WO2024007474A1 - 一种热学数据确定方法、装置和设备 - Google Patents

一种热学数据确定方法、装置和设备 Download PDF

Info

Publication number
WO2024007474A1
WO2024007474A1 PCT/CN2022/125225 CN2022125225W WO2024007474A1 WO 2024007474 A1 WO2024007474 A1 WO 2024007474A1 CN 2022125225 W CN2022125225 W CN 2022125225W WO 2024007474 A1 WO2024007474 A1 WO 2024007474A1
Authority
WO
WIPO (PCT)
Prior art keywords
heat flow
flow density
round
regularization
sampling
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Ceased
Application number
PCT/CN2022/125225
Other languages
English (en)
French (fr)
Inventor
黄明鸣
衡益
杨青青
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Sun Yat Sen University
Original Assignee
Sun Yat Sen University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Sun Yat Sen University filed Critical Sun Yat Sen University
Priority to GB2312112.2A priority Critical patent/GB2623404B/en
Publication of WO2024007474A1 publication Critical patent/WO2024007474A1/zh
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08—Thermal analysis or thermal optimisation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation

Definitions

  • the present application relates to the technical field of computer processing of thermal data, and in particular to a thermal data determination method, device and equipment.
  • thermal data such as heat flux density or temperature
  • the instantaneous heat flow density in a short period of time during laser, microwave and other hyperthermia treatments is large, and it is necessary to obtain information such as temperature field changes in relevant target areas of human tissue in real time.
  • temperature estimation of the target area around communications equipment can help optimize the installation location and architecture of communications equipment and achieve better heat dissipation.
  • evaluating the heat flow density in the target area of the heated component can help further optimize the heating strategy.
  • monitoring the heat flow density in target areas of pipeline fluids can help ensure safety and increase the service life of equipment.
  • the temperature data of limited measurement points on a part of the surface of the target area can only be obtained through temperature sensing components such as infrared temperature sensors or thermocouple sensors.
  • the target area cannot be detected by these temperature sensing components.
  • the temperature or heat flow density of the sensed part requires the use of auxiliary means such as computers to obtain indirect estimates.
  • the key part is to calculate and solve the inverse heat transfer problems (IHTP, Inverse heat transfer problems).
  • embodiments of the present application disclose a method for determining thermal data, which includes: determining a Tikhonov regularized functional model, the functional model is used to solve the inverse heat conduction problem in the target area, and outputs Estimate the heat flow density distribution of the area to be solved; obtain the known conditions of the variables in the functional model, which include boundary conditions, thermal property parameters and temperature distribution measurements of the target area; perform more than two rounds of calculations based on the functional model
  • the regularization parameter selection operation is performed to obtain the optimal solution of the last round of regularization parameters; based on the optimal solution of the last round of regularization parameters, the final selected regularization parameters are determined; and based on the final selected regularization parameters, the final selected regularization parameters are determined.
  • a thermal data determination device which includes: a model determination module for determining a Tikhonov regularized functional model, and the functional model is used to solve the thermal conductivity of the target area. Inverse problem, output the estimated value of heat flow density distribution in the area to be solved in the target area;
  • the known condition acquisition module is used to obtain the known conditions of the variables in the functional model.
  • the known conditions include the boundary conditions of the target area, thermal property parameters and temperature distribution measurements;
  • the optimal solution acquisition module is used to obtain the known conditions according to the functional model.
  • Execute more than two rounds of regularization parameter selection operations to obtain the optimal solution of the last round of regularization parameters;
  • the regularization parameter determination module is used to determine the final selected regularization parameters based on the optimal solution of the last round of regularization parameters. ;
  • an estimation module used to determine the final estimated value of the heat flow density distribution in the area to be solved based on the final selected regularization parameters.
  • the optimal solution acquisition module includes: a sampling value determination sub-module, used in each round of regularization parameter selection operation to determine multiple sampling values of this round according to the set sampling range value and sampling interval of the regularization parameter;
  • the model running sub-module is used to input multiple sampling values and known conditions into the functional model to obtain the heat flow density distribution estimate corresponding to each sampling value;
  • the L-curve determination sub-module is used to estimate the heat flow density distribution based on multiple value to determine the coordinate data of the L curve;
  • the optimal solution determination sub-module is used to determine the sampling values corresponding to the multiple coordinate data at the corners of the L curve as the optimal solution for the regularization parameters of this round;
  • the sampling parameter adjustment sub-module Module used to determine the sampling range value of the regularization parameters of the next round based on the optimal solution range of the regularization parameters of the current round when the current round is not the last round, and reduce the sampling range of the regularization parameters of the next round. interval.
  • embodiments of the present application disclose a computer device, which includes a memory and one or more processors.
  • Computer-readable instructions are stored in the memory.
  • processors When the computer-readable instructions are executed by one or more processors, One or more processors are caused to perform the steps of the thermal data determination method in any embodiment.
  • embodiments of the present application disclose a thermal data determination device, including a temperature measurement component and a processor; the temperature measurement component is used to measure the temperature distribution of the target area and generate the temperature distribution measurement value of the target area; the processor is used to Perform the steps of the thermal data determination method in any embodiment.
  • embodiments of the present application disclose one or more non-volatile computer-readable storage media storing computer-readable instructions. When executed by one or more processors, the computer-readable instructions cause one or more A processor performs the steps of the thermal data determination method in any embodiment.
  • Figure 1 is an application environment diagram of a thermal data determination method according to one or more embodiments
  • Figure 2(a) is a schematic flowchart of a method for determining thermal data according to one or more embodiments
  • Figure 2(b) is a schematic flowchart of the regularization parameter selection operation involved in Figure 2(a);
  • Figure 3 is a schematic flowchart of steps related to obtaining target coefficients according to one or more embodiments
  • FIG. 4 is a flowchart illustrating steps involved in determining a preferred solution for regularization parameters in accordance with one or more embodiments
  • Figure 5 is a schematic flowchart of steps involving calculation using the conjugate gradient method according to one or more embodiments
  • Figure 6 is a schematic flowchart of steps involving obtaining known conditions according to one or more embodiments
  • FIG. 7 is a flowchart illustrating steps related to determining a temperature distribution function of a target area in accordance with one or more embodiments
  • Figure 8 is a structural block diagram of a thermal data determination device according to one or more embodiments.
  • Figure 9 is an internal structure diagram of a computer device according to one or more embodiments.
  • FIG. 10 is a schematic diagram illustrating changes in estimated heat flux density distribution over observation time according to one or more embodiments.
  • the thermal data determination method disclosed in this application can be applied in the application environment as shown in Figure 1.
  • the processor 101 can communicate with the temperature measurement component 102 through the network, thereby obtaining the temperature distribution measurement value of the target area generated by the temperature measurement component 102.
  • the processor 101 may adopt at least one of a programmable logic array (PLA), a field programmable gate array (FPGA), a digital signal processor (DSP), an application specific integrated circuit (ASIC), a general-purpose processor or other programmable logic devices. implemented in hardware form.
  • the temperature measurement component 102 may include contact or non-contact temperature sensors for measuring the actual temperature of the target area, for measuring the temperature at the actual measurement point of the target area. These temperature sensors include, but are not limited to, thermocouple temperature sensors, thermal resistance temperature sensors, and infrared temperature sensors.
  • the present application discloses a method for determining thermal data, which is explained by taking the method applied to the processor 101 in Figure 1 as an example, including The processor 101 can execute steps S201 to S205, and each step will be described below.
  • Step S201 Determine the Tikhonov regularized functional model. This functional model is used to solve the inverse heat conduction problem in the target area and output an estimate of the heat flow density distribution in the area to be solved in the target area.
  • determining the functional model of Tikhonov regularization refers to the expression required to determine the functional model.
  • the specific expressions can be diverse and are not particularly limited here.
  • the functional model can include a prediction residual term and a regularization penalty term.
  • the prediction residual term includes the norm of the residual of the temperature distribution function.
  • the temperature distribution function is used to describe the temperature distribution of the target area in time and space.
  • Regularization The penalty term includes the regularization parameter and the norm of the unknown heat flow density function.
  • formula (1) can be used as the expression of the functional model.
  • L(Q u ) represents the target functional; can be regarded as the prediction residual term, It can be regarded as a regularization penalty term, ⁇ is the regularization parameter to be determined; ⁇ (x,t,Q u ) represents the temperature distribution function, x represents the space vector, t represents time, and Q u represents the heat flow density of the area to be solved Distribution, the solution of Q u is the solution of the inverse problem of heat conduction in the target area; ⁇ m (x, t) represents the temperature distribution measurement value; t max represents the final moment in a certain observation period, ⁇ I represents the first boundary of the target area, ⁇ u represents the second boundary of the target area.
  • the target area is an area composed of the boundary between the heating surface and the unknown heat flow
  • the first boundary can refer to the boundary of the lower surface of the area
  • the second boundary can refer to the boundary of the upper surface of the area.
  • the target area also includes a third boundary
  • the third boundary is the boundary of the side surface of the region.
  • the above functional model does not need to consider the influence of heat conduction on the side surface.
  • it is assumed that the first boundary and the second boundary of the area may or may not intersect, and the details may be determined based on the actual structure of the target area.
  • the second boundary can also be located inside the target area, mainly depending on which area is regarded as the area to be solved. If the heat flow density distribution on the outer surface of the target area is known and you want to know the heat flow density distribution in a certain area inside, then at this time
  • the boundary of the outer surface can be used as the first boundary, and the boundary of the inner region can be used as the second boundary.
  • the target area mentioned in this article includes target areas of living or non-living organisms, such as areas where physical quantities to be estimated are located in human tissues, animal tissues, plant tissues, industrial fluids and gas spaces, etc.
  • the target area may also refer to the entire area of living organisms or non-living entities, that is, the spatial area where the entirety of living organisms or non-living entities are located can be regarded as the target area.
  • the temperature distribution function in the functional model is essentially the solution to the forward problem of the heat conduction equation. It can use the heat conduction equation that has been proposed in the research field corresponding to the target area; of course, the existing heat conduction equation can also be modified according to actual needs. Optimization is performed to obtain the temperature distribution function.
  • the solid area being studied in reality (such as the internal area of a container carrying liquid, the biological sample tissue area, the spatial area of an industrial site, etc.) can be modeled, and the surface of the solid area can be smoothed, Obtain the smoothed target area.
  • the target area after smoothing still possesses the thermophysical properties of the solid area.
  • the heat flow density distribution of the area to be solved in the target area can reflect the heat flow density distribution of the corresponding position in the solid area.
  • the temperature distribution function is a solution to the forward problem of the heat conduction equation consisting of equation (2), equation (3), equation (4), equation (5), and equation (6).
  • ⁇ represents the temperature distribution function of the target area
  • ⁇ represents the density in the target area
  • c P represents the heat capacity of the target area
  • a represents the thermal conductivity of the target area
  • ⁇ represents the gradient operator
  • ⁇ represents the three-dimensional computational domain
  • ⁇ 0 ( ⁇ ) represents the initial temperature of a certain space point
  • ⁇ I represents the first boundary of the target area
  • ⁇ U represents the second boundary of the target area
  • ⁇ R represents the target area The third boundary of That is, the heat flux density distribution within the second boundary.
  • Step S202 Obtain known conditions of variables in the functional model.
  • the known conditions include boundary conditions, thermal property parameters and temperature distribution measurements of the target area.
  • the boundary conditions of the target area may include the boundary position of the target area in the spatial coordinate system. Specifically, it can be determined by establishing a three-dimensional model for the target area by measuring the cross-sectional perimeter, surface area or volume of the target area. The specific measurement method of the boundary length of the target area can be determined according to the properties of the target area.
  • the boundary conditions can be obtained by measuring the boundary lengths of the liquid area with calipers and other instruments;
  • the boundary length of the real human tissue can be calculated proportionally by taking an image of the human tissue and based on the boundary length of the human tissue in the image.
  • Thermal property parameters including but not limited to density, heat capacity and thermal conductivity of the target area. Temperature distribution measurements include temperature data read by various temperature sensors.
  • the known conditions include ⁇ , c P , a, ⁇ , ⁇ 0 ( ⁇ ), ⁇ I , ⁇ U , ⁇ R , n, t max ,
  • the values or vectors corresponding to Qi can be preset or obtained through measurement, query, or other reasonable methods in the existing technology.
  • Step S203 According to the functional model, more than two rounds of regularization parameter selection operations are performed to obtain the optimal solution of the final round of regularization parameters.
  • the aforementioned two or more rounds include the original number of two rounds.
  • the regularization parameter selection operation in each round includes:
  • Step S2031 determine multiple sampling values of this round according to the set sampling range value and sampling interval of the regularization parameter
  • Step S2032 input multiple sampled values and known conditions into the functional model to obtain an estimated heat flow density distribution corresponding to each sampled value;
  • Step S2033 determine the coordinate data of the L curve based on multiple heat flux density distribution estimates
  • Step S2034 determine the sampling values corresponding to the multiple coordinate data at the corner of the L curve as the optimal solution for the regularization parameters of this round;
  • Step S2035 when the current round is not the last round, determine the sampling range value of the regularization parameters of the next round based on the range of the optimal solution of the regularization parameters of this round, and reduce the sampling interval of the regularization parameters of the next round.
  • step S2035 includes: determining that the current round is not the last round, determining the sampling range value of the regularization parameters of the next round based on the range of the preferred solution of the regularization parameters of this round, and reducing The sampling interval of the regularization parameters for the next round.
  • the L-curve method was originally proposed by Hansen. Its principle is to determine the regularization parameters by determining the points at the corners of the L-curve.
