CN116562091A - Mild moxibustion multi-target optimization design method considering heat penetrability - Google Patents
Mild moxibustion multi-target optimization design method considering heat penetrability Download PDFInfo
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- G—PHYSICS
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- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/08—Thermal analysis or thermal optimisation
Abstract
The invention provides a mild moxibustion multi-target optimization design method considering heat penetrability, which comprises the steps of firstly, utilizing numerical simulation software COMSOL to realize parameterized modeling of mild moxibustion temperature field simulation; secondly, carrying out global sensitivity analysis on parameters such as moxa stick combustion temperature, moxa stick thickness, skin distance, ambient temperature and the like in mild moxibustion treatment, and simultaneously obtaining global sensitivity indexes of different parameters by adopting a function decomposition strategy so as to accurately evaluate sensitivity values of different operation parameters; and finally, establishing a mild moxibustion multi-target design optimization model, and solving the model by adopting a second generation non-dominant order genetic algorithm (NSGA-II) to obtain a Pareto optimal front boundary. The method of the embodiment provides the optimal operation parameters for the multi-target parameter problem selection in the mild moxibustion treatment process, thereby achieving the optimal treatment effect and further promoting the development of the mild moxibustion treatment theory and the more efficient method.
Description
Technical Field
The invention relates to the technical field of traditional Chinese medicine processing, in particular to a mild moxibustion multi-target optimal design method considering heat penetrability.
Background
Moxibustion is prepared from folium Artemisiae Argyi by making into moxibustion cone or grass, igniting the grass, burning and ironing on acupoints or affected parts, and is mainly based on heat effect, non-heat radiation effect and pharmacological effect. The moxibustion has the effect of enhancing the function and preventing and treating diseases. The moxibustion is ignited to heat part of acupoints on human body surface, and the diseases are treated by regulating the functions of channels and collaterals and viscera.
Mild moxibustion is one of moxibustion treatments that uses the result of warming to act on the skin to modulate the functioning of the nervous system by stimulating skin receptors.
In order to study the influence of the mild moxibustion operation parameters on the target parameters and quantitatively describe the influence degree of different operation parameters on different target parameters, global sensitivity analysis is required to be carried out on the influence between different operation parameters and the target parameters of the mild moxibustion.
However, the current mild moxibustion treatment process lacks corresponding guidance research, and has the following problems:
1. two main target parameters during mild moxibustion therapy, mild moxibustion heat penetrability HPM and patient mild moxibustion therapy comfort CMT, which jointly reflect the therapeutic efficacy of mild moxibustion. The treatment efficacy is influenced by moxa stick combustion highest temperature, moxa stick thickness, moxa stick distance from the skin surface, ambient temperature and other influencing factors, and the influence of the influencing factors on the mild moxibustion treatment effect is not quantitatively analyzed and compared.
2. What we want is that two target parameters are optimal solutions, but at the time of actual treatment, such results are almost impossible to obtain due to the contradiction between target parameters.
Disclosure of Invention
Aiming at the defects existing in the mild moxibustion treatment process, the invention provides a mild moxibustion multi-target optimal design method considering heat penetrability, which is characterized by comprising the following steps:
step 1, establishing a mild moxibustion combustion mathematical model;
the formula of radiation heat transfer of moxa stick combustion to the skin surface is as follows:
J＝εe b (T)+ρ d G
e b (T)＝n 2 δT 4
wherein J is effective radiation, G is input radiation, e b (T) is the radiant heat flux density of the black body as a function of temperature, ε is the surface emissivity of the body to radiation, ρ d Is the reflectance of the surface, T is the temperature of the object, sigma is the blackbody radiation constant, and n is the refractive index of the transparent medium;
the biological tissue heat conduction simulation is solved by adopting a Pennes equation, wherein the Pennes equation is as follows:
wherein T, ρ, c and k are the temperature, density, specific heat and thermal conductivity, ω, respectively, of the tissue b For blood perfusion rate, C b And T b For the specific heat capacity and the temperature of the blood, q m For tissue metabolism heat generation rate, q r Is an external heat source item;
step 2, performing global sensitivity analysis on moxa stick combustion temperature, moxa stick thickness, skin distance and environmental temperature parameters, and simultaneously obtaining global sensitivity indexes of different parameters by adopting a function decomposition strategy so as to accurately evaluate sensitivity values of different operation parameters;
step 3, latin hypercube design sampling;
50 experimental design points are obtained by adopting an optimal Latin hypercube sampling method within the design range of the operation parameters;
step 4, establishing a radial basis function neural network model;
according to the result of the sampling point, developing a proxy model to obtain a response surface of the whole design field;
step 5, calculating and solving by using NSGA-II algorithm
The mild moxibustion optimization problem is written as the following multi-objective optimization design model:
wherein: HPM-mild moxibustion heat penetrability; CMT-mild moxibustion treatment comfort; t is t 1 -maximum moxa stick combustion temperature; d-moxa stick thickness, h-distance of moxa stick from skin surface and t 2 -ambient temperature.
