WO2024007474A1 - Thermal data determination method, apparatus and device - Google Patents

Abstract

The present application relates to a thermal data determination method, apparatus and device. The method comprises: determining a functional model for Tikhonov regularization, acquiring known conditions for variables in the functional model, executing two or more rounds of regularization parameter selection operation according to the functional model, so as to obtain a preferred solution for a regularization parameter in the last round; according to the preferred solution for the regularization parameter in the last round, determining a finally selected regularization parameter; and determining, according to the finally selected regularization parameter, a final estimated value of a heat flux density distribution in a region to be solved.

Description

A method, device and equipment for determining thermal data

Cross-references to related applications

This application requests the priority of the Chinese patent application submitted to the China Patent Office on July 4, 2022, with the application number CN202210777855. incorporated in this application.

Technical field

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.

Background technique

In many fields such as biomedicine, communications, energy, industrial manufacturing, agriculture, forestry, fishery, and animal husbandry, it is often necessary to measure or estimate thermal data (such as heat flux density or temperature) in target areas of living or non-living organisms. , to improve technology, protect the target area to maintain it in a reasonable and normal state, or understand the heat conduction rules in the target area.

For example, in the field of biomedicine and clinical medicine, 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.

For example, in the field of preventive medicine, considering the temperature difference between diseased tissues such as human tumors and surrounding normal tissues, it is necessary to obtain heat flow density data of relevant target areas for subsequent determination of the location or boundary of the diseased tissue.

For example, in the field of agricultural planting and breeding, when developing intensive high-density breeding, effective and convenient monitoring of important physiological indicators reflected in heat flow density data can timely evaluate and adjust breeding technology to achieve better breeding benefits.

For example, in the field of bionics, when designing bionic components, by analyzing the heat flow density changes in target areas in key parts of the bionic components, it is helpful to quickly evaluate the heat dissipation or insulation effect in real time.

For example, in the field of communications, 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.

For example, in the field of industrial manufacturing, evaluating the heat flow density in the target area of the heated component can help further optimize the heating strategy.

For example, in the energy field, monitoring the heat flow density in target areas of pipeline fluids can help ensure safety and increase the service life of equipment.

However, in most cases, 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).

The mathematical ill-posedness and high-performance computing strategies to solve the transient heat transfer inverse problem face many challenges. Traditional methods are no longer suitable in terms of computational efficiency and accuracy when facing complex situations such as three-dimensional and transient conditions.

Regularization methods have received relatively more research attention. Mathematical methods such as classical Tikhonov regularization and iterative regularization have been widely used to solve inverse problems in mathematical physics that are common in fields such as science and engineering. For Tikhonov regularization methods, choosing appropriate regularization parameters is crucial to obtain stable and accurate solutions.

However, in practical applications, it is usually difficult to obtain accurate optimal regularization parameters in a short time, which results in low efficiency in accurately estimating the heat flow density distribution in the area to be solved.

Contents of the invention

In a first aspect, 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. Get a final estimate of the heat flux distribution in the solution area. Among them, in each round of regularization parameter selection operation, multiple sampling values of this round are determined according to the set sampling range value and sampling interval of the regularization parameters, and the multiple sampling values and known conditions are input into the functional model, Obtain the heat flow density distribution estimate corresponding to each sampling value, determine the coordinate data of the L curve based on multiple heat flow density distribution estimates, and determine the sampling values corresponding to the multiple coordinate data at the corners of the L curve as the regularity of this round When this 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 preferred solution of the regularization parameters of this round, and reduce the regularization parameters of the next round. sampling interval.

In a second aspect, embodiments of the present application disclose 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. ; and, 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. Among them, 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; and, 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.

In a third aspect, 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. 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.

In a fourth aspect, 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.

In a fifth aspect, 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.

The details of one or more embodiments of the application are set forth in the accompanying drawings and the description below. Other features and advantages of the application will be apparent from the description, drawings, and claims.

Description of the drawings

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;

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;

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.

Detailed ways

In order to make the technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

The thermal data determination method disclosed in this application can be applied in the application environment as shown in Figure 1. Wherein, 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.

In one embodiment, as shown in Figure 2(a) and Figure 2(b), 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.

