Deep learning-based transient thermal field inversion method and system

Abstract

The invention discloses a transient thermal field inversion method and system based on deep learning, and the method comprises the steps: firstly obtaining thermal field evolution data and space grid coordinates of a measured object in a cooling process, and then designing a thermal field evolution network model composed of two sub-networks, the second sub-network outputs a deduced evolution thermal field, and deduces real material parameters of an object based on a finite difference deep learning model through joint optimization and fusion of internal and boundary thermal evolution equations as physical constraints so as to improve precision and robustness; on the basis, a time-containing inversion operator model is constructed, discrete cosine transform is utilized to map a thermal diffusion coefficient, a time step size and a final-state temperature field evolution sequence to a frequency domain, and accurate reasoning of an initial temperature field is realized through iterative optimization of an operator learning framework. The method has a good application prospect in material science and engineering detection, and can effectively assist in analysis and prediction of a complex heat conduction process.

Description

Technical Field

[0001] This invention belongs to the field of transient thermal inverse problem measurement technology, specifically involving a transient thermal field inversion method based on deep learning. Background Technology

[0002] Thermal diffusion is a ubiquitous physical phenomenon in nature and engineering, and its precise control and inversion are of great significance in many fields (such as heat dissipation of electronic devices, energy system optimization, and industrial non-destructive testing). Taking modern chips as an example, with the continuous shrinking of integrated circuit size and the continuous increase in power density, thermal management has become a key factor restricting their performance and reliability. The thermal diffusion problem in complex structures often involves high-dimensional, non-uniform materials and nonlinear boundary conditions, which poses a great challenge to the computational efficiency and accuracy of traditional numerical methods.

[0003] In the field of materials design, the emergence of thermal metamaterials has provided innovative ideas for thermal field manipulation: some studies have proposed radiation camouflage strategies based on structural thermal surfaces, achieving thermal stealth against external objects; others have used anisotropic element helmets to map background temperature distribution onto material surfaces, further expanding the application scope of thermal camouflage; still others have developed intelligent design frameworks for thermal metamaterials, significantly improving the optimization efficiency of functional structures. However, the widespread application of thermal metamaterials also places higher demands on thermal field inversion, and traditional iterative calculation-based methods often fall short when dealing with complex structures. In the field of intelligent algorithms, the rapid development of deep learning technology has provided new tools for solving thermal diffusion problems. The introduction of methods such as diffusion models and operator learning has opened up new avenues for solving inverse problems. For example, some studies have used diffusion models to achieve inverse design of periodic lattices of thermal metamaterials, effectively alleviating the ill-conditioned nature of inverse problems; other studies have significantly reduced the dependence on large-scale datasets by embedding physical equations into neural networks.

[0004] However, existing methods still have some limitations: on the one hand, data-driven models may lose interpretability in the absence of physical constraints; on the other hand, existing research is mostly focused on homogeneous materials or simplified scenarios, which are difficult to directly extend to practical applications of complex structures. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a transient thermal field inversion method based on deep learning. This method is a thermal field inversion framework based on the fusion of deep learning and physical models, aiming to overcome the limitations of traditional methods in non-uniform materials and time-dependent thermal fields, as well as the inference problem of complex non-uniform materials in time-dependent thermal fields. It is particularly applicable in industrial non-destructive testing, and the initial state is derived in reverse through the evolution of the finite final state thermal field.

[0006] To achieve the above-mentioned objectives, the present invention specifically adopts the following technical solution: In a first aspect, the present invention provides a transient thermal field inversion method based on deep learning, comprising the following steps: S1. Construct a spatial mesh based on the geometric model of the object under test to obtain the spatial mesh coordinates, and obtain the thermal field evolution data of the object under test during the cooling process to form a dataset. S2. Based on the heat conduction control equation, design a thermal field evolution network model containing two sub-networks. Train the thermal field evolution network model on the dataset and incorporate the thermal evolution equation and boundary thermal evolution equation as physical constraints. Construct a loss function using the mean square error of the obtained real temperature field and the evolved thermal field derived by the model. Based on minimizing the loss function, jointly optimize the two sub-networks to obtain the trained thermal field evolution network model. S3. The thermal diffusivity derived from the thermal field evolution network model is used as the inversion parameter. The time step, the final state evolution sequence in the dataset and the inversion parameter are input into the time-dependent inversion operator model. The operator learning framework is used to train it. The optimized time-dependent inversion operator model is obtained by iteratively optimizing the model parameters. S4. Determine if the materials of the tested object and the target detection object are the same: If they are the same, obtain the final state evolution sequence of the target detection object and use it as the actual evolution sequence. Use the time step, inversion parameters, and the actual evolution sequence as input to the optimized time-dependent inversion operator model, and inversely reason to obtain the actual initial thermal field distribution. If they are different, replace the tested object with the target detection object, generate a new dataset according to S1, retrain the thermal field evolution network model according to S2, and re-optimize the time-dependent inversion operator model according to S3. The retrained thermal field evolution network model derives a new thermal diffusivity coefficient as a new inversion parameter based on the new dataset, obtains a new actual evolution sequence from the new dataset, and uses the time step, the new inversion parameters, and the new actual evolution sequence as input to the second-optimized time-dependent inversion operator model, and inversely reason to obtain the actual initial thermal field distribution.

[0007] Based on the above scheme, each step can be implemented in the following preferred manner.

[0008] As a preferred embodiment of the first aspect mentioned above, in S1, a local heat source is simulated by a laser spot, and thermal field evolution data of different materials during the cooling process are obtained through laser heating experiments or numerical simulations. The thermal field evolution data from the initial state to after cooling time T1 is used as the initial evolution sequence, and the final state thermal field evolution data is used as the final state evolution sequence. Thus, multiple sets of thermal field evolution data are obtained by changing the laser position and power to form a dataset. The final state evolution sequence consists of thermal field evolution data at time T2. T1 and T2 represent the preset first time length and second time length, respectively.

