KR101295859B1 - SVRC Model Predicting Thermal Conductivity of Gas of Pure Organic Compound - Google Patents

Abstract

The present invention consists of up to five elements such as hydrogen (H), carbon (C), nitrogen (N), oxygen (O), and sulfur (S), and is composed of pure molecules consisting of up to 25 atoms except hydrogen. A mathematical model for predicting the thermal conductivity of organic compounds with high accuracy is provided. The above model is a scaled variable reduced coordinate (SVRC) model, which allows the SVRC equation to determine the value of gas thermal conductivity at each temperature. These calculations require values of several parameters, which are values uniquely given to each compound. In order to obtain them, the present invention is based on experimental values of gas thermal conductivity of a plurality of compounds satisfying the above-mentioned conditions. By using multiple linear regression and neural network technique, QSPR (quantitative structure-property relationship) prediction models for each parameter were established. Therefore, the above model predicts the gas thermal conductivity of a compound composed purely of this molecule, as long as the specific values of the molecular descriptors included in the model are known. As such, the present invention provides a method for predicting a reliable gas thermal conductivity value even for a large number of compounds in which the experimental value is not known, thereby saving the cost and time required for the experiment, thereby facilitating the R & D activities of related industries. It produces effects such as making it.

Description

SVRC Model Predicting Thermal Conductivity of Gas of Pure Organic Compound

The present invention belongs to a field of physical chemistry called physical property prediction and relates to a method for predicting gas thermal conductivity, which is one of several physical properties of a compound, with high accuracy.

Knowing the exact values of the various properties of a compound specifically involves the entire process of production and consumption, such as reviewing the feasibility of the use of the substance, designing the synthesis and purification processes, and establishing methods and conditions for storage, transport, use and disposal. It is an important issue, both industrially and academically, because it is crucial for all decision making. The most accurate way of knowing the value of the property of interest of the compound of interest is also an experiment, but it is true that it is quite costly and time consuming in many aspects, including the preparation of purified samples and the construction of an environment for accurate measurements. May not be possible. Thus, as an alternative, many researchers have long been trying to predict the exact value of various properties of a compound. As such, the prediction of physical properties has a long history, and new prediction methods are constantly appearing. At present, several prediction models with different accuracy and application range coexist.

를 통해서 1초동안에 흐르는 열량을 줄(joule)로 측정한 값을 말한다. 기체 열전도율의 예측에 대한 그간의 연구결과들은 문헌[Poling B. E., Prausnitz J. M., O’Connell J. P., The Properties of Gases and Liquids(5 ed.), New York, McGraw Hill, (2000).]에 간략히 소개되어 있다. Several prediction models have been proposed to date for gas thermal conductivity, which is a property of interest of the present invention. Thermal Conductivity of Gas is the ratio of the amount of heat flowing vertically in unit time through the unit area of an isothermal surface inside a pure object and the temperature gradient in this direction, ie the degree of heat conduction in the material. If the temperature difference of 1K is on both sides of a plate 1m thick as a value,

It is the value measured by joule of the amount of heat flowing in 1 second through. The results of previous studies on the prediction of gas thermal conductivity are briefly described in Polling BE, Prausnitz JM, O'Connell JP, The Properties of Gases and Liquids (5 ed.) , New York, McGraw Hill, (2000). It is.

, 분자량

을 이용하여 임의의 온도에 대한 기체 열전도율을 계산할 수 있게 해준다. The well-known and widely used models for predicting gas thermal conductivity at present are mainly mathematical models developed based on the principle of response state. The following equation, known as the Eucken relation, is the most classic and widely used model [Poling BE, Prausnitz JM, O'Connell JP, The Properties of Gases and Liquids (5 ed.) , New York, McGraw Hill, (2000)]. Viscosity η Heat capacity of the second phase body

, Molecular Weight

Allows to calculate the gas thermal conductivity for any temperature.

This method is known to be less accurate for polar molecules.

환산온도

, 임계 온도

, 임계 압력

, 분자량 M을 이용하여 임의의 온도에 대한 기체 열전도율을 계산할 수 있게 해준다.One similar method of calculating thermal conductivity using other properties is the Misic-Thodos method [Misic, D., G. Thodos, Atmospheric Thermal Conductivity for Gases of Simple Molecular Structure , J. Chem. Eng. Data, 8 (1963), 540] heat capacity of ideal gas

Conversion temperature

Critical temperature

Critical pressure

Using the molecular weight M, it is possible to calculate the gas thermal conductivity for any temperature.

가 0.355이상일 때와 탄화수소 분자들 이외의 상황에서는 대해서는 정확도가 떨어지는 것으로 알려져 있다.This method is more than 273K or converted temperature

Is less than 0.355 and in situations other than hydrocarbon molecules.

가 온도

의 다음과 같은 함수로 주어진다고 가정한다.One of the alternatives for building a predictive model of gas thermal conductivity is the scaled variable reduced coordinates (SVRC) method. This method has been proposed in Shaver RD, Robinson RL Jr., Gasem KAM, Fluid Phase Equilibria , 64: 141 (1991) as an integrated framework for dealing with the saturation properties of compounds based on the principle of correspondence. There is no example of applying this method to gas thermal conductivity. This method is basically a saturation property of a compound

Temperature

Suppose that is given by

와

는 각각correlating 함수, scaling 지수라고 불리는 양들이며

는 일종의 환산온도(reduced temperature)이다. 아래첨자 c와 b는 각각 임계점과 끓는점을 의미하는 것으로

는 각각 임계점과 끓는점에서의 온도를,

는 각각 임계점과 끓는점에서의

값을,

는각각 임계점과 끓는점에서의 물성값을 뜻한다. 또한 A, B, C는 각 물성에 고유하게 주어지는 보편상수들(universal constants)로서 본 발명에서는 기체 열전도율을 예측하기 위해 그 값을 각각1.07068, 0.325, 0으로 정하였으며

