CN109299560B - A Determination Method of Optimal Exhaust Pressure Characteristic Variable of CO2 System - Google Patents

Abstract

The present invention provides a method for determining an optimal exhaust pressure characteristic variable of a CO ₂ system, comprising: the first step, determining a data sample set to construct an efficiency prediction model; the second step, for the 9-input single-output determined in the first step The sample data set, determine the reference function; the third step, determine the calculation formula of the outer criterion; the fourth step: construct the binary linear function y=ax ₁ +bx ₂ as the transfer function to generate an intermediate model and perform layer-by-layer screening to form the optimal Complexity model structure. The invention is based on real-time data-driven efficiency decision-making, and uses the method of data mining to mine the characteristic variables affecting the operation in the transcritical CO ₂ heat pump system, thereby overcoming the subjective experience and judgment of researchers, and not relying on the experience of researchers, Intuition, the real-time data generated by the system itself makes judgments and choices.

Description

A Determination Method of Optimal Exhaust Pressure Characteristic Variable of CO2 System

technical field

The invention belongs to the technical field of heat pumps, and in particular relates to a method for determining an optimal exhaust pressure characteristic variable of a CO ₂ heat pump.

Background technique

With the further development of economy and society, environmental protection and sustainable development issues have become the common concern of all human society. The signing of the Montreal Agreement marks the first time that the impact of refrigerants on the environment has been paid attention to on a global scale, and the replacement of refrigerants has since become the first element to guide the development of the refrigeration and air-conditioning industry. The new environmental protection and refrigeration issues that have emerged during the development and promotion of new synthetic refrigerants have convinced more and more researchers that natural refrigerants will become the end of this round of replacement. Among natural refrigerants, carbon dioxide has become a research hotspot in the heat pump industry due to its excellent thermophysical properties and the promotion of transcritical devices.

In the research of the transcritical CO ₂ heat pump water heater system, the research of the optimal exhaust pressure of the system is one of the core contents, and it is determined which parameters have specific effects on the optimal exhaust pressure of the system and the corresponding parameters have an impact on the optimal exhaust pressure of the system. The degree of influence of the optimal exhaust pressure is the basis for realizing the optimal exhaust pressure control of the system under variable working conditions. Many scholars have made significant contributions in this field, and proposed the optimal exhaust pressure correlation for transcritical CO ₂ heat pump system. In the development process of the transcritical CO ₂ heat pump system unit, researchers also follow this model. After the selection of system components is completed, when designing the control system, the calculation formula of the optimal exhaust pressure fitted by a large number of experimental data is generally selected as . However, the most suitable calculation formula for a large number of experimental data is the optimal exhaust pressure of the experimental prototype system. In the actual engineering background, even if the exact same accessories are used for assembly and production, it may be due to the installation process. The performance difference of the secondary products makes the performance of the final unit vary greatly, which brings the following problems to the development of the unit control system:

(1) Controlling the unit through the conventional optimal control algorithm of the prototype cannot fully adapt to the external working conditions.

(2) There is a large deviation in predicting the optimal pressure based on the existing empirical equations, and the performance degradation of the unit will increase such differences over time.

In order to realize the accurate control of the optimal exhaust pressure by the control system, it is necessary to use the real-time data-driven efficiency decision-making to extract the classification features and predict the efficiency of the variables that affect the optimal exhaust pressure of the system.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for determining the optimal exhaust pressure characteristic variable of a CO ₂ system to solve the above technical problems.

