Intelligent design method of floor heating insulation module based on swarm optimization algorithm

Abstract

The present invention relates to the technical field of computer-aided design or optimization algorithms, and further to an intelligent design method for floor heating insulation modules based on a group optimization algorithm. The method comprises: step 1: creating a multi-scale heat conduction model based on fractal theory; step 2: parameterizing the porous medium structure using the level set method; step 3: performing homogenization according to the multi-scale expansion results of temperature and the multi-scale expansion results of heat conductivity coefficient; step 4: defining a topological optimization problem according to the obtained homogenization results and the effective heat conductivity coefficient, and extracting the level set function corresponding to the parameterization result at this time as the optimized porous structure. The present invention can improve the heat conduction efficiency or temperature uniformity of the floor heating system.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer-aided design or optimization algorithm, and specifically relates to an intelligent design method for floor heating insulation modules based on a group optimization algorithm. Background Art

[0002] As an important component of modern building heating systems, the design and performance of floor heating insulation modules directly affect indoor thermal comfort and energy efficiency. With the global energy shortage and the increasing awareness of environmental protection, how to improve the energy efficiency of floor heating systems and reduce energy consumption has become an important research direction in heating technology. In the existing technology, porous media structures are widely used in the design of floor heating insulation modules due to their good thermal conductivity and heat transfer efficiency. However, there are some problems in the design of traditional porous media floor heating systems that need to be solved, which limits their energy efficiency performance and user experience in practical applications.

[0003] In the prior art, the thermal conductivity of porous media is usually improved by selecting materials with higher thermal conductivity. For example, traditional floor heating insulation modules mostly use high thermal conductivity materials such as graphite and aluminum alloy, which can improve the thermal conductivity efficiency to a certain extent and ensure that the surface temperature of the floor is evenly distributed. However, this method has obvious limitations. First, the thermal conductivity only depends on the physical properties of the material itself, while ignoring the influence of the microstructure and multi-scale characteristics of the material on the thermal conductivity efficiency. In practical applications, the internal structure of porous media is complex and diverse, and different porosity and pore size distributions will significantly affect the conduction path and speed of heat flow, making the heat energy unevenly distributed inside the material, resulting in local overheating or overcooling. This uneven heat distribution not only reduces the energy efficiency of the overall system, but also may cause discomfort to users and affect the comfort of the indoor environment. Secondly, most of the existing optimization methods are based on single-scale models, which usually assume that the thermal conductivity of the material is uniform, ignoring the thermal conductivity characteristics at different scales and their influence on macroscopic performance. In reality, the heat conduction process inside porous media involves multiple levels, including microscale (e.g., heat flow inside pores), mesoscale (e.g., heat exchange between pores and solid phases), and macroscale (e.g., heat conduction of the entire material). This multi-scale characteristic makes the heat conduction path more complex and diverse. Traditional single-scale models are difficult to accurately describe these complex physical processes, and thus cannot fully consider the impact of material structure on heat conduction in optimization design. Summary of the invention

[0004] The main purpose of the present invention is to provide an intelligent design method for floor heating insulation modules based on a group optimization algorithm, thereby improving the heat conduction efficiency or temperature uniformity of the floor heating system.

[0005] In order to solve the above problems, the technical solution of the present invention is achieved as follows:

[0006] An intelligent design method for floor heating insulation modules based on a group optimization algorithm, the method comprising: step 1: creating a multi-scale heat conduction model based on fractal theory, performing multi-scale expansion of the temperature field and the multi-scale heat conduction coefficient in the multi-scale heat conduction model, and obtaining the multi-scale expansion results of the temperature and the multi-scale expansion results of the heat conduction coefficient; step 2: parameterizing the porous medium structure using the level set method to obtain the parameterization results; step 3: performing homogenization processing according to the multi-scale expansion results of the temperature and the multi-scale expansion results of the heat conduction coefficient, integrating the micro-scale information into the macro-scale equation, obtaining an effective heat conduction equation of the macro-scale as the homogenization result, and calculating the effective heat conduction coefficient based on the homogenization result; step 4: defining a topology optimization problem according to the obtained homogenization results and the effective heat conduction coefficient, wherein the optimization goal of the topology optimization problem is to maximize the heat conduction efficiency or maximize the uniformity of the temperature distribution, and defining the objective function of the topology optimization problem; substituting the parameterization results into the topology optimization problem for solving, so that the effective heat conduction coefficient is maximized, and extracting the level set function corresponding to the parameterization result at this time as the optimized porous structure.

[0007] Furthermore, the multi-scale heat conduction model based on fractal theory created in step 1 is expressed using the following formula:

[0008] ;

[0009] in, represents the temperature field; Indicates time; It is a three-dimensional space vector, representing a position coordinate in three-dimensional space; Indicates the material density; represents specific heat capacity; represents the multi-scale heat transfer coefficient; represents the heat source term; represents the latent heat of phase change; represents the phase change function; represents the scale parameter; represents the fractal dimension; represents the Laplace operator.

[0010] Furthermore, the multi-scale heat transfer coefficient is calculated using the following formula:

[0011] ;

[0012] in, Indicates the reference scale, which is the set value; Indicates the base thermal conductivity, which is the set value; Represents the temperature gradient sensitivity coefficient, which is the set value; phase change function Use the smoothed Heaviside function to describe the representation:

[0013] ;

[0014] in, represents the phase transition temperature; Indicates the phase change temperature range.

[0015] Furthermore, in step 1, the temperature field and multi-scale heat conduction coefficient in the multi-scale heat conduction model are multi-scale expanded to obtain the temperature multi-scale expansion result and the multi-scale expansion results of the heat conductivity coefficient The method is:

[0016] ;

[0017] ;

[0018] in, It is a fast variable; is the multi-scale thermal conductivity order expansion term; It is the temperature field order expansion term; is a natural number ranging from 0 to 2; Indicates that all The set of terms whose order of variation is greater than or equal to 3.

[0019] Furthermore, the level set function used in step 2 is expressed using the following formula:

[0020] ;

[0021] in, is the level set function; represents a solid area; represents the fluid region; Represents the interface; using the level set function, define a smooth Heaviside function to represent the material distribution as a parameterized result:

[0022] ;

[0023] in, To define the smoothing parameter, it is a positive number.