, 즉

라고 가정하였다. 위의 수식을 통해 기화열을 계산하기 위해서는 각 화합물에 대한 이와 같은 매개 변수들의 값을 알아야 하는데 이를 해결하는 한가지 방법은 각 매개 변수에 대한 QSPR 예측모형을 확립하는 것이다.here

Wow

Are the quantities called the correlating function and the scaling exponent

Is a reduced temperature. The subscripts c and b mean the critical point and the boiling point, respectively

Is the temperature at the critical and boiling points, respectively,

At the critical and boiling points, respectively

Value,

Is the property value at the critical point and the boiling point, respectively. In addition, A, B, and C are universal constants uniquely given to each physical property. In the present invention, the values are set to 1.07068, 0.325, and 0 to predict gas thermal conductivity.

, In other words

Is assumed. In order to calculate the heat of vaporization through the above formula, we need to know the values of these parameters for each compound. One way to solve this problem is to establish a QSPR prediction model for each parameter.

QSPR (quantitative structure-property relationship) basically starts with the assumption that the properties of a compound are a function of the structural properties of the molecule and uses various molecular descriptors that reflect different structural properties. The number of molecular descriptors proposed to date has been thousands, and many kinds of molecular descriptors range from simple ones such as the number of carbons or hydrogens in a molecule to complex ones such as the shape, connection state, and electrochemical properties of molecules. Calculation methods have been developed [Todeschini R., V. Consonni V., Molecular Descriptors for Chemoinformatics: Second, Revised and Enlarged Edition: Volume I / II , Wiley-VCH, 2009]. The QSPR prediction model is presented in the form of a function that includes some of these molecular descriptors and sometimes, in addition, some of the other physicochemical properties of the compound, which are also functions of structural properties.

들의 선형 결합 함수이며 각 계수

들은 주로 다중선형회귀분석을 통해 실험데이터로부터 결정된다.The most frequently adopted form of such a function is

Linear coupling function of each coefficient

These are mainly determined from experimental data through multiple linear regression analysis.

이 부여되어 있다. 은닉층과 출력층의 각 노드들은 전 단계의 노드들로부터 이러한 연결들을 통해 입력을 받은 뒤 이를 가공하여 출력값을 만드는데 이때 활성화 함수(activation function)라 불리는 함수

를 적용한다. 이러한 인공신경망을 실제로 활용하려면 먼저, 다양한 입력값과 그 입력값에 대응하는 출력값을 함께 묶어 놓은 샘플집합을 이용하여 인공신경망을 훈련시키는 과정이 필요한데 이는 주어진 입력에 대한 인공신경망의 출력과 원하는 출력의 차이가 최소가 되도록 역전파(back propagation) 알고리즘을 사용하여 각 연결의 가중치를 최적화 하는 것을 말한다. 이러한 훈련을 거친 인공신경망은 문제해결에 필요한 규칙이나 지식을 따로 제공하지 않아도 학습을 통해서 스스로 일반적인 규칙을 수립하여 미지의 입력에 대해서도 타당성 있는 출력을 내주므로 화합물의 물성예측과 같이 기반 이론이 결여되어 있는 분야에 매우 유용한 수단으로 널리 이용되고 있다.
Another way to create a QSPR model is to use an artificial neural network. Artificial neural network technology is one of the long-standing research results of human beings who want to make intelligent machines by modeling human nerve cells with intelligence, and is an information processing technology that has been applied in various fields since the mid 20th century. . 4 shows a typical example of an artificial neural network. As can be seen, the artificial neural network has an input layer for receiving input data, an output layer for producing output data, and a hidden layer located between them, each layer having one or more nodes. ) Each node in the hidden layer is connected to nodes in the input and output layers, and each connection has a quantity called a weight.

Is granted. Each node in the hidden and output layers receives input through these connections from the nodes in the previous stage and then processes it to produce an output, which is called an activation function.

Is applied. In order to actually use such an artificial neural network, first, the neural network is trained using a sample set in which various input values and output values corresponding to the input values are bundled together. This means optimizing the weight of each connection using a back propagation algorithm to minimize the difference. The neural network that has undergone such training does not provide the necessary rules or knowledge to solve the problem, but it establishes general rules through learning and gives valid output for unknown inputs. It is widely used as a very useful means in the field.

The technical problem to be solved by the present invention is to overcome the limitations of the various models mentioned above and to show more broad and more accurate predictive performance, hydrogen (H), carbon (C), nitrogen (N), oxygen (O) and sulfur. The SVRC model is constructed for the gas thermal conductivity of a pure organic compound composed of less than five elements such as (S) and molecules having 25 or less atoms except hydrogen.

We achieved this goal by constructing QSPR models that predicted the values of the parameters in the SVRC equation, taking into account a wider variety of molecular descriptors based on more experimental data. Some of these are multilinear regression-artificial neural network hybrid models obtained by combining a combination of multiple linear regression and artificial neural network techniques. Especially, artificial neural networks have a nonlinear functional relationship between independent and dependent variables that cannot be reflected It has the advantage of being able to reflect, which makes it possible to implement a model with higher prediction performance. However, the artificial neural network has a disadvantage in that its stability is lower than that of the multiple linear regression model due to its high degree of freedom in rule setting. In the present invention, when the prediction value of the artificial neural network model and the prediction value of the multiple linear regression model show a large difference, the method of adopting the prediction value of the multiple linear regression model compensates for these shortcomings. We established an excellent prediction model that takes advantage of the neural network model.

The reason for the limitations mentioned above on the range of compounds to which the predictive model can be applied is mainly to the current state of the art, if any of the molecular descriptors used require quantum mechanical calculations to obtain their values. Is due to the fact that for compounds outside the stated range, troubles arise in terms of accuracy and calculation time. However, even within the above limitations, since there are a great many compounds and industrially important compounds are included in a large amount, it is determined that the present invention can greatly benefit human society.

