CN111898299A - PCR base manufacturing parameter optimization method based on finite element model numerical simulation - Google Patents

PCR base manufacturing parameter optimization method based on finite element model numerical simulation Download PDF

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CN111898299A
CN111898299A CN202010727847.5A CN202010727847A CN111898299A CN 111898299 A CN111898299 A CN 111898299A CN 202010727847 A CN202010727847 A CN 202010727847A CN 111898299 A CN111898299 A CN 111898299A
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pcr
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CN111898299B (en
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李建兴
杨睿宁
罗堪
马莹
陈炜
黄靖
沈亮
蔡聪
赖智晨
刘肖
黄炳法
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Fujian Piaofutong Information Technology Co ltd
Fujian University Of Science And Technology
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Abstract

The invention relates to a PCR base manufacturing parameter optimization method based on finite element model numerical simulation, which constructs a numerical simulation method through common finite element software COMSOL Multiphysics and a with MATLAB interface thereof, gives out the actual temperature control process of the PCR base finite element model by a transient analysis method, and carries out manufacturing parameter optimization design according to the result so as to ensure that the PCR base can obtain the optimal dynamic and static performance in the actual thermal cycle process. The invention can obtain optimized manufacturing parameters such as the optimal size of the heat-insulating material and the like under the condition of meeting the temperature performance index of the PCR base, can be used for guiding the actual base processing, and ensures that the PCR base has good thermal uniformity on the premise of keeping quick temperature response in the thermal cycle process. The invention can greatly save the time and the material cost for the research and development of the novel PCR base.

Description

PCR base manufacturing parameter optimization method based on finite element model numerical simulation
Technical Field
The invention relates to the technical field of PCR base temperature performance optimization design, in particular to a PCR base manufacturing parameter optimization method based on finite element model numerical simulation.
Background
Heat transfer performance is central to PCR base design concerns. Currently, how to optimize PCR base parameters is a difficult point in the design in PCR base manufacturing. The method through actual processing and real heat transfer experiments has the defects of long period and great waste of manpower and material resources. Most of the existing simulation optimization design methods aim at the simulation of the temperature uniformity of a PCR base finite element model. Most focus is on solving for the steady state temperature performance of the susceptor. Meanwhile, the models and the methods simply realize the heat transfer simulation of the given temperature as a heat source, and the influence of system sensing lag and control links on the temperature performance is not considered. The dynamic response description progress of the models and the methods with limitations to the object is poor, and the thermal field distribution of the base cannot be accurately solved and the change situation of the dynamic temperature in the circulation of the three temperature zones of 94-55-72 ℃ can be reflected.
The existing PCR improvement base is designed with the following schemes:
(1) directly using the bare substrate to carry out reaction
(2) The periphery of the side wall of the PCR base is coated with 30mm polyethylene foam to eliminate convection heat transfer of the side wall and improve temperature uniformity, and the temperature difference between the highest temperature and the lowest temperature of the base can be improved from 1.2 ℃ to 0.34 ℃ when the given temperature is 94 ℃ in a 96-hole PCR base.
(3) The reaction in the vacuum drying box provides a stable internal environment for the circulation process, and eliminates the influence of air convection heat transfer.
In the method, in the scheme of (1) exposing the base, although the temperature responsiveness is fastest, the base and the ambient temperature have faster heat exchange, so that the temperature uniformity of the base is poor; (2) although the steady-state thermal uniformity performance of the base can be improved by introducing the thermal insulation material package, if proper thermal insulation material package design parameters cannot be correctly selected, the dynamic performance of the base can be reduced, the temperature response of the base generates large lag, and the temperature rising and falling speed is greatly influenced. Whether the heat-insulating material is used for wrapping and the wrapping thickness are problems to be solved in the manufacturing of the base. (3) Because the volume of the vacuum drying oven is limited, when the heat source needs an external circuit to maintain the circulation condition and when the environment meets specific requirements, the reaction in the vacuum drying oven cannot be realized, and the proposal has great limitation on the PCR base and is difficult to popularize for the basic health department. The traditional experimental method has the defects of long time period, difficulty in finding the optimal design and great waste of manpower and material resources.
Interpretation of terms:
a base: generally, a metal material with good thermal conductivity, such as copper, aluminum, etc., is selected to enable the heat source temperature to be better transferred to the surface of the base in the thermal cycle process
Manufacturing parameters are as follows: the method refers to a series of entity design parameters such as PCR base model material, size, hole number, whether a thermal insulation material is coated or not, type selection of the thermal insulation material, thickness and the like.
Thermal insulation material: according to the method, materials (such as foam, EVA (ethylene-vinyl acetate), aluminum silicate fibers, polyethylene and the like) with heat resistance meeting requirements are selected during actual temperature circulation, and the influence of the external environment on the temperature of the base is greatly reduced in the circulation process.
And (3) PCR: the Polymerase Chain Reaction (PCR) is a molecular biological technique for amplifying and amplifying specific DNA fragments, which can be regarded as special DNA replication in vitro, and the biggest characteristic of the PCR is that trace amount of DNA can be greatly increased under three process cycles of denaturation (94 ℃), annealing (55 ℃) and primer extension (72 ℃).
Finite element: finite Element Method (FEM) is a numerical technique that approximates a solution to the problem of side values of partial differential equations. When solving, the whole problem area is decomposed, and each sub-area becomes a simple part.
Disclosure of Invention
In view of the above, the present invention provides a method for optimizing PCR base manufacturing parameters based on finite element model numerical simulation, which solves the PCR base manufacturing parameter optimization data by a finite element model numerical analysis method, so as to meet the temperature performance requirement, greatly reduce the cost in each aspect during the research and development, and have better adaptability without being limited by the environment.