[0024] Furthermore, in step 3, the macro-scale effective heat conduction equation obtained by homogenizing the temperature multi-scale expansion results and the heat conductivity coefficient multi-scale expansion results is expressed using the following formula:

[0025] ;

[0026] in, represents the average temperature field at the macroscopic scale and is defined as:

[0027] ,

[0028] in is a representative volume unit; is the effective heat transfer coefficient, calculated by the following formula:

[0029] ;

[0030] in The multi-scale expansion results Order item, are shape functions defined at different scales; Represents the volume of the fluid region in the microstructure. During the homogenization process, Represents the volume of the fluid region inside the porous medium where heat conduction occurs.

[0031] Furthermore, based on the homogenization results, the calculated effective heat transfer coefficient is expressed using the following formula:

[0032] ;

[0033] in, is the effective heat conductivity coefficient at the macroscopic scale, which describes the equivalent heat conduction capacity of the porous medium at the macroscopic scale; : The absolute value of the gradient of the temperature field, indicating the spatial rate of temperature change; is the volume differential element, which means the integral operation is in the volume On.

[0034] Furthermore, when the optimization goal is to maximize the heat transfer efficiency, the objective function of the topology optimization problem defined in step 4 is Use the following formula to express it:

[0035] ;

[0036] in, Indicates the first weight coefficient that is set.

[0037] Furthermore, when the optimization goal is to maximize the heat transfer efficiency, the objective function of the topology optimization problem defined in step 4 is Use the following formula to express it:

[0038] ;

[0039] in, is the average temperature; is the maximum temperature; is the minimum temperature; is the second weight coefficient set.

[0040] The intelligent design method of floor heating insulation module based on group optimization algorithm of the present invention has the following beneficial effects:

[0041] The present invention significantly improves the thermal conduction efficiency of the floor heating insulation module. By introducing fractal theory and multi-scale expansion methods, the present invention can accurately describe the thermal conduction behavior inside the porous medium and optimize it to a state of maximum thermal conduction efficiency. In porous media, the transfer of heat not only depends on the thermal conductivity of the material itself, but is also significantly affected by the complex geometric structure inside the material. The multi-scale expansion method of the present invention can capture the heat flow characteristics at the microscopic scale, especially the heat conduction path inside the pores and the heat exchange process at the microscopic scale. Through precise modeling and optimized design of these multi-scale characteristics, the present invention can more effectively guide the heat flow to transfer along the optimal path, thereby greatly improving the overall thermal conduction efficiency of the floor heating system.

[0042] Secondly, the present invention achieves a high degree of uniformity in temperature distribution. The uniformity of temperature distribution is an important indicator for measuring the performance of floor heating systems, which directly affects the comfort of the indoor environment and the energy efficiency. In the optimization design, the present invention not only takes into account the maximization of heat conduction efficiency, but also effectively reduces the local fluctuations and non-uniformities in the temperature field by introducing high-order derivative terms and normalization of temperature gradients. In particular, through the application of topological optimization methods and level set functions, the present invention can finely adjust the microstructure and interface shape of the material to ensure that the temperature field achieves optimal uniformity throughout the floor heating module. This highly uniform temperature distribution not only improves the energy efficiency of the floor heating system, but also significantly improves the indoor thermal comfort and reduces the discomfort caused by uneven cold and heat.

[0043] Again, the present invention effectively solves the problem of optimizing the interface conditions of porous media. The interface shape and position of the solid and fluid regions inside the porous medium have an important influence on the heat conduction path and efficiency. In traditional design methods, the processing of interface conditions is often relatively simple, and it is difficult to flexibly adapt to complex geometric changes and topological structures. However, by introducing the level set method, the present invention can flexibly adjust the shape and position of the interface to achieve the optimal heat conduction path in complex porous structures. The use of the level set function makes the representation of the interface more flexible and continuous, avoiding instability in numerical calculations. At the same time, the smoothed Heaviside function ensures the smoothness and differentiability of the interface transition, which helps to reasonably adjust the interface shape during the optimization process. The application of this method allows the present invention to more accurately control the material distribution and interface conditions in the process of optimizing the floor heating module structure, thereby improving the overall thermal conductivity performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A schematic diagram of a method flow of an intelligent design method for floor heating insulation modules based on a group optimization algorithm provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0046] Example 1: Reference Figure 1, an intelligent design method for floor heating insulation module based on group optimization algorithm, the method comprising: step 1: creating a multi-scale heat conduction model based on fractal theory, performing multi-scale expansion of the temperature field and the multi-scale heat conduction coefficient in the multi-scale heat conduction model, and obtaining the multi-scale expansion results of temperature and the multi-scale expansion results of heat conduction coefficient; step 2: parameterizing the porous medium structure using the level set method to obtain the parameterization results; step 3: performing homogenization processing according to the multi-scale expansion results of temperature and the multi-scale expansion results of heat conduction coefficient, integrating the micro-scale information into the macro-scale equation, obtaining a macro-scale effective heat conduction equation as the homogenization result, and calculating the effective heat conduction coefficient based on the homogenization result; step 4: defining a topology optimization problem according to the obtained homogenization results and the effective heat conduction coefficient, the optimization goal of the topology optimization problem is to maximize the heat conduction efficiency or maximize the uniformity of temperature distribution, and defining the objective function of the topology optimization problem; substituting the parameterization results into the topology optimization problem for solving, so that the effective heat conduction coefficient is maximized, and extracting the level set function corresponding to the parameterization result at this time as the optimized porous structure.