In order to achieve the above object, the present invention adopts the following technical solutions:

A method for determining an optimal exhaust pressure characteristic variable of a CO ₂ system, comprising the following steps:

The first step: collect the samples obtained during the working condition test of the transcritical CO ₂ heat pump water heater system to obtain a sample data set; build an efficiency prediction model, the input is the ambient temperature, the evaporator outlet temperature, the suction temperature, the exhaust temperature, the water pump Inlet water temperature, water pump outlet temperature, air cooling outlet temperature, evaporator coil temperature and suction pressure, the output is the exhaust pressure;

Divide the data sample set, use the letter A to represent the training set, which is used to generate the competitive model; use the letter B to represent the test set; use the external criterion to screen the competitive model: w _n =N _A +N _B , w=A∪B, where w represents all data samples;

为自变量和因变量的映射关系，并以其子项v1＝a₀,v2＝a₁x₁,v3＝a₂x₂,……，v55＝a₅₄x₈x₉作为建模网络中的55个初始模型；Step 2: For the 9-input single-output sample data set determined in the first step, determine the reference function

is the mapping relationship between the independent variable and the dependent variable, and its sub-items v1=a ₀ , v2=a ₁ x ₁ , v3=a ₂ x ₂ ,..., v55=a ₅₄ x ₈ x ₉ as the modeling network 55 initial models of ;

式中y_t为第t个实际输出值；

为在数据集K上得到的模型估计的第t个输出值，在建模中K取A,B及A∪B＝w；The third step: determine the calculation formula of the outer criterion is:

where y _t is the t-th actual output value;

is the t-th output value estimated by the model obtained on the data set K, and K takes A, B and A∪B=w in the modeling;

Step 4: Build a binary linear function y=ax _i +x _j as a transfer function to generate an intermediate model and perform layer-by-layer screening to finally form an optimal complexity model structure.

There are 9 related variables of the optimal exhaust pressure. The purpose of the GMDH algorithm is to use the method of genetic variation selection to evaluate these 9 variables, and to determine the most relevant variable in the final optimal exhaust pressure correlation. The purpose of this transfer function is to generate an intermediate model, and to inherit and mutate the model of the upper layer. The specific method is: pre-shuffle the sample order of the training set and the test set, perform the process randomly 50 times, and perform GMDH in each process to obtain the optimal complexity model, and count each element as the principal component. Probability; 50 random experimental results are counted for each experiment, and the average value of 50 trials is obtained, so as to obtain the ranking of the most relevant variables according to the probability of occurrence from large to small.

表示在第一层由自组织过程自适应产生36个竞争模型，且彼此因所含变量个数、函数结构的差异性而不同；同时在训练集A上估计w_k的参数a,b；Further, in the fourth step, the transfer function w _k =ax _i +bx _j is the first-layer intermediate model, and the size of the number of competing models k is related to the number m of items in the previous layer, m=9, then according to the formula have to

It means that 36 competing models are adaptively generated by the self-organizing process in the first layer, and they are different from each other due to the difference in the number of variables and the functional structure; at the same time, the parameters a and b of w _k are estimated on the training set A;

再次通过检测集B对第二层中间模型进行筛选，选中的竞争模型进入第三层；The intermediate model builds the competition model of the second layer on the basis of the intermediate model of the first layer; the input variable of the second layer is equal to the output variable _wk of the first layer, and the number of constructed competition models is

The second-layer intermediate model is screened again through the detection set B, and the selected competitive model enters the third layer;

取得全局最小值。Starting from the second layer, the number of models with the same structure that are generated in the second selection layer and enter the next layer is determined by the external criterion; by continuously generating competing models and screening according to the value of the external criterion, the complexity of the model continues to increase. At the same time, by calculating The external criterion value improves the quality of the model; when the quality of the model cannot be improved again, the modeling process stops and the optimal model is found; at this time, the minimum fitting variance calculated on the detection set is

Get the global minimum.

Further, a loop is added to the GMDH algorithm to ensure that the training set and the test set are divided into different ways to generate a combination of samples containing more transcritical CO ₂ system variables; assuming that n is the total number of samples in the training set, it is taken from 2 loops. The value to n-1 ensures the completeness of the sample distribution ratio of the training set and the prediction set in the same sample distribution order.

Further, in order to compare the fairness of the analysis and ensure the completeness of the sample sequence; count the number of occurrences of the elements as the principal components, scramble the sample sequence of the training set and the test set in advance, and perform the process randomly 50 times, and perform each time. In the process, GMDH is carried out, and the probability of each element as the principal component is counted; 50 random experimental results are counted for each experiment, and the average value of the 50 experiments is obtained.