The invention is realized by adopting the following scheme: a PCR base manufacturing parameter optimization method based on finite element model numerical simulation comprises the following steps:
step S1: and (3) designing a base 3D model: drawing a 3D model of the PCR base according to the number and the size of holes required by actual design;
step S2: initializing simulation conditions;
step S3: setting and simulating the initialization condition of the finite element model;
step S4: setting an optimization method, judging whether constraint conditions are met, if so, continuing to execute the step S5, otherwise, updating variables and returning to the step S3;
step S5: save the result O1k{0<k≤n2| k ∈ Z } to an optimization set O;
step S6: judging whether the stop condition formulas (1) and (2) are met, if so, outputting an optimization set O, processing an optimization result, and finishing the optimization of the manufacturing parameters of the PCR base, otherwise, updating the variables and returning to the step S3;
further, the step S2 specifically includes the following steps:
step S21: initializing static and dynamic indexes of a PCR base as constraint conditions, wherein the steady-state error is essOvershoot is sigma, and heating rate is vupThe cooling rate is vdownThe temperature uniformity coefficient is xi;
steady state error essA, b, a rate of temperature increase vupC, cooling rate vdownD, temperature uniformity coefficient xi f; and the constraint conditions in the finite element simulation are as follows (1):
ess≤a、σ≤b、vup≥c、vdown≥d、ζ≤f (1)
wherein a, b, c, d and f all represent design index coefficients; the establishment of index coefficients is completed according to the performance of the existing PCR base: a is more than or equal to 0 and less than or equal to 0.5, b is more than or equal to 0 and less than or equal to 10 percent, v is more than or equal to 2 ℃/sup≤4℃/s,1.5℃/s≤vdownn≤3℃/s，0.4≤ξ≤1；
Step S22: initializing a manufacturing parameter to be optimized to a variable V1、V2、V3…VnWherein V is1Type of material for base, V2Type V of insulating material3Thickness of the insulating material, V4… Vn refers to parameters including base size, test tube hole size, whether the surface is provided with plum blossom holes or not, which may affect the PCR base; setting the step length corresponding to the variable according to the selection of the actual material type;
step S23: the realization of sensing and the selection of a control method are carried out, the real-time temperature sensing is measured by adding a domain point probe ppb1 at the midpoint of any side wall of the PCR base to be used as the input of an adopted control algorithm, and the control method can adopt PID control, fuzzy control, internal model control or Smith estimation control intelligent control algorithm as a system control scheme;
step S24: an optimized cost performance coefficient theta is formulated according to the actual manufacturing cost, and the optimized cost performance coefficient theta is initialized and usedThe expression is given as formula (2), and the variable V is defined according to the manufacturing cost1、V2、V3、…、VnIs given by a weight coefficient P1、P2、P3、…、Pn；
θ＝P1×V1+P2×V2+P3×V3+…+Pn×Vn(2)
Step S25: initializing a stopping condition and simulation searching times; the stop conditions were set as follows: the number of operating iterations reaches the maximum number of iterations: n is1＞n2
The objective function F falls with gradient convergence: i.e. Fk-Fk-1＜T
Wherein n is1For this time, the number of iterations for optimizing the data of the manufacturing parameters, n2And 500-10000 is selected for the maximum data optimization iteration times formulated according to the calculation resources in the actual optimization process. FkRepresents the target value obtained by k times of iterative calculation, T is a set threshold constant and is set to be 10-6。
Further, the specific content of step S3 is:
step S31: setting of the 3D model:
import the drawn bare base model into COMSOLULTIPhysics as C4Drawing three cuboids C in COMSOLULTIPHYSICS1、C2、C3(ii) a Wherein C is1、C2、C3With bare base C introduced from the outside4Has a length, width and height of (a)1，b1，c1)、(a2，b2，c2)、(a3，b3，c3)、(a4，b4，c4) (ii) a Let C1、C2Coordinate of center point (x)1，y1，z1)、(x2，y2，z2) And C4Center point coordinate (x)4，y4，z4) Are in agreement with C3The coordinate of the center point is (x)4,，y4，z4+0.5c3+0.5c4) In relation theretoThe formula is shown as formula (3):
a1≥a2＝a4，b1≥b2＝b4，c1＝c2＝c4，(a1-a2)＝(b1-b2) (3)
wherein (a)3，b3，c3) Set according to the size of the selected heat source, so 2 (a)1-a2) Is the thickness of the thermal insulation material; let C1And C2Form a difference set C5Namely a heat insulating material coated on the periphery of the base and a pair C3、C4、C5Constructing a united body to form a PCR base finite element geometric model of which the periphery of a bare base is wrapped by a heat-insulating material and the bottom of which is provided with a heat source; wherein, the C3Represents a heat source, C4Representing a bare base, C5Represents a heat insulating material;
step S32: analyzing the PCR base heat transfer model, selecting a physical field capable of realizing the temperature field characteristic of the PCR base in a COMSOL Multiphy sics heat transfer module to carry out finite element numerical simulation:
because the PCR base is complex in shape and has no internal heat source, the heat conduction problem is described by a heat conduction differential equation under the conditions of a stable state and no internal heat source in a Cartesian coordinate system, as shown in a formula (4):
Figure BDA0002601863420000061
the base steady state thermal analysis boundary conditions include: the first type boundary condition of the bottom surface of the base and the third type boundary condition of the convection heat exchange of the side wall of the base; because the bottom surface of the base is contacted with the heat source, when the temperature rises/falls to a constant value, the contact surface of the bottom surface of the base and the heat source keeps constant temperature, the side wall of the base and air have natural convection heat exchange, and the boundary condition is shown as the formula (5):
Figure BDA0002601863420000062
wherein, twIs the base temperature, tfIs the ambient air temperature, h is the convective heat transfer coefficient, λ0Is the heat conduction coefficient, and n is the normal direction of the side wall of the base; the temperature control of the PCR base is to control the heating power P of a heat source by taking the heat source heating value P arranged at the bottom of the PCR base and the base side wall measuring point ppb1 as input and transmit the heat to the PCR base to complete temperature change circulation; analyzing the temperature field of the P CR base to obtain a solid heat transfer physical field in a heat transfer module in COMSOL Multiphysics for completing finite element numerical simulation;
step S33: completing the material types and parameter settings of the base, the heat source and the heat insulation material in a solid heat transfer physical field;
directly searching or self-defining a hollow material by using a built-in material library in COMSOL Multiphysics, and needing to enter constant-pressure heat capacity C of the materialp[J/(kg·K)]Thermal conductivity lambda0[W/(m·K)]And density rho (kg/m)3)；
Step S34: setting a probe and a heat source heat rate in a solid heat transfer physical field:
arranging a temperature sensor on any side wall of the PCR base and adding a one-field point probe ppb at the center of the side wall1(ii) a According to the selected control algorithm, including alternative PID control, fuzzy control, internal model control or Smith predictive control intelligent control algorithm, the control of the heating power P of the heat source is completed so as to change the heat consumption rate Q of the heat source and realize the three-temperature-zone cycle control; the heat source heat rate Q expression is shown in formula (6):
Figure BDA0002601863420000071
wherein P is the heat source power, and V is the heat source volume;
step S35: setting of boundary conditions in a solid heat transfer physical field:
setting natural convection heat exchange between the side wall of the base and air, if the base is a bare base, the natural convection heat exchange between the side wall of the base and the air does not need to be calculated according to formula (5), selecting external natural convection heat exchange in a COMSOL Multiphysics heat flux module, and typing in the height L (m) of a vertical wall,External temperature Text(K) Absolute pressure PA(Pa) and selecting the fluid species to be air; if the heat insulating material exists on the side wall of the base, the natural convection heat exchange between the side wall and the air is negligible, so the temperature of the side wall of the heat insulating material is defined as room temperature T0Then the method is finished; the upper surface of the base is regarded as heat insulation because a constant temperature hot cover at about 104 ℃ can be placed in the actual reaction process of the PCR base to prevent the volatilization of the reagent;
for the partitioning of the grid: dividing a mesh by using a free tetrahedron with best geometric adaptability; because the hole part of the test tube in the PCR base is a link with a more complex shape, a free tetrahedral grid is firstly created for global drawing in order to save computing resources, and then the hole surface and the connection part of the test tube are refined through a refining function, so that the grid drawing is completed;
step S36: the configuration of a solver in a solid heat transfer physical field is as follows: selecting a transient solver, and setting the relative tolerance of the solver to be 0.01; selecting a generalized alpha by a time stepping method, selecting a middle-level by a step length, uniformly initializing in algebraic variable setting, selecting a backward Eulerian method, and finishing solver configuration, saving a file, wherein the format is stored as m format for preparing for subsequently calling a with Matlab interface;
step S37: finite element numerical simulation is carried out in a solid heat transfer physical field: performing numerical simulation according to the set finite element model to obtain the dynamic thermal field distribution of the PCR base in the heat exchange process, and calculating the steady state error e of the ppb1 temperature value curve of the domain point probessOvershoot sigma up-down, temperature rate vup、vdownAnd calculating an optimized cost performance coefficient xi according to the formula (2), and storing all results as output O1k{V1、V2、V3…Vn、essk、σk、vupk、vdownk、ξk、θk}{0<k≤n2︱k∈Z}。
Further, the specific content of step S4 is:
the m file is used with the finite element model set in the COMSOL Multiphysics generation step S35The MATLAB interface pair, the m file is processed in the formula (1) as a constraint condition, the (1) and the (2) in the S25 are stop conditions, and the number of searching times is n2T is the definition of a set threshold constant; implementing variable V in (2) each time according to set search strategy1、V2、V3Is selected, the calculation result O in step S361k{V1、V2、V3…Vn、essk、σk、vupk、vdownk、ξk、θk}{0<k≤n2| k ∈ Z } output; judging whether the iteration stopping conditions (1) and (2) are met, if so, exiting the loop and entering the step S5; otherwise, according to the constraint of equation (1), the updated simulation parameters are input to step S3 to re-perform the finite element numerical simulation.
Further, the set search strategy comprises grid search, particle swarm optimization, simulated annealing or ant colony optimization.
Further, the specific content of step S6 is: judging whether the stop condition expressions (1) and (2) are met, if so, stopping the calculation and outputting an optimized set O { V }1、V2、V3…Vn、ess、σ、vup、vdownXi and theta, and carrying out optimization result processing to complete the optimization of the manufacturing parameters of the PCR base; otherwise, the update variable returns to step S3.
Further, the specific content of the optimization result processing is as follows:
based on the calculation result, all the output values O conforming to the formula (1) are calculated1k{V1、V2、V3…Vn、essk、σk、vupk、vdownk、ξk、θk}{0<k≤n2| k ∈ Z } input set O, according to θk{0＜k≤n2I k belongs to Z, reordering the set in a mode from large to small, and outputting a set O to submit to a user; according to the optimization principle customized by the user, in the set O, according to the actual requirement, namely when the cost performance is expected to be higher, the cost performance coefficient theta is taken as the main selection basis, and if the better temperature uniformity is expected, the uniformity coefficient xi is taken as the main selection basisSimilarly, v is considered when a faster ramp rate is desiredupk、vdownkThe optimization of ess, σ needs to be prioritized in hopes of better temperature accuracy.
Compared with the prior art, the invention has the following beneficial effects:
(1) the method completes the solution of the optimized data of the PCR base manufacturing parameters by a finite element model numerical analysis method, can meet the temperature performance requirement, greatly reduces the cost in all aspects during the research and development period, is not limited by the environment, and has better adaptability.
(2) The invention solves the problem that the temperature uniformity is improved only by studying the steady state analysis in the prior PCR base finite element model numerical simulation, and the invention can directly observe the temperature dynamic and static performance of the PCR base and make analysis.
(3) The invention adds sensing and control into finite element numerical simulation, so that the simulation is extremely close to a real environment, and the simulation result has great guiding significance for actual research and development.
Drawings
FIG. 1 is a flow chart of a method according to an embodiment of the present invention.
FIG. 2 is a temperature step plot of an embodiment of the present invention.
FIG. 3 is an engineering drawing of a 96-well PCR base according to an embodiment of the present invention.
FIG. 4 is a flowchart of initializing simulation conditions according to an embodiment of the present invention.
FIG. 5 is a flowchart illustrating initialization condition setting of finite elements according to an embodiment of the present invention.
FIG. 6 is a design engineering drawing of a 96-well base PCR base according to an embodiment of the present invention.
FIG. 7 is a geometric model diagram of a finite element model of a 96-well PCR base according to an embodiment of the present invention.
FIG. 8 is an exemplary grid division of a 96-well PCR base according to an embodiment of the present invention.
FIG. 9 is a flowchart of a method for optimizing manufacturing parameters of a 96-well PCR base according to an embodiment of the present invention.
FIG. 10 is a graph of the steady state thermal field at 94 ℃ given after optimization of the manufacturing parameters for a 96-well PCR base according to an embodiment of the present invention.
FIG. 11 is a graph of the steady state thermal field at 72 ℃ given after optimization of the manufacturing parameters for a 96-well PCR base according to an embodiment of the present invention.
