CN109299560A - A Determining Method of Optimal Exhaust Pressure Characteristic Variable of Transcritical CO2 System Based on GMDH Algorithm - Google Patents

A Determining Method of Optimal Exhaust Pressure Characteristic Variable of Transcritical CO2 System Based on GMDH Algorithm Download PDF

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CN109299560A
CN109299560A CN201811174422.5A CN201811174422A CN109299560A CN 109299560 A CN109299560 A CN 109299560A CN 201811174422 A CN201811174422 A CN 201811174422A CN 109299560 A CN109299560 A CN 109299560A
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曹锋
崔策
殷翔
王琳玉
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Xian Jiaotong University
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Abstract

本发明提供一种基于GMDH算法的跨临界CO2系统最优排气压力特征变量的确定方法，包括：第一步，确定数据样本集以构建效能预测模型；第二步，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；第三步，确定外准则的计算公式；第四步：构建二元线性函数y＝ax1+bx2作为传递函数产生中间模型并且进行逐层筛选，形成最优复杂度模型结构。本发明是基于实时数据驱动的效能决策，利用数据挖掘的方法去挖掘跨临界CO2热泵系统中影响运行的特征变量，从而克服了研究人员的主观经验和判断，不依赖于研究者的经验、直觉，由系统产生的实时数据自身进行判断和选择。

The invention provides a method for determining the optimal exhaust pressure characteristic variable of a transcritical CO 2 system based on the GMDH algorithm, including: the first step, determining a data sample set to construct an efficiency prediction model; The determined 9-input single-output sample data set is determined, and the reference function is determined; the third step, the calculation formula of the outer criterion is determined; the fourth step: the binary linear function y=ax 1 +bx 2 is constructed as the transfer function to generate an intermediate model and perform step by step. 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 kind of Trans-critical cycle CO based on GMDH algorithm2System optimal pressure at expulsion characteristic variable Determine method
Technical field
The invention belongs to technical field of heat pumps, in particular to a kind of CO2The determination of the optimal pressure at expulsion characteristic variable of heat pump Method.
Background technique
With the further development of economic society, the common pass of environmental protection and sustainable development as whole mankind society It cuts.The signing of Montreal Agreement indicates that influence problem of the refrigerant for environment obtains weight in the world for the first time Depending on the substitution of refrigerant also becomes the first element of guidance refrigerating and air conditioning industry development since then.In grinding for novel synthesis refrigerant The novel environment friendly and refrigeration problem occurred in hair and extension process allows more and more researchers to firmly believe that natural refrigerant will The terminal of this wheel substitution can be become.In natural refrigerant, carbon dioxide by its own excellent thermophysical property and across The popularization of critical assembly becomes the research hotspot of heat pump industry instantly.
In Trans-critical cycle CO2In the research of heat pump water heater system, the research of system optimal pressure at expulsion is that its is most crucial One of content, and wherein determining which parameter has specific influence and corresponding parameter to optimal row system optimal pressure at expulsion Atmospheric pressure effect is the basis that system optimal pressure at expulsion controls under the conditions of realizing variable working condition.Numerous scholars are herein Significant contribution is made in field, and proposes Trans-critical cycle CO2The optimal pressure at expulsion correlation of heat pump system.In Trans-critical cycle CO2 In the development process of heat pump system unit, also mode controls after system unit selects to complete in design researcher like this The calculation formula conduct for the optimal pressure at expulsion being fitted by lot of experimental data is typically chosen when system.But a large amount of experiment What the calculation formula of data fitting was most adapted to is the optimal pressure at expulsion of experimental prototype system, in actual engineering background, i.e., Make to carry out assembling production using identical accessory, it is also possible to which, because of mounting process, the performance difference of different batches of product makes The performance difference that shows of final unit is very big, this just brings following problems to the exploitation of unit control system:
(1) go control unit that cannot be adapted to external work condition environment completely by the conventional optimal control algorithm to model machine.
