Method and device for temperature field inversion inside wall of thick-walled component
By employing sliding window inversion and hierarchical recursion methods, the accuracy and stability issues of temperature field information in the inverse problem of heat conduction in thick-walled components were resolved, achieving high-precision and high-stability temperature field reconstruction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTH CHINA ELECTRIC POWER UNIV
- Filing Date
- 2026-03-12
- Publication Date
- 2026-06-12
AI Technical Summary
In the inverse problem of heat conduction in thick-walled components, subtle changes in the temperature of the outer wall cause huge differences in heat flow inversion on the inner wall, resulting in low accuracy and poor stability of the temperature field information solution.
The sliding window inversion method is adopted. The objective function is constructed in each time window, and the initial temperature field information and boundary condition parameters are updated based on the adjoint method until the gradient value change is less than the threshold. A time overlap region is set between adjacent windows, and the temperature field of the thick-walled component is inverted segment by segment by combining the hierarchical recursive method.
This improves the accuracy and stability of the temperature field distribution results for thick-walled components, effectively solves the problems of spurious heat flow and convergence difficulties, and ensures the physical reliability and computational robustness of the inversion solution.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of heat conduction technology, and in particular to a method and apparatus for inverting the temperature field inside the wall of a thick-walled component. Background Technology
[0002] The Inverse Heat Conduction Problem (IHCP) refers to the problem of inverting and inferring the complete temperature field information within a component under test based on limited temperature measurement data. Currently, the IHCP is widely used in the calculation of the internal temperature field of metal cylinders subjected to high pressure, including the temperature field reconstruction calculation of thick-walled pipes and headers under high pressure in coal-fired boilers.
[0003] However, in the inverse problem of heat conduction in thick-walled components, the sensitivity of thick-walled components is low. Slight changes in temperature on the outer wall can cause huge differences in heat flow inversion on the inner wall, resulting in false heat flow. The accuracy and stability of the temperature field information solution are low.
[0004] Therefore, there is an urgent need in this field to develop a new technical solution to solve the above-mentioned technical problems. Summary of the Invention
[0005] This invention provides a method and apparatus for inverting the temperature field inside the wall of a thick-walled component, which can improve the accuracy and stability of the solution of the temperature field information distribution results of the thick-walled component.
[0006] In a first aspect, the present invention provides a method for inverting the temperature field inside the wall of a thick-walled component, comprising: Each time window in the temperature field inversion process is determined. The time windows are sequentially connected in chronological order to form the total inversion time from the outer wall to the inner wall of the thick-walled component. Each time window includes a finite retention interval determined according to a preset thermal diffusion threshold. There is a time overlap region between adjacent time windows. The temperature field information at the beginning of the finite retention interval of each time window is used as the initial temperature field information of the next adjacent time window. An objective function is constructed to characterize the difference between the simulated value of the outer wall temperature and the temperature measurement data, as well as the difference between the initial temperature field information and the boundary condition parameters and the preset prior conditions. The temperature measurement data is the temperature measurement data of the temperature measuring points on the outer wall of the thick-walled component. The simulated value of the outer wall temperature is obtained based on the initial temperature field information, boundary condition parameters and heat conduction equation within the time window. The gradient of the objective function with respect to the initial temperature field information and boundary condition parameters is obtained based on the adjoint method. The initial temperature field information and boundary condition parameters are updated according to the gradient class method until the change in the gradient value of the initial temperature field information and boundary condition parameters is less than a preset threshold, and the temperature field distribution result within the time window is obtained. By stitching together the temperature field distribution results within the limited retention interval of all time windows, the temperature field distribution results inside the wall of the thick-walled component within the total inversion time are obtained.
[0007] In a second aspect, the present invention provides a temperature field inversion device for the interior of a thick-walled component, comprising: The time window division module determines each time window in the temperature field inversion process. The time windows are sequentially connected in chronological order to form the total inversion time from the outer wall to the inner wall of the thick-walled component. Each time window includes a limited retention interval determined according to a preset thermal diffusion threshold. There is a time overlap area between adjacent time windows. The temperature field information at the beginning of the limited retention interval of each time window is used as the initial temperature field information of the next adjacent time window. The objective function establishment module, connected to the time window division module, constructs an objective function. The objective function is used to characterize the difference between the simulated value of the outer wall temperature and the temperature measurement data, as well as the difference between the initial temperature field information and the boundary condition parameters and the preset prior conditions. The temperature measurement data is the temperature measurement data of the temperature measuring points on the outer wall of the thick-walled component. The simulated value of the outer wall temperature is obtained based on the initial temperature field information, boundary condition parameters, and heat conduction equation within the time window. The temperature field inversion module is connected to the objective function establishment module. Based on the adjoint method, it obtains the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters. It updates the initial temperature field information and boundary condition parameters according to the gradient class method until the change in the gradient values of the initial temperature field information and boundary condition parameters is less than a preset threshold, thereby obtaining the temperature field distribution result within the time window. The time window stitching module, connected to the temperature field inversion module, stitches together the temperature field distribution results within the limited retention interval of all time windows to obtain the temperature field distribution results inside the wall of the thick-walled component within the total inversion time.
[0008] Thirdly, the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the method described in the first aspect of the present invention.
[0009] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method described in the first aspect of the present invention.