[0047] Specifically, the core idea of ​​multi-scale heat conduction is to consider the complex structure and multi-scale effects inside the material. Porous media usually have complex geometric forms, which often show different physical properties at different scales. Therefore, the traditional single-scale model cannot accurately describe these characteristics, thereby limiting the effect of design and optimization. In order to solve this problem, the present invention introduces fractal theory to construct a multi-scale heat conduction model. Fractal theory provides a mathematical basis for multi-scale models by describing the self-similarity and irregularity of porous media. In this model, the temperature field and thermal conductivity coefficient are respectively multi-scale expanded, so that physical phenomena at different scales can be accurately captured and described. This multi-scale expansion method is actually a process of decomposing a complex problem into multiple relatively simple sub-problems. Each sub-problem corresponds to a specific scale, so that the solution of the entire problem becomes more efficient and accurate. Mathematically, the multi-scale expansion of the temperature field and thermal conductivity coefficient can be expressed by a series of expansions. Although these formulas are not listed in detail in this explanation, it can be understood that they contribute corresponding physical quantities at each different scale, so that the model can comprehensively reflect the influence of microscopic and mesoscopic scales at the macroscopic scale. Secondly, parameterization of porous media is one of the key steps to achieve optimal design. The structure of porous media is complex and irregular, and traditional geometric parameterization methods are difficult to accurately describe this complexity. Therefore, the present invention adopts the level set method to perform parametric design of porous media. The core of the level set method is to use an implicit function to represent the position and shape of the interface. This method can flexibly and accurately describe the evolution of the interface. In specific applications, the level set function is used to distinguish between the areas of pores and solid materials. By adjusting the value of the function, the geometric morphology of the porous media structure can be controlled. Since the level set method has high flexibility and can adapt to changes in complex structures, it is very suitable for geometric parameterization in optimal design. By parameterizing the porous media structure, the present invention can achieve smooth changes in structural morphology during the topological optimization solution process, thereby avoiding the geometric mutation problem that may occur in traditional methods.

[0048] After completing the construction of the multi-scale heat conduction model and the parameterization of the porous medium, the system needs to be homogenized next. The purpose of the homogenization process is to integrate the information of the microscale into the macroscale model, so as to obtain an effective macroscale heat conduction equation. The homogenization process can be understood as a process of information integration, that is, by normalizing and comprehensively processing the multi-scale expansion results of the temperature field and the heat conductivity coefficient, an effective heat conductivity coefficient that can reflect the microscopic characteristics on the macroscale is obtained. This effective heat conductivity coefficient not only takes into account the influence of the microstructure, but also integrates the heat conduction behavior at various scales, so that the macro model can accurately describe the overall heat conduction performance of the floor heating insulation module. In this process, the homogenization process simplifies the complexity of the microscale into an effective parameter on the macroscale through a series of mathematical operations. This parameter is then used to solve the macroscopic heat conduction equation, thereby laying the foundation for the subsequent optimization design. Finally, step 4 is the core of the entire system and the key link in realizing the optimization of the porous medium structure. In the present invention, the goal of the optimization design is to maximize the heat conduction efficiency of the floor heating insulation module or to optimize the uniformity of the temperature distribution. To this end, the system first needs to define a topology optimization problem. The optimization goal can be expressed as an objective function, which is usually related to the distribution of the temperature field and its gradient. After setting the optimization goal, the system substitutes the parameterization results of the porous medium into the topology optimization problem for solution. The solution process of topology optimization is actually an iterative process. In each iteration, the system will calculate the corresponding thermal conductivity performance based on the current parameterization results, and adjust the structural parameters accordingly, so that the value of the objective function gradually approaches the optimal solution. In this process, the system will also use numerical solution techniques such as the finite element method to discretize and solve the heat conduction equation, so as to obtain the temperature distribution and thermal conductivity coefficient under the current structure. After multiple iterations, the system will eventually obtain an optimized porous medium structure, which has the best thermal conductivity or temperature distribution uniformity on a macro scale.

[0049] Example 2: The multi-scale heat conduction model based on fractal theory created in step 1 is expressed using the following formula:

[0050] ;

[0051] in, represents the temperature field; Indicates time; It is a three-dimensional space vector, representing a position coordinate in three-dimensional space; Indicates the material density; represents specific heat capacity; represents the multi-scale heat transfer coefficient; represents the heat source term; represents the latent heat of phase change; represents the phase change function; represents the scale parameter; represents the fractal dimension; represents the Laplace operator.

[0052] Specifically, the core part of the formula is to describe the temperature field Over time The change of is the core of the heat conduction equation. First of all, the basic principle of the heat conduction process is based on the law of conservation of energy, that is, energy can neither be created nor destroyed, but can only be transferred or transformed within the system. Represents the time rate of change of the temperature field, which involves the density of the material and specific heat capacity , which together determine the heat capacity of the material. The significance of heat capacity is that it reflects the ability of the material to change temperature when absorbing or releasing a certain amount of heat. For porous media, the distribution and change of heat capacity directly affects the overall thermal performance of the floor heating system. The first item on the right Describes the conduction diffusion of heat in porous media. Here, the thermal conductivity is a key factor that depends not only on the spatial position , but also depends on the scale parameter and fractal dimension . Fractal dimension Used to describe the geometric complexity of porous media, especially those with self-similar structures. This complexity is difficult to describe in the traditional Euclidean geometry framework, but fractal theory provides an effective tool that can be used to more accurately describe the heat conduction characteristics inside the material. This reflects the heat conduction characteristics of different scales in the material, which enables the model to capture the heat conduction behavior at different scales from microscopic to macroscopic, thus providing a basis for optimizing the design of porous media. In addition, the formula also includes the heat source term , which is a representation of external heat, which may come from electric heating elements or other forms of internal heating sources. The introduction of heat source terms enables the model to simulate the influence of external or internal heating sources on the temperature field in reality. This is especially important for the design of floor heating insulation modules, because the module needs to take into account the influence of multiple heat sources and optimize their distribution to make the distribution of the temperature field more uniform and effective. The last term of the formula Describes the thermal effect during phase change, which is a significant nonlinear effect, especially in floor heating systems where phase changes such as freezing and melting of water may be involved. It represents the amount of heat absorbed or released per unit mass when a material undergoes a phase change. This is a key physical quantity. describes the degree of phase change, which is usually a function of temperature, indicating that the material is in different phases at different temperatures. The phase change process plays a significant role in the heat conduction of porous media, because the phase change not only involves a large amount of latent heat exchange, but also significantly changes the physical properties of the material, such as thermal conductivity and density. Therefore, the heat conduction model that takes into account the phase change effect can more accurately predict and describe the thermal behavior of porous media under different working conditions.

[0053] Example 3: The multi-scale thermal conductivity coefficient is calculated using the following formula:

[0054] ;

[0055] in, Indicates the reference scale, which is the set value; Indicates the base thermal conductivity, which is the set value; Represents the temperature gradient sensitivity coefficient, which is the set value; phase change function Use the smoothed Heaviside function to describe the representation:

[0056] ;

[0057] in, represents the phase transition temperature; Indicates the phase change temperature range.