(2) there are biggish deviations when going prediction optimum pressure based on existing empirical equation, and over time The performance degradation of unit will increase such otherness.
In order to realize control system accurately controlling for optimal pressure at expulsion, the efficiency based on Real-time data drive is used Decision carries out characteristic of division extraction to the variable for influencing system optimal pressure at expulsion and Effectiveness Forecast is necessary.
Summary of the invention
The purpose of the present invention is to provide a kind of Trans-critical cycle CO based on GMDH algorithm2System optimal pressure at expulsion feature becomes Method for determination of amount, to solve the above technical problems.
To achieve the goals above, the present invention adopts the following technical scheme:
A kind of Trans-critical cycle CO based on GMDH algorithm2The determination method of system optimal pressure at expulsion characteristic variable, including with Lower step:
Step 1: acquisition Trans-critical cycle CO2Sample obtained in heat pump water heater system working condition measurement process obtains sample number According to collection；Construct Effectiveness Forecast model, input for environment temperature, evaporator outlet temperature, suction temperature, delivery temperature, water pump into Coolant-temperature gage, water pump water outlet temperature, air cooling outlet temperature, evaporator coil temperature and pressure of inspiration(Pi), export as pressure at expulsion；
Set of data samples is divided, training set is indicated with alphabetical A, for generating competitive model；It indicates to examine with letter b Test collection；There is w using outer criterion to screen competitive modeln=NA+NB, w=A ∪ B, wherein w indicates all data samples；
Step 2: determining reference function for the single output sample data set of 9 inputs determined in the first step For the mapping relations of independent variable and dependent variable, and with its subitem v1=a0, v2=a1x1, v3=a2x2... .., v55=a54x8x9 As 55 initial models in modeled network；
Step 3: determining the calculation formula of outer criterion are as follows: Y in formulatFor t-th of real output value；T-th of the output for the model estimation obtained on data set K Value, K takes A, B and A ∪ B=w in modeling；
Step 4: building binary linearity function y=axi+bxjMid-module is generated as transmission function and is carried out layer-by-layer Screening, ultimately forms optimal complexity model structure.
The correlated variables of optimal pressure at expulsion has 9, and GMDH algorithm purpose is the method pair selected using hereditary variation This 9 variables are evaluated, and determine the most correlated variables in final optimal pressure at expulsion correlation.The purpose of the transmission function It is to generate mid-module, heredity and variation is carried out to upper one layer of model.Specific practice are as follows: upset training set, detection in advance Collect sample order, which is carried out 50 times at random, and during carrying out each time, carries out GMDH, obtain optimal complexity Model counts probability of the every kind of element as main composition；Random 50 experimental results are counted for each experiment, and are taken The average values for obtaining 50 tests, thus according to the sequence for obtaining most correlated variables from big to small of probability of occurrence.
Further, in the 4th step, transmission function wk=axi+bxjFor first layer mid-module, wherein competitive model number The size of k is related with the item number m of preceding layer, m=9, then obtains according to formulaIt indicates in first layer by self-organizing Process adaptive generates 36 competitive models, and different due to contained variable number, the otherness of function structure each other；Exist simultaneously W is estimated on training set AkParameter a, b；
Mid-module builds the competitive model of the second layer in turn in first layer mid-module ground foundation；The input of the second layer The output variable w of variable and first layerkEqual, the number for constructing competitive model isCollect B again by detection Second layer mid-module is screened, the competitive model chosen enters third layer；
It is true by outer criterion in the identical pattern number of structure that the second selection layer generation enters next layer since the second layer It is fixed；By constantly generating competitive model and being screened according to outer criterion value, the complexity of model is continuously increased, while passing through meter It calculates outer criterion value and improves model quality；When model quality can not improve again, modeling process stops, and optimal models are found；This When detection collection on the minimum fitting variance that calculatesObtain global minimum.
