model: ; in, Based on specific heat capacity, As a rate-sensitive factor for specific heat capacity, This is the rate of temperature change, used to compensate for non-equilibrium heat capacity fluctuations during rapid heating.

[0009] Preferably, the method for obtaining the predicted temperature field data and inverted thermal property parameters based on a variable cross-section one-dimensional heat conduction finite element mesh model, combined with the laser power time series data, the local physical parameters, and the equivalent density, using a lumped mass scheme and implicit time integration algorithm, includes: ; in, for n Temperature vector at time +1 for n Temperature vector at time, To diagonalize the quality matrix, Here is the stiffness matrix. For time step, Explicitly includes laser heat flow and dynamic heat loss.

[0010] Preferably, the method further includes: The deviation between the calculated temperature field data and the measured temperature data is used to calculate the gradient of the deviation with respect to the output parameters of the geometric feature encoding neural network using an automatic differentiation mechanism, and the weights of the geometric feature encoding neural network are updated. End-to-end physical parameter inversion is achieved through the backpropagation algorithm.

[0011] The present invention also provides a real-time prediction and parameter inversion system for laser soldering temperature field, the system being used to implement the aforementioned method, the system comprising: a data acquisition module, a first construction module, a second construction module, a third construction module, and a prediction and inversion module; The data acquisition module is used to acquire the geometric and physical parameters of the solder paste to be tested, and at the same time acquire the laser power timing data of the laser processing process; The first construction module is used to construct a geometric feature encoding neural network based on a deep residual architecture, and obtain local physical parameters by combining the geometric physical parameters; The second construction module is used to construct a spherical cap geometric model and, in combination with the geometric physical parameters, obtain the equivalent density; The third construction module is used to construct a one-dimensional thermal conduction finite element mesh model with mass conservation constraints based on the geometric physical parameters and the equivalent density. The prediction and inversion module is used to obtain the predicted temperature field data and the inverted thermal property parameters based on the variable cross-section one-dimensional thermal conduction finite element mesh model, combined with the laser power time series data, the local physical parameters and the equivalent density, using a lumped mass scheme and implicit time integration algorithm.

[0012] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned method.

[0013] The present invention also provides a computer-readable storage medium storing a computer program that, when executed, implements the aforementioned method.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: Physical consistency and high accuracy: The innovative introduction of equivalent density correction based on mass conservation solves the problem of thermal capacity mismatch caused by geometric approximation at the microscale; combined with the lumped mass scheme, it effectively suppresses numerical oscillations in the phase transition process, significantly improving the physical realism and accuracy of temperature prediction.

[0015] Powerful geometric generalization capability: By using deep residual networks to extract dimensionless geometric features, the model can adapt to solder paste morphologies with different diameters, masses, and aspect ratios. This enables one-time training and application to multiple solder pad sizes, overcoming the drawback of traditional models that require repeated modeling for a single size.

[0016] Balancing real-time performance and interpretability: Employing a dimension-reduced one-dimensional variable cross-section model and an efficient tridiagonal matrix solving algorithm, millisecond-level real-time prediction is achieved. Simultaneously, the microarchitecture supports end-to-end parameter inversion, enabling the output of process parameters with clear physical meaning, such as contact thermal resistance and absorption rate, providing transparent decision-making basis for welding quality monitoring.

[0017] Strong adaptability to operating conditions: Through the parameterized boundary condition model, it can automatically identify and adapt to complex operating conditions such as grounded and ungrounded conditions, solving the problem of predicting failure when the boundary conditions change in existing models. Attached Figure Description

