A three-dimensional temperature field soft measurement method and system based on multi-source heterogeneous data fusion and boundary self-adaptation

Abstract

The application discloses a kind of based on multi-source heterogeneous data fusion and boundary self-adapting three-dimensional temperature field soft measurement method and system, method includes: obtaining infrared time series temperature field data and discrete thermocouple time series temperature data;Establish three-dimensional tetrahedral finite element grid model, and the solution domain is divided into the sub-region with independent thermal physical property parameters;Adaptive Robin boundary condition with virtual control gain is constructed, and the initial value of global three-dimensional simulation temperature field of current time step is obtained;Based on the pre-constructed spatial hierarchical index structure, the corresponding simulation temperature value at the position of discrete thermocouple is extracted;Temperature residual is calculated, and the equivalent thermal diffusivity of each sub-region is independently updated using asymmetric parameter identification law;The updated equivalent thermal diffusivity is fed back to the next iteration round, and when the set convergence condition is reached, the measured object three-dimensional transient temperature field and the identified thermal physical property parameters are output.The application improves the numerical stability of multi-source data assimilation solution.

Description

Technical Field

[0001] This invention relates to the field of numerical heat transfer and laser soldering modeling technology, and in particular to a three-dimensional temperature field soft measurement method and system based on multi-source heterogeneous data fusion and boundary adaptation. Background Technology

[0002] In modern high-density electronic manufacturing and microelectronic packaging soldering processes, the transient temperature changes of solder paste determine the metallurgical forming quality of solder joints and the electrical reliability of the system. Especially under grounding conditions during laser soldering, the localized high-intensity heat source applied during soldering is conducted along the ground plane to the surrounding printed circuit boards. This grounding effect makes it difficult for traditional one-dimensional ungrounded thermodynamic models to accurately describe the actual heat flow distribution, leading to decreased accuracy in temperature field prediction. In this process, improper control of the surrounding heat field diffusion can cause irreversible thermal damage to nearby heat-sensitive components. Furthermore, in actual observations, non-contact infrared thermometry can only acquire the surface temperature of the solder paste and substrate. During dynamic heating, a significant temperature gradient often exists between the surface and interior of the solder paste, and the core parameter truly reflecting the phase transition process and metallurgical state of the solder paste is its internal true temperature. Limited by the geometric dimensions of tiny solder joints, traditional contact thermocouples are difficult to implant to achieve effective measurement of the internal temperature. Therefore, achieving accurate prediction of the true internal temperature of the solder paste and simultaneously estimating the transient temperature evolution of the surrounding PCB board is a crucial step in improving the yield of microelectronic manufacturing. Based on this, the present invention proposes a three-dimensional temperature field soft measurement method and system based on multi-source heterogeneous data fusion and boundary adaptation. Summary of the Invention

[0003] To address the technical problems existing in the prior art, this invention proposes a three-dimensional temperature field soft measurement method and system based on multi-source heterogeneous data fusion and boundary adaptation. This method constructs a physical evolution model of solder paste and printed circuit board based on the three-dimensional transient heat conduction equation, and simultaneously identifies the equivalent thermophysical parameters of the system during dynamic heating. By establishing a spatial mapping and assimilation mechanism between surface infrared temperature measurement data and internal thermocouple observation data, the physical reconstruction of the surface two-dimensional temperature to the internal three-dimensional temperature field under grounding conditions is realized, ultimately achieving the goal of high-precision prediction of the true internal temperature of solder paste and the distribution of the surrounding thermal field.

[0004] On the one hand, to achieve the above objectives, this invention provides a three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation, comprising: Acquire infrared time-series temperature field data of the surface of the object under test and time-series temperature data of the thermocouple at key internal locations; A three-dimensional tetrahedral finite element mesh model of the object under test is established, and the solution domain is divided into several sub-regions with independent thermophysical parameters, including the heat source excitation region and the thermal inertia conduction region. An adaptive Robin boundary condition with virtual control gain is constructed, and the infrared time-series temperature field data is assimilated into the three-dimensional tetrahedral finite element mesh model as a soft constraint. The initial value of the global three-dimensional simulation temperature field at the current time step is obtained by solving the weak form of the transient heat conduction equation. Based on a pre-built spatial hierarchical index structure, the simulated temperature value corresponding to the location of the thermal couple is extracted. Calculate the temperature residual between the simulated temperature value and the time-series temperature data of the thermal coupler, and based on the temperature residual, apply asymmetric parameter identification laws with different dynamic response characteristics to the heat source excitation region and the thermal inertia conduction region respectively, and independently update the equivalent thermal diffusivity of each sub-region. The updated equivalent thermal diffusivity is fed back to the next iteration. When the set convergence condition is met or the solution is completed, the three-dimensional transient temperature field of the measured object and the identified thermal property parameters are output.

[0005] Preferably, the adaptive Robin boundary condition with virtual control gain is: ; In the formula, The thermal conductivity of the surface medium, For the outer normal of the boundary, The coefficient of heat dissipation by natural convection. For ambient temperature, To simulate temperature, For the first m The time-varying sequence of virtual assimilation gain during round iterations. The measured surface temperature is obtained using infrared technology.

[0006] Preferably, the weak form of the transient heat conduction equation is discretized in time using a backward Euler fully implicit difference scheme and in space using the Galerkin method. In the discretized algebraic equation system, the boundary convection matrix and boundary load vector related to the adaptive Robin boundary conditions explicitly contain a virtual assimilation gain sequence.

