CN116884618A - Human body bladder focusing electric stimulation method based on finite element modeling and simulated annealing optimization algorithm - Google Patents
Human body bladder focusing electric stimulation method based on finite element modeling and simulated annealing optimization algorithm Download PDFInfo
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Abstract
The invention provides a human bladder focusing electric stimulation method based on finite element modeling and simulated annealing optimization algorithm, belonging to the field of urinary function rehabilitation electric stimulation treatment. The method specifically comprises the following steps: s1: and constructing a human finite element electrical simulation model. S2: and carrying out iterative computation on the finite element model of the human body by using a simulated annealing optimization algorithm to obtain the optimal electrical stimulation parameters. The method is proved to have certain feasibility in searching the optimal parameter scheme of the bladder percutaneous focusing electric stimulation, and a reliable reference method and scheme are provided for corresponding clinical application.
Description
Technical Field
The invention belongs to the field of urinary function rehabilitation electric stimulation treatment, and particularly relates to a human bladder focusing electric stimulation method based on finite element modeling and simulated annealing optimization algorithm.
Background
Urinary system dysfunction, such as urinary frequency, urinary incontinence, urine retention, etc., can be caused by various causes, including aging, spinal cord injury, complications of related diseases, etc. Corresponding treatment methods include drug therapy, surgical therapy, electrical stimulation therapy, and the like. The electric stimulation treatment realizes the regulation and intervention of the urinary system function by stimulating and controlling the nerve (sympathology, parasympathetic or somatic nerve) or the smooth muscle cells of the bladder wall and the urethral sphincter through the current, thereby achieving the purpose of treating and recovering the corresponding function.
Bioelectric stimulation has been studied and applied very widely. In 1871, hermann successfully measured the resistance of skeletal muscle in different current directions, and was the precursor for bioelectric stimulation studies. The bioelectric stimulation aims to improve the condition of the human body or to treat diseases by applying microcurrent stimulation to the human body. Bioelectric stimulation can be classified into various methods depending on the site of action, the mode of action, and the purpose of action. For example, bioelectric stimulation can be classified into in vivo (also referred to as implantable), in vitro (also referred to as noninvasive) and semi-implantable depending on electrode placement; according to the function and purpose of the electric stimulation, the electric stimulation can be divided into direct treatment type electric stimulation and auxiliary rehabilitation type electric stimulation; according to the electric stimulation part, the human body electric stimulation can be divided into various different human body electric stimulation, such as brain stimulation, stomach electric stimulation, heart electric stimulation and the like.
The electrical stimulation has remarkable treatment effect on various diseases, but at the same time, the electrical stimulation also causes damage (namely electrical damage, including thermal damage, electrochemical effect, abnormal physiological response of neurohormones and the like) to human bodies. The study of electrical injury dates back to 1964, when researchers began to study the effects of small direct currents on neuronal excitability after acting on biological tissues. Although the stimulation current used is already small to milliamp level, the micro-current still causes some slight damage to human tissues, whether in laboratory research or clinical application; some electrical stimulation requires a large enough stimulation current to ensure therapeutic effects, such as defibrillation and other percutaneous electrical stimulation methods, and the large current necessarily increases the extent and extent of damage to the tissue. How to reduce the stimulating current and relieve the bowels on the basis of ensuring the treatment effect becomes one of the very necessary consideration and solving problems. A simple and effective idea is to concentrate the stimulation current to the target tissue region, reduce the current density or electric field strength of the non-target tissue region, i.e. to achieve focused electrical stimulation (Focal Electrical Stimulation) of the target tissue region. In view of the fact that the focusing electric stimulation can ensure the stimulation effect and reduce the damage of current to human tissues, many biological electric stimulation applications have been studied for focusing electric stimulation, including brain focusing electric stimulation, heart focusing electric stimulation, eye focusing electric stimulation, bladder focusing electric stimulation and the like.
For focused electrical stimulation of the bladder, current maturation protocols are mostly implantable or semi-implantable. Implantable electrical stimulators are required to be surgically implanted in the body, and the stimulators are required to be periodically charged (typically by wireless charging) and, after a certain period of time, to be surgically serviced again. The semi-implantation type stimulation probe is needed to be arranged at the anus or the urethra for electric stimulation, and the stimulation probe is connected with a controller and a power supply outside the body in a wired mode. Obviously, both schemes have inconvenience, and the use cost and the cost are relatively high. The body surface stimulation mode is more acceptable to patients and has obvious advantages in portability. However, due to the heterogeneity and distribution complexity of human tissues, the body surface electrical stimulation is difficult to ensure the stimulation effect. Therefore, to achieve focused electrical stimulation of the body surface bladder, it is currently highly desirable to find a suitable body surface electrical stimulation regimen.