Using the Tikhonov regularization method to construct functional models can draw on many existing techniques, for example, "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.), "Tikhonov regularization method for the inverse problem of the heat conduction equation" (Computer and Digital Engineering, Issue 307, 2015 Issue 5, author He Junhong), "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.) and many other documents have been recorded, and will not be repeated here.

In step S201, 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. Generally, 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.

In some embodiments, formula (1) can be used as the expression of the functional model.

In formula (1), L(Q _u ) represents the target functional;

can be regarded as the prediction residual term,

It can be regarded as a regularization penalty term, α is the regularization parameter to be determined; Φ(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; Φ _m (x, t) represents the temperature distribution measurement value; t _max represents the final moment in a certain observation period, Λ _I represents the first boundary of the target area, Λ _u represents the second boundary of the target area.

Generally, if 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, and the second boundary can refer to the boundary of the upper surface of the area. At this time, the target area also includes a third boundary, The third boundary is the boundary of the side surface of the region. However, when the upper surface and the lower surface of the region are very close to each other, the above functional model does not need to consider the influence of heat conduction on the side surface. In some other cases, 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. In addition, 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. Of course, in some cases, 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.

In some embodiments, 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.

In some embodiments, 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).

Φ(·,0)＝Φ ₀ (·),in Ω (3)

Among them, Φ represents the temperature distribution function of the target area, ρ 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, Ω represents the three-dimensional computational domain, Φ ₀ (·) represents the initial temperature of a certain space point, Λ _I represents the first boundary of the target area, Λ _U represents the second boundary of the target area, Λ _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.

Those skilled in the art will understand that the aforementioned known conditions can be obtained using a variety of means in the prior art. 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. For example, when the target area is a liquid area in a container, the boundary conditions can be obtained by measuring the boundary lengths of the liquid area with calipers and other instruments; When the target area is human tissue, 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.

Taking the heat conduction equation, that is, formula (2) to formula (6) as an example, the known conditions include ρ, c _P , a, Ω, Φ ₀ (·), Λ _I , Λ _U , Λ _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. Among them, as shown in Figure 2(b), 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. . In some optional implementations, 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.

When selecting regularization parameters through the L-curve method, if you only rely on the operator's experience and use the Hansen regularization toolbox (an application to assist in determining regularization parameters), select a coordinate point at the corner of the L-curve, so that Determine the corresponding regularization parameters. Usually, there is a certain deviation between the selected regularization parameters and the optimal regularization parameters. The difference is that step S203 (including step S2031 to step S2035) 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.

In step S2031, 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. In each round, when the sampling interval is constant, the sampling performed is constant step sampling. When the sampling interval is not constant, the sampling performed is variable step sampling. Those skilled in the art can set the corresponding settings according to actual needs. sampling interval.

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.

In step S2034, 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. In some cases, 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.

In step S2035, 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. In addition, 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.

In some embodiments, as shown in Figure 3, 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).

S ^k+1 ＝C ^k gS ^k , C ^k ∈(0,1) (7)

In step S301, 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. Of course, in step S301, 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.

When performing step S204, 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, α 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.

In some embodiments, 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.

In some embodiments, as shown in Figure 4, 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. During execution, 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.

It should be noted that the deviation mentioned in this article, unless otherwise emphasized, can be understood as the difference in value between the two objects being compared. This difference can be reflected by direct subtraction, and can be calculated by The error can be reflected in other ways, and it can also be reflected in other ways of expressing differences. There is no special restriction here.

In some embodiments, 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).

in,

represents the optimal sampling value of this round, α _m represents a sampling value among other sampling values, and is determined by the sampling range [α _min , α _max ] and the sampling interval ^Sk ,

represents the estimated value of heat flux density distribution corresponding to α _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 α _m . Of course, 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. In some optional implementations, 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 ε represent the preset deviation threshold, then the elements of the optimal solution of the kth round include

as well as

In some embodiments, as shown in Figure 5, 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. In some optional implementations, 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.

The equations involved in the iterative regularization calculation model based on the conjugate gradient method can be found in formula (9) to formula (22).

