KR102139706B1 - Method for providing gas pipeline control information through statistical learning - Google Patents

Abstract

According to an embodiment of the present invention, a state information collection step of collecting and database state information measured at a plurality of points in a gas pipeline network, based on the state information, selecting an input variable and estimating a regression coefficient to obtain a regression model. Providing a method for providing gas pipeline network operation information, including a model establishment step for establishing, and an information providing step for providing operation information necessary for operation of the gas pipeline network using the regression model. Economics can be improved.

Description

Method for providing gas pipeline control information through statistical learning}

The present invention relates to a method for providing gas pipeline network operation information through statistical learning.

Natural gas is imported through LNG carriers, etc., and is supplied to various customers through pipe networks. In order to efficiently and safely operate the pipe network supplying natural gas, it is necessary to predict the gas demand and maintain the pressure of the main pipe properly. If the pressure is high or low compared to demand, the safety, stability, and economics of pipe network operation may be deteriorated.

The operation of the pipe network to determine and adjust the appropriate level of main pipe pressure is influenced by various variables. In particular, the pressure distribution of the main pipe changes frequently due to various pipe network changes that occur in most periods of the year, resulting in a problem that the main pipe pressure becomes excessively high or low. Sudden fluctuations in the main pipe pressure deteriorate the safety or stability of the pipe network operation, and in order to cope with the pressure change, there is a problem in that the equipment with high operation cost is additionally operated in the process of rapidly reducing and rapidly increasing the gas delivery amount, thereby lowering economic efficiency.

On the other hand, in the process of gas direct introduction operators using the pipe network together, related facilities are required to draw gas into the pipe network, and a problem arises in that the local pressure of the pipe network connected to the Boryeong base is excessively increased. This is because the gas withdrawal points of gas direct import operators are distributed throughout the country, but the inflow point is concentrated in Boryeong base, causing bottlenecks due to excessive gas inflow compared to the capacity of the pipe network.

As gas direct introduction increases, bottlenecks and pressure rises in the pipeline network where the incoming facilities are connected will become more severe. When the pressure of the main pipe reaches the limit due to gas inlet, it is expected that the process of requiring gas to be returned through additional intake will occur frequently when the gas intake of gas direct import operators is limited and the limited gas is not a bottleneck. Therefore, the contract for the use of the gas inlet facility should be concluded within the range in which the restriction and return of the gas can be smoothly implemented throughout the year, but there is no problem in making decisions regarding the contract by the related agencies because there is no estimate for this range.

JP 2000-265184 A

An object according to an embodiment of the present invention is to establish and use a regression model that can predict the average gas pressure to be supplied to the main pipe in order to predict the average pressure of the main pipe and to adjust the average pressure of the main pipe, to operate the gas pipeline network It is intended to provide a method and apparatus for providing necessary information.

In addition, the object according to an embodiment of the present invention, establishing and using a regression model that can predict the capacity of the gas supply point connected to the gas pipeline network, the annual demand of the gas pipeline network, and the annual facility utilization rate of the direct gas operator, It is intended to provide a method and apparatus for providing information necessary for decision-making related to the direct gas import business and operation of the gas pipeline network.

According to an embodiment of the present invention, a method for providing operation information of a gas piping network is a state information collection step of collecting and databaseting state information measured at a plurality of points in a gas piping network, and selecting an input variable based on the state information. A model establishment step of establishing a regression model by estimating a regression coefficient, and an information providing step of providing operation information necessary for the operation of the gas pipeline network using the regression model may be included.

In addition, the status information may include at least one item of pressure, demand, maximum demand, minimum demand, gas intake amount, average pressure at the plurality of points, and temperature at a plurality of points in the gas pipe network. .

In addition, the model establishing step is a preliminary input variable of a combination of individual items included in the state information or items having a linear relationship with each other in order to establish a first regression model predicting the average pressure of the plurality of points at a specific time point. A first regression model establishment step of establishing the first regression model by selecting an input variable from the preliminary input variables using all possible regression methods and estimating a regression coefficient using a least squares method, And time series included in the status information to establish a second regression model that predicts the amount of gas input to be supplied to the gas piping network in order to achieve the average pressure at the specific time point predicted by the first regression model. It may include a second regression model establishment step of establishing a regression model with an average pressure change as an input variable and a gas filling amount change as a dependent variable.