[0018] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the physical information fusion and geometric feature generalization architecture of an embodiment of the present invention; Figure 2 This is a schematic diagram of the node division of a one-dimensional variable cross-section finite element according to an embodiment of the present invention; Figure 3 This is a comparison chart of predicted temperature data and measured temperature data under the following conditions in an embodiment of the present invention: a 1.5×10⁻³ m solder pad radius, a 2.2×10⁻⁵ kg solder paste mass, and a constant power heating of 8.01 W for 5 seconds in an ungrounded working condition. Figure 4 This is a comparison chart of predicted temperature data and measured temperature data under the following conditions in an embodiment of the present invention: a 2×10⁻³ m solder pad radius, a solder paste mass of 3.9×10⁻⁵ kg, a constant power heating capacity of 14.83 W for 6 seconds, without grounding. Figure 5 This is a comparison chart of predicted temperature data and measured temperature data under the following conditions in an embodiment of the present invention: a 2.5×10⁻³ m solder pad radius, a 6×10⁻⁵ kg solder paste mass, and a constant power heating of 16.22 W for 9 seconds in an ungrounded working condition. Figure 6 This is a comparison chart of predicted temperature data and measured temperature data under the grounding condition of this invention, with a solder pad radius of 1.5×10-3m, a solder paste mass of 2×10-5kg, and a constant power heating of 14.83W for 9s. Figure 7 This is a comparison chart of predicted temperature data and measured temperature data under the grounding condition of this invention, with a solder pad radius of 1.5×10-3m, a solder paste mass of 2×10-5kg, and a constant power heating of 15.75W for 8s. Figure 8This is a comparison chart of predicted temperature data and measured temperature data under the grounding condition of this invention, with a 2×10⁻³ m solder pad radius, 4×10⁻⁵ kg solder paste mass, 19.635 W constant power heating for 11 s. Figure 9 This is a comparison chart of predicted temperature data and measured temperature data under the grounding condition of this invention, with a 2×10⁻³ m solder pad radius, a solder paste mass of 4.1×10⁻⁵ kg, a constant power heating of 20.33 W for 9 seconds. Figure 10 This is a comparison chart of predicted temperature data and measured temperature data under the following conditions in Embodiment 2 of the present invention: a solder pad radius of 6.3×10-5m, a solder paste mass of 25.683W, and constant power heating for 8.5s. Figure 11 This is a comparison chart of predicted temperature data and measured temperature data under the following conditions in Embodiment 2.5×10-3m solder pad radius, 6.3×10-5kg solder paste mass, 26.388W constant power heating for 8.5s. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] Example 1 This invention provides a method for real-time prediction of temperature field and parameter inversion in laser soldering, including: The geometric and physical parameters of the solder paste to be tested are obtained, and the laser power timing data of the laser processing process are also obtained. A geometric feature encoding neural network based on a deep residual architecture is constructed, and local physical parameters are obtained by combining the geometric physical parameters. Construct a spherical cap geometric model and, in conjunction with the aforementioned geometric and physical parameters, obtain the equivalent density; Based on the aforementioned geometric and physical parameters and the equivalent density, a one-dimensional thermal conduction finite element mesh model with mass conservation constraints is constructed. Based on a variable cross-section one-dimensional thermal conduction finite element mesh model, combined with the laser power time series data, the local physical parameters, and the equivalent density, the predicted temperature field data and the inverted thermal property parameters are obtained using a lumped mass scheme and implicit time integration algorithm.

[0023] The specific implementation process of this invention is as follows: like Figure 1 As shown in the figure, this embodiment discloses a real-time prediction and parameter inversion method for laser soldering based on geometric feature generalization and physical information fusion, which mainly includes four core links: geometric feature extraction and parameter prediction, variable cross-section physical mechanism modeling, mass conservation constraint correction, and differentiable finite element solution and inversion.