[0007] Preferably, based on a pre-constructed spatial hierarchical index structure, the simulated temperature value corresponding to the location of the thermocouple is extracted, including: In the offline preprocessing stage, a directed bounding box tree is established for the three-dimensional tetrahedral finite element mesh; The directed bounding box tree is used to perform collision detection on the physical coordinates of each thermocouple and locate the tetrahedral cell to which the physical coordinates of the thermocouple belong. Centered on the nominal coordinates of the thermocouple, grid nodes are collected within a preset plane radius and thickness tolerance range, and the arithmetic mean temperature of the grid nodes is used as the equivalent simulation temperature of the corresponding thermocouple. The mapping relationship between the equivalent simulation temperature and the mesh node number is cached as a sparse matrix for direct use in online iteration.

[0008] Preferably, the conditions for collecting grid nodes within a preset planar radius and thickness tolerance range, centered on the nominal coordinates of the thermocouple, are as follows: and ; In the formula, These are the grid nodes within the region. x axis, y axis, z axis coordinate values, These are thermocouple measuring points. x axis, y axis, z axis coordinate values, r The preset plane radius, dz for z Directional layer thickness tolerance range.

[0009] Preferably, the asymmetric parameter identification law includes: For the heat source excitation region, a gradient descent method with an adaptive decay learning rate is used to update the inverse of the equivalent thermal diffusivity of the corresponding region based on the temperature residual at the heating point. For the aforementioned thermal inertia conduction region, a proportional-differential iterative learning control algorithm with time memory effect is adopted to update the reciprocal of the equivalent thermal diffusivity coefficient of the corresponding region based on the signed L2 composite residual from multiple measurement points.

[0010] Preferably, the adaptive decay learning rate decays exponentially with each iteration to balance the convergence speed and stability of parameter identification; the differential term in the proportional-differential iterative learning control algorithm is used to provide advance phase compensation for the response lag of the large thermal inertial system, suppressing overshoot and oscillation during the identification process.

[0011] Preferably, the asymmetric parameter identification law further includes: For the virtual control gain sequence, an inter-round proportional iterative learning control strategy is used for global updates.

[0012] On the other hand, to achieve the above objectives, the present invention also provides a three-dimensional temperature field soft measurement system based on multi-source heterogeneous data fusion and boundary adaptation, comprising: The data acquisition module is used to acquire infrared time-series temperature field data of the surface of the object under test and time-series temperature data of the thermocouple at key internal locations. The multiphysics assimilation solution module is used to construct adaptive Robin boundary conditions with iterative variable virtual control gain, assimilate infrared time-series temperature field data as soft constraints into a three-dimensional tetrahedral finite element mesh model, and solve to obtain the global simulation temperature field. The spatial addressing mapping module is used to extract the simulation temperature value corresponding to the location of the thermocouple based on a pre-built spatial hierarchical index structure. The asymmetric parameter identification module is used to update the equivalent thermal diffusivity of each region based on the residual between the simulated temperature and the measured temperature, using different closed-loop update laws for different thermal property regions, and then feeding the updated parameters back to the multiphysics assimilation solution module.

[0013] 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. When the processor executes the computer program, it implements the aforementioned three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation.

[0014] Compared with the prior art, the present invention has the following advantages and technical effects: (1) Improved numerical stability of multi-source data assimilation solution: This invention constructs an adaptive Robin boundary condition with virtual control gain, and introduces infrared measurement data into the partial differential equation in the form of soft constraints. Compared with directly imposing surface temperature (first type boundary condition), this mechanism effectively suppresses spatial gradient divergence and heat loss distortion, and avoids numerical oscillation problems in the finite element solution process.

[0015] (2) A dynamic collaborative compensation mechanism for surface boundaries and internal parameters was constructed, achieving accurate reconstruction of the global thermal field: Addressing the challenge of highly coupled surface heat transfer and internal heat conduction in complex systems, making independent identification difficult, this invention abandons the traditional approach of forced decoupling. Instead, it constructs a dual feedback compensation mechanism using "surface virtual boundary gain" and "internal multi-region parameter identification law." During the dynamic solution process, surface boundary assimilation and internal parameter optimization work in synergy and compensate for each other, ultimately converging to a global physical equilibrium state in the iteration. This mechanism not only reconstructs the transient temperature of the core solder paste area with high fidelity (ensuring soldering quality) but also simultaneously estimates the thermal diffusion boundary of the surrounding PCB board, providing reliable data support for preventing thermal damage to sensitive components.

[0016] (3) Significantly reduced computational overhead of 3D finite element soft measurement: To address the bottleneck of time-consuming spatial addressing of multiple measurement points in 3D mesh models, this invention introduces bounding box collision tree and mapping topology caching technology. This method avoids global traversal of the mesh in finite element iterative solutions, greatly improves the computational efficiency of single-step multi-point joint evaluation, and meets the timeliness requirements of soft measurement systems in practical engineering applications.