  • the coordinate data of the L curve that is, the abscissa and ordinate, are usually determined by the prediction residual term and the regularization penalty term. Since existing technology can be used, the relevant details will not be elaborated here.
  • step S203 ensures that by performing more than two rounds of regularization parameter selection operations, each round continuously narrows the sampling range of the regularization parameter and refines the sampling interval of the regularization parameter. The selection of regularization parameters is sufficiently detailed and efficient.
  • the sampling range and sampling interval of the regularization parameters in the first round can be obtained by reading preset data; the sampling range and sampling interval of the regularization parameters in the second round or after the second round can be obtained by reading preset data. It is determined based on the sampling range and sampling interval set in the previous round.
  • the sampling range of this round is used to represent the numerical range of the optional regularization parameters of this round.
  • the sampling interval of this round represents the interval between the values of the optional regularization parameters, that is, the interval between sampling values. For example, when the sampling range is the numerical interval [0.0010, 0.0020] and the sampling interval is 0.0001, the multiple sampling values in this round are 0.0010, 0.0011, 0.00012, 0.0013,..., 0.0020.
  • the sampling performed is constant step sampling.
  • the sampling performed is variable step sampling. Those skilled in the art can set the corresponding settings according to actual needs. sampling interval.
  • step S2032 When performing step S2032, multiple sampling values can be input into the functional model in sequence, and combined with known conditions, the heat flow density distribution estimate corresponding to each sampling value can be obtained in sequence; a multi-thread parallel method can also be used to combine the multiple sampling values. The values are divided into batches, and calculations are performed simultaneously on each batch of sampled values. In any case, it is enough to finally obtain multiple heat flow density distribution estimates corresponding to multiple sampling values.
  • the estimated value of heat flow density distribution in step S2032 refers to the estimated value of heat flow density distribution in the area to be solved.
  • the range of the L-curve corner can be determined according to the Hansen (Hansen) regularization toolbox.
  • the specific range can be selected or determined according to actual needs. Within this range, multiple heat flow density distributions within a certain numerical range are selected.
  • the estimated values, and the sampling values corresponding to the estimated values of these heat flux density distributions, can be determined as the optimal solution for the regularization parameters of this round.
  • an estimate of the heat flow density distribution for reference may be determined, and the estimate, as well as other estimates of the heat flow density distribution that deviate from the estimate within a preset range, may be regarded as the aforementioned "Estimates of multiple heat flux density distributions within a certain range of values.”
  • the estimated value of the heat flow density distribution used for reference can be determined based on the regularization parameter corresponding to a selected coordinate point at the corner of the L curve.
  • the selected coordinate point can be determined based on the slope of the tangent line at each coordinate point at the corner of the L curve. The principle is to minimize the functional model.
  • the sampling range value of the regularization parameter of the next round is determined based on the range of the preferred solution of the regularization parameter of this round. This may be based on the maximum value and minimum value of the preferred solution of this round to determine the sampling range of the next round.
  • the maximum and minimum values of the next round of sampling range can also be determined based on the mode, average or median value of the current round of optimal solutions. The specific selection can be made according to actual needs.
  • the sampling interval of the regularization parameters of the next round can be reduced according to actual needs. For example, the sampling interval of the next round can be changed to one-tenth, one-fifth, or one-half of the sampling interval of the current round. etc.
  • step S2035 includes step S301 and step S302.
  • Step S301 Obtain a preset target coefficient. The value of the target coefficient is greater than 0 and less than 1.
  • Step S302 The product of the target coefficient and the sampling interval of the regularization parameter of this round is determined as the sampling interval of the regularization parameter of the next round. For example, when k represents the round, Sk k represents the sampling interval of the kth round, and C k represents the target coefficient function, the sampling interval S k+1 of the k+1th round can be determined by formula (7).
  • a preset target coefficient is obtained.
  • the specific target coefficient of this round can be determined according to the preset target coefficient function. Specifically, after running the target coefficient function, a constant greater than 0 and less than 1 can be obtained as the target coefficient. .
  • the objective coefficient function can be linear or nonlinear.
  • the target coefficient obtained in each round can be constant, in which case C k can be a constant; the target coefficient obtained in each round can also be changed, and can be preset according to actual needs.
  • Step S204 Determine the final selected regularization parameters based on the optimal solution of the last round of regularization parameters.
  • a preferred solution can be selected from the preferred solutions of the last round of regularization parameters and determined as the final selected regularization parameter; it can also be based on the maximum value of the preferred solution of the regularization parameters of the last round. and the minimum value, select a value in the interval formed by the maximum value and the minimum value as the final regularization parameter.
  • Step S205 Determine the final estimated value of the heat flow density distribution of the area to be solved based on the finally selected regularization parameter. This refers to the estimated value of the heat flow density distribution within a certain observation period. Since the final regularization parameter is determined, that is, ⁇ in the functional model is determined, the heat flow density in the area to be solved is determined as time goes by. Distributions can also be estimated in real time.
  • 2 to 5 rounds of regularization parameter selection operations may be performed. Of course, more rounds of regularization parameter selection operations may also be performed, depending on actual requirements.
  • the above thermal data determination method uses the coordinate data of the L curve in a round of regularization parameter selection operation to determine that the sampling values corresponding to the multiple coordinate data at the corners of the L curve are the optimal solutions for the regularization parameters of this round, and Use the optimal solution of this round to determine the sampling range value of the regularization parameter in the next round of regularization parameter selection operation, and reduce the sampling interval of the regularization parameter in the next round, so that the calculations involved in the next round of regularization parameter selection operation are
  • the quantity is greatly reduced and the accuracy of the regularization parameter search is improved, which can help determine the appropriate regularization parameters in a short time, thereby quickly obtaining an accurate estimate of the heat flow density distribution in the solution area.
  • step S2034 includes steps S401 to S403.
  • Step S401 according to the coordinate data of the L-curve of this round, determine the optimal sampling value for reference from multiple sampling values of this round, and use the optimal sampling value of this round as the optimal solution of the regularization parameters of this round. element.
  • the optimal sampling value of this round can be determined by analyzing the tangent slope at the coordinate point of the L curve corresponding to multiple sampling values. You can also determine the coordinate point corresponding to the coordinate data closest to the inflection point by determining the inflection point closest to the corner of the L curve, thereby determining the sampling value corresponding to the coordinate data as the optimal sampling value of this round.
  • Step S402 Determine the deviations between the estimated heat flow density distribution values corresponding to other sampling values in this round and the estimated heat flow density distribution values corresponding to the optimal sampling values in this round.
  • step S402 includes: determining the norm of the difference between the estimated heat flow density distribution corresponding to other sampling values and the estimated heat flow density distribution corresponding to the optimal sampling value of this round as the first norm; determining the first norm of this round; The norm of the heat flow density distribution estimate corresponding to the optimal sampling value is used as the second norm; the deviation is determined based on the ratio of the first norm and the second norm. Specifically, the deviation in step S402 can be determined according to formula (8).
  • ⁇ m represents a sampling value among other sampling values, and is determined by the sampling range [ ⁇ min , ⁇ max ] and the sampling interval Sk , represents the estimated value of heat flux density distribution corresponding to ⁇ m and
  • the deviation of the corresponding heat flow density distribution estimate, k represents the current round, express
  • the corresponding estimated value of heat flux density distribution Indicates the estimated value of heat flux density distribution corresponding to ⁇ m .
  • the deviation in step S402 can also be determined based on other calculation methods.
  • Step S403 When the deviation does not exceed the preset deviation threshold, the corresponding other sample values are used as elements of the preferred solution of the regularization parameters of this round.
  • step S403 includes: in response to the deviation not exceeding the preset deviation threshold, using corresponding other sample values as elements of the preferred solution of the regularization parameters of this round.
  • the preset deviation threshold can be set according to actual needs, such as 0.01, 0.1 or other values. Let ⁇ represent the preset deviation threshold, then the elements of the optimal solution of the kth round include as well as
  • step S2032 includes:
  • Step S501 for each sampling value, use an iterative regularization calculation model based on the conjugate gradient method to determine the heat flow density distribution estimate corresponding to multiple iteration cycles;
  • Step S502 When the deviation between the heat flow density distribution estimate obtained in the current iteration cycle and the heat flow density distribution estimate obtained in the previous iteration cycle is within the preset iteration deviation threshold range, the heat flow density distribution estimate obtained in the current iteration cycle is used as The estimated value of heat flow density distribution corresponding to this sample value.
  • step S502 includes: determining that the deviation is within a preset iteration deviation threshold range, and using the heat flow density distribution estimate obtained in the current iteration cycle as the heat flow density distribution estimate corresponding to the sampling value.
  • Formula (9) is the iterative update formula for the heat flux density distribution estimate
  • Formula (13) to Formula (16) are the solution equations for the adjoint problem
  • Formula (19) to Formula (22) are the solution equations for the sensitivity problem.
  • r represents the number of iterations, Represents the estimated heat flow density distribution of the area to be solved, R r (x,t), R r represents the conjugate search direction, ⁇ r represents the conjugate coefficient, ⁇ r represents the step size of the conjugate search, and L r represents the target functional , H r represents the solution to the adjoint problem, h represents the error between the estimated temperature distribution function ⁇ (x, t, Q u ) on ⁇ I and the temperature distribution measurement value ⁇ m (x, t), v r represents the sensitivity problem solution.
  • the iterative regularization based on the conjugate gradient method is used in the solution.
  • the serial number of the current iteration cycle is r
  • the serial number of the previous iteration cycle is r-1
  • the preset iteration deviation threshold range in step S502 can mean that the deviation is less than or equal to The heat flow density estimation error in the iteration.
  • the heat flow density estimation error in the iteration can be expressed as ⁇ .
  • the heat flow density distribution estimate obtained in the current iteration cycle and the heat flow density distribution estimate obtained in the previous iteration cycle can be calculated according to the formula (23 )to make sure.
  • r max can be 200, 300 or others, which can be set according to actual needs.
  • the functional model includes a prediction residual term and a regularization penalty term.
  • the prediction residual term includes a norm of a residual of a temperature distribution function.
  • the temperature distribution function is used to describe the temperature of the target area in time and space.
  • distribution, the regularization penalty term includes the regularization parameter and the norm of the unknown heat flow density function; understood in conjunction with Figure 6 and Figure 7,
  • step S202 includes: step S601, obtaining the thermal attribute parameters of the target area; step S602, obtaining the boundary of the target area Conditions; Step S603, obtain the temperature distribution measurement value of the target area; Step S604, obtain the initial temperature distribution of the target area; Step S605, obtain the heat flow density data of the first boundary of the target area within the preset observation time.
  • step S2032 includes: step S701, using the heat flow density distribution of the second boundary of the target area as the heat flow density distribution of the area to be solved, based on the thermal attribute parameters, boundary conditions, initial temperature distribution, heat flow density data and the second boundary Heat flow density distribution, determine the temperature distribution function of the target area; step S702, use the difference between the temperature distribution function of the target area and the temperature distribution measurement value as the residual of the temperature distribution function, and determine the heat flow density distribution estimate corresponding to each sampling value. .
  • the residual of the temperature distribution function of the functional model can be combined with the known conditions and sampling values to calculate the corresponding heat flow density distribution estimate.
  • step S605 the execution order of each step in step S601 to step S605 can be reasonably designed by those skilled in the art according to actual needs, and is not particularly limited here.
  • the heat flux density data of the first boundary can be calculated based on the temperature distribution measurement value, or can be calculated based on the heating power of the heat source, or can be obtained by measuring the heat generation of the heat source by other means.
  • step S701 includes: solving the heat conduction forward problem in parallel according to the thermal property parameters, boundary conditions, initial temperature distribution, heat flow density data and the heat flow density distribution at the second boundary, and using the solution of the heat conduction forward problem as the target area Temperature distribution function. Solving the heat conduction forward problem in parallel, combined with the selection method of regularization parameters, achieves the purpose of high-throughput data processing and can effectively improve the efficiency of solving the final estimate of heat flow density distribution.
  • step S701 and step S702 can be understood by referring to formula (1) to formula (6).
  • the thermal data determination method further includes: determining the temperature distribution of the area to be solved at a specified moment based on the final estimate of the heat flux density distribution and the initial temperature distribution of the area to be solved.
  • the aforementioned designated time may include a time within a past observation period, or may include the latest observation time.
  • the thermal data determination method further includes: determining the temperature distribution of the area to be solved at the latest moment based on the final estimate of the heat flow density distribution and the initial temperature distribution of the area to be solved;
  • the component emits a regulation signal, which is used to control the heat flux applied by the heating component to the target area.
  • an existing three-dimensional transient heat conduction equation solver can be used to calculate the equations involved in the aforementioned forward problem, inverse problem, adjoint problem or sensitivity problem.
  • DROPS a computational fluid dynamics software for simulating two-phase flow
  • NGSolve a high-performance multiphysics finite element software
  • COMSOL Multiphysics an advanced numerical simulation software
  • OpenFoam a software based on C++ object-oriented computational fluid dynamics software
  • other software with the function of solving heat conduction partial differential equations can be used to numerically solve partial differential equations such as forward problems, adjoint problems, and sensitivity problems that arise during the calculation of the inverse problems mentioned above.
  • each step in the flowcharts of FIG. 2(a) to FIG. 7 is shown in sequence as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows.
  • the steps shown in Figure 2(a) to Figure 7 and the steps disclosed in other embodiments are not strictly limited to the order in which these steps are performed, and these steps can be performed in other orders unless explicitly stated herein.