FIG. 12 is a graph of steady-state thermal field at 55 ℃ given after optimization of manufacturing parameters for a 96-well PCR base according to an embodiment of the present invention
FIG. 13 is a graph showing the temperature dynamics of the manufacturing parameters of a 96-well PCR base after optimization.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
As shown in fig. 1, the present embodiment provides a PCR base manufacturing parameter optimization method based on finite element model numerical simulation, which includes the following steps:
step S1: and (3) designing a base 3D model: drawing a 3D model of the PCR base according to the number and the size of holes required by actual design;
step S2: initializing simulation conditions;
step S3: setting and simulating the initialization condition of the finite element model;
step S4: setting an optimization method, judging whether constraint conditions are met, if so, continuing to execute the step S5, otherwise, updating variables and returning to the step S3;
step S5: save the result O1k{0<k≤n2| k ∈ Z } to an optimization set O;
step S6: judging whether the stop condition formulas (1) and (2) are met, if so, outputting an optimization set O, processing an optimization result, and finishing the optimization of the manufacturing parameters of the PCR base, otherwise, updating the variables and returning to the step S3;
as shown in fig. 4, in this embodiment, the step S2 specifically includes the following steps:
step S21: taking the given static and dynamic design indexes of the PCR base as constraint conditions, initializing the static and dynamic indexes of the PCR base by using a ppb1 point (the position of which is shown in a 396-hole PCR base engineering drawing, and taking a central point by taking the actual PCR base as the reference and arranging the actual PCR base on any side wall surface of the sensor), wherein the steady-state error is essOvershoot is sigma, and heating rate is vupThe cooling rate is vdownThe temperature uniformity coefficient is xi;
steady state error essA, b, a rate of temperature increase vupC, cooling rate vdownD, temperature uniformity coefficient xi f; FIG. 2 is a graph of temperature step increase and decrease, where T1、T4Given target temperature values, T, for the temperature rise and temperature fall intervals, respectively2、T5For a steady-state temperature value in a temperature rise and fall interval, a steady-state error essIs the difference between the target temperature value and the steady-state temperature value, and the steady-state error of the temperature rise interval is essup＝T1-T2The steady state error of the cooling interval is essdown＝T5-T4. Overshoot refers to the maximum extent to which the parameter being tuned dynamically deviates from a given value, where T3、T6Respectively, the temperature rise and fall interval dynamically deviates from the highest temperature value, so the overshoot of the temperature rise interval
Figure BDA0002601863420000121
And overshoot of the cooling interval
Figure BDA0002601863420000122
The temperature increase/decrease rate refers to the rate from the starting value to the first time a given temperature value is reachedRate of change of time and temperature, where t1For the temperature rise time, t2For the time of cooling, Δ T1、ΔT2For the temperature variation during the temperature raising and lowering period, since the initial temperature of the diagram is 20, Δ T1＝T1-20，ΔT2＝T4-T2Rate of temperature rise
Figure BDA0002601863420000131
Cooling rate in the same way
Figure BDA0002601863420000132
For the temperature uniformity evaluation index, the method defines a temperature uniformity coefficient xi, taking a 96-hole PCR base as an example, as shown in FIG. 3, a point a is a central region point of the upper surface of the base, a point b is an end side region point of the upper surface of the base, and the temperature uniformity deviation coefficient is
Figure BDA0002601863420000133
Wherein T isa1、Tb1Refers to the temperature values of the point a and the point b of the upper surface base in the PCR base temperature rising and falling interval, i.e. the temperature rising and falling time t in FIG. 21And t2Is an interval; t isa2、Tb2The temperature values of the central domain point and the edge domain point on the upper surface of a static interval for reaction at a given temperature are maintained, wherein the static interval refers to the period from the moment that the temperature reaches a steady-state temperature value and then the temperature fluctuation range does not exceed 5% to the end of the reaction in the temperature interval, t in figure 23、t4Representing a static interval. And lambda is a weight coefficient of the dynamic process and the static process, if the temperature of the PCR base has a large steady-state error in the simulation process of the finite element model of the bare base, the lambda is less than 1, and similarly, if the temperature rising and falling speed is slow, the lambda is more than 1, and the specific value of the lambda is given according to the severity of the insufficiency of the temperature performance of the PCR base in the simulation of the bare base.
And the constraint conditions in the finite element simulation are as follows (1):
ess≤a、σ≤b、vup≥c、vdown≥d、ζ≤f (1)
wherein a, bC, d and f all represent design index coefficients; the establishment of index coefficients is completed according to the performance of the existing PCR base: a is more than or equal to 0 and less than or equal to 0.5, b is more than or equal to 0 and less than or equal to 10 percent, v is more than or equal to 2 ℃/sup≤4℃/s,1.5℃/s≤vdownn≤3℃/s，0.4≤ξ≤1；
Step S22: initializing a manufacturing parameter to be optimized to a variable V1、V2、V3…VnWherein V is1Type of material for base, V2Type V of insulating material3Thickness of the insulating material, V4、…、VnThe index includes the base size, the test tube hole size, and whether the surface is provided with the quincuncial holes which may influence the PCR base; setting the step length corresponding to the variable according to the selection of the actual material type;
the type of the material manufactured by the V1 base can be selected from any metal with better heat conductivity such as (aluminum and copper) according to the actual parameter selection range, the type of the V2 heat-insulating material is selected from materials with better heat-insulating property such as (foam cotton, polyethylene and aluminum silicate), and the thickness of the V3 heat-insulating material meets the actual thickness range (0,100) [ mm ] to complete the setting of the optimized parameter step length;
step S23: the realization of sensing and the selection of a control method are carried out, the real-time temperature sensing is measured by adding a domain point probe ppb1 at the midpoint of any side wall of the PCR base to be used as the input of an adopted control algorithm, and the control method can adopt PID control, fuzzy control, internal model control or Smith estimation control intelligent control algorithm as a system control scheme;
step S24: an optimized cost performance coefficient theta is formulated according to the actual manufacturing cost, the optimized cost performance coefficient theta is initialized, and the expression formula (2) defines a variable V according to the manufacturing cost1、V2、V3…VnIs given by a weight coefficient P1、P2、P3…Pn；
θ＝P1×V1+P2×V2+P3×V3+…+Pn×Vn(2)
Step S25: initializing a stopping condition and simulation searching times; the stop conditions were set as follows:
1) the number of operating iterations reaches the maximum number of iterations: n is1＞n2
2) The objective function F falls with gradient convergence: i.e. Fk-Fk-1＜T
Wherein n is1For this time, the number of iterations for optimizing the data of the manufacturing parameters, n2500-10000 can be taken for the maximum data optimizing iteration times formulated according to the calculation resources in the actual optimization process. FkRepresenting the target value calculated by k iterations, T is a set threshold constant, and is suggested to be set to 10-6。