[0024] 1. Geometric feature encoding and adaptive prediction of physical parameters In laser soldering, even minute fluctuations in the shape (diameter, height) and mass of a small amount of solder paste can significantly alter the internal thermal resistance distribution. Although the actual solder paste morphology is random, in this embodiment, its geometry is approximated as a variable cross-section spherical cap geometric model uniquely determined by its diameter (D) and height (H). To achieve adaptive generalization for different geometric morphologies, this embodiment constructs a geometric feature encoding neural network based on a deep residual architecture, including a geometric feature encoding module. This module first performs dimensionless processing on the input geometric physical parameters (which include at least the solder paste diameter, solder paste mass, and dot height) and the calculated height-to-diameter ratio. Then, by constructing a deep feature extraction network based on a cascaded residual architecture, it adaptively extracts nonlinear geometric features strongly correlated with the physical parameters. Finally, it maps and outputs local physical parameters, which include at least the interface contact thermal resistance, dynamic absorptivity parameter, and specific heat capacity correction parameter, as detailed below: Input layer processing: First, obtain the geometric and physical parameters of the solder paste: solder paste diameter. Actual measured solder paste quality and dot height To eliminate the dimensional difference, dimensionless eigenvectors are calculated. ,in , , , These are the diameter, mass, volume, and aspect ratio of the solder paste for the spherical crown after Z-Score standardization.

[0025] Deep feature extraction: The main body of the network consists of cascaded residual processing units. Each residual processing unit contains a fully connected layer. Adaptive Layer Normalization (LayerNorm) SiLU activation function The path is "Dropout" and superimposed with a skip connection of the identity mapping. This structure effectively solves the gradient vanishing problem and can decouple the nonlinear relationship between geometric shape and boundary condition parameters in high-dimensional feature space.

[0026] Physical parameter mapping: The output layer projects latent features onto a physically meaningful positive range using a Softplus or Sigmoid activation function, outputting the predicted local physical parameters: interface contact thermal resistance. Initial laser absorption rate Thermal conductivity correction factor and specific heat capacity rate sensitive factor .

[0027] 2. Modeling of one-dimensional unsteady-state heat conduction mechanism with variable cross-section This step establishes a one-dimensional thermal conductivity finite element mesh model with variable cross-section based on geometric physical parameters: the total geometric volume of the mesh is calculated, and the equivalent density is calculated based on the ratio of solder paste mass to the total geometric volume. This equivalent density is then used as the material density parameter in the thermal conductivity equation to force the model to satisfy the mass conservation constraint. Specifically: Based on solder paste diameter and dot height Construct a geometric model of the spherical cap and calculate the first... Each grid cell is at height Average cross-sectional area at And calculate the equivalent density based on the grid. The calculation formula is: (1) in, The measured physical quality of the solder paste. The geometric volume of the finite element mesh. For the number of grid cells, For the first The axial height of each unit; This embodiment establishes a mathematical model describing the evolution of the solder paste temperature field based on the thermodynamic law of conservation of energy. An energy balance analysis is performed on a micro-element of the solder paste along the height direction (Z-axis), and the equivalent density is calculated. With cross-sectional area Substituting the values, we establish the governing equation for one-dimensional variable cross-section unsteady heat conduction: (2) in: For temperature, For time; The equivalent density is calculated based on the law of conservation of mass. This represents the dynamic specific heat capacity that varies with temperature and heating rate. Thermal conductivity as a function of temperature; As the axial height z A changing cross-sectional area function; The internal heat source generation rate per unit volume ( (), representing the energy generated inside the material due to chemical reactions, Joule heating, or microwave heating.

[0028] In the laser soldering scenario of this embodiment, since the solder paste is mainly heated by external laser energy, and violent exothermic chemical reactions are not considered within the studied temperature range, an internal heat source term is set. At this point, the governing equation for unsteady heat conduction in a one-dimensional variable cross-section can be simplified to a purely heat conduction form: (3) Let the total length of the solder paste in the Z-axis direction be... Divide it into equal parts Section (in this embodiment, it is taken as) That is, the length between each divided section is ,common Each node, as shown in the diagram. Figure 2 As shown.

[0029] Define the test function as Then the weak form of equation (3) is: (4) Integrating by parts on the right-hand side of equation (4) reduces the second derivative to a lower order, and introduces natural boundary conditions: (5) In equation (5), the first term on the right side This corresponds to the system's boundary heat flux conditions. In this embodiment, the external laser input from the top... Heat dissipation through contact with the bottom The natural boundary load is transformed into the equation.