[0009] As a preferred embodiment of the first aspect, in the thermal field evolution network model of S2, the first sub-network takes the spatial grid coordinates and dataset of the measured object as input and outputs the thermal diffusivity coefficient; the second sub-network takes the spatial grid coordinates and dataset of the measured object with time information as input, incorporates the internal thermal evolution equation and the boundary thermal evolution equation as physical constraints into the second sub-network, and outputs the evolved thermal field derived by the model; wherein, both the first sub-network and the second sub-network adopt convolutional neural networks with finite difference constraints.

[0010] As a preferred embodiment of the first aspect, in step S2, by calculating the gradient of the thermal diffusivity coefficient and the derived divergence of the evolving thermal field, the gradient and divergence are substituted into the internal thermal evolution equation and the boundary thermal evolution equation, and the thermal field evolution network model is jointly constrained and optimized by combining the loss function, thereby achieving joint optimization of the first sub-network and the second sub-network.

[0011] As a preferred embodiment of the first aspect mentioned above, the final state evolution sequence in S3 is input into the time-dependent inversion operator model for training using a sliding window method. The specific steps are as follows: S31. The continuous multi-frame final state evolution sequence from time step (t-Q) to time t is used as the input sequence. The operator learning framework updates the time-dependent inversion operator model parameters based on the input sequence and outputs the predicted temperature field data at time step (t+1); where t represents time; Q is the preset maximum prediction step size. S32. The predicted temperature field data at time (t+1) is incorporated into the input sequence, and the predicted temperature field data at time (t-Q) is deleted. The final state evolution sequence of multiple consecutive frames from time (t-Q+1) to time (t+1) is obtained as a new input sequence. The time-dependent inversion operator model parameters are updated by the operator learning framework, and the predicted temperature field data at time step (t+2) is further output. S33. Repeat S32 continuously until the predicted temperature field data at the initial moment is output, and obtain the optimized time-dependent inversion operator model.

[0012] As a preferred embodiment of the first aspect above, the internal thermal evolution equation is: ; In the formula, Let represent the temperature field of the pixel with coordinates (x, y) at time t. This represents the temperature field of the pixel with coordinates (x, y) at time t+1. Indicates the time step. Where is the ambient temperature, h is the convective heat transfer coefficient, and d is the thickness of the object being measured. The density of the object being measured. For constant pressure heat capacity, Thermal conductivity, This represents the divergence of the derived evolutionary thermal field. The gradient represents the thermal diffusivity, and T represents the temperature of the object being measured. It represents the product of the temperature gradient and the thermal conductivity.

[0013] As a preferred embodiment of the first aspect above, the boundary thermal evolution equation is: ; In the formula, This represents the temperature of the nth pixel to be measured. This represents the temperature of the (n+1)th pixel plus one pixel in the x-direction. This represents the temperature of the (n-1)th pixel minus the temperature of one pixel in the y-direction. This represents the temperature of the (n+1)th pixel in the y-direction plus one pixel. This represents the distance between two adjacent coordinates in the x-direction. This represents the distance between two adjacent coordinates in the y-direction. This represents the distance between two adjacent coordinates in the z-direction.

[0014] As a preferred embodiment of the first aspect above, the time-dependent inversion operator model is: ; In the formula, Let represent the temperature field of the pixel with coordinates (x, y) at time t. This represents the temperature field of the pixel with coordinates (x, y) at time t+1. Indicates the assignment operator. Represents a non-linear activation function. Indicates a correction term. It is a function The cosine transform of the equation, where D represents the thermal diffusivity, and → represents the mapping relationship. express The real space of dimension 1 It is a constant. yes The reverse, Let H represent the eigenvalues ​​corresponding to the characteristic basis, H represent the height of the Cartesian coordinate system, W represent the width of the Cartesian coordinate system, and m and n represent the coordinates in the characteristic space. Indicates time 0. This indicates that a cosine transform of the thermal diffusivity is performed. This indicates a cosine transform of the temperature field.

[0015] Secondly, the present invention provides a transient thermal field inversion system based on deep learning, comprising: The data acquisition module is used to acquire the spatial grid coordinates of the object to be inferred and its thermal field evolution data during the cooling process; The result acquisition module is used to obtain the actual initial thermal field distribution by reverse reasoning based on the spatial grid coordinates of the object to be reasoned and the thermal field evolution data, according to the deep learning-based transient thermal field inversion method described in any of the first aspects above.

[0016] Thirdly, the present invention provides a computer electronic device, including a memory and a processor; The memory is used to store computer programs; The processor is configured to, when executing the computer program, implement the deep learning-based transient thermal field inversion method as described in any of the first aspects above.

[0017] Compared with the prior art, the present invention has the following advantages: The method provided in this invention, by simulating the evolution of local thermal fields caused by different heat sources and combining actual infrared thermal imaging data, demonstrates the accuracy of this method in deriving the thermal diffusivity of materials and inferring the initial thermal field. Furthermore, this invention proposes a time-dependent inversion operator model based on DCT correction, significantly improving the accuracy and efficiency of thermal field inversion for complex structures. This invention achieves accurate estimation of material thermal parameters through the finite difference method, providing a reliable foundation for thermal field inversion of non-uniform materials. By using a convolutional neural network instead of a traditional fully connected neural network, the model can better preserve spatial information and accurately learn the evolution of the temperature field in both space and time. Furthermore, the strategy of combining operator learning and a diffusion model not only improves the robustness of the inference results but also effectively reduces noise interference, improving the accuracy of the model for time-dependent thermal field inversion. Numerical simulations and experimental scenarios verify the effectiveness of the proposed method, providing a new solution for practical applications such as chip heat dissipation and 3D printed devices. Through simulation and experimental verification, the method of this invention has an error of less than 5% in deriving the thermal diffusivity and less than 8% in numerical error in thermal field inversion. Furthermore, the initial heat source distribution and point heat source locations are clearly visible in the inversion results. This invention further advances the understanding of complex thermal field evolution and reverse diffusion mechanisms, laying a theoretical and technical foundation for subsequent applications in advanced materials design, industrial non-destructive testing, and other fields. Attached Figure Description