As shown in fig. 5, in this embodiment, the specific content of step S3 is:
step S31: setting of the 3D model:
import the drawn bare base model into COMSOLULTIPhysics as C4Drawing three cuboids C in COMSOLULTIPHYSICS1、C2、C3(ii) a Wherein C is1、C2、C3With bare base C introduced from the outside4Has a length, width and height of (a)1，b1，c1)、(a2，b2，c2)、(a3，b3，c3)、(a4，b4，c4) (ii) a Let C1、C2Coordinate of center point (x)1，y1，z1)、(x2，y2，z2) And C4Center point coordinate (x)4，y4，z4) Are in agreement with C3The coordinate of the center point is (x)4,，y4，z4+0.5c3+0.5c4) And the relation is shown as formula (3):
a1≥a2＝a4，b1≥b2＝b4，c1＝c2＝c4，(a1-a2)＝(b1-b2) (3)
wherein (a)3，b3，c3) Set according to the size of the selected heat source, so 2 (a)1-a2) Is the thickness of the thermal insulation material; let C1And C2Form a difference set C5Namely a heat insulating material coated on the periphery of the base and a pair C3、C4、C5Constructing a united body to form a PCR base finite element geometric model of which the periphery of a bare base is wrapped by a heat-insulating material and the bottom of which is provided with a heat source; wherein, the C3Represents a heat source, C4Representing a bare base, C5Represents a heat insulating material;
step S32: analyzing the PCR base heat transfer model, selecting a physical field capable of realizing the temperature field characteristic of the PCR base in a COMSOL Multiphy sics heat transfer module to carry out finite element numerical simulation:
because the PCR base is complex in shape and has no internal heat source, the heat conduction problem can only be described by a heat conduction differential equation under the conditions of a stable state and no internal heat source in a Cartesian coordinate system, as shown in formula (4):
Figure BDA0002601863420000161
the base steady state thermal analysis boundary conditions include: the first type boundary condition of the bottom surface of the base and the third type boundary condition of the convection heat exchange of the side wall of the base; because the bottom surface of the base is contacted with the heat source, when the temperature rises/falls to a constant value, the contact surface of the bottom surface of the base and the heat source keeps constant temperature, the side wall of the base and air have natural convection heat exchange, and the boundary condition is shown as the formula (5):
Figure BDA0002601863420000162
wherein, twIs the base temperature, tfIs the ambient air temperature, h is the convective heat transfer coefficient, λ0Is the heat conduction coefficient, and n is the normal direction of the side wall of the base; the temperature control of the PCR base is to control the heating power P of a heat source by taking the heat source heating value P arranged at the bottom of the PCR base and the base side wall measuring point ppb1 as input and transmit the heat to the PCR base to complete temperature change circulation; the physical field of solid heat transfer in the heat transfer module in COMSOL Multiphysics is obtained by analyzing the temperature field of the P CR baseFor completing finite element numerical simulation;
step S33: completing the material types and parameter settings of the base, the heat source and the heat insulation material in a solid heat transfer physical field;
directly searching or self-defining a hollow material by using a built-in material library in COMSOL Multiphysics, and needing to enter constant-pressure heat capacity C of the materialp[J/(kg·K)]Thermal conductivity lambda0[W/(m·K)]And density rho (kg/m)3)；
Step S34: setting a probe and a heat source heat rate in a solid heat transfer physical field:
arranging a temperature sensor on any side wall of the PCR base and adding a one-field point probe ppb at the center of the side wall1The arrangement position of the domain point probe is shown in figure 3;
according to the selected control algorithm (PID control algorithm is adopted in the example), the control of the heating power P of the heat source is completed so as to change the heat consumption rate Q of the heat source and realize the three-temperature-zone cycle control; the heat source heat rate Q is expressed by the formula (6), and P in this example is expressed by the formula (7):
Figure BDA0002601863420000171
Figure BDA0002601863420000172
wherein P is heat source power, V is heat source volume, Tppb1Temperature value, T, measured for the Domain Point probe ppb1iIs an input temperature value; when the heat sources are different, the formula (6) can be modified according to the actual heat generation condition.
Step S35: setting of boundary conditions in a solid heat transfer physical field:
setting natural convection heat exchange between the side wall of the base and air, if the base is a bare base, the natural convection heat exchange between the side wall of the base and the air does not need to be calculated according to formula (5), selecting external natural convection heat exchange in a COMSOL Multiphysics heat flux module, and typing in the wall height L (m) and the external temperature T into the vertical wallext(K) Absolute pressure PA(Pa) and selecting the fluid species to be air; if the heat insulating material exists on the side wall of the base, the natural convection heat exchange between the side wall and the air is negligible, so the temperature of the side wall of the heat insulating material is defined as room temperature T0Then the method is finished; the upper surface of the base is regarded as heat insulation because a constant temperature hot cover at about 104 ℃ can be placed in the actual reaction process of the PCR base to prevent the volatilization of the reagent;
for the partitioning of the grid: dividing a mesh by using a free tetrahedron with best geometric adaptability; because the hole part of the test tube in the PCR base is a link with a more complex shape, a free tetrahedral grid is firstly created for global drawing in order to save computing resources, and then the hole surface and the connection part of the test tube are refined through a refining function, so that the grid drawing is completed;
step S36: the configuration of a solver in a solid heat transfer physical field is as follows: selecting a transient solver, and setting the relative tolerance of the solver to be 0.01; selecting a generalized alpha by a time stepping method, selecting a middle-level by a step length, uniformly initializing in algebraic variable setting, selecting a backward Eulerian method, and finishing solver configuration, saving a file, wherein the format is stored as m format for preparing for subsequently calling a with Matlab interface;
step S37: finite element numerical simulation is carried out in a solid heat transfer physical field: performing numerical simulation according to the set finite element model to obtain the dynamic thermal field distribution of the PCR base in the heat exchange process, and calculating the steady state error e of the ppb1 temperature value curve of the domain point probessOvershoot sigma up-down, temperature rate vup、vdownAnd calculating an optimized cost performance coefficient xi according to the formula (2), and storing all results as output O1k{V1、V2、V3…Vn、essk、σk、vupk、vdownk、ξk、θk}{0<k≤n2︱k∈Z}。
In this embodiment, the specific content of step S4 is:
the m file using the with MATLAB is generated using COMSOL Multiphysics to the finite element model set up in step S35The formula (1) of the m file is a constraint condition, the formula (1) and the formula (2) of S25 are stop conditions, and the number of searching times is n2T is the definition of a set threshold constant; implementing variable V in (2) each time according to set search strategy1、V2、V3Is selected, the calculation result O in step S371k{V1、V2、V3…Vn、essk、σk、vupk、vdownk、ξk、θk}{0<k≤n2| k ∈ Z } output; judging whether the iteration stopping conditions (1) and (2) are met, if so, exiting the loop and entering the step S5; otherwise, according to the constraint of equation (1), the updated simulation parameters are input to step S3 to re-perform the finite element numerical simulation.