[0017] (4) Overcoming the distortion caused by parameter drift in pure mechanism simulation models: The closed-loop feedback architecture of this invention can adaptively adjust parameters according to the change in thermal resistance of materials during dynamic heating. It effectively overcomes the error accumulation problem caused by material phase change and batch differences in traditional open-loop finite element simulation, making the algorithm have strong engineering generalization ability when dealing with complex grounding conditions. Attached Figure Description

[0018] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of a three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a printed circuit board according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the mesh model of the object under test in an embodiment of the present invention (taking a pad radius of 1.5mm and a solder paste mass of 0.02g as an example). Figure 4 This is a schematic diagram of the three-dimensional transient temperature field of an embodiment of the present invention (taking a pad radius of 1.5mm and a solder paste mass of 0.02g as an example). Figure 5 This is a schematic diagram comparing the heating point temperatures of a pad with a radius of 1.5 mm and a solder paste mass of 0.03 g under constant power heating of 26.72 W for 11.5 s according to an embodiment of the present invention. Figure 6 This is a schematic diagram showing the temperature error changes at all measuring points for a solder pad with a radius of 1.5 mm and a solder paste mass of 0.03 g under constant power heating of 26.72 W for 11.5 s according to an embodiment of the present invention. Figure 7 This is a schematic diagram of the virtual boundary gain used in the simulation to verify the specifications of 1.5mm pad radius and 0.03g solder paste mass in an embodiment of the present invention. Figure 8 This is a statistical chart of the root mean square error at various measuring points for a solder pad with a radius of 1.5 mm and a solder paste mass of 0.03 g under constant power heating of 26.72 W for 11.5 s according to an embodiment of the present invention. Figure 9 This is a schematic diagram comparing the heating point temperatures of a pad with a radius of 2mm and a solder paste mass of 0.045g under constant power heating at 32.82W for 9.5s according to an embodiment of the present invention. Figure 10 This is a schematic diagram showing the temperature error changes at all measuring points under constant power heating of 32.82W for 9.5s with a pad radius of 2mm and a solder paste mass of 0.045g, according to an embodiment of the present invention. Figure 11 This is a schematic diagram of the virtual boundary gain used in the verification simulation of a solder pad radius of 2mm and a solder paste mass of 0.045g in an embodiment of the present invention. Figure 12 This is a statistical chart of the root mean square error at each measuring point under constant power heating of 32.82W for 9.5s with a pad radius of 2mm and a solder paste mass of 0.045g in an embodiment of the present invention. Figure 13 This is a schematic diagram comparing the heating point temperatures of a pad with a radius of 2.5 mm and a solder paste mass of 0.085 g under constant power heating at 33.79 W for 10.5 s according to an embodiment of the present invention. Figure 14 This is a schematic diagram showing the temperature error changes at all measuring points under constant power heating of 33.79W for 10.5s with a pad radius of 2.5mm and a solder paste mass of 0.085g in an embodiment of the present invention. Figure 15 This is a schematic diagram of the virtual boundary gain used in the verification simulation of an embodiment of the present invention with a pad radius of 2.5 mm and a solder paste mass of 0.085 g. Figure 16 This is a statistical chart of the root mean square error at each measuring point under the condition of constant power heating at 33.79W for 10.5s with a pad radius of 2.5mm and a solder paste mass of 0.085g in an embodiment of the present invention. Detailed Implementation

[0019] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0020] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0021] This embodiment proposes a three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation, such as... Figure 1 ,include: Acquire infrared time-series temperature field data of the surface of the object under test and time-series temperature data of the thermocouple at key internal locations; A three-dimensional tetrahedral finite element mesh model of the object under test is established, and the solution domain is divided into several sub-regions with independent thermophysical parameters, including the heat source excitation region and the thermal inertia conduction region. An adaptive Robin boundary condition with virtual control gain is constructed, and the infrared time-series temperature field data is assimilated into the three-dimensional tetrahedral finite element mesh model as a soft constraint. The initial value of the global three-dimensional simulation temperature field at the current time step is obtained by solving the weak form of the transient heat conduction equation. Based on a pre-built spatial hierarchical index structure, the simulated temperature value corresponding to the location of the thermal couple is extracted. Calculate the temperature residual between the simulated temperature value and the time-series temperature data of the thermal coupler, and based on the temperature residual, apply asymmetric parameter identification laws with different dynamic response characteristics to the heat source excitation region and the thermal inertia conduction region respectively, and independently update the equivalent thermal diffusivity of each sub-region. The updated equivalent thermal diffusivity is fed back to the next iteration. When the set convergence condition is met or the solution is completed, the three-dimensional transient temperature field of the measured object and the identified thermal property parameters are output.

[0022] Specifically, step S1, acquiring multi-source heterogeneous temperature observation data, includes: In laser soldering applications, the object under test (including the core solder paste area and the surrounding PCB substrate) faces two distinctly different temperature observation methods. First, non-contact infrared sensors acquire infrared time-series temperature field data of the object's surface. Infrared time-series temperature field data has high spatial resolution and can continuously reflect the two-dimensional distribution of surface temperature, but due to the opacity of the medium, it cannot directly characterize the true internal temperature state of the object. Second, miniature thermocouples embedded in key locations within the temperature measuring plate acquire internal time-series temperature data at several discrete points. Thermocouple data has high measurement accuracy and can directly reflect the temperature evolution of local points, but it cannot describe the global temperature distribution in three-dimensional space. These two types of data together constitute the multi-source heterogeneous temperature observation dataset required in this embodiment, providing a dual source of information for subsequent three-dimensional temperature field reconstruction: boundary assimilation and internal correction.

