KR101325124B1 - QSPR Model Predicting Surface Tension of Liquid 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 surface tension of organic compounds with high accuracy is provided. The above model is an example of a quantitative structure-property relationship (QSPR) model, and it is possible to know the value of the surface tension at each temperature through an equation. These calculations require the values of several parameters, which are values unique to each compound, and are based on experimental values of the surface tension of a number of compounds that satisfy the conditions mentioned above to obtain them in the present invention. 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 surface tension of a compound composed purely of this molecule, as long as it knows only the specific values of the molecular descriptors included in the model. As such, the present invention provides a method for predicting a reliable surface tension 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

QSPR Model Predicting Surface Tension of Liquid 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, with high accuracy, surface tension, which is one of several physical properties of a compound.

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 its use, 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 tried 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.

Several prediction models have been proposed to date for surface tension, which is a property of interest of the present invention. Surface tension refers to the force acting to reduce the surface area of a pure material's liquid surface. The results of previous studies on the prediction of surface tension are briefly introduced in Polling BE, Prausnitz JM, O'Connell JP, The Properties of Gases and Liquids (5 ed.) , New York, McGraw Hill, (2000). It is.

, 기체의 밀도

, 파라코르(온도에 독립적인 변수, [P])의 값을 이용하여 임의의 온도에 대한 표면장력 σ의 값을 계산해 준다. Currently known and widely used models for predicting surface tension are mathematical models developed based on the principle of response state. The following equation, known as the Macleod-Sugden equation, is the most classical model [Macleod, DB, Trans. Faraday Soc , 19: 38 (1923)., Sugden, S., J. Chem. Soc. , 32, 1177, (1924)], density of liquids

, Gas density

Using the values of paracor (temperature independent variable, [P]), calculate the surface tension σ for any temperature.

, 임계온도

, 환산온도

, 압축인자

를 도입한 다음의 수식을 제안하였다[Brock J. R., Bird R., B, AIChE J, 1: 174 (1955).].After this, Brock-Bird is the critical pressure

, Critical temperature

, Conversion temperature

, Compression factor

The following formula was proposed to introduce [Brock JR, Bird R., B, AIChE J , 1: 174 (1955).].

이다.Using other parameters instead of compression factors in the Brock-Bird equation above, Miller proposed the following equation [Miller, DG, Ind. Eng. Chem. Fundam., 2: 78 (1963)]

to be.

One of the alternatives to constructing the predictive model of surface tension is to find a general equation that can represent the graph deformation of surface tension and calculate the variables of the equation. The formula of surface tension to be used in this method is determined by the following function.

Where A and N are predicted using QSPR as constants uniquely given to each molecule.

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 입력을받은 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 최적화하는 것을 말한다. 이러한 훈련을거친 인공신경망은 문제해결에 필요한규칙이나 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-time research results of human beings to make artificially intelligent machines by modeling human nerve cells with intelligence, and is an information processing technology that has been applied in various fields since it appeared in the middle of the 20th century. . 3 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 is called a weight.

Is granted. Each node in the hidden and output layers receives inputs from these nodes and processes them to produce output values. This 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. Such trained artificial neural network does not provide the necessary rules or knowledge for problem solving, but it establishes general rules through learning and gives valid output even for unknown input, so it lacks the basic theory like the physical property prediction of compound. 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 QSPR model is constructed for the surface tension 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 included in the surface tension general formula, taking into account a wider variety of molecular descriptors based on more experimental data. These are the multiple linear regression-artificial neural network hybrid models obtained by properly combining the multiple linear regression analysis and the neural network technique. Especially, the neural network reflects the nonlinear functional relationship between independent and dependent variables that the multiple linear regression model cannot reflect. It has the advantage of being able to implement a model with higher predictive 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, surface tension 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, and international regulations on the production and consumption of compounds such as REACH are required. do. 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 the surface tension of a large number of compounds with high accuracy without any experiments, not only saves 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 building a QSPR prediction model for surface tension provided by the present invention.
2 is a flowchart illustrating a process of constructing a multiple linear regression-artificial neural network hybrid model for each parameter required for the present invention.
Figure 3 is a view showing the structure of the artificial neural network used in the present invention.
4 to 7 are diagrams comparing the prediction performance of the prediction model provided by the present invention, for example, Brock-Bird model and Miller model, among the existing prediction methods for some compounds.
8 is a histogram diagram of 7923 experimental data of the Brock-Bird model.
9 is a histogram plot of 7923 experimental data of the Miller model.
10 is a histogram plot of 7923 experimental data of the QSPR model.