Disclosure of Invention
Aiming at the requirement of body surface bladder focusing electric stimulation, the invention provides an effective method, and provides a proper focusing electric stimulation scheme which is calculated by iteration through finite element modeling simulation and simulated annealing optimization algorithm.
The technical scheme of the invention is as follows:
a human body bladder focusing electric stimulation method based on finite element modeling and simulated annealing optimization algorithm specifically comprises the following steps:
s1: construction of human finite element electrical simulation model
The method comprises the steps of constructing a human body three-dimensional finite element model, wherein the model comprises information of various tissues and organs in a human body, specifically comprises three-dimensional information of muscles, bones, organs and blood vessels of the human body, and comprises surface grid information. The source model is simplified, and the processing flow is as follows: the method comprises the steps of carrying out segmentation treatment on a source model, segmenting and extracting a hip and abdomen model, and then carrying out smoothing treatment on the segmented model, so as to remove overlapped patches and too narrow cracks, unclosed patches and sharp surfaces contained in partial parts of the segmented model.
The simplified model is subjected to finite element analysis, including electrode configuration scheme design, electrode and human body three-dimensional model coupling, electrical characteristic parameter injection, meshing and final finite element calculation. The specific process is as follows: (1) Generating a solid model on the basis of the model after the simplification treatment, and constructing an array electrode model; model-to-model coupling between different tissues and organs and between electrodes and tissues is then performed, i.e., a complex is constructed. (2) Material property characteristics including electrical conductivity and relative permittivity are imparted into individual tissue organs of the model. (3) performing physical field setting: the physical field selects a current physical field in the AC/DC module. The shell of the model is electrically insulated, and the whole model ensures current conservation; then, different electrodes are given different potential values for corresponding analysis. (4) And performing grid subdivision to realize proper grid setting so as to reduce the calculation complexity and ensure certain calculation precision. (5) And (3) carrying out solver configuration, and selecting steady-state research or transient state research according to the calculated amount. A default configuration is selected for the solver configuration. And then carrying out finite element calculation and solving to obtain the electric field distribution condition inside the human body model under the stimulation of the external electrode.
S2: iterative calculation is carried out on the finite element model of the human body by utilizing an optimization algorithm to obtain the optimal electrical stimulation parameters
And (2) designing a proper objective function according to the electric field distribution condition inside the human body model under the external electrode stimulation obtained in the step (S1), so that the objective function value can represent the focusing stimulation degree of the current on the bladder in the model. And (3) modifying the electric stimulation parameters on the stimulation electrode according to the focusing stimulation degree, and then continuously repeating the finite element calculation solving process in the step S1. And selecting a simulated annealing algorithm to perform iterative optimization on the objective function value, and finally obtaining a proper focusing electric stimulation scheme.
The invention has the beneficial effects that: the invention realizes the percutaneous focusing electric stimulation of the human bladder by finite element modeling and simulated annealing optimization algorithm, and improves the focusing property of the electric stimulation of the bladder. By using the method of the invention, the bladder electrical stimulation focal power is increased from 0.4 to 0.76, which is approximately 2 times. The invention provides a possible scheme for regulating and controlling the functions of the urinary system by using a percutaneous electrical stimulation method to treat the related diseases of the urinary system.
Drawings
FIG. 1 is a flowchart for iterative calculation of optimal electrical stimulation parameters by an optimization algorithm
FIG. 2 is a diagram showing the iterative computation of a finite element electrical model of a human body using a simulated annealing algorithm
FIG. 3 is a graph of the change in objective function value during an iterative process
Detailed Description
Aiming at the body surface bladder focusing electric stimulation, the method mainly comprises two steps:
s1: and constructing a human finite element electrical simulation model.
S2: and carrying out iterative computation on the finite element model of the human body by using a simulated annealing optimization algorithm to obtain the optimal electrical stimulation parameters.
For step S1, the specific steps for constructing the finite element model are as follows:
s11: simplifying the source model. Finite element simulation of the method is performed on a COMSOL platform. Because the platform has a shortage of processing capability for complex nonlinear three-dimensional models, which is a common disadvantage of most other finite element analysis platforms, the method of the invention simplifies and smoothes the source human three-dimensional model. Meanwhile, the invention mainly aims at the human bladder to carry out finite element simulation analysis, and a complete human three-dimensional model is not needed, so that the model of the human hip abdomen part is separated, processed and analyzed.
