CN114896747B - Microchannel structure optimization design method based on sensitivity calculation - Google Patents
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Abstract
The invention discloses an optimization design method of micro-channel structural parameters based on sensitivity calculation, which is mainly applied to optimizing a channel size structure and solves the problem that an accompanying method cannot be directly applied to the field of machine learning when an objective function and parameters are in a hidden function relation. The invention combines the reverse automatic differential method in the machine learning field with the accompanying method, and can directly utilize the reverse automatic differential method to calculate the sensitivity and utilize the machine learning method to optimize the flow channel when the objective function and the input variable are in the hidden function relation.
Description
Technical Field
The invention relates to the field of optimized design of flow channel structures, in particular to an optimized design method of micro-flow channel structural parameters based on sensitivity calculation.
Background
Sensitivity analysis is a method for researching and analyzing the sensitivity degree of the state or output change of a system (or model) to the change of system parameters or surrounding conditions, is an effective tool for quantifying the influence of input variables on output response in a complex system, can determine which parameters have larger influence on the system or model through sensitivity analysis, and can solve the optimization problem of partial differential equation constraint.
According to patent CN201510464147.0, the sensitivity analysis method comprises: limited differential, concomitant, perturbation, direct differential, and the like. The adjoint method only needs to solve one set of control equations and one set of adjoint equations with the same specification in the process of adopting the adjoint variable method no matter how many variables are designed, the calculated amount is only equal to twice of that of a single control equation, and the adjoint method has remarkable advantages in the face of the problem of huge variable number. However, when the objective function and the parameter are in a hidden function relationship, the conventional accompanying method cannot be directly applied to the field of machine learning.
In the flow channel optimization engineering, in order to minimize the flow resistance thereof, it is necessary to optimize the flow channel size structure according to the sensitivity of the objective function. However, in the application of channel optimization, the objective function and the input variable are in a hidden function relationship, and the channel cannot be optimized by directly using a machine learning method.
Disclosure of Invention
The invention overcomes the defects of the prior art and provides a microchannel structure optimization design method based on sensitivity calculation.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a microchannel structure optimization design method based on sensitivity calculation comprises the following steps:
Step 1: determining a runner design variable gamma and setting an initial value;
gamma is 0-1, 0 represents solid, 1 represents fluid;
Step 2: determining the positions and the sizes of a calculation domain, a liquid inlet and a liquid outlet to be solved, and dividing grids in the X direction and the Y direction, wherein the grids are divided into Nelx multiplied by Nely finite element units;
Nelx: number of units in X direction;
nely: the number of units in the Y direction;
Step 3: determining a mathematical model F (u (gamma), gamma) =0 of the model about the design variable gamma, and determining a boundary condition G (x) =0 of the mathematical model and a runner volume constraint condition ≡ Ωγ≤V0;
the boundary condition G (x) =0 includes: speed, pressure, flow information of inlet and outlet;
The flow channel volume constraint condition is ≡ Ωγ≤V0:
Omega is the design field;
v 0 is the flow channel volume;
The mathematical model F (u (γ), γ) =0 is a modified form of the Navier-Stokes equation:
wherein:
ρ is the density of the liquid in the flow channel;
u is a velocity vector;
p is pressure;
μ is hydrodynamic viscosity;
alpha (gamma) is the reverse permeability in the porous medium and is determined by the following equation:
wherein:
Alpha min is the minimum value of reverse osmosis rate, and 0Pa.s/m 2 is taken;
Alpha max is the maximum value of reverse osmosis rate, taking 1×10 4～1×107Pa.s/m2;
q is a penalty parameter, and a constant is taken, and the range is 0.01-1;
Step 4: f (u (γ), γ) =0 is changed to its variant form;
step 5: solving a variational equation by using a finite element method;
Step 6: according to the velocity field obtained by solving, solving an objective function J;
The objective function J is formed by two parts, j=j 1+J2,J1 is one of a fluid inlet and outlet differential pressure function, a countercurrent and forward flow differential pressure ratio function and a flow channel flow viscosity dissipation function, and J 2 is a volume constraint function.
Step 7: solving the sensitivity of the objective function on the design variable gamma by using a reverse automatic differentiation method;
Step 8: judging whether a convergence condition is reached, if so, ending optimization, and outputting a flow channel optimization result; if not, updating the design variable gamma by using the neural network according to the sensitivity, jumping to the step 5 until the convergence condition is reached, and outputting the flow channel optimization result.
The further technical scheme is as follows: the variation of the momentum equation described in step 4 is:
Wherein: v and s are test functions of u and P, respectively, the test functions being defined as continuous functions of coordinates inside the cell;
u is a velocity vector;
p is the pressure.
