CN113672850A - Refrigeration system construction method based on refrigerant general vapor pressure equation - Google Patents

Refrigeration system construction method based on refrigerant general vapor pressure equation Download PDF

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CN113672850A
CN113672850A CN202111121376.4A CN202111121376A CN113672850A CN 113672850 A CN113672850 A CN 113672850A CN 202111121376 A CN202111121376 A CN 202111121376A CN 113672850 A CN113672850 A CN 113672850A
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equation
vapor pressure
refrigerant
objective function
equations
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CN113672850B (en
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尹建国
可晋军
赵贯甲
马素霞
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Taiyuan University of Technology
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    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/12—Computing arrangements based on biological models using genetic models
    • G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
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    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B30/00—Energy efficient heating, ventilation or air conditioning [HVAC]
    • Y02B30/70—Efficient control or regulation technologies, e.g. for control of refrigerant flow, motor or heating

Abstract

The invention relates to a construction method of a refrigeration system based on a refrigerant general vapor pressure equation, and relates to the optimization calculation of the form and parameters of a high-precision vapor pressure equation of an environment-friendly substitute refrigerant in the fields of refrigeration air conditioners, heat pumps, chemical engineering and the like, so as to solve the problem that the high-precision equation is obtained by a novel refrigerant on the basis of vapor pressure experimental data. The method comprises the following steps: establishing a novel refrigerant vapor pressure equation term library and determining the number N of equation terms to be optimized; establishing an optimization algorithm objective function; initializing an equation set; carrying out equation set variation; performing regression analysis; and (5) judging the iteration end. The invention enhances the ability of the original biological evolution optimization algorithm to jump out the local optimal solution by changing the variation rule; by adopting new control parameters, the optimization result of the genetic algorithm is retained to the maximum extent, and the algorithm searching efficiency is improved.