[0058] Specifically, the multi-scale thermal conductivity formula described is the key to the entire floor heating insulation module porous media optimization design system. It reflects the thermal conduction behavior under the influence of material microstructure characteristics and temperature gradient. This formula not only takes into account the complex geometric morphology of porous media, but also accurately describes the changes in thermal conductivity at different scales through fractal theory and temperature sensitivity factors. In the formula, the multi-scale thermal conductivity The core idea of ​​the fractal theory is to deal with the complex structure of porous media. In the process of heat conduction, the microstructure of the material directly affects how heat is transmitted in the medium. It is used to characterize the complex geometric characteristics of porous media, which describes the space filling capacity of the medium at different scales. In the traditional Euclidean geometry framework, complex porous structures are often difficult to describe with simple geometric parameters, and fractal dimension provides an effective quantitative tool for this complexity. By introducing fractal dimension, the formula can reflect the heat transfer characteristics of porous media at different scales, making It shows different values ​​at different scales. This means that as the scale parameter The thermal conductivity will change accordingly with the change of , thus more realistically simulating the heat transfer behavior of porous media at different scales. In addition, the exponential term in the formula Introduced sensitivity to temperature gradient. During heat conduction, the temperature gradient It directly affects the direction and speed of heat transfer. This exponential term expresses how the thermal conductivity coefficient adjusts with changes in temperature gradient. Specifically, when the temperature gradient is large, the value of this term will be significantly reduced, which means that under strong temperature gradients, the thermal conductivity efficiency of the material will decrease. This temperature sensitivity reflects the thermal response characteristics of the material when facing drastic temperature changes, especially in complex porous structures, this effect is more significant. By adjusting the temperature gradient sensitivity coefficient , it is possible to control the material's response speed to temperature changes, thereby optimizing the material's thermal conductivity and making it more suitable for specific application scenarios. and the base thermal conductivity Together they provide a standardized framework for formulas. As a reference scale, it provides a scale benchmark for normalizing multi-scale parameters This normalization process enables the formula to uniformly handle heat conduction behaviors at different scales, avoiding the computational complexity caused by scale changes. At the same time, the benchmark heat conduction coefficient As the thermal conductivity of the material under a certain reference state, it provides a benchmark for the entire model, so that the adjustment of other parameters is performed relative to this benchmark, so that the thermal conductivity performance of different materials and structures can be compared and optimized in the same framework. In addition, in this embodiment, the phase change function The introduction of further enhances the applicability of the model. In porous media, temperature changes not only affect the thermal conductivity of the material, but may also induce phase change, thereby significantly changing the physical properties of the material. In order to accurately describe this phase change effect, the formula uses a smoothed Heaviside function to characterize the phase change process. This function is based on the temperature and phase transition temperature The relationship between the phase transition temperature and the phase change temperature is described as the smooth transition of the material from one phase to another during the phase change process. , the smoothness of the phase change can be controlled to better simulate the actual phase change process. This treatment enables the model to not only accurately predict the change of thermal conductivity at different temperatures, but also capture the sudden change of thermal conductivity caused by phase change.

[0059] Example 4: In step 1, the temperature field and the multi-scale heat conduction coefficient in the multi-scale heat conduction model are multi-scale expanded to obtain the temperature multi-scale expansion result and the multi-scale expansion results of the heat conductivity coefficient The method is:

[0060] ;

[0061] ;

[0062] in, It is a fast variable; is the multi-scale thermal conductivity order expansion term; It is the temperature field order expansion term; is a natural number ranging from 0 to 2; Indicates that all The set of terms whose order of variation is greater than or equal to 3.

[0063] Specifically, the core idea of ​​the multi-scale expansion of temperature field and thermal conductivity is to use the scale parameter The power series expansion of can decompose the originally complex multi-scale heat conduction problem into several relatively simple sub-problems. Specifically, in porous media, the temperature field and thermal conductivity The distribution of is not uniform and linear, but is significantly affected by the microstructure of the material. This influence often exhibits different characteristics at different scales. For example, the microstructure may cause local temperature gradient changes at the micrometer or even nanometer scale, while at the macroscale it manifests as a change in the overall thermal conductivity. Therefore, by expanding these physical quantities into The number of levels can be used to examine the heat conduction characteristics at each scale. In the multi-scale expansion of the temperature field, is represented as In the power series form, each expansion term is , and Represent the temperature distribution characteristics at different scales. Here, is a so-called fast variable, which is used to describe rapid changes on a relatively small scale. The introduction of this fast variable enables the change of the temperature field to be captured more accurately at the microscopic scale. In particular, the zero-order expansion term Usually represents the average temperature distribution on a macroscopic scale, while higher-order terms such as and The subtle temperature fluctuations caused by the microstructure and the more complex nonlinear effects are considered separately. The expansion of also follows this principle, and its expansion terms of each order are as follows and They reflect the changes in thermal conductivity at different scales. It plays a key role here, as it relates the structural characteristics of porous media to thermal conduction behavior by describing the geometric complexity of the material. This is because in porous media, the thermal conductivity coefficient depends not only on the physical properties of the material, but is also strongly affected by its geometric morphology, and this effect is particularly evident at different scales. The multi-scale expansion of can concretize this complex dependency, so that in the heat conduction analysis, the interaction between different scales can be described more accurately. Another important role of multi-scale expansion is that it provides a systematic framework for subsequent numerical calculations. Since the expansion contains terms of different orders, each order can be solved independently and gradually superimposed to finally obtain an approximate solution for the entire system. This processing method not only improves the efficiency of the calculation, but also can gradually approach the actual physical situation, thereby providing a more accurate basis for the design and optimization of floor heating insulation modules. Especially in the heat conduction optimization design of porous media, this method can help designers understand and predict the thermal response behavior of different materials and structures under various conditions, so as to carry out targeted optimization. In addition, the higher-order terms in the expansion, such as and , although their contribution is small in most cases, they are crucial to understanding the subtle heat conduction characteristics in porous media. These higher-order terms reflect more complex physical processes, such as nonlinear thermal effects and multi-scale coupling. These effects may significantly affect the overall thermal performance of the material under some extreme conditions. Therefore, ignoring these terms in the design of floor heating systems may lead to underestimation or instability of performance. By taking these higher-order terms into account, the system can provide more accurate design parameters to ensure that the floor heating insulation module can maintain efficient and stable thermal conductivity under different environmental conditions.

[0064] Example 5: The level set function used in step 2 is expressed using the following formula:

[0065] ;

[0066] in, is the level set function; represents a solid area; represents the fluid region; Represents the interface; using the level set function, define a smooth Heaviside function to represent the material distribution as a parameterized result:

[0067] ;

[0068] in, To define the smoothing parameter, it is a positive number.

