A boiling surface heat flux soft measurement method and system based on a TransUNet fusion forward proxy operator loss

Abstract

The application belongs to the technical field of heat flux measurement, and proposes a boiling surface heat flux soft measurement method and system based on a TransUNet fusion forward proxy operator loss, which comprises the following steps: constructing a heat flux density function containing multiple random parameters, substituting the heat flux density function as a boundary condition into a three-dimensional transient heat conduction partial differential equation model for solving, training a TransUNet model based on training set data constructed based on the solving result, optimizing network parameters of the TransUNet model based on a physical information constraint loss function containing a forward proxy operator until convergence is achieved, and obtaining a trained TransUNet model; and predicting and calculating the boiling surface heat flux of a to-be-measured object based on the trained TransUNet model. Compared with the prior art, the application greatly improves the measurement accuracy while achieving non-contact measurement.

Description

Technical Field

[0001] This application belongs to the field of heat flux measurement technology, and proposes a soft measurement method and system for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss. Background Technology

[0002] Boiling heat transfer is widely used in energy, chemical, and electronic fields, including boilers in thermal power units, cooling of nuclear reactors, distillation columns, and chip cooling in electronic devices. In these applications, the core parameter "heat flux" directly determines the operating efficiency and safety of the equipment. For example, if the boiling heat flux of a nuclear reactor core exceeds a critical value, it can lead to wall burn-out; uneven heat flux distribution on the heating surface of a thermal power unit boiler can cause localized overheating and deformation. Therefore, achieving high-resolution, physically consistent, and data-efficient measurement of boiling surface heat flux is a key supporting technology for ensuring the safe operation of high-end equipment and optimizing thermal management design.

[0003] However, existing heat flux measurement and inversion techniques still have significant shortcomings in engineering applications. Traditional measurement techniques struggle to balance resolution and physical consistency. Contact heat flux meters are prone to interfering with the boiling flow field and have limited spatial resolution. While non-contact infrared thermal imaging can achieve field measurement, it is susceptible to measurement errors due to variations in detector hardware and surface emissivity. Secondly, soft measurement methods using the inverse heat transfer problem (IHTP) generally suffer from ill-posed limitations, being highly sensitive to measurement noise and exhibiting extremely unstable numerical solutions. Furthermore, although deep learning inversion methods, such as Physical Information Neural Networks (PINN), have emerged in recent years, existing models still suffer from insufficient inversion accuracy, low computational efficiency, and a lack of physical consistency guarantees in pool boiling heat flux density inversion scenarios, failing to achieve high-precision and high-efficiency engineering-grade inversion. Summary of the Invention

[0004] To overcome the shortcomings of poor measurement accuracy in the prior art, this invention proposes a soft measurement method and system for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss.

[0005] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows:

[0006] A soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss, the method comprising:

[0007] S1. Construct a heat flux density function containing multiple random parameters, substitute the heat flux density function as a boundary condition into the three-dimensional transient heat conduction partial differential equation model for solution, and obtain the simulated temperature field. Then, traverse the heat flux density function and the simulated temperature field to construct a simulated temperature-heat flux tensor pair.

[0008] S2. Undersample the tensor pairs based on zero values ​​to obtain training set data;

[0009] S3. Construct a TransUNet model, build a physical information constraint loss function containing forward surrogate operators, train the TransUNet model based on the training set data, optimize the network parameters of the TransUNet model based on the loss function during the training process until convergence, and obtain the trained TransUNet model.

[0010] S4. Input the temperature field of the object to be measured into the trained TransUNet model to obtain the boiling surface heat flux density distribution field of the object to be measured, and calculate the boiling surface heat flux based on the boiling surface heat flux density distribution field.

[0011] As a preferred embodiment, the multivariate random parameters include one or more parameters among the following: the position of the center of the control ring within the heat flux density function, the inner and outer radii of the ring, the peak heat flux, the phase, the start time of the peak, the end time of the peak, or the number of peaks.

[0012] As a preferred embodiment, the step of constructing a heat flux density function containing multivariate random parameters includes: randomly combining and sampling the multivariate random parameters to obtain multiple sets of heat flux density functions with different forms, the expressions of which are as follows:

[0013]

[0014] in, For the first i A heat flux density function, ( x,y,t ) represents a three-dimensional spatiotemporal independent variable; Let be the space of Cartesian product, and let represent the independent variable ( x,y,t The complete domain of ) a ( t ) is a bimodal time-periodic function; b ( x,y ) represents the annular space function simulating heat flow; To control the position of the center of the ring; and To control the inner and outer radii of the ring; To control the peak value of heat flux; To control the phase value of the heat flux periodic function; These are the start and end times of the first heat flux peak. These are the start and end times of the second heat flux peak; This represents the number of heat flux peaks.