[0010] This invention provides a method and apparatus for inverting the temperature field inside the wall of a thick-walled component. By introducing techniques such as segmented inversion using a sliding window, splicing finite retention intervals within the window, and joint inversion of temperature field information and boundary condition parameters, the numerical stability and efficiency of the inversion solution are maximized, ensuring stable and reliable temperature field reconstruction results even in low-sensitivity scenarios involving thick-walled components. It effectively solves problems such as spurious heat flow and convergence difficulties in the reverse heat conduction problem of thick-walled structures, improving the physical reliability and computational robustness of the inversion solution. It is widely applicable to various scenarios requiring temperature field reconstruction from temperature measurement data, including thick-walled pipes in power plants and components in steam systems. Attached Figure Description
[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0012] Figure 1 This is a flowchart of a method for inverting the temperature field inside the wall of a thick-walled component according to an embodiment of the present invention; Figure 2 A schematic block diagram of a temperature field inversion device inside the wall of a thick-walled component according to one embodiment is shown. Figure 3 This is a schematic diagram illustrating the layering of a thick-walled component from the outside in, according to one embodiment; Figure 4 This is a schematic diagram illustrating a temperature measuring point distribution according to one embodiment; Figure 5 This is a schematic diagram illustrating the division of discrete moments within a time window according to one embodiment; Figure 6 This is a schematic diagram illustrating a comparison between a temperature inversion result and temperature measurement data according to one embodiment; Figure 7 This is a schematic diagram illustrating a comparison between a temperature inversion result and temperature measurement data according to one embodiment; Figure 8 This is a schematic diagram illustrating a comparison between a temperature inversion result and temperature measurement data according to one embodiment; Figure 9This is a schematic diagram illustrating a comparison between a temperature inversion result and temperature measurement data according to one embodiment; Figure 10 This is a schematic diagram illustrating a comparison between a temperature inversion result and temperature measurement data according to one embodiment; Figure 11 This is a schematic diagram illustrating a comparison between a temperature inversion result and temperature measurement data according to one embodiment. Detailed Implementation
[0013] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0014] Please refer to Figure 1 This invention provides a method for inverting the temperature field inside the wall of a thick-walled component, the method comprising: Step 100: Determine each time window in the temperature field inversion process; The time windows are sequentially connected in chronological order to form the total inversion time from the outer wall to the inner wall of the thick-walled component. Each time window includes a finite retention interval determined according to a preset thermal diffusion threshold. There is a time overlap area between adjacent time windows. The temperature field information at the beginning of the finite retention interval of each time window is used as the initial temperature field information of the next adjacent time window. Step 102: Construct the objective function; The objective function is used to characterize the difference between the simulated value of the outer wall temperature and the temperature measurement data, as well as the difference between the initial temperature field information and the boundary condition parameters and the preset a priori conditions. The temperature measurement data is the temperature measurement data of the temperature measuring points on the outer wall of the thick-walled component. The simulated value of the outer wall temperature is obtained based on the initial temperature field information, boundary condition parameters and heat conduction equation within the time window. Step 104: Obtain the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters based on the adjoint method, update the initial temperature field information and boundary condition parameters according to the gradient class method until the change in the gradient values of the initial temperature field information and boundary condition parameters is less than the preset threshold, and obtain the temperature field distribution result within the time window. Step 106: Segment the temperature field distribution results within the limited retention interval of all time windows to obtain the temperature field distribution results inside the wall of the thick-walled component within the total inversion time.
[0015] In this embodiment of the invention, the temperature field information inversion from the outer wall to the inner wall of a thick-walled component can be divided into online inversion and offline inversion. In offline inversion, the total inversion time (the total time period for which heat conduction analysis needs to be performed, such as the temperature change process of the pipe wall during several hours of operation of the thick-walled component) is divided into multiple time windows that are sequentially connected in chronological order, so that independent temperature field inversion calculations are performed within each time window. The online inversion process involves receiving temperature measurement data returned by temperature sensors located on the outer wall of the thick-walled component in real time, dividing the time windows online, and performing independent temperature field inversion calculations within each time window. After the inversion is completed, all time windows constitute the total inversion time. The temperature sensors correspond to preset temperature measurement points. The temperature measurement points can be set at any location on the thick-walled component according to the specific application scenario requirements. They can be symmetrically set on the left and right sides of the thick-walled component, asymmetrically set, or only set on the left side or one of the left sides. In this embodiment of the invention, the location of the temperature measurement points is not specifically limited. The accurate temperature field at a certain moment obtained by the inversion of the previous time window is used as the initial temperature field of the next time window, and the temperature field reconstruction of the long-term sequence is completed segment by segment. After the inversion solution for each time window is completed, only the inversion results corresponding to the finite retention interval within that time window are retained for output and stitching. This is equivalent to discarding the part that may be distorted due to boundary effects and missing end information at the beginning of that time window. By setting a finite retention interval, the error caused by window boundary effects can be reduced, achieving smooth stitching and transition of results from each time window. The temperature field information at the beginning of the finite retention interval of each time window is used as the initial temperature field information for the next adjacent time window. For example, if the previous time window includes discrete times 1-40 and the finite retention interval is 10-20, then the temperature field information at the beginning of the finite retention interval of the previous window at 10s is used as the initial temperature field information for the next time window. It should be noted that the next time window also includes discrete times 1-40, i.e., 1s-40s, while the time corresponding to the initial temperature field information is... Time. That is, each time window includes not only 1-40 discrete moments, but also a... The initial conditions are given at time 1 second. However, for the sake of convenience in subsequent calculations, we will still use 1 second as the start time of this time window and 40 seconds as the end time of the time window. This only corresponds to the moment of the initial temperature field information.
[0016] In each sliding window, a joint inversion strategy is employed to simultaneously identify unknown parameters in the initial temperature field and boundary condition parameter set within that time period. The initial temperature field distribution within the window, along with one or more boundary condition parameters, are uniformly incorporated into the parameters to be inverted. These boundary condition parameters may include, but are not limited to, boundary heat flux density, fluid temperature, and convective heat transfer coefficients (heat transfer intensity between the boiler tube inner wall and steam, ambient temperature outside the tube, or radiative heat transfer parameters can all be used as boundary conditions to be inverted). By jointly inverting the initial conditions (initial temperature field information) and boundary conditions, non-physical fluctuations occurring in the initial stage of inversion can be effectively suppressed, making the temperature field calculation more stable and reliable. The low-dimensional parameter vector is iteratively optimized within the sliding window to ensure that the simulated outer wall temperature obtained from the initial temperature field information and boundary condition parameters within the time window approximates the actual measured value. The initial temperature field information and boundary condition parameters for each time window are used as the variables to be optimized to construct an objective function. The gradient of the objective function with respect to the variables to be optimized is obtained based on the adjoint method. The initial temperature field information and boundary condition parameters are updated according to the obtained gradient information (including curvature approximation and historical gradients) until the change in the gradient value is less than a preset threshold. At this point, the inversion converges, and the temperature field distribution results within the time window are obtained. The temperature field distribution results within the limited retention intervals of all time windows are stitched together to obtain the temperature field distribution results inside the wall of the thick-walled component within the total inversion time.