Today, humans depend on a wide variety of compounds, including plastics, fibers, rubber, paints, fertilizers, medicines and fuels, and this trend is expected to intensify. According to the American Chemical Society (ACS), as of July 2010, the total number of compounds registered was over 54,000,000. In comparison, even if the physical property value is only one, the number of experimentally known compounds is only tens of thousands. The physical property value of compounds is essential for the better life of mankind, such as the development of new materials and new drugs, the optimal design of chemical plants, the improvement of the productivity of existing facilities, the development and saving of resources, the securing of safety, and the protection of the environment. In particular, the gas thermal conductivity is a property that commercial programs such as AspenPlus and Pro / II, which are well known as optimal design programs for chemical plants, are urgently requesting the exact values. However, at present, the number of compounds whose experimental values are known is only a few thousand, and depending on the compounds, the work of obtaining data through experiments may be past due to toxicity, instability, and difficulty of purification. From this point of view, the present invention, which can obtain gas thermal conductivity of a large number of compounds with high accuracy without any experiments, not only reduces the cost and time required for experiments, but also makes it possible to estimate the value even when the experiments are impossible. In addition to facilitating the R & D activities of the University, it will also provide the information that is appropriate to all places that need it, such as academics and academia, so that the activities can be carried out more smoothly.

1 is a flowchart illustrating a process of constructing an SVRC prediction model for a gas thermal conductivity provided by the present invention.
2 is a flowchart illustrating a process of constructing a multilinear regression model for α among parameters required for an SVRC model.
3 is a flowchart illustrating a process of constructing a multiple linear regression-artificial neural network hybrid model for λ _b and λ _3b among parameters required for an SVRC model.
Figure 4 is a view showing the structure of the artificial neural network used in the present invention.
5 to 8 illustrate, for example, the prediction performances of the Misic-Thodos model, the modified Eucken model, and the prediction model provided by the present invention.
9 is a histogram diagram of 6090 experimental data of the Misic-Thodos model.
10 is a histogram plot of 6090 experimental data of the modified Eucken model.
11 is a histogram diagram of 6090 experimental data of the SVRC model.

Figure 1 is a simplified representation of the process of building the SVRC model for gas thermal conductivity.

The first thing to do when building an SVRC model is to collect and review the experimental data as specified in step 1. As a result of extensive research on all literatures and data that can be referred to through various papers, books, and Internet sites for the present invention, 9730 data of 910 compounds were collected. The collected data were examined in a variety of ways to determine whether they were truly valid values that could be used to build the model.They were not experimental values, errors in data notation, or values for similar temperatures of the same compound. If the values are unreliably distant from the values or if the values for the molecular descriptors are data on a compound that is difficult to prepare immediately, the data is corrected or deleted. Data were selected. In the present invention, the 'organic compound' or 'compound' is composed of five elements such as hydrogen (H), carbon (C), nitrogen (N), oxygen (O), and sulfur (S). Refers to a substance consisting of molecules with 25 or fewer atoms excluded.

The next step is to prepare the values of the molecular descriptors for these compounds. The values for various molecular descriptors totaling up to 1978 are computed in batches using a computer from files containing information on the molecules of each compound. In order to calculate the electronic structure of molecules, the Schrodinger equation is usually solved by a pure theory to solve the electron energy. However, in the case of systems with many electrons, Hartley uses an approximation method that ignores electron correlation. Hartree-Fock (HF) method [CC J. Roothan, Rev. Mod. Phys. 23, 69 (1951)]. This approximation introduces a fundamental error in the calculated results and adds a multidimensional theoretical perturbation term to the Post Hartree-Fock method [C. Moller and M. S. Plesset, Phys. Rev. 46, 618 (1934)], to obtain a more accurate solution, but require a relatively large amount of computation. In this way, it is too costly or time-consuming to calculate large molecules.

In addition, the Gaussian method that combines Hartley-Fork and Post Hartley-Fork [L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem. Phys. 94, 7221 (1991); L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, and J. A. Pople, J. Chem. Phys. 109, 7764 (1998) show very little error in energy prediction, but more computation is required because it performs energy calculations for several post-Hartley-Fork methods.

Density functional theory is used to find the ground state using the function of the total energy using the electron density function instead of the wave function with the multidimensional perturbation term to consider the correlation between the electrons of the molecules of many electrons. R. Seeger and JA Pople, J. Chem. Phys. 66, 3045 (1977). The advantage of the density functional theory is that the electron density only needs to be taken into account so that more accurate results can be obtained with comparable calculations to the Hartree-Fock method. The combination of exchange functions and correlation functions for calculating the exchange-correlation energy of the electrons is used to obtain more improved results without increasing the calculation amount.

The computational theories previously attempted to select an optimal quantum mechanical calculation method are the density ranges of the aforementioned Hartley-Fork method, various Post-Hartley-Fork methods, Gaussian (G2, G3) methods, and various combinations of functional functions. Function theory. Among them, one method of density functional theory, which is the best performance calculation time, was selected.

Therefore, in the present invention, the optimization of the molecular structure and the frequency calculation are performed by applying the calculation method of the specified density functional theory using a commercial quantum mechanical calculation program.

In the optimized structure, not only the above physical information but also molecular descriptors represented by various meaningful values reflecting the characteristics of the molecules can be obtained. Some molecular descriptors can express the characteristics of two-dimensional structures, while others represent the characteristics of three-dimensional structures. Divided into 24 categories, including detailed presenters in each category. After calculating the molecular descriptor values, we picked out those that were not suitable, that is, the values were the same for all sample compounds and could not be independent variables in the model. This is because it prevents irrelevant molecular expressions from being included in the prediction model, thereby increasing the reliability of the model and reducing the computation time required to find the optimal model by reducing the number of molecular expressions.