[0069] Specifically, the core of the level set method is to use an implicit function To indicate the shape and position of the interface. is defined as a level set function that can distinguish different regions: , indicating that the position is in the solid area ;when , indicating that the position is at the interface between the solid and the fluid ; and when , it indicates that the position is in the fluid region . The advantage of this method is that it can describe complex interface shapes with a simple scalar function without explicitly tracking the position and shape changes of the interface. This is particularly important for the optimal design of floor heating insulation modules, because the interface morphology inside the porous medium has a direct impact on the overall thermal conductivity performance. Through the level set method, these interfaces can be easily represented and adjusted to meet different design requirements and optimization goals. In order to handle the material distribution near the interface in the numerical calculation, Example 5 introduces a smoothed Heaviside function , which is used to represent the distribution of materials between the solid and fluid regions and to achieve a smooth transition near the interface. The smoothed Heaviside function is a three-segment function: hour, , indicating that the region is completely occupied by solid material; when hour, This part is defined according to a smooth trigonometric function expression, which describes the transition area between solid and fluid. This smooth transition is achieved by smoothing the originally steep Heaviside function, avoiding numerical instability or oscillation caused by sudden changes in material properties at the interface in numerical simulation. This smoothing process not only helps to improve the stability and accuracy of numerical calculations, but also can more accurately describe the physical behavior of materials at the interface, which is of great significance, especially for the complex interaction between solids and fluids in porous media.

[0070] In the optimization design of porous media for floor heating insulation modules, the distribution of materials and the shape of interfaces directly affect the path and efficiency of heat conduction. The thermal conductivity of the solid region is usually much higher than that of the fluid region. Therefore, heat is mainly conducted through the solid part, while the fluid part may cause heat loss or slow conduction. By using the level set function to accurately control the distribution of solid and fluid regions, and combining the smoothed Heaviside function to achieve a smooth transition of material properties at the interface, the present invention can optimize the structure of the porous medium so that it can minimize heat loss and maintain uniformity of temperature distribution while maintaining efficient thermal conductivity. In addition, the smoothing parameter The introduction of provides greater freedom for optimized design. As a positive number, it defines the range of smooth transition, and its size directly affects the smoothness of the Heaviside function. , the smoothness of the transition between the solid and fluid regions can be controlled. This is particularly critical in the design of floor heating insulation modules, because the thermal conductivity of the module depends not only on the thermal conductivity of the material itself, but also on the microstructure of the material. By adjusting the smoothing parameters, the material distribution near the interface can be flexibly controlled, thereby optimizing the thermal conductivity characteristics of the entire system.

[0071] Compared with the traditional explicit interface tracking method, the advantage of the level set method is that it can naturally handle the topological changes of the interface. Since the pore structure in porous media can be very complex, traditional explicit methods often require complex meshing and tedious calculations when tracking and describing these interfaces. The level set method uses an implicit function It is possible to flexibly represent any complex interface, and when the interface undergoes topological changes (such as splitting or merging), the stability and accuracy of the numerical calculation can still be maintained. This is particularly important for the optimal design of floor heating insulation modules, because the optimization process of the pore structure is essentially a process of constantly adjusting and optimizing the interface, and changes in the interface are inevitable. Through the level set method, the present invention can perform these optimization calculations more efficiently and stably, thereby significantly improving the efficiency and effect of the optimization process.

[0072] Example 6: In step 3, the macroscopic effective heat conduction equation obtained by homogenizing the temperature multi-scale expansion results and the heat conductivity coefficient multi-scale expansion results is expressed by the following formula:

[0073] ;

[0074] in, represents the average temperature field at the macroscopic scale and is defined as:

[0075] ,

[0076] in is a representative volume unit; is the effective heat transfer coefficient, calculated by the following formula:

[0077] ;

[0078] in The multi-scale expansion results Order item, are shape functions defined at different scales; Represents the volume of the fluid region in the microstructure. During the homogenization process, Represents the volume of the fluid region inside the porous medium where heat conduction occurs.

[0079] Specifically, in porous media, the temperature field Due to the multi-scale structure inside the material, it exhibits a complex spatial distribution. At the microscopic scale, the pore structure and the distribution of solid materials may cause significant temperature fluctuations in local areas. This fluctuation is not only related to the physical properties of the material, but also closely related to the thermal conductivity of the fluid area and the solid area. In order to simplify this complexity at the macroscopic scale, the present invention adopts a homogenization method to convert the temperature field into a macroscopic average temperature field. This average temperature field is defined as a representative volume unit The temperature integral average within the porous medium is obtained by spatially averaging the temperature distribution at the microscopic scale to obtain a temperature field that is smoother and easier to handle at the macroscopic scale. This homogenization process not only simplifies the description of the temperature field, but also lays the foundation for subsequent heat conduction analysis. In porous media, the complexity of the microstructure makes it very difficult to directly solve the complete heat conduction problem. Therefore, by homogenizing the temperature field, a simplified macroscopic model is obtained, which can more effectively describe the overall heat conduction behavior. And this macroscopic average temperature field , becomes one of the main variables of heat conduction analysis in the present invention, which can accurately reflect the temperature distribution characteristics of the whole material, thus providing a reliable basis for the optimal design of floor heating insulation modules. Next, the homogenization process also involves the heat conduction coefficient Due to the complex structure of porous media, the thermal conductivity coefficient will show significant heterogeneity at the microscopic scale. The thermal conductivity between materials and fluids in different regions is different, so it is unreasonable to use a unified thermal conductivity coefficient directly at the macroscopic scale. In order to solve this problem, the present invention uses multi-scale expansion to express the thermal conductivity coefficient as a series of scale-dependent parameters. , where each order term All reflect the heat conduction characteristics at the corresponding scale. This expansion method can capture the physical properties at different scales and integrate them into a unified macroscopic model.