[0018] Figure 1 A schematic diagram of the transient thermal field inversion method based on deep learning provided in this embodiment; Figure 2 This is a schematic diagram of the data acquisition experiment in this embodiment; Figure 3 This is a schematic diagram of the thermal field evolution network model in this embodiment, along with a schematic diagram of its derivation. Figure 4 The schematic diagram and experimental comparison diagram of the time-dependent inversion operator model provided in this embodiment are shown. Detailed Implementation

[0019] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in the various embodiments of the present invention can be combined accordingly without mutual conflict.

[0020] In the description of this invention, it should be understood that the terms "first" and "second" are used only for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first" and "second" may explicitly or implicitly include at least one of those features.

[0021] like Figure 1 As shown, in a preferred embodiment of the present invention, the above-mentioned deep learning-based transient thermal field inversion method includes the following steps S1 to S4. The specific implementation process of each step will be described in detail below.

[0022] like Figure 1 As shown in Figure a, the initial state during the forward thermal diffusion process is often difficult to observe and unknown. It is necessary to infer the initial state from the final state of the diffusion process. Therefore, this invention constructs a time-dependent inversion operator model based on Discrete Cosine Transform (DCT) correction. This model inputs the final state thermal evolution data into the time-dependent inversion operator model, i.e. Figure 1 The time-reversal operator network in 'a' maps the heat conduction equation to a cosine basis to characterize complex dissipation processes. Even with noise and nonlinear perturbations, it can still efficiently and accurately infer the initial thermal field distribution. Its model flow is as follows: Figure 1 As shown in b. For the heat conduction process, different objects will exhibit different characteristics due to their varying thermal parameters, the most important of which is the thermal diffusivity of the object. This invention constructs a Thermal Field Evolution Network (TE-Net) to propagate the cooling process of the object forward. Combining convective heat transfer and boundary treatment, the thermal diffusivity of the object is derived and trained. Based on the grid information, the thermal diffusivity and thermal field information are derived, the derived thermal field is compared with the actual thermal field, and the obtained thermal diffusivity is fed into a time inversion operator network to guide the model, providing prior knowledge input for inversion. The model flow is as follows: Figure 1 As shown in c.

[0023] Specifically, as a preferred embodiment of the present invention, this embodiment provides a transient thermal field inversion method based on deep learning, including the following steps: S1. Construct a spatial mesh based on the geometric model of the object under test to obtain the spatial mesh coordinates and acquire the thermal field evolution data of the object under test during the cooling process to form a dataset.

[0024] It should be noted that a local heat source can be simulated using a laser spot, and thermal field evolution data of different materials during the cooling process can be obtained through laser heating experiments or numerical simulations. To simulate this process, it is crucial to reproduce as realistically as possible the situation where an object experiences an abnormal heat source, such as... Figure 2 As shown in the figure, in this embodiment, the following is constructed: Figure 2 The experimental platform shown in the lower left corner uses a laser to continuously output laser light to simulate the continuous heating of an abnormal heat source in an object. The laser outputs infrared light, which, through a prism, alters its optical path so that it strikes the object under test vertically from bottom to top. Finally, it is focused by a lens to achieve the effect of point heat source generation. After stabilization, the changes in the surface thermal field during cooling are observed using an infrared microscope. The initial state of the thermal field change is altered by changing the laser position. In this embodiment, measurements show that the actual laser spot diameter is less than 1 mm, and the propagation loss in air is less than 5%, thus simulating localized heating caused by defects in a chip.

[0025] During the experiment, a laser of a certain power was used to irradiate the sample until it reached a steady state, followed by a 5-second cooling period. The time step of the experiment was 0.125 seconds. This invention only observed the cooling period, meaning that 40 frames of data could be obtained per experiment. By continuously modifying the position of the laser hitting the object under test, a series of thermal field evolution data under different heat source conditions were obtained. These thermal field evolution data serve as the dataset for subsequent derivation of the thermal diffusivity parameter. Furthermore, the thermal field evolution obtained during cooling was further divided. First, the thermal field evolution data from the initial state to after cooling time T1 was used as the initial evolution sequence. Then, after cooling for another T2 time, the final state thermal field evolution data after cooling time T2 was used as the final state evolution sequence. Figure 2 Dataset 1 in the dataset represents the final-state thermal field evolution data after cooling for time T2. T1 and T2 represent the preset first and second time lengths, respectively, which can be set according to actual experimental requirements. The initial and final-state evolution sequences within the T1+T2 time interval constitute the dataset. Figure 2Dataset 2 in the dataset consists of T1 and T2. In the thermal field inversion stage, this invention uses the final state evolution sequence data of time period T2 to deduce the thermal field evolution of the forward time from the end to the beginning, and compares it with the actual thermal field evolution data to verify the inference accuracy of the method of this invention.

[0026] S2. Based on the heat conduction control equation, design a thermal field evolution network model containing two sub-networks. Train the thermal field evolution network model on the dataset and incorporate the thermal evolution equation and boundary thermal evolution equation as physical constraints. Construct a loss function using the mean square error of the obtained real temperature field and the evolved thermal field derived by the model. Based on minimizing the loss function, jointly optimize the two sub-networks to obtain the trained thermal field evolution network model.