[0015] As a preferred embodiment, the step of undersampling the tensor pairs based on zero values ​​to obtain the training set data includes:

[0016] Calculate the proportion of heat flux sample amplitudes in any tensor pair that are less than a first threshold as the zero-value ratio; classify tensor pairs with the zero-value ratio greater than a second threshold as a high zero-value sample set, and classify the remaining tensor pairs as a normal sample set.

[0017] A portion of samples is randomly selected from the high zero-value sample set and combined with the normal sample set to obtain the training set data, the expression of which is as follows:

[0018]

[0019]

[0020]

[0021]

[0022] in, The tensor pairs constitute the (th)th element in the heat flux matrix. i, j ) heat flow samples, r i The proportion of zero value The first threshold, The second threshold, For a high zero-value sample set, For the normal sample set, This represents the proportion of a sample drawn. For the extracted sample, For training set data, The sample set data consisting of all tensor pairs; N The tensor pairs constitute the total number of heat flux nodes in each column of the heat flux matrix; For indicator functions; This is the floor function.

[0023] As a preferred embodiment, the forward surrogate operator is the mapping relationship between the heat flow predicted by the TransUNet model and the corresponding temperature field, and its expression is:

[0024]

[0025] Where q and T represent the input and output variables during the TransUNet model training process, respectively, and A is the regularization matrix. H represents the regular coefficients, H is the coefficient matrix, and N is the non-homogeneous matrix.

[0026] As a preferred embodiment, the regularization matrix is ​​determined by a sparse diagonal matrix generated by a Markov random field four-neighborhood model.

[0027] As a preferred embodiment, the steps for determining the coefficient matrix and the non-homogeneous matrix include: extracting a two-dimensional region along a preset direction from the three-dimensional spatial solution domain corresponding to the three-dimensional transient heat conduction partial differential equation model; constructing finite element basis functions by discretizing the boundary of the two-dimensional region using finite element methods; and substituting the finite element basis functions into the corresponding partial differential equation model, the expression of which is as follows:

[0028]

[0029] Where s is a three-dimensional spatial coordinate node, t It is a time coordinate node; These are finite element basis functions. M It is the order of the matrix. T L It is a non-homogeneous PDE linear system; T U It is a linear system of PDEs with coefficient matrix terms. T L and T U Derived from ray-like transformations; N is a non-homogeneous matrix, which is composed of elements The first element in the matrix represents the first element. i One element, i It is the element index, with values ​​ranging from 1 to... M H is the coefficient matrix, which consists of elements The first element in the matrix represents the first element. i OK j Column elements, i and j These are the row and column indices of the element, respectively.

[0030] As a preferred embodiment, the physical information constraint loss function includes data loss and physical loss; wherein, the data loss is used to quantify the difference between the heat flow predicted by the TransUNet model and the simulated heat flow, and the physical loss maps the predicted heat flow to a temperature field based on the forward surrogate operator and measures the difference between the temperature field and the measured temperature data, and its expression is as follows:

[0031]

[0032] in, For training parameters, and These are the training weights. For the total loss function, For data loss, For the surrogate model loss, Let be the temperature field vector, defined as =[ ], Refers to the first i Temperature node values; Let the measured temperature vector be defined as follows: =[ ], For the first i Measured temperature node values; n For the finite element discrete dimension of heat flow, q It is a discrete heat flow vector, defined as q =[ q 1, q 2,...], q i For the first i Each heat flow node value; The heat flow estimation vector generated during network training is defined as follows: =[ ], For the first i Each heat flux is estimated at a node value.

[0033] As a preferred embodiment, after outputting the boiling surface heat flux density distribution field, the method further includes using mean absolute error, structural similarity, and peak signal-to-noise ratio to evaluate the prediction results.

[0034] This invention also proposes a soft measurement system for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss. The application of the aforementioned soft measurement method for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss includes:

[0035] The data acquisition module is used to generate a heat flux density function through multivariate parameterized random combination, and substitute the heat flux density function into a three-dimensional transient heat conduction partial differential equation model for parallel solution to obtain the corresponding simulated temperature field data and construct a simulated temperature-heat flux tensor pair.

[0036] The training dataset preprocessing module is used to calculate the proportion of zero values ​​in each sample of the tensor pair, divide the samples into high zero value samples and normal samples according to a preset threshold, and perform undersampling on the high zero value samples to obtain a balanced training set.

[0037] The model training module is used to build the TransUNet model, construct a physical information constraint loss function containing forward surrogate operators, and train the TransUNet model based on the training set data.