[0017] Furthermore, for thick-walled structures or inversion regions with extremely low sensitivity, a spatially layered recursive method can be used to improve convergence and observability. For example... Figure 3 As shown, layered recursion refers to dividing the region to be inverted into at least two layers along the thickness direction and recursively inverting in a predetermined direction (from outside to inside or from inside to outside). Taking the outside-to-inside approach as an example, the outer layer region is inverted and solved first, and then the interface temperature and / or heat flow obtained from the outer layer are used as known boundary conditions or equivalent observation constraints for the inversion of the inner layer. Physical conditions such as temperature continuity and heat flow continuity should also be satisfied between layers to ensure the physical consistency of the solutions at each layer. Layered recursive solutions can effectively reduce the thickness of a single layer and enhance the feasibility and accuracy of the solution. This invention combines the layered strategy with joint inversion and finite retention intervals, ensuring the convergence advantage of the layered method while avoiding the distortion of the initial temperature field caused by the adiabatic assumption at the interface, thus improving the stability and accuracy of inversion in thick-walled scenarios.
[0018] In one embodiment of the present invention, each time window includes multiple equally spaced discrete moments, each moment corresponds to a first thermal diffusion parameter and a second thermal diffusion parameter, and the thermal diffusion threshold includes a first thermal diffusion threshold and a second thermal diffusion threshold. The earliest moment when the first thermal diffusion parameter is greater than or equal to the preset first thermal diffusion threshold is taken as the start moment of the finite retention interval, and the latest moment when the second thermal diffusion parameter is greater than or equal to the preset second thermal diffusion threshold is taken as the end moment of the finite retention interval. The first thermal diffusion parameter is expressed by the following formula:
[0019] The second thermal diffusion parameter is expressed by the following formula:
[0020] The first thermal diffusion parameter, This is the second thermal diffusion parameter. The thermal diffusivity of the wall material for thick-walled components. For any discrete moment within the time window. This is the start time of the time window. This is the last moment of the time window. The characteristic length of the thick-walled component. , For the volume of thick-walled components, This refers to the surface area of the inner wall of a thick-walled component.
[0021] In this embodiment, each time window includes multiple equally spaced discrete moments. For example, with one second as a discrete moment, a 40-second time window includes 40 discrete moments. The thermal diffusivity corresponding to each moment is calculated, i.e., in the formula above, Within these 40 time points, the first thermal diffusion parameter gradually increases, while the second thermal diffusion parameter gradually decreases. The earliest time when the first thermal diffusion parameter is greater than or equal to a preset first thermal diffusion threshold is taken as the starting time of the finite retention interval, and the latest time when the second thermal diffusion parameter is greater than or equal to a preset second thermal diffusion threshold is taken as the ending time of the finite retention interval. For example, When the first thermal diffusion parameter is less than the first thermal diffusion threshold, starting from 10s, the first thermal diffusion parameter becomes greater than or equal to the first thermal diffusion threshold. 10s is considered the earliest time when the first thermal diffusion parameter exceeds the first thermal diffusion threshold, and the overlapping region begins after 10s, marking the start of the finite retention interval. From 1 to 20s, the second thermal diffusion parameter exceeds the second thermal diffusion threshold. Starting from the 21st second, the second thermal diffusion parameter becomes less than the second thermal diffusion threshold, and 20s is considered the latest time when the second thermal diffusion parameter exceeds the second thermal diffusion threshold, marking the end of the finite retention interval. The finite retention interval for this time window is from 10s to 20s. It should be noted that, in a preferred embodiment, the initial temperature location of the next time window is within the finite retention interval of this time window (preferably the start of the finite retention interval of this time window), meaning there is an overlapping region between this time window and the next time window.
[0022] like Figure 3 As shown, in an embodiment where the thick-walled component is spatially layered, both the inner and outer layers are defined within finite intervals with reference to a first thermal diffusion threshold and a second thermal diffusion threshold. The first thermal diffusion parameter is calculated using the following formula:
[0023] In this formula, This is the characteristic length of the thick-walled component within this layer. , This represents the volume of the thick-walled component within this layer. This refers to the surface area of the inner wall of the thick-walled component within this layer.
[0024] The second thermal diffusion parameter is solved using the following formula:
[0025] In this formula, The characteristic length of the thick-walled component. , For the volume of thick-walled components, The surface area of the inner wall of a thick-walled component can be understood as... .
[0026] This can be understood as meaning that, without layering, .
[0027] In one embodiment of the present invention, the objective function is expressed as:
[0028] in, Let be the objective function. For a moment, For the first on the outer wall surface One temperature measuring point, The first circumferential direction of the calculation region for thick-walled components discrete points, For thick-walled components, calculate the radial direction of the region. discrete points, These are the boundary condition regularization coefficients. Here is the initial temperature field regularization coefficient. These are boundary condition parameters. For the first Simulated values of the outer wall temperature corresponding to each temperature measuring point for The radial coordinates of the position point on the outer wall surface of the thick-walled component at that moment. This refers to the temperature measurement data of the outer wall surface. For the calculation area Time of the first The circumferential position, the first Temperature values of the initial temperature field information at each radial position. To calculate the preset prior values of the initial temperature field within the calculation region, The boundary condition parameters to be inverted are... Pre-set prior conditions for boundary conditions.