[0027] It should be noted that, in order to help those skilled in the art better understand the present invention, the theoretical derivation of the thermal diffusivity is explained below.

[0028] For a non-uniform material, during its cooling process after heating, in addition to the internal convection between materials, convective heat transfer with the air is also a significant influencing factor. Therefore, this embodiment designs a thermal field evolution network model based on the heat conduction control equation. The heat conduction control equation is: ; In the formula, h is the convective heat transfer coefficient, and d is the thickness of the object being measured. The density of the object being measured. For constant pressure heat capacity, Thermal conductivity, The ambient temperature is T, and the temperature of the object being measured is T. This represents the divergence of the derived evolutionary thermal field. The gradient represents the thermal diffusivity. The product of the temperature gradient and thermal conductivity is given by t, where t represents time.

[0029] In this embodiment, it is assumed that the thermal diffusivity does not change with time during the evolution process, and only calculations need to be performed on it in the Cartesian coordinate system. However, the thermal field evolution is closely related to time. Therefore, based on the heat conduction control equation, a thermal field evolution network model (TE-Net) containing two sub-networks is designed, such as... Figure 3 As shown in figure a, the first subnetwork net1 takes the spatial grid coordinates of the measured object and the dataset as input, and outputs the thermal diffusivity D, where The second subnetwork, net2, takes the time-informed spatial grid coordinates of the measured object and the dataset as input, and incorporates the internal thermal evolution equation (i.e. Figure 3 The thermal diffusion equation (internal) and the boundary thermal evolution equation (i.e., ...) in a Figure 3The thermal diffusion equation (boundary) in a is incorporated into the second sub-network as a physical constraint, and the evolved thermal field derived from the output model is output.

[0030] In existing technologies, fully connected neural networks (FCNNs) are mostly used to build thermal field evolution network models. However, the spatial and temporal positional information of the input grid in fully connected neural networks cannot be well learned by the model; that is, the fully connected network unfolds the grid into vectors, resulting in the loss of spatial information. For the research content of this invention, especially when detecting the non-uniform or anisotropic thermal diffusivity of an object, spatial information is particularly important. Furthermore, it has been verified that using FCNNs only yields approximately equal numerical results and cannot learn the specific spatial distribution. Therefore, this invention chooses convolutional neural networks (CNNs), whose convolution operations extract features from the input data, enabling the thermal field evolution network model to learn the spatial relationships between its grids. Based on the above analysis, in this embodiment, both the first and second sub-networks employ finite-difference constrained convolutional neural networks. The two sub-networks can extract features from the input data to calculate the gradient of the thermal diffusivity and the derived divergence of the evolving thermal field. Furthermore, this invention adds physical constraints to each evolution process of the model, formulates internal thermal evolution equations and boundary thermal evolution equations respectively, substitutes the physical quantities obtained from model reasoning into them, compares them with the real physical field, and finally modifies the model parameters through backpropagation to satisfy both equations, thereby deriving the correct thermal diffusivity.

[0031] Specifically, in this embodiment, the gradient and divergence are substituted into the internal thermal evolution equation and the boundary thermal evolution equation, and the loss function is combined to constrain and optimize the thermal field evolution network model, thereby achieving joint optimization of the first sub-network and the second sub-network.

[0032] The internal thermal evolution equation is as follows: ; In the formula, Let represent the temperature field of the pixel with coordinates (x, y) at time t. This represents the temperature field of the pixel with coordinates (x, y) at time t+1. Indicates the time step. Where is the ambient temperature, h is the convective heat transfer coefficient, and d is the thickness of the object being measured. The density of the object being measured. For constant pressure heat capacity, Thermal conductivity, This represents the divergence of the derived evolutionary thermal field. The gradient represents the thermal diffusivity, and T represents temperature. It represents the product of the temperature gradient and the thermal conductivity.

[0033] The boundary thermal evolution equation is: ; In the formula, This represents the temperature of the nth pixel to be measured. This represents the temperature of the (n+1)th pixel plus one pixel in the x-direction. This represents the temperature of the (n-1)th pixel minus the temperature of one pixel in the y-direction. This represents the temperature of the (n+1)th pixel in the y-direction plus one pixel. This represents the distance between two adjacent coordinates in the x-direction. This represents the distance between two adjacent coordinates in the y-direction. This represents the distance between two adjacent coordinates in the z-direction.

[0034] In this embodiment, other boundary evolution equations can be derived similarly. Through the above derivation, the evolution process of the object during cooling can be fully described, thereby guiding the model inference to obtain the correct thermal diffusivity distribution. The overall process is as follows: Figure 3 As shown in a, the thermal diffusivity obtained this time will serve as prior knowledge for the inversion model below.

[0035] In this embodiment, writing the evolutionary equation has the advantage of eliminating the need for temporal calculations of the data, requiring only spatial calculations, thus reducing model complexity. Theoretically, knowing only the temperature field at t=0 allows for the inference of the temperature field at any other time, facilitating parallel computation and accelerating the training process. Clearly, after obtaining the derived evolutionary thermal field through the second sub-network, the actual temperature field (i.e., ...) is then used to infer the temperature field at any other time. Figure 3 The mean square error of the actual thermal field (in model a) and the derived evolved thermal field is used to construct a loss function, which guides the model inference to obtain the correct thermal diffusivity. The loss function is: ; In the formula, Let x and y represent the true temperature field, where x and y represent the horizontal and vertical coordinates of the true temperature field. Let i and j represent the derived evolutionary thermal field, and let N represent the x and y coordinates of the derived evolutionary thermal field.