The method comprises the steps of constructing a human body three-dimensional finite element model, comprising information of various tissues and organs in the human body, specifically comprising three-dimensional information of muscles, bones, organs, blood vessels and the like of the human body, deriving and storing model files into an STL format, and comprising surface grid information. The surface mesh of the source STL model is too complex and the model patches overlap, and the source STL file is correspondingly simplified. Segmentation reduction of the source model is performed on MIMICS and 3-matic platforms. The specific segmentation simplifying process is as follows: (1) The method comprises the steps of importing a source model (STL format) into MIICS software, processing a model file by utilizing the segmentation and smoothing functions of the software, segmenting and extracting a hip and abdomen model, smoothing the model file to remove overlapped patches contained in part of the segmented model, too narrow cracks between the patches, unclosed patches (ensuring that the patches are closed to facilitate the generation of a solid model later) and other geometric structures, and then exporting the model into the STL format file. (2) And importing the model file after preliminary processing into the 3-material software, and manually processing the sharp points of the model surface which cannot be processed by the MIICS software through the smoothing function of the 3-material software. The MIMICS and 3-matic processes ensure smooth subsequent COMSOL generation of surface mesh files and solid models. The 3-matic result export is then stored as an STL format file.
S12: and constructing a geometric module in the finite element model. The construction of the geometric module mainly comprises three steps: (1) Importing the STL format file of each model component after the simplification treatment into COMSOL to form a corresponding surface grid file; (2) Generating a solid model by using the imported surface mesh file; (3) constructing an electrode geometric model; the electrode array in the embodiment is designed into a circular array electrode form; (4) constructing a complex model. If the previous simplification step does not perform a suitable and effective simplification process on the source model, there is a possibility that the processing failure is caused by geometrical internal calculation errors in all three steps (1), (2) and (4). The reason for the processing failure is that the three-dimensional model of the human body contains an abnormal geometric surface structure, and the size of gaps between different structures in the model also changes nonlinearly, so that the processing failure can be caused by the complex structure of the input model no matter the surface grid is divided, the entity model is generated from the surface grid or each model component is constructed as a complex model. The model can be simplified again by using MIICS and 3-matic software after failure. For the construction of the electrode geometric model in the step (3), the method is realized by utilizing a CAD processing module embedded in COMSOL software, a cylindrical model is constructed first, and then useless parts are removed by utilizing Boolean operation (the thickness of the patch electrode is ignored in the method), so that the final geometric module comprises the patch electrode array part.
S13: and constructing a material attribute module in the finite element model. This step imparts electrical parameters to the model, including conductivity and relative permittivity. Different human tissues include different electrical characteristic parameters. According to the electrical characteristic parameters of each tissue of the human body obtained by searching the related papers, creating blank material properties in a material module of COMSOL software, endowing the obtained electrical characteristic parameters, and applying the created material module to each geometric structure of the model; it is also possible to find the desired material properties from a library of materials embedded in COMSOL and modify the relevant material property values before applying to the relevant geometry.
S14: and constructing a physical field module in the finite element model. The method involves electro-stimulation simulation, whereby the physical field selects the current physical field in the AC/DC module. For the convenience of calculation, the shell of the model is set to be electrically insulated, and the whole model ensures current conservation; then, different electrodes are given different potential values for corresponding analysis. Considering the problem of the calculation amount, only the steady-state method is considered. Only the ground electrode and other input electrodes are provided in this module. The voltage of the input electrode is randomly generated, and the size of the input electrode is continuously corrected by the subsequent iterative optimization part.
S15: dividing a finite element model grid. The grid division is very important in finite element simulation, and the grid division with high precision can obtain more accurate results, but the calculated amount is very huge; while a less accurate meshing may lose some of the accuracy of the result. Therefore, a suitable meshing parameter is necessary, considering the trade-off between accuracy of the result and the amount of computation. The model in the embodiment is complex, and the accuracy of the mesh subdivision is ensured by independently adjusting the size of each parameter in the mesh subdivision. In the COMSOL platform, the grid is divided into four different grid cells and nine default configurations with different accuracies. For grid cells, the method selects the most commonly used tetrahedral cells, which have very good applicability in the grid division of complex three-dimensional geometries. For grid size, selecting only any one of nine default configurations may result in grid partition failure due to geometric internal decomposition errors. For the case where the default configuration is not satisfactory, the COMSOL platform provides more specific parameter control including five parameters, maximum cell size, minimum cell size, maximum cell growth rate, curvature factor, and narrow region resolution. In the method, the sizes of the five parameters are respectively as follows: 36.9, 4, 1.5, 0.6, 0.5.