[0029] In this embodiment, the objective function not only includes the simulated value of the outer wall temperature and the temperature measurement data, but also incorporates a regularization term to mitigate the influence of noise. Within each sliding window, a corresponding inverse problem model and objective function are established. The initial condition is taken as the temperature field of the entire solution domain at the time preceding the start of that time window (for the first window, this is a known initial condition, such as uniform room temperature; for subsequent windows, the result of stitching together the previous window is used as the initial estimate). The set of parameters to be inverted within the time window includes: initial temperature field parameters (describing the distribution of the pipe wall temperature along the thickness direction at the time preceding the start of the window); and inner wall boundary condition parameters (describing the heat transfer between the inner wall and the fluid within that time window, such as the equivalent heat flux of the inner wall as a function of time).
[0030] In one embodiment of the present invention, obtaining the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters based on the adjoint method includes: Based on the objective function, initial temperature field information, boundary condition parameters, and heat conduction equation, the Lagrange equation is constructed, and the adjoint equation is obtained by variational derivation of the Lagrange equation. Solving the adjoint equation yields the gradient of the objective function with respect to the initial temperature field and boundary condition parameters.
[0031] In this embodiment, the inverse problem of heat conduction is an optimization process, which is optimized using the gradient descent method. The gradient of the objective function with respect to the parameters to be inverted (initial temperature field and boundary condition parameters) is obtained based on the Lagrange equation. This embodiment constructs the Lagrange function using the adjoint method, transforming the optimization of the objective function under two hard constraints (hard constraints of the heat conduction equation; hard constraints that the initial temperature field must be equal to the ambient temperature field or the precise temperature field obtained in the previous time period) into an optimization equation for the Lagrange function under unconstrained conditions.
[0032] In one embodiment of the present invention, the Lagrange equation is expressed by the following formula:
[0033] in, Let be the objective function. These are the accompanying variables introduced for the heat conduction equation. The accompanying variable introduced for the initial temperature field, For temperature field information, For the solution domain in space, This refers to the time corresponding to the initial temperature field information within the time window. This is the start time of the time window. This is the last moment of the time window. For the density of thick-walled components, For the specific heat capacity of thick-walled components, The thermal conductivity of the thick-walled component is given. It serves as the internal heat source for thick-walled components. It is a spatial position coordinate vector. , for The radial coordinates of the position point inside the wall of the thick-walled component at that moment. for The circumferential, radial, and circumferential coordinates of the position point inside the wall of the thick-walled component at the given time are located in a cylindrical coordinate system established with the central axis of the thick-walled component as the reference. The heat conduction equation is established in the cylindrical coordinate system.
[0034] In this embodiment, the constrained optimization problem is transformed into an unconstrained problem by introducing Lagrange multiplier functions (i.e., adjoint variables). An augmented Lagrange functional is constructed. Variational operations are then performed on the aforementioned Lagrange functional. By using all variations related to the temperature field in the variational expression The sum of the coefficients of the multiplied terms is zero, so they can be eliminated. The influence of this, and from this, the accompanying variables are derived. The required differential equations—i.e., the adjoint equations—along with the corresponding terminal and boundary conditions, must be satisfied. The boundary conditions of the adjoint equations are determined by the type of boundary conditions in the original heat conduction problem. After solving the adjoint equations to obtain the adjoint variable field, the Lagrange functional variational equations are then solved. Variation that depends only on the variable to be optimized and From this, the Lagrange function can be extracted. Regarding the functional gradients of these variables: the extrema of the Lagrange function are also the extrema of the original objective function, thus realizing a complete mathematical derivation from the objective function and physical constraints to the specific gradient expression, providing the core computational basis for subsequent gradient-based method optimization.
[0035] In one embodiment of the present invention, the gradient of the objective function with respect to the initial temperature field information is:
[0036] The gradient of the objective function with respect to the boundary condition parameters is: .
[0037] In this embodiment, after obtaining the gradient expression of the objective function with respect to the initial temperature field and boundary condition parameters using the adjoint method, the optimal parameters for each window are solved iteratively. Specifically, based on the currently estimated initial temperature field and boundary conditions, the forward heat conduction problem is solved to obtain the temperature field within the window. Using this temperature field and measurement data, the adjoint equation is solved in reverse to obtain the adjoint variable field. Substituting the adjoint variable field into the gradient formula, the gradient of the objective function with respect to the initial temperature field and boundary conditions is calculated.
[0038] In one embodiment of the present invention, the initial temperature field information and boundary condition parameters are updated according to a gradient-based method until the gradient value change of the initial temperature field information and boundary condition parameters is less than a preset threshold, thereby obtaining the temperature field distribution result within the time window, including: The update direction and step size of the corresponding parameters are determined based on the gradient information of the objective function with respect to the initial temperature field information and the boundary condition parameters, respectively. The initial temperature field information and boundary condition parameters are iteratively updated; After each iteration, the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters is recalculated until the change in the gradient values of the initial temperature field information and boundary condition parameters is less than a preset threshold, thus obtaining the temperature field information and boundary condition parameters within the time window.
[0039] In this embodiment, gradient descent and a quasi-Newton trust region with damped updates can be used. Methods such as the conjugate gradient method are used to update the initial temperature field and boundary condition parameters. Based on the gradient information of the objective function with respect to the initial temperature field information and boundary condition parameters (which may include their transformation, curvature approximation, and historical gradients), the update direction of the corresponding parameters is determined; and based on the gradient information alone or in combination with the function value information of the objective function, the step size of the corresponding parameters is determined. The gradient value of the objective function with respect to the parameters to be inverted is recalculated using the updated parameters. It is determined whether the change in gradient value, the change in objective function value, or the change in parameters is less than a preset threshold. If convergence is not achieved, the iteration returns to the previous embodiment; if convergence is achieved, the final inverted initial temperature field, boundary conditions, and complete temperature field history for that window are output.