  • at least some of the steps in the foregoing embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but may be executed at different times. The order of execution is not necessarily sequential, but may be performed in turn or alternately with other steps or sub-steps of other steps or at least part of the stages.
  • This application also discloses a thermal data determination device, as shown in Figure 8, including: a model determination module 810, used to determine the Tikhonov regularized functional model, and the functional model is used to solve the heat conduction inverse of the target area. problem, output the heat flow density distribution estimate of the area to be solved in the target area; the known condition acquisition module 820 is used to obtain the known conditions of the variables in the functional model.
  • a model determination module 810 used to determine the Tikhonov regularized functional model
  • the functional model is used to solve the heat conduction inverse of the target area. problem, output the heat flow density distribution estimate of the area to be solved in the target area
  • the known condition acquisition module 820 is used to obtain the known conditions of the variables in the functional model.
  • the known conditions include the boundary conditions of the target area, thermal property parameters and Temperature distribution measurement value; the optimal solution acquisition module 830 is used to perform more than two rounds of regularization parameter selection operations according to the functional model to obtain the optimal solution of the last round of regularization parameters; the regularization parameter determination module 840 is used to The final selected regularization parameter is determined based on the optimal solution of the last round of regularization parameters; the estimation module 850 is used to determine the final estimated value of the heat flow density distribution of the area to be solved based on the final selected regularization parameter.
  • the optimal solution acquisition module 830 includes: a sampling value determination sub-module 831, which is used in each round of regularization parameter selection operation to determine multiple samples of this round according to the set sampling range value and sampling interval of the regularization parameter. value; the model operation sub-module 832 is used to input multiple sampling values and known conditions into the functional model to obtain the heat flow density distribution estimate corresponding to each sampling value; the L-curve determination sub-module 833 is used to calculate the The heat flow density distribution estimate is used to determine the coordinate data of the L curve; the optimal solution determination sub-module 834 is used to determine the sampling values corresponding to the multiple coordinate data at the corners of the L curve as the optimal solution for the regularization parameters of this round; sampling Parameter adjustment sub-module 835 is used to determine the sampling range value of the regularization parameters of the next round based on the optimal solution range of the regularization parameters of this round when the current round is not the last round, and reduce the regularization of the next round. Sampling interval for parameterization.
  • the preferred solution determination sub-module 834 includes: a reference value determination unit, configured to determine the optimal sampling value for the reference from multiple sampling values according to the coordinate data of the L-curve of this round, The optimal sampling value of this round is used as an element of the optimal solution of the regularization parameters of this round; the first deviation estimation unit is used to determine the heat flow density distribution estimate corresponding to other sampling values of this round and the optimal sampling value of this round respectively. The deviation of the heat flow density distribution estimate corresponding to the value; the optimal solution determination unit is used to use the corresponding other sampled values as elements of the optimal solution for the regularization parameters of this round when the deviation does not exceed the preset deviation threshold.
  • the first deviation estimation unit includes: a first norm determination subunit, used to determine the heat flow density distribution estimate corresponding to other sampling values and the heat flow density distribution estimate corresponding to the optimal sampling value of this round.
  • the norm of the difference is used as the first norm
  • the second norm determination subunit is used to determine the norm of the heat flow density distribution estimate corresponding to the optimal sampling value of this round as the second norm
  • the deviation determination subunit is used to determine The deviation is determined based on the ratio of the first norm to the second norm.
  • the sampling parameter adjustment sub-module 835 includes: a target coefficient acquisition unit, used to obtain a preset target coefficient, the value of the target coefficient is greater than 0 and less than 1; a sampling interval adjustment unit, used to compare the target coefficient with the current The product of the sampling intervals of the regularization parameters of one round is determined as the sampling interval of the regularization parameters of the next round.
  • the model running sub-module 832 includes: an inverse problem calculation unit, used for each sampling value to use an iterative regularization calculation model based on the conjugate gradient method to determine the heat flow density distribution estimate corresponding to multiple iteration cycles. ; Iterative error calculation unit, used to calculate the heat flow obtained in the current iteration cycle when the deviation between the heat flow density distribution estimate obtained in the current iteration cycle and the heat flow density distribution estimate obtained in the previous iteration cycle is within the preset iteration deviation threshold range. The density distribution estimate is used as the heat flow density distribution estimate corresponding to the sampling value.
  • the functional model includes a prediction residual term and a regularization penalty term.
  • the prediction residual term includes a norm of a residual of a temperature distribution function.
  • the temperature distribution function is used to describe the temperature of the target area in time and space.
  • Distribution, the regularization penalty term includes the regularization parameter and the norm of the unknown heat flow density function.
  • the known condition acquisition module 820 includes: an attribute parameter acquisition sub-module, used to acquire the thermal attribute parameters of the target area; a boundary data acquisition sub-module, used to acquire the boundary conditions of the target area; and a measurement value acquisition sub-module, used to acquire the target area
  • the temperature distribution measurement value is used to obtain the initial temperature distribution of the target area
  • the heat flow density data acquisition sub-module is used to obtain the heat flow density data of the first boundary of the target area within the preset observation time.
  • the model running sub-module 832 includes: a temperature distribution function solving unit, used to use the heat flow density distribution of the second boundary of the target area as the heat flow density distribution of the area to be solved, according to the thermal attribute parameters, boundary conditions, initial temperature distribution, and heat flow density data. and the heat flow density distribution at the second boundary to determine the temperature distribution function of the target area; the functional model solving unit is used to use the difference between the temperature distribution function of the target area and the measured temperature distribution value as the residual of the temperature distribution function to determine each The estimated value of heat flux density distribution corresponding to a sample value.
  • the temperature distribution function solving unit includes a parallel solving subunit, and the parallel solving subunit is used to solve the heat conduction in parallel according to the thermal property parameters, boundary conditions, initial temperature distribution, heat flow density data and the heat flow density distribution of the second boundary. Forward problem, the solution to the forward problem of heat conduction is used as the temperature distribution function of the target area.
  • the thermal data determination device further includes a temperature distribution estimation module (not shown), which is used to determine the temperature of the area to be solved at a specified moment based on the final estimate of the heat flow density distribution and the initial temperature distribution of the area to be solved. distributed.
  • a temperature distribution estimation module (not shown), which is used to determine the temperature of the area to be solved at a specified moment based on the final estimate of the heat flow density distribution and the initial temperature distribution of the area to be solved. distributed.
  • the thermal data determination device further includes: a temperature estimation module (not shown), used to determine the temperature of the area to be solved at the latest moment based on the final estimated value and the initial temperature distribution of the heat flow density distribution of the area to be solved. Distribution; the temperature control module (not shown) is used to send an adjustment signal to the heating component according to the temperature distribution at the latest moment. The adjustment signal is used to control the heat flux density applied by the heating component to the target area.
  • a temperature estimation module (not shown), used to determine the temperature of the area to be solved at the latest moment based on the final estimated value and the initial temperature distribution of the heat flow density distribution of the area to be solved. Distribution
  • the temperature control module (not shown) is used to send an adjustment signal to the heating component according to the temperature distribution at the latest moment.
  • the adjustment signal is used to control the heat flux density applied by the heating component to the target area.
  • the thermal data determination device can implement the steps of the thermal data determination method in any of the foregoing embodiments.
  • Each module in the above thermal data determination device can be implemented in whole or in part by software, hardware and combinations thereof.
  • Each of the above modules may be embedded in or independent of the processor of the computer device in the form of hardware, or may be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.
  • embodiments of the present application also disclose a computer device, which includes a memory and one or more processors.
  • Computer-readable instructions are stored in the memory, and the computer-readable instructions are processed by one or more processors. When executed, one or more processors are caused to execute the steps of the thermal data determination method in any of the previous embodiments.
  • the computer device may be a server, and its internal structure diagram may be as shown in Figure 9.
  • the computer device includes a processor, a memory, and a network interface connected through a system bus.
  • the computer device's processor is used to provide computing and control capabilities.
  • the memory of the computer device includes non-volatile storage media and internal memory.
  • the non-volatile storage medium stores an operating system and computer-readable instructions.
  • This internal memory provides an environment for the execution of an operating system and computer-readable instructions in a non-volatile storage medium.
  • the network interface of the computer device is used to communicate with external terminals through a network connection.
  • the computer-readable instructions implement the thermal data determination method in any of the foregoing embodiments.
  • FIG. 9 is only a block diagram of a partial structure related to the solution of the present application, and does not constitute a limitation on the computer equipment to which the solution of the present application is applied.
  • the specific computer equipment may include more than what is shown in the figure. More or fewer parts, or combining certain parts, or having different parts arrangements.
  • the thermal data determination device includes the processor 101 and the temperature measurement component 102 shown in FIG. 1 .
  • the temperature measurement component 102 is used to measure the temperature distribution of the target area and generate the temperature distribution measurement value of the target area.
  • the processor 101 may be configured to perform the steps of the thermal data determination method in any of the foregoing embodiments.
  • the thermal data determination device further includes a heating component (not shown) for heating the target area.
  • the processor 101 may also be used to perform the following steps: obtain the preset initial temperature distribution of the area to be solved; update the area to be solved based on the final estimated value of the heat flow density distribution of the area to be solved and the preset initial temperature distribution of the area to be solved. The temperature distribution of the area at the latest moment; according to the temperature distribution of the area to be solved at the latest moment, adjust the heat flow density applied by the heating component to the target area.
  • the initial temperature distribution of the target area can be regarded as the initial temperature distribution of the area to be solved.
  • the room temperature can be considered as the initial temperature distribution of the target area.
  • the initial temperature distribution of the target area may be estimated or preset according to actual conditions.
  • Embodiments of the present application also disclose one or more non-volatile computer-readable storage media storing computer-readable instructions.
  • the computer-readable instructions When executed by one or more processors, the computer-readable instructions cause one or more processors to Perform the steps of the thermal data determination method in any of the previous embodiments.
  • Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory.
  • Volatile memory may include random access memory (RAM) or external cache memory.
  • RAM random access memory
  • DRAM dynamic RAM
  • SDRAM synchronous DRAM
  • DDRSDRAM double data rate SDRAM
  • ESDRAM enhanced SDRAM
  • SLDRAM synchronous chain Synchlink DRAM
  • RDRAM direct RAM
  • DRAM direct memory bus dynamic RAM
  • RDRAM memory bus dynamic RAM
  • thermal data determination devices can be applied according to the fields in which the thermal data determination method can be applied.
  • thermal data determination device Due to the thermal data determination method, thermal data determination device, computer equipment and thermal data determination equipment, the applicable fields are rich, for example, they can be applied to the biomedical field, communication field, energy field, industrial manufacturing field and agriculture, forestry, fishery and animal husbandry. In order to facilitate intuitive understanding, a simple explanation is given here, taking the temperature study of the target area applied to living organisms as an example.
  • mosquitoes When faced with the threat of heat stress, body temperature regulation of insects and other organisms is critical. Taking mosquitoes as an example, existing research has shown that high temperatures caused by blood sucking can endanger the physiological condition of mosquitoes. Mosquitoes lower their body temperature by expelling, maintaining and evaporating droplets at the end of their abdomen during feeding. As one of the most important physical quantities, the high transient heat flux density at the end of the abdomen is crucial to better understand the dissipation mechanism of the studied object. It is still difficult to directly obtain the accurate value of this physical quantity with existing measurement technology, but the unknown heat flow density distribution that is difficult to measure can be estimated by establishing and solving the transient heat transfer inverse problem.
  • the inventor studied the problem of estimating the heat flow density distribution during the blood-sucking process of mosquitoes.
  • a functional model is established on x ⁇ [0,16]mm (the mosquito’s body length range, that is, the target area).
  • the actual transient temperature data of the mosquito head (that is, the heat flow density data of the first boundary) is based on the experimental data published by Lahondère and others.
  • the specific source is: C Lahondère, Lazzari C. Mosquitoes Cool Down during Blood Feeding to Avoid Overheating[J ].Current biology:CB,2011,22(1):40-45.
  • the value range of the regularization parameter is set to [0,0.001].
  • the optimal solution for the regularization parameters was finally obtained, namely ⁇ m
  • the inventor finally determined the value of the regularization parameter to be 0.000296.
  • the final appropriate value of the regularization parameter can be determined based on the smoothness of the curve of the heat flow density distribution estimate corresponding to a limited number of regularization parameters in ⁇ m
  • Choosing appropriate regularization parameters is important to deal with ill-posed problems. Choosing regularization parameters that are too large or too small instead of appropriate will lead to overly smooth or oscillatory results, which are inconsistent with physical phenomena.
  • the abscissa represents the observation time
  • the ordinate represents the estimated heat flow density distribution of the area to be solved (i.e., the end of the mosquito's abdomen, within the second boundary), and the estimated heat flow at the end of the mosquito's abdomen.
  • the heat exchange situation is shown, and it can be seen that the high transient heat flow density at the end of the abdomen is closely related to the complex temperature changes of the mosquito head, and the heat flow peak may occur when the mosquito gradually loses the droplets at the end of the abdomen.