S16: and carrying out solver configuration. The steady state method is selected by the method in consideration of the calculation amount, and compared with the transient method, the calculation amount is greatly reduced. And selecting a default value by the solver, carrying out finite element calculation and solving to obtain the electric field distribution condition inside the human body model under the stimulation of the external electrode, and obtaining a result data set. The result data set can be subjected to drawing, display and observation, and can also be exported for subsequent processing by using other platforms. The method selects an MATLAB platform for post-processing, namely, focusing degree calculation.
The steps of constructing the human finite element electrical simulation model are as above. After the finite element model is constructed, the voltage input of the electrode in the finite element model is continuously and iteratively changed and corrected by using an optimization algorithm, and then the process is repeatedly calculated. The implementation process of the optimization algorithm comprises the following specific steps:
s21: a decision optimization algorithm is selected. The optimization process of the method is mainly used for solving the electrical stimulation parameters, the specific process comprises the steps of randomly generating initial conditions (the number of electrode positions and the current magnitude), solving the whole function, correcting relevant parameter values according to the solved result, and then iterating the process until the solved solution meets the focusing condition, as shown in fig. 1. In this process, the objective function and the optimization method determine the quality of the research result. The objective function is a measure of the quality of the result of each iteration calculation, and generally consists of the following parts: target area current density, target area electric field, least squares error between target area electric field and achievable electric field, etc. After the objective function is determined, the proper optimization method can enable iteration to converge to the optimal solution more quickly, and the optimal initial condition can be solved more quickly. In the related research, the selection of the optimization algorithm has different considerations, and genetic algorithm, least square method, internal penalty algorithm, branch-and-bound algorithm, superposition principle, evolution strategy algorithm and the like are all tried and feasible algorithms. The invention selects a simulated annealing algorithm (Simulated Annealing, SA) to realize optimization solution.
S22: and realizing a simulated annealing algorithm. Simulated annealing is an extension of the local search algorithm and is characterized by accepting solutions with a probability that the result does not meet the requirements, and the probability gradually decays with an increase in certain parameters (temperature) and iteration number. This feature can increase the flexibility of the algorithm search process, preventing the algorithm from being trapped in a locally optimal solution. Furthermore, it is limited to the last solution for the search interval of the new solution, not to a breadth-wise random search in the global solution space like a genetic algorithm. This may speed up the convergence of the algorithm to some extent. In addition, algorithm control parameters are introduced, so that the optimization process can be divided into two stages, one is to optimize the optimal solution under the parameter (temperature) after fixing the parameter, and the other is to reduce the parameter and improve the acceptance criterion, so that the probability of accepting the disfigurement solution is reduced. The other characteristics are that the requirement on the objective function is less, the derivative value of the objective function cannot be calculated because the finite element simulation process is not tiny, so that the searching direction cannot be determined, and the simulated annealing is only randomly searched in the neighborhood space of the last solution, thereby avoiding uncontrollable global random searching and ensuring smooth proceeding of searching.
S23: and constructing an optimization model. The simulated annealing optimization model in the method mainly comprises the following parts:
(1) Objective function
A model objective function is first determined. The objective function may measure the goodness of a solution. The objective function in the present invention is expressed by the ratio of the mean current density model of bladder tissue at the input of body surface voltage to the mean current density model of the whole model. The larger the ratio, the larger the current transferred to the bladder tissue by the current on the body surface, the better the current focusing effect on the bladder tissue. The objective function F is calculated as follows:
wherein, sigma is the electrical conductivity,represents potential gradient, J represents current density, mean (|J) bladder I) represents the average current density of the bladder induced by percutaneous focused electrical stimulation, mean (|j) all I) represents the average current density in tissue organs induced by percutaneous focused electrical stimulation.
(2) Electrical stimulation parameter solution and solution space
The solution space comprises the proper voltage input values of 16 electrodes on the model body surface so that the current is converged to the bladder as much as possible, and the model solution is an array with the size of 16. The voltage input range of each electrode is set to be-10.0V, and the voltage is accurate to the position behind the decimal point, and the parameter setting can ensure that the damage of the current to the human body is in a safe range. Number of solutions in solution spaceScale of quantity 200 16 The iterative solution of the optimization model is to search the optimal solution in the solution space.