Figure 1 is a simplified representation of the process of building a QSPR model for the surface tension.

The first thing to do when building the 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, a total of 26767 data for 2181 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 too reliably compared to the values, or if the values for the molecular expressions are data about a compound that is difficult to prepare immediately, then the data is corrected or deleted, and finally 11455 for a total of 502 compounds are obtained. 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. In total, 1978 values for various molecular descriptors are collectively calculated using a computer from files containing information about 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.

으로 표면장력을 계산하기 위해서는 그래프의 기울기에 해당하는 A와 온도항에 대한 지수 N 값이 필요하다. 식에서 변수 값이 2개이므로 두 점에서의 표면장력을 알면 각 분자별 A와 N을 구할 수 있다. 이 모형에서는 삼중점과 정상 끓는점에서의 표면장력

의 값을 계산하여 다른 변수를 알아내는 방법을 선택하였다. 삼중점의 온도를 정확히 예측하는 것은 일반적으로 매우 어려운 일임이 잘 알려져 있으며, 따라서 본 발명에서는 삼중점 대신 정상끓는점의 0.55배(

)를 표면장력곡선의 시작 온도로 잡았는데, 샘플 화합물들에 대해 이 지점들의 평균은 삼중점의 평균과 거의 일치한다. QSPR모형을 완성하기 위해서는 매개변수들인

,

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

와

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

와

가 되는 지점의 값을 취하였다.Step 4 is followed by preparing data needed to establish a QSPR model for each parameter based on the experimental data. Surface tension general formula

In order to calculate the surface tension, we need the A corresponding to the slope of the graph and the exponent N for the temperature term. Since there are two variable values in the equation, if we know the surface tension at two points, we can find A and N for each molecule. In this model, the surface tension at triple and normal boiling points

We chose the method of finding other variables by calculating the value of. It is well known that it is generally very difficult to accurately predict the temperature of the triple point, so in the present invention, 0.55 times the normal boiling point instead of the triple point (

) Is taken as the starting temperature of the surface tension curve, for the sample compounds the mean of these points is almost identical to the mean of the triple point. To complete the QSPR model, the parameters

,

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.

Wow

For, we first fit a typical curve of surface tension to the experimental data of each compound, and then

Wow

The value of the point at which is taken is taken.

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 that have relatively little experimental data satisfying these conditions exists, the number of compounds participating in the QSPR prediction model of each parameter is significantly smaller than the total number of compounds.

Step 5 is to build a QSPR model for each parameter. Figure 2 is a simplified representation of the process of building a QSPR model for each parameter. The specific detailed steps are as follows.

In detail step 1, the sample compounds are divided into two parts: the training set used to search the prediction model and the test set used to test the predictive performance of the model determined by the training set. 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.

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 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 the parent chromosome is given as (24, 262, 343, 789, 1290), (38, 454, 554, 1322, 1449), and there is a crossing point 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 cases where there is no appropriate solution within the initial set of combinations.

In this way, a new generation of populations are created by replacing some or all of the existing populations with newly acquired individuals. 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 found model is evaluated using a test set 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 samples thus prepared are divided into training sets, validation sets, and test sets in a roughly 6: 2: 2 ratio.

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. In this case, 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. 3, and the three layers are connected only in a feed forward direction, that is, in a direction from an input to an output. It was. The input layer is composed of the same number of nodes that receive the values of the molecular markers included in the already established multilinear regression model, and the output layer is composed of one node that outputs the surface tension. 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(보통 1000세트이내)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 weight them by repeatedly training the neural networks initialized with each set using the back-up 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 이보다작을 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 artificial neural networks give wrong answers to unknown inputs as a result of excessive training.

), And when 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, 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 surface tension with the value calculated by the surface tension formula. At this time, the normal boiling point value is required to calculate the predicted value by the surface tension formula. For this information, a value obtained by a known method or a calculation method based on a QSPR model is used.

,

의 값을 예측하는 QSPR 모형을 간단히 기술한것이며 이들을 바탕으로 탄화수소의 표면장력을 예측하는 QSPR 모형과 그 성능에 대한 결과는 표 3에 나와 있다. 또한 비탄화수소의 표면장력을 예측하는 QSPR 모형과그 성능에 대한 결과는 표 4에 나와 있다.
The results of the QSPR model established through this process are summarized in Tables 1-4. Tables 1 and 2 respectively

,

The QSPR model for predicting the value of is briefly described and based on these results, the QSPR model for predicting the surface tension of hydrocarbons and the performance results are shown in Table 3. In addition, the QSPR model for predicting the surface tension of non-hydrocarbons and the results of the performance are shown in Table 4.