[0036] It should also be noted that the above theoretical derivations are all based on two-dimensional models, but in reality, the targets being detected are all three-dimensional structures. However, since infrared cameras can only capture data from two-dimensional surfaces, using sensors to obtain three-dimensional data is too costly, and the model computation cost would also increase significantly. This method can also be used for three-dimensional models, except that the material parameters obtained are equivalent to the two-dimensional equivalent thermal conductivity and thermal diffusivity of the three-dimensional model, but this does not affect the subsequent steps of this invention.

[0037] Based on the above principles, this embodiment uses COMSOL Multiphysics 6.2 simulation software to verify the theoretical feasibility of the thermal field evolution model. Since this embodiment uses a laser to continuously output laser light to simulate the continuous heating of an abnormal heat source in the object, a point heat source with the same cross-section as the laser is defined as the heat source term in the simulation, and a material is selected from the material library for simulation. Furthermore, to ensure the representativeness of the results inferred from the thermal field evolution model, this embodiment defines the thermal conductivity of the thermal field evolution model as cosine in the x-direction and sinusoidal in the y-direction, with the specific expression as follows: In the formula, L represents the length and width of the simulated material, and its thermophysical properties are: density = 6000 kg / m3, specific heat = 420 J / (kg K ).

[0038] In the simulation experiment, this embodiment performs a 10-second simulation, with the heat source heating time being 5 seconds, and the time step being... The time interval is set to 0.1s, the total size of the simulated material is 8mm × 8mm × 1mm, and the size of each discrete voxel is... = =0.08mm. For the simulation process, this embodiment defines a coordinate grid on the upper surface of the cuboid, taking only the surface readings from the simulation. Since the thermal imager can only provide surface readings, this embodiment uses these simulated surface profiles as ground truth values ​​to train the model and test its performance.

[0039] The theoretical thermal diffusivity distribution obtained from COMSOL simulation data modeling and the actual thermal diffusivity distribution (true thermal diffusivity distribution) in COMSOL simulation are as follows: Figure 3 b and Figure 3As shown in Figure c, the thermal diffusivity distribution inferred by this invention is very close to the true value. Furthermore, in this embodiment, considering the high integration level of existing chips, most of which are in the millimeter range or even smaller, an infrared microscope is used to observe the thermal field evolution of the object under test. Each pixel of the microscope is 50µm × 50µm in size. The object is observed by 3D printing an 8mm × 8mm perforated structure with concentric circles at its center, as shown in Figure c. Figure 3 d. It uses internal drilling to prevent the model from obtaining information about its material parameters through surface structure.

[0040] In this embodiment, the initial and final evolution sequences during its thermal evolution process are fed into the model, and its thermal diffusivity distribution can be inferred as follows: Figure 3 As shown in figure e, the thermal diffusivity distribution is also two concentric circles with different radii, and its value is similar to that of the photosensitive resin. This proves that the thermal field evolution network model provided by this invention can accurately derive the thermal diffusivity distribution of the tested item and obtain an accurate thermal diffusivity coefficient.

[0041] S3. The thermal diffusivity derived from the thermal field evolution network model is used as the inversion parameter. The time step, the final state evolution sequence in the dataset and the inversion parameter are input into the time-dependent inversion operator model, and the operator learning framework is used to train it. The optimized time-dependent inversion operator model is obtained by iteratively optimizing the model parameters.

[0042] It's worth noting that diffusion models are currently very popular in the field of image generation. These models first define a Markov chain of diffusion steps to slowly add random noise to the data, and then learn the reverse diffusion process to construct the desired data samples from the noise. This invention is inspired by this; if an evolutionary equation can be defined and the time-dependent thermal field reverse diffusion process of a real physical field can be learned, then the initial state can be solved in reverse from the final-state temperature field.

[0043] Inspired by the above, and corresponding to S3, this invention proposes a time-dependent inversion operator (TRO) model for guiding the thermal field based on prior knowledge. The motivation for this design is that after deriving the material parameters, these parameters are used as prior knowledge input into another deep learning model. This model utilizes the final-state temperature field and material parameters, and learns through a deep learning model to infer the initial temperature field distribution.

[0044] Specifically, such as Figure 4 As shown in a, the construction and derivation process of the time-dependent inversion operator model is as follows: This invention starts from the parameterless partial differential equation of heat conduction, and based on the partial differential model, incorporates the temperature field with time and spatial information. Expressed in the form of evolutionary equations: ; In the formula, Let represent the temperature field of the pixel with coordinates (x, y) at time t. For evolution operators, Indicates time 0. Represents the Laplace operator. This represents the temperature field of the pixel with coordinates (x, y) at time 0.

[0045] An operator is a mapping from one function space to another. In a general sense, any operation performed on any function can be considered an operator. In neural networks, convolutional layers and fully connected layers can be considered operators. Existing PINN work samples x and the corresponding y from a given function and builds a neural network to learn. Unlike some previous PINN works, the evolutionary operator mentioned in this embodiment aims to learn the mapping from one cluster of functions to another.

[0046] The Graph Neural Operator (PDE) is a powerful operator model that uses a learning operator structured into a form similar to a Green's function as a solution method for PDEs. Since thermal field evolution in actual experiments inevitably involves the introduction of noise, this invention, inspired by the FNO network, introduces a correction term in this embodiment to better learn its evolutionary process, based on the aforementioned evolution equations. ,Will Updated to : ; In the formula, it is assumed that For a bounded open set, Representative is The real space of dimension 1 Represents a constant. Describes a bounded open set. It is mapped to Bounded linear operators on, and by Parameterization Represents a number parameterized from a finite space. Represents a linear transformation. For a finite-dimensional parameter space, and They are in and The space of separable Banach functions taking values ​​in, where and They represent as and The real space of dimension 1 and Represents a constant. The correction term is a linear transformation. This is a non-linear activation function. The effect of a non-linear activation function is defined by its components, and → indicates a mapping relationship. express The real space of dimension 1 It is a constant. Represents the real number space, This represents the assignment operator.