[0040] In a specific embodiment, a thick-walled pressure pipeline of a power plant boiler is used as the object to demonstrate the temperature field information solution process of the method of the present invention under a thick-walled structure. The object under test is a section of thick-walled cylinder (such as a superheater header pipe section), made of heat-resistant alloy steel, approximately 1m in length, with an inner diameter of approximately 0.193m, an outer diameter of approximately 0.273m, and a wall thickness of approximately 0.04m. High-temperature and high-pressure superheated steam flows inside the pipeline, and the outer wall is usually covered with an insulation layer (which can be regarded as approximate insulation). During operation, the temperature change curve of the outer wall over time can be obtained by an array of temperature sensors embedded on the outer surface of the pipe wall. However, the temperature of the inner wall cannot be directly measured due to the harsh environment (the inverse problem of heat conduction does not require temperature measurement points on the inner wall, but in order to verify the effectiveness of the inverse problem of heat conduction, temperature measurement points are added to the inner wall to verify the effectiveness of the heat conduction inversion results, such as...). Figure 4 As shown, Figure 4 The temperature measuring points are evenly distributed on both the inner and outer wall surfaces. Since the thick-walled component in this embodiment has a symmetrical structure... Figure 4 Temperature measuring points are only set on the right wall surface. The boundary thermal state (e.g., the intensity of convective heat transfer with steam or equivalent heat flux density) and the initial temperature field of the pipe wall are parameters to be identified.
[0041] For the aforementioned working condition of thick-walled cylinders, the implementation steps of the method of the present invention are as follows: A two-dimensional heat conduction model of the cylindrical wall is established. The governing equations, initial conditions, and boundary conditions are shown below.
[0042]
[0043] in It's a temperature value, the unit is... , It is a radial coordinate, and the unit is 1 / 2. , These are the coordinates of the inner wall surface, in units of... , These are the coordinates of the outer wall surface, in units of... . It is the thermal conductivity, and its unit is 1000 kilometres per second (kJ / m²). , It is the circumferential angle. It is time, the unit is , It is the initial time point. The heat flux density of the inner wall is expressed in units of 1. , It is the heat flux (internal heat source) of electric heat tracing, and the unit is _____. Initial conditions refer to the temperature distribution of the pipe wall at the initial moment. Boundary conditions include the heat transfer boundary between the inner wall and the steam (in this example, the unknown heat flux density) and the outer wall boundary (considered adiabatic in this example). Figure 5 The diagram shows a numerical discretization method for the model using the finite volume method to divide the mesh and select an appropriate time step (e.g., one time step every 2 seconds).
[0044] Due to the relatively thick pipe wall, in this embodiment of the invention, the solution domain is divided into two layers along the radial thickness direction: an outer layer and an inner layer. The outer layer is a portion of the thickness near the outer wall, and the inner layer is the remaining thickness near the inner wall, with the interface between the two located near the middle of the wall thickness. The outer layer region is inverted first, followed by the inner layer region. The inversion processes for the outer and inner layers follow a time-window inversion procedure, ensuring physical continuity between layers. Specifically, the interface temperature and heat flux obtained from the outer layer inversion are used as known boundary conditions for the inner layer inversion, while ensuring consistency of the interface temperature and heat flux density between the outer and inner layer solutions, achieving interlayer coupling. This layered, progressive solution reduces the thickness of a single layer, alleviates the difficulty caused by low sensitivity, and improves the convergence of gradient optimization.
[0045] Determine the total time range for the inversion analysis (e.g., pipe wall temperature changes over several hours or online monitoring), and divide it into continuous sliding time windows. Each window contains a fixed number of time steps (e.g., each window covers 40 time steps of data). Adjacent windows slide forward with partial overlap, for example, sliding forward 10 time steps each time, resulting in 75% time overlap between adjacent windows. This sliding window design ensures a smooth transition between results from adjacent windows and allows for subsequent correction of results at the end of the window.
[0046] Within each sliding window, a corresponding inverse problem model and objective function are established. The model within each window uses governing equations and a discrete mesh, but the initial conditions are taken as the temperature field of the entire solution domain at the time step preceding the start of that window (for the first window, this can be from known initial conditions, such as uniform room temperature; for subsequent windows, the result of stitching together the previous window is used as the initial estimate). The set of parameters to be inverted within each window includes: initial temperature field parameters (describing the distribution of pipe wall temperature along the circumferential and thickness directions at the start of the window); inner wall boundary condition parameters (describing the heat transfer between the inner wall and the fluid within the window time range, such as the equivalent heat flux of the inner wall as a function of time); and other potentially unknown boundary condition parameters (in this example, the outer wall is adiabatic, and the thick-walled component is symmetrical, so there are no additional unknown boundaries; however, a wall heating source can also be included). The objective function is constructed from the measured historical data of the outer wall temperature, for example, using the least squares form, with the sum of the squares of the differences between the simulated outer wall temperature and the actual measured value as the objective function.
[0047] The objective function can be expressed as:
[0048] The objective function not only includes the error of the outer wall measurement points at each time step within the window, but also allows for the addition of necessary regularization terms to mitigate the effects of noise.
[0049]
[0050] The inverse problem of heat conduction is an optimization process, which is optimized using a gradient-based method in this embodiment. First, the gradient of the objective function with respect to the parameters to be inverted (initial temperature field and inner wall heat flux density) must be obtained. This embodiment constructs a Lagrangian function using the adjoint method, transforming the optimization process under hard constraints—namely, the hard constraints that the objective function must be equal to the ambient temperature field or the precise temperature field obtained in the previous time period—into an optimization process under unconstrained conditions using the Lagrangian function. The Lagrangian function is shown below:
[0051] Lagrange function It is a temperature field as well as Initial temperature field at time The functional, now for Variational calculus yields the following equation:
[0052] The boundary conditions of the heat conduction equation are varied and used as part of the boundary conditions of the above variation:
[0053] For functionals By performing a distributional integral, making the discrete terms continuous, and substituting the boundary conditions, we obtain the following equation:
[0054] In order to eliminate The influence of heat flow through the inner wall makes the Lagrangian function only affected by the heat flow through the inner wall. and initial temperature field The impact. Treatment. By forcing the coefficients of relevant terms to zero, we obtain the Lagrange multipliers. Initial conditions, boundary conditions, source terms, governing equations, and Lagrange multipliers The expression is as follows:
[0055] Lagrange function Regarding the initial temperature field and internal wall heat flow The functional derivative is shown in the equation:
[0056] Once the derivative of the functional is obtained, the gradient information of the Lagrangian function with respect to the parameters to be inverted can be obtained. Based on the gradient information, the parameters to be inverted can be updated using gradient-based optimization methods (such as the conjugate gradient method, gradient descent method, quasi-Newton method, etc.). As long as the Lagrangian function reaches its minimum value, the objective function will inevitably reach its minimum value under constraints, thus completing the optimization. Through the above model, the in-window inversion problem is transformed into an optimization problem with the initial temperature field and boundary condition parameters as decision variables and the temperature measurement matching error as the objective.