의 값과

의 값이 필요하다. 끝점인 임계온도에서의 기체 열전도율를 정확히 예측하는 것은 어려운 일이다. 따라서 본 발명에서는 임계온도 대신 정상끓는점의 3배(

)를 기체 열전도율곡선의 끝 온도로 잡았는데, 샘플 화합물들에 대해 실험값 끝점 온도의 평균은 정상끓는점의 3배의 평균과 거의 일치한다. 이제 SVRC 모형을 완성하기 위해서는 나머지 매개변수들인 α,

,

에 대한 QSPR 예측모형을 확립하여야 한다. 이러한 QSPR 예측모형을 확립하기 위해서는 각 매개변수 별로 여러 화합물들에 대한 해당 값들의 집합을 마련하여야 하는데,

에 대해서는 먼저 기체 열전도율의 전형적인 곡선을 각 화합물의 실험데이터에 맞춘 뒤, 그 곡선에서 온도가

(또는

)가 되는 지점의 값을 취하였으며, α에 대해서는 비선형방정식의 수치해법을 통하여 아래의 식에서

의 값을 각 온도에 대해 구한 뒤, 이러한 값들이 이루는 선에서 온도가

인 지점의 값을 각각 취하였다.Step 4 is followed by preparing data needed to establish a QSPR model for each parameter based on the experimental data. In order to calculate the gas thermal conductivity with the SVRC formula, the gas thermal conductivity at the critical temperature and boiling point

And the value of

The value of is required. It is difficult to accurately predict the gas thermal conductivity at the critical temperature, which is the end point. Therefore, in the present invention, three times the normal boiling point instead of the critical temperature (

) Is taken as the end temperature of the gas thermal conductivity curve, for the sample compounds the mean of the experimental endpoint temperature is nearly identical to the average of three times the normal boiling point. Now, to complete the SVRC model, the remaining parameters α,

,

You should establish a QSPR prediction model for. In order to establish the QSPR prediction model, a set of corresponding values for various compounds should be prepared for each parameter.

For, we first fit a typical curve of gas thermal conductivity to the experimental data of each compound, and then

(or

Is taken as the value of), and for α, through the numerical solution of the nonlinear equation,

Is obtained for each temperature, and then the temperature

The value of the phosphorus point was taken respectively.

In order to be able to obtain the value of each parameter from the experimental data of a compound to use as a data for establishing the QSPR prediction model, the experimental data of the compound is distributed evenly over a relatively wide temperature range, Since the number of compounds with relatively few experimental data satisfying these conditions exists, the number of compounds participating in the QSPR prediction model of each parameter is significantly reduced than the total number of compounds.

에 대해서는 다중선형회귀-인공신경망 혼성모형을 채택하였다. 도 2는 다중선형회귀모형을 구축하는 과정을, 도 3은 다중선형회귀-인공신경망 혼성모형을 구축하는 과정을 흐름도로 간략히 표현한 것이다. 그 구체적인 세부 단계들은 다음과 같다.Step 5 is to build a QSPR model for each parameter. In the present invention, such a QSPR model, for the α linear multiple regression model,

We adopted the multiple linear regression-artificial neural network hybrid model. 2 is a flowchart illustrating a process of constructing a multiple linear regression model, and FIG. 3 is a process of constructing a multiple linear regression-artificial neural network hybrid model. The specific detailed steps are as follows.

In detail step 1, the sample compounds are divided into two parts: the training set used to explore the predictive model, and the test set used to test the predicted performance of the determined model. The samples were divided in a ratio of 5: 5 to 8: 2, preferably 6 to 4, taking care not to distribute similar molecules on one side only.

이며 이들을 다 조사하는 것은 현실적으로 불가능하다.We then find the best multiple linear regression model based on the training set. The term 'best' is used in the sense of relative meaning that it can be obtained in a relatively short time and has a performance very close to the optimal solution in the absolute sense. The reason for not finding the optimal solution directly is because of the long computation time. For example, when there are 1700 suitable molecular representations out of 1978 molecular representations, you can choose from five different linear regression models. The total number is

It is practically impossible to investigate them all.

In order to obtain useful results within a limited time, the present invention provides a genetic algorithm [Judson, "Genetic Algorithms and Their Uses in Chemistry", Reviews in Computational Chemistry, Lipkowitz & Boyd, Eds., Vol. 10, pp. 1 -73 (VCH Publishers, NY, 1997)]. First, a population of multiple linear regression models is created by randomly drawing a certain number of molecular descriptors from a pool of molecular descriptors. For example, let's say we created a population of 1000 different polylinear regression models that were randomly drawn from 5 of the 1700 suitable molecular descriptors.

Individuals, called chromosomes, are coded by combining the numbers of extracted molecular descriptors. For example, the chromosome of the multiple linear regression model formed by the 45th, 167, 684, 1033, and 1502th molecular descriptors among 1700 molecular descriptors can be expressed as (45, 167, 684, 1033, 1502). Two parent chromosomes are selected from the populations thus generated and crossed over to generate children. In the present invention, the Roulette Wheel method is adopted as a selection method for selecting the parent chromosomes.

) 또는 평균절대오차(average absolute error: AAE)를 활용하였다. 즉 결정계수값이 크거나 평균절대오차값이 작은 것이 선택확률이 높도록 하였다.The Roulette Wheel method is the most commonly used selection algorithm, which allocates a roulette region to the chromosome in proportion to the fitness of each chromosome, and then rotates the roulette to select the chromosome of the corresponding region. Therefore, in this method, the higher the fit, the more likely it is to be selected. The coefficient of determination of the regression model is used to calculate the goodness of fit for each chromosome that determines the probability of selection.