(3) Initial temperature and attenuation factor
The initial temperature of the model is set to 100, which is a common choice for most similar models, and the attenuation factor K is set to 0.96, so that the temperature is ensured to drop with the increase of the iteration number N at a proper speed, and the probability of accepting the malignant solution is reduced. The temperature change at each iteration is as follows:
T←K*T
(4) Metropolis sampling criteria
Wherein S is value1 Represents the objective function value corresponding to the current solution (each solution is a group of electrode input parameters), S value2 Representing the objective function value corresponding to the last solution, u is the control parameter, and p represents the probability of accepting the current solution. If S value1 ＞S value2 The objective function value corresponding to the current solution is larger than the objective function value corresponding to the previous solution, namely the current solution is more optimal, and the current solution is accepted as a new solution; otherwise, accept the current solution as a new solution with probability p. u is present for regulating the amplitude of the variation of the probability p, due to the adjacency S value The difference between the two is small, so that the value of p is still large (close to 1) after iterating for many times without u participations, which violates the basic idea of simulated annealing, and the existence of u can lead p to steadily decrease along with the progress of the iterating, and the specific value of the p is set to consider adjacent S value The values of the difference between them, the decay factor K of the temperature T and the number of iterations N need to be guaranteed to reduce the p-value to a level close to 0 before reaching the defined number of iterations.
(5) Step size factor
The step size factor determines the size of the scope of the search each time a new solution is searched. Since the data accuracy of the solution in the present model is only reserved to one bit after the decimal point, the step factor is set to 0.1.
(6) Stop criterion
In general, the algorithm stopping criterion for simulated annealing is set to a suitable temperature threshold, i.e., the iteration stops when the temperature drops to the temperature threshold. However, since the temperature threshold is typically set close enough to zero, it cannot be guaranteed later whether a more optimal solution exists, at which point the iteration has stopped and the search is not complete. Thus, the algorithm stopping criteria in this model are: a suitable iteration number threshold while ensuring that the temperature has fallen to approximately 0 before the iteration threshold is reached. Thus, after the temperature is reduced to be small enough, iteration can still be performed for a certain number of times, and the completion of searching is ensured.
The above optimization model procedure is shown in fig. 2. Based on the Matlab interface provided by COMSOL, the finite element model construction process of the method is realized in a code running mode. The construction of each module of the COMSOL has related interface functions, and the related interface functions are operated in Matlab to realize the function of calling each module of the COMSOL. The finite element model construction process is packaged into Matlab functions, and the Matlab functions are input into electrode stimulation parameters of the model and output into objective function values. And (3) compiling a main code of an optimization algorithm based on Matlab, and calling the packed finite element model function to realize the construction of a model and the calculation of corresponding indexes. After the iteration control parameters are set, the operation model and the optimization calculation process are started, and the related calculation results including indexes and the like are obtained as shown in fig. 3. The objective function value steadily increases along with the increase of the iteration times (figure 3), namely the degree of focus increases along with the increase of the iteration times, which shows that the method of the invention has certain feasibility in searching the optimal parameter scheme of the bladder percutaneous focusing electric stimulation, and provides a reliable reference method and scheme for corresponding clinical application.
The present invention has been described in terms of the preferred embodiments thereof, and it should be understood by those skilled in the art that various modifications can be made without departing from the principles of the invention, and such modifications should also be considered as being within the scope of the invention.