[0057] To reduce the optimization dimensionality, improve the efficiency of inversion calculations, and make the boundary conditions more consistent with physical laws, the embodiments employ a low-dimensional parameterization method for the unknown boundary condition parameters within the window. For the inner wall heat flux density... The time-varying nature of the equations is represented using a finite-order polynomial basis function expansion. The variation of the circumferential angle is represented using the Fourier cosine basis function expansion:
[0058] The gradient of the Lagrange function with respect to the parameters to be inverted is shown below:
[0059] After establishing the parameterized representation, iterative optimization algorithms (such as gradient method, trust region method, etc.) are used to solve for the optimal parameter vector within the current window, minimizing the objective function. During the calculation process, as the parameters are iteratively updated, the forward problem simulation within this window can be repeatedly solved until the error between the calculated temperature and the observed temperature of the outer wall converges within the allowable range.
[0060] After completing the optimization solution within a certain window, only a finite number of intervals within that window are retained. The inversion results for the specified time period are adopted, while results for other time periods are discarded. Specifically, the results near the end of the window are used. Subsequent time steps, lacking sufficient supporting information, yielded results with lower reliability and were therefore discarded. In this embodiment, a total window length of 40 steps was chosen. For 10, Step 20 of retrieving the window, which is to keep only the window in the window. to The results of the 10 steps are used to stitch together the output. The temperature field and parameter estimates within the retention interval will be used as the final inversion output for that window, including the temperature field history at various locations on the pipe wall during that time period and the curve of the heat flux density on the inner wall over time. Then, the temperature distribution obtained at the beginning of the retention interval (time) is passed to the next window as the initial temperature field condition for the inversion of the next window.
[0061] For the thick-walled cylinder in this embodiment, after the inversion of the outer region is completed at each time interval, a similar time-window inversion is performed on the inner region. The outer wall boundary conditions required for the inner layer inversion are provided by the interface temperature / heat flux obtained from the outer layer inversion: that is, the interface acts as a "known boundary" for the inner layer, and the change of temperature or heat flux over time is determined by the outer layer results and incorporated into the inner layer objective function as observation data to provide constraints. The inversion steps for the inner layer are similar to those for the outer layer, including window division, finite retention, and joint optimization of initial field and boundary condition parameters. After iterative calculation to obtain the results of each window retention interval in the inner layer, the thermodynamic information of the entire thick-walled pipe from the outer wall to the inner wall over the entire time interval is obtained. The thermodynamic information from different time intervals is spliced together to obtain the temperature field evolution history for the entire time period.
[0062] Through the above steps, the embodiment ultimately reconstructs the transient temperature field of the thick-walled cylinder under complex boundary conditions. In particular, the temperature change over time at the inner wall can serve as an important output of the method of this invention, used to compare with temperature measurement points to verify the effectiveness of the method. In this example, based on several data points obtained from the experimental setup, the inverted inner wall temperature-time curve was compared with the measured temperatures at a few thermocouple measurement points embedded in the inner wall (e.g., ...). Figures 6-11(As shown in the figure). The results show that the overall trend of the inverted curve matches the measured curve well, accurately capturing temperature changes during transient processes such as sudden increases or decreases in steam temperature. Meanwhile, the inverted inner wall heat flux density curve is stable without significant non-physical oscillations, and there are no spurious peaks as seen in traditional methods. This verifies the effectiveness and superiority of the method of this invention in thick-walled scenarios: it ensures numerical stability in calculations while improving the physical reliability and usability of the results.
[0063] According to another embodiment, the present invention provides a temperature field inversion device inside the wall of a thick-walled component. Figure 2 A schematic block diagram of a temperature field inversion apparatus inside the wall of a thick-walled component is shown according to one embodiment. It will be understood that this apparatus can be implemented using any device, apparatus, platform, or cluster of devices with computing and processing capabilities. Figure 2 As shown, the device includes: a time window division module 200, an objective function establishment module 202, a temperature field inversion module 204, and a time window splicing module 206. The main functions of each component are as follows: The time window division module determines each time window in the temperature field inversion process. The time windows are sequentially connected in chronological order to form the total inversion time from the outer wall to the inner wall of the thick-walled component. Each time window includes a limited retention interval determined according to a preset thermal diffusion threshold. There is a time overlap area between adjacent time windows. The temperature field information at the beginning of the limited retention interval of each time window is used as the initial temperature field information of the next adjacent time window. The objective function establishment module, connected to the time window division module, constructs an objective function. The objective function is used to characterize the difference between the simulated value of the outer wall temperature and the temperature measurement data, as well as the difference between the initial temperature field information and the boundary condition parameters and the preset prior conditions. The temperature measurement data is the temperature measurement data of the temperature measuring points on the outer wall of the thick-walled component. The simulated value of the outer wall temperature is obtained based on the initial temperature field information, boundary condition parameters, and heat conduction equation within the time window. The temperature field inversion module is connected to the objective function establishment module. Based on the adjoint method, it obtains the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters. It updates the initial temperature field information and boundary condition parameters according to the gradient class method until the change in the gradient values of the initial temperature field information and boundary condition parameters is less than a preset threshold, thereby obtaining the temperature field distribution result within the time window. The time window stitching module, connected to the temperature field inversion module, stitches together the temperature field distribution results within the limited retention interval of all time windows to obtain the temperature field distribution results inside the wall of the thick-walled component within the total inversion time.