The invention has the beneficial effects that:
(1) The importance of the influence of different operation parameters on the treatment efficacy in the mild moxibustion treatment process is provided. In order to accurately evaluate the sensitivity of the operating parameters, a global sensitivity analysis is performed using a function decomposition method. The effect of mild moxibustion operating parameters including maximum moxa stick firing temperature, moxa stick thickness, moxa stick distance from the skin surface and ambient temperature on heat penetration HPM and therapeutic comfort CMT was studied. The results show that the factors with the biggest influence on the mild moxibustion heat penetrability are moxa stick thickness, ambient temperature and moxa stick burning temperature.
(2) Provides a method for researching the energy efficiency of mild moxibustion treatment. In the mild moxibustion design and optimization process, the heat penetration HPM and the therapeutic comfort CMT are considered as target parameters for its optimization. In order to optimize the mild moxibustion heat penetration and the patient treatment comfort, and also to save the calculation cost, the embodiment adopts Latin hypercube sampling technology and radial basis network (RBNN) method to develop a multi-objective optimal design model. The result obtained by the model is well matched with experimental data, and the error between the actually measured established model and the experimental data is within 5 percent and is in the allowable range. The optimization model is then solved using the non-dominant genetic algorithm NSGA-II. Finally, a group of optimal solutions of Pareto boundaries are obtained, so that an optimal reference is provided for patients to receive mild moxibustion treatment, and development and research of the mild moxibustion are promoted.
Drawings
FIG. 1 is a simulation model of mild moxibustion treatment over skin tissue;
FIG. 2 shows the results of mild moxibustion parameter sensitivity analysis;
FIG. 3 solves a computational flow diagram;
FIG. 4 is a graph showing the results of a mild moxibustion Pareto front iteration;
FIG. 5 Mild moxibustion Multi-objective optimal design Pareto optimal front
Detailed Description
In order to better understand the technical solutions of the present application, the present invention will be further described in detail below with reference to specific embodiments and drawings.
The embodiment provides a mild moxibustion multi-target optimal design method considering heat penetrability, which comprises the following steps of;
step 1, establishing a mild moxibustion combustion mathematical model and establishing a simulation model
The heat transfer from the burning place of moxa stick to the biological tissue of the treatment place is mainly carried out by the surface to the surface radiation heat transfer, then the heat generated by the absorption of the skin to the heat radiation becomes a heat source item of the biological heat transfer, and then the calculation of the heat transfer of the biological tissue of the tissue is carried out, thus obtaining the temperature field distribution of the whole treatment tissue after the completion of the calculation.
The formula of radiation heat transfer of moxa stick combustion to the skin surface is as follows:
J＝εe b (T)+ρ d G
e b (T)＝n 2 δT 4
wherein J is effective radiation, G is input radiation, e b (T) is the radiant heat flux density of the black body as a function of temperature, ε is the surface emissivity of the body to radiation, ρ d Is the reflectance of the surface, T is the temperature of the object, σ is the blackbody radiation constant, and n is the refractive index of the transparent medium.
Biological tissue heat conduction simulation is solved by adopting Pennes equation [11] The Pennes equation is:
wherein T, ρ, c and k are the temperature, density, specific heat and thermal conductivity, ω, respectively, of the tissue b For blood perfusion rate, C b And T b For the specific heat capacity and the temperature of the blood, q m For tissue metabolism heat generation rate, q r Is an external heat source item.