Description

Refrigeration system construction method based on refrigerant general vapor pressure equation
Technical Field
The invention relates to the technical field of refrigeration air conditioners, heat pumps and chemical engineering, in particular to a method for constructing a refrigeration system based on a refrigerant general vapor pressure equation.
Background
The saturated vapor pressure is one of important physical and chemical properties of substances, is basic data for system design and process parameter optimization in the fields of refrigeration air conditioners, heat pumps, chemical engineering and the like, and is also an important parameter for screening of environment-friendly alternative refrigeration working media. The vapor pressure equation plays an important role in theoretical research and engineering application of thermodynamic properties such as a fluid state equation, a gas-liquid phase change law and the like. Wagner obtains two widely used 4-parameter vapor pressure equations, Wagner2.5,5 and Wagner3,6, by performing optimization analysis on general equations based on a term library. The general vapor pressure equation form based on the term library is as follows:
Figure BDA0003277323550000011
the equations of Wagner2.5,5 and Wagner3,6 can reproduce experimental data of most substances in a whole area from a three-phase point to a critical point, and vapor pressure equations of different forms can be constructed by changing index values and equation terms for different substances so as to improve the reproduction accuracy of the experimental data.
In order to select the optimal combination term from the term library and keep the equation concise as much as possible, a reasonable optimization algorithm is needed for analysis and calculation. Setzmann and Wagner synthesize respective advantages of a stepwise regression analysis method and a biological evolution algorithm on the basis of earlier-stage work, develop a more advanced OPTIM algorithm, and can simultaneously optimize the number and the structure of terms of an equation. But the OPTIM algorithm is easy to have the problems of premature convergence and slow convergence speed in the biological evolution process. Through optimization regression analysis, Chinese academy Lihui accelerates the convergence speed of the algorithm, but does not improve the global search capability.
Disclosure of Invention
The invention provides a method for constructing a refrigeration system based on a refrigerant general vapor pressure equation, which is a new improved algorithm obtained by changing variation rules and using new control parameters on the basis of the existing algorithm, effectively avoids the premature convergence problem in the optimization process, and greatly improves the convergence speed and precision of the algorithm.
The invention provides a method for constructing a refrigeration system based on a universal vapor pressure equation of a refrigerant, which comprises the following steps:
the method comprises the following steps: establishing a corresponding novel refrigerant vapor pressure equation item library aiming at a novel refrigerant adopted by a refrigeration system to be constructed, and determining the number N of equation items to be optimized;
step two: establishing an optimization algorithm objective function;
step three: initializing a new refrigerant vapor pressure equation set: randomly combining an equation with N terms from a new refrigerant vapor pressure equation term library, repeating NS times, selecting the equation with the minimum objective function, and repeating the process to obtain an initial equation set consisting of NP equations;
step four: the vapor pressure equation system of the novel refrigerant is changed:
(1) randomly selecting a term p in the initial equation setn,oldAnd random term p in the item library remainder termnExchanging to generate a new equation;
(2) repeating the item changing process NM times for each initial equation, selecting the equation with the minimum objective function value, and if the objective function value is smaller than the objective function of the original equation, replacing the original equation with a new equation, otherwise, keeping the original equation unchanged;
(3) repeatedly executing the processes for NP equations to obtain a new variation equation set;
step five: regression analysis: selecting NR +1 equations with the minimum target function in the NP equations, finding out terms of NR +1 times, NR times and NR-1, …, 2 times which simultaneously appear in the NP equations, taking the terms as pre-options of regression analysis, respectively carrying out the regression analysis to generate NR regression equations, replacing the NR equations in the initial equation set, and forming a new generation equation set;
step six: if the NP equations are the same or reach the preset iteration times, the algorithm is ended to obtain a novel refrigerant vapor pressure equation, the refrigeration parameters of the refrigerant are determined according to the novel refrigerant vapor pressure equation, and a refrigeration system is constructed according to the refrigeration parameters of the refrigerant.
Wherein, in the step of establishing the optimization algorithm objective function,
the refrigerant vapor pressure equation is of the general form:
Figure BDA0003277323550000031
wherein p iscalCalculated for the refrigerant vapor pressure equation, T is the thermodynamic temperature, pcAnd TcRespectively critical pressure and temperature of the refrigerant, I is the number of equation terms, aiIs a parameter to be optimized;
based on the vapor pressure equation, an equal-weight nonlinear objective function is established as follows:
Figure BDA0003277323550000032
wherein p isexpThe refrigerant vapor pressure experimental value is shown, and n is the number of vapor pressure data points;
establishing a linear objective function with weights as follows:
Figure BDA0003277323550000033
wherein the variance σmCalculating by a Gaussian error transfer formula;
or other forms of objective function that establish the accuracy of the data reproduction of the reaction equation.
Wherein, the convergence speed and precision of the algorithm are optimized by modifying the control parameters NP, NR and NS.
In the step of modifying the control parameters, the parameter modification mode is as follows:
3≤NP≤9，NR＝1，150≤NS≤300。
different from the prior art, the method for constructing the refrigeration system based on the refrigerant general vapor pressure equation aims at the problems that the existing optimization algorithm is easy to premature convergence and has low convergence speed, and enhances the capability of jumping out of a local optimal solution of the original biological evolution optimization algorithm by changing the variation rule of the optimization algorithm; by adopting new control parameters, the optimization result of the genetic algorithm is retained to the maximum extent, and the algorithm searching efficiency is improved.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart illustrating the absence of pre-options when using the conventional OPTIM algorithm in an exemplary embodiment.
FIG. 2 is a diagram illustrating the inability to obtain an optimal solution in an embodiment using the prior OPTIM algorithm.
Fig. 3 and 4 are comparison graphs of the calculation efficiency of the optimization method of the invention and the literature algorithm in the specific embodiment respectively.
FIG. 5 is a graph of the deviation of various terms of vapor pressure equations and experimental data obtained by the optimization method of the present invention in a specific example.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
The invention provides a method for constructing a refrigerating system based on a universal vapor pressure equation of a refrigerant, which comprises the following steps:
the method comprises the following steps: establishing a novel refrigerant vapor pressure equation item library, wherein the item library comprises 21 items, and determining the item number N of an equation to be optimized;
step two: establishing an optimization algorithm objective function:
the novel refrigerant vapor pressure equation has the general form:
Figure BDA0003277323550000041
wherein p iscalCalculated for the refrigerant vapor pressure equation, T is the thermodynamic temperature, pcAnd TcRespectively critical pressure and temperature of the refrigerant, I is the number of equation terms, aiAre the parameters to be optimized. Based on the vapor pressure equation, an equal-weight nonlinear objective function is established as follows:
Figure BDA0003277323550000042
wherein p isexpAnd n is the number of points of the vapor pressure data.
Step three: initializing a system of equations: randomly combining an equation with N terms from the term library, repeating NS times, selecting the equation with the minimum target function, and repeating the process to obtain an initial equation set consisting of NP equations;
the values of NP and NS are different according to N and I, and specifically as follows:
(1) when N is less than or equal to 10 and I is less than or equal to 200:
NP: the value is 8, NS: the value is 250.
(2) When N is less than or equal to 30 and I is less than or equal to 400:
NP: the value is 7, NS: the value is 250.
(3) When N is less than or equal to 60 and I is less than or equal to 700:
NP: the value is 6, NS: the value is 250.
Step four: variation of the equation set: (1) randomly selecting a term p in the initial equationn,oldAnd random term p in the item library remainder termnThe exchange is performed to generate a new equation. (2) And repeating the item changing process NM times for each initial equation, selecting the equation with the minimum objective function value, and if the objective function is smaller than the objective function of the original equation, replacing the original equation with a new equation, otherwise, keeping the original equation unchanged. (3) Repeatedly executing the processes for NP equations to obtain a new variation equation set;
step five: regression analysis: selecting NR +1 equations with the minimum target function in NP equations, finding out terms of NR +1 times, NR times and NR-1, …, 2 times which simultaneously appear in the NP equations, using the terms as pre-options of regression analysis, respectively carrying out regression analysis to generate NR regression equations, replacing NR equations in an initial equation set to form a new generation equation set, wherein the NR value is 1;
step six: if the NP equations are the same or reach the preset iteration times, the algorithm is ended to obtain a novel refrigerant vapor pressure equation, the refrigeration parameters of the refrigerant are determined according to the novel refrigerant vapor pressure equation, and a refrigeration system is constructed according to the refrigeration parameters of the refrigerant.
In this embodiment, when the OPTIM algorithm is used to fit the vapor pressure equation of the novel refrigerant, it is found that there may be no pre-selected item when performing regression analysis on the equation set, as shown in fig. 1, which may result in loss of the optimization result of the biological evolution algorithm, thereby reducing the convergence rate of the algorithm and increasing the calculation time. As can be seen from fig. 1, no term appearing 3 times is found in the 4 equations with the minimum objective function in the varied equation set, so that the second equation has no pre-selection during regression analysis, and needs to be searched again to determine the regression equation, thereby reducing the algorithm efficiency. Aiming at the situation, the Lihuya adopts a strategy of deleting a regression equation without pre-options and changing related parameters, so that the aim of improving the algorithm searching efficiency is fulfilled, but the problem that the number of the pre-selected items exceeds the maximum number of the items of the equation may occur in the actual optimization process.
In addition, in the OPTIM optimization method, the number of equation terms exchanged by the biological evolution optimization algorithm in the mutation operation is large, so that the mutation rate of each generation is large, the algorithm is degenerated into random search, the search capability is reduced, the early-maturing and convergence condition of the algorithm occurs, and the method is particularly obvious for the condition of large number of equation terms. As shown in FIG. 2, it can be seen that the final variation result has reached the convergence condition of "NP equations are all the same" required by the algorithm, but the "optimal solution" given by the algorithm is (2, 3, 5, 7), and the corresponding objective function value is 5.75 × 10-7And the actual optimal solution of the equation is (2, 3, 4, 5), corresponding to an objective function value of 5.55 × 10-7. The analysis shows that the algorithm 'optimal solution' and the actual optimal solutionOnly 1 item is different between the two items, the actual optimal solution can not be achieved through item changing operation, and the problem of premature convergence occurs.
The improved optimization algorithm of the invention does not have the problems, and the optimization efficiency comparison of different algorithms is respectively shown in fig. 3 and fig. 4, wherein fig. 3 is the rule that the calculation time of each algorithm changes along with the number of terms of the equation when the number of experimental data points is 75, and fig. 4 is the rule that the calculation time of each algorithm changes along with the number of experimental data points when the number of terms of the equation is 5. The poor stability of the OPTIM algorithm is easily found from the graph, the Lei-Hui-ya algorithm is improved on the basis of the OPTIM algorithm, the convergence rate of the optimization algorithm is obviously superior to that of other 2 algorithms, and the optimization algorithm has obvious advantages in stability.
Table 1 shows the calculation time of the algorithm when the number of experimental data points ranges from 35 to 236 and the number of equation terms N ranges from 4 to 8. From the results in the table, it can be found that when the optimization algorithm is adopted, the increase of the number of the experimental data points needs to consume more computing resources than the increase of the number of the equation terms, but the algorithm can still keep higher computing efficiency.
Figure BDA0003277323550000061
TABLE 1 optimization algorithm calculation time of the invention
The data reproduction accuracy of the optimization results of the steam pressure equations with different terms is shown in table 2 and fig. 5, and the results in the table show that for 3-7 steam pressure equations, the optimal terms are not included, that is, the importance among the terms in the term library is coupled and related, so that the optimization algorithm is particularly important in equation fitting. In addition, the optimal terms 2 and 3, namely the exponential terms of 1 and 1.5 times in the equation, are contained in all the equations, which are also completely consistent with the equations of Wagner2.5,5 and Wagner3,6, and show the important roles of the two terms in the vapor pressure equation. In addition, the 3 steam pressure equations and the Wagner equation have equivalent fitting accuracy, the equation calculation accuracy can be improved by increasing the number of the equation terms, the deviation value of the 5 steam pressure equations is minimum, the fitting accuracy is improved by 10.2% compared with the Wagner2.5 and 5 type equations, and then the equation terms are increased without great improvement on the data reproduction accuracy.
Figure BDA0003277323550000071
TABLE 2 fitting results and deviations of the general vapor pressure equation and Wagner equation
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (4)