[0023] Further, step S2, establishing a three-dimensional tetrahedral finite element mesh model of the object under test, includes: The printed circuit board used in this embodiment is shown in the image below. Figure 2As shown, it is composed of a copper foil layer with a thickness of approximately 25 μm, an FR-4 insulating substrate with a thickness of approximately 1.5 mm, and a green oil coating on the surface. For the geometry of the object under test, the spatial solution domain Ω is discretized using an unstructured tetrahedral mesh. Tetrahedral meshes possess strong geometric adaptability and can accurately fit complex curved surface geometric boundaries. For example... Figure 3 The mesh model constructed using a 3mm pad diameter as an example. Figure 3 The dark blue area is the heat source activation zone of the solder paste. The shape is a spherical cap; the lower area is the PCB's large thermal inertia conduction area ( ), Figure 3 The marked points indicate the spatial distribution of the embedded thermocouples. For the test objects with 4mm and 5mm pad diameters, the mesh construction method is the same as in this embodiment, only the pad diameter and the geometric dimensions of the spherical cap are different.

[0024] Based on the fundamental differences in the physical properties of materials, the global solution domain Ω is divided into the following two independent sub-regions: (1) Heat source activation zone (solder paste, denoted as) This region is located at the welding point and directly bears the local high-density heat flow input from the laser heat source. It is small in size but has an extremely high heat flow density, and is accompanied by nonlinear phase change latent heat absorption during the welding process.

[0025] (2) Large thermal inertia conduction area (PCB substrate, denoted as Due to the low thermal conductivity of the FR-4 substrate and the thermal insulation effect of the green oil coating on the surface, the overall equivalent heat dissipation capability of the PCB substrate is limited. Considering the significant differences in the thickness of each layer and the difficulty in accurately measuring the interfacial thermal resistance, this embodiment treats the above composite structure as a whole and obtains its comprehensive equivalent thermal property parameters through parameter identification, rather than modeling each layer individually. This region is responsible for conducting heat along the ground plane to the surrounding structure. The heat conduction process has significant spatial and temporal hysteresis effects, and its equivalent thermal property parameters tend to stabilize and converge during the iterative identification process.

[0026] The two sub-regions mentioned above will be updated independently using different optimization strategies in the subsequent parameter identification steps to achieve refined identification of multi-regional thermal properties.

[0027] Further, step S3 involves constructing adaptive Robin boundary conditions with virtual control gain, assimilating the infrared time-series temperature field data as a soft constraint into the three-dimensional tetrahedral finite element mesh model, and obtaining the initial value of the global three-dimensional simulation temperature field at the current time step by solving the weak form of the transient heat conduction equation, including: Based on the law of conservation of energy and Fourier's law of heat conduction, the governing equations for the three-dimensional unsteady-state heat conduction inside the object under test are as follows: (1); In the formula, ρ For density, c For specific heat capacity, λ Thermal conductivity, T Let be the temperature distribution function. t For time, This is the gradient operator. In this embodiment, the internal heat source term (Q=0) is ignored. Expanding and rearranging equation (1), we obtain its Cartesian coordinate form: (2); The boundaries of the solution domain Ω are classified into the following categories: Top infrared heated surface ( Apply the innovative adaptive Robin boundary condition (third type boundary condition) with virtual control gain proposed in this embodiment: (3); In the formula, The thermal conductivity of the surface medium, For the outer normal of the boundary, The coefficient of heat dissipation by natural convection. For ambient temperature, To simulate temperature, The surface temperature is measured using infrared radiation. For the first m The virtual assimilation gain sequence that changes over time during the iterations is used to assimilate infrared measurement data into the finite element model in the form of soft constraint penalties, effectively suppressing spatial gradient divergence and thermal loss caused by imposing first-type Dirichlet boundary conditions.

[0028] The contact surface between the solder paste and the PCB substrate is treated using a shared node approach to ensure temperature continuity and heat flow conservation at the contact surface.

[0029] The four sides and bottom of the object under test are covered with insulating green oil, which is considered the insulating boundary, i.e.: .

[0030] Define the test function as v(x,y,z), and perform a volume integral of equation (2) over the entire domain Ω: (4); Applying the vector identity to the right side of equation (4), we have: (5); Substituting equation (5) into equation (4), and applying the divergence theorem (Gauss formula) to the first term on the right, the volume integral is transformed into the boundary surface integral, yielding the weak form of the system: (6); In the formula, For the calculation area The boundary, Let be the area element of the boundary.

[0031] Substituting the Robin boundary conditions defined in equation (3) into the area fractions on the right side of equation (6), and rearranging, we obtain the continuous weak form containing the boundary conditions: (7); Furthermore, the weak form of the transient heat conduction equation is discretized in time using a backward Euler fully implicit difference scheme and in space using the Galerkin method. In the discretized algebraic equation system, the boundary convection matrix and boundary load vector related to the adaptive Robin boundary conditions explicitly contain a virtual assimilation gain sequence.

[0032] Specifically, the time derivative term is discretized using an unconditionally stable backward Euler fully implicit difference scheme. Let the time step be Δt, then: (8); in, k Indicates the current time step. and These represent the temperature fields of the current step and the previous step, respectively.