Further, circulation is added in GMDH algorithm, it is ensured that the different partitioning schemes of training set, inspection set, generation contain There are more Trans-critical cycle CO2The sample combination of system variable；It is assumed that n is the total number of samples of training set, from 2 circulation values to n- 1, it is ensured that training set and completeness of the forecast set sample allocation proportion under same sample distribution sequence.
Further, for the fairness of comparative analysis, it is ensured that the completeness of sample order；Statistics is wanted as main composition Plain frequency of occurrence upsets training set, detection collection sample order in advance, which is carried out 50 times at random, and carries out each time In the process, GMDH is carried out, then counts probability of the every kind of element as main composition；It is counted random 50 times for each experiment Experimental result, and obtain the average value of 50 tests.
Further, the sample that sample data is concentrated is Trans-critical cycle CO2It is recorded under heat pump water heater system COP stable state System operation data.
Further, it is 5000 that sample data, which concentrates the quantity of sample,.
Compared with prior art, the invention has the following advantages:
The optimal control algorithm of traditional Control System Design is the optimal pressure at expulsion based on the fitting of experimental prototype data Formula fails to consider to give Trans-critical cycle system the problems such as device aging in device otherness and operational process in Practical Project manufacture Bring performance difference.A kind of Trans-critical cycle CO based on GMDH algorithm provided by the invention2System optimal pressure at expulsion feature becomes Method for determination of amount is the efficiency decision based on Real-time data drive, goes to excavate Trans-critical cycle CO using the method for data mining2Heat The characteristic variable that operation is influenced in pumping system, so that subjective experience and the judgement of researcher is overcome, independent of researcher Experience, intuition, judged and selected by the real time data itself that system generates.
Compared with other data digging methods, GMDH algorithm has the advantages that following some:
(1) modeling process intelligence degree is high.Modeler is outside providing sample data and outer criterion, to guarantee it in mould Objectivity in type selection, is no longer participate in remaining modeling process, to ensure that the freedom of computer software.
(2) compared with the implicit models such as ANN (neural network), SVM, grey relational grade, GMDH can obtain display expression mould Type is conducive to the influence factor of people's identifying system.
(3) anti-interference is stronger, precision of prediction is relatively high.GMDH algorithm is using data-driven as starting point, to improve The fitting accuracy of model guarantees that algorithm finds the model for meeting true inherent law under data noise disturbance state, passes through Selection criterion makes the complexity that network structure is optimal.
Detailed description of the invention
In order to illustrate more clearly of a kind of Trans-critical cycle CO based on GMDH algorithm provided by the invention2System optimal exhaust pressure The determination method of power characteristic variable below will be briefly described required attached drawing in present invention description.
Fig. 1 is the optimal pressure at expulsion characteristic variable extraction step flow chart based on GMDH algorithm；
Fig. 2 is that GMDH generates optimal models process schematic.
Specific embodiment
Refering to Figure 1, a kind of Trans-critical cycle CO based on GMDH algorithm provided by the invention2System optimal pressure at expulsion The determination method of characteristic variable, comprising the following steps:
Step 1: determining data sample collection, to construct Effectiveness Forecast model, selection obtains during unit working condition measurement 5000 sample data sets, input for environment temperature (DEG C), evaporator outlet temperature (DEG C), suction temperature (DEG C), exhaust temperature Spend (DEG C), water feeding of water pump temperature (DEG C), water pump water outlet temperature (DEG C), air cooling outlet temperature (DEG C), evaporator coil temperature (DEG C) With pressure of inspiration(Pi) (MPa), export as pressure at expulsion (MPa).
The control program using optimum pressure of unit in actual operation, it is primary every acquisition in 5 minutes.Identical The case where being tested under test condition, unit, which reaches test stable state, to be needed to undergo a period of time, this is unit operating condition in stabilization The data recorded in the case where reaching measurement condition.Wherein, water feeding of water pump temperature and water pump water outlet temperature belong in unit data The operation data of exterior meets physical condition by changing the frequency of water route water pump.According to actual operating condition, because Need to do a series of working condition measurement experiments for single energization test experiments, temperature and inlet and outlet temperature have the case where variation, number According to eliminated be not keyed up and be just switched on do not access optimum pressure operation data.Institute selectively data be Trans-critical cycle CO under test macro2The system operation data recorded under heat pump system COP stable state, at this time inlet and outlet temperature and environment Temperature is stationary value.