[0038] The measurement module inputs the temperature field of the object to be measured into the trained TransUNet model to obtain the boiling surface heat flux density distribution field of the object to be measured, and calculates the boiling surface heat flux based on the boiling surface heat flux density distribution field.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] This invention efficiently captures the nonlinear mapping relationship between the temperature field and the heat flow field by fusing a forward surrogate operator with the TransUNet model network. Furthermore, it transforms physical laws into loss constraints using the forward surrogate model, ensuring that the inversion results are both highly accurate and consistent with actual heat conduction logic. In addition, this invention eliminates the dependence on explicit expressions of partial differential equations, making the TransUNet model widely applicable to boundary condition inversion problems in any flat plate geometry, demonstrating strong cross-domain generalization potential. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating the implementation of a soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss proposed in Example 1.

[0042] Figure 2 This is a schematic diagram of the thermophysical process corresponding to the heat conduction partial differential equation model in Example 1;

[0043] Figure 3 This is a flowchart of the heat flux soft measurement method in Example 1;

[0044] Figure 4 This is a diagram of a soft measurement system architecture for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss, as shown in Example 2.

[0045] Figure 5 This is a schematic diagram of the single-bubble boiling experimental apparatus of Example 3;

[0046] Figure 6 The single-bubble boiling prediction results and error heatmap for Example 3;

[0047] Figure 7 This is a graph showing the multi-dimensional error analysis and performance verification of Example 3;

[0048] Figure 8 This is a graph showing the correlation and interval distribution between the prediction error and the true value in Example 3.

[0049] Figure 9 This is a schematic diagram of the multi-scale decomposition of the prediction error space in Example 3 of this embodiment;

[0050] Figure 10 This is a schematic diagram of the prediction results for Example 4;

[0051] Figure 11 This is a schematic diagram of the prediction results for Example 5. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0053] Example 1

[0054] This embodiment proposes a soft measurement method for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss, and the implementation flowchart is as follows. Figure 1 As shown.

[0055] A soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss, the method comprising:

[0056] A heat flux density function containing multiple random parameters is constructed. The heat flux density function is used as a boundary condition and substituted into a three-dimensional transient heat conduction partial differential equation model for solution to obtain a simulated temperature field. The simulated temperature-heat flux tensor pair is constructed by traversing the heat flux density function and the simulated temperature field.

[0057] The tensor pairs are undersampled based on zero values ​​to obtain training set data;

[0058] Construct a TransUNet model, build a physical information constraint loss function containing forward surrogate operators, train the TransUNet model based on the training set data, optimize the network parameters of the TransUNet model based on the loss function during the training process until convergence, and obtain the trained TransUNet model.

[0059] The temperature field of the object to be measured is input into the trained TransUNet model to obtain the boiling surface heat flux density distribution field of the object to be measured, and the boiling surface heat flux is calculated based on the boiling surface heat flux density distribution field.

[0060] In this embodiment, a temperature-heat flux dataset is constructed by solving the three-dimensional transient heat conduction partial differential equation, and undersampling of the data based on zero values ​​is performed during the preprocessing stage, effectively alleviating the imbalance problem in boiling heat transfer data. Furthermore, this scheme innovatively incorporates prior knowledge of forward surrogate operators containing physical mechanisms into the loss function of the TransUNet model for constrained training, combining the feature extraction capabilities of deep learning with physical laws, significantly improving the accuracy, robustness, and generalization ability of boiling surface heat flux measurement under complex and unknown conditions.

[0061] Furthermore, the 3D transient heat conduction partial differential equation model is expressed as follows:

[0062]

[0063] in, Indicates with position s and time t The temperature field, which is related to variables, is defined over a time interval. and 3D spatial domain Above; (s, t ) represents the spacetime domain. Define a 3D spatial domain and time domain The product space; , and They were defined separately and The product space of the boundary and the time domain; Indicates the initial time ( t The temperature field at (=0), express The initial condition values ​​are as follows: Let represent the normal vector outside the corresponding boundary; as a Newman boundary condition, it is assumed that the boundary heat flux under consideration is a function of time and space variables, where and Representing the upper and lower boundaries respectively and surrounding boundaries Heat flux on; k It is the thermal conductivity coefficient. It is the density of the material. It is specific heat capacity. It is the Laplace operator; It is the time partial derivative. It is along the outer normal of the boundary. The partial derivatives of .

[0064] like Figure 2 The figure shown is a schematic diagram of the thermophysical process corresponding to the partial differential equation model of heat conduction.

[0065] Figure 2 The green flat geometric part corresponds to the regular heating foil. The area, the lower surface of the area Apply a constant heat flux Heat will be transferred from the bottom up to the upper surface through the heating foil. This achieves the effect of heat dissipation for the system.

[0066] In an optional embodiment, the multivariate random parameters include one or more parameters within the heat flux density function, such as the position of the control ring center, the inner and outer radii of the ring, the peak heat flux, the phase, the peak start time, the peak end time, or the number of peaks.