[0033] Substituting equation (8) into equation (7), we obtain the first... k The time-discrete weak form of the time step: (9); In spatial terms, the Galerkin method is employed, introducing first-order finite element basis functions. (i=1,2,...,m, where m is the total number of nodes), consider the i-th k The time step node temperature is Then the temperature field interpolation is approximately: (10); Among them, the first-order finite element basis functions It satisfies the following interpolation properties: (11); Let the test function ,Right now: (12); Substituting equations (10) and (12) into equation (9), and assembling node by node, we obtain the first... k The global linear algebraic equations for each time step: (13); The definitions of matrices and vectors are as follows: Mass matrix M: (14); Stiffness matrix K: (15); Boundary convection matrix : (16); Boundary load vector : (17); In equation (14), Describes the first mass matrix M. i Line number j Column elements; In equation (15), The first term of the stiffness matrix K represents the first term of the stiffness matrix K. i Line number j Column elements; In equation (16), Represents the boundary convection matrix The i Line number j Column elements; In equation (17), Indicates the first k Time step boundary load vector The i One element, S For the boundary area, d S For the boundary The area of ​​the element is a micro-element.

[0034] By solving the system of linear equations shown in equation (13), the first... k Temperature vector of nodal points in the global 3D simulation temperature field at time step .

[0035] In three-dimensional finite element discretization, tetrahedral elements are used as the basic computational units. For any tetrahedral element in physical space... Let the physical coordinates of its four vertices be respectively , , , .

[0036] To facilitate the unified calculation of numerical integration and shape functions, a local reference tetrahedral element is introduced. The reference element is the standard parent element of a three-dimensional linear tetrahedral element, and the domain of the local reference coordinate system (ξ, η, ζ) is: ξ ≥ 0, η ≥ 0, ζ ≥ 0 and ξ + η + ζ ≤ 1; the four vertices of the reference element are respectively... , , , , corresponding to the four linear shape functions defined in equation (18).

[0037] In the local coordinate system (ξ, η, ζ) of the reference element, four linear shape functions (basis functions) are defined as follows: (18); The four shape functions mentioned above satisfy the interpolation property, that is ; In the formula, For the reference unit's first j The interpolation property ensures that the shape function can accurately interpolate the physical quantities at the element vertices, providing a foundation for finite element discretization.

[0038] A one-to-one mapping relationship is established between the physical coordinate system (x, y, z) and the local reference coordinate system (ξ, η, ζ) through affine coordinate transformation. This is based on the tetrahedral linear shape function defined in equation (18). (i=1,2,3,4), perform linear interpolation on the vertex coordinates of the physical unit, and the physical coordinates can be expressed as: (19); Substituting equation (18) into equation (19), we get: (20); Among them, the Jacobian matrix J Defined as: (twenty one); For a geometrically reasonable tetrahedral element J If J is a non-singular matrix (i.e., det(J) ≠ 0), its inverse matrix is... It exists, and the physical coordinates can be transformed back to local coordinates: (twenty two); Physical volume of a tetrahedral unit Ve It can be directly calculated from the determinant of the Jacobian matrix: (twenty three); Since the temperature field is interpolated using the finite element method in the physical coordinate system, it is necessary to transform the partial derivatives of the shape function in the reference coordinate system to the physical coordinate system. According to the chain rule for finding the derivative of a composite function, the relationship between the partial derivatives of the shape function in the reference coordinate system with respect to local coordinates and the partial derivatives of the shape function in the physical coordinate system with respect to global coordinates is as follows: (twenty four); In the formula, Let the transpose of the Jacobian matrix be represented. By inversely solving equation (24), we obtain the formula for calculating the gradient of the shape function in the physical coordinate system: (25); In the formula, Let be the transpose of the inverse of the Jacobian matrix. For physical coordinate system Lower shape function gradient vector, Reference coordinate system Lower shape function The gradient vector.

[0039] The gradient vectors of the four shape functions on the reference unit with respect to the local coordinates can be directly obtained from equation (18): (26); Substituting equations (25) and (26) into equation (15), we obtain the formula for calculating the element stiffness matrix: (27); In the formula, The element stiffness matrix The i Line number j Column elements are used to characterize the coupling properties of heat conduction within a unit. , Local reference coordinate systems Next i , j The gradient vector of a linear function.

[0040] Similarly, the formula for calculating the element mass matrix can be obtained: (28); In the formula, Unit mass matrix The i Line number j Column elements are used to characterize the transient thermal inertia of the unit; , These are the first two digits in the local reference coordinate system. i , j A linear function.

[0041] For linear tetrahedral elements, the integral in the reference coordinate system in equation (28) can be precisely calculated analytically using the Dirichlet integral formula for the standard reference tetrahedron (the centroid coordinate integral formula), without the need for numerical Gaussian integration. Its general form is: (29); In the formula, Representing the reference unit, the diagonal and off-diagonal elements of the mass matrix can be calculated separately using equation (29), such as correspond If a=2, then: Similarly, we can find the off-diagonal elements.

[0042] Therefore, the unit mass matrix can be rearranged as follows: (30); Stiffness matrices of all elements With the mass matrix and the convection matrix of the top boundary surface element. With load vector The system is assembled unit by unit according to the global node number, and finally forms a system of global linear algebraic equations (13) that can be directly solved.

[0043] Further, step S4, based on the pre-built spatial hierarchical index structure, extracts the simulation temperature value corresponding to the location of the thermal coupler, including: In the offline preprocessing stage, a directed bounding box tree is established for the three-dimensional tetrahedral finite element mesh; The directed bounding box tree is used to perform collision detection on the physical coordinates of each thermocouple and locate the tetrahedral cell to which the physical coordinates of the thermocouple belong. Centered on the nominal coordinates of the thermocouple, grid nodes are collected within a preset plane radius and thickness tolerance range, and the arithmetic mean temperature of the grid nodes is used as the equivalent simulation temperature of the corresponding thermocouple. The mapping relationship between the equivalent simulation temperature and the mesh node number is cached as a sparse matrix for direct use in online iteration.