[0080] The final effective heat transfer coefficient on a macro scale By combining these expansions with the shape functions in the microstructure It is obtained by integration. This process actually summarizes the detailed information of the microstructure and converts it into an equivalent parameter on the macro scale through integration. This equivalent thermal conductivity coefficient not only takes into account the complex heat conduction path inside the porous medium, but also integrates the characteristics at different scales into a unified model through multi-scale expansion. Through this homogenization process, an effective heat conduction equation is obtained that can accurately describe the thermal conduction behavior of the material on a macro scale. The final form of the effective heat conduction equation is a partial differential equation on a macro scale, which describes the evolution of the temperature field on a macro scale and the transfer of heat in the material. The left-hand side of the equation Describes the time variation of the temperature field, that is, the storage and release of energy, which in part reflects the heat capacity characteristics of the material. The first term on the right describes the diffusion of heat, which is the transfer of heat from high temperature area to low temperature area, and this diffusion process is affected by the effective thermal conductivity The final heat source term It represents the influence of the heat source inside the material on the temperature field, which may come from external heating or internal physical and chemical reactions. The significance of this effective heat conduction equation is that it provides a simplified and accurate model for engineering design and practical applications. In the actual design of floor heating insulation modules, due to the complexity of porous media, it is often unrealistic to directly use micro-scale models for simulation and optimization. Through homogenization treatment, the present invention converts the complex behavior of the micro-scale into effective parameters on the macro-scale, so that calculation and optimization can be performed more conveniently during the design process. At the same time, this processing method also retains the key information of the microstructure, so that the final macro model can still accurately reflect the true thermal conductivity performance of the material, thereby providing higher energy efficiency and performance stability in the design of floor heating insulation modules.

[0081] Example 7: Based on the homogenization results, the calculated effective heat transfer coefficient is expressed using the following formula:

[0082] ;

[0083] in, is the effective heat conductivity coefficient at the macroscopic scale, which describes the equivalent heat conduction capacity of the porous medium at the macroscopic scale; : The absolute value of the gradient of the temperature field, indicating the spatial rate of temperature change; is the volume differential element, which means the integral operation is in the volume On.

[0084] Specifically, the effective thermal conductivity The calculation formula takes into account the thermal conductivity of the porous medium through the integration operation. The formula not only simply averages the microscopic thermal conductivity, but also takes into account the non-uniformity caused by the temperature gradient. This is particularly important because in porous media, changes in temperature gradients often lead to changes in the heat flow path, which in turn affects the overall thermal conductivity. Introduced into the formula and squared, the formula captures the spatial rate of temperature change and its effect on thermal conductivity. The square of the temperature gradient is multiplied by a small parameter This treatment reflects the modification effect of the microstructure on the macroscopic heat conduction behavior. Usually represents the ratio between microscopic scale and macroscopic scale, The term reflects the weight of the influence of the microstructure in the porous medium as it changes with scale. This treatment method can better describe the nonlinear heat conduction phenomenon in actual materials, thereby improving the accuracy of the model. In the calculation process of the thermal conductivity coefficient, the integral operation is performed on the volume This means that the formula takes into account the effect of all microstructures in the fluid region on heat conduction. Usually represents the fluid area in the porous medium, which has a significant impact on the overall thermal conductivity. The presence of fluid areas may reduce the overall thermal conductivity efficiency because the thermal conductivity of fluids is usually lower than that of solid materials. By integrating these areas in the formula, all influencing factors can be taken into account, making the calculated effective thermal conductivity closer to the actual situation. In addition, the introduction of volume integrals also means that this method can handle a variety of complex structures and is suitable for porous media of various shapes and sizes, and has a wide range of applications.

[0085] The denominator of the formula It plays a normalization role. By integrating the weight function within the volume of the entire fluid area, it ensures that the calculation result of the effective thermal conductivity coefficient is a weighted average. This normalization process not only ensures the physical meaning of the calculation results, but also enhances its versatility under different materials and structural conditions. By performing such a weighted average treatment on the thermal conductivity coefficient, the formula can give a more comprehensive effective thermal conductivity coefficient on a macro scale based on the consideration of the thermal conduction contribution of different microscopic regions. In the optimal design of floor heating insulation modules, the determination of the effective thermal conductivity coefficient is crucial. Since floor heating systems usually need to achieve uniform heat conduction and temperature distribution in a larger area, it is particularly important to understand and optimize the overall thermal conductivity performance of the material. The homogenization method of the present invention provides a powerful tool for designers by accurately calculating the effective thermal conductivity coefficient on a macro scale. By adjusting the microstructure and material distribution of the porous medium, the thermal conductivity performance of the floor heating module can be effectively optimized to ensure that the best temperature distribution effect is achieved under the premise of minimum energy consumption. The application of this formula in the homogenization process enables designers to more intuitively understand the heat flow characteristics in porous media, so that more accurate optimization adjustments can be made during the design stage. At the same time, this method of calculating the thermal conductivity coefficient based on the homogenization results also provides a new way to solve complex heat conduction problems in porous media. Traditional heat conduction analysis methods are often limited to single-scale or simple structural models, and their accuracy and applicability are limited for complex porous structures. Through homogenization, the complex behavior of the microscopic scale and the overall effect of the macroscopic scale are combined, and the present invention realizes an accurate description of the thermal conduction behavior of porous media at a higher scale. This method is not only of great significance in theory, but also provides valuable guidance for practical engineering design. Through this method, the design of the floor heating insulation module can be based on the consideration of the complex internal structure of the material and the multi-scale effect, and more optimized material selection and structural design can be carried out, thereby improving the overall performance and reliability of the system.

[0086] Example 8: When the optimization goal is the maximum heat transfer efficiency, the objective function of the topology optimization problem defined in step 4 is Use the following formula to express it:

[0087] ;

[0088] in, Indicates the first weight coefficient that is set.