Further, the samples in the sample data set are all the system operation data recorded under the steady state of COP of the transcritical CO ₂ heat pump water heater system.

Further, the number of samples in the sample data set is 5000.

Compared with the prior art, the present invention has the following beneficial effects:

The optimal control algorithm of the traditional control system design is based on the optimal exhaust pressure formula fitting the experimental prototype data, which fails to take into account the differences of devices in actual engineering manufacturing and the aging of devices during operation. performance difference. The method for determining the optimal exhaust pressure characteristic variable of the CO ₂ system provided by the present invention is based on real-time data-driven efficiency decision-making, and uses the method of data mining to mine the characteristic variables affecting the operation in the transcritical CO ₂ heat pump system, thereby It overcomes the subjective experience and judgment of researchers, does not rely on the experience and intuition of researchers, and judges and selects itself by real-time data generated by the system.

Compared with other data mining methods, the GMDH algorithm has the following advantages:

(1) The modeling process is highly intelligent. In addition to providing sample data and external criteria, the modeler will no longer participate in the rest of the modeling process in order to ensure the objectivity of model selection, thus ensuring the freedom of computer software.

(2) Compared with implicit models such as ANN (neural network), SVM, and gray correlation degree, GMDH can obtain an explicit expression model, which is helpful for people to identify the influencing factors of the system.

(3) The anti-interference is relatively strong and the prediction accuracy is relatively high. The GMDH algorithm is data-driven. In order to improve the fitting accuracy of the model and ensure that the algorithm finds a model that conforms to the real internal laws in the state of data noise interference, the network structure can achieve the optimal complexity through the selection criteria.

Description of drawings

In order to more clearly illustrate a method for determining an optimal exhaust pressure characteristic variable of a CO ₂ system provided by the present invention, the accompanying drawings required in the description of the present invention will be briefly introduced below.

Fig. 1 is the flow chart of the extraction steps of the optimal exhaust pressure characteristic variable based on the GMDH algorithm;

Figure 2 is a schematic diagram of the process of generating the optimal model for GMDH.

Detailed ways

Please refer to FIG. 1 , a method for determining the optimal exhaust pressure characteristic variable of a CO ₂ system provided by the present invention includes the following steps:

Step 1: Determine the data sample set to build an efficiency prediction model, select 5000 sample data sets obtained during the unit operating condition test, and input the ambient temperature (°C), evaporator outlet temperature (°C), suction temperature ( °C), exhaust temperature (°C), water pump inlet temperature (°C), water pump outlet temperature (°C), air cooling outlet temperature (°C), evaporator coil temperature (°C) and suction pressure (MPa), output is the exhaust pressure (MPa).

In the actual operation of the unit, the optimal pressure control scheme is adopted, which is collected every 5 minutes. In the case of testing under the same test conditions, it takes a period of time for the unit to reach the test steady state, which is the data recorded when the unit operating condition reaches the test condition stably. Among them, the pump inlet water temperature and pump outlet water temperature in the unit data belong to the operating data outside the system, and the actual conditions can be met by changing the frequency of the water pump. According to the actual operation situation, because a single power-on test experiment needs to do a series of working condition test experiments, the temperature and the temperature of the inlet and outlet water have changed, the data have been excluded from the data that are not powered on and not connected to the optimal pressure operation just after booting. data. All the selected data are the system operation data recorded under the COP steady state of the transcritical CO ₂ heat pump system under the test system, at which time the inlet and outlet water temperature and the ambient temperature are stable values.

Divide the data sample set, the training set (represented by the letter A) is used to generate the competitive model, that is, to determine the model parameters and structure, and the test set (represented by the letter B) uses the external criteria to screen the competitive model; there is w _n =N _{A +} NB , w= _A∪B , where _wn represents the number of all data samples, NA represents the number of training set samples, and _NB represents the number of test set samples.