H ^r (x,t _max )＝0,in Ω (14)

h(x,t,Q _u )=Φ(x,t,Q _u )-Φ _m (x,t) (17)

v ^r (·,0)＝0,in Ω (20)

When running the conjugate gradient method and performing a conjugate search, you can set an initial estimate

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, and Formula (19) to Formula (22) are the solution equations for the sensitivity problem. In formula (9) to formula (22), 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, ξ ^r represents the conjugate coefficient, ε ^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 Φ (x, t, Q _u ) on Λ _I and the temperature distribution measurement value Φ _m (x, t), v ^r represents the sensitivity problem solution. For parameters in formula (9) to formula (22) that have already appeared in formula (1) to formula (8), please refer to the previous description for understanding, and no further explanation will be given here.

Assume that in the current round of regularization parameter selection operation, one of the multiple sampling values is α _m , and α _m is in the sampling range [α _min , α _max ]. The iterative regularization based on the conjugate gradient method is used in the solution. When solving the heat flow density distribution estimate corresponding to α _m using the computational model, the serial number of the current iteration cycle is r, and the serial number of the previous iteration cycle is r-1; then 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 η. At this time, 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.

in,

and

Respectively represent 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.

When formula (23) is satisfied, the corresponding

is regarded as the estimated value of heat flux density distribution of α _m , that is

At this time, the calculation of the iterative regularization calculation model based on the conjugate gradient method for α _m can be stopped. Subsequently, the calculation of the iterative regularization calculation model based on the conjugate gradient method can be performed for the next sampled value.

When formula (23) is not satisfied, the next iteration is entered, and then whether formula (23) is satisfied is judged until the number of iterations reaches the preset maximum number r _max . If the maximum number of times r _max is reached and formula (23) is still not satisfied, the iteration loop will be jumped out. The value of r _max can be 200, 300 or others, which can be set according to actual needs.

It should be noted that in addition to using the aforementioned conjugate gradient method to determine the heat flow density distribution estimate, you can also use methods based on space marching algorithm (Space marching), sequence function method (Function specification), and Bayes method (Bayes). , artificial neural network method (ANN, Artificial Neural Networks), Kalman filter (KF, Kalman filter) method, Levenberg-Marquardt (LM, Levenberg–Marquardt) algorithm, truncated singular value decomposition (SVD, Singular value decomposition) ) method, Tikhonov regularization method and other methods or algorithms to calculate the inverse problem and determine the heat flow density distribution estimate.

In some embodiments, 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. Correspondingly, 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. . Specifically, 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.

It should be noted that 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. In step S605, 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.

In some embodiments, 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.

In some cases, the calculation formulas involved in performing step S701 and step S702 can be understood by referring to formula (1) to formula (6).

In some embodiments, 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.

In some embodiments, 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. Considering that in various heating environments such as manufacturing or heating biological tissue, in order to meet the need to control the temperature distribution on the second boundary of the target area, this embodiment can be implemented to execute thermal data through the processor 101 Determine the method to control the heating component to achieve the purpose of temperature control.

In some embodiments, 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. For example, 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) and 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.

Although 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. Moreover, 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. 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.

Among them, 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.

In some embodiments, 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.

In some embodiments, 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.

In some embodiments, 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.

In some embodiments, 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.

In some embodiments, 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; the initial temperature acquisition sub-module 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.

In some embodiments, 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.

In some embodiments, 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.

In some embodiments, 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.

For specific limitations on the thermal data determination device, please refer to the above limitations on the thermal data determination method, which will not be described again here. Specifically, 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.

In some embodiments, 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. In some 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. When executed by the processor, the computer-readable instructions implement the thermal data determination method in any of the foregoing embodiments.

The structure shown in Figure 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.

This application also discloses a thermal data determination device. 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.

In some 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.

In some embodiments, the initial temperature distribution of the target area can be regarded as the initial temperature distribution of the area to be solved. Specifically, the room temperature can be considered as the initial temperature distribution of the target area. Of course, in other embodiments, 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. When the computer-readable instructions are 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.

Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through computer readable instructions. The aforementioned computer readable instructions can be stored in a non-volatile computer. When the computer-readable instructions are read from the storage medium and executed, they may include the processes of the embodiments of the above methods. Any reference to memory, storage, database or other media used in the embodiments provided in this application may include non-volatile and/or volatile memory. 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. By way of illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous chain Synchlink DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

Those skilled in the art can understand that from the perspective of technical feasibility, thermal data determination devices, computer equipment or thermal data determination equipment can be applied according to the fields in which the thermal data determination method can be applied.