Number of sample compounds 497 Number of molecular descriptors 13 Names of Molecular Presenters P ₁ : leverage-weighted autocorrelation of lag 2 / Weighted by atomic polarizability
P ₂ : 1st component shape directional WHIM index / weighted by atomic Sanderson electronegativity
P ₃ : Polarity parameter / square distance
P ₄ : average connectivity index chi-3
P ₅ : Narumi harmonic topological index
P ₆ : highest level occupied molecular orbital energy (HOMO energy)
P ₇ : RRCG Relative positive charge (QMPOS / QTPLUS)
P ₈ : hydrogen bond receptor charge surface area fraction (HACA-1 / TMSA)
P ₉ : number of Nitrogen atoms
P ₁₀ : 3D molecular representation of electron diffraction based on 3D-MoRSE-signal 14 / weighted by atomic Sanderson electronegativity
P ₁₁ : Minimum partial charge for a H atom
P ₁₂ : R maximal autocorrelation of lag 6 / Weighted by atomic masses
P ₁₃ : R autocorrelation of lag 7 / Weighted by atomic polarizability Regression Model Decision Coefficients 0.902166 Regression Model AAE 0.001369 N / m Regression model

Artificial Neural Network Determination Coefficient 0.907183 Artificial Neural Network AAE 0.001353 N / m Artificial Neural Network Model

Overconformity Prevention Criteria 0.003 N / m

Number of sample compounds 498 Number of molecular descriptors 13 Names of Molecular Presenters P ₁ : leverage-weighted autocorrelation of lag 2 / Weighted by atomic masses
P ₂ : frequency of O-O at topological distance 02
P ₃ : Narumi harmonic topological index
P ₄ : folding degree index
P ₅ : R maximal autocorrelation of lag 6 / Weighted by atomic masses
P ₆ : number of secondary alcohols
P ₇ : shape profile order6
P ₈ : number of sulfides
P ₉ : sum of topological distances between N..N
P ₁₀ : number of double bonds
P ₁₁ : R autocorrelation of lag 3 / Weighted by atomic van der Waals volumes
P ₁₂ : Minimum partial charge for a H atom
P ₁₃ : hydrophilic factor Regression Model Decision Coefficients 0.882471 Regression Model AAE 0.001018 N / m Regression model

Artificial Neural Network Determination Coefficient 0.918365 Artificial Neural Network AAE 0.000847 N / m Artificial Neural Network Model

Overconformity Prevention Criteria 0.003 N / m

Number of sample compounds 138 Number of experiment data 2641 Coefficient of determination 0.984788 Mean Absolute Error 0.000613 N / m model

위식에 앞에 구한

,

값과 각 값에서의 환산 온도

를 넣고 분자마다 A와 N을 구한다.

Obtained before on the common sense

,

Value and converted temperature at each value

Add A and N for each molecule.

Number of sample compounds 786 Number of experiment data 6986 Coefficient of determination 0.880922 Mean Absolute Error 0.001914 N / m model

위식에 앞에 구한

,

값과 각 값에서의 환산 온도

를 넣고 분자마다 A와 N을 구한다.

Obtained before on the common sense

,

Value and converted temperature at each value

Add A and N for each molecule.

의 평균절대오차값을 보이고 Miller 모형은 0.040329의 결정계수값과 0.005457

의 평균절대오차값을 보일 반면, 본 발명의 QSPR 모형은 0.925291의 결정계수값과 0.001343

의 평균절대오차값을 보여 현저히 우수함을 알게 되었다. 도 4~7은 예로 몇몇 화합물에 대해 각 모형의 예측성능을 비교한 도면들이다. 이 도면들로부터 QSPR 모형이 기존 모형보다 우수한 성능을 가짐을 눈으로 확인할 수 있다. 한편 7923개의 실험데이터에 대해 실험값과 예측값 사이의 오차를 히스토그램으로 그린 것이 도 8, 9, 10이다. 이 도면들은, Brock-Bird 모형은 48.37%, Miller 모형은 48.53%, QSPR 모형은 64.42%의 확률로 5%오차 이내로 표면장력을 예측하고 있음을 보여주어 QSPR 모형이 보다 정확함을 증명해준다.
In order to show that the present invention is superior to the existing technology, the predicted performance of the Brock-Bird model and the Miller model, which was mentioned above as the conventional model widely used with the QSPR model of the present invention, was compared with 7923 experimental data of 916 compounds. As a result, the Brock-Bird model has a coefficient of determination of 0.034519 and 0.005855.