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Data Mining & Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Geometry (AREA)
  • Operations Research (AREA)
  • Evolutionary Computation (AREA)
  • Algebra (AREA)
  • Computer Hardware Design (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • Investigating Or Analyzing Materials Using Thermal Means (AREA)

Abstract

本申请涉及一种热学数据确定方法、装置和设备，前述方法包括：确定吉洪诺夫正则化的泛函模型，获取泛函模型中变量的已知条件，根据泛函模型，执行两轮以上的正则化参数选取操作，获得最后一轮的正则化参数的优选解；根据最后一轮的正则化参数的优选解，确定最终选用的正则化参数；根据最终选用的正则化参数，确定待求解区域的热流密度分布的最终估计值。

Description

一种热学数据确定方法、装置和设备
相关申请的交叉引用
本申请要求于2022年7月4日提交中国专利局，申请号为CN202210777855.X，申请名称为“一种热学数据确定方法、装置和设备”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本申请涉及计算机处理热学数据的技术领域，特别是涉及一种热学数据确定方法、装置和设备。
背景技术
在生物医学领域、通信领域、能源领域、工业制造领域和农林渔牧业领域等诸多领域，经常需要对生物体或非生物体的目标区域进行热学数据(如热流密度或温度)的测量或估计，以供改进技术、保护目标区域使其维持在合理正常的状态下或了解目标区域内的热传导规律。
例如，在生物医学领域，在临床医学中，激光、微波等热疗过程中的短时间内瞬时热流密度大，需要实时获得人体组织相关目标区域的温度场变化等信息。
例如，在预防医学领域，考虑到人体肿瘤等病灶组织与周围正常组织之间存在温度差异，需要通过获取相关目标区域的热流密度数据以供后续确定病灶组织的位置或边界。
例如，在农业种植养殖领域，在发展集约化高密度养殖时，有效、方便的监测热流密度数据所反映的重要生理指标，可及时评估和调整养殖技术，实现更好的养殖效益。
例如，在仿生学领域，在设计生物仿生构件时，通过分析生物仿生构件关键部位中目标区域的热流密度变化，可利于实时迅速的评估散热或保温效果。
例如，在通信领域，对通信设备周围的目标区域进行温度估计，有利于优化通信设备的安装位置和架构，实现更好的散热效果。
例如，在工业制造领域，对被加热的零部件的目标区域的热流密度进行评估，有利于进一步优化加热策略。
例如，在能源领域，对管道流体的目标区域进行热流密度的监控，有利于保障安全度和提高设备使用寿命。
然而，在多数情况下，通常只能通过红外温度传感器或热电偶传感器等温度传感组件，获取到目标区域的一部分表面上有限的测量点的温度数据，对于目标区域无法被这些温度传感组件感测到的部位的温度或热流密度，需要使用计算机等辅佐手段来获得间接的估计值，其关键的一环，就是计算求解瞬态传热反问题(IHTP,Inverse heat transfer problems)。
解决瞬态传热反问题的数学不适定性和高性能计算策略面临诸多挑战，传统方法在面对三维、瞬态等复杂情况时，在计算效率和精度方面不再适用。
正则化方法获得了相对更多的研究关注，经典吉洪诺夫(Tikhonov)正则化和迭代正则化等数学 方法已经广泛应用于求解科学与工程等领域普遍存在的数学物理反问题。对于吉洪诺夫正则化方法，选择合适的正则化参数对获得稳定的、精确的解至关重要。
然而，实际应用过程中，通常难以在短时间内获得精确的最优正则化参数，这导致对待求解区域的热流密度分布的精准估算效率较低。
发明内容
在第一方面，本申请实施例公开了一种热学数据确定方法，其包括：确定吉洪诺夫正则化的泛函模型，泛函模型用于求解目标区域的热传导反问题，输出目标区域中待求解区域的热流密度分布估计值；获取泛函模型中变量的已知条件，已知条件包括目标区域的边界条件、热学属性参数和温度分布测量值；根据泛函模型，执行两轮以上的正则化参数选取操作，获得最后一轮的正则化参数的优选解；根据最后一轮的正则化参数的优选解，确定最终选用的正则化参数；以及，根据最终选用的正则化参数，确定待求解区域的热流密度分布的最终估计值。其中，在每轮正则化参数选取操作中，根据设定的正则化参数的采样范围值和采样间隔，确定本轮的多个采样值，将多个采样值和已知条件输入泛函模型，获得与每一采样值对应的热流密度分布估计值，根据多个热流密度分布估计值确定L曲线的坐标数据，将L曲线拐角处的多个坐标数据对应的采样值，确定为本轮的正则化参数的优选解，在本轮为非最后一轮时，以本轮的正则化参数的优选解的范围，确定下轮的正则化参数的采样范围值，并减小下轮的正则化参数的采样间隔。
在第二方面，本申请实施例公开了一种热学数据确定装置，其包括：模型确定模块，用于确定吉洪诺夫正则化的泛函模型，泛函模型用于求解目标区域的热导反问题，输出目标区域中待求解区域的热流密度分布估计值；
已知条件获取模块，用于获取泛函模型中变量的已知条件，已知条件包括目标区域的边界条件、热学属性参数和温度分布测量值；优选解获取模块，用于根据泛函模型，执行两轮以上的正则化参数选取操作，获得最后一轮的正则化参数的优选解；正则化参数确定模块，用于根据最后一轮的正则化参数的优选解，确定最终选用的正则化参数；以及，估计模块，用于根据最终选用的正则化参数，确定待求解区域的热流密度分布的最终估计值。其中，优选解获取模块包括：采样值确定子模块，用于在每轮正则化参数选取操作中，根据设定的正则化参数的采样范围值和采样间隔，确定本轮的多个采样值；模型运行子模块，用于将多个采样值和已知条件输入泛函模型，获得与每一采样值对应的热流密度分布估计值；L曲线确定子模块，用于根据多个热流密度分布估计值，确定L曲线的坐标数据；以及，优选解确定子模块，用于将L曲线拐角处的多个坐标数据对应的采样值，确定为本轮的正则化参数的优选解；采样参数调整子模块，用于在本轮为非最后一轮时，以本轮的正则化参数的优选解的范围，确定下轮的正则化参数的采样范围值，并减小下轮的正则化参数的采样间隔。
在第三方面，本申请实施例公开了一种计算机设备，其包括存储器及一个或多个处理器，存储器中储存有计算机可读指令，计算机可读指令被一个或多个处理器执行时，使得一个或多个处理器执行任一实施例中的热学数据确定方法的步骤。
在第四方面，本申请实施例公开了一种热学数据确定设备，包括温度测量组件和处理器；温度测量组件用于测量目标区域的温度分布，生成目标区域的温度分布测量值；处理器用于执行任一实施例 中的热学数据确定方法的步骤。
在第五方面，本申请实施例公开了一个或多个存储有计算机可读指令的非易失性计算机可读存储介质，计算机可读指令被一个或多个处理器执行时，使得一个或多个处理器执行任一实施例中的热学数据确定方法的步骤。
本申请的一个或多个实施例的细节在下面的附图和描述中提出。本申请的其它特征和优点将从说明书、附图以及权利要求书变得明显。
附图说明
图1为根据一个或多个实施例中热学数据确定方法的应用环境图；
图2(a)为根据一个或多个实施例中热学数据确定方法的流程示意图；
图2(b)为图2(a)中涉及正则化参数选取操作的流程示意图；
图3为根据一个或多个实施例中涉及获取目标系数的步骤的流程示意图；
图4为根据一个或多个实施例中涉及确定正则化参数的优选解的步骤的流程示意图；
图5为根据一个或多个实施例中涉及采用共轭梯度法进行计算的步骤的流程示意图；
图6为根据一个或多个实施例中涉及获取已知条件的步骤的流程示意图；
图7为根据一个或多个实施例中涉及确定目标区域的温度分布函数的步骤的流程示意图；
图8为根据一个或多个实施例中热学数据确定装置的结构框图；
图9为根据一个或多个实施例中计算机设备的内部结构图；
图10为根据一个或多个实施例中热流密度分布估计值随观测时间变化的示意图。
具体实施方式
为了使本申请的技术方案及优点更加清楚明白，以下结合附图及实施例，对本申请进行进一步详细说明。应当理解，此处描述的具体实施例仅仅用以解释本申请，并不用于限定本申请。
本申请公开的热学数据确定方法，可以应用于如图1所示的应用环境中。其中，处理器101可以通过网络与温度测量组件102通信，从而获取温度测量组件102生成的目标区域的温度分布测量值。处理器101可以采用可编程逻辑阵列(PLA)、现场可编程门阵列(FPGA)、数字信号处理器(DSP)、专用集成电路(ASIC)、通用处理器或者其他可编程逻辑器件中的至少一种硬件形式来实现。温度测量组件102可以包括接触式或非接触式温度传感器，这些温度传感器用于测量目标区域的实际温度，用于测量目标区域的实际测量点上的温度。这些温度传感器包括但不限于热电偶温度传感器、热电阻温度传感器、红外线温度传感器。
在一个实施例中，如图2(a)和图2(b)所示，本申请公开了一种热学数据确定方法，以该方法应用于图1中的处理器101为例进行说明，包括处理器101可执行的步骤S201至步骤S205，下文对各步骤进行说明。
步骤S201，确定吉洪诺夫正则化的泛函模型。该泛函模型用于求解目标区域的热传导反问题，输出目标区域中待求解区域的热流密度分布估计值。
利用吉洪诺夫正则化法来构造泛函模型，可以借鉴诸多已有的技术，例如，《Analysis of discrete ill-posed problems by means of the L-curve》(Hansen,P.C.(1992):Analysis of discrete ill-posed problems by means of the L-curve,SIAM Rev.34(4),561–580.)、《热传导方程反问题的Tikhonov正则化法》(计算机与数字工程，总第307期，2015年第5期，作者何俊红)、《Efficient reconstruction of local heat fluxes in pool boiling experiments by goal-oriented adaptive mesh refinement》(DOI：10.1007/s00231-010-0683-6)、《MODEL FUNCTION APPROACH IN THE MODIFIED L-CURVE  METHOD FOR THE CHOICE OF REGULARIZATION PARAMETER》(2000 Mathematics Subject Classification.65J20,65M30.)等诸多文献均有记载，在此不作赘述。
步骤S201中，确定吉洪诺夫正则化的泛函模型，是指确定泛函模型所需采取的表达式。具体的表达式可以是多样化的，在此不作特别限制。通常，泛函模型可以包括预测残差项和正则化惩罚项，预测残差项包括温度分布函数的残差的范数，温度分布函数用于描述目标区域在时间和空间上的温度分布，正则化惩罚项包括正则化参数和未知热流密度函数的范数。
在一些实施例中，可以采用公式(1)作为泛函模型的表达式。
Figure PCTCN2022125225-appb-000001
公式(1)中，L(Q u)表示目标泛函；
Figure PCTCN2022125225-appb-000002
可被视为预测残差项，
Figure PCTCN2022125225-appb-000003
可被视为正则化惩罚项，α是待确定的正则化参数；Φ(x,t,Q u)表示温度分布函数，x表示空间向量，t表示时间，Q u表示待求解区域的热流密度分布，Q u的解是目标区域热传导反问题的解；Φ m(x,t)表示温度分布测量值；t max表示某一观测时段内的最终时刻，Λ I表示目标区域的第一边界，Λ u表示目标区域的第二边界。
通常，若目标区域为受热面与未知热流所在边界等构成的区域，第一边界可以指区域下表面的边界，第二边界可以指区域上表面的边界，此时目标区域还包括第三边界，第三边界是区域侧表面的边界，但在区域上表面和下表面距离很近的情况下，上述的泛函模型可以不用考虑侧表面的热传导影响。在其他一些情况下，假设区域第一边界和第二边界可以有交集也可以没有交集，具体可以根据目标区域的实际结构来确定。另外，第二边界也可以位于目标区域内部，主要取决于将哪个区域视为待求解区域，如果已知目标区域外表面的热流密度分布，希望获知内部某个区域的热流密度分布，则此时外表面的边界可以作为第一边界，内部的区域的边界可以作为第二边界。
本文所说的目标区域，包括生物体或非生物体的目标区域，例如人体组织、动物组织、植物组织、工业流体和气体空间中的待估算物理量所在区域等等。当然，在一些情况下，目标区域也可以指生物体或非生物体的整体区域，即，可以将生物体或非生物体的整体所在的空间区域视为目标区域。泛函模型中的温度分布函数，其本质是热传导方程的正问题的解，它可以采用目标区域所对应的研究领域已提出的热传导方程；当然，也可以根据实际需要，对已有的热传导方程进行优化而获得温度分布函数。
在一些实施例中，可以对现实中被研究的实体区域(例如承载液体的容器内部区域、生物样本组织区域、工业场所空间区域，等等)进行建模，将实体区域的表面平滑化处理，得到经平滑化处理后的目标区域。经平滑化处理后的目标区域仍具备了实体区域的热物理性质，该目标区域中待求解区域的热流密度分布，可以反映出实体区域的相应位置的热流密度分布。
在一些实施例中，温度分布函数是公式(2)、公式(3)、公式(4)、公式(5)和公式(6)组成的热传导方程的正问题的解。
Figure PCTCN2022125225-appb-000004
Φ(·,0)＝Φ 0(·),in Ω      (3)
Figure PCTCN2022125225-appb-000005
Figure PCTCN2022125225-appb-000006
Figure PCTCN2022125225-appb-000007
其中，Φ表示目标区域的温度分布函数，ρ表示目标区域内的密度，c P表示目标区域的热容，a表示目标区域的热导率，
Figure PCTCN2022125225-appb-000008
表示梯度算子，Ω表示三维计算域，Φ 0(·)表示某一个空间点的初始温度，Λ I表示目标区域的第一边界，Λ U表示目标区域的第二边界，Λ R表示目标区域的第三边界，n表示穿过边界的外法线，t max表示某一观测时段内的最终时刻，Q i表示第一边界内的热流密度分布，Q u表示待求解区域的热流密度分布，即第二边界内的热流密度分布。
步骤S202，获取泛函模型中变量的已知条件。该已知条件包括目标区域的边界条件、热学属性参数和温度分布测量值。
本领域技术人员可以理解，前述的已知条件可以采用现有技术中的多种手段来获得。目标区域的边界条件，可以包括目标区域在空间坐标系中所处的边界位置。具体可以通过采用测量目标区域的截面周长、表面积或体积等多种方式，为目标区域建立三维模型而确定。目标区域的边界长度，具体测量方式可以根据目标区域的属性而定，例如，当目标区域为容器内的液体区域时，可以通过卡尺等仪器测量该液体区域的各边界长度，而获得边界条件；当目标区域为人体组织时，可以通过拍摄人体组织图像，根据图像中人体组织的边界长度，按比例计算得到现实中人体组织的边界长度。热学属性参数，包括但不限于目标区域的密度、热容和热导率。温度分布测量值，包括由各类温度传感器读取到的温度数据。