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.

In one embodiment, it can be applied to study the cooling process of mosquitoes when sucking blood. 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.

Specifically, the inventor studied the problem of estimating the heat flow density distribution during the blood-sucking process of mosquitoes. In order to approximate the actual problem, a functional model is established on x∈[0,16]mm (the mosquito’s body length range, that is, the target area). The total observation time is set to 180 seconds, the observation time interval is Δt=2s, and the thermal conductivity is a=0.58W/(m·K). The initial temperature distribution of the target area is set to Φ(g,0)=24°C. The constant applied input heat flow was set to Q _i (x, t) = 0.000386 W/mm ² to reflect the direct contact between the mosquito and the blood-sucking organism. 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.

Applying the steps of the thermal data determination method, in the first round of regularization parameter selection operation, the value range of the regularization parameter is set to [0,0.001]. After more than two rounds of regularization parameter selection operations, the optimal solution for the regularization parameters was finally obtained, namely {α _m |0.000295≤α _m ≤0.000315}, which quickly narrowed the selection range of the regularization parameters and ensured the area to be solved The error in the heat flux distribution estimate is small. On the basis of {α _m |0.000295≤α _m ≤0.000315}, the inventor finally determined the value of the regularization parameter to be 0.000296. Specifically, 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 {α _m |0.000295 ≤ α _m ≤ 0.000315}. 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.

When the regularization parameter is selected to be 0.000296, as shown in Figure 10, 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.

The technical features of the above embodiments can be combined in any way. To simplify the description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, all possible combinations should be used. It is considered to be within the scope of this manual. The above embodiments only express several implementation modes of the present application, and their descriptions are relatively specific and detailed, but should not be construed as limiting the protection scope of the present application. For those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all fall within the protection scope of the present application. Therefore, the scope of protection of this application should be determined by the appended claims.

Claims (20)

1. A thermal data determination method, characterized in that the method includes:

   Determine the Tikhonov regularized functional model, which is used to solve the inverse heat conduction problem in the target area, and output the estimated value of the heat flow density distribution of the area to be solved in the target area;

   Obtain known conditions of variables in the functional model, where the known conditions include boundary conditions, thermal property parameters and temperature distribution measurements of the target area;

   According to the functional model, perform more than two rounds of regularization parameter selection operations to obtain the optimal solution of the final round of regularization parameters;

   Determine the final selected regularization parameters based on the optimal solution of the last round of regularization parameters; and

   According to the finally selected regularization parameter, determine the final estimated value of the heat flow density distribution of the area to be solved;

   Among them, in each round of regularization parameter selection operation, multiple sampling values of this round are determined according to the set sampling range value and sampling interval of the regularization parameter, and the multiple sampling values and the known conditions are input The functional model obtains the heat flow density distribution estimate corresponding to each sampling value, determines the coordinate data of the L curve based on multiple heat flow density distribution estimates, and compares the sampling values corresponding to the multiple coordinate data at the corner of the L curve, Determine it as the optimal solution of the regularization parameters of this round. When this round is not the last round, use the range of the optimal solution of the regularization parameters of this round to determine the sampling range value of the regularization parameters of the next round, and reduce The sampling interval of the regularization parameters for the next round.
2. The method according to claim 1, characterized in that determining the sampling values corresponding to the multiple coordinate data at the corner of the L curve as the optimal solution of the regularization parameters of this round includes:

   According to the coordinate data of the L-curve of this round, the optimal sampling value of this round is determined from the plurality of sampling values for reference, and the optimal sampling value of this round is used as the regularization parameter of this round. elements of the preferred solution;

   Determine the deviation of the estimated heat flow density distribution corresponding to other sampling values in this round from the estimated heat flow density distribution corresponding to the optimal sampling value in this round; and

   When the deviation does not exceed the preset deviation threshold, the corresponding other sampled values are used as elements of the preferred solution of the regularization parameters of this round.
3. The method according to claim 2, characterized in that determining the deviation of the estimated heat flow density distribution corresponding to other sampling values of this round and the estimated heat flow density distribution corresponding to the optimal sampling value of this round respectively includes:

   Determine 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;