Step 2: When establishing a self-organizing model, an initial organization (initial model set) is generated according to the reference function of the mapping relationship between the independent variable (input) and the dependent variable (output), and this type of system is described through the self-evolution of the organization. For the system with limited memory points, the reference function adopts Kolmogorov-Gabor (referred to as K-G) polynomial, and its expression is:

为多项式子项的系数。将该多项式的子项作为建模网络结构中的m个初始模型，对于n个输入的K-G多项式，建模网络结构中的初始模型m＝1+2n+(n(n-1))/2个。对于第一步中确定的9输入单输出样本数据集，确定参考函数

为自变量和因变量的映射关系，其中x₁～x₉为环境温度(℃)、蒸发器出口温度(℃)、吸气温度(℃)、排气温度(℃)、水泵进水温度(℃)、水泵出水温度(℃)、气冷出口温度(℃)、蒸发器盘管温度(℃)和吸气压力(MPa)，f(x₁,x₂,..,x₉)表示作为输出量的排气压力(MPa)， a₀～a₅₄为多项式子项的系数，将多项式子项v1＝a₀,v2＝a₁x₁,v3＝a₂x₂,……,v55＝ a₅₄x₈x₉作为建模网络中的55个初始模型。where x ₁ ～x _n are related variables,

are the coefficients of the polynomial subterms. The subterms of the polynomial are used as m initial models in the modeling network structure. For n input KG polynomials, the initial models in the modeling network structure are m=1+2n+(n(n-1))/2 . For the 9-input single-output sample dataset identified in the first step, determine the reference function

is the mapping relationship between the independent variable and the dependent variable, where x ₁ ~ x ₉ are the ambient temperature (°C), the outlet temperature of the evaporator (°C), the suction temperature (°C), the exhaust temperature (°C), and the water inlet temperature of the pump ( °C), water pump outlet temperature (°C), air cooling outlet temperature (°C), evaporator coil temperature (°C) and suction pressure (MPa), f(x ₁ , x ₂ ,.., x ₉ ) is expressed as The exhaust pressure (MPa) of the output volume, a ₀ to a ₅₄ are the coefficients of the polynomial sub-terms, and the polynomial sub-terms v1=a ₀ , v2=a ₁ x ₁ , v3=a ₂ x ₂ ,...,v55= a ₅₄ x ₈ x ₉ as the 55 initial models in the modeling network.

Step 3: In the process of building the system model, build an intermediate model on the training data set and perform parameter estimation, that is, the screening process is to use the quality of different competing models to distinguish. The outer criterion is the mathematical description of these specific requirements, by calculating the outer criterion value (by the difference between the output y ^M and the actual observed value of the output y), the "best" model is selected from a simple class of candidate models, The "best" model is then obtained by limiting the external conditions. The external criterion calculation formula is: J(C)＝E{Q(y ^M ,y,C)}, where y ^M is the output value of the reference function, y is the actual observed value, J(C) is the external criterion value, C is the dataset, Q is the loss function, and E is the expected value.

式中y_t为第t个实际输出值；

为在数据集K上得到的模型估计的第t个输出值，在建模中K取A,B及A∪B＝w，式中A表示训练集，B表示检验集，w表示所有数据样本。Common external criteria include accuracy criteria, correlation criteria, compatibility criteria, variable balance criteria and so on. In terms of selection of external criteria, Ivakhnenko emphasized that specific selection should be made in the process of feature extraction according to the specific characteristics of the problem, so as to improve the fitting accuracy. In the process of building the system model, in order to improve the prediction accuracy, the calculation formula of the prediction criterion is as follows:

where y _t is the t-th actual output value;

It is the t-th output value estimated by the model obtained on the data set K. In the modeling, K takes A, B and A∪B=w, where A represents the training set, B represents the test set, and w represents all data samples .

Step 4: Build a binary linear function y=ax _i +bx _j as a transfer function to generate an intermediate model and perform layer-by-layer screening to form an optimal complexity model structure, where x _i , x _j represent the model of the previous layer, y Represents the newly generated intermediate model of this layer, a and b are parameters.