The biological tissue model in the simulation model of the invention is divided into three layers: the first layer is a skin tissue model and has a thickness of 2.2mm; the second layer is fat with thickness of 12.4mm; the third layer was a muscle tissue model, taken to a thickness of 10.4mm. The material parameters are provided by the material library of COMSOL, and the parameters of specific biological tissues are shown in the following Table 1.
TABLE 1 biological tissue characterization parameters
As shown in fig. 1, the modeling of the combustion portion of the moxa stick is a part of a sphere, and because the influence of natural convection heat transfer of air is not considered, two convection heat transfer can be ignored: 1) The convection heat exchange between the upper half cylinder and the air caused by the solid heat transfer between the moxa stick combustion area and the upper half cylinder has negligible effect on the skin tissue temperature field distribution; 2) Convective heat transfer between the moxa stick burning zone and the skin tissue through the air is also negligible. Therefore, the air area above the skin surface can be omitted during modeling, and meanwhile, in order to ensure the authenticity of the model as much as possible, a finite element simulation model obtained after the cylindrical part above the moxa stick burning part is reserved.
Step 2, performing sensitivity analysis of operation parameters related to mild moxibustion
In order to obtain sensitivity of mild moxibustion performance to operating parameters, a global sensitivity analysis was performed on mild moxibustion. In the field of global sensitivity analysis, there are mainly two types of methods, regression-based methods and variance-based methods. The function decomposition method is a variance-based method and is widely applied to global sensitivity analysis. In the invention, four influencing factors of the maximum burning temperature of the moxa stick, the thickness of the moxa stick, the distance between the moxa stick and the skin surface and the ambient temperature are studied.
Let the model have k input parameters in total, the output function y=f (x 1 ,x 2 ,…x k ) Mapping the variation range of each input parameter to the interval [0,1 ]]In which it is discretized and thenWherein p is a preset number of sample levels. And selecting m groups of vectors as input of the system, wherein m=k+1, forming an m-k matrix as the input matrix of the system, and according to the design principle of the OAT, only one of two adjacent rows of parameter values of the input matrix is different. Let the output result of two adjacent lines of parameters be y n ,y n+1 The sensitivity of the unique variation parameters of two adjacent rows to the output index parameter y is as follows:
wherein the method comprises the steps ofs is a change factor, so the system can obtain the sensitivity of all parameters by only sampling once, and the calculated amount is greatly reduced. The specific method comprises the following steps:
1) Construction of m x k matrix B
In the matrix, the first row elements are all 0, representing the basic state of the input parameters, where the parameters are selected fromAnd (3) taking the value. Only one parameter value of two adjacent rows of input parameters changes, and from the second row, the number 1 in the matrix represents the changed input parameter, and the number 0 represents the unchanged input parameter.
2) Inputting two adjacent rows from top to bottom as parameters of a model, and assuming that the two adjacent rows only have j-th column elements which are different, namely:
the basic impact of the j-th parameter is:
3) In order to ensure reliability, repeated sampling is needed, and the steps (1) and (2) are repeated r times, so that r S values can be obtained for each input parameter, and an average value of r basic influence values is taken. The larger the average value is, the larger the influence degree of the parameter on the system response is, and the importance degree of the input parameter of the system on the system response can be quantitatively evaluated by calculating the average value.
As shown in figure 2, a sensitivity result graph of the corresponding parameters is calculated.
Step 3, latin hypercube design sampling
A flow chart for solving mild moxibustion parameters is shown in fig. 3. The goal of the multi-objective optimization design is to accurately find the set of optimal solutions for the entire design space response surface. Because of the numerous and complex finite element models, the calculation cost for directly optimizing and analyzing the whole numerical simulation model is high. In order to simplify the multi-objective optimization problem, firstly, a response surface approximation model between the selected optimization parameters and the maximum deformation and quality needs to be established, then the model is trained to be mature, and finally the mature model is used for multi-objective optimization design. Latin hypercube design is a multi-dimensional hierarchical sampling method, and the basic steps of sampling are as follows:
firstly, dividing each layer of space of an n-dimensional space into m sections according to the principle of equal probability;
secondly, randomly taking out and only taking one sample point in m intervals, and ensuring that n levels can be researched and only researched once;
finally, the n extracted sample points are randomly paired to generate an n+m matrix.