   Determine the norm of the heat flow density distribution estimate corresponding to the optimal sampling value of this round as the second norm; and

   The deviation is determined based on the ratio of the first norm and the second norm.
4. The method according to any one of claims 1 to 3, characterized in that when the current round is not the last round, the regularization parameters of the next round are determined based on the range of the optimal solution of the regularization parameters of the current round. Sampling range value, and reducing the sampling interval of the regularization parameters of the next round, including:

   Obtain the preset target coefficient, the value of the target coefficient is greater than 0 and less than 1; and

   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.
5. The method according to any one of claims 1 to 4, characterized in that the plurality of sampled values and the known conditions are input into the functional model to obtain the heat flow density distribution corresponding to each sampled value. Estimates include:

   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; and

   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 sampling value Corresponding heat flow density distribution estimate.
6. The method according to any one of claims 1 to 5, characterized in that the functional model includes a prediction residual term and a regularization penalty term, and 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, and the regularization penalty term includes regularization parameters and the norm of the unknown heat flow density function;

   The obtaining the known conditions of the variables in the functional model includes: obtaining the thermal attribute parameters of the target area; obtaining the boundary conditions of the target area; obtaining the temperature distribution measurement value of the target area; obtaining the The initial temperature distribution of the target area; and, obtaining the heat flow density data of the first boundary of the target area within a preset observation time;

   Inputting the plurality of sampled values and the known conditions into the functional model to obtain an estimate of the heat flow density distribution corresponding to each sampled value includes: converting the heat flow density of the second boundary of the target area Distributed as the heat flow density distribution of the area to be solved, the target is determined based on the thermal property parameters, the boundary conditions, the initial temperature distribution, the heat flow density data and the heat flow density distribution of the second boundary The temperature distribution function of the area; and, using 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, determine the heat flow density distribution estimate corresponding to each sampling value.
7. The method according to claim 6, characterized in that: determining based on the thermal property parameters, the boundary condition, the initial temperature distribution, the heat flow density data and the heat flow density distribution of the second boundary. The temperature distribution function of the target area includes: solving the heat conduction forward problem in parallel according to the thermal property parameters, the boundary conditions, the initial temperature distribution, the heat flow density data and the heat flow density distribution of the second boundary. , using the solution to the forward heat conduction problem as the temperature distribution function of the target area;
8. The method according to claim 6 or 7, further comprising: determining the temperature of the area to be solved at a specified moment based on the final estimate of the heat flow density distribution of the area to be solved and the initial temperature distribution. distributed.
9. A thermal data determination device, characterized in that the device includes:

   A model determination module, used to determine the Tikhonov regularized functional model, the functional model is used to solve the inverse heat conduction problem in the target area, and output the estimated value of the heat flow density distribution of the area to be solved in the target area;

   A known condition acquisition module, used to acquire known conditions of variables in the functional model, where the known conditions include boundary conditions, thermal property parameters and temperature distribution measurements of the target area;

   The preferred solution acquisition module is used to perform more than two rounds of regularization parameter selection operations based on the functional model to obtain the preferred solution of the last round of regularization parameters;

   A regularization parameter determination module, configured to determine the final selected regularization parameter based on the optimal solution of the last round of regularization parameters; and

   An estimation module, configured to determine the final estimated value of the heat flow density distribution of the area to be solved based on the finally selected regularization parameter;

   Wherein, the preferred solution acquisition module includes:

   The sampling value determination submodule is used in each round of regularization parameter selection operation to determine multiple sampling values of this round based on the set sampling range value and sampling interval of the regularization parameter;

   A model running submodule, used to input the plurality of sampled values and the known conditions into the functional model to obtain an estimate of the heat flow density distribution corresponding to each sampled value;

   The L-curve determination submodule is used to determine the coordinate data of the L-curve based on multiple heat flux density distribution estimates;

   The optimal solution determination submodule is used to determine the sampling values corresponding to multiple coordinate data at the corners of the L curve as the optimal solution for the regularization parameters of this round; and

   The sampling parameter adjustment submodule is used to 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 when the current round is not the last round, and reduce the regularization of the next round. Sampling interval for parameterization.
10. The device according to claim 9, characterized in that the preferred solution sub-module includes:

    A reference value determination unit, configured to determine an optimal sampling value for reference from the plurality of sampling values according to the coordinate data of the L curve of this round, and use the optimal sampling value of this round as the The elements of the optimal solution for the regularization parameters of this round;

    The first deviation estimation unit is used to determine the deviation of the estimated heat flow density distribution corresponding to other sampling values in this round from the estimated heat flow density distribution corresponding to the optimal sampling value in this round; and

    The preferred solution determination unit is configured to use corresponding other sample values as elements of the preferred solution for the regularization parameters of this round when the deviation does not exceed the preset deviation threshold.
11. The device according to claim 10, characterized in that the first bias estimation unit includes:

    The first norm determination subunit is used to determine 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;

    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; and

    The deviation determination subunit is used to determine the deviation according to the ratio of the first norm and the second norm.
12. The device according to any one of claims 9 to 11, characterized in that the sampling parameter adjustment sub-module includes:

    A target coefficient acquisition unit, used to obtain a preset target coefficient, the value of the target coefficient being greater than 0 and less than 1; and

    The sampling interval adjustment unit is configured to determine the product of the target coefficient and the sampling interval of the regularization parameter of this round as the sampling interval of the regularization parameter of the next round.
13. The device according to any one of claims 9 to 12, characterized in that the model running sub-module includes:

    An inverse problem calculation unit, used for each sampling value, using an iterative regularization calculation model based on the conjugate gradient method to determine the heat flow density distribution estimate corresponding to multiple iteration cycles; and

    An iteration error calculation unit, used to calculate the heat flow density 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 distribution estimate is used as the heat flow density distribution estimate corresponding to the sampled value.
14. The device according to any one of claims 9 to 13, wherein the functional model includes a prediction residual term and a regularization penalty term, and 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, and the regularization penalty term includes regularization parameters and the norm of the unknown heat flow density function;

    The known condition acquisition module includes:

    The attribute parameter acquisition sub-module is used to obtain the thermal attribute parameters of the target area;

    The boundary data acquisition submodule is used to obtain the boundary conditions of the target area;

    A measurement value acquisition submodule is used to obtain the temperature distribution measurement value of the target area;

    An initial temperature acquisition submodule is used to acquire the initial temperature distribution of the target area; and

    The heat flow density data acquisition submodule is used to acquire the heat flow density data of the first boundary of the target area within the preset observation time;

    The model running sub-module includes:

    A temperature distribution function solving unit, configured 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, the boundary conditions, the initial temperature distribution, The heat flow density data and the heat flow density distribution of the second boundary determine a temperature distribution function of the target area; and

    A functional model solving unit is used to 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 sampled value.
15. The device according to claim 14, characterized in that the temperature distribution function solving unit includes:

    Parallel solving subunit, used to solve the heat conduction forward problem in parallel according to the thermal property parameters, the boundary condition, the initial temperature distribution, the heat flow density data and the heat flow density distribution of the second boundary, and convert the heat conduction into a normal problem. The solution to the problem is as a function of the temperature distribution in the target area.
16. The device according to claim 14 or 15, further comprising:

    A temperature distribution estimation module, configured to determine the temperature distribution of the area to be solved at a specified moment based on the final estimate of the heat flow density distribution of the area to be solved and the initial temperature distribution.
17. A computer device, characterized in that it includes a memory and one or more processors. Computer-readable instructions are stored in the memory. When the computer-readable instructions are executed by the one or more processors, the computer-readable instructions cause the The one or more processors perform the steps of the method according to any one of claims 1 to 8.
18. A thermal data determination device, characterized by 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 configured to perform the steps of the method according to any one of claims 1 to 8.
19. The device according to claim 18, wherein the device further includes a heating component for heating the target area;

    The processor is also used to:

    Update the temperature distribution of the region to be solved at the latest moment according to the final estimate of the heat flow density distribution of the region to be solved and the preset initial temperature distribution of the region to be solved; and

    The heat flux density applied by the heating component to the target area is adjusted according to the temperature distribution of the area to be solved at the latest moment.
20. One or more non-volatile computer-readable storage media storing computer-readable instructions, characterized in that, when executed by one or more processors, the computer-readable instructions cause the one or more processors to Carry out the steps of the method according to any one of claims 1 to 8.

Images