[0064] In a preferred embodiment, each time window includes multiple equally spaced discrete moments, each moment corresponding to a first thermal diffusion parameter and a second thermal diffusion parameter. The thermal diffusion threshold includes a first thermal diffusion threshold and a second thermal diffusion threshold. The earliest moment when the first thermal diffusion parameter is greater than or equal to the preset first thermal diffusion threshold is taken as the start moment of the finite retention interval, and the latest moment when the second thermal diffusion parameter is greater than or equal to the preset second thermal diffusion threshold is taken as the end moment of the finite retention interval. The first thermal diffusion parameter is expressed by the following formula:
[0065] The second thermal diffusion parameter is expressed by the following formula:
[0066] The first thermal diffusion parameter, This is the second thermal diffusion parameter. The thermal diffusivity of the wall material of the thick-walled component. For any discrete moment within the time window. This is the start time of the time window. This refers to the end of the time window. The characteristic length of the thick-walled component. , The volume of the thick-walled component. The surface area of the inner wall of the thick-walled component is given.
[0067] In a preferred embodiment, the objective function is expressed as:
[0068] in, Let be the objective function. For a moment, For the first on the outer wall surface One temperature measuring point, The first circumferential direction of the calculation region for thick-walled components discrete points, For thick-walled components, calculate the radial direction of the region. discrete points, These are the boundary condition regularization coefficients. Here is the initial temperature field regularization coefficient. These are boundary condition parameters. For the first Simulated values of the outer wall temperature corresponding to each temperature measuring point for The radial coordinates of the position point on the outer wall surface of the thick-walled component at that moment. This refers to the temperature measurement data of the outer wall surface. For the calculation area Time of the first The circumferential position, the first Temperature values of the initial temperature field information at each radial position. The initial temperature field within the calculation region is a preset prior value. The boundary condition parameters to be inverted are... Pre-set prior conditions for boundary conditions.
[0069] As a preferred embodiment, obtaining the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters based on the adjoint method includes: Based on the objective function, the initial temperature field information, the boundary condition parameters, and the heat conduction equation, the Lagrange equation is constructed, and the adjoint equation is obtained by variational derivation of the Lagrange equation. Solving the adjoint equation yields the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters.
[0070] In a preferred embodiment, the Lagrange equation is expressed by the following formula:
[0071] in, Let be the objective function. These are the accompanying variables introduced for the heat conduction equation. The accompanying variable introduced for the initial temperature field, For temperature field information, For the solution domain in space, This refers to the time corresponding to the initial temperature field information of the time window. This is the start time of the time window. This refers to the end of the time window. For the density of thick-walled components, For the specific heat capacity of thick-walled components, The thermal conductivity of the thick-walled component is given. It serves as the internal heat source for thick-walled components. It is a spatial position coordinate vector. , for The radial coordinates of the position point inside the wall of the thick-walled component at that moment. for The circumferential coordinates of the position point inside the wall of the thick-walled component at the given time are given. The radial and circumferential coordinates are located in a cylindrical coordinate system established with the central axis of the thick-walled component as the reference. The heat conduction equation is established in the cylindrical coordinate system.
[0072] In a preferred embodiment, the gradient of the objective function with respect to the temperature field information at the initial time is:
[0073] The gradient of the objective function with respect to the boundary condition parameters is: .
[0074] In a preferred embodiment, updating the initial temperature field information and boundary condition parameters according to a gradient-based method until the gradient value change of the initial temperature field information and boundary condition parameters is less than a preset threshold, to obtain the temperature field distribution result within the time window, includes: The update direction and step size of the corresponding parameters are determined based on the gradient information of the objective function with respect to the initial temperature field information and the boundary condition parameters, respectively. The initial temperature field information and the boundary condition parameters are iteratively updated; After each iteration, the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters is recalculated until the change in the gradient values of the initial temperature field information and boundary condition parameters is less than a preset threshold, thereby obtaining the temperature field information and boundary condition parameters within the time window.
[0075] According to another embodiment, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed in a computer, causes the computer to perform a combination Figure 1 The method described.
[0076] According to another embodiment, an electronic device is also provided, including a memory and a processor, wherein executable code is stored in the memory, and when the processor executes the executable code, it implements a combination... Figure 1 The method.
[0077] The various embodiments in this invention are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the device embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.
[0078] Those skilled in the art will recognize that, in one or more of the examples above, the functions described in this invention can be implemented using hardware, software, firmware, or any combination thereof. When implemented in software, these functions can be stored in a computer-readable medium or transmitted as one or more instructions or code on a computer-readable medium.
[0079] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made on the basis of the technical solution of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for inverting the temperature field inside the wall of a thick-walled component, characterized in that, include: Each time window in the temperature field inversion process is determined. The time windows are sequentially connected in chronological order to form the total inversion time from the outer wall to the inner wall of the thick-walled component. Each time window includes a finite retention interval determined according to a preset thermal diffusion threshold. There is a time overlap region between adjacent time windows. The temperature field information at the beginning of the finite retention interval of each time window is used as the initial temperature field information of the next adjacent time window. An objective function is constructed to characterize the difference between the simulated value of the outer wall temperature and the temperature measurement data, as well as the difference between the initial temperature field information and the boundary condition parameters and the preset prior conditions. The temperature measurement data is the temperature measurement data of the temperature measuring points on the outer wall of the thick-walled component. The simulated value of the outer wall temperature is obtained based on the initial temperature field information, boundary condition parameters and heat conduction equation within the time window. The gradient of the objective function with respect to the initial temperature field information and boundary condition parameters is obtained based on the adjoint method. The initial temperature field information and boundary condition parameters are updated according to the gradient class method until the change in the gradient value of the initial temperature field information and boundary condition parameters is less than a preset threshold, and the temperature field distribution result within the time window is obtained. By stitching together the temperature field distribution results within the limited retention interval of all time windows, the temperature field distribution results inside the wall of the thick-walled component within the total inversion time are obtained.