Claims (3)
1. The human body bladder focusing electric stimulation method based on finite element modeling and simulated annealing optimization algorithm is characterized by comprising the following steps:
s1: construction of human finite element electrical simulation model
Constructing a human body three-dimensional finite element model, wherein the model comprises three-dimensional information of all tissues and organs in a human body, specifically comprises three-dimensional information of muscles, bones, organs and blood vessels of the human body, and comprises surface grid information; the source model is simplified, and the processing flow is as follows: the method comprises the steps of carrying out segmentation treatment on a source model, segmenting and extracting a hip belly model, then carrying out smoothing treatment on the segmented model, and removing overlapped patches, too narrow cracks between the patches, unclosed patches and sharp surfaces contained in part of the segmented model;
performing finite element analysis on the model after the simplification processing, wherein the finite element analysis comprises electrode configuration scheme design, coupling of electrodes and a human body three-dimensional model, electrical characteristic parameter injection, grid division and final finite element calculation; the specific process is as follows: (1) Generating a solid model on the basis of the model after the simplification treatment, and constructing an array electrode model; then, carrying out model-to-model coupling between different tissues and organs and between the electrodes and tissues, namely constructing a combination body; (2) Imparting material property characteristics to each tissue organ of the model, the material property characteristics including electrical conductivity and relative permittivity; (3) performing physical field setting: the physical field selects a current physical field in the AC/DC module; the shell of the model is electrically insulated, and the whole model ensures current conservation; then, giving different potential values to different electrodes for corresponding analysis; (4) Performing grid subdivision to realize proper grid setting so as to reduce the calculation complexity and ensure certain calculation precision; (5) Carrying out solver configuration, and selecting steady-state research or transient-state research according to the calculated amount; selecting a default configuration for the solver configuration; then carrying out finite element calculation and solving to obtain the electric field distribution condition inside the human body model under the stimulation of the external electrode;
s2: iterative calculation is carried out on the finite element model of the human body by utilizing an optimization algorithm to obtain the optimal electrical stimulation parameters
Designing a proper objective function according to the electric field distribution condition inside the human body model under the external electrode stimulation obtained in the step S1, so that the objective function value can represent the focusing stimulation degree of current on the bladder in the model; modifying the electric stimulation parameters on the stimulation electrode according to the focusing stimulation degree, and then continuously repeating the finite element calculation solving process in the step S1; and selecting a simulated annealing algorithm to perform iterative optimization on the objective function value, and finally obtaining a proper focusing electric stimulation scheme.
2. The human bladder focusing electro-stimulation method based on finite element modeling and simulated annealing optimization algorithm as claimed in claim 1, wherein the optimization process is divided into two stages: one is to optimize the optimal solution under the fixed parameter, and the other is to reduce the parameter and improve the acceptance criterion, so that the probability of accepting the disfigurement solution is reduced.
3. The human bladder focusing electro-stimulation method based on finite element modeling and simulated annealing optimization algorithm as claimed in claim 1, wherein the optimization model is as follows:
(1) Objective function
The objective function is expressed by the ratio of the average current density module value of bladder tissue under the input of body surface voltage to the average current density module value of the integral model; the larger the ratio is, the larger the current transmitted to the bladder tissue by the current on the body surface is, and the better the current focusing effect on the bladder tissue is; the objective function F is calculated as follows:
wherein, sigma is the electrical conductivity,represents potential gradient, J represents current density, mean (|J) bladder I) represents the average current density of the bladder induced by percutaneous focused electrical stimulation, mean (|j) all I) represents percutaneous focusingMean current density in tissue organs induced by electrical stimulation;
(2) Electrical stimulation parameter solution and solution space
The solution space comprises proper voltage input values of the model body surface electrodes so that the current is converged to the bladder as much as possible, and the model solution is an array which is equal to the electrode voltage input values in number; the voltage input range of each electrode is set to be-10.0V, and the voltage is accurate to the position behind the decimal point, so that the damage of the current to the human body is ensured to be in a safe range; the number of solutions in the solution space is 200 in scale 16 The iterative solution of the optimization model is to search the optimal solution in the solution space;
(3) Initial temperature and attenuation factor
The initial temperature of the model is selected and set, and meanwhile, an attenuation factor K is set, so that the temperature is ensured to be reduced along with the increase of the iteration times N at a proper speed, and the probability of receiving the malignant solution is further reduced; the temperature change at each iteration is as follows:
T←K*T
(4) Metropolis sampling criteria
Wherein S is value1 Representing the objective function value corresponding to the current solution, S value2 Representing the objective function value corresponding to the last solution, u is a control parameter, and p represents the probability of accepting the current solution; if S value1 ＞S value2 The objective function value corresponding to the current solution is larger than the objective function value corresponding to the previous solution, namely the current solution is more optimal, and the current solution is accepted as a new solution; the presence of u can cause p to steadily decrease as the iteration proceeds, the specific value of which should be set taking into account the adjacent S value The difference value, the attenuation factor K of the temperature T and the iteration number N need to ensure that the p value is reduced to the degree close to 0 before the limit iteration number is reached;
(5) Setting a proper step factor
(6) Stop criterion
The algorithm stopping criterion is set to a suitable iteration number threshold while ensuring that the temperature has fallen close to 0 before the iteration threshold is reached.
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| CN117438039B (en) * | 2023-12-19 | 2024-03-22 | 湖南安泰康成生物科技有限公司 | Method and device for determining application distribution of electrode plates |
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