) Or average absolute error (AAE). In other words, the larger the coefficient of determination or the smaller the mean absolute error, the higher the probability of selection.

The single point crossover method is adopted as the breeding method. The most common breeding method is to generate a child by selecting one crossing point on the parent chromosome and exchanging chromosomal parts before and after the point. For example, if a parent chromosome is given as (24, 262, 343, 789, 1290), (38, 454, 554, 1322, 1449) and a cross point is placed between the third and fourth elements, then the child chromosomes are (24, 262, 343, 1322, 1449), (38, 454, 554, 789, 1290).

When the offspring are created, they have a chance of mutating a portion of their chromosomes, which randomly replaces several elements with completely new values. This new information does not exist in the current population. It is a process that makes it possible to search to compensate for the case where there is no proper solution in the initial set combination.

In this way, a new generation of populations are created by replacing some or all of the existing populations with newly obtained entities. Repeat this process until the number of generations reaches a pre-determined value (usually between 10 and 1000), and then select and end up the regression model with the best predictive performance.

Once this best multiple linear regression model has been selected, the next step is to examine its validity. If a problem is found that the t-test value of the molecular descriptors included in the model is not good, go back and look for another model. For example, if the number of sample compounds is 1005 and the selected model consists of five molecular descriptors, if the t-test for one of the molecular descriptors is 3.3 or higher, then the probability that the molecular descriptor is irrelevant to that property is 0.1 It means less than%. In the present invention, when there is a molecular presenter having a t-test value of less than about 3, the selected model is discarded and another model is found. In addition, even if the values of the molecular descriptors for the sample compounds are the same except for a few few compounds, they are not considered to be reliable models. In general, increasing the number of molecular expressions included in the model increases the predictive performance, but such problems occur. Therefore, the final model is usually obtained by repeating these steps through several trials and errors while changing the number of molecular expressions. If the problem no longer appears in the selected model, proceed to the next step.

In the final detail, Step 4, the predictive performance of the model is assessed using test sets that did not participate in model formation. If a problem is found in the training set, such as a lot of poor predictive performance or a significant drop in prediction, go to detail step 1, readjust the training set and the test set, and then proceed with the detailed steps. If the difference between the training set and the test set does not exceed 20% of the absolute mean error (AAE) obtained for the training set, it is judged that the predictive performance is satisfied.

In this way, once the multiple linear regression model for a parameter has been constructed, first the standardization of the data of the molecular presenters and the parameters of the parameters, ie, subtracting the mean of the corresponding data from each value, is needed to build an artificial neural network model. Proceed to divide by deviation. The total sample thus prepared is divided into a training set, a validation set, and a test set in a ratio of approximately 6: 2: 2.

을, 출력층의 활성화 함수로는 선형함수 즉

를 채택하였다. 따라서 입력층의 각 노드들이 받는 입력값들을

라 할 때 은닉층의 j번째 노드의 출력값은

와 같이 주어지며 은닉층이

개의 노드로 이루어져 있을 때 출력층 출력노드의 최종 출력값은

와 같이 주어진다. 여기서

는 문턱 가중치(threshold weight)를 의미한다.We then use them to find the best artificial neural network model. At this time, the search range is limited to a neural network having a hidden layer between the input layer and the output layer as shown in FIG. 4 and having three structures connected only in a feed forward direction, that is, in a direction from the input to the output. It was. The input layer consisted of the same number of nodes that received the values of the molecular markers included in the already established multiple linear regression model, and the output layer consisted of one node that outputs the gas thermal conductivity. In addition, as the activation function of the hidden layer, the Sigmoid function,

, The activation function of the output layer is a linear function

Was adopted. Therefore, the input values that each node in the input layer receives

In this case, the output value of the j th node of the hidden layer is

Is given by

The final output value of the output layer output node when composed of four nodes

As shown in Fig. here

Denotes a threshold weight.

들의 다양한 초기값세트(보통1000세트이내)를 마련하고, 훈련집합을 사용하여 각 세트로 초기화된 신경망을 역전파 알고리즘을 통해 반복 훈련함으로써 가중치

들의 최적화된 값을 찾는다. 최적화에 대한 판단은 매 훈련 후 경신된 가중치들의 값으로 정해지는 모형을 검증집합에 적용하였을 때 그 평균제곱오차(mean square error)의 값이 최소가 되는 것으로 한다. 보통은 3000~5000번의 반복훈련 내에 이러한 시점이 나오게 된다. 이렇게 얻어진 각 초기값세트에 대응하는 최적화된 신경망모형을 훈련집합, 검증집합, 시험집합에 각각 적용하여 그 평균제곱오차들이 모두 다중선형회귀모형의 그것들보다 작은 것만을 모은다. 이러한 것이 여러 개 있을 경우, 결정계수나 평균절대오차 등을 기준으로 가장 우수한 모형을 선택한다.The search proceeds from increasing the number of hidden nodes to one in order. Usually, the search proceeds to twice the number of input nodes. However, if a satisfactory model is not found, the search proceeds further. The detailed procedure is as follows. First, the weight generated by using random number generation function for each number of hidden nodes

Prepare different sets of initial values (usually within 1000 sets), and then use the training set to repeatedly train the neural networks initialized in each set using a backpropagation algorithm.

Find the optimal value for these. The judgment of the optimization is that the mean square error is minimized when the model, which is determined by the updated weights after each training, is applied to the test set. Normally this will occur within 3000 to 5000 repetitions. The optimized neural network model corresponding to each set of initial values thus obtained is applied to the training set, the test set, and the test set, respectively, to collect only those whose mean square errors are smaller than those of the multiple linear regression model. If there are several of these, choose the best model based on the coefficient of determination or the absolute absolute error.