[0067] Further optionally, the step of constructing a heat flux density function containing multivariate random parameters includes: randomly combining and sampling the multivariate random parameters to obtain multiple sets of heat flux density functions with different forms, the expressions of which are as follows:

[0068]

[0069] in, For the first i A heat flux density function, ( x,y,t ) represents a three-dimensional spatiotemporal independent variable; Let be the space of Cartesian product, and let represent the independent variable ( x,y,t The complete domain of ) a ( t ) is a bimodal time-periodic function; b ( x,y ) represents the annular space function simulating heat flow; To control the position of the center of the ring; and To control the inner and outer radii of the ring; To control the peak value of heat flux; To control the phase value of the heat flux periodic function; These are the start and end times of the first heat flux peak. These are the start and end times of the second heat flux peak; This represents the number of heat flux peaks.

[0070] In this embodiment, by introducing multi-dimensional random variables such as the center position, radius, peak heat flux, and time parameters, and constructing a heat flux density function with a specific mathematical expression based on the random combination and sampling of these parameters, the morphological diversity of the heat flux boundary conditions is enriched, making the generated training dataset more statistically close to the real physical scene.

[0071] In an optional embodiment, the step of undersampling the tensor pairs based on zero values ​​to obtain training set data includes:

[0072] Calculate the proportion of heat flux sample amplitudes in any tensor pair that are less than a first threshold as the zero-value ratio; classify tensor pairs with the zero-value ratio greater than a second threshold as a high zero-value sample set, and classify the remaining tensor pairs as a normal sample set.

[0073] A portion of samples is randomly selected from the high zero-value sample set and combined with the normal sample set to obtain the training set data, the expression of which is as follows:

[0074]

[0075]

[0076]

[0077]

[0078] in, The tensor pairs constitute the (th)th element in the heat flux matrix. i, j ) heat flow samples, r i The proportion of zero value The first threshold, The second threshold, For a high zero-value sample set, For the normal sample set, This represents the proportion of a sample drawn. For the extracted sample, For training set data, The sample set data consisting of all tensor pairs; N The tensor pairs constitute the total number of heat flux nodes in each column of the heat flux matrix; For indicator functions; This is the floor function.

[0079] In this embodiment, to address the long-tail effect of data caused by the excessive proportion of non-boiling regions throughout the boiling heat transfer cycle, a dual threshold is set to quantify the proportion of zero values ​​and divide the sample set. Undersampling is specifically performed on high zero-value samples, thereby avoiding the influence of invalid data on the neural network during training.

[0080] In an optional embodiment, the forward surrogate operator is the mapping relationship between the heat flow predicted by the TransUNet model and the corresponding temperature field, and its expression is:

[0081]

[0082] Where q and T represent the input and output variables during the TransUNet model training process, respectively, and A is the regularization matrix. H represents the regular coefficients, H is the coefficient matrix, and N is the non-homogeneous matrix.

[0083] Further, optionally, the regularization matrix is ​​determined by a sparse diagonal matrix generated by a Markov random field four-neighborhood model.

[0084] Optionally, the steps for determining the coefficient matrix and the non-homogeneous matrix include: extracting a two-dimensional region along a preset direction from the three-dimensional solution domain corresponding to the three-dimensional transient heat conduction partial differential equation model; constructing finite element basis functions by discretizing the boundary of the two-dimensional region using finite element methods; and substituting the finite element basis functions into the corresponding partial differential equation model, the expression of which is as follows:

[0085]

[0086] Where s is a three-dimensional spatial coordinate node, t It is a time coordinate node; These are finite element basis functions. M It is the order of the matrix. T L It is a non-homogeneous PDE linear system; T U It is a linear system of PDEs with coefficient matrix terms. T L and T U Derived from ray-like transformations; N is a non-homogeneous matrix, which is composed of elements The first element in the matrix represents the first element. i One element, i It is the element index, with values ​​ranging from 1 to... M H is the coefficient matrix, which consists of elements The first element in the matrix represents the first element. i OK j Column elements, i and j These are the row and column indices of the element, respectively.

[0087] In this embodiment, the mapping relationship between predicted heat flow and temperature field is used as a forward modeling surrogate operator, and a Markov random field four-neighborhood model is introduced to generate a regularization matrix. By utilizing the physical correlation of spatially adjacent nodes, the inherent mathematical ill-posedness problem in the inverse heat conduction problem is effectively overcome, ensuring the continuity and smoothness of the predicted heat flow field in spatial distribution.

[0088] As an example, the regularization matrix A={ a ij} is a sparse diagonal matrix generated by a Markov random field (MRF) four-neighborhood model, and the calculation formula for each element is defined as follows:

[0089]

[0090] The coefficient matrix H is the matrix of finite element basis functions B. j Substituting the results into the PDE equation and then integrating them, the expression for the PDE equation is as follows:

[0091]

[0092] The PDE model for a nonhomogeneous matrix N is:

[0093]

[0094] in, k It is the thermal conductivity coefficient. It is the density of the material. It is specific heat capacity. It is the Laplace operator.