以热传导方程，即公式(2)-公式(6)为例，已知条件包括ρ、c P、a、Ω、Φ 0(·)、Λ I、Λ U、Λ R、n、t max、Q i对应的数值或向量，这些数值或向量可以是预设的，也可以通过测量、查询或采用现有技术中的其他合理方式得到的。
步骤S203，根据泛函模型，执行两轮以上的正则化参数选取操作，获得最后一轮的正则化参数的优选解。前述的两轮以上，包括两轮本数。其中，如图2(b)所示，每轮的正则化参数选取操作，包括：
步骤S2031，根据设定的正则化参数的采样范围值和采样间隔，确定本轮的多个采样值；
步骤S2032，将多个采样值和已知条件输入泛函模型，获得与每一采样值对应的热流密度分布估计值；
步骤S2033，根据多个热流密度分布估计值，确定L曲线的坐标数据；
步骤S2034，将L曲线拐角处的多个坐标数据对应的采样值，确定为本轮的正则化参数的优选解；
步骤S2035，在本轮为非最后一轮时，以本轮的正则化参数的优选解的范围，确定下轮的正则化参数的采样范围值，并减小下轮的正则化参数的采样间隔。在一些可选的实施方式中，步骤S2035包括：确定本轮为非最后一轮，以本轮的正则化参数的优选解的范围，确定下轮的正则化参数的采样范围值，并减小下轮的正则化参数的采样间隔。
L曲线法最初由汉森(Hansen)提出，其原理是通过确定L曲线的拐角处的点，从而确定正则化参数。L曲线的坐标数据，即横坐标和纵坐标，通常由预测残差项和正则化惩罚项来确定，由于可以采用现有技术，相关细节在此不作过多展开。
通过L曲线法选取正则化参数时，如果仅仅凭借操作人员的经验，借助汉森(Hansen)正则化工具箱(一个辅助确定正则化参数的应用程序)在L曲线拐角处选取一个坐标点，从而确定对应的正则化参数，通常，选取出来的正则化参数与最优的正则化参数存在一定偏差。不同的是，步骤S203(含步骤S2031-步骤S2035)通过执行两轮以上的正则化参数选取操作，通过每一轮不断限缩正则化参数的采样范围以及细化正则化参数的采样间隔，确保正则化参数的选取操作足够细致以及高效。
步骤S2031中，最初一轮的正则化参数的采样范围和采样间隔，可以通过读取预先设定的数据而获得；第二轮或第二轮以后的正则化参数的采样范围和采样间隔，可以根据上一轮设定的采样范围和采样间隔而进行确定。本轮的采样范围用于表示本轮可选的正则化参数的数值范围，本轮的采样间隔，表示可选的正则化参数的取值之间的间隔，即采样值之间的间隔。例如，当采样范围是数值区间[0.0010，0.0020]，采样间隔是0.0001时，本轮的多个采样值便是0.0010，0.0011，0.00012，0.0013，……，0.0020。在每一轮中，当采样间隔是常数时，执行的采样是恒定步长的采样，当采样间隔不是常数时，执行的采样是变步长采样，本领域技术人员可以根据实际需要设置相应的采样间隔。
执行步骤S2032时，可以依次将多个采样值输入泛函模型，结合已知条件，依次获得与每一采样值对应的热流密度分布估计值；也可以采用多线程并行的方式，将多个采样值分为多批，每一批采样值被同时执行计算。无论如何，最后能获得多个采样值对应的多个热流密度分布估计值即可。步骤S2032中的热流密度分布估计值，是指待求解区域的热流密度分布估计值。
在步骤S2034中，可以根据汉森(Hansen)正则化工具箱确定L曲线拐角的范围，具体范围可以根据实际需要选取或确定，在此范围内，选取一定数值范围内的多个热流密度分布的估计值，这些热流密度分布的估计值对应的采样值，便可以被确定为本轮的正则化参数的优选解。在一些情况下，可以确定一个用于参考的热流密度分布的估计值，该估计值，以及与该估计值的偏差在预设范围内的其他热流密度分布的估计值，可以被视为前述的“一定数值范围内的多个热流密度分布的估计值”。该用于参考的热流密度分布的估计值，可以根据L曲线的拐角处的一个被选定的坐标点所对应的正则化参数来确定。该被选定的坐标点，可以根据L曲线的拐角处各坐标点处切线的斜率来确定，原则是使泛函模型最小化。
在步骤S2035中，以本轮的正则化参数的优选解的范围，确定下轮的正则化参数的采样范围值，可以是根据本轮优选解的最大值和最小值，确定下轮的采样范围的最大值和最小值；还可以是根据本轮优选解的众数、平均值或中位值等数值来确定下轮采样范围的最大值和最小值，具体可以根据实际需要进行选择。另外，可以根据实际需要，减小下轮的正则化参数的采样间隔，例如可以使下轮的采样间隔变为本轮的采样间隔的十分之一、五分之一或二分之一，等等。
在一些实施例中，如图3所示，步骤S2035包括步骤S301和步骤S302。步骤S301，获取预设的目标系数。该目标系数的取值大于0小于1。步骤S302，将目标系数与本轮的正则化参数的采样间隔 的乘积，确定为下轮的正则化参数的采样间隔。例如，以k表示轮次，以S k表示第k轮的采样间隔，以C k表示目标系数函数时，第k+1轮的采样间隔S k+1可以由公式(7)来确定。
S k+1＝C kgS k，C k∈(0,1)         (7)
步骤S301中，获取预设的目标系数，可以根据预设的目标系数函数来确定本轮具体的目标系数，具体地，运行目标系数函数后，可以获得一个大于0且小于1的常数作为目标系数。目标系数函数可以是线性的，也可以是非线性的。当然，步骤S301中，每轮获取的目标系数既可以是不变的，此时C k可以是一个常数；每轮获取的目标系数也可以是变化的，具体可以根据实际需求进行预设。
步骤S204，根据最后一轮的正则化参数的优选解，确定最终选用的正则化参数。
执行步骤S204时，可以从最后一轮的正则化参数的优选解中选择一个优选解，将其确定为最终选用的正则化参数；也可以根据最后一轮的正则化参数的优选解的最大值和最小值，在最大值和最小值形成的区间中选择一个数值作为最终选用的正则化参数。
步骤S205，根据最终选用的正则化参数，确定待求解区域的热流密度分布的最终估计值。此处指的是在某个观测时段内的热流密度分布估计值，由于确定了最终选用的正则化参数，即确定了泛函模型中的α，因此随着时间推移，待求解区域的热流密度分布也可以被实时估计得到。
在一些实施例中，可以执行2至5轮的正则化参数选取操作，当然，还可以执行更多轮次的正则化参数选取操作，具体取决于实际需求。
上述热学数据确定方法，在一轮的正则化参数选取操作中，利用L曲线的坐标数据，确定L曲线的拐角处多个坐标数据对应的采样值为本轮的正则化参数的优选解，并以本轮的优选解来确定下轮的正则化参数选取操作中的正则化参数的采样范围值，以及减小下轮的正则化参数的采样间隔，使得下轮正则化参数选取操作涉及的计算量大幅降低，并提高了正则化参数搜索的精确度，能有利于在短时间内确定出合适的正则化参数，从而快速获得精确的求解区域的热流密度分布估计值。
在一些实施例中，如图4所示，步骤S2034包括步骤S401至步骤S403。
步骤S401，根据本轮的L曲线的坐标数据，从多个采样值中，确定用于参考的本轮最优采样值，将本轮最优采样值作为本轮的正则化参数的优选解的元素。执行时，可以通过分析多个采样值对应的L曲线的坐标点处的切线斜率，从而确定本轮最优采样值。也可以通过确定最接近L曲线拐角处的拐点，确定离拐点最近的一个坐标数据对应的坐标点，从而确定该坐标数据对应的采样值作为本轮最优采样值。
步骤S402，确定本轮的其他采样值所对应的热流密度分布估计值分别与本轮最优采样值对应的热流密度分布估计值的偏差。
需要注意，本文所说的偏差，除非有其他特别强调，否则都可以理解为被比较偏差的两个对象之间在取值上的差距，这种差距可以通过直接相减进行体现，可以通过计算误差的方式进行体现，也可以通过其他表现差值的方式进行体现，在此不作特别限制。
在一些实施例中，步骤S402包括：确定其他采样值所对应的热流密度分布估计值与本轮最优采样值对应的热流密度分布估计值之差的范数作为第一范数；确定本轮最优采样值对应的热流密度分布估计值的范数作为第二范数；根据第一范数和第二范数之比确定偏差。具体地，可以根据公式(8)来确定步骤S402中的偏差。
Figure PCTCN2022125225-appb-000009
其中，
Figure PCTCN2022125225-appb-000010
表示本轮最优采样值，α m表示其他采样值中的一个采样值，由采样范围[α min,α max]和采样间隔S k来确定，
Figure PCTCN2022125225-appb-000011
表示α m所对应的热流密度分布估计值与
Figure PCTCN2022125225-appb-000012
对应的热流密度分布估计值的偏差，k表示当前的轮次，
Figure PCTCN2022125225-appb-000013
表示
Figure PCTCN2022125225-appb-000014
对应的热流密度分布估计值，
Figure PCTCN2022125225-appb-000015
表示α m所对应的热流密度分布估计值。当然，步骤S402中的偏差，也可以根据其他计算方式进行确定。
步骤S403，在偏差不超出预设偏差阈值时，将相应的其他采样值作为本轮的正则化参数的优选解的元素。在一些可选的实施方式中，步骤S403包括：响应于偏差不超出预设偏差阈值，将相应的其他采样值作为本轮的正则化参数的优选解的元素。预设偏差阈值可以根据实际需要进行取值，例如取0.01、0.1或其他数值。以ε表示预设偏差阈值，则第k轮的优选解的元素，包括了
Figure PCTCN2022125225-appb-000016
以及
Figure PCTCN2022125225-appb-000017
在一些实施例中，如图5所示，步骤S2032包括：
步骤S501，对于每个采样值，采用基于共轭梯度法的迭代正则化计算模型确定多个迭代周期对应的热流密度分布估计值；
步骤S502，在当前迭代周期获得的热流密度分布估计值与上一迭代周期获得的热流密度分布估计值的偏差在预设迭代偏差阈值范围内时，将当前迭代周期获得的热流密度分布估计值作为该采样值对应的热流密度分布估计值。在一些可选的实施方式中，步骤S502包括：确定该偏差在预设迭代偏差阈值范围内，将当前迭代周期获得的热流密度分布估计值作为该采样值对应的热流密度分布估计值。
基于共轭梯度法的迭代正则化计算模型涉及的方程可参见公式(9)至公式(22)。
Figure PCTCN2022125225-appb-000018
Figure PCTCN2022125225-appb-000019
Figure PCTCN2022125225-appb-000020
Figure PCTCN2022125225-appb-000021
Figure PCTCN2022125225-appb-000022
H r(x,t max)＝0,in Ω     (14)
Figure PCTCN2022125225-appb-000023
Figure PCTCN2022125225-appb-000024
h(x,t,Q u)＝Φ(x,t,Q u)-Φ m(x,t)       (17)
Figure PCTCN2022125225-appb-000025
Figure PCTCN2022125225-appb-000026
v r(·,0)＝0,in Ω     (20)
Figure PCTCN2022125225-appb-000027
Figure PCTCN2022125225-appb-000028
在运行共轭梯度法，进行共轭搜索时，可以设定初始估算值
Figure PCTCN2022125225-appb-000029
公式(9)是热流密度分布估计值的迭代更新公式，公式(13)至公式(16)是伴随问题的求解方程，公式(19)至公式(22)是灵敏度问题的求解方程。公式(9)至公式(22)中，r表示迭代次数，
Figure PCTCN2022125225-appb-000030
表示估计的待 求解区域的热流密度分布，R r(x,t)、R r表示共轭搜索方向，ξ r表示共轭系数，ε r表示共轭搜索的步长，L r表示目标泛函，H r表示伴随问题的解，h表示Λ I上估计的温度分布函数Φ(x,t,Q u)和温度分布测量值Φ m(x,t)之间的误差，v r表示灵敏度问题的解。公式(9)至公式(22)中的参数，已在公式(1)至公式(8)中出现过的，请参照前文说明进行理解，在此不作过多解释。
假设当前轮次的正则化参数选取操作中，多个采样值中的某一个采样值为α m，α m处于采样范围[α min,α max]，在求解采用基于共轭梯度法的迭代正则化计算模型求解α m对应的热流密度分布估计值时，当前迭代周期的序号为r，上一迭代周期的序号为r-1；则步骤S502中的预设迭代偏差阈值范围可以指偏差小于等于迭代中的热流密度估计误差，迭代中的热流密度估计误差可以表示为η，此时，当前迭代周期获得的热流密度分布估计值与上一迭代周期获得的热流密度分布估计值可以根据公式(23)来确定。
Figure PCTCN2022125225-appb-000031
其中，
Figure PCTCN2022125225-appb-000032
和
Figure PCTCN2022125225-appb-000033
分别表示当前迭代周期获得的热流密度分布估计值和上一迭代周期获得的热流密度分布估计值。
当公式(23)被满足时，对应的
Figure PCTCN2022125225-appb-000034
则被视为α m的热流密度分布估计值，即
Figure PCTCN2022125225-appb-000035
此时，可以停止针对α m的基于共轭梯度法的迭代正则化计算模型的计算。随后，可以针对下一个采样值，执行基于共轭梯度法的迭代正则化计算模型的计算。
当公式(23)不被满足，则进入下一次迭代，再判断公式(23)是否被满足，直至迭代的次数达到预设的最大次数r max。若达到最大次数r max，公式(23)仍未被满足，则跳出迭代的循环。r max的取值可以是200、300或其他，具体可根据实际需求设置。
需要注意的是，除了可以采用前述的共轭梯度法来确定热流密度分布估计值以外，还可以采用基于空间推进算法(Space marching)、序列函数法(Function specification)、贝叶斯方法(Bayes)、人工神经网络方法(ANN,Artificial Neural Networks)、卡尔曼滤波(KF,Kalman filter)方法、莱文格-马夸特(LM,Levenberg–Marquardt)算法、截断奇异值分解(SVD,Singular value decomposition)方法、Tikhonov正则化方法等方法或算法来进行反问题计算，并确定热流密度分布估计值。
在一些实施例中，泛函模型包括预测残差项和正则化惩罚项，预测残差项包括温度分布函数的残差的范数，温度分布函数用于描述目标区域在时间和空间上的温度分布，正则化惩罚项包括正则化参数和未知热流密度函数的范数；结合图6和图7理解，步骤S202包括：步骤S601，获取目标区域的热学属性参数；步骤S602，获取目标区域的边界条件；步骤S603，获取目标区域的温度分布测量 值；步骤S604，获取目标区域的初始温度分布；步骤S605，获取目标区域的第一边界在预设观测时间内的热流密度数据。相应地，步骤S2032包括：步骤S701，将目标区域的第二边界的热流密度分布作为待求解区域的热流密度分布，根据热学属性参数、边界条件、初始温度分布、热流密度数据和第二边界的热流密度分布，确定目标区域的温度分布函数；步骤S702，将目标区域的温度分布函数与温度分布测量值的差值作为温度分布函数的残差，确定每一采样值对应的热流密度分布估计值。具体地，可以将泛函模型的温度分布函数的残差，结合已知条件和采样值，计算得到对应的热流密度分布估计值。