Set of data samples is divided, training set (being indicated with alphabetical A) determines model ginseng for generating competitive model Several and structure, inspection set (being indicated with letter b) screen competitive model using outer criterion；There is wn=NA+NB, w=A ∪ B, wherein wnIndicate all data sample numbers, NAIndicate training set number of samples, NBIndicate inspection set number of samples.
Step 2: reference when establishing self-organizing model, according to independent variable (input) and dependent variable (output) mapping relations Function generates initial tissu (initial model set), and this kind of systems are described by self evolving for tissue.For The system of finite memory point, reference function use Kolmogorov-Gabor (abbreviation K-G) multinomial, expression formula are as follows:
Wherein x1~xnFor relevant different variables,For the coefficient of multinomial subitem.By the multinomial Subitem as m initial model in modeled network structure, the K-G multinomial inputted for n, in modeled network structure Initial model m=1+2n+ (n (n-1))/2.For the single output sample data set of 9 inputs determined in the first step, reference is determined Function For the mapping relations of independent variable and dependent variable, wherein x1~x9For environment temperature (DEG C), evaporator Outlet temperature (DEG C), suction temperature (DEG C), delivery temperature (DEG C), water feeding of water pump temperature (DEG C), water pump water outlet temperature (DEG C), air cooling Outlet temperature (DEG C), evaporator coil temperature (DEG C) and pressure of inspiration(Pi) (MPa), f (x1, x2.., x9) indicate as output quantity Pressure at expulsion (MPa), a0~a54For the coefficient of multinomial subitem, by multinomial subitem v1=a0, v2=a1x1, v3= a2x2..., v55=a54x8x9As 55 initial models in modeled network.
Step 3: constructing mid-module on training dataset in system model build process, and carries out parameter and estimate Meter, i.e., screening process is distinguished using the quality of different competitive models.And outer criterion is exactly the number of these particular requirements Description is learned, by calculating outer criterion value (by exporting yMWith the difference of the actual observed value of output y), from simple candidate family " optimal " model is selected in class, then the model of " best " is obtained by the restriction of external condition.Outer criterion calculation formula are as follows: J (C)=E { Q (yM, y, C) }, y in formulaMFor the output valve of reference function, y is actual observed value, and J (C) is outer criterion value, and C is indicated Data set, Q indicate that loss function, E indicate desired value.
Common outer criterion includes accuracy criteria, correlation criterion, compatibility criterion, variable balance criterion etc..It is quasi- outside Aspect is then selected, Ivakhnenko emphasizes specifically be chosen during feature extraction according to the specific features of problem, And then improve fitting precision.During this system model buildings, in order to improve precision of prediction, the calculation formula of criteria for prediction is such as Under:Y in formulatFor t-th of real output value；For t-th of output valve of the model estimation obtained on data set K, K takes A, B and A ∪ B=w, A in formula in modeling Indicate that training set, B indicate that inspection set, w indicate all data samples.
Step 4: building binary linearity function y=axi+bxjMid-module is generated as transmission function and is carried out layer-by-layer Screening, forms optimal complexity model structure, wherein xi, xjIndicate that one layer of model, y indicate this layer of newly generated centre Model, a, b are parameter.
Further, as shown in Fig. 2, in the 4th step, transmission function wk=axi+bxjFor first layer mid-module, wherein competing The size for striving Number of Models k is related with the item number of preceding layer, such as m=9, then can obtain according to formulaIt indicates the One layer is adaptively generated 36 neurons (competitive model) by self-organizing process, and each other because of contained variable number, function structure Otherness and it is different.W is estimated on training set A simultaneouslykParameter a, b.