)을 정하여 인공신경망모형과 다중선형회귀모형의 예측값들 차이의 절대값이 기준값을 넘을 경우 다중선형회귀모형의 예측값을 채택하고 이보다 작을 경우 인공신경망모형의 값을 채택하게 하는 것을 말한다.When the artificial neural network model is selected, an overfitting prevention standard is finally set. This is a measure to improve the instability that the artificial neural network gives wrong answers to unknown inputs as a result of overtraining, a reference value (e.g. 0.003 for hydrocarbon starting point gas thermal conductivity).

), Which means that if the absolute value of the difference between the predicted values of the artificial neural network model and the multiple linear regression model exceeds the reference value, the predicted value of the multiple linear regression model is adopted.

After this process, the QSPR model for each parameter is constructed. Next, in step 6, a test is conducted to compare the entire experimental data of each compound with respect to the gas thermal conductivity with the values calculated through the SVRC equation. At this time, the normal boiling point value is required to calculate the predicted value by SVRC formula. For this information, the value obtained by the known method or the calculation method based on the QSPR model is used. If the error between the experimental and predicted values is larger than the acceptable level (approximately 20% more than the predicted error is greater than the experimental mean error), go back to step 5 and re-establish the QSPR model for each parameter. If it passes the test, it is adopted as the completed SVRC model.

,

, α의 값을 예측하는 QSPR 모형은 표 1(

에 대한 QSPR 예측모델의 주요 내용), 표 2(

에 대한 QSPR 예측모델의 주요 내용) 및 표 3(α에 대한 QSPR 예측모델의 주요 내용)에 간단히 기술되어 있으며 이들을 바탕으로 기체 열전도율을 예측하는 SVRC 모형과 그 성능에 대한 결과는 표 4(SVRC 예측모델의 주요 내용)에 나와 있다.The results of the SVRC model established through this process are summarized in Tables 1-4. each

,

, QSPR model for predicting the value of α is shown in Table 1 (

Highlights of the QSPR predictive model for

The main contents of the QSPR predictive model for KSPR) and Table 3 (the main contents of the QSPR predictive model for α) are summarized in Table 4 (SVRC forecasting). The main contents of the model).

의 평균절대오차값을 보이고 Eucken 변형모형은 0.822973의 결정계수값과 0.011201

의 평균절대오차값을 보이는 반면, 본 발명의 SVRC 모형은 0.979691의 결정계수값과 0.003665

의 평균절대오차값을 보여 현저히 우수함을 알게 되었다. 도 5~8은 예로 몇몇 화합물에 대해 각 모형의 예측성능을 비교한 도면들이다. 이 도면들로부터 SVRC 모형이 기존 모형보다 우수한 성능을 가짐을 눈으로 확인할 수 있다. 한편 6090개의 실험데이터에 대해 실험값과 예측값 사이의 오차를 히스토그램으로 그린 것이 도 9, 10, 11이다. 이 도면들은, Misic-Thodos모형은 60.44%, Eucken 변형모형은 49.83%, SVRC 모형은 73.2%의 확률로 6% 오차 이내로 기체의 열전도율을 예측하고 있음을 보여주어 SVRC 모형이 보다 정확함을 증명해준다.In order to show that the present invention is superior to the existing technology, we compared the predictive performance of the Misic-Thodos model and Eucken's deformation model mentioned above as the existing model widely used with the SVRC model of the present invention on 6090 experimental data of 609 compounds. . As a result, the Misic-Thodos model has a coefficient of determination of 0.80743 and 0.010691.

The average absolute error of and Eucken's deformation model is 0.822973 and 0.011201

While the mean absolute error of is shown, the SVRC model of the present invention has a coefficient of determination of 0.979691 and 0.003665

The average absolute error of was found to be remarkably excellent. 5 to 8 are examples for comparing the predictive performance of each model for some compounds. From these drawings, it can be seen that the SVRC model has better performance than the existing model. Meanwhile, FIGS. 9, 10, and 11 show a histogram of the error between the experimental value and the predicted value for 6090 experimental data. These figures show that the SVRC model is more accurate, showing that the Misic-Thodos model is 60.44%, the Eucken deformation model is 49.83%, and the SVRC model predicts the thermal conductivity of the gas within 6% error.

The present invention is not limited to the above-described embodiments, and any person having ordinary skill in the art to which the present invention pertains may make various modifications without departing from the gist of the present invention as claimed in the claims. Such changes are intended to fall within the scope of the claims.

Claims (15)

A first step of inputting experimental data of collected sample organic compounds;
Preparing a molecular presenter value for a gas thermal conductivity of an organic compound of the sample compounds;
Third step of obtaining parameters required for SVRC equation described in Equation (1) below