[0047] In this embodiment, the selection As a kernel integral transform for neural network parameterization, its corresponding evolution operator The function, This represents the coefficient changes in a higher-dimensional space. Returning to the evolution equation itself, we can also consider more general (pseudo)differential operators to replace the Laplace operator to describe more complex dissipative processes. When under the Neumann boundary conditions, the evolution operator is explicitly written. The result of its action will Transform into: ; in, Initial state Projection to feature function The coefficients, m and n represent the coordinates in the feature space. Let H represent the eigenvalues ​​corresponding to the characteristic basis, where H represents the height of the Cartesian coordinate system and W represents the width of the Cartesian coordinate system.

[0048] Under cosine basis conditions, the thermal field evolution process can be described by eigenvalue evolution. If the kernel integral operator can be mapped to the frequency domain for processing, it can be given meaning at the frequency domain physical level. Since the derivation process does not include material parameters such as thermal diffusivity, this embodiment needs to introduce the mapping of the material parameters derived in the previous step after cosine transformation into the evolution process, and assume that the material parameters do not change with time, so the cosine transformation can be directly multiplied by the above equation.

[0049] Therefore, based on the above derivations, this embodiment uses discrete cosine transform to map the thermal diffusivity and thermal field evolution data to the frequency domain. By introducing a linear operator based on eigenvalue evolution and a thermal diffusivity mapping term, the time-dependent inversion operator model is obtained as follows: ; In the formula, Indicates a correction term. It is a function The cosine transform of the equation, where D represents the thermal diffusivity, and → represents the mapping relationship. express The real space of dimension 1 Represents a constant. yes The reverse, This indicates that a cosine transform of the thermal diffusivity is performed. This indicates a cosine transform of the temperature field.

[0050] It should be noted that since the energy of the thermal field is mainly concentrated in the low-frequency range, some high-frequency noise can be appropriately removed later to obtain the most useful information. Through the above derivation, the physical properties of the model can be incorporated into its structure, making the model more interpretable. The specific model structure is as follows: Figure 4 As shown in a. Figure 4 In a, M is the evolution operator for multiplying the result of the DCT transform, i.e. The R part of the operation is to re-introduce the result from the previous step into the mapping of the material parameters after cosine transformation, i.e. This method not only improves the accuracy of inferring the initial temperature field but also significantly reduces computation time. In this way, rapid and accurate prediction of complex heat conduction processes can be achieved, providing reliable technical support for industrial applications.

[0051] It should be noted that in this embodiment, the final state evolution sequence is input into the time-dependent inversion operator model for training using a sliding window approach. The specific steps are as follows: S31. The continuous multi-frame final state evolution sequence from time step (t-Q) to time t is used as the input sequence. The operator learning framework updates the time-dependent inversion operator model parameters based on the input sequence and outputs the predicted temperature field data at time step (t+1); where t represents time; Q is the preset maximum prediction step size. S32. The predicted temperature field data at time (t+1) is incorporated into the input sequence, and the predicted temperature field data at time (t-Q) is deleted. The final state evolution sequence of multiple consecutive frames from time (t-Q+1) to time (t+1) is obtained as a new input sequence. The time-dependent inversion operator model parameters are updated by the operator learning framework, and the predicted temperature field data at time step (t+2) is further output. S33. Repeat S32 continuously until the predicted temperature field data at the initial moment is output, and obtain the optimized time-dependent inversion operator model.

[0052] S4. Determine if the materials of the tested object and the target detection object are the same: If they are the same, obtain the final state evolution sequence of the target detection object and use it as the actual evolution sequence. Use the time step, inversion parameters, and the actual evolution sequence as input to the optimized time-dependent inversion operator model, and inversely reason to obtain the actual initial thermal field distribution. If they are different, replace the tested object with the target detection object, generate a new dataset according to S1, retrain the thermal field evolution network model according to S2, and re-optimize the time-dependent inversion operator model according to S3. The retrained thermal field evolution network model derives a new thermal diffusivity coefficient as a new inversion parameter based on the new dataset, obtains a new actual evolution sequence from the new dataset, and uses the time step, the new inversion parameters, and the new actual evolution sequence as input to the second-optimized time-dependent inversion operator model, and inversely reason to obtain the actual initial thermal field distribution.

[0053] In this embodiment, verification is first performed on simulation data. One layer of the model is selected, and the input thermal field is compared with the thermal field at the next moment after passing through one layer of the model. The result is as follows: Figure 4 As shown in Figure a, it can be seen that directly using eigenvalues ​​to evolve the thermal field still results in some error compared to the actual thermal field evolution. This is because after performing a cosine transform on the thermal field distribution, factors such as environmental radiation and heat conduction, which cannot be ignored, interfere with the results. Therefore, a correction term is used... This can effectively correct this process and improve the inversion accuracy of the model. After the correction term... With the correction, the experimental error can be reduced by about 10%, indicating that the environmental influence is still significant.

[0054] After model training is complete, the error estimate of the thermal field inversion results is quantitatively estimated by observing the experimental results obtained from different detected objects, and a horizontal comparison is performed under different initial states to verify the accuracy and robustness of the model in learning thermal field evolution. In this embodiment, a perforated structure obtained by 3D printing is first used for verification, such as... Figure 4 b and Figure 4 As shown in the left figure (d), due to the photosensitive resin material, its thermal conductivity is relatively low, and the lateral heat diffusion is weak, so its point heat source is very obvious. The actual initial thermal field distribution is obtained through reverse reasoning using an optimized time-dependent inversion operator model, which is basically consistent with the actual results and can reconstruct the location of the heat source quite well.