[0044] Specifically, after solving the finite element equation in step S3, it is necessary to quickly extract the internal simulation temperature corresponding to the thermocouple physical coordinates from the global node temperature vector for parameter identification in step S5.

[0045] In the offline preprocessing stage, a directed bounding box tree needs to be constructed for the 3D tetrahedral finite element mesh. The directed bounding box tree is a hierarchical spatial acceleration data structure that recursively partitions the axis-aligned bounding boxes (AABBs) of all tetrahedral elements according to spatial hierarchy, forming a binary tree structure. For any query point, by traversing this tree structure from top to bottom, branch nodes that do not contain the query point are quickly excluded, reducing the time complexity of spatial search from O(n) of global traversal to O(log n), where n is the total number of elements. Subsequently, the known physical 3D coordinates of the embedded thermocouples are... Input the data into the bounding box tree above for collision detection, and quickly locate the target tetrahedral element e containing the coordinates.

[0046] After locking the target element, perform inverse coordinate transformation using equation (22): (31); The physical coordinates of the thermocouple Local reference coordinates mapped to the target cell .Will Substituting the basis functions defined in equation (18), the interpolation weights of the measurement point at the four vertices of the target unit are calculated. (i=1,2,3,4).

[0047] Considering the geometric uncertainty of thermocouple welding positions in actual working conditions, and the susceptibility of single-node temperature extraction to mesh discretization errors, this embodiment further proposes a robust temperature extraction strategy based on node averaging within a circular region. This is achieved using the nominal physical coordinates of the thermocouple. Define a neighborhood radius in the XY plane centered on the x-axis. r And set the layer thickness tolerance in the Z direction. dz Collect all grid nodes that meet the following conditions: and (32); In the formula, These are the grid nodes within the region. x axis, y axis, z axis coordinate values, These are thermocouple measuring points. x axis, y axis, z axis coordinate values, All N within the cylindrical neighborhood n The arithmetic mean of the temperatures at each grid node is taken as the equivalent simulation temperature of the thermocouple measuring point. : (33); The node coordinate selection and weight calculation processes described above are both completed in one step during the offline preprocessing stage and stored as a sparse matrix in cache. In the iterative solution at each time step, the aforementioned offline cached sparse mapping matrix is ​​directly called, along with the global node temperature vector of the current step. By performing dot product and mean calculations, the equivalent simulation temperature corresponding to each thermocouple measuring point can be obtained quickly. This eliminates the need to repeatedly perform any spatial search or interpolation calculations, greatly reducing online computational overhead and meeting the real-time requirements of soft measurement systems.

[0048] Furthermore, step S5, dynamic updating of thermal property parameters based on the multi-region asymmetric identification law, includes: Define the measured temperature data of the internal thermocouple. The equivalent simulation temperature extracted in step S4 The residuals between them are: (34); In the complex heat transfer system involved in this embodiment, the material's density ρ, specific heat capacity c, and thermal conductivity λ are coupled together. Identifying these three independent parameters simultaneously using only temperature response data would constitute an underdetermined problem, making it impossible to obtain a unique and definite solution. To solve this parameter coupling problem, this embodiment mathematically reduces the dimensionality of the parameters, defining the reciprocal of the equivalent thermal diffusivity as the single core identification target, denoted as: .

[0049] To address the fundamental difference in thermal response characteristics between the heat source excitation region and the large thermal inertia conduction region of the tested object, this embodiment employs a multi-region asymmetric dual-closed-loop iterative identification law to update the parameters in the time domain, as detailed below: The heat source excitation region is small in volume and extremely sensitive to changes in local heat sources, and it undergoes nonlinear latent heat absorption during welding. Based on the transient temperature residual at the heating point, this embodiment employs a gradient descent method with an adaptive decay learning rate α(t) for parameter updating, with the update law being: (35); in, The value is the reciprocal of the thermal diffusivity of the solder paste, (m) represents the outer iteration number of the algorithm, and t represents the current time step. This represents the temperature residual at the heating point.

[0050] Learning rate The learning rate gradually decreases with each iteration; α0 is the initial learning rate, and β is the decay coefficient.

[0051] To ensure the physical validity of the parameters, the updated parameters were... Apply physical upper and lower bound constraints: (36); In the formula, This is a preset lower bound constraint value for the reciprocal of the thermal diffusivity of the solder paste. This is a preset upper bound constraint value for the reciprocal of the thermal diffusivity of the solder paste.

[0052] For virtual control gain sequence Global updates are performed using an inter-round proportional iterative learning control (ILC) strategy. (37); In the formula, The gain is learned for the inter-round ratio; the updated gain sequence is smoothed by Gaussian and subjected to upper and lower bound constraints, and then used as the boundary condition input for the next round of finite element solution. It should be noted that, due to the surface virtual gain With internal equivalent thermal diffusivity Both factors influence the temperature evolution of the heating region, and they form a mutually synergistic dual-closed-loop compensation mechanism during the iterative process. Specifically, Primarily responsible for flexibly assimilating infrared surface observation data and suppressing boundary heat flow dispersion; Then in Based on this, the internal heat conduction rate is further refined to approximate the measured value of the thermocouple. The two compensate for each other and converge synergistically, jointly ensuring the high fidelity of the solder paste internal temperature prediction.