[0030] Consider the following linear basis functions: (6) in, i , j For node index variables.

[0031] Taking first-order basis functions, the expressions for the basis functions are: (7) The derivative expressions of the basis functions are: (8) In this embodiment, the definition is as follows: for t Time of the first i The temperature of each node, based on the one-dimensional thermal conduction assumption, represents its altitude. The average temperature across the entire cross-section, and the overall temperature, can be approximated as: (9) The summation symbol represents assembly summation in the finite element method, which means that matrix assembly is completed by embedding the stiffness matrices of each local element into the corresponding positions of the global stiffness matrix, rather than directly adding the values.

[0032] Let the stiffness matrix elements mass matrix elements , Therefore: (10) as well as: (11) in, For time step; Substituting equations (10) and (11) into equation (5), we get: (12) when At that time, it can be seen from equation (7) that From equation (8), we can see that ,so , .

[0033] when At that time, it can be seen from equation (7) that for the e-th unit (interval) ), due to the unit length It is very small, so the average cross-sectional area of ​​the unit can be taken. Alternative Therefore: (13) Similarly: (14) when Similarly, the above process can be followed to obtain... , .

[0034] when At that time, if From equation (7), it can be seen that only in hour, We can obtain: (15) From equation (8), it can be seen that only in hour, Therefore: (16) when As can be seen from equation (7), only in hour, We can obtain: (17) As can be seen from equation (8), only in hour, Therefore: (18) when At that time, as can be seen from equation (7), only when hour, Therefore: (19) From equation (8), it can be seen that only in hour, Therefore: (20) Based on the aforementioned Galerkin weak form derivation, for the... Each grid cell (corresponding node) With nodes Its physical properties are determined by the average cross-sectional area of ​​the unit. Thermal conductivity and equivalent volumetric heat capacity Decide.

[0035] From the previous integral derivation, the element stiffness matrix can be obtained as follows: (twenty one) Similarly, the uniform quality matrix is ​​obtained as follows: (twenty two) Among them, the off-diagonal terms (1 / 6 coefficient terms) represent the dynamic coupling between nodes.

[0036] Given that the laser soldering process involves millisecond-level rapid heating and phase transformation, the above Off-diagonal coupling terms in the equation are prone to causing numerical oscillations. Therefore, this embodiment addresses this issue. Row-sum lumping is used to sum the contributions of off-diagonal terms onto the main diagonal, resulting in the optimized diagonalized quality matrix: (twenty three) This approach endows the finite element model with monotonicity and conservation properties similar to the finite volume method (FVM), significantly improving numerical stability while ensuring computational accuracy.

[0037] Based on the optimized unit matrix, a full-field assembly is performed using the implicit time-difference scheme (Backward Euler). Due to the one-dimensional chain topology of the mesh, the resulting overall system matrix exhibits a significant tridiagonal banded structure, ultimately constructing a system of linear algebraic equations for solving the full-field temperature: (twenty four) Abbreviated as .

[0038] in, This is the assembled tridiagonal coefficient matrix; Let be the temperature vector to be determined at the next moment, i.e. n Temperature vector at time +1 for n Temperature vector at time, To diagonalize the quality matrix, Here is the stiffness matrix; The vector on the right-hand side contains not only the temperature information from the previous moment, but also the boundary integral term from equation (5). Transformed load vector Specifically, at the top boundary Boundary conditions Substituted into the boundary integral term, where Let be the laser heat flux density at time t. The heat loss of the solder paste surface at time t; at the bottom boundary place, Substituted into the boundary terms, where Let be the heat flow from the bottom contact at time t. The above boundary conditions are introduced into the weak form equations, transforming into the right-hand load vector of the finite element equations. This enables the coupled solution of boundary heat flux load and internal temperature field.

[0039] 3. Adaptive Correction of Equivalent Density Based on Mass Conservation For small-scale calculations, the volume of a spherical cap is determined by the geometric assumptions. Compared with the actual weighing mass of solder paste To address the common mismatch issue, this embodiment introduces an equivalent density correction mechanism.