In addition, the information providing step is a conversion information providing step of standardizing and providing items selected as the input variable so that the degree of the effect of the input variable on the dependent variable in the first regression model is compared, and at the specific point in time In order to achieve the average pressure predicted by the first regression model, it may include a supply information provision step of predicting and providing a change in the gas filling amount using the second regression model.

In addition, the first regression model establishment step divides the day into at least two or more sections based on the shift of the manager's work shift and the highest average pressure of the day, and establishes the first regression model for each section. The average pressure can be predicted at the reference point of division.

In addition, the model establishing step establishes the third regression model by estimating a regression coefficient using Bayes' theorem and temperature as an input variable to establish a third regression model for predicting the annual demand of the gas pipeline network. The third regression model establishment step, in order to establish a fourth regression model for predicting the capacity of the gas supply point of the gas piping network, the gas demand is used as an input variable and the Bayes' theorem is used to estimate the regression coefficient to obtain the fourth In order to establish the fourth regression model establishment step of establishing the regression model and the fifth regression model predicting the annual facility utilization rate of gas direct import operators, the gas demand is used as an input variable and the Bayes' theorem is used to estimate the regression coefficient. And a fifth regression model establishment step of establishing the fifth regression model.

In addition, the information provision step includes the capacity of the gas supply point of the gas pipeline network predicted using the fourth regression model, and the facility utilization rate predicted using the fifth regression model in the contract capacity of the direct gas supplier. It may be to provide long-term information by comparing the expected amount of input calculated by multiplying by and calculating the restriction date of gas input and the possible additional gas input date.

In addition, the third regression model establishment step and the fifth regression model establishment step are divided into sections on weekdays, Saturdays, and Sundays (including holidays), and each regression model is established for each section, and the fourth regression model establishment step is in the summer. In the winter season, sections can be divided, and regression models can be established for each section.

Features and advantages of the present invention will become more apparent from the following detailed description based on the accompanying drawings.

Prior to this, the terms or words used in the specification and claims should not be interpreted in a conventional and lexical sense, and the inventor can appropriately define the concept of terms in order to best describe his or her invention. It should be interpreted as meaning and concept consistent with the technical idea of the present invention based on the principle of being there.

According to an embodiment of the present invention, regardless of the system change operation of the gas piping network, predict the average pressure of the main piping and predict the amount of gas input to be supplied to the main piping to adjust the average pressure of the main piping, thereby operating information of the gas piping network. Since it provides, the safety, stability and economics of the gas pipeline network can be improved.

In addition, according to an embodiment of the present invention, when a gas direct import operator uses a gas piping network facility, a gas intake limit date and a time limit in which gas is drawn in and less than the amount in which the gas is drawn out are restricted and the rest of the gas could not be introduced It is possible to reliably predict and provide operational information, such as the date when additional gas can be added, which can additionally draw in the remaining gas.

1 is a view schematically showing a gas piping network.
2 is a flow chart showing the steps of the gas pipe network operating information providing method according to an embodiment of the present invention.
Figure 3 is a flow chart showing the detailed steps of the gas pipe network operating information providing method according to an embodiment of the present invention.
4 is a residual diagram of the morning section of the first regression model according to an embodiment of the present invention.
5 is a residual diagram of an afternoon section of a first regression model according to an embodiment of the present invention.
6 is a residual diagram of a dawn section of a first regression model according to an embodiment of the present invention.
7 is a flowchart illustrating detailed steps of a method for providing operation information of a gas piping network according to an embodiment of the present invention.
8 is a view showing an estimation of a regression coefficient of a fourth regression model in a summer section according to an embodiment of the present invention.
9 is a view showing estimated spare capacity for each time of a gas supply point connected to a gas piping network according to an embodiment of the present invention.