The experimental design is performed by first selecting sampling points. The sampling points are typically in full factor methods such as full factor designs, latin hypercube and center complex designs. The embodiment adopts Latin hypercube to sample the design points, which is beneficial to the uniform distribution of the samples. The study obtained 50 experimental design points by adopting an optimal Latin hypercube sampling method within the design range of the operation parameters.
Step 4, establishing a radial basis function neural network model
And developing a proxy model according to the result of the sampling point to obtain a response surface of the whole design field. The present study uses RBNN model regression to build a proxy model for the objective function. In the whole design space, objective parameters of any design point can obtain the accuracy of the proxy model according to the established parameters.
By modeling the Relative Error (RE) between the result y (x) and the approximation of the regression function f (x), it can be expressed as:
meanwhile, the accuracy of the established proxy model is also evaluated by Root Mean Square Error (RMSE), which can be expressed as:
wherein:
SSE is the sum of squares of errors;
k is the number of sampling points, 50 in this embodiment;
SST is the sum of the total squares;
y i -an ith sample point real model response value;i i sample point model response value;
average value of (2).
The error analysis results of the established approximation model are shown in table 2 below.
TABLE 2 model error analysis results
From the error results of the established approximation model, the established model of RBNN has enough accuracy in medical practice for the penetration and comfort of mild moxibustion during mild moxibustion treatment.
Step 5, calculating and solving by using NSGA-II algorithm
According to the result of global sensitivity analysis, considering these different influencing factors, the mild moxibustion optimization problem can be written as the following multi-objective optimization design model:
wherein: HPM-mild moxibustion heat penetrability; CMT-mild moxibustion treatment comfort.
The invention adopts NSGA-II to carry out high-efficiency solving on the multi-objective optimized mathematical model. For contradictions between HPM and CMT, the solution of the optimization model is a set of non-dominant solutions, called Pareto solutions.
As shown in fig. 4, the NSGA-II algorithm was used for solving. The algorithm is used for iterating the moxibustion therapy to 500 generations, the abscissa is a comfort coefficient of the mild moxibustion therapy of a patient, and the ordinate is skin penetrability during moxibustion combustion, namely temperature at a certain depth in the skin. From the above analysis, it is clear that the moxa stick thickness has the greatest sensitivity to the effects of both targets, while the effect of ambient temperature is negligible. Each point on the Pareto boundary can be treated as an optimal solution. Thus, the choice of optimal design depends on the therapeutic comfort of the different patients, and the physician further obtains the corresponding optimal therapeutic heat penetration according to Pareto boundaries.
And solving the established optimization model by adopting an NSGA-II algorithm. The results after the 5O, 200, 400, 500 iterations are shown in figure 4 above. It can be seen that the result of the 200 th iteration is slowly approaching a true solution. After the 400 th generation, the iteration result basically has no change and is converged, and the 500 th generation iteration result is accurate enough to be used as an optimization result.
As shown in fig. 5, every point can be theoretically treated as an optimal solution according to the optimal front of the mild moxibustion Pareto after 500 generations. It can be seen that the maximum HPM is present at point 1 and the maximum CMT is present at point 3, which is typically the optimal point for single objective optimization. The thermal penetration or therapeutic comfort of mild moxibustion at each point is greatly improved, while other properties are worse than standard conditions. Multiple targets can be simultaneously reached to a relatively optimal level on Pareto boundary with point 2 as the optimal design target.
While the principles of the invention have been described in detail in connection with the preferred embodiments thereof, it should be understood by those skilled in the art that the foregoing embodiments are merely illustrative of the implementations of the invention and are not intended to limit the scope of the invention. The details of the embodiments are not to be taken as limiting the scope of the invention, and any obvious modifications based on equivalent changes, simple substitutions, etc. of the technical solution of the invention fall within the scope of the invention without departing from the spirit and scope of the invention.