The further technical scheme is that the function selectable by J 1 in the step 6 is specifically:
Fluid inlet-outlet differential pressure function: j=p in-Pout
In the middle of
P in is the flow channel inlet pressure;
p out is the flow channel outlet pressure;
reverse flow to forward flow differential pressure ratio function:
wherein:
Δp r is the inlet and outlet pressure differential for the flow path counter-current flow;
Δp f is the inlet and outlet pressure differential for the flow path to flow in the forward direction;
flow viscous dissipation function of flow channel:
wherein:
μ is hydrodynamic viscosity;
Omega is the design field.
The volume constraint function J 2 is:
wherein:
w is a constant in the range of 0.0001-10000;
n is the number of finite element units;
gamma is a design variable;
V 0 is the flow channel volume.
The further technical scheme is as follows: and (8) the convergence condition is the relative variation of the objective function value or the number of iterations or the number of intermediate values of the design variables.
The invention calculates the sensitivity of the micro-channel optimization objective function to the design variable by using a reverse automatic differential method, and because the objective function and the design variable are difficult to solve by a general method with a hidden function relationship, the method which can be solved, such as a concomitant method, cannot be combined with machine learning, and the like, the invention has the advantages that the sensitivity of the micro-channel optimization objective function to the design variable can be automatically solved, and the micro-channel structure is optimized by using a machine learning method.
Drawings
Fig. 1 is a schematic flow chart of a microchannel structure optimization design method based on sensitivity calculation.
Fig. 2 is a schematic diagram of a microchannel design domain according to an embodiment of the present invention.
FIG. 3 shows an optimized flow channel according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Referring to fig. 1, a method for optimizing a micro-channel structure based on sensitivity calculation specifically includes the following steps:
Step 1: determining a runner design variable gamma and setting an initial value;
gamma is 0-1, 0 represents solid, 1 represents fluid;
The design variable is a calculation variable of calculation sensitivity, and the initial value of the design variable gamma is 0.5.
Step 2: determining a calculation domain to be solved, determining the positions and the sizes of a liquid inlet and a liquid outlet, and dividing a grid into Nelx multiplied by Nely finite element units;
Nelx: number of units in X direction;
nely: the number of units in the Y direction;
referring to FIG. 2, a microchannel design field is selected to be 75mm long and 50mm wide, the grid is divided into 75X 50 units, two selected liquid inlets are positioned on the left short side of the design field, the distance from the end point of the short side is 12.5mm, 37.5mm, and the inlet width is 8mm; the selected liquid outlet was 8mm wide at the mid-point of the right short side of the design field.
Step 3: determining a mathematical model F (u (gamma), gamma) =0 of the model about the design variable gamma, and determining a boundary condition G (x) =0 of the mathematical model and a runner volume constraint condition ≡ Ωγ≤V0;
The boundary condition is the inlet velocity: u=0.001 m/s;
Outlet pressure: p=0 Pa;
the flow channel volume constraint conditions are as follows: v 0 = 0.3.
The mathematical model F (u (γ), γ) =0 is a modified form of the Navier-Stokes equation:
wherein:
ρ is the density ρ=1000 kg/m 3,
U is a velocity vector;
p is pressure;
μ is hydrodynamic viscosity, taking μ=0.001pa.s;
alpha (gamma) is the reverse permeability in the porous medium and is determined by the following equation:
Alpha min is the minimum value of reverse osmosis rate, and 0Pa.s/m 2 is taken;
Alpha max is the maximum value of reverse osmosis rate, the value range is 1×10 4～1×107Pa.s/m2,, and 1×10 5Pa.s/m2 is adopted in the embodiment;
q is a penalty parameter, the value range is 0.01-1, and 0.1 is taken in the embodiment;
the flow channel volume constraint conditions are as follows: v 0 = 0.3.
Step 4: change F (u (γ), γ) =0 to the variation form
The mathematical model F (u (γ), γ) =0 is changed into a variation form, and the variation form of the momentum equation is:
wherein: v and s are test functions of u and P, respectively, which are defined as continuous functions of coordinates inside the cell.
U is a velocity vector;
p is the pressure.
Step 5: solving a variational equation by using a finite element method;
and solving a variational equation by using a finite element method to obtain a speed vector u.
Step6: according to the velocity field u obtained by solving, solving an objective function J;
The objective function J consists of two parts, J=J 1+J2, wherein J 1 is a runner flow viscous dissipation function, the obtained velocity field u is brought into the runner flow viscous dissipation function, and J 2 is a volume constraint function;
Summing the resulting objective function J:
wherein:
μ is hydrodynamic viscosity;
Omega is the design field;
w is a constant, the value range is 0.0001-10000, 10 is taken in the embodiment;
n is the number of finite element units, and the value is 3750;
gamma is a design variable;
V 0 is the flow channel volume, and the value is 0.3.