[0095] In an optional embodiment, the physical information constraint loss function includes data loss and physical loss; wherein, the data loss is used to quantify the difference between the heat flow predicted by the TransUNet model and the simulated heat flow, and the physical loss maps the predicted heat flow to a temperature field based on the forward surrogate operator and measures the difference between the temperature field and the measured temperature data, and its expression is as follows:

[0096]

[0097] in, For training parameters, and These are the training weights. For the total loss function, For data loss, For the surrogate model loss, Let be the temperature field vector, defined as =[ ], Refers to the first i Temperature node values; Let the measured temperature vector be defined as follows: =[ ], For the first i Measured temperature node values; n For the finite element discrete dimension of heat flow, q It is a discrete heat flow vector, defined as q =[ q 1, q 2,...], q i For the first i Each heat flow node value; The heat flow estimation vector generated during network training is defined as follows: =[ ], For the first i Each heat flux is estimated at a node value.

[0098] More specifically, the temperature-heat flux tensor pair is undersampled and balanced and then input into the TransUNet model, with the temperature tensor used as the feature input of the neural network and the heat flux tensor used as the benchmark data for supervised learning.

[0099] A forward modeling surrogate operator is constructed from the 2D solution domain of the three-dimensional transient heat conduction partial differential equation after dimensionality reduction. The intermediate temperature field is then calculated based on the temperature-heat flux tensor pair using the forward modeling surrogate operator.

[0100] Calculate the data loss between predicted heat flow and simulated heat flow, the physical loss between intermediate temperature field and measured temperature field, and then sum the two by weight to obtain the total loss function.

[0101] The AdamW optimizer is used to perform backpropagation based on the total loss function to continuously update the network parameters until convergence and the optimal TransUNet model is output.

[0102] In this embodiment, a composite loss function is constructed that includes data loss and physical loss. The data loss ensures the model's ability to fit existing samples, while the physical loss substitutes the predicted heat flow into the forward surrogate operator to generate a temperature field and performs cross-verification in the temperature dimension.

[0103] In an optional embodiment, after outputting the boiling surface heat flux density distribution field, the method further includes using mean absolute error, structural similarity and peak signal-to-noise ratio to evaluate the prediction results.

[0104] In this embodiment, after obtaining the heat flux density distribution field, mean absolute error is introduced to evaluate the global numerical deviation, structural similarity is used to evaluate the spatial structure and texture features, and peak signal-to-noise ratio is used to evaluate the local distortion of the prediction results. This allows for a comprehensive and three-dimensional quantification of the soft sensor model's performance.

[0105] like Figure 3 The diagram shown is a flowchart of the heat flux soft measurement method in this embodiment.

[0106] Example 2

[0107] This embodiment proposes a soft measurement system for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss, applying the soft measurement method for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss proposed in Embodiment 1. For example... Figure 4The diagram shown is an architecture diagram of a soft measurement system for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss in this embodiment.

[0108] This embodiment proposes a soft measurement system for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss, including:

[0109] The data acquisition module is used to generate a heat flux density function through multivariate parameterized random combination, and substitute the heat flux density function into a three-dimensional transient heat conduction partial differential equation model for parallel solution to obtain the corresponding simulated temperature field data and construct a simulated temperature-heat flux tensor pair.

[0110] The training dataset preprocessing module is used to calculate the proportion of zero values ​​in each sample of the tensor pair, divide the samples into high zero value samples and normal samples according to a preset threshold, and perform undersampling on the high zero value samples to obtain a balanced training set.

[0111] The model training module is used to build the TransUNet model, construct a physical information constraint loss function containing forward surrogate operators, and train the TransUNet model based on the training set data.

[0112] The measurement module inputs the temperature field of the object to be measured into the trained TransUNet model to obtain the boiling surface heat flux density distribution field of the object to be measured, and calculates the boiling surface heat flux based on the boiling surface heat flux density distribution field.

[0113] It is understood that the system in this embodiment corresponds to the method in Embodiment 1 above, and the options in Embodiment 1 above are also applicable to this embodiment, so they will not be described again here.

[0114] Example 3

[0115] This embodiment implements the soft measurement method for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss proposed in Embodiment 1 under single-bubble boiling conditions.

[0116] like Figure 5 The diagram shown is a schematic of a single-bubble boiling experimental setup.

[0117] This embodiment primarily models the heating foil region (the green area in Figure 5). The metal heating foil is considered the computational domain, and a constant heat flux density is applied as a boundary condition on its bottom surface. The simulated spatiotemporal high-resolution measurement data are taken from the temperature values ​​calculated by the forward model at the bottom surface.