The objects, specific advantages and novel features of an embodiment of the present invention will become more apparent from the following detailed description and preferred embodiments associated with the accompanying drawings. In addition, it should be noted that, in addition to reference numerals to the components of each drawing in the present specification, the same components have the same numbers as possible, even if they are displayed on different drawings. In addition, the terms "one side", "other side", "first", "second", etc. are used to distinguish one component from another component, and the component is limited by the terms no. Hereinafter, in describing one embodiment of the present invention, detailed descriptions of related well-known technologies that may unnecessarily obscure the subject matter of one embodiment of the present invention are omitted.

Hereinafter, an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

1 is a view schematically showing a gas piping network 10, and FIG. 2 is a flow chart showing steps of a method for providing operation information of a gas piping network 10 according to an embodiment of the present invention, and FIG. 3 is an embodiment of the present invention. It is a flow chart showing the detailed steps of the method for providing operation information of the gas piping network 10 according to an example.

As shown in FIG. 1, the gas pipeline 10 (Gas Pipeline) refers to a supply chain that transports natural gas (Natural Gas) to a consumer (Fout) of a home or business. The gas piping network 10 may be divided into a main pile (Main Pileline, Pm) and a sub-pipe (Sub Pipeline, Ps). The main pipe (Pm) refers to the non-decompression section where the gas inlet facility (Fin) is connected and the gas is injected into the pipe network, and the sub-pipe (Ps) is branched from the high-pressure main pipe (Pm) to decompress the gas to low pressure to accommodate the gas (Fout) It means the decompression section supplied by ). In order to operate the gas piping network 10 stably and economically, an embodiment of the present invention establishes a regression model using statistical learning of a supervised learning method having data of input variables and dependent variables to be estimated. Using the regression model, it is possible to provide operation information necessary for the operation of the gas piping network 10.

As illustrated in FIG. 2, the method for providing operation information of the gas piping network 10 according to an embodiment of the present invention collects state information collected from a plurality of points of the gas piping network 10 and databased Step (S100), a model establishment step (S200) of selecting an input variable based on state information and estimating a regression coefficient to establish a regression model, and operation information required to operate the gas piping network 10 using the regression model It may include an information providing step (S300) for providing.

In the state information collection step (S100), various measurement devices such as pressure gauges, flowmeters, and thermometers installed at each point of the main pipe (Pm) or sub-pipe (Ps) of the gas pipe network (10) collect and measure the data in real time. Can be angry. Each point of the gas piping network 10 includes points that require state measurement of the gas piping network 10, such as a gas inlet facility (Fin), a main pipe (Pm) and a sub-pipe (Ps) branching point, and an acceptor (Fout). The status information may include at least one item of pressure, demand, maximum demand, minimum demand, gas intake amount, average pressure at the plurality of points, and temperature at a plurality of points in the gas piping network 10. The status information may further include various items in addition to the items listed above. In the state information collection step (S100), the temperature of each gas pipeline network 10 can be collected and databased from the Korea Meteorological Administration.

The model establishment step (S200) is a step of selecting an input variable based on state information and estimating a regression coefficient to establish a regression model, and may establish a short-term regression model (S200a) and a long-term regression model (S200b). First, the short-term regression model establishment (S200a) will be described.

Since the operation of the gas piping network 10 is usually operated by shift work, it is possible to divide the day into at least two or more sections based on the shift of the manager who controls the gas piping network 10 and the highest average pressure during the day. For example, if the peak pressure of the main pipe (Pm) is at the highest average hour of the day at 06 o'clock and the shift time is at 8 o'clock, 15 o'clock, and 21 o'clock, the day is morning (08 a.m.-5 p.m.) City), and can be divided into three sections: early morning (21 o'clock to 6 o'clock). When the shift work and the maximum pressure during the day are different, it may be desirable to classify the end point of the dawn section of the day as the highest average pressure in order not to exceed the maximum pressure limit of the gas piping network 10. At this time, the regression model can be established by dividing the period from 06 to 08 into separate sections, or it can be operated as a section for managing the average pressure peak without establishing the regression model. Or, if the end point of the early morning section is divided into 06:00, the start time of the morning section is set to 06:00, and the morning (from 6:00 to 15:00), the afternoon (from 15:00 to 21:00), and the morning (from 21:00 to 06:00) It can also be divided into three sections.