[0053] The large thermal inertial conduction region is mainly responsible for heat diffusion and conduction, exhibiting significant spatial and temporal lag effects. If proportional feedback is used alone, overshoot and oscillations in the optimization process are easily caused by the phase lag of heat conduction. Therefore, this embodiment introduces a proportional-differential iterative learning control (PD-ILC) algorithm with time memory effect for parameter updates, with the update law as follows: (38); In the formula, It is the reciprocal of the equivalent thermal diffusivity in the large thermal inertial conduction region; For iteration rounds, For time steps, Nothers represents the combined signed L2 norm of the residuals at each measurement point in the PCB area, and Nothers represents the number of measurement points in the PCB area. and These represent the proportional learning gain and the differential learning gain, respectively. This signed L2 norm comprehensively considers the directionality and magnitude of the residuals from multiple measurement points, providing a more complete reflection of the overall temperature deviation across the PCB area. (Differential term) Advanced damping compensation is provided to effectively suppress numerical oscillations in the identification of large thermal inertial systems, ensuring smooth convergence of the substrate's equivalent thermal properties in the time domain. Similarly, physical upper and lower bound constraints are applied to the updated parameters: (39).

[0054] In the formula, This is a preset lower bound constraint value for the reciprocal of the thermal diffusivity of the PCB board. This is a preset upper bound constraint value for the reciprocal of the thermal diffusivity of the PCB board.

[0055] Furthermore, the output of step S6, parameter closed-loop feedback, and three-dimensional global temperature field reconstruction results includes: The reciprocal of the equivalent thermal diffusivity of each region after the update in step S5 and the gain sequence updated in step S3 One-dimensional Gaussian filtering is applied to smooth the data to eliminate local high-frequency numerical noise, ensuring the physical continuity of the time series parameters. The smoothed parameters are then substituted back into the finite element stiffness and mass matrices from step S3 for the next iteration. The overall root mean square error (RMSE) of the system in the current iteration (m) is defined as: (40); The system exits the iteration loop when any of the following convergence conditions are met: (1) The overall RMSE(m) is less than the preset absolute convergence threshold ε.

[0056] (2) The change in RMSE in three consecutive iterations is very small, i.e. max(RMSE(m),RMSE(m-1),RMSE(m-2))-min(RMSE(m),RMSE(m-1),RMSE(m-2))<δ, triggering the oscillation convergence judgment.

[0057] After the convergence condition is met, the system will eventually output the following two types of results: (1) High-fidelity three-dimensional transient global temperature field of the measured object It can be used to evaluate the true temperature profile inside the solder paste and the thermal diffusion boundary of the surrounding PCB area; (2) The equivalent thermophysical parameters of each physical region as it evolves during the dynamic heating process, i.e. and The time series, and the converged virtual control gain sequence. This provides a reference for optimizing process parameters and analyzing material properties.

[0058] To verify the generalization ability of this embodiment under complex and variable grounding conditions, three-dimensional temperature field soft measurement experiments were conducted on printed circuit board (PCB) assemblies with diameters of 3mm, 4mm, and 5mm. The experiments only required input of non-contact infrared measured surface two-dimensional temperature field data and a small amount of discrete point temperature data from internal thermocouples; no precise material property parameter dictionary was required.

[0059] The specific verification scheme is as follows: For each pad diameter, two independent sets of experimental data were used to execute the complete identification process of steps S1 to S6 above, obtaining the converged equivalent thermal property parameters corresponding to each set of data. Then, the parameters of the two sets of identification results were arithmetically averaged over time steps to obtain the final equivalent thermal property constant for that pad diameter. This average parameter was then used to perform a pure forward simulation (i.e., without any parameter updates) on a third independent set of verification data, and the simulated temperature was compared with the measured thermocouple temperature in the verification data. The results show that, for all three pad diameters, the temperature curves of the pure forward verification simulation are highly consistent with the experimental data, and the verification error of the core heating point remains at a low level, thus verifying the effectiveness and accuracy of this technical solution. Figure 4 The output shows a schematic diagram of the three-dimensional transient temperature field distribution of the tested object, which intuitively illustrates the temperature gradient distribution between the solder paste heat source excitation area and the PCB conduction area. Specific results are shown in Tables 1 and 2. Figures 5-16 As shown.

[0060] Table 1 Table 2 This embodiment also provides a three-dimensional temperature field soft measurement system based on multi-source heterogeneous data fusion and boundary adaptation, used to implement the aforementioned three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation, including: The data acquisition module is used to acquire time-series temperature data of the surface of the object under test collected by non-contact infrared sensors, as well as discrete point time-series temperature data collected by internally embedded thermocouples, and to perform time synchronization and format standardization processing on the two types of data. The multiphysics assimilation solution module is used to construct adaptive Robin boundary conditions with iterative variable virtual control gain, assimilate infrared time-series temperature field data as soft constraints into a three-dimensional tetrahedral finite element mesh model, and solve to obtain the global simulation temperature field. The spatial addressing mapping module is used to extract the simulation temperature value corresponding to the location of the thermocouple based on a pre-built spatial hierarchical index structure. The asymmetric parameter identification module is used to update the equivalent thermal diffusivity of each region based on the residual between the simulated temperature and the measured temperature, using different closed-loop update laws for different thermal property regions, and then feeding the updated parameters back to the multiphysics assimilation solution module.

[0061] This embodiment also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation. The processor can be a central processing unit (CPU), a graphics processing unit (GPU), or a multiprocessor cluster to meet the parallel computing requirements of three-dimensional finite element solution.