[Where [lambda] is gas thermal conductivity, [lambda] _3b is gas thermal conductivity at temperature T _3b three times the normal boiling point, [lambda] _b is gas thermal conductivity at normal boiling point T _b , and [alpha] is a scaling index .;
A fourth step of constructing a QSPR model for gas thermal conductivity at a temperature three times the parameter normal boiling point, gas thermal conductivity at a normal boiling point, and α obtained in the third step;
A fifth step of testing predictive performance with the experimental data; And
If the test of the fifth step is satisfied, the organic compound is determined by the SVRC model including the sixth step of adopting the gas thermal conductivity predicted value by the searched model as the gas thermal conductivity value and not satisfying the fourth and fifth steps. How to find the gas thermal conductivity of
The method of claim 1, wherein the method of obtaining a QSPR model for gas thermal conductivity at a temperature three times the normal boiling point and gas thermal conductivity at the normal boiling point
A step 4-0 of extracting gas thermal conductivity at a temperature three times the normal boiling point, gas thermal conductivity at a normal boiling point, and optimal molecular descriptors for α;
Step 4-1 separating the experimental data into a training set and a test set;
Step 4-2 of searching for an optimal multiple linear regression model for the training set;
Steps 4-3 to review the validity of the selected model;
Step 4-3, if the validity in step 4-3, and repeats step 4-2, step 4-3, and if valid, step 4-4 of testing the predictive performance of the model against the test set;
If the performance does not meet the criteria in the 4-4 test for the test set, repeat steps 4-2 to 4-4, and if the performance satisfies the criteria, separate the data into three sets after sample standardization. 4-5 steps;
Step 4-6 of dividing the entire sample into three sets and searching for an optimal artificial neural network model;
Predicted gas thermal conductivity at a temperature which is three times the normal boiling point and the normal boiling point obtained by the optimal multiple linear regression model satisfying the performance test in the fourth to fifth stages, and the optimum artificial value found in the fourth to sixth stages. Steps 4-7 of comparing the absolute value of the difference between the predicted values of the gas thermal conductivity at a temperature which is three times the normal boiling point and the normal boiling point obtained by the neural network model with a preset overfit prevention reference value; And
If the difference is greater than the reference value for preventing overfitting, the gas thermal conductivity predicted value at the temperature of three times the normal boiling point and the normal boiling point by the multiple linear regression model obtained in steps 4-5 is three times the normal boiling point and the normal boiling point. If the gas thermal conductivity value is smaller than the reference value for preventing overfitting, the predicted value of the gas thermal conductivity at a temperature which is three times the normal boiling point and the normal boiling point by the artificial neural network model detected in steps 4-6 is 3 of the normal boiling point and the normal boiling point. 4 to 8 steps of adopting the gas thermal conductivity value at the temperature of vane,
In the fourth step, a method for obtaining a QSPR model for α is
If the performance does not meet the criteria in the above-described steps 4-1 to 4-4 and the test set 4-4 for the test set, the steps 4-2 to 4-4 are repeated, and the performance is the standard. Step 4-5-1 to determine the optimal multiple linear regression model if satisfied;
Method for obtaining the gas thermal conductivity of the organic compound by the SVRC model comprising the step 4-6-1 to obtain the α value through the multiple linear regression model that satisfies the performance test in step 4-5-1.
3. The method according to claim 2, wherein in step 4-0, the gas thermal conductivity at the temperature three times the normal boiling point, the gas thermal conductivity at the normal boiling point, and the optimal molecular expression for α are not the same for all the sample compounds. A method of obtaining the gas thermal conductivity of an organic compound by an SVRC model characterized in that it is an independent molecular presenter.
The method of claim 2, wherein the training set and the test set are divided by a ratio of 5: 5 to 8: 2 in step 4-1.
The method according to claim 2, wherein in step 4-2, the multiple linear regression model is derived from the SVRC model by searching for the multiple linear regression model by applying a genetic algorithm to the training set. A method of obtaining the gas thermal conductivity of a compound.
The method of claim 5, wherein the genetic algorithm generates a population composed of a plurality of multiple linear regression models randomly drawn from a predetermined number of molecular expressions in a pool of molecular expressions. Making; Encoding each individual by combining the numbers of the extracted molecular presenters; Selecting two parent chromosomes from the created population by the Roulette Wheel method and generating offspring by a single point crossover method; A method of obtaining gas thermal conductivity of an organic compound by an SVRC model, comprising: generating a new population by mutating a portion of chromosomes of the generated offspring with a certain probability and then replacing a portion of the existing population with them. .
3. The method of claim 2, wherein the step 4-2 is to determine the gas thermal conductivity of the organic compound by the SVRC model comprising determining the predictive performance by the coefficient of determination or the mean absolute error of the regression model.
The method of claim 2, wherein the validity in the step 4-3 is to determine the gas thermal conductivity of the organic compound by the SVRC model to determine the validity by the t-test value.
The method of claim 2, wherein in step 4-5, if the predictive performance of the test set is similar to the predicted performance of the training set, a multiple linear regression model is determined, and the predictive performance of the test set is predicted performance of the training set. And the thermal conductivity of the organic compound by the SVRC model that reclassifies the training set and the test set.
[4] The SVRC model of claim 2, wherein the search range by the artificial neural network in step 4-6 has one hidden layer between the input layer and the output layer and is connected only in a feed forward. To obtain the gas thermal conductivity of an organic compound.
11. The method of claim 10, wherein a sigmoid function is used as the activation function of the hidden layer.
3. The method of claim 2, wherein the reference value for preventing overfitting for the gas thermal conductivity at a temperature three times the normal boiling point in steps 4-7 is 0.05 W / (m * K), and for the gas thermal conductivity thermal conductivity at the normal boiling point. The overfit prevention reference value is 0.006 W / (m * K) method for obtaining the gas thermal conductivity of the organic compound by the SVRC model.
According to claim 2, wherein the molecular descriptors for the gas thermal conductivity at the normal boiling point extracted in step 4-0
P ₁ : Max net atomic charge for a H atom,
P ₂ : hydrogen bond dependent hydrogen bond base charge surface area fraction (HA dependent HDCA-1 / TMSA),
P ₃ : Edgevalue 12 from edge adjacency matrix weighted by edge degrees,
P ₄ : Broto-Moreau autocorrelation of a topological structure-lag 3 / Weighted by atomic masses,
P ₅ : R maximal autocorrelation of lag 5 / Weighted by atomic polarizabilities,
P ₆ : H autocorrelation of lag 6 / Weighted by atomic masses,
P ₇ : Al-O-Ar / Ar-O-Ar / R..O..R / ROC = X Number of functional groups (Al-O-Ar / Ar-O-Ar / R..O..R / ROC = X),
P ₈ : Kier & Hall index (order 1),
P ₉ : atomic charge weighted partial negative charge surface area fraction (FNSA-3 Fractional PNSA (PNSA-3 / TMSA)), and
P ₁₀ : contains the moment of inertia B,
Molecular descriptors for the gas thermal conductivity at temperatures three times the normal boiling point
P ₁ : topological charge index of order 9,
P ₂ : Tokyo Distribution Function-10.0 / Radial Distribution Function-10.0 / weighted by atomic masses,
P ₃ : Spectral moment 09 from edge adjacency matrix weighted by dipole moments,
P ₄ : Average electrophilic reactivity index for a O atom,
P ₅ : Broto-Moreau autocorrelation of a topological structure-lag 2 / Weighted by atomic van der Waals volumes,
P ₆ : Geary's autocorrelation-lag 1 / Weighted by atomic Sanderson electronegativity,
P ₇ : Radial Distribution Function-13.5 / weighted by atomic Sanderson electronegativity,
P ₈ : sp3 carbon / sp2 carbon bonded hydrogen (H attached to C1 (sp3) / C0 (sp2)),
P ₉ : Geary's autocorrelation-lag 2 / Weighted by atomic polarizability,
P ₁₀ : hydrogen bonding charged surface area fraction (FHBCA Fractional HBCA (HBCA / TMSA)), and
P _{11 includes the} frequency of C-O at topological distance 08
The optimal molecular expression for α extracted in step 4-0 is
P ₁ : Max partial charge for a C atom,
P ₂ : Image of the Onsager-Kirkwood solvation energy,
P ₃ : Spectral moment 13 from edge adjacency matrix weighted by dipole moments,
P ₄ : lowest eigenvalue n. 1 of Burden matrix / weighted by atomic masses,
P ₅ : HACA H-acceptors charged surface area,
P ₆ : Randic index (order 2),
P ₇ : topological charge index of order 9,
P ₈ : Total charge weighted partial negative charge surface area fraction weight (WNSA-2 Weighted PNSA (PNSA2 * TMSA / 1000)),
P ₉ : Tokyo Distribution Function-10.0 / Radial Distribution Function-10.0 / weighted by atomic masses, and
P ₁₀ : hydrogen donor surface area fraction (FHDSA Fractional HDSA (HDSA / TMSA))
Method for obtaining the gas thermal conductivity of the organic compound by the SVRC model comprising a.
A computer-readable storage medium having recorded thereon a program for executing on a computer a method for obtaining the gas thermal conductivity of an organic compound according to any one of claims 1 to 13.
About SVRC model described in following formula (2)