需要注意的是，步骤S601至步骤S605中的各步骤的执行顺序，本领域技术人员可以根据实际需要进行合理地设计，在此不作特别限制。步骤S605中，第一边界的热流密度数据，可以根据温度分布测量值计算得到，也可以根据热源的加热功率计算得到，也可以通过其他手段对热源的发热进行测量而获得。
在一些实施例中，步骤S701包括：根据热学属性参数、边界条件、初始温度分布、热流密度数据和第二边界的热流密度分布，并行求解热传导正问题，将热传导正问题的解作为目标区域的温度分布函数。并行求解热传导正问题，结合正则化参数的选取方式，实现了高通量数据处理的目的，能有效提升对热流密度分布的最终估计值求解的效率。
在一些情况下，执行步骤S701和步骤S702所涉及的计算公式，可参见公式(1)至公式(6)进行理解。
在一些实施例中，热学数据确定方法还包括：根据待求解区域的热流密度分布的最终估计值和初始温度分布，确定待求解区域在指定时刻的温度分布。前述的指定时刻可以包括过去一段观测时段内的某个时刻，也可以包括最新的观测时刻。
在一些实施例中，热学数据确定方法还包括：根据待求解区域的热流密度分布的最终估计值和初始温度分布，确定待求解区域在最新时刻的温度分布；根据最新时刻的温度分布，向加热组件发出调节信号，调节信号用于控制加热组件对目标区域施加的热流密度。考虑到在生产制造或对生物组织加热等各种加热环境中，出于满足对目标区域的第二边界上的温度分布进行控制的需求，可以通过实施该实施例，通过处理器101执行热学数据确定方法，控制加热组件，从而实现控温的目的。
在一些实施例中，可采用现有的三维瞬态热传导方程求解器来运算前述的正问题、反问题、伴随问题或灵敏度问题涉及的方程。例如，DROPS(一款用于模拟两相流的计算流体力学软件)、NGSolve(一款高性能的多物理场有限元软件)、COMSOL Multiphysics(一款高级数值仿真软件)、OpenFoam(一款基于C++的面向对象计算流体力学软件)等具有求解热传导偏微分方程功能的软件可以用来数值求解前文提及的反问题计算时所产生的正问题、伴随问题和灵敏性问题等偏微分方程。
虽然图2(a)至图7的流程图中的各个步骤按照箭头的指示依次显示，但是这些步骤并不是必然按照箭头指示的顺序依次执行。图2(a)至图7展示的步骤以及其他实施例公开的步骤，除非本文中有明确的说明，这些步骤的执行并没有严格的顺序限制，这些步骤可以以其它的顺序执行。而且，前述各实施例的至少一部分步骤可以包括多个子步骤或者多个阶段，这些子步骤或者阶段并不必然是在同一时刻执行完成，而是可以在不同的时刻执行，这些子步骤或者阶段的执行顺序也不必然是依次进行，而是可以与其它步骤或者其它步骤的子步骤或者阶段的至少一部分轮流或者交替地执行。
本申请还公开了一种热学数据确定装置，如图8所示，包括：模型确定模块810，用于确定吉洪诺夫正则化的泛函模型，泛函模型用于求解目标区域的热传导反问题，输出目标区域中待求解区域的热流密度分布估计值；已知条件获取模块820，用于获取泛函模型中变量的已知条件，已知条件包括目标区域的边界条件、热学属性参数和温度分布测量值；优选解获取模块830，用于根据泛函模型，执行两轮以上的正则化参数选取操作，获得最后一轮的正则化参数的优选解；正则化参数确定模块 840，用于根据最后一轮的正则化参数的优选解，确定最终选用的正则化参数；估计模块850，用于根据最终选用的正则化参数，确定待求解区域的热流密度分布的最终估计值。
其中，优选解获取模块830包括：采样值确定子模块831，用于在每轮正则化参数选取操作中，根据设定的正则化参数的采样范围值和采样间隔，确定本轮的多个采样值；模型运行子模块832，用于将多个采样值和已知条件输入泛函模型，获得与每一采样值对应的热流密度分布估计值；L曲线确定子模块833，用于根据多个热流密度分布估计值，确定L曲线的坐标数据；优选解确定子模块834，用于将L曲线拐角处的多个坐标数据对应的采样值，确定为本轮的正则化参数的优选解；采样参数调整子模块835，用于在本轮为非最后一轮时，以本轮的正则化参数的优选解的范围，确定下轮的正则化参数的采样范围值，并减小下轮的正则化参数的采样间隔。
在一些实施例中，优选解确定子模块834包括：参考值确定单元，用于根据本轮的L曲线的坐标数据，从多个采样值中，确定用于参考的本轮最优采样值，将本轮最优采样值作为本轮的正则化参数的优选解的元素；第一偏差估计单元，用于确定本轮的其他采样值所对应的热流密度分布估计值分别与本轮最优采样值对应的热流密度分布估计值的偏差；优选解确定单元，用于在偏差不超出预设偏差阈值时，将相应的其他采样值作为本轮的正则化参数的优选解的元素。
在一些实施例中，第一偏差估计单元包括：第一范数确定子单元，用于确定其他采样值所对应的热流密度分布估计值与本轮最优采样值对应的热流密度分布估计值之差的范数作为第一范数；第二范数确定子单元，用于确定本轮最优采样值对应的热流密度分布估计值的范数作为第二范数；偏差确定子单元，用于根据第一范数和第二范数之比确定偏差。
在一些实施例中，采样参数调整子模块835包括：目标系数获取单元，用于获取预设的目标系数，目标系数的取值大于0小于1；采样间隔调整单元，用于将目标系数与本轮的正则化参数的采样间隔的乘积，确定为下轮的正则化参数的采样间隔。
在一些实施例中，模型运行子模块832包括：反问题计算单元，用于对于每个采样值，采用基于共轭梯度法的迭代正则化计算模型确定多个迭代周期对应的热流密度分布估计值；迭代误差计算单元，用于在当前迭代周期获得的热流密度分布估计值与上一迭代周期获得的热流密度分布估计值的偏差在预设迭代偏差阈值范围内时，将当前迭代周期获得的热流密度分布估计值作为该采样值对应的热流密度分布估计值。
在一些实施例中，泛函模型包括预测残差项和正则化惩罚项，预测残差项包括温度分布函数的残差的范数，温度分布函数用于描述目标区域在时间和空间上的温度分布，正则化惩罚项包括正则化参数和未知热流密度函数的范数。已知条件获取模块820包括：属性参数获取子模块，用于获取目标区域的热学属性参数；边界数据获取子模块，用于获取目标区域的边界条件；测量值获取子模块，用于获取目标区域的温度分布测量值；初始温度获取子模块，用于获取目标区域的初始温度分布；热流密度数据获取子模块，用于获取目标区域的第一边界在预设观测时间内的热流密度数据。模型运行子模块832包括：温度分布函数求解单元，用于将目标区域的第二边界的热流密度分布作为待求解区域的热流密度分布，根据热学属性参数、边界条件、初始温度分布、热流密度数据和第二边界的热流密度分布，确定目标区域的温度分布函数；泛函模型求解单元，用于将目标区域的温度分布函数与温度分布测量值的差值作为温度分布函数的残差，确定每一采样值对应的热流密度分布估计值。
在一些实施例中，温度分布函数求解单元包括并行求解子单元，并行求解子单元用于根据热学属性参数、边界条件、初始温度分布、热流密度数据和第二边界的热流密度分布，并行求解热传导正问题，将热传导正问题的解作为目标区域的温度分布函数。
在一些实施例中，热学数据确定装置还包括温度分布估计模块(未图示)，用于根据待求解区域的热流密度分布的最终估计值和初始温度分布，确定待求解区域在指定时刻的温度分布。
在一些实施例中，热学数据确定装置还包括：温度估计模块(未图示)，用于根据待求解区域的热流密度分布的最终估计值和初始温度分布，确定待求解区域在最新时刻的温度分布；控温模块(未图示)，用于根据最新时刻的温度分布，向加热组件发出调节信号，调节信号用于控制加热组件对目标区域施加的热流密度。
关于热学数据确定装置的具体限定可以参见上文中对于热学数据确定方法的限定，在此不再赘述。具体地，热学数据确定装置可以实现前述任一实施例中热学数据确定方法的步骤。上述热学数据确定装置中的各个模块可全部或部分通过软件、硬件及其组合来实现。上述各模块可以硬件形式内嵌于或独立于计算机设备中的处理器中，也可以以软件形式存储于计算机设备中的存储器中，以便于处理器调用执行以上各个模块对应的操作。
在一些实施例中，本申请实施例还公开了一种计算机设备，其包括存储器及一个或多个处理器，存储器中储存有计算机可读指令，该计算机可读指令被一个或多个处理器执行时，使得一个或多个处理器执行前文任一实施例中的热学数据确定方法的步骤。在一些实施例中，该计算机设备可以是服务器，其内部结构图可以如图9所示。该计算机设备包括通过系统总线连接的处理器、存储器、网络接口。该计算机设备的处理器用于提供计算和控制能力。该计算机设备的存储器包括非易失性存储介质、内存储器。该非易失性存储介质存储有操作系统、计算机可读指令。该内存储器为非易失性存储介质中的操作系统和计算机可读指令的运行提供环境。该计算机设备的网络接口用于与外部的终端通过网络连接通信。该计算机可读指令被处理器执行时以实现前文任一实施例中的热学数据确定方法。
图9中示出的结构，仅仅是与本申请方案相关的部分结构的框图，并不构成对本申请方案所应用于其上的计算机设备的限定，具体的计算机设备可以包括比图中所示更多或更少的部件，或者组合某些部件，或者具有不同的部件布置。
本申请还公开了一种热学数据确定设备，热学数据确定设备包括图1所示的处理器101和温度测量组件102。温度测量组件102用于测量目标区域的温度分布，生成目标区域的温度分布测量值。处理器101可用于执行前文任一实施例中的热学数据确定方法的步骤。
在一些实施例中，热学数据确定设备还包括加热组件(未图示)，加热组件用于加热目标区域。处理器101还可以用于执行以下步骤：获取预设的待求解区域的初始温度分布；根据待求解区域的热流密度分布的最终估计值和预设的待求解区域的初始温度分布，更新待求解区域在最新时刻的温度分布；根据待求解区域在最新时刻的温度分布，调节加热组件向目标区域施加的热流密度。
在一些实施例中，可以将目标区域的初始温度分布，视为待求解区域的初始温度分布。具体地，可以将室温视为目标区域的初始温度分布。当然，在其他实施例中，可以根据实际情况，估计或预设目标区域的初始温度分布。
本申请实施例还公开了一个或多个存储有计算机可读指令的非易失性计算机可读存储介质，该计算机可读指令被一个或多个处理器执行时，使得一个或多个处理器执行前文任一实施例中的热学数据确定方法的步骤。
本领域普通技术人员可以理解实现上述实施例方法中的全部或部分流程，是可以通过计算机可读指令来指令相关的硬件来完成，前述的计算机可读指令可存储于一非易失性计算机可读取存储介质中，该计算机可读指令在被执行时，可包括如上述各方法的实施例的流程。其中，本申请所提供的各实施例中所使用的对存储器、存储、数据库或其它介质的任何引用，均可包括非易失性和/或易失性存储器。非易失性存储器可包括只读存储器(ROM)、可编程ROM(PROM)、电可编程ROM(EPROM)、电可擦除可编程ROM(EEPROM)或闪存。易失性存储器可包括随机存取存储器(RAM)或者外部高速缓冲存储器。作为说明而非局限，RAM以多种形式可得，诸如静态RAM(SRAM)、动态RAM(DRAM)、同步DRAM(SDRAM)、双数据率SDRAM (DDRSDRAM)、增强型SDRAM(ESDRAM)、同步链路(Synchlink)DRAM(SLDRAM)、存储器总线(Rambus)直接RAM(RDRAM)、直接存储器总线动态RAM(DRDRAM)、以及存储器总线动态RAM(RDRAM)等。
本领域技术人员可以理解，从技术可行性的角度考虑，可以按照与热学数据确定方法所能应用的领域，应用热学数据确定装置、计算机设备或热学数据确定设备。
由于热学数据确定方法、热学数据确定装置、计算机设备和热学数据确定设备，可应用的领域是丰富的，例如，可应用于生物医学领域、通信领域、能源领域、工业制造领域和农林渔牧业领域等诸多领域，为便于直观理解，在此以应用于生物体的目标区域的温度研究为例，作简单说明。
在一个实施例中，可以应用于蚊子吸食血液时的降温过程研究。在面临热胁迫的威胁时，昆虫等生物的体温调控十分关键。以蚊子为例，已有的研究表明，吸血引起的高温会危及蚊子的生理状况，蚊子通过在进食过程中排出、维持和蒸发腹部末端的液滴来降低体温。作为最重要的物理量之一，腹部末端的高瞬态热流密度对于更好地理解研究对象的耗散机制至关重要。现有测量技术仍难以直接获得该物理量的准确值，但可以通过建立和求解瞬态传热反问题来估计难以测量的未知热流密度分布。
具体地，发明人研究了蚊子吸血过程中的热流密度分布估算问题。为对实际问题做近似处理，在x∈[0,16]mm(蚊子的身体长度范围，即目标区域)上建立泛函模型。总观测时间设定为180秒，观测时间间隔为Δt＝2s，导热系数为a＝0.58W/(m·K)。目标区域的初始温度分布设定为Φ(g,0)＝24℃。恒定施加的输入热流设定为Q i(x,t)＝0.000386W/mm 2，以反映蚊子和被吸血生物之间的直接接触。蚊子头部的实际瞬态温度数据(即第一边界的热流密度数据)，采用了Lahondère等公开的实验数据，具体出处为：C Lahondère,Lazzari C.Mosquitoes Cool Down during Blood Feeding to Avoid Overheating[J].Current biology:CB,2011,22(1):40-45。
应用热学数据确定方法的步骤，第一轮的正则化参数选取操作中，正则化参数的取值范围被设定为[0,0.001]。经过两轮以上的正则化参数选取操作，最后得到正则化参数的优选解，即{α m|0.000295≤α m≤0.000315}，实现了对正则化参数选取范围的快速缩小，并确保待求解区域的热流密度分布估计值的误差较小。在{α m|0.000295≤α m≤0.000315}的基础上，发明人最终将正则化参数的取值确定为0.000296。具体地，可以根据{α m|0.000295≤α m≤0.000315}中有限个数的正则化参数所对应的热流密度分布估计值的曲线的平滑度，确定最终合适的正则化参数的取值。选择合适的正则化参数对处理不适定问题很重要。选择过大或过小而不是合适的正则化参数，将导致过于平滑或振荡的结果，这与物理现象不相符。
选取正则化参数为0.000296时，如图10所示，横坐标表示观测时间，纵坐标表示待求解区域(即蚊子腹部末端、第二边界内)的热流密度分布估计值，蚊子腹部末端的估算热流显示了热交换情况，可见腹部末端高瞬态热流密度与蚊子头部复杂的温度变化密切相关，热流峰值可能出现在蚊子逐渐失去腹部末端液滴时。
以上实施例的各技术特征可以进行任意的组合，为使描述简洁，未对上述实施例中的各个技术特征所有可能的组合都进行描述，然而，只要这些技术特征的组合不存在矛盾，都应当认为是本说明书记载的范围。以上实施例仅表达了本申请的若干实施方式，其描述较为具体和详细，但并不能因此而理解为对本申请的保护范围的限制。对于本领域的普通技术人员来说，在不脱离本申请构思的前提下，还可以做出若干变形和改进，这些都属于本申请的保护范围。因此，本申请的保护范围应以所附权利要求为准。