[0040] Mesh volume calculation: Calculate the total geometric volume based on finite element mesh. ,in For the first Average cross-sectional area of ​​each unit.

[0041] Equivalent density inversion: Force the total mass of the model to be equal to the measured mass, and inversely deduce the equivalent density from equation (1); Equation correction: the reverse calculation Substitute this into the transient term of the heat conduction equation. This step ensures that, regardless of how approximate the geometric model, the average temperature rise of the system after absorbing energy strictly obeys the law of conservation of energy.

[0042] 4. Dynamic physical parameters and differentiability solutions In order to realistically reflect the complex thermophysical processes accompanied by phase transitions in a single thermal conductivity model (variable cross-section one-dimensional thermal conduction finite element mesh model), this model integrates dynamically evolving constitutive relations in the computational graph and constructs a full-process differentiable finite element solver.

[0043] Laser heat flux density: (25) in, Let be the dynamic laser absorption rate at time t. Let be the laser power at time t. This is the equivalent projected area of ​​the laser spot on the top of the spherical cap, which is determined by the geometric parameters of the spherical cap (radius of the sphere). Solder paste application height The effective size of the laser spot is determined by the height of the spherical cap and the effective size of the laser spot, representing the equivalent area of ​​the actual area where the laser energy acts on the top of the spherical cap.

[0044] Dynamic absorption rate: laser absorption rate With the liquid phase fraction at the top of the solder paste Attenuation, simulating the melting and brightening effect: (26) in, The initial solid-state absorptivity, i.e., the initial laser absorptivity, is predicted by the neural network. This is the absorption rate attenuation coefficient, used to simulate the light absorption attenuation caused by the melting and brightening of solder paste; This represents the liquid phase fraction at the top of the solder paste, calculated based on the current temperature and the solid-liquid phase temperature.

[0045] Non-equilibrium specific heat capacity: In order to capture the non-equilibrium thermodynamic effects under rapid laser heating, the heating rate (temperature change rate) is introduced. Nonlinear correction for contrast heat capacity: (27) in, Based on specific heat capacity; The rate-sensitive factor is predicted by the neural network; The function is used to limit the correction amount to a physically reasonable saturation range.

[0046] The differentiable finite element solver employs a lumped mass scheme and an implicit time integration algorithm, specifically including: Based on the geometric assumption of a one-dimensional spherical cap with variable cross-section, the thermal conductivity terms between nodes are calculated to form the off-diagonal elements of the stiffness matrix. By using a lumped mass scheme, the element heat capacity contributions are superimposed on the main diagonal to form a mass matrix, thus eliminating non-physical numerical oscillations. Construct a system of tridiagonal linear equations , where the matrix The system coefficient matrix, which includes thermal conductivity stiffness and heat capacity mass terms, is a vector. The matrix is ​​a load vector containing the right-hand side of the temperature field information from the previous moment and the generalized heat source term; and the matrix... sum vector The entire construction process is implemented within an automatic differentiation framework, supporting backpropagation of gradients between time steps. Specifically: Based on discrete matrices, assemble a system of tridiagonal linear equations within the PyTorch automatic differentiation framework: (28) System coefficient matrix : From the optimized diagonalized mass matrix and stiffness matrix It is composed of linear combinations, and its expression is: .because It is a diagonal matrix and It is a tri-diagonal matrix, therefore Strictly maintaining the tridiagonal sparse structure lays the foundation for efficient solution.

[0047] Right-hand term load vector : It integrates historical moment information and current boundary conditions, and the expression is: .in The explicit expression includes the time-varying laser heat flux determined by equation (5). and dynamic heat loss.

[0048] For matrix Given the tridiagonal property, this embodiment employs the differentiable pursuit method (Thomas Algorithm / TDMA) for solving the problem. Compared to the general matrix inversion algorithm, its computational complexity is reduced from... Reduce to The temperature field at the next moment is obtained by solving. It will continue to participate in the next time step iteration. Since all the matrix construction and solution operations mentioned above preserve the gradient path in the computational graph, the model supports calculating the loss function (Loss) on the neural network output parameters (…). The gradient of (etc.) is used to achieve end-to-end physical parameter inversion through the backpropagation algorithm.