In this embodiment, the set search strategy includes a grid search, a particle swarm algorithm, a simulated annealing, or an ant colony algorithm. (the method and the flowchart 1 are described by genetic algorithm)
In this embodiment, the specific content of step S6 is: judging whether the stop conditions (1) and (2) are met, if so, stopping the calculation, and outputting an optimized set O { V }1、V2、V3…Vn、ess、σ、vup、vdownXi and theta, and carrying out optimization result processing to complete the optimization of the manufacturing parameters of the PCR base; otherwise, the update variable returns to step S3.
In this embodiment, the specific content of the optimization result processing is as follows:
based on the calculation result, all the output values O conforming to the formula (1) are calculated1k{V1、V2、V3…Vn、essk、σk、vupk、vdownk、ξk、θk}{0<k≤n2| k ∈ Z } input set O, according to θk{0＜k≤n2I k belongs to Z, reordering the set in a mode from large to small, and outputting a set O to submit to a user; according to the optimization principle customized by the user, in the set O, according to the actual requirement, namely when the cost performance is expected to be higher, the cost performance coefficient theta is taken as the main selection basis, and if the better temperature is expectedUniformity takes uniformity coefficient xi as the main basis for selection, and v is considered when a faster temperature rise and fall rate is expected in the same wayupk、vdownkE is considered in hopes of better temperature accuracyssk、σkAnd further screening to obtain an optimal manufacturing parameter result, and completing optimization.
Preferably, in the embodiment, a numerical simulation method is constructed through common finite element software COMSOL Multiphysics and a witmatlab interface thereof, an actual temperature control process of a finite element model of the PCR base is given by a transient analysis method, and manufacturing parameter optimization design is performed according to the result, so as to ensure that the PCR base can obtain optimal dynamic and static performances in an actual thermal cycle process. The embodiment can obtain optimized manufacturing parameters such as the optimal size of the heat-insulating material and the like under the condition of meeting the temperature performance index of the PCR base, and can be used for guiding the actual base processing, so that the good thermal uniformity is ensured on the premise of keeping the rapid temperature response in the thermal cycle process. To facilitate understanding of the method of the present invention, we use the optimization of 96-well PCR susceptor manufacturing parameters as an example to perform numerical solution using COMSOL Multiphysics and its WithMATLAB interface to obtain susceptor surrounding parameters meeting the design specification requirements. The invention can greatly save the time and material cost for the research and development of the novel PCR base.
The optimization was performed by taking a 96-well PCR base as an example, and the 3D model design engineering drawing thereof is shown in FIG. 6.
Initializing simulation conditions, wherein in the constraint condition (1), a is 0.2, b is 5%, and v isup＝2.5℃/s,vdownn2 ℃/s, xi is 0.8, λ is 1.2; let variable V1、V2、V3Is (aluminum, copper), (aluminum silicate cotton, polyethylene foam), (0,100, 1); the method comprises the following steps of (1) adopting a carbon fiber heating sheet as a heat source, and adopting a PID control algorithm as a control algorithm; let P in formula (2)1、P2、P30.5, 2 and 3 respectively, so that n in the stop condition2Is 1000, T is 10-6。
And thirdly, setting and numerical simulation of finite element initialization conditions are completed. Setting the initial condition of the finite element to 20 ℃ according to the method of step S2, wherein the P CR base hasThe finite element geometric model is shown in FIG. 7, the parameters of the introduced material are shown in Table 1, the ppb1 position of the domain point probe is shown in FIG. 3, the gridding example is shown in FIG. 8, the heat source power expression P is shown in formula (7), wherein T isppb1Temperature value, T, measured for the Domain Point probe ppb1iFor inputting temperature values, the three temperature zones in the PCR base model are respectively 94-55-72 ℃, so that P is defined in CO MSOL Multiphysics94、P55、P72In this embodiment, it is specified that 0-90s is 94 ℃ temperature region, 90-180s is 55 ℃ temperature region, and 180-240s is 72 ℃ temperature region, the power P input expression in the calculation of heat consumption rate Q of the heat source in solid heat transfer is shown in formula (8), and the formula is modified according to the actual heating condition when the selected heat source is changed. Wherein due to not being directly defined
Figure BDA0002601863420000211
It is defined as algebraic I and is referred to in formula (7), and then global differential and ordinary differential equations in COMSOL Multiphysics mathematical physical field are selected for defining I expression.
Figure BDA0002601863420000212
P＝P94*(t＞＝0&t＜＝90)+P55*(t＞90&t＜180)+P72*(t＞＝180&t＜＝240) (8)
TABLE 1 import materials parameter Table
Figure BDA0002601863420000213
And fourthly, finishing the setting of the optimization method. Generating a model m file, setting initial conditions, searching by taking a particle swarm algorithm as an example after stopping the conditions, and obtaining a variable V1、V2、V3Set as three particles, when result O1k(essk、σk、vupk、vdownk、ξk、θk){0<k≤n2If | k ∈ Z } satisfies constraint conditional expression (1), the optimization result is savedThe set O. In the method, the stopping condition is that the number of iterations exceeds n2Or the objective function F converges with decreasing gradient. And outputting the data set O to the user after the iteration is completed. The flow chart of the optimization method is shown in fig. 9. The thermal field diagram of the PCR base three temperature zone obtained after optimization is (aluminum, aluminum silicate cotton, 40mm) as shown in FIGS. 10-12, the dynamic temperature curve of the base measuring point, i.e. the ppb1 point position in FIG. 3, as shown in FIG. 13, and the steady state error e of the base can be calculated according to the method in step S2ss94＝0.117℃、ess55＝0.130℃、ess720.108 ℃ overshoot σ94＝3.8％、σ55＝4.5％、σ724.2%, and the heating and cooling rates are v94＝2.96℃/s、v55＝2.13℃/s、v942.64 ℃/s and xi is 0.74, which meets the index specified in advance, so the optimized data set meets the requirement.