[0055] Furthermore, to ensure the optimized model has universality in real-world applications, this invention uses a chip as the test object, yielding a series of results such as... Figure 4 c and Figure 4As shown in the right figure (d), its internal structure means that the actual heat source effect is not an idealized point heat source. However, the model can still correctly reproduce the forward thermal field of the chip, proving the effectiveness and robustness of the model. The inversion results also highlight local heat sources, which is beneficial for the subsequent detection of heat sources in this invention.

[0056] The method provided in this embodiment has been verified in simulation experiments and practical applications, showing that the time-dependent inversion model based on the final state temperature field can accurately reconstruct the thermal field distribution and has good application prospects, especially in the fields of materials science, engineering testing and industrial non-destructive testing.

[0057] In summary, the deep learning-based transient thermal field inversion method provided in this embodiment aims to solve the inference problem of complex heterogeneous materials in time-dependent thermal fields, particularly in industrial non-destructive testing. Since thermally conductive materials undergo complex physical and chemical changes during heat transfer, the study of their heat transfer performance inevitably becomes a hot topic in thermal analysis. This invention addresses the time-dependent thermal field inversion problem by analyzing the time evolution of the temperature field to derive material parameters and infer the initial temperature field. A deep learning model based on finite difference is designed to derive the true material parameters of the object, improving accuracy and robustness. In the initial temperature field inference, an operator model is introduced, using its characteristic basis thermal field evolution equations and employing discrete cosine transform to learn the time-dependent evolution law of the inverse diffusion of the thermal field, while enhancing the physical interpretability of the model, ultimately accurately predicting the temperature field at previous moments. Specifically, this invention uses discrete cosine transform (DCT) to correct the traditional thermal diffusion model, enabling it to effectively invert the initial temperature field distribution. This method not only enhances the physical interpretability of the model but also significantly improves the inference speed and accuracy for complex cooling processes. This study simulates the evolution of local thermal fields caused by different heat sources and combines this with actual infrared thermal imaging data to demonstrate the accuracy of this method in deriving the thermal diffusivity of materials and inferring the initial thermal field. By using a convolutional neural network (CNN) instead of a traditional fully connected neural network (FCNN), the model can better preserve spatial information and accurately learn the spatial and temporal evolution of the temperature field. Furthermore, the strategy of combining operator learning and a diffusion model not only improves the robustness of the inference results but also effectively reduces noise interference, thereby enhancing the accuracy of the model in temporally inverting the thermal field.

[0058] The method of this invention has been validated in simulation experiments and practical applications, demonstrating that the time-dependent inversion model based on the final-state temperature field can accurately reconstruct the thermal field distribution and has promising application prospects, particularly in materials science, engineering testing, and industrial non-destructive testing. This invention showcases how to solve problems in traditional numerical simulations by combining deep learning with physical models, providing an efficient and accurate tool for thermal field analysis and defect detection in practical engineering.

[0059] It should also be noted that the deep learning-based transient thermal field inversion method in the above embodiments can essentially be executed by a computer program or module. Therefore, similarly, based on the same inventive concept, another preferred embodiment of the present invention provides a deep learning-based transient thermal field inversion system corresponding to the deep learning-based transient thermal field inversion method provided in the above embodiments, comprising: The data acquisition module is used to acquire the spatial grid coordinates of the object to be inferred and its thermal field evolution data during the cooling process; The result acquisition module is used to obtain the actual initial thermal field distribution by reverse reasoning based on the spatial grid coordinates of the object to be reasoned and the thermal field evolution data, according to the transient thermal field inversion method based on deep learning described in the above embodiments.

[0060] Similarly, based on the same inventive concept, another preferred embodiment of the present invention also provides a computer electronic device corresponding to the physical perception-based generative 3D reverse design method provided in the above embodiments, which includes a memory and a processor; The memory is used to store computer programs; The processor is configured to implement the deep learning-based transient thermal field inversion method in the above embodiments when executing the computer program.

[0061] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention.

[0062] It is understood that the processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0063] It should also be noted that those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here. In the embodiments provided in this application, the division of steps or modules in the system and method is merely a logical functional division, and there may be other division methods in actual implementation. For example, multiple modules or steps may be combined or integrated together, and a module or step may also be split.

[0064] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A transient thermal field inversion method based on deep learning, characterized in that, Includes the following steps: S1. Construct a spatial mesh based on the geometric model of the object under test to obtain the spatial mesh coordinates, and obtain the thermal field evolution data of the object under test during the cooling process to form a dataset. S2. Based on the heat conduction control equation, design a thermal field evolution network model containing two sub-networks. Train the thermal field evolution network model on the dataset and incorporate the thermal evolution equation and boundary thermal evolution equation as physical constraints. Construct a loss function using the mean square error of the obtained real temperature field and the evolved thermal field derived by the model. Based on minimizing the loss function, jointly optimize the two sub-networks to obtain the trained thermal field evolution network model. S3. The thermal diffusivity derived from the thermal field evolution network model is used as the inversion parameter. The time step, the final state evolution sequence in the dataset and the inversion parameter are input into the time-dependent inversion operator model. The operator learning framework is used to train it. The optimized time-dependent inversion operator model is obtained by iteratively optimizing the model parameters. S4. Determine whether the material of the tested object and the target detection object are the same: If they are the same, obtain the final state evolution sequence of the target detection object and use it as the actual evolution sequence. Use the time step, inversion parameters and the actual evolution sequence to input the optimized time-dependent inversion operator model, and inversely reason to obtain the actual initial thermal field distribution. If they are different, the detected object is used to replace the object being tested. A new dataset is generated according to S1, and the thermal field evolution network model is retrained according to S2. The time-dependent inversion operator model is re-optimized according to S3. The retrained thermal field evolution network model derives a new thermal diffusivity coefficient as a new inversion parameter based on the new dataset. A new actual evolution sequence is obtained from the new dataset. The time step, the new inversion parameter, and the new actual evolution sequence are input into the second-optimized time-dependent inversion operator model, and the actual initial thermal field distribution is obtained through reverse reasoning.