[0049] 5. Standardized description of complex working conditions This embodiment utilizes the interface contact thermal resistance based on bottom boundary condition parameters. The numerical range of these values ​​uniformly describes different heat conduction conditions: The interfacial contact thermal resistance predicted by the geometric feature encoding neural network is an equivalent lumped parameter characterizing the heat dissipation capacity of the solder paste at the bottom; the bottom boundary condition is described by the following heat flux density equation: (29) in, The heat flux density at the bottom is... For interfacial contact thermal resistance, This refers to the temperature at the bottom of the solder paste. The ambient temperature is used; the value of this parameter is continuously distributed to cover different bottom boundary conditions. When the interfacial contact thermal resistance is in a relatively high range, it indicates that the heat flow channel is a highly thermally conductive metal connection or grounded state: the model adaptively predicts high... The value simulates the rapid conduction of heat to highly thermally conductive strata; When the interfacial contact thermal resistance is in a relatively low range, it indicates that the heat flow channel is in a non-grounded contact state limited by the diffusion thermal resistance of the insulating substrate: the model predicts low... The value simulates adiabatic or natural convection conditions.

[0050] 6. Model Training and Prediction In this embodiment, the method for real-time prediction of laser soldering temperature field and parameter inversion further includes: During the model training phase, the deviation between the obtained temperature field data and the measured temperature data is calculated. The gradient of the deviation with respect to the output parameters of the geometric feature encoding neural network is calculated using an automatic differentiation mechanism, and the weights of the geometric feature encoding neural network are updated. End-to-end physical parameter inversion is achieved through the backpropagation algorithm. During the prediction phase, the millisecond-level temperature field prediction results and the inverted thermal property parameters are directly output.

[0051] Specifically, the model training phase employs a multi-objective physical consistency loss function, including: Temperature mean square error term: constrains the numerical deviation between the predicted temperature and the measured temperature; Derivative term: Constrains the consistency between the time derivative of the predicted temperature curve and the time derivative of the measured curve to accurately capture the phase transition inflection point; Physical prior constraints include range constraints on predicted physical parameters and correlation constraints based on physical laws. The correlation constraints include at least the positive correlation between solder paste diameter and interfacial contact thermal resistance.

[0052] To further verify the effectiveness and robustness of the method proposed in this invention, this embodiment selected multiple sets of experimental data covering different solder paste geometries (including different solder pad diameters, dotting heights, and solder paste quality) and different operating conditions (grounded and ungrounded) for prediction and verification. The comparison results are as follows: Figures 3-11 As shown, the temperature prediction curve output by the model maintains a high degree of consistency with the real-time temperature data collected in the experiment in terms of heating rate, peak temperature, and cooling trend. Particularly at the solid-liquid phase transition inflection point, the model can accurately capture the temperature plateau characteristics caused by latent heat release. These results fully demonstrate the model's high accuracy in handling variable cross-section heat conduction problems and its excellent adaptive generalization ability to handle fluctuations in geometry and boundary conditions.

[0053] In summary, this invention discloses a real-time prediction and parameter inversion method for the temperature field of laser soldering based on geometric feature generalization and physical information fusion. Addressing the characteristics of variable solder paste geometry and complex boundary conditions during laser soldering, this method constructs a hybrid differentiable architecture that integrates a deep residual network and a mechanistic model. First, a geometric feature encoding network is used to extract features such as the diameter, mass, and aspect ratio of the solder paste, adaptively predicting key nonlinear parameters such as interface contact thermal resistance and dynamic laser absorptivity evolving with phase transition states. Second, a one-dimensional unsteady-state heat conduction physical model with variable cross-section based on the spherical cap assumption is established, introducing an equivalent density correction mechanism based on mass conservation to effectively compensate for thermal capacity errors caused by geometric approximation, and employing a lumped mass scheme technique to eliminate phase transition numerical oscillations. Finally, an end-to-end calculation of the thermal and phase transition processes is performed using a differentiable finite element solver, supporting automatic inversion of physical parameters based on gradients. This invention, through flexible configuration of bottom boundary conditions, is applicable to both solder paste grounding and ungrounding conditions. Furthermore, thanks to the dimensionality-reduced physical model and efficient numerical algorithm, it achieves millisecond-level real-time temperature field prediction, significantly improving the efficiency and accuracy of welding process parameter optimization.