[0089] Specifically, the objective function The design of is based on the maximization of heat conduction efficiency, and its main parts include the two terms in the numerator and the normalized term in the denominator. Represents the effective thermal conductivity of the material in a temperature gradient field. Effective thermal conductivity It is obtained by homogenization method and reflects the overall thermal conductivity of porous media on a macro scale. It combines the microstructure and material properties of porous media, converting these microscopic characteristics into macroscopic average performance, so that the coefficient can represent the thermal conductivity of the entire system. It reflects the distribution of heat flux density in space. Areas with high heat flux density are usually key areas for efficient heat conduction, so the introduction of this term in the objective function can help the optimization algorithm identify and enhance the structural characteristics of these areas. is a high-order correction for microscale heat conduction effects. This term further captures the complex heat conduction behavior of porous media by considering the interaction between temperature gradient and thermal conductivity gradient. Specifically, when the temperature gradient changes, the thermal conductivity may also change, and this change may have a nonlinear effect on the overall heat flow. This high-order correction term can provide more detailed structural optimization guidance to ensure that the heat transfer efficiency is maximized in the context of multiple scales. The denominator of the objective function Normalization is introduced to ensure the stability and comparability of the objective function under different design parameters. The introduction of normalization allows the optimization algorithm to run stably even in high temperature difference areas, without being affected by excessive or insufficient temperature gradients. This processing method enhances the robustness of the optimization process, making it more practical and stable. The last term in the objective function is a crucial part of the optimization process. is the level set function, which is used to describe the interface shape and position in the porous media structure. represents the boundary between the solid and fluid regions, and is a smooth Heaviside function that represents the distribution of material between solid and fluid regions. By solving the objective function , the optimization algorithm is actually adjusting the level set function The shape and position of , in order to find the interface shape that optimizes the objective function value. In other words, The optimization process is to find a material distribution that maximizes the heat conduction efficiency while satisfying other physical and geometric constraints. Specifically, the optimization process can be understood as a process of finding the optimal solution in a high-dimensional space. Due to the complex structure of porous media, its optimization problem is often a nonlinear, multi-constrained optimization problem. By introducing the level set method, the optimization algorithm can flexibly adjust the interface shape of the material distribution, and as the iterative process proceeds, these interfaces are continuously optimized to achieve the optimal value of the objective function. Level set function The adjustment and optimization of the solid and fluid areas make the shape and position of the solid and fluid areas constantly change, and these changes directly affect the heat conduction path of the entire floor heating insulation module. , can optimize the structure of porous media, making the transfer of heat energy in the material more efficient. Smoothed Heaviside function It plays an important bridging role here, which transforms the level set function Combined with the physical model of material distribution. The smooth nature of the Heaviside function ensures that the transition at the interface is continuous, thus avoiding instabilities in the numerical calculations. This is crucial for the convergence and accuracy of the optimization algorithm, because in practical applications, the material interface is usually not a perfect boundary, but a transition area with a certain thickness. By introducing a smooth Heaviside function, the model can more accurately simulate the actual material transition characteristics and avoid numerical oscillations or instabilities during the optimization process. Weight coefficients in the optimization objective function It also plays a key role. It controls the weight of the interface shape optimization item in the overall optimization process. The value of can balance the maximization of heat conduction efficiency and the rationality of interface shape during the optimization process. When a larger value is taken, the optimization process pays more attention to the smoothness and rationality of the interface to avoid irregular or discontinuous interfaces; When the value is smaller, the optimization process focuses more on maximizing the heat transfer efficiency, which may result in a more complex interface morphology. , the designer can flexibly control the direction and focus of the optimization process, so that the optimization results can meet the engineering requirements and achieve the highest heat conduction efficiency. The optimization solution of the objective function usually adopts numerical methods, such as gradient descent method, conjugate gradient method or topology optimization algorithm based on Lagrange multiplier method. These methods gradually adjust the level set function through repeated iterations. The shape and position of the objective function are constantly approaching the optimal value. In each iteration, the algorithm calculates the objective function value and its gradient information based on the current material distribution and interface shape, and updates the As the number of iterations increases, the optimization algorithm gradually converges to an optimal solution, that is, the interface shape that maximizes the heat conduction efficiency is found. . The end point of this process is the optimized porous media structure, which can provide the highest heat conduction efficiency and the best energy utilization effect. In the design of floor heating insulation modules, the application of this optimization design method has significant practical value. The porous media structure obtained by optimization can not only achieve the best heat conduction efficiency under certain material and geometric conditions, but also ensure the stability and reliability of the system under various working conditions. The optimized structure usually has a better heat conduction path, a more uniform temperature distribution and higher energy efficiency, which is of great significance to improving the overall performance of the floor heating system. In addition, by adjusting the weight coefficient in the objective function , the optimization results can be further customized according to specific engineering needs to meet different design requirements and usage conditions.

[0090] Example 9: When the optimization goal is to maximize the uniformity of temperature distribution, the objective function of the topology optimization problem defined in step 4 is Use the following formula to express it:

[0091] ;

[0092] in, is the average temperature; is the maximum temperature; is the minimum temperature; is the second weight coefficient set.

[0093] Specifically, in the design of the objective function, the first term of the numerator is It still plays a role in measuring the thermal conductivity of materials. Effective thermal conductivity It is obtained by homogenization method, which represents the equivalent heat conduction capacity of porous media on a macro scale. This term combines the square of the temperature gradient , which directly reflects the intensity of heat flow inside the material. For floor heating insulation modules, efficient heat conduction is the basic condition for uniform temperature distribution, so the introduction of this term in the objective function is still crucial. It ensures that the heat conduction efficiency of the material will not be ignored during the optimization process, while maintaining a reasonable distribution of the overall temperature field. The second term in the numerator of the objective function is a key high-order correction term, which enables the optimization algorithm to adjust the material structure more finely to achieve a more uniform temperature distribution. represents the third-order gradient of the temperature field, which is able to capture local variations and subtle inhomogeneities in the temperature field. This is done by normalizing the square of the high-order derivative and multiplying it by a small parameter , the objective function effectively amplifies smaller non-uniformities in the temperature field, encouraging the optimization algorithm to make subtle structural adjustments to eliminate these non-uniformities. The physical significance of this correction term is that when the temperature gradient is large, the higher-order derivative terms can provide greater weights, thereby guiding the optimization process to focus on reducing these gradients to smooth the entire temperature field. This treatment is crucial to achieving uniform temperature distribution because it can effectively reduce fluctuations in the temperature field and ensure that the temperature distribution tends to be stable throughout the module. The normalization treatment of the denominator further ensures the physical rationality of the optimization results and their operability in practical applications. The expression introduced in the denominator Used to normalize the overall fluctuation of the temperature field. is the average temperature over the entire domain, and Represent the highest temperature and the lowest temperature respectively. This normalization process normalizes the non-uniformity of the temperature field into a dimensionless ratio, making the comparison between different design schemes more intuitive and fair. In this way, the optimization algorithm can maintain the stability and comparability of the calculation results under different temperature ranges and gradient conditions. Especially in practical engineering applications, this normalization process can help designers avoid unstable results caused by extreme temperature differences during the optimization process. The last term in the objective function Introduced optimization constraints on interface shape and position, similar to the previous objective function The interface optimization items in . Is a weight coefficient that controls the influence of this item in the overall optimization process. Level set function Describes the shape and position of the interface between the solid and fluid regions, the Heaviside function It is used to make smooth transition in the interface area. By optimizing the objective function , the solution algorithm is constantly adjusted The shape and position of the surface are adjusted to maximize the uniformity of the temperature distribution. The smooth Heaviside function plays an important role here again. By ensuring the continuity and differentiability of the interface transition, the optimization process can avoid numerical oscillations and instabilities. This smoothing process is particularly important for the design optimization of floor heating insulation modules because it can avoid discontinuous material distribution or unreasonable geometry in the optimization results. In this optimization process, solving the objective function The actual goal is to find an optimal level set function , which describes the shape and position of the interface between the solid and fluid regions in the porous medium. The optimization algorithm iterates and adjusts , gradually find the interface shape that makes the temperature distribution most uniform. This process involves the application of complex numerical calculations and optimization algorithms, such as gradient descent method, Lagrange multiplier method, etc. In each iteration, the algorithm calculates the objective function value and its gradient information, and then adjusts the As the number of iterations increases, the algorithm continues to approach the optimal solution, that is, it finds an interface shape that makes the temperature distribution most uniform. . In the design of floor heating insulation modules, temperature distribution uniformity is a key performance indicator because it is directly related to the comfort of the indoor environment and the energy efficiency of the system. By optimizing the design and finding a porous media structure that makes the temperature distribution most uniform, the overall performance and user experience of the floor heating system can be significantly improved. The optimized porous media structure can usually provide a more stable heat flow path and a more uniform temperature field, thereby reducing local overheating or overcooling. This can not only improve the energy efficiency of the system, but also extend the service life of the equipment and reduce maintenance costs.