2. The transient thermal field inversion method based on deep learning according to claim 1, characterized in that, In S1, a local heat source is simulated by a laser spot. Thermal field evolution data of different materials during the cooling process are obtained through laser heating experiments or numerical simulations. The thermal field evolution data from the initial state to after cooling time T1 is used as the initial evolution sequence, and the thermal field evolution data of the final state is used as the final state evolution sequence. By changing the laser position and power, multiple sets of thermal field evolution data are obtained to form a dataset. The final state evolution sequence consists of thermal field evolution data at time T2. T1 and T2 represent the preset first time length and second time length, respectively.

3. The transient thermal field inversion method based on deep learning according to claim 1, characterized in that, In the S2 thermal field evolution network model, the first sub-network takes the spatial grid coordinates and dataset of the measured object as input and outputs the thermal diffusivity coefficient; the second sub-network takes the spatial grid coordinates and dataset of the measured object with time information as input, incorporates the internal thermal evolution equation and the boundary thermal evolution equation as physical constraints into the second sub-network, and outputs the evolved thermal field derived by the model; wherein, both the first sub-network and the second sub-network adopt convolutional neural networks with finite difference constraints.

4. The transient thermal field inversion method based on deep learning according to claim 1, characterized in that, In step S2, by calculating the gradient of the thermal diffusivity coefficient and the derived divergence of the evolving thermal field, the gradient and divergence are substituted into the internal thermal evolution equation and the boundary thermal evolution equation, and the thermal field evolution network model is jointly constrained and optimized by combining the loss function, so as to achieve joint optimization of the first sub-network and the second sub-network.

5. The transient thermal field inversion method based on deep learning according to claim 1, characterized in that, The final state evolution sequence in S3 is input into the time-dependent inversion operator model for training using a sliding window approach. The specific steps are as follows: S31. The continuous multi-frame final state evolution sequence from time step (t-Q) to time t is used as the input sequence. The operator learning framework updates the time-dependent inversion operator model parameters based on the input sequence and outputs the predicted temperature field data at time step (t+1); where t represents time; Q is the preset maximum prediction step size. S32. The predicted temperature field data at time (t+1) is incorporated into the input sequence, and the predicted temperature field data at time (t-Q) is deleted. The final state evolution sequence of multiple consecutive frames from time (t-Q+1) to time (t+1) is obtained as a new input sequence. The time-dependent inversion operator model parameters are updated by the operator learning framework, and the predicted temperature field data at time step (t+2) is further output. S33. Repeat S32 continuously until the predicted temperature field data at the initial moment is output, and obtain the optimized time-dependent inversion operator model.

6. The transient thermal field inversion method based on deep learning according to claim 1, characterized in that, The internal thermal evolution equation is: ； In the formula, Let represent the temperature field of the pixel with coordinates (x, y) at time t. This represents the temperature field of the pixel with coordinates (x, y) at time t+1. Indicates the time step. Where is the ambient temperature, h is the convective heat transfer coefficient, and d is the thickness of the object being measured. The density of the object being measured. For constant pressure heat capacity, Thermal conductivity, This represents the divergence of the derived evolutionary thermal field. The gradient represents the thermal diffusivity, and T represents the temperature of the object being measured. It represents the product of the temperature gradient and the thermal conductivity.

7. The transient thermal field inversion method based on deep learning according to claim 6, characterized in that, The boundary thermal evolution equation is: ； In the formula, This represents the temperature of the nth pixel to be measured. This represents the temperature of the (n+1)th pixel plus one pixel in the x-direction. This represents the temperature of the (n-1)th pixel minus the temperature of one pixel in the y-direction. This represents the temperature of the (n+1)th pixel in the y-direction plus one pixel. This represents the distance between two adjacent coordinates in the x-direction. This represents the distance between two adjacent coordinates in the y-direction. This represents the distance between two adjacent coordinates in the z-direction.

8. The transient thermal field inversion method based on deep learning according to claim 1, characterized in that, The time-dependent inversion operator model is as follows: ； In the formula, Let represent the temperature field of the pixel with coordinates (x, y) at time t. This represents the temperature field of the pixel with coordinates (x, y) at time t+1. Indicates the assignment operator. Represents a non-linear activation function. Indicates a correction term. It is a function The cosine transform of the equation, where D represents the thermal diffusivity, and → represents the mapping relationship. express The real space of dimension 1 It is a constant. yes The reverse, Let H represent the eigenvalues ​​corresponding to the characteristic basis, H represent the height of the Cartesian coordinate system, W represent the width of the Cartesian coordinate system, and m and n represent the coordinates in the characteristic space. Indicates time 0. This indicates that a cosine transform of the thermal diffusivity is performed. This indicates a cosine transform of the temperature field.

9. A transient thermal field inversion system based on deep learning, characterized in that, include: The data acquisition module is used to acquire the spatial grid coordinates of the object to be inferred and its thermal field evolution data during the cooling process; The result acquisition module is used to obtain the actual initial thermal field distribution by reverse reasoning based on the spatial grid coordinates of the object to be reasoned and the thermal field evolution data according to the deep learning-based transient thermal field inversion method described in any one of claims 1 to 8.

10. A computer electronic device, characterized in that, Including memory and processor; The memory is used to store computer programs; The processor is configured to implement the deep learning-based transient thermal field inversion method as described in any one of claims 1 to 8 when executing the computer program.

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