[0054] Example 2 Based on the same inventive concept, the present invention also provides a real-time prediction and parameter inversion system for laser soldering temperature field, used to implement the aforementioned method. The system includes: a data acquisition module, a first construction module, a second construction module, a third construction module, and a prediction and inversion module. The data acquisition module is used to acquire the geometric and physical parameters of the solder paste to be tested, and at the same time acquire the laser power timing data of the laser processing process; The first construction module is used to construct a geometric feature encoding neural network based on a deep residual architecture, and obtain local physical parameters by combining the geometric physical parameters. The second construction module is used to construct the geometric model of the spherical cap and obtain the equivalent density by combining the geometric physical parameters; The third construction module is used to construct a one-dimensional thermal conduction finite element mesh model with mass conservation constraints based on the geometric physical parameters and the equivalent density. The prediction and inversion module is used to obtain the predicted temperature field data and the inverted thermal property parameters based on the variable cross-section one-dimensional thermal conduction finite element mesh model, combined with the laser power time series data, the local physical parameters and the equivalent density, using the lumped mass scheme and implicit time integration algorithm.

[0055] Example 3 The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any of the foregoing embodiments.

[0056] Example 4 The present invention also provides a computer-readable storage medium (such as ROM / RAM, magnetic disk, optical disk) storing a computer program thereon. When the computer program is executed by a processor (such as CPU, GPU, or TPU) in a computer device, it can implement the methods described in any of the foregoing embodiments.

[0057] Specifically, when the computer program is executed by the processor, it performs the following operations: Data acquisition: Read the solder paste geometric and physical parameters and laser power timing; Network inference: Call the pre-stored deep residual geometric feature encoding network weights to calculate local physical parameters; Physical modeling: Construct a variable cross-section finite element model based on in-memory mesh data and perform mass conservation corrections; Solution operation: Assemble the tridiagonal system matrix under the automatic differentiation framework, and use a sparse solver to calculate the temperature field evolution; Backpropagation (in training mode): Calculate the gradient of the loss function and update the network parameters.

[0058] Furthermore, those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the above method embodiments.

[0059] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for real-time prediction of temperature field and parameter inversion in laser soldering, characterized in that, The method includes: The geometric and physical parameters of the solder paste to be tested are obtained, and the laser power timing data of the laser processing process are also obtained. A geometric feature encoding neural network based on a deep residual architecture is constructed, and local physical parameters are obtained by combining the geometric physical parameters. Construct a spherical cap geometric model and, in conjunction with the aforementioned geometric and physical parameters, obtain the equivalent density; Based on the aforementioned geometric and physical parameters and the equivalent density, a one-dimensional thermal conduction finite element mesh model with mass conservation constraints is constructed. Based on a variable cross-section one-dimensional thermal conduction finite element mesh model, combined with the laser power time series data, the local physical parameters, and the equivalent density, the predicted temperature field data and the inverted thermal property parameters are obtained using a lumped mass scheme and implicit time integration algorithm.

2. The method according to claim 1, characterized in that, The geometric feature encoding neural network includes: a geometric feature encoding module; The geometric feature encoding module first performs dimensionless processing on the input geometric physical parameters and the height-to-diameter ratio calculated therefrom, then adaptively extracts nonlinear geometric features that are strongly correlated with the physical parameters, and finally maps and outputs local physical parameters.