Claims (5)
1. The multi-target mild moxibustion optimization design method considering heat penetrability is characterized by comprising the following steps of:
step 1, establishing a mild moxibustion combustion mathematical model;
the formula of radiation heat transfer of moxa stick combustion to the skin surface is as follows:
J＝εe b (T)+ρ d G
e b (T)＝n 2 δT 4
wherein J is effective radiation, G is input radiation, e b (T) is the radiant heat flux density of the black body as a function of temperature, ε is the surface emissivity of the body to radiation, ρ d Is the reflectance of the surface, T is the temperature of the object, sigma is the blackbody radiation constant, and n is the refractive index of the transparent medium;
the biological tissue heat conduction simulation is solved by adopting a Pennes equation, wherein the Pennes equation is as follows:
wherein T, ρ, c and k are the temperature, density, specific heat and thermal conductivity, ω, respectively, of the tissue b For blood perfusion rate, C b And T b For the specific heat capacity and the temperature of the blood, q m For tissue metabolism heat generation rate, q r Is an external heat source item;
step 2, performing global sensitivity analysis on moxa stick combustion temperature, moxa stick thickness, skin distance and environmental temperature parameters, and simultaneously obtaining global sensitivity indexes of different parameters by adopting a function decomposition strategy so as to accurately evaluate sensitivity values of different operation parameters;
step 3, latin hypercube design sampling;
50 experimental design points are obtained by adopting an optimal Latin hypercube sampling method within the design range of the operation parameters;
step 4, establishing a radial basis function neural network model;
according to the result of the sampling point, developing a proxy model to obtain a response surface of the whole design field;
step 5, calculating and solving by using NSGA-II algorithm
The mild moxibustion optimization problem is written as the following multi-objective optimization design model:
wherein: HPM-mild moxibustion heat penetrability; CMT-mild moxibustion treatment comfort; t is t 1 -maximum moxa stick combustion temperature; d-moxa stick thickness, h-distance of moxa stick from skin surface and t 2 -ambient temperature.
2. The mild moxibustion multi-objective optimal design method considering heat penetrability according to claim 1, wherein: the biological tissue model in the simulation model is divided into three layers: the first layer is a skin tissue model and has a thickness of 2.2mm; the second layer is fat with thickness of 12.4mm; the third layer was a muscle tissue model, taken to a thickness of 10.4mm.
3. The mild moxibustion multi-objective optimal design method considering heat penetrability according to claim 1, wherein: in step 2:
let the model have k input parameters in total, the output function y=f (x 1 ,x 2 ,nx k ) Mapping the variation range of each input parameter to the interval [0,1 ]]In which it is discretized and thenWherein p is a preset sampling level number;
m sets of vectors are selected as inputs to the system, where m=k+1, and a matrix of m×k is formed as an input matrix to the system. Let the output result of two adjacent lines of parameters be y n ,y n+1 The sensitivity of the unique variation parameters of two adjacent rows to the output index parameter y is as follows:
in the middle ofs is a variation factor; y is n ,y n+1 Two adjacent rows of parameters; p is a preset sampling level number; n is a natural number and is the number of selected parameter lines.
4. The mild moxibustion multi-objective optimal design method considering heat penetrability according to claim 1, wherein in step 3:
firstly, dividing each layer of space of an n-dimensional space into m sections according to the principle of equal probability;
secondly, randomly taking out and only taking one sample point in m intervals, and ensuring that n levels can be researched and only researched once;
finally, the n extracted sample points are randomly paired to generate an n multiplied by m matrix.
5. The mild moxibustion multi-objective optimal design method considering heat penetrability according to claim 1, wherein: in step 4:
by modeling the Relative Error (RE) between the result y (x) and the approximation of the regression function f (x), it can be expressed as:
meanwhile, the accuracy of the established proxy model is also evaluated by Root Mean Square Error (RMSE), which can be expressed as:
wherein:
SSE is the sum of squares of errors;
k is the number of sampling points, 50 in this embodiment;
SST is the sum of the total squares;
y i -an ith sample point real model response value;
-an ith sample point model response value;
-y i average value of (2).
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