Where λ is the gas thermal conductivity, λ _3b is the gas thermal conductivity at temperature T _3b three times the normal boiling point, λ _b is the gas thermal conductivity at normal boiling point T _b , and α is the scaling index.
The molecular descriptor for the gas thermal conductivity at the normal boiling point
P ₁ : Max net atomic charge for a H atom,
P ₂ : hydrogen bond dependent hydrogen bond base charge surface area fraction (HA dependent HDCA-1 / TMSA),
P ₃ : Edgevalue 12 from edge adjacency matrix weighted by edge degrees,
P ₄ : Broto-Moreau autocorrelation of a topological structure-lag 3 / Weighted by atomic masses,
P ₅ : R maximal autocorrelation of lag 5 / Weighted by atomic polarizabilities,
P ₆ : H autocorrelation of lag 6 / Weighted by atomic masses,
P ₇ : Al-O-Ar / Ar-O-Ar / R..O..R / ROC = X Number of functional groups (Al-O-Ar / Ar-O-Ar / R..O..R / ROC = X),
P ₈ : Kier & Hall index (order 1)
P ₉ : atomic charge weighted partial negative charge surface area fraction (FNSA-3 Fractional PNSA (PNSA-3 / TMSA)),
P ₁₀ : contains the moment of inertia B,
Molecular descriptors for the gas thermal conductivity at temperatures three times the normal boiling point
P ₁ : topological charge index of order 9,
P ₂ : Tokyo Distribution Function-10.0 / Radial Distribution Function-10.0 / weighted by atomic masses,
P ₃ : Spectral moment 09 from edge adjacency matrix weighted by dipole moments,
P ₄ : Average electrophilic reactivity index for a O atom,
P ₅ : Broto-Moreau autocorrelation of a topological structure-lag 2 / Weighted by atomic van der Waals volumes,
P ₆ : Geary's autocorrelation-lag 1 / Weighted by atomic Sanderson electronegativity,
P ₇ : Radial Distribution Function-13.5 / weighted by atomic Sanderson electronegativity,
P ₈ : sp3 carbon / sp2 carbon bonded hydrogen (H attached to C1 (sp3) / C0 (sp2)),
P ₉ : Geary's autocorrelation-lag 2 / Weighted by atomic polarizability,
P ₁₀ : hydrogen bonding charged surface area fraction (FHBCA Fractional HBCA (HBCA / TMSA)), and
P _{11 includes the} frequency of C-O at topological distance 08
The optimal molecular expression for the scaling factor α is
P ₁ : Max partial charge for a C atom,
P ₂ : Image of the Onsager-Kirkwood solvation energy,
P ₃ : Spectral moment 13 from edge adjacency matrix weighted by dipole moments,
P ₄ : lowest eigenvalue n. 1 of Burden matrix / weighted by atomic masses,
P ₅ : HACA H-acceptors charged surface area,
P ₆ : Randic index (order 2),
P ₇ : topological charge index of order 9,
P ₈ : Total charge weighted partial negative charge surface area fraction weight (WNSA-2 Weighted PNSA (PNSA2 * TMSA / 1000)),
P ₉ : Tokyo Distribution Function-10.0 / Radial Distribution Function-10.0 / weighted by atomic masses, and
P ₁₀ : A method for determining the gas thermal conductivity of an organic compound by an SVRC model comprising a hydrogen donor surface area fraction (FHDSA Fractional HDSA (HDSA / TMSA)).

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