2. The method according to claim 1, characterized in that, Each time window includes multiple equally spaced discrete moments, each moment corresponding to a first thermal diffusion parameter and a second thermal diffusion parameter. The thermal diffusion threshold includes a first thermal diffusion threshold and a second thermal diffusion threshold. The earliest moment when the first thermal diffusion parameter is greater than or equal to the preset first thermal diffusion threshold is taken as the start moment of the finite retention interval, and the latest moment when the second thermal diffusion parameter is greater than or equal to the preset second thermal diffusion threshold is taken as the end moment of the finite retention interval. The first thermal diffusion parameter is expressed by the following formula: The second thermal diffusion parameter is expressed by the following formula: The first thermal diffusion parameter, This is the second thermal diffusion parameter. The thermal diffusivity of the wall material of the thick-walled component. For any discrete moment within the time window. This is the start time of the time window. This refers to the end of the time window. The characteristic length of the thick-walled component. , The volume of the thick-walled component. The surface area of the inner wall of the thick-walled component is given.
3. The method according to claim 1, characterized in that, The objective function is expressed as: in, Let be the objective function. For a moment, For the first on the outer wall surface One temperature measuring point, The first circumferential direction of the calculation region for thick-walled components discrete points, For thick-walled components, calculate the radial direction of the region. discrete points, These are the boundary condition regularization coefficients. Here is the initial temperature field regularization coefficient. These are boundary condition parameters. For the first Simulated values of the outer wall temperature corresponding to each temperature measuring point for The radial coordinates of the position point on the outer wall surface of the thick-walled component at that moment. This refers to the temperature measurement data of the outer wall surface. For the calculation area Time of the first The circumferential position, the first Temperature values of the initial temperature field information at each radial position. The initial temperature field within the calculation region is a preset prior value. The boundary condition parameters to be inverted are... Pre-set prior conditions for boundary conditions.
4. The method according to claim 3, characterized in that, The step of obtaining the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters based on the adjoint method includes: Based on the objective function, the initial temperature field information, the boundary condition parameters, and the heat conduction equation, the Lagrange equation is constructed, and the adjoint equation is obtained by variational derivation of the Lagrange equation. Solving the adjoint equation yields the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters.
5. The method according to claim 4, characterized in that, The Lagrange equation is expressed by the following formula: in, Let be the objective function. These are the accompanying variables introduced for the heat conduction equation. The accompanying variable introduced for the initial temperature field, For temperature field information, For the solution domain in space, This refers to the time corresponding to the initial temperature field information of the time window. This is the start time of the time window. This refers to the end of the time window. For the density of thick-walled components, For the specific heat capacity of thick-walled components, The thermal conductivity of the thick-walled component is given. It serves as the internal heat source for thick-walled components. It is a spatial position coordinate vector. , for The radial coordinates of the position point inside the wall of the thick-walled component at that moment. for The circumferential coordinates of the position point inside the wall of the thick-walled component at the given time are given. The radial and circumferential coordinates are located in a cylindrical coordinate system established with the central axis of the thick-walled component as the reference. The heat conduction equation is established in the cylindrical coordinate system.
6. The method according to claim 5, characterized in that, The gradient of the objective function with respect to the initial temperature field information is: The gradient of the objective function with respect to the boundary condition parameters is: .
7. The method according to claim 6, characterized in that, The step of updating the initial temperature field information and boundary condition parameters according to the gradient method until the gradient value change of the initial temperature field information and boundary condition parameters is less than a preset threshold, to obtain the temperature field distribution result within the time window, includes: The update direction and step size of the corresponding parameters are determined based on the gradient information of the objective function with respect to the initial temperature field information and the boundary condition parameters, respectively. The initial temperature field information and the boundary condition parameters are iteratively updated; After each iteration, the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters is recalculated until the change in the gradient values of the initial temperature field information and boundary condition parameters is less than a preset threshold, thereby obtaining the temperature field information and boundary condition parameters within the time window.
8. A temperature field inversion device for the interior of a thick-walled component, characterized in that, include: The time window division module determines each time window in the temperature field inversion process. The time windows are sequentially connected in chronological order to form the total inversion time from the outer wall to the inner wall of the thick-walled component. Each time window includes a limited retention interval determined according to a preset thermal diffusion threshold. There is a time overlap area between adjacent time windows. The temperature field information at the beginning of the limited retention interval of each time window is used as the initial temperature field information of the next adjacent time window. The objective function establishment module, connected to the time window division module, constructs an objective function. The objective function is used to characterize the difference between the simulated value of the outer wall temperature and the temperature measurement data, as well as the difference between the initial temperature field information and the boundary condition parameters and the preset prior conditions. The temperature measurement data is the temperature measurement data of the temperature measuring points on the outer wall of the thick-walled component. The simulated value of the outer wall temperature is obtained based on the initial temperature field information, boundary condition parameters, and heat conduction equation within the time window. The temperature field inversion module is connected to the objective function establishment module. Based on the adjoint method, it obtains the gradient of the objective function with respect to the initial temperature field information and boundary condition parameters. It updates the initial temperature field information and boundary condition parameters according to the gradient class method until the change in the gradient values of the initial temperature field information and boundary condition parameters is less than a preset threshold, thereby obtaining the temperature field distribution result within the time window. The time window stitching module, connected to the temperature field inversion module, stitches together the temperature field distribution results within the limited retention interval of all time windows to obtain the temperature field distribution results inside the wall of the thick-walled component within the total inversion time.
9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program, implements the method as described in any one of claims 1-7.
10. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the method of any one of claims 1-7.