Fifthly, optimizing result processing
And sequencing the data set O from large to small according to the manufacturing optimization weight coefficient theta, selecting the data set with the largest theta as an optimization result for processing, and storing the optimized data set O to facilitate subsequent experimental verification. And finishing the optimization of the manufacturing parameters.
Preferably, the thermal field of the PCR base in the whole cycle period can be monitored by using a finite element transient analysis method, and the optimization indexes of the manufacturing parameters of the manufactured base can be optimized according to the manufacturing parameters of the manufactured base while the actual conditions are greatly fitted, so that the optimized manufacturing parameters of the base can be obtained. And the temperature dynamic and static performance of the PCR base is improved. The working requirement is met, and the research and development cost of the novel PCR instrument is greatly reduced. By adding sensing and control into finite element numerical simulation, dynamic simulation closer to real temperature control is realized.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (7)

1. A PCR base manufacturing parameter optimization method based on finite element model numerical simulation is characterized in that: the method comprises the following steps:
step S1: and (3) designing a base 3D model: drawing a 3D model of the PCR base according to the number and the size of holes required by actual design;
step S2: initializing simulation conditions;
step S3: setting and simulating the initialization condition of the finite element model;
step S4: setting an optimization method, judging whether constraint conditions are met, if so, continuing to execute the step S5, otherwise, updating variables and returning to the step S3;
step S5: save the result O1k{0<k≤n2| k ∈ Z } to an optimization set O;
step S6: and (3) judging whether the stop condition expressions (1) and (2) are met, if so, outputting an optimization set O, processing an optimization result, and finishing the optimization of the manufacturing parameters of the PCR base, otherwise, updating the variables and returning to the step S3.
2. The method of claim 1, wherein the method comprises the steps of: the step S2 specifically includes the following steps:
step S21: initializing static and dynamic indexes of a PCR base as constraint conditions, wherein the steady-state error is essOvershoot is sigma, and heating rate is vupThe cooling rate is vdownThe temperature uniformity coefficient is xi;
steady state error essA, b, a rate of temperature increase vupC, cooling rate vdownD, temperature uniformity coefficient xi f; and the constraint conditions in the finite element simulation are as follows (1):
ess≤a、σ≤b、vup≥c、vdown≥d、ζ≤f (1)
wherein a, b, c, d and f all represent design index coefficients; the establishment of index coefficients is completed according to the performance of the existing PCR base: a is more than or equal to 0 and less than or equal to 0.5, b is more than or equal to 0 and less than or equal to 10 percent, v is more than or equal to 2 ℃/sup≤4℃/s,1.5℃/s≤vdownn≤3℃/s，0.4≤ξ≤1；
Step S22: initializing a manufacturing parameter to be optimized to a variable V1、V2、V3…VnWherein V is1Type of material for base, V2Type V of insulating material3Thickness of the insulating material, V4… and Vn refer to parameters including base size, test tube hole size, and whether the surface is provided with plum blossom holes which may influence the PCR base; setting the step length corresponding to the variable according to the selection of the actual material type;
step S23: the realization of sensing and the selection of a control method are carried out, the real-time temperature sensing is measured by adding a domain point probe ppb1 on the side wall of the PCR base as the input of the adopted control algorithm, and the control method can adopt PID control, fuzzy control, internal model control or Smith estimation control intelligent control algorithm as a system control scheme;
step S24: an optimized cost performance coefficient theta is formulated according to the actual manufacturing cost, the optimized cost performance coefficient theta is initialized, and the expression formula (2) defines a variable V according to the manufacturing cost1、V2、V3、…、VnIs given by a weight coefficient P1、P2、P3、…、Pn；
θ＝P1×V1+P2×V2+P3×V3+…+Pn×Vn(2)
Step S25: initializing a stopping condition and simulation searching times; the stop conditions were set as follows:
the number of operating iterations reaches the maximum number of iterations: n is1＞n2
The objective function F falls with gradient convergence: i.e. Fk-Fk-1＜T
Wherein n is1For this time, the number of iterations for optimizing the data of the manufacturing parameters, n2500-10000 are selected for the maximum data optimizing iteration times formulated according to the calculation resources in the actual optimization process; fkRepresents the target value obtained by k times of iterative calculation, T is a set threshold constant and is set to be 10-6。
3. The method of claim 2, wherein the method comprises the steps of: the specific content of step S3 is:
step S31: setting of the 3D model:
import the drawn bare base model into COMSOL Multiphysics which is C4Drawing three cuboids C in COMSOL Multiphysics1、C2、C3(ii) a Wherein C is1、C2、C3With bare base C introduced from the outside4Has a length, width and height of (a)1，b1，c1)、(a2，b2，c2)、(a3，b3，c3)、(a4，b4，c4) (ii) a Let C1、C2Coordinate of center point (x)1，y1，z1)、(x2，y2，z2) And C4Center point coordinate (x)4，y4，z4) Are in agreement with C3The coordinate of the center point is (x)4,，y4，z4+0.5c3+0.5c4) And the relation is shown as formula (3):
a1≥a2＝a4，b1≥b2＝b4，c1＝c2＝c4，(a1-a2)＝(b1-b2) (3)
wherein (a)3，b3，c3) Set according to the size of the selected heat source, so 2 (a)1-a2) Is the thickness of the thermal insulation material; let C1And C2Form a difference set C5Namely a heat insulating material coated on the periphery of the base and a pair C3、C4、C5Constructing a united body to form a PCR base finite element geometric model of which the periphery of a bare base is wrapped by a heat-insulating material and the bottom of which is provided with a heat source; wherein, the C3Represents a heat source, C4Representing a bare base, C5Represents a heat insulating material;
step S32: analyzing the PCR base heat transfer model, selecting a physical field capable of realizing the temperature field characteristic of the PCR base in a COMSOL Multiphy sics heat transfer module to carry out finite element numerical simulation:
because the PCR base is complex in shape and has no internal heat source, the heat conduction problem is described by a heat conduction differential equation under the conditions of a stable state and no internal heat source in a Cartesian coordinate system, as shown in a formula (4):
Figure FDA0002601863410000041
the base steady state thermal analysis boundary conditions include: the first type boundary condition of the bottom surface of the base and the third type boundary condition of the convection heat exchange of the side wall of the base; because the bottom surface of the base is contacted with the heat source, when the temperature rises/falls to a constant value, the contact surface of the bottom surface of the base and the heat source keeps constant temperature, the side wall of the base and air have natural convection heat exchange, and the boundary condition is shown as the formula (5):