表示在第一层由自组织过程自适应产生36个神经元(竞争模型)，且彼此因所含变量个数、函数结构的差异性而不同。同时在训练集A上估计w_k的参数a,b。Further, as shown in Figure 2, in the fourth step, the transfer function w _k =ax _i +bx _j is the first-layer intermediate model, and the size of the number of competing models k is related to the number of items in the previous layer, such as m =9, then according to the formula we can get

It means that 36 neurons (competitive model) are adaptively generated by the self-organizing process in the first layer, and they are different from each other due to the difference in the number of variables and the functional structure. At the same time, the parameters a and b of w _k are estimated on the training set A.

Among them, the partial competition model structure generated by the first layer is as follows:

w ₁ =a ₁ x ₁ +b ₁ x ₂ , w ₂ =a ₂ x ₁ +b ₂ x ₃ ,...,w ₇ =a ₇ x ₁ +b ₇ x ₈ ,w ₈ =a ₈ x ₁ + b ₈ x ₉

w ₉ =a ₉ x ₂ +b ₉ x ₃ , ..., w ₁₄ =a ₁₄ x ₂ +b ₁₄ x ₈ , w ₁₅ =a ₁₅ x ₂ +b ₁₅ x ₉

...

w ₃₄ =a ₃₄ x ₇ +b ₃₄ x ₈ , w ₃₅ =a ₃₅ x ₇ +b ₃₅ x ₉

w ₃₆ = a ₃₆ x ₈ + b ₃₆ x ₉

再次通过检测集B对第二层中间模型进行筛选，选中的竞争模型进入第三层。The intermediate model will build the competition model of the second layer on the basis of the intermediate model of the first layer, that is, the input variable of the second layer is equal to the output variable _wk of the first layer, and the number of the constructed competition model is

The second-layer intermediate model is screened again through the detection set B, and the selected competitive model enters the third layer.

取得全局最小值。Starting from the second layer, the number of models with the same structure in the second selection layer that goes into the next layer is determined by the outer criterion. By constantly generating competing models and screening them according to the external criterion values, the complexity of the models is increasing, and the model quality is improved by calculating the external criterion values. When the model quality cannot be improved again, the modeling process stops and the optimal model is found. The minimum fitted variance computed on the detection set at this time

Get the global minimum.

Further, in order to verify the combination of various variables of the system under various working conditions, extract the main features that affect the optimal exhaust pressure under different working conditions, and perform cyclic processing in the system. A loop is added to the GMDH algorithm to ensure that the training set and the test set are divided into different ways to generate a combination of samples containing more transcritical CO ₂ system variables. In order to identify and sort different transcritical CO ₂ heat pump units, the corresponding occurrence probability is calculated according to the number of feature extractions. Assuming that n is the total number of samples in the training set, it can cycle from 2 to n-1 to ensure the completeness of the distribution ratio of samples in the training set and the prediction set in the same sample distribution order.

Further, in order to compare the fairness of the analysis, the completeness of the sample order is ensured. Count the number of occurrences of the elements as the principal components, scramble the sample order of the training set and the detection set in advance, and perform the process randomly 50 times, and in each process, perform GMDH, and then count (the frequency of a single element as the principal component/ The total number of all principal components) counts the probability of each element as a principal component. For each experiment, 50 random experimental results were counted, and the average value of the 50 experiments was obtained.

By selecting the elements ranked in the forefront of the statistical results as the characteristic variables of the optimal exhaust pressure, it provides a basis for the subsequent optimal exhaust pressure formula fitting and control strategy formulation. By comparing the effect of the final control strategy and the previous control strategy obtained by fitting formulas from experimental data, the GMDH method can select characteristic variables more objectively from the data itself and avoid the researchers' subjective guesses about the unknown model, so as to obtain Relatively good control effect, in addition, by updating the database in real time, it can also realize the adjustment of the control strategy most suitable for the current database.