The average absolute error of is shown and the Miller model has a coefficient of determination of 0.040329 and 0.005457

While the mean absolute error of is shown, the QSPR model of the present invention has a coefficient of determination of 0.925291 and 0.001343.

The average absolute error of was found to be remarkably excellent. 4 to 7 are examples for comparing the predictive performance of each model for some compounds. From these figures it can be seen that the QSPR model outperforms the existing model. 8, 9, and 10 show a histogram of the error between the experimental value and the predicted value for 7923 experimental data. These figures demonstrate that the QSPR model is more accurate, showing that the Brock-Bird model is 48.37%, the Miller model is 48.53%, and the QSPR model has a 64.42% probability of predicting surface tension within 5%.

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 the surface tension of the organic compounds of the sample compounds;
The third step of obtaining the parameters required for the equation described in the following formula (1)

Equation (1)

Where σ is the surface tension, A and N are constant values that depend on each molecule, T is temperature, T _c is critical temperature,

Silver conversion temperature];
QSPR model for the surface tension (σ _b , σ _0.55b ) at a temperature of 0.55 times the normal boiling point and the normal boiling point obtained from the third step was constructed and the calculated σ _b , σ _0.55b was calculated from the above equation ( A fourth step of obtaining the surface tension by constant values A and N obtained by substituting 1);
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 QSPR model including the sixth step of adopting the surface tension predicted value by the searched model as the surface tension value and not satisfying the fourth and fifth steps. To get the surface tension
The method of claim 1, wherein the method for obtaining a QSPR model for surface tension at a temperature that is 0.55 times the normal boiling point and the normal boiling point is
Step 4-0 of extracting optimal molecular _descriptors for surface tension (σ _b , σ _0.55b ) at a temperature of 0.55 times the normal boiling point and the normal boiling point;
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;
Surface tension predicted value at a temperature of 0.55 times normal boiling point and normal boiling point obtained by the optimal multilinear regression model satisfying the performance test in steps 4-5, and the optimal artificial searched in steps 4-6. Step 4-7 comparing the absolute value of the difference between the surface tension predicted value at a temperature of 0.55 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 surface tension predicted value at the temperature point of 0.55 times the normal boiling point and the normal boiling point by the multiple linear regression model obtained in steps 4-5 is at a temperature of 0.55 times the normal boiling point and the normal boiling point. If the surface tension value is smaller than the reference value for the prevention of overfitting, the surface tension predicted value at the temperature of 0.55 times the normal boiling point and the normal boiling point by the artificial neural network model detected in the above steps 4-6 is determined between the normal boiling point and the normal boiling point. A method of obtaining the surface tension of an organic compound by a QSPR model including steps 4-8, which is adopted as the surface tension value at a temperature of 0.55 times.
The optimal molecular expression of surface tension (σ _b , σ _0.55b ) at a temperature of 0.55 times the normal boiling point and the normal boiling point in steps 4-0 is the same for all the sample compounds. A method of obtaining surface tension of an organic compound by a QSPR 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 the multilinear regression model is searched for by the QSPR model, wherein the multilinear regression model is searched by applying a genetic algorithm to the training set. How to find the surface tension 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 surface tension of an organic compound by a QSPR model, comprising: generating a new population by mutating a portion of the 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 comprises determining the predictive performance based on the coefficient of determination or the mean absolute error of the regression model. 4.
The method of claim 2, wherein the validity in the step 4-3 is obtained by calculating the surface tension of the organic compound by the QSPR model to determine the validity by the t-test value.
The method of claim 2, wherein in step 4-5, if the predicted performance of the test set is similar to the predicted performance of the training set, the multiple linear regression model is determined, and the predicted performance of the test set is the predicted performance of the training set. And the surface tension of organic compounds by QSPR model that reclassifies the training set and the test set.
The QSPR model according to claim 2, wherein in step 4-6, the search range by the artificial neural network has one hidden layer between the input layer and the output layer and is connected only in a feed forward. To obtain the surface tension of organic compounds.
The method of claim 10, wherein a sigmoid function is used as a function of activation of the hidden layer.
3. The method of claim 2, wherein the reference value for preventing overfitting in step 4-7 is 0.003 N / m.
According to claim 2, wherein the optimum molecular expression for the surface tension at the normal boiling point extracted in the step 4-0
P ₁ : leverage-weighted autocorrelation of lag 2 / Weighted by atomic masses,
P ₂ : frequency of O-O at topological distance 02,
P ₃ : Narumi harmonic topological index,
P ₄ : folding degree index,
P ₅ : R maximal autocorrelation of lag 6 / Weighted by atomic masses,
P ₆ : number of secondary alcohols,
P ₇ : shape profile order 6 (shape profile no. 06),
P ₈ : number of sulfides,
P ₉ : sum of topological distances between N..N,
P ₁₀ : number of double bonds,
P ₁₁ : R autocorrelation of lag 3 / Weighted by atomic van der Waals volumes,
P1 ₂ : Minimum partial charge for a H atom, and
P ₁₃ : contains a hydrophilic factor,
The molecular presenter for surface tension at a temperature of 0.55 times the normal boiling point for step 4-0
P ₁ : leverage-weighted autocorrelation of lag 2 / Weighted by atomic polarizability,
P ₂ : 1st component shape directional WHIM index / weighted by atomic Sanderson electronegativity,
P ₃ : Polarity parameter / square distance,
P ₄ : average connectivity index chi-3,
P ₅ : Narumi harmonic topological index,
P ₆ : highest level occupied molecular orbital energy (HOMO energy),
P ₇ : RRCG Relative positive charge (QMPOS / QTPLUS),
P ₈ : hydrogen bond receptor charged surface area fraction (HACA-1 / TMSA),
P _{9 is the} number of Nitrogen atoms,
P ₁₀ : 3D molecular representation of electron diffraction based on 3D-MoRSE-signal 14 / weighted by atomic Sanderson electronegativity,
P ₁₁ : Minimum partial charge for a H atom,
P ₁₂ : R maximal autocorrelation of lag 6 / Weighted by atomic masses, and
P ₁₃ : Method of obtaining the surface tension of an organic compound by a QSPR model comprising R autocorrelation of lag 7 / Weighted by atomic polarizability.
A computer-readable storage medium having recorded thereon a program for executing on a computer a method for obtaining the surface tension of an organic compound according to any one of claims 1 to 13.
About the model described in following formula (2)