Wherein, the partial competition model structure that first layer generates is as follows:
w1=a1x1+b1x2, w2=a2x1+b2x3... ..., w7=a7x1+b7x8, w8=a8x1+b8x9
w9=a9x2+b9x3... ..., w14=a14x2+b14x8, w15=a15x2+b15x9
……
w34=a34x7+b34x8, w35=a35x7+b35x9
w36=a36x8+b36x9
Mid-module in first layer mid-module ground foundation and then will build the competitive model of the second layer, i.e. the second layer The output variable w of input variable and first layerkEqual, the number for constructing competitive model isAgain by inspection It surveys collection B to screen second layer mid-module, the competitive model chosen enters third layer.
It is true by outer criterion in the identical pattern number of structure that the second selection layer generation enters next layer since the second layer It is fixed.By constantly generating competitive model and being screened according to outer criterion value, the complexity of model is being continuously increased, and is passed through simultaneously It calculates outer criterion value and improves model quality.When model quality can not improve again, modeling process stops, and optimal models are found. The minimum fitting variance calculated on detection collection at this timeObtain global minimum.
Further, in order to verify the combinations of the various variables of system under various working, extracting influences most under different operating conditions The main feature of excellent row pressure, has done circular treatment in systems.Circulation is added in GMDH algorithm, it is ensured that training set, inspection set Different partitioning schemes, generate contain more Trans-critical cycle CO2The sample combination of system variable.In order to different Trans-critical cycles CO2Heat pump unit carries out identification sequence, calculates its corresponding probability of happening according to feature extraction number.It is assumed that n is training set Total number of samples can ensure that training set and forecast set sample allocation proportion in same sample distribution from 2 circulation values to n-1 Completeness under sequence.
Further, for the fairness of comparative analysis, it is ensured that the completeness of sample order.Statistics is wanted as main composition Plain frequency of occurrence upsets training set, detection collection sample order in advance, which is carried out 50 times at random, and carries out each time In the process, GMDH is carried out, then counts (frequency/all main composition sum of the single element as main composition) and counts every kind and want Probability of the element as main composition.Random 50 experimental results are counted for each experiment, and obtain being averaged for 50 tests Value.
Characteristic variable of the element stood out by selection statistical result as optimal pressure at expulsion, is subsequent optimal The formulation of pressure at expulsion formula fitting and control strategy provides basis.By comparing final control strategy with previous by experiment number From the point of view of effect according to control strategy made of fitting formula, GMDH method selected characteristic variable can be more objectively from data sheet The subjective guess that body sets out and avoids researcher for Unknown Model, so that relatively good control effect is obtained, this Outside, the adjustment of the control strategy of current database is most adapted to by can also voluntarily realize for the update of database in real time.

Claims (6)