Figure FDA0002601863410000042
wherein, twIs the base temperature, tfIs the ambient air temperature, h is the convective heat transfer coefficient, λ0Is the heat conduction coefficient, and n is the normal direction of the side wall of the base; the temperature control of the PCR base is to control the heating power P of a heat source by taking the heat source heating value P arranged at the bottom of the PCR base and the base side wall measuring point ppb1 as input and transmit the heat to the PCR base to complete temperature change circulation; analyzing the temperature field of the PCR base to obtain a solid heat transfer physical field in a heat transfer module in COMSOL Multiphysics to complete finite element numerical simulation;
step S33: completing the material types and parameter settings of the base, the heat source and the heat insulation material in a solid heat transfer physical field;
directly searching or self-defining a hollow material by using a built-in material library in COMSOL Multiphysics, and needing to enter constant-pressure heat capacity C of the materialp[J/(kg·K)]Thermal conductivity lambda0[W/(m·K)]And density rho (kg/m)3)；
Step S34: setting a probe and a heat source heat rate in a solid heat transfer physical field:
on the PCR baseA temperature sensor is arranged on the side wall, and a one-domain point probe ppb is added at the central position of the side wall1(ii) a According to the selected control algorithm, including alternative PID control, fuzzy control, internal model control or Smith predictive control intelligent control algorithm, the control of the heating power P of the heat source is completed so as to change the heat consumption rate Q of the heat source and realize the three-temperature-zone cycle control; the heat source heat rate Q expression is shown in formula (6):
Figure FDA0002601863410000051
wherein P is the heat source power, and V is the heat source volume;
step S35: setting of boundary conditions in a solid heat transfer physical field:
setting natural convection heat exchange between the side wall of the base and air, if the base is a bare base, the natural convection heat exchange between the side wall of the base and the air does not need to be calculated according to formula (5), selecting external natural convection heat exchange in a COMSOL Multiphysics heat flux module, and typing in the wall height L (m) and the external temperature T into the vertical wallext(K) Absolute pressure PA(Pa) and selecting the fluid species to be air; if the heat insulating material exists on the side wall of the base, the natural convection heat exchange between the side wall and the air is negligible, so the temperature of the side wall of the heat insulating material is defined as room temperature T0Then the method is finished; the upper surface of the base is regarded as heat insulation because a constant temperature hot cover at about 104 ℃ can be placed in the actual reaction process of the PCR base to prevent the volatilization of the reagent;
for the partitioning of the grid: dividing a mesh by using a free tetrahedron with best geometric adaptability; because the hole part of the test tube in the PCR base is a link with a more complex shape, a free tetrahedral grid is firstly created for global drawing in order to save computing resources, and then the hole surface and the connection part of the test tube are refined through a refining function, so that the grid drawing is completed;
step S36: the configuration of a solver in a solid heat transfer physical field is as follows: selecting a transient solver, and setting the relative tolerance of the solver to be 0.01; selecting a generalized alpha by a time stepping method, selecting a middle-level by a step length, uniformly initializing in algebraic variable setting, selecting a backward Eulerian method, and finishing solver configuration, saving a file, wherein the format is stored as m format for preparing for subsequently calling a with Matlab interface;
step S37: finite element numerical simulation is carried out in a solid heat transfer physical field: performing numerical simulation according to the set finite element model to obtain the dynamic thermal field distribution of the PCR base in the heat exchange process, and calculating the steady state error e of the ppb1 temperature value curve of the domain point probessOvershoot σ, rise and fall rate vup、vdown(ii) a And calculating an optimized cost performance coefficient xi according to the formula (2), and storing all results as output O1k{V1、V2、V3、…、Vn、essk、σk、vupk、vdownk、ξk、θk}{0<k≤n2︱k∈Z}。
4. The method of claim 3, wherein the method comprises the steps of: the specific content of step S4 is:
generating the finite element model set in the step S35 by utilizing COMSOL Multiphysics, wherein the m file uses a WithMATLAB interface to carry out the formula (1) of the m file as a constraint condition, the formula (1) and the formula (2) of the S25 as stop conditions, and the searching times are n2T is the definition of a set threshold constant; implementing variable V in (2) each time according to set search strategy1、V2、V3Is selected, the calculation result O in step S371k{V1、V2、V3、…、Vn、essk、σk、vupk、vdownk、ξk、θk}{0<k≤n2| k ∈ Z } output; judging whether the iteration stopping conditions (1) and (2) are met, if so, exiting the loop and entering the step S5; otherwise, according to the constraint of equation (1), the updated simulation parameters are input to step S3 to re-perform the finite element numerical simulation.
5. The method of claim 4, wherein the method comprises the steps of: the set search strategy comprises grid search, particle swarm algorithm, simulated annealing or ant colony algorithm.
6. The method of claim 2, wherein the method comprises the steps of: the specific content of step S6 is: judging whether the stop conditions (1) and (2) are met, if so, stopping the calculation, and outputting an optimized set O { V }1、V2、V3…Vn、ess、σ、vup、vdownXi and theta, and carrying out optimization result processing to complete the optimization of the manufacturing parameters of the PCR base; otherwise, the update variable returns to step S3.
7. The method of claim 5, wherein the method comprises the steps of: the specific content of the optimization result processing is as follows:
based on the calculation result, all the output values O conforming to the formula (1) are calculated1k{V1、V2、V3…Vn、essk、σk、vupk、vdownk、ξk、θk}{0<k≤n2| k ∈ Z } input set O, according to θk{0＜k≤n2I k belongs to Z, reordering the set in a mode from large to small, and outputting a set O to submit to a user; and according to an optimization principle customized by a user, selecting the most reasonable manufacturing parameters according to design requirements in the set O, and completing optimization.
When the cost performance is expected to be higher, the cost performance coefficient theta is taken as the main basis, if better temperature uniformity is expected, the uniformity coefficient xi is taken as the main basis, and similarly, if a faster temperature rise and fall rate is expected, v is consideredupk、vdownkPreference is given to e in the hope of better temperature accuracyssσ is minimized.
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CN117272715A (en) * 2023-08-14 2023-12-22 中国人民解放军63723部队 System thermal insulation performance simulation test method under severe cold condition

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