[0118] The geometric parameters and material thermophysical parameters used in the forward model in this embodiment are shown in Table 1.

[0119] Table 1. Geometric domain dimensions and material parameters for Example 3

[0120]

[0121] Based on the experimental setup, the stainless steel heating foil in the boiling device was modeled as a three-dimensional spatial domain. The observation duration was set to 0.05 seconds, corresponding to the complete growth cycle of a single bubble. An annular heat flux function was used as the heat flux on the upper surface. Qu ( x , y , t The theoretical distribution of ) has the following specific functional form:

[0122]

[0123] Among them, the function characterizing the change of peak heat flux with time Defined as:

[0124]

[0125] This function a ( t The peak variation of the boiling surface heat flux was simulated over one cycle, with the heat flux reaching its maximum value of 0.2 MW / m² at 0.025 seconds. 2 The spatially annular distribution of heat flux is determined by a function. describe:

[0126]

[0127] in It defines the ring-shaped physical structure of heat flow in space.

[0128] The analysis was conducted within a time interval of 0.016 seconds to 0.031 seconds. The time frequency of the numerical simulation was set to 1000 Hz, and the spatial resolution was 63 × 63. The heat flux at the bottom surface was assumed to be... Q L Keep the time constant, set to 5×10 -3 MW / m 2 From the bottom Γ L Input from bottom to top into the computational domain.

[0129] like Figure 6 The figure shows the single-bubble boiling prediction results and error heatmap of this embodiment.

[0130] like Figure 7 The figure shown is a diagram illustrating the multi-dimensional error analysis and performance verification of this embodiment.

[0131] from Figure 6 and Figure 7 As can be seen, the FPO-TransUNet model proposed in this application exhibits extremely high spatial feature fitting and numerical prediction accuracy in single-frame heat flux density field prediction. The overall error is extremely low and the distribution has good stochastic stability. Individual relative error extremes mainly originate from the numerical amplification effect of local zero-gravity pixels and do not affect the overall evaluation. At the same time, it also has a clear algorithm optimization path for small systematic deviations in local high gradient regions.

[0132] like Figure 8 The figure shown is a graph illustrating the correlation and interval distribution between the prediction error and the true value in this embodiment.

[0133] from Figure 8 As shown in the left figure, the mean absolute error generally increases with the increase of the actual heat flux value, reaching a peak (approximately 0.035) when the actual value is 0.15, and then slightly decreasing. The model has a larger error when predicting high heat flux densities because high-value regions usually correspond to areas with larger heat flux gradients (such as the annular enhancement zone of boiling bubbles), which are more difficult to fit and result in more obvious deviations. Figure 8 The right-hand figure shows that as the range of actual heat flux values ​​increases, both the median (orange line) and upper and lower quartiles of the error increase significantly, with greater error fluctuations (longer boxes) in the high-value range (e.g., 0.15-0.17). The error remains positive (both boxes are above the 0 red line), indicating a systematic positive bias in the high-value heat flux region (predicted values ​​are generally higher than actual values), and the error stability is worse in the high-value region.

[0134] like Figure 9 The diagram shown is a schematic diagram of the spatial multi-scale decomposition of prediction error in this embodiment.

[0135] Figure 9 The red positive error region at the center of the original error field and the alternating red and blue fluctuations around it reflect that the error is concentrated in the core high gradient region and that there is local random noise. The dense contour lines at the center of the error contour lines indicate that the error is highly concentrated in the core region, while the sparse contour lines on the periphery indicate that the model has higher fitting accuracy in the low gradient region at the edge, and the error mainly comes from the core high gradient region.

[0136] Example 4

[0137] This embodiment is another specific implementation of the soft measurement method for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss proposed in Embodiment 1, based on Embodiment 3.

[0138] The geometric parameters and material thermophysical parameters used in the forward model in this embodiment are shown in Table 2.

[0139] Table 2 Geometric domain dimensions and material parameters for Example 4

[0140]

[0141] like Figure 10 The image shown is a schematic diagram of the prediction results in this embodiment.

[0142] Figure 10 contains 8 time frames (frames 9-16), each frame is divided into two parts: "lower surface temperature field (input)" and "upper surface predicted heat flow field (output)," which fully presents the dynamic process of single-bubble boiling from bubble initiation → development → maturity → dissipation.