3. The method according to claim 1, characterized in that, Methods for constructing a spherical cap geometric model and obtaining the equivalent density by combining the aforementioned geometric and physical parameters include: ； in, For equivalent density, The measured physical quality of the solder paste. The geometric volume of the finite element mesh. The number of elements in the finite element mesh. The average cross-sectional area, For the first The axial height of each unit.

4. The method according to claim 3, characterized in that, The method for constructing a one-dimensional thermal conduction finite element mesh model with mass conservation constraints based on the aforementioned geometric and physical parameters and the equivalent density includes: Substituting the equivalent density and cross-sectional area into the one-dimensional variable cross-section unsteady heat conduction control equation: ； in, This represents the dynamic specific heat capacity that varies with temperature and heating rate. As the axial height z The changing cross-sectional area function, For temperature, For time, Thermal conductivity as a function of temperature; The formula for calculating laser heat flux density is: ； in, For dynamic laser absorption rate, For laser power, The equivalent projected area of ​​the laser spot at the top of the spherical cap; Coupled top boundary conditions: ； in, For dot painting height, This is the surface heat loss term; By using the equivalent density in the one-dimensional variable cross-section unsteady heat conduction control equation This ensures that the variable cross-section one-dimensional heat conduction finite element mesh model satisfies the energy conservation constraint.

5. The method according to claim 4, characterized in that, The one-dimensional variable cross-section unsteady-state heat conduction control equation adopts a dynamic physical parameter model that evolves with the phase transition state, including: Dynamic laser absorptivity model: ； in, The initial laser absorption rate, This is the attenuation coefficient, used to simulate the light absorption attenuation caused by the melting and brightening of solder paste. The liquid phase fraction at the top of the solder paste; Non-equilibrium specific heat capacity model: ； in, Based on specific heat capacity, As a rate-sensitive factor for specific heat capacity, This is the rate of temperature change, used to compensate for non-equilibrium heat capacity fluctuations during rapid heating.

6. The method according to claim 5, characterized in that, Based on a variable cross-section one-dimensional thermal conductivity finite element mesh model, and combining the laser power time-series data, the local physical parameters, and the equivalent density, a method for obtaining predicted temperature field data and inverted thermal property parameters using a lumped mass scheme and implicit time integration algorithm includes: ； in, for n Temperature vector at time +1 for n Temperature vector at time, To diagonalize the quality matrix, Here is the stiffness matrix. For time step, Explicitly includes laser heat flow and dynamic heat loss.

7. The method according to claim 1, characterized in that, The method further includes: The deviation between the calculated temperature field data and the measured temperature data is used to calculate the gradient of the deviation with respect to the output parameters of the geometric feature encoding neural network using an automatic differentiation mechanism, and the weights of the geometric feature encoding neural network are updated. End-to-end physical parameter inversion is achieved through the backpropagation algorithm.

8. A real-time prediction and parameter inversion system for laser soldering temperature field, said system being used to implement the method described in any one of claims 1-7, characterized in that, The system includes: a data acquisition module, a first construction module, a second construction module, a third construction module, and a prediction and inversion module; The data acquisition module is used to acquire the geometric and physical parameters of the solder paste to be tested, and at the same time acquire the laser power timing data of the laser processing process; The first construction module is used to construct a geometric feature encoding neural network based on a deep residual architecture, and obtain local physical parameters by combining the geometric physical parameters; The second construction module is used to construct a spherical cap geometric model and, in combination with the geometric physical parameters, obtain the equivalent density; The third construction module is used to construct a one-dimensional thermal conduction finite element mesh model with mass conservation constraints based on the geometric physical parameters and the equivalent density. The prediction and inversion module is used to obtain the predicted temperature field data and the inverted thermal property parameters based on the variable cross-section one-dimensional thermal conduction finite element mesh model, combined with the laser power time series data, the local physical parameters and the equivalent density, using a lumped mass scheme and implicit time integration algorithm.

9. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed, implements the method described in any one of claims 1-7.

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