Claims (6)

1. CO (carbon monoxide)₂The method for determining the optimal exhaust pressure characteristic variable of the system is characterized by comprising the following steps:

the first step is as follows: collecting transcritical CO₂Obtaining a sample data set by a sample obtained in the process of testing the working condition of the heat pump water heater system; constructing an efficiency prediction model, inputting the environment temperature, the outlet temperature of the evaporator, the air suction temperature, the exhaust temperature, the water inlet temperature of the water pump, the water outlet temperature of the water pump, the air cooling outlet temperature, the temperature of an evaporator coil and the air suction pressure, and outputting the exhaust pressure;

dividing a data sample set, and using a letter A to represent a training set for generating a competition model; the test set is denoted by the letter B; using the external criteria to screen competition models has w_n＝N_A+N_BW ═ a ═ u β, where w denotes all data samples;

the second step is that: for the 9-input single-output sample data set determined in the first step, a reference function is determined

Is the mapping relation between independent variable and dependent variable, and its sub-item v1 ═ a₀,v2＝a₁x₁,v3＝a₂x₂，……，v55＝a₅₄x₈x₉As 55 initial models in the modeled network;

the third step: the calculation formula for determining the external criterion is:

in the formula y_tIs the t actual output value;

for the tth output value of the model estimate obtained on the dataset K, K takes a, B and atou B ═ w in the modeling;

the fourth step: construction of a binary Linear function y ═ ax_i+bx_jAnd generating an intermediate model as a transfer function and carrying out layer-by-layer screening to finally form an optimal complexity model structure.

2. CO according to claim 1₂The method for determining the optimum exhaust pressure characteristic variable of the system is characterized in that in the fourth step, the transfer function w_k＝ax_i+bx_jThe intermediate model of the first layer, wherein the number k of the competitive models is related to the number m of the terms of the previous layer, and m is 9, the intermediate model is obtained according to the formula

The method comprises the steps that 36 competitive models are generated in a self-organizing process in a self-adapting mode in a first layer, and the competitive models are different from each other due to the number of contained variables and the difference of function structures; simultaneous estimation on training set Aw_kThe parameters a, b;

the intermediate model builds a competition model of a second layer on the basis of the first layer of intermediate model foundation; input variables of the second layer and output variables w of the first layer_kEqual, the number of the constructed competition models is

Screening the middle models of the second layer again through the detection set B, and enabling the selected competitive models to enter a third layer;

starting from the second layer, generating the number of models with the same structure entering the next layer at the second selection layer, wherein the number of the models is determined by the external criterion; by continuously generating competition models and screening according to the external criterion values, the complexity of the models is continuously increased, and meanwhile, the quality of the models is improved by calculating the external criterion values; when the quality of the model cannot be improved again, the modeling process is stopped, and the optimal model is found; at this point the minimum fitting variance calculated on the detection set

A global minimum is taken.

3. CO according to claim 1₂The method for determining the optimal exhaust pressure characteristic variable of the system is characterized in that a cycle is added in a GMDH algorithm to ensure different segmentation modes of a training set and a test set to generate a model containing more transcritical COs₂Sample combination mode of system variables; and assuming that n is the total number of samples in the training set, and circularly taking values from 2 to n-1, so as to ensure the completeness of the sample distribution proportion of the training set and the prediction set under the same sample distribution sequence.

4. CO according to claim 1₂The method for determining the optimal exhaust pressure characteristic variable of the system is characterized in that the completeness of a sample sequence is ensured for the fairness of comparative analysis; counting the occurrence frequency of the main components, pre-scrambling the sequence of the training set and the detection set, randomly performing the process for 50 times, performing GMDH in each process,then, counting the probability of each element as a main component; for each experiment, the results of the random 50 experiments were counted, and the average of the 50 experiments was obtained.

5. CO according to claim 1₂The method for determining the optimal exhaust pressure characteristic variable of the system is characterized in that all samples in the sample data set are transcritical CO₂And recording system operation data under the COP steady state of the heat pump water heater system.

6. CO according to claim 1₂The method for determining the optimal exhaust pressure characteristic variable of the system is characterized in that the number of samples in a sample data set is 5000.

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