1. A method for constructing a refrigeration system based on a universal vapor pressure equation of a refrigerant is characterized by comprising the following steps:
the method comprises the following steps: establishing a corresponding novel refrigerant vapor pressure equation item library aiming at a novel refrigerant adopted by a refrigeration system to be constructed, and determining the number N of equation items to be optimized;
step two: establishing an optimization algorithm objective function;
step three: initializing a new refrigerant vapor pressure equation set: randomly combining an equation with N terms from a new refrigerant vapor pressure equation term library, repeating NS times, selecting the equation with the minimum objective function, and repeating the process to obtain an initial equation set consisting of NP equations;
step four: the vapor pressure equation system of the novel refrigerant is changed:
(1) randomly selecting one term in the initial equation setp n,oldAnd random entries in the item library remainder entriesp n Exchanging to generate a new equation;
(2) repeating the item changing process NM times for each initial equation, selecting the equation with the minimum objective function value, and if the objective function value is smaller than the objective function of the original equation, replacing the original equation with a new equation, otherwise, keeping the original equation unchanged;
(3) repeatedly executing the processes for NP equations to obtain a new variation equation set;
step five: regression analysis: selecting NR +1 equations with minimum objective function from NP equations, and finding out simultaneous occurrence of NR +1 times, NR times and NR times-The 1, …, 2-degree terms are used as the pre-options of regression analysis, the regression analysis is respectively carried out, NR regression equations are generated, and NR equations in the initial equation set are replaced to form a new generation of equation set;
step six: if the NP equations are the same or reach the preset iteration times, the algorithm is ended to obtain a novel refrigerant vapor pressure equation, the refrigeration parameters of the refrigerant are determined according to the novel refrigerant vapor pressure equation, and a refrigeration system is constructed according to the refrigeration parameters of the refrigerant.
2. The refrigerant system construction method based on refrigerant universal vapor pressure equation according to claim 1, wherein, in the step of establishing an optimization algorithm objective function,
the refrigerant vapor pressure equation is of the general form:
Figure 852139DEST_PATH_IMAGE002
wherein the content of the first and second substances,p cal a value is calculated for a refrigerant vapor pressure equation,Tis a thermodynamic temperature, and is characterized in that,p candT crespectively the critical pressure and the temperature of the refrigerant,Iis the number of the terms of the equation,a iis a parameter to be optimized;
based on the vapor pressure equation, an equal-weight nonlinear objective function is established as follows:
Figure 956230DEST_PATH_IMAGE004
wherein the content of the first and second substances,p exp for the experimental value of the vapor pressure of the refrigerant,ncounting the number of the steam pressure data points;
establishing a linear objective function with weights as follows:
Figure 673650DEST_PATH_IMAGE006
wherein the varianceσ m Calculating by a Gaussian error transfer formula;
or other forms of objective function that establish the accuracy of the data reproduction of the reaction equation.
3. The refrigerant system construction method based on the refrigerant universal vapor pressure equation as recited in claim 1, wherein the convergence speed and accuracy of the algorithm are optimized by modifying the control parameters NP, NR, NS.
4. A method as claimed in claim 3, wherein the step of modifying the control parameter comprises the following steps:
3≤NP≤9，NR=1，150≤NS≤300。
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US5735134A (en) * 1996-05-30 1998-04-07 Massachusetts Institute Of Technology Set point optimization in vapor compression cycles
US20150277444A1 (en) * 2014-03-28 2015-10-01 Mitsubishi Electric Research Laboratories, Inc. Time-Varying Extremum Seeking for Controlling Vapor Compression Systems
CN104778338A (en) * 2015-05-03 2015-07-15 长春工业大学 Optimization method for set value of low-energy-consumption molecular distillation process

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