1.一种基于GMDH算法的跨临界CO2系统最优排气压力特征变量的确定方法，其特征在于，包括以下步骤：1. a determination method based on the transcritical CO 2 system optimal exhaust pressure characteristic variable of GMDH algorithm, is characterized in that, comprises the following steps: 第一步：采集跨临界CO2热泵热水器系统工况测试过程中得到的样本，获得样本数据集；构建效能预测模型，输入为环境温度、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，输出为排气压力；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; 对数据样本集进行划分，用字母A表示训练集，用于产生竞争模型；用字母B表示检验集；利用外准则来筛选竞争模型有wn＝NA+NB，w＝A∪B，其中w表示所有数据样本；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; 第二步：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，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 are used as the modeling network 55 initial models of ; 第三步：确定外准则的计算公式为： 式中yt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; 第四步：构建二元线性函数y＝axi+bxj作为传递函数产生中间模型并且进行逐层筛选，最终形成最优复杂度模型结构。Step 4: Construct a binary linear function y=ax i +bx j as a transfer function to generate an intermediate model and perform layer-by-layer screening, and finally form an optimal complexity model structure. 2.根据权利要求1所述的一种基于GMDH算法的跨临界CO2系统最优排气压力特征变量的确定方法，其特征在于，第四步中，传递函数wk＝axi+bxj为第一层中间模型，其中竞争模型个数k的大小和前一层的项数m有关，m＝9，则依据公式得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wk的参数a,b；2. The method for determining the optimal exhaust pressure characteristic variable of a transcritical CO 2 system based on a GMDH algorithm according to claim 1, wherein in the fourth step, the transfer function w k =ax i +bx j is the first-layer intermediate model, in which the size of the number of competing models k is related to the number of items m in the previous layer, m=9, then according to the formula 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; 中间模型在第一层中间模型地基础上进而搭建第二层的竞争模型；第二层的输入变量与第一层的输出变量wk相等，构建竞争模型的个数为再次通过检测集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; 从第二层开始，在第二选择层产生进入下一层的结构相同的模型数由外准则确定；通过不断产生竞争模型及根据外准则值进行筛选，模型的复杂度不断增加，同时通过计算外准则值提高模型质量；当模型质量无法再次提高时，建模过程停止，最优模型找到；此时检测集上计算的最小拟合方差取得全局最小值。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. 3.根据权利要求1所述的一种基于GMDH算法的跨临界CO2系统最优排气压力特征变量的确定方法，其特征在于，在GMDH算法中加入循环，确保训练集、检验集的不同分割方式，生成含有更多跨临界CO2系统变量的样本组合方式；假定n为训练集的总样本数，从2循环取值到n-1，确保训练集与预测集样本分配比例在同一种样本分布顺序下的完备性。3. the method for determining the optimal exhaust pressure characteristic variable of a transcritical CO 2 system based on the GMDH algorithm according to claim 1, is characterized in that, in the GMDH algorithm, add circulation to ensure the difference between training set and inspection set The split method generates a sample combination method that contains more transcritical CO 2 system variables; assumes n is the total number of samples in the training set, and takes the value from 2 to n-1 to ensure that the distribution ratio of the training set and the prediction set samples is the same. Completeness under sample distribution order. 4.根据权利要求1所述的一种基于GMDH算法的跨临界CO2系统最优排气压力特征变量的确定方法，其特征在于，为了比较分析的公平性，确保样本顺序的完备性；统计作为主成份的要素出现次数，预先打乱训练集、检测集样本顺序，将该过程随机进行50次，并在每一次进行过程中，进行GMDH，再统计出每种要素作为主成份的概率；针对每次实验均统计随机50次的实验结果，并取得50次试验的平均值。4. the method for determining the optimal exhaust pressure characteristic variable of a transcritical CO 2 system based on a GMDH algorithm according to claim 1, characterized in that, in order to compare the fairness of the analysis, ensure the completeness of the sample sequence; statistics The number of occurrences of the elements as the principal components, the order of the samples in the training set and the test set is disrupted in advance, the process is randomly performed 50 times, and in each process, GMDH is performed, and then the probability of each element as the principal component is counted; For each experiment, 50 random experimental results were counted, and the average value of the 50 experiments was obtained. 5.根据权利要求1所述的一种基于GMDH算法的跨临界CO2系统最优排气压力特征变量的确定方法，其特征在于，样本数据集中的样本均为跨临界CO2热泵热水器系统COP稳态下记录的系统运行数据。5. The method for determining the optimal exhaust pressure characteristic variable of a transcritical CO 2 system based on a GMDH algorithm according to claim 1, wherein the samples in the sample data set are all transcritical CO 2 heat pump water heater system COP System operating data recorded at steady state. 6.根据权利要求1所述的一种基于GMDH算法的跨临界CO2系统最优排气压力特征变量的确定方法，其特征在于，样本数据集中样本的数量为5000。6 . The method for determining the optimal exhaust pressure characteristic variable of a transcritical CO 2 system based on the GMDH algorithm according to claim 1 , wherein the number of samples in the sample data set is 5000. 7 .
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