Claims (20)

  1. 一种热学数据确定方法，其特征在于，所述方法包括：
    确定吉洪诺夫正则化的泛函模型，所述泛函模型用于求解目标区域的热传导反问题，输出所述目标区域中待求解区域的热流密度分布估计值；
    获取所述泛函模型中变量的已知条件，所述已知条件包括所述目标区域的边界条件、热学属性参数和温度分布测量值；
    根据所述泛函模型，执行两轮以上的正则化参数选取操作，获得最后一轮的正则化参数的优选解；
    根据所述最后一轮的正则化参数的优选解，确定最终选用的正则化参数；以及
    根据所述最终选用的正则化参数，确定所述待求解区域的热流密度分布的最终估计值；
    其中，在每轮正则化参数选取操作中，根据设定的正则化参数的采样范围值和采样间隔，确定本轮的多个采样值，将所述多个采样值和所述已知条件输入所述泛函模型，获得与每一采样值对应的热流密度分布估计值，根据多个热流密度分布估计值确定L曲线的坐标数据，将L曲线拐角处的多个坐标数据对应的采样值，确定为本轮的正则化参数的优选解，在本轮为非最后一轮时，以本轮的正则化参数的优选解的范围，确定下轮的正则化参数的采样范围值，并减小下轮的正则化参数的采样间隔。
  2. 根据权利要求1所述的方法，其特征在于，所述将L曲线拐角处的多个坐标数据对应的采样值，确定为本轮的正则化参数的优选解，包括：
    根据本轮的L曲线的坐标数据，从所述多个采样值中，确定用于参考的本轮最优采样值，将所述本轮最优采样值作为所述本轮的正则化参数的优选解的元素；
    确定本轮的其他采样值所对应的热流密度分布估计值分别与本轮最优采样值对应的热流密度分布估计值的偏差；以及
    在偏差不超出预设偏差阈值时，将相应的其他采样值作为本轮的正则化参数的优选解的元素。
  3. 根据权利要求2所述的方法，其特征在于，所述确定本轮的其他采样值所对应的热流密度分布估计值分别与本轮最优采样值对应的热流密度分布估计值的偏差，包括：
    确定其他采样值所对应的热流密度分布估计值与本轮最优采样值对应的热流密度分布估计值之差的范数作为第一范数；
    确定本轮最优采样值对应的热流密度分布估计值的范数作为第二范数；以及
    根据第一范数和第二范数之比确定所述偏差。
  4. 根据权利要1至3任一所述的方法，其特征在于，所述在本轮为非最后一轮时，以本轮的正则化参数的优选解的范围，确定下轮的正则化参数的采样范围值，并减小下轮的正则化参数的采样间隔，包括：
    获取预设的目标系数，所述目标系数的取值大于0小于1；以及
    将所述目标系数与本轮的正则化参数的采样间隔的乘积，确定为下轮的正则化参数的采样间隔。
  5. 根据权利要1至4任一所述的方法，其特征在于，所述将所述多个采样值和所述已知条件输入所述泛函模型，获得与每一采样值对应的热流密度分布估计值，包括：
    用于对于每个采样值，采用基于共轭梯度法的迭代正则化计算模型确定多个迭代周期对应的热流密度分布估计值；以及
    在当前迭代周期获得的热流密度分布估计值与上一迭代周期获得的热流密度分布估计值的偏差在预设迭代偏差阈值范围内时，将当前迭代周期获得的热流密度分布估计值作为该采样值对应的热流密度分布估计值。
  6. 根据权利要1至5任一所述的方法，其特征在于，所述泛函模型包括预测残差项和正则化惩罚项，所述预测残差项包括温度分布函数的残差的范数，所述温度分布函数用于描述目标区域在时间和空间上的温度分布，所述正则化惩罚项包括正则化参数和未知热流密度函数的范数；
    所述获取所述泛函模型中变量的已知条件，包括：获取所述目标区域的热学属性参数；获取所述目标区域的边界条件；获取所述目标区域的温度分布测量值；获取所述目标区域的初始温度分布；以及，获取所述目标区域的第一边界在预设观测时间内的热流密度数据；
    所述将所述多个采样值和所述已知条件输入所述泛函模型，获得与每一采样值对应的热流密度分布估计值，包括：将所述目标区域的第二边界的热流密度分布作为所述待求解区域的热流密度分布，根据所述热学属性参数、所述边界条件、所述初始温度分布、所述热流密度数据和所述第二边界的热流密度分布，确定所述目标区域的温度分布函数；以及，将所述目标区域的温度分布函数与所述温度分布测量值的差值作为温度分布函数的残差，确定每一采样值对应的热流密度分布估计值。
  7. 根据权利要6所述的方法，其特征在于，所述根据所述热学属性参数、所述边界条件、所述初始温度分布、所述热流密度数据和所述第二边界的热流密度分布，确定所述目标区域的温度分布函数，包括：根据所述热学属性参数、所述边界条件、所述初始温度分布、所述热流密度数据和所述第二边界的热流密度分布，并行求解热传导正问题，将热传导正问题的解作为所述目标区域的温度分布函数；
  8. 根据权利要6或7所述的方法，其特征在于，还包括：根据所述待求解区域的热流密度分布的最终估计值和所述初始温度分布，确定所述待求解区域在指定时刻的温度分布。
  9. 一种热学数据确定装置，其特征在于，所述装置包括：
    模型确定模块，用于确定吉洪诺夫正则化的泛函模型，所述泛函模型用于求解目标区域的热传导反问题，输出所述目标区域中待求解区域的热流密度分布估计值；
    已知条件获取模块，用于获取所述泛函模型中变量的已知条件，所述已知条件包括所述目标区域的边界条件、热学属性参数和温度分布测量值；
    优选解获取模块，用于根据所述泛函模型，执行两轮以上的正则化参数选取操作，获得最后一轮的正则化参数的优选解；
    正则化参数确定模块，用于根据所述最后一轮的正则化参数的优选解，确定最终选用的正则化参数；以及
    估计模块，用于根据所述最终选用的正则化参数，确定所述待求解区域的热流密度分布的最终估计值；
    其中，所述优选解获取模块包括：
    采样值确定子模块，用于在每轮正则化参数选取操作中，根据设定的正则化参数的采样范围值和采样间隔，确定本轮的多个采样值；
    模型运行子模块，用于将所述多个采样值和所述已知条件输入所述泛函模型，获得与每一采样值对应的热流密度分布估计值；
    L曲线确定子模块，用于根据多个热流密度分布估计值，确定L曲线的坐标数据；
    优选解确定子模块，用于将L曲线拐角处的多个坐标数据对应的采样值，确定为本轮的正则化参数的优选解；以及
    采样参数调整子模块，用于在本轮为非最后一轮时，以本轮的正则化参数的优选解的范围，确定下轮的正则化参数的采样范围值，并减小下轮的正则化参数的采样间隔。
  10. 根据权利要求9所述的装置，其特征在于，所述优选解确定子模块包括：
    参考值确定单元，用于根据本轮的L曲线的坐标数据，从所述多个采样值中，确定用于参考的本轮最优采样值，将所述本轮最优采样值作为所述本轮的正则化参数的优选解的元素；
    第一偏差估计单元，用于确定本轮的其他采样值所对应的热流密度分布估计值分别与本轮最优采样值对应的热流密度分布估计值的偏差；以及
    优选解确定单元，用于在偏差不超出预设偏差阈值时，将相应的其他采样值作为本轮的正则化参数的优选解的元素。
  11. 根据权利要求10所述的装置，其特征在于，所述第一偏差估计单元包括：
    第一范数确定子单元，用于确定其他采样值所对应的热流密度分布估计值与本轮最优采样值对应的热流密度分布估计值之差的范数作为第一范数；
    第二范数确定子单元，用于确定本轮最优采样值对应的热流密度分布估计值的范数作为第二范数；以及
    偏差确定子单元，用于根据第一范数和第二范数之比确定所述偏差。
  12. 根据权利要求9至11任一所述的装置，其特征在于，所述采样参数调整子模块包括：
    目标系数获取单元，用于获取预设的目标系数，所述目标系数的取值大于0小于1；以及
    采样间隔调整单元，用于将所述目标系数与本轮的正则化参数的采样间隔的乘积，确定为下轮的正则化参数的采样间隔。
  13. 根据权利要求9至12任一所述的装置，其特征在于，所述模型运行子模块包括：
    反问题计算单元，用于对于每个采样值，采用基于共轭梯度法的迭代正则化计算模型确定多个迭代周期对应的热流密度分布估计值；以及
    迭代误差计算单元，用于在当前迭代周期获得的热流密度分布估计值与上一迭代周期获得的热流密度分布估计值的偏差在预设迭代偏差阈值范围内时，将当前迭代周期获得的热流密度分布估计值作为该采样值对应的热流密度分布估计值。
  14. 根据权利要求9至13任一所述的装置，其特征在于，所述泛函模型包括预测残差项和正则化惩罚项，所述预测残差项包括温度分布函数的残差的范数，所述温度分布函数用于描述目标区域在时间和空间上的温度分布，所述正则化惩罚项包括正则化参数和未知热流密度函数的范数；
    所述已知条件获取模块包括：
    属性参数获取子模块，用于获取所述目标区域的热学属性参数；
    边界数据获取子模块，用于获取所述目标区域的边界条件；
    测量值获取子模块，用于获取所述目标区域的温度分布测量值；
    初始温度获取子模块，用于获取所述目标区域的初始温度分布；以及
    热流密度数据获取子模块，用于获取所述目标区域的第一边界在预设观测时间内的热流密度数据；
    所述模型运行子模块包括：
    温度分布函数求解单元，用于将所述目标区域的第二边界的热流密度分布作为所述待求解区域的热流密度分布，根据所述热学属性参数、所述边界条件、所述初始温度分布、所述热流密度数据和所述第二边界的热流密度分布，确定所述目标区域的温度分布函数；以及
    泛函模型求解单元，用于将所述目标区域的温度分布函数与所述温度分布测量值的差值作为温度分布函数的残差，确定每一采样值对应的热流密度分布估计值。
  15. 根据权利要求14所述的装置，其特征在于，所述温度分布函数求解单元包括：
    并行求解子单元，用于根据所述热学属性参数、所述边界条件、所述初始温度分布、所述热流密度数据和所述第二边界的热流密度分布，并行求解热传导正问题，将热传导正问题的解作为所述目标区域的温度分布函数。
  16. 根据权利要求14或15所述的装置，其特征在于，还包括：
    温度分布估计模块，用于根据所述待求解区域的热流密度分布的最终估计值和所述初始温度分布，确定所述待求解区域在指定时刻的温度分布。
  17. 一种计算机设备，其特征在于，包括存储器及一个或多个处理器，所述存储器中储存有计算机可读指令，所述计算机可读指令被所述一个或多个处理器执行时，使得所述一个或多个处理器执行如权利要求1至8任一所述方法的步骤。
  18. 一种热学数据确定设备，其特征在于，包括温度测量组件和处理器；
    所述温度测量组件用于测量目标区域的温度分布，生成所述目标区域的温度分布测量值；
    所述处理器用于执行如权利要求1至8任一所述方法的步骤。
  19. 根据权利要求18所述的设备，其特征在于，所述设备还包括加热组件，所述加热组件用于加热所述目标区域；
    所述处理器还用于：
    根据所述待求解区域的热流密度分布的最终估计值和预设的待求解区域的初始温度分布，更新所述待求解区域在最新时刻的温度分布；以及
    根据待求解区域在最新时刻的温度分布，调节所述加热组件向所述目标区域施加的热流密度。
  20. 一个或多个存储有计算机可读指令的非易失性计算机可读存储介质，其特征在于，所述计算机可读指令被一个或多个处理器执行时，使得所述一个或多个处理器执行如权利要求1至8任一所述方法的步骤。
PCT/CN2022/125225 2022-07-04 2022-10-13 一种热学数据确定方法、装置和设备 Ceased WO2024007474A1 (zh)