[0143] In this design, purple represents the low-temperature region (corresponding to the low-temperature liquid film region below the bubble), and orange represents the surrounding high-temperature wall surface. From frames 9 to 12, the central purple low-temperature region gradually expands and deepens in color (bubbles are generated and grow); from frames 13 to 16, the purple low-temperature region gradually shrinks and lightens in color (bubbles detach and disappear), clearly reflecting the temporal evolution of single-bubble boiling. Cyan / yellow-green represents high heat flux density regions (boiling heat transfer enhancement regions), and purple represents low heat flux density regions. Completely synchronized with the temperature field: from frames 9 to 12, as the central low-temperature region expands, a ring-shaped high heat flux region appears on the upper surface (local heat transfer enhancement during bubble generation), and the ring structure gradually becomes clearer with an increase in heat flux value; from frames 13 to 16, as the low-temperature region shrinks, the ring-shaped heat flux region gradually weakens and disappears, and the heat flux value decreases.

[0144] The prediction results of this example show that the application can predict the evolution of the heat flow field in complete synchronization with the temporal changes of the input temperature field. Throughout the entire cycle from bubble initiation to dissipation, the appearance, enhancement, and weakening of the heat flow field strictly correspond to the changes in the low-temperature region of the temperature field. Furthermore, the application demonstrates good small-scale feature fitting ability. At low spatial resolution, the model can clearly capture the fine structure of the annular heat flow (such as the edge details of the annular high-value region at frames 12 and 14), which can meet the needs of refined studies of boiling heat transfer.

[0145] Example 5

[0146] This embodiment is another specific implementation of the soft measurement method for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss proposed in Embodiment 1, based on Embodiment 3.

[0147] The geometric parameters and material thermophysical parameters used in the forward model in this embodiment are shown in Table 3.

[0148] Table 3. Geometric domain dimensions and material parameters for Example 5

[0149]

[0150] like Figure 11 The image shown is a schematic diagram of the prediction results in this embodiment.

[0151] exist Figure 11 The model comprises eight time frames (frames 1-4 and 13-16), each frame consisting of a lower surface temperature field (input) and a predicted upper surface heat flow field (output), showcasing the dynamic process of single-bubble boiling. Full-cycle temporal analysis and spatial feature evaluation demonstrate that the FPO-TransUNet model in this application can accurately, stably, and physically consistently reconstruct the dynamic evolution of single-bubble boiling. In the temporal dimension, the predicted heat flow loop evolution is strictly synchronized with the bubble's initiation (frames 1-2), development (frames 3-4), and regression (frames 13-16) stages. In terms of physical mechanisms and spatial distribution, the model, at high resolution, clearly captures the fine annular structure of the low-temperature liquid film region below the bubble (purple center) and the edge heat transfer enhancement region (yellow-green ring) (as shown by the clear outlines and smooth gradients in frames 2 and 14), and the overall spatial distribution perfectly matches the boiling heat transfer theory.

[0152] In summary, this application demonstrates extremely high reliability in engineering applications in terms of spatiotemporal dynamic tracking, accurate fitting of small-scale features, and physical consistency.

[0153] The terminology used in the accompanying drawings is for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0154] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss, characterized in that, The method includes: A heat flux density function containing multiple random parameters is constructed. The heat flux density function is used as a boundary condition and substituted into a three-dimensional transient heat conduction partial differential equation model for solution to obtain a simulated temperature field. The simulated temperature-heat flux tensor pair is constructed by traversing the heat flux density function and the simulated temperature field. The tensor pairs are undersampled based on zero values ​​to obtain training set data; Construct a TransUNet model, build a physical information constraint loss function containing forward surrogate operators, train the TransUNet model based on the training set data, optimize the network parameters of the TransUNet model based on the loss function during the training process until convergence, and obtain the trained TransUNet model. The temperature field of the object to be measured is input into the trained TransUNet model to obtain the boiling surface heat flux density distribution field of the object to be measured, and the boiling surface heat flux is calculated based on the boiling surface heat flux density distribution field. The physical information constraint loss function includes data loss and physical loss; wherein, the data loss is used to quantify the difference between the heat flow predicted by the TransUNet model and the simulated heat flow, and the physical loss is based on the forward surrogate operator to map the predicted heat flow to a temperature field and measure the difference between the temperature field and the measured temperature data, and its expression is as follows: in, For training parameters, and These are the training weights. For the total loss function, For data loss, For the surrogate model loss, Let be the temperature field vector, defined as =[ ], Refers to the first i Temperature node values; Let the measured temperature vector be defined as follows: =[ ], For the first i Measured temperature node values; n For the finite element discrete dimension of heat flow, q It is a discrete heat flow vector, defined as q =[ q 1, q 2,...], q i For the first i Each heat flow node value; The heat flow estimation vector generated during network training is defined as follows: =[ ], For the first i Each heat flux is estimated at a node value.

2. The soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss according to claim 1, characterized in that, The multivariate random parameters include one or more of the following parameters within the heat flux density function: the position of the control ring center, the inner and outer radii of the ring, the peak heat flux, the phase, the peak start time, the peak end time, or the number of peaks.