[0094] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An intelligent design method for floor heating insulation modules based on group optimization algorithm, characterized in that: The method comprises: Step 1: Create a multi-scale heat conduction model based on fractal theory, perform multi-scale expansion on the temperature field and multi-scale heat conduction coefficient in the multi-scale heat conduction model, and obtain the multi-scale expansion results of temperature and heat conduction coefficient; Step 2: Use the level set method to parameterize the porous media structure and obtain the parameterization results; Step 3: Perform homogenization processing based on the multi-scale expansion results of temperature and heat conductivity, integrate the micro-scale information into the macro-scale equation, and obtain a macro-scale effective heat conduction equation as the homogenization result. Calculate the effective heat conductivity based on the homogenization result; Step 4: Based on the homogenization results and the effective heat conduction coefficient, define a topology optimization problem, the optimization goal of which is to maximize the heat conduction efficiency or the uniformity of the temperature distribution, and define the objective function of the topology optimization problem; substitute the parameterized results into the topology optimization problem for solving, so that the effective heat conduction coefficient is maximized, and extract the level set function corresponding to the parameterized results at this time as the optimized porous structure; The multi-scale heat conduction model based on fractal theory created in step 1 is expressed using the following formula: ； in, represents the temperature field; Indicates time; It is a three-dimensional space vector, representing a position coordinate in three-dimensional space; Indicates the material density; represents specific heat capacity; represents the multi-scale heat transfer coefficient; represents the heat source term; represents the latent heat of phase change; represents the phase change function; represents the scale parameter; represents the fractal dimension; represents the Laplace operator; The multi-scale thermal conductivity is calculated using the following formula: ； in, Indicates the reference scale, which is the set value; Indicates the base thermal conductivity, which is the set value; Represents the temperature gradient sensitivity coefficient, which is the set value; phase change function Use the smoothed Heaviside function to describe the representation: ； in, represents the phase transition temperature; Indicates the phase change temperature range.

2. The intelligent design method for floor heating insulation module based on group optimization algorithm according to claim 1 is characterized in that: In step 1, the temperature field and the multi-scale heat conduction coefficient in the multi-scale heat conduction model are multi-scale expanded to obtain the multi-scale expansion results of temperature and the multi-scale expansion results of heat conduction coefficient as follows: ； ； in, It is a fast variable; is the multi-scale thermal conductivity order expansion term; It is the temperature field order expansion term; is a natural number ranging from 0 to 2; Indicates all The set of terms whose order of variation is greater than or equal to 3.

3. The intelligent design method of floor heating insulation module based on group optimization algorithm according to claim 2 is characterized in that: The level set function used in step 2 is expressed as follows: ； in, is the level set function; represents a solid area; represents the fluid region; Represents the interface; using the level set function, define a smooth Heaviside function to represent the material distribution as a parameterized result: ； in, To define the smoothing parameter, it is a positive number.

4. The intelligent design method for floor heating insulation module based on group optimization algorithm according to claim 3 is characterized in that: In step 3, the macro-scale effective heat conduction equation obtained by homogenizing the temperature multi-scale expansion results and the heat conductivity coefficient multi-scale expansion results is expressed as follows: ； in, represents the average temperature field at the macroscopic scale and is defined as: ， in is a representative volume unit; is the effective heat transfer coefficient, calculated by the following formula: ； in The multi-scale expansion results Order item, are shape functions defined at different scales; Represents the volume of the fluid region in the microstructure. During the homogenization process, Represents the volume of the fluid region inside the porous medium where heat conduction occurs.

5. The intelligent design method of floor heating insulation module based on group optimization algorithm according to claim 4 is characterized in that: Based on the homogenization results, the calculated effective heat transfer coefficient is expressed using the following formula: ； in, is the effective heat conductivity coefficient at the macroscopic scale, which describes the equivalent heat conduction capacity of the porous medium at the macroscopic scale; : The absolute value of the gradient of the temperature field, indicating the spatial rate of temperature change; is the volume differential element, which means the integral operation is in the volume On.

6. The intelligent design method for floor heating insulation module based on group optimization algorithm according to claim 5, characterized in that: When the optimization goal is to maximize the heat transfer efficiency, the objective function of the topology optimization problem defined in step 4 is Use the following formula to express it: ； in, Indicates the first weight coefficient that is set.

7. The intelligent design method for floor heating insulation module based on group optimization algorithm according to claim 6, characterized in that: When the optimization goal is to maximize the uniformity of temperature distribution, the objective function of the topology optimization problem defined in step 4 is Use the following formula to express it: ； in, is the average temperature; is the maximum temperature; is the minimum temperature; is the second weight coefficient set.

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