Priority Applications (1)

Application Number Priority Date Filing Date Title
GB2312112.2A GB2623404B (en) 2022-07-04 2022-10-13 Thermotics data determining method, apparatus and device

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN202210777855.X 2022-07-04
CN202210777855.XA CN114841023B (zh) 2022-07-04 2022-07-04 一种热学数据确定方法、装置和设备

Publications (1)

Publication Number Publication Date
WO2024007474A1 true WO2024007474A1 (zh) 2024-01-11

Family

ID=82573693

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2022/125225 Ceased WO2024007474A1 (zh) 2022-07-04 2022-10-13 一种热学数据确定方法、装置和设备

Country Status (2)

Country Link
CN (1) CN114841023B (zh)
WO (1) WO2024007474A1 (zh)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118350257A (zh) * 2024-06-18 2024-07-16 电子科技大学成都学院 基于三角形单元的瞬态热传导仿真方法及系统
CN118655175A (zh) * 2024-08-21 2024-09-17 南通市富捷隔热材料有限公司 隔热材料瑜伽柱品质智能检测方法及系统
CN119614852A (zh) * 2025-02-12 2025-03-14 航昇船机(大连)有限公司 一种热处理炉温度自适应调控方法
CN120461800A (zh) * 2025-07-14 2025-08-12 中国计量大学 一种自适应塑料相框热弯温度控制方法
CN120578862A (zh) * 2025-08-04 2025-09-02 国家海洋信息中心 一种针对高分辨率海底原位热流数据的处理方法及系统

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114841023B (zh) * 2022-07-04 2022-09-09 中山大学 一种热学数据确定方法、装置和设备
GB2623404B (en) * 2022-07-04 2024-10-16 Univ Sun Yat Sen Thermotics data determining method, apparatus and device
CN115950916B (zh) * 2023-03-14 2023-05-26 中国空气动力研究与发展中心计算空气动力研究所 一种物体表面热流密度检测方法、装置以及设备
CN119861575A (zh) * 2025-03-24 2025-04-22 北京涵鑫盛科技有限公司 一种大规模服务器集群的环境控制系统及控制方法

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108416723A (zh) * 2018-02-07 2018-08-17 南京理工大学 基于全变分正则化和变量分裂的无透镜成像快速重构方法
CN113255181A (zh) * 2021-04-27 2021-08-13 北京航空航天大学 基于深度学习的传热学反问题识别方法及装置
CN114841023A (zh) * 2022-07-04 2022-08-02 中山大学 一种热学数据确定方法、装置和设备

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2014144168A2 (en) * 2013-03-15 2014-09-18 Ion Geophysical Corporation Method and system for seismic inversion
CN103902834B (zh) * 2014-04-14 2017-01-25 重庆大学 一种基于岭估计和l曲线法的结构损伤识别方法
CN113390602B (zh) * 2021-05-25 2022-09-09 中国科学院力学研究所 一种基于内嵌式温敏漆的气动热全场测量系统及方法
CN114117864B (zh) * 2021-12-03 2024-06-28 厦门大学 自适应时间步长有限元法在电子器件热仿真中的应用方法

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108416723A (zh) * 2018-02-07 2018-08-17 南京理工大学 基于全变分正则化和变量分裂的无透镜成像快速重构方法
CN113255181A (zh) * 2021-04-27 2021-08-13 北京航空航天大学 基于深度学习的传热学反问题识别方法及装置
CN114841023A (zh) * 2022-07-04 2022-08-02 中山大学 一种热学数据确定方法、装置和设备

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
HE, JUNHONG: "Tikhonov Regularization Method on Inverse Problem of Heat Conduction Equation", JISUANJI YU SHUZI GONGCHENG - COMPUTER AND DIGITAL ENGINEERING, ZHONGGUO CHUANBO ZHONGGONG JITUAN GONGSI. DI-709 YANJIUSUO, CN, vol. 43, no. 5, 31 May 2015 (2015-05-31), CN , pages 776 - 780, XP009552485, ISSN: 1672-9722, DOI: 10.3969/j.issn1672-9722.2015.05.006 *
HENG, YI; JIU, LUO; QINGQING, YANG; DONGCHUAN, MO; SHUSHEN, LYU: "Three-dimensional Transient Inverse Heat Conduction Problems in the Enhanced Pool Boiling Heat Transfer", SCIENCE BULLETIN, KEXUE CHUBANSHE, BEIJING, CN, vol. 65, no. 18, 30 June 2020 (2020-06-30), CN , pages 1857 - 1874, XP009552484, ISSN: 0023-074X, DOI: 10.1360/TB-2019-0352 *
SUN YAO: "A meshless method based on the method of fundamental solution for solving the steady-state heat conduction problems", INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, ELSEVIER, AMSTERDAM, NL, vol. 97, 15 March 2016 (2016-03-15), AMSTERDAM, NL , pages 891 - 907, XP029474930, ISSN: 0017-9310, DOI: 10.1016/j.ijheatmasstransfer.2016.03.002 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118350257A (zh) * 2024-06-18 2024-07-16 电子科技大学成都学院 基于三角形单元的瞬态热传导仿真方法及系统
CN118655175A (zh) * 2024-08-21 2024-09-17 南通市富捷隔热材料有限公司 隔热材料瑜伽柱品质智能检测方法及系统
CN119614852A (zh) * 2025-02-12 2025-03-14 航昇船机(大连)有限公司 一种热处理炉温度自适应调控方法
CN120461800A (zh) * 2025-07-14 2025-08-12 中国计量大学 一种自适应塑料相框热弯温度控制方法
CN120578862A (zh) * 2025-08-04 2025-09-02 国家海洋信息中心 一种针对高分辨率海底原位热流数据的处理方法及系统

Also Published As

Publication number Publication date
CN114841023B (zh) 2022-09-09
CN114841023A (zh) 2022-08-02

Similar Documents

Publication Publication Date Title
WO2024007474A1 (zh) 一种热学数据确定方法、装置和设备
Huang et al. A two-dimensional inverse problem in imaging the thermal conductivity of a non-homogeneous medium
Huang et al. An inverse problem in estimating simultaneously the effective thermal conductivity and volumetric heat capacity of biological tissue
Lee et al. An inverse hyperbolic heat conduction problem in estimating surface heat flux of a living skin tissue
Chen et al. Predicting the thermophysical properties of skin tumor based on the surface temperature and deep learning
Feng et al. A two-state cell damage model under hyperthermic conditions: theory and in vitro experiments
Jamil et al. Evaluation of meshless radial basis collocation method (RBCM) for heterogeneous conduction and simulation of temperature inside the biological tissues
CN111680444B (zh) 基于单纯形算法的磁纳米粒子临界产热值自动定位方法
Zhang et al. Real-time computation of bio-heat transfer in the fast explicit dynamics finite element algorithm (FED-FEM) framework
Manuel Luna et al. Procedure to estimate thermophysical and geometrical parameters of embedded cancerous lesions using thermography
Grabski et al. Identification of a time-dependent bio-heat blood perfusion coefficient
Abdelhamid et al. Simultaneous reconstruction of the time-dependent Robin coefficient and heat flux in heat conduction problems
Jin et al. Convergence rate analysis of Galerkin approximation of inverse potential problem
Mohebbi et al. Parameter estimation in heat conduction using a two-dimensional inverse analysis
Cotta et al. Hybrid integral transforms analysis of the bioheat equation with variable properties
Shah et al. A computational wavelet method for solving dual‐phase‐lag model of bioheat transfer during hyperthermia treatment
Iljaž et al. Blood perfusion estimation in heterogeneous tissue using BEM based algorithm
Alekseev et al. On estimation of temperature uncertainty using the second order adjoint problem
Bozzoli et al. Comparative application of CGM and Wiener filtering techniques for the estimation of heat flux distribution
Wang Inverse estimation of heat flux and temperature field for a nonlinear heat transfer system using step-renewed two-stage Kalman filter
Mohebbi et al. An inverse analysis for determination of space-dependent heat flux in heat conduction problems in the presence of variable thermal conductivity
Chen et al. Identification of boundary conditions for non-Fourier heat conduction problems by differential transformation DRBEM and improved cuckoo search algorithm
Dai et al. A FOURTH-ORDER COMPACT FINITE-DIFFERENCE SCHEME FOR SOLVING A 1-D PENNES'BIOHEAT TRANSFER EQUATION IN A TRIPLE-LAYERED SKIN STRUCTURE
Majchrzak et al. Numerical modelling of hyperthermia and hypothermia processes
Aviles et al. Exploring the effects of dimensionality reduction in deep networks for force estimation in robotic-assisted surgery

Legal Events

Date Code Title Description
ENP Entry into the national phase

Ref document number: 202312112

Country of ref document: GB

Kind code of ref document: A

Free format text: PCT FILING DATE = 20221013

WWE Wipo information: entry into national phase

Ref document number: 2312112.2

Country of ref document: GB

121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 22950035

Country of ref document: EP

Kind code of ref document: A1

WWP Wipo information: published in national office

Ref document number: 2312112.2

Country of ref document: GB

WWG Wipo information: grant in national office

Ref document number: 2312112.2

Country of ref document: GB

NENP Non-entry into the national phase

Ref country code: DE

32PN Ep: public notification in the ep bulletin as address of the adressee cannot be established

Free format text: NOTING OF LOSS OF RIGHTS PURSUANT TO RULE 112(1) EPC (EPO FORM 1205A DATED 06/05/2025)

122 Ep: pct application non-entry in european phase

Ref document number: 22950035

Country of ref document: EP

Kind code of ref document: A1