3. The soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss according to claim 2, characterized in that, The step of constructing a heat flux density function containing multivariate random parameters includes: randomly combining and sampling the multivariate random parameters to obtain multiple sets of heat flux density functions with different forms, the expressions of which are as follows: in, For the first i A heat flux density function, ( x,y,t ) represents a three-dimensional spatiotemporal independent variable; Let be the space of Cartesian product, and let represent the independent variable ( x,y,t The complete domain of ) a ( t ) is a bimodal time-periodic function; b ( x,y ) represents the annular space function simulating heat flow; To control the position of the center of the ring; and To control the inner and outer radii of the ring; To control the peak value of heat flux; To control the phase value of the heat flux periodic function; These are the start and end times of the first heat flux peak. These are the start and end times of the second heat flux peak; The number of heat flux peaks; t It is a time coordinate node.

4. The soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss according to claim 1, characterized in that, The steps for undersampling the tensor pairs based on zero values ​​to obtain the training set data include: Calculate the proportion of heat flux sample amplitudes in any tensor pair that are less than a first threshold as the zero-value ratio; classify tensor pairs with the zero-value ratio greater than a second threshold as a high zero-value sample set, and classify the remaining tensor pairs as a normal sample set. A portion of samples is randomly selected from the high zero-value sample set and combined with the normal sample set to obtain the training set data, the expression of which is as follows: in, The tensor pairs constitute the (th)th element in the heat flux matrix. i, j ) heat flow samples, r i The proportion of zero value The first threshold, The second threshold, For a high zero-value sample set, For the normal sample set, This represents the proportion of a sample drawn. For the extracted sample, For training set data, The sample set data consisting of all tensor pairs; N The tensor pairs constitute the total number of heat flux nodes in each column of the heat flux matrix; For indicator functions; This is the floor function.

5. The soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss according to claim 1, characterized in that, The forward surrogate operator is the mapping relationship between the heat flow predicted by the TransUNet model and the corresponding temperature field, and its expression is: Where q and T represent the input and output variables during the TransUNet model training process, respectively, and A is the regularization matrix. H represents the regular coefficients, H is the coefficient matrix, and N is the non-homogeneous matrix.

6. The soft measurement method for boiling surface heat flux based on TransUNet fused forward surrogate operator loss according to claim 5, characterized in that, The regularization matrix is ​​determined by a sparse diagonal matrix generated by a Markov random field four-neighborhood model.

7. The soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss according to claim 5, characterized in that, The steps for determining the coefficient matrix and the non-homogeneous matrix include: extracting a two-dimensional region along a preset direction from the three-dimensional solution domain corresponding to the three-dimensional transient heat conduction partial differential equation model; constructing finite element basis functions by discretizing the boundary of the two-dimensional region using finite element methods; and substituting the finite element basis functions into the corresponding partial differential equation model, the expression of which is as follows: Where s is a three-dimensional spatial coordinate node, t It is a time coordinate node; These are finite element basis functions. M It is the order of the matrix. T L It is a non-homogeneous PDE linear system; T U It is a linear system of PDEs with coefficient matrix terms. T L and T U Derived from ray-like transformations; N is a non-homogeneous matrix, which is composed of elements The first element in the matrix represents the first element. i One element, i It is the element index, with values ​​ranging from 1 to... M H is the coefficient matrix, which consists of elements The first element in the matrix represents the first element. i OK j Column elements, i and j These are the row and column indices of the element, respectively.

8. The soft measurement method for boiling surface heat flux based on TransUNet fused forward modeling surrogate operator loss according to any one of claims 1 to 7, characterized in that, After outputting the boiling surface heat flux density distribution field, the method further includes using mean absolute error, structural similarity and peak signal-to-noise ratio to evaluate the prediction results.

9. A soft measurement system for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss, applied to the soft measurement method for boiling surface heat flux based on TransUNet fusion forward modeling surrogate operator loss as described in any one of claims 1 to 8, characterized in that, The system includes: The data acquisition module is used to generate a heat flux density function through multivariate parameterized random combination, and substitute the heat flux density function into a three-dimensional transient heat conduction partial differential equation model for parallel solution to obtain the corresponding simulated temperature field data and construct a simulated temperature-heat flux tensor pair. The training dataset preprocessing module is used to calculate the proportion of zero values ​​in each sample of the tensor pair, divide the samples into high zero value samples and normal samples according to a preset threshold, and perform undersampling on the high zero value samples to obtain a balanced training set. The model training module is used to build the TransUNet model, construct a physical information constraint loss function containing forward surrogate operators, and train the TransUNet model based on the training set data. The measurement module inputs the temperature field of the object to be measured into the trained TransUNet model to obtain the boiling surface heat flux density distribution field of the object to be measured, and calculates the boiling surface heat flux based on the boiling surface heat flux density distribution field.

Images