Step 7: solving the gamma sensitivity of the objective function with respect to the design variable by using the inverse automatic differentiation method
Performing inverse automatic differentiation on the objective function J by using an open source code Jax Fenics, and solving the gradient of the objective function relative to the design variable gamma, wherein the solved gradient is the sensitivity of the objective function J (u (gamma), gamma) relative to the design variable gamma;
Step 8: judging whether a convergence condition is reached, and setting the convergence condition as whether the relative variation of the objective function J is smaller than 0.001 or the iteration number reaches 1800. In this embodiment, after the first iteration of the program, the relative variation of the objective function J is 0.58, the convergence condition is not reached, the design variable γ is updated by using the neural network according to the sensitivity, and the process goes to step 5 to continue the calculation. The program is run for 1200 times in total, the relative change amount of the final objective function J is 0.0009, the program is converged, the calculation is finished, and the flow channel optimization result is output. In this embodiment, the number of layers of the neural network is 8, the number of nodes in each layer is 20, and the update optimization method of the neural network is Adam.
After reaching the convergence condition, an optimized microchannel structure is obtained, see fig. 3. The sensitivity of the micro-channel optimization objective function to the design variable can be automatically solved, so that the channel optimization result can be obtained by using a machine learning method.
Although the application has been described herein with reference to illustrative embodiments thereof, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within the scope and spirit of the principles of this disclosure. More specifically, various modifications and improvements may be made to the component parts and/or arrangements of the subject combination layout within the scope of the disclosure. In addition to variations and modifications in the component parts and/or arrangements, other uses will be apparent to those skilled in the art.
Claims (3)
1. The microchannel structure optimization design method based on sensitivity calculation is characterized by comprising the following steps:
Step 1: determining a runner design variable gamma and setting an initial value;
gamma is 0-1, 0 represents solid, 1 represents fluid;
step 2: determining the positions and the sizes of a calculation domain, a liquid inlet and a liquid outlet to be solved, and dividing a grid into Nelx multiplied by Nely finite element units;
Nelx: number of units in X direction;
nely: the number of units in the Y direction;
Step 3: determining a mathematical model F (u (gamma), gamma) =0 of the model about the design variable gamma, and determining a boundary condition G (x) =0 of the mathematical model and a runner volume constraint condition ≡ Ωγ≤V0;
the boundary condition G (x) =0 includes: speed, pressure, flow information of inlet and outlet;
The flow channel volume constraint condition is ≡ Ωγ≤V0:
Omega is the design field;
v 0 is the flow channel volume;
The mathematical model F (u (γ), γ) =0 is a modified form of the Navier-Stokes equation:
wherein:
ρ is the density of the liquid in the flow channel;
u is a velocity vector;
p is pressure;
μ is hydrodynamic viscosity;
alpha (gamma) is the reverse permeability in the porous medium and is determined by the following equation:
wherein:
Alpha min is the minimum value of reverse osmosis rate, and 0Pa.s/m 2 is taken;
Alpha max is the maximum value of reverse osmosis rate, taking 1×10 4～1×107Pa.s/m2;
q is a penalty parameter, and a constant is taken, and the range is 0.01-1;
step 4: changing the mathematical model F (u (γ), γ) =0 of the design variable γ into a variation form;
the variational form equation is:
Wherein: v and s are test functions of u and P, respectively, the test functions being defined as continuous functions of coordinates inside the cell;
u is a velocity vector;
p is pressure;
step 5: solving the variational form equation by using a finite element method;
step6: according to the velocity field u obtained by solving, solving an objective function J;
The objective function J consists of two parts, wherein J=J 1+J2,J1 is one of a fluid inlet and outlet differential pressure function, a countercurrent and forward flow differential pressure ratio function and a flow channel flow viscosity dissipation function, and J 2 is a volume constraint function;
step 7: solving the sensitivity of the objective function on the design variable gamma by using a reverse automatic differentiation method;
Step 8: judging whether a convergence condition is reached, if so, ending optimization, and outputting a flow channel optimization result; if not, updating the design variable gamma by using the neural network according to the sensitivity, jumping to the step 5 until the convergence condition is reached, and outputting the flow channel optimization result.
2. The optimization design method of the micro-channel structure based on sensitivity calculation according to claim 1, wherein the function selectable by J 1 in the step 6 is specifically:
Fluid inlet-outlet differential pressure function: j 1＝Pin-Pout
Wherein:
p in is: flow channel inlet pressure;
p out is: flow channel outlet pressure;
reverse flow to forward flow differential pressure ratio function:
wherein:
Δp r is the inlet and outlet pressure differential for the flow path counter-current flow;
Δp f is the inlet and outlet pressure differential for the flow path to flow in the forward direction;
flow viscous dissipation function of flow channel:
wherein:
μ is hydrodynamic viscosity;
Omega is the design field;
the volume constraint function J 2 is:
wherein:
w is a constant in the range of 0.0001-10000;
n is the number of finite element units;
gamma is a design variable;
V 0 is the flow channel volume.
3. The optimization design method of the micro-channel structure based on the sensitivity calculation according to claim 1, wherein the convergence condition in the step 8 is a relative variation amount of the objective function value or the number of iterations or the number of intermediate design variables.
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