Equation (2)
Where σ is the surface tension, A and N are constant values that depend on each molecule, T is temperature, T _c is critical temperature,

Silver conversion temperature];
The optimal molecular expression for surface tension at normal boiling point is
P ₁ : leverage-weighted autocorrelation of lag 2 / Weighted by atomic masses,
P ₂ : frequency of O-O at topological distance 02,
P ₃ : Narumi harmonic topological index,
P ₄ : folding degree index,
P ₅ : R maximal autocorrelation of lag 6 / Weighted by atomic masses,
P ₆ : number of secondary alcohols,
P ₇ : shape profile order 6 (shape profile no. 06),
P ₈ : number of sulfides,
P ₉ : sum of topological distances between N..N,
P ₁₀ : number of double bonds,
P ₁₁ : R autocorrelation of lag 3 / Weighted by atomic van der Waals volumes,
P ₁₂ : Minimum partial charge for a H atom, and
P ₁₃ : contains a hydrophilic factor,
Molecular descriptors for surface tension at temperatures 0.55 times normal boiling point
P ₁ : leverage-weighted autocorrelation of lag 2 / Weighted by atomic polarizability,
P ₂ : 1st component shape directional WHIM index / weighted by atomic Sanderson electronegativity,
P ₃ : Polarity parameter / square distance,
P ₄ : average connectivity index chi-3,
P ₅ : Narumi harmonic topological index,
P ₆ : highest level occupied molecular orbital energy (HOMO energy),
P ₇ : RRCG Relative positive charge (QMPOS / QTPLUS),
P ₈ : hydrogen bond receptor charged surface area fraction (HACA-1 / TMSA),
P _{9 is the} number of Nitrogen atoms,
P ₁₀ : 3D molecular representation of electron diffraction based on 3D-MoRSE-signal 14 / weighted by atomic Sanderson electronegativity,
P ₁₁ : Minimum partial charge for a H atom,
P ₁₂ : R maximal autocorrelation of lag 6 / Weighted by atomic masses, and
P ₁₃ : R autocorrelation of lag 7 / Weighted by atomic polarizability, which includes surface tensions at temperatures of 0.55 times normal and normal boiling points (σ _b , A method for obtaining the surface tension of an organic compound by the QSPR model, characterized in that the surface tension is calculated from the constant values A and N obtained by substituting [sigma] _0.55b ) into the above formula (2).

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