[0062] This embodiment also provides a computer-readable storage medium storing a computer program. When the computer program is executed, it implements the three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation. The computer-readable storage medium may include, but is not limited to, various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0063] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation, characterized in that, include: Acquire infrared time-series temperature field data of the surface of the object under test and time-series temperature data of the thermocouple at key internal locations; A three-dimensional tetrahedral finite element mesh model of the object under test is established, and the solution domain is divided into several sub-regions with independent thermophysical parameters, including the heat source excitation region and the thermal inertia conduction region. An adaptive Robin boundary condition with virtual control gain is constructed, and the infrared time-series temperature field data is assimilated into the three-dimensional tetrahedral finite element mesh model as a soft constraint. The initial value of the global three-dimensional simulation temperature field at the current time step is obtained by solving the weak form of the transient heat conduction equation. Based on a pre-built spatial hierarchical index structure, the simulated temperature value corresponding to the location of the thermal couple is extracted. Calculate the temperature residual between the simulated temperature value and the time-series temperature data of the thermal coupler, and based on the temperature residual, apply asymmetric parameter identification laws with different dynamic response characteristics to the heat source excitation region and the thermal inertia conduction region respectively, and independently update the equivalent thermal diffusivity of each sub-region. The updated equivalent thermal diffusivity is fed back to the next iteration. When the set convergence condition is met or the solution is completed, the three-dimensional transient temperature field of the measured object and the identified thermal property parameters are output. The adaptive Robin boundary condition with virtual control gain is: ； In the formula, The thermal conductivity of the surface medium, For the outer normal of the boundary, The coefficient of heat dissipation by natural convection. For ambient temperature, To simulate temperature, For the first m The time-varying sequence of virtual control gain during round iteration. The measured surface temperature is obtained using infrared technology. The asymmetric parameter identification law includes: For the heat source excitation region, a gradient descent method with an adaptive decay learning rate is used to update the inverse of the equivalent thermal diffusivity of the corresponding region based on the temperature residual at the heating point. For the aforementioned thermal inertia conduction region, a proportional-differential iterative learning control algorithm with time memory effect is adopted to update the reciprocal of the equivalent thermal diffusivity coefficient of the corresponding region based on the signed L2 composite residual from multiple measurement points.

2. The three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation according to claim 1, characterized in that, The weak form of the transient heat conduction equation is discretized in time using a backward Euler fully implicit difference scheme and in space using the Galerkin method. In the discretized algebraic equation system, the boundary convection matrix and boundary load vector related to the adaptive Robin boundary conditions explicitly contain the virtual control gain sequence.

3. The three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation according to claim 1, characterized in that, Based on a pre-built spatial hierarchical index structure, the simulated temperature values ​​corresponding to the location of the thermal couple are extracted, including: In the offline preprocessing stage, a directed bounding box tree is established for the three-dimensional tetrahedral finite element mesh; The directed bounding box tree is used to perform collision detection on the physical coordinates of each thermocouple and locate the tetrahedral cell to which the physical coordinates of the thermocouple belong. Centered on the nominal coordinates of the thermocouple, grid nodes are collected within a preset plane radius and thickness tolerance range, and the arithmetic mean temperature of the grid nodes is used as the equivalent simulation temperature of the corresponding thermocouple. The mapping relationship between the equivalent simulation temperature and the mesh node number is cached as a sparse matrix for direct use in online iteration.

4. The three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation according to claim 3, characterized in that, The conditions for collecting grid nodes within a preset plane radius and thickness tolerance range, centered on the nominal coordinates of the thermocouple, are as follows: and ; In the formula, These are the grid nodes within the region. x axis, y axis, z axis coordinate values, These are thermocouple measuring points. x axis, y axis, z axis coordinate values, r The preset plane radius, dz for z Directional layer thickness tolerance range.

5. The three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation according to claim 1, characterized in that, The adaptive decay learning rate decays exponentially with each iteration to balance the convergence speed and stability of parameter identification; the differential term in the proportional-derivative iterative learning control algorithm is used to provide advance phase compensation for the response lag of the large thermal inertial system and suppress overshoot and oscillation during the identification process.

6. The three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation according to claim 1, characterized in that, The asymmetric parameter identification law also includes: For the virtual control gain sequence, an inter-round proportional iterative learning control strategy is used for global updates.

7. A three-dimensional temperature field soft measurement system based on multi-source heterogeneous data fusion and boundary adaptation, used to implement the three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation as described in any one of claims 1-6, characterized in that, include: The data acquisition module is used to acquire infrared time-series temperature field data of the surface of the object under test and time-series temperature data of the thermocouple at key internal locations. The multiphysics assimilation solution module is used to construct adaptive Robin boundary conditions with iterative variable virtual control gain, assimilate infrared time-series temperature field data as soft constraints into a three-dimensional tetrahedral finite element mesh model, and solve to obtain the global simulation temperature field. The spatial addressing mapping module is used to extract the simulation temperature value corresponding to the location of the thermocouple based on a pre-built spatial hierarchical index structure. The asymmetric parameter identification module is used to update the equivalent thermal diffusivity of each region based on the residual between the simulated temperature and the measured temperature, using different closed-loop update laws for different thermal property regions, and then feeding the updated parameters back to the multiphysics assimilation solution module.

8. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the three-dimensional temperature field soft measurement method based on multi-source heterogeneous data fusion and boundary adaptation as described in any one of claims 1-6.

Images