The gas piping network 10 is modified such as blocking, closing, bypassing, or establishing a part of the piping network due to the establishment or closing of some sections or replacement of old piping. Such various pipe network changes may cause a problem in which the pressure distribution of the main pipe (Pm) is frequently changed and the pressure of the main pipe (Pm) becomes too high or low.

In order to minimize the effect of such a change on the pipe network on the operation of the gas pipe network 10, a model for predicting the average pressure (MPa) of the main pipe (Pm) is established. If the average pressure is not affected by changes in the pipe network and the national gas demand (ton/hour, t/h) prediction is accurate, unlike the individual point pressure, the national gas intake (t/h) is adjusted to achieve an accuracy of about 99% or more. Because it is adjustable. In addition, the relationship between the average pressure and the amount of gas input is suitable as an appropriate pressure index because it has a reliable tendency despite various types of pipe network changes.

One embodiment of the present invention uses a linear regression model of supervised learning and a least-squares method suitable for real-time prediction to predict in real time the appropriate average pressure of the main pipe (Pm).

As shown in FIG. 3, in the model establishment step, in order to establish a first regression model for predicting the average pressure of a plurality of points of the gas piping network 10 at a specific time point, individual items included in the state information or linear relationships with each other The first regression model is established by selecting the input variable from the preliminary input variables using all possible regression methods, and using the least squares method to estimate the regression coefficients. Establishing a first regression model (S210), and establishing a second regression model predicting the amount of gas input to be supplied to the gas piping network 10 in order to achieve an average pressure at a specific time point predicted by the first regression model To this end, a second regression model establishment step (S220) of establishing a regression model having a change in average pressure for each time period included in the state information as an input variable and a change in gas inflow as a dependent variable may be included. Here, the specific time point may be the end time of a section dividing the day into at least two or more.

In the first regression model establishment step (S210), regression models of various input variable combinations among various preliminary input variables are generated using all possible regression methods, and regression coefficients are estimated and adjusted using the least square method for each regression model. A model selection step (S211) of selecting a regression model using a determination coefficient index, a model diagnosis step (S212) of diagnosing whether a hypothesis hypothesized to establish a selected regression model is established, and a value of a value predicted by the regression model. It may include a predictive power test step (S213) for evaluating the accuracy. In the first regression model establishment step (S210 ), a first regression model may be established for each section in which a day is divided into two or more sections. Therefore, one first regression model may be established for each morning section, afternoon section, and dawn section.

In the following, the model selection step (S211) will be described.

In the model selection step (S211), all possible regression methods are used to find a combination of input variables considering simplicity and accuracy at the same time based on the adjusted coefficient of determination index among the preliminary input variables. When establishing a regression model, if the input variable is excessively large, the model explains the past dependent variable well, but the predictive power of the dependent variable tends to decrease in the future. In order to solve the problem of overfitting, one of the methods that can simultaneously consider the fit and the simplicity of the model is all possible regression. This is to establish a plurality of regression models with all possible combinations of preliminary input variables, and then select one regression model with the optimal combination of input variables through indicators that can simultaneously evaluate accuracy and simplicity.

와 오차항 i의 선형결합으로 나타낼 수 있는 모형이다. i는 i번째 측정자료를 의미한다.The linear regression model is the input variable k of k as in Equation 1.

And a model of error term i. i means i-th measurement data.

To establish a model, state information such as the operating pressure and flow rate data of the past gas piping network 10 is acquired for each time zone at a plurality of points in the gas piping network 10 and processed to make a preliminary variable. Table 1 illustrates some of the status information. The preliminary input variables may be the average pressure, the national gas intake amount by time, and the maximum and minimum values of the national gas intake amount. First, a plurality of regression models having a combination of all possible input variables are generated using preliminary input variables, and a regression model is established by estimating a regression coefficient for each regression model.

Pause Average pressure (MPa) National gas intake (t/h) 10-19 o'clock minimum 36~48 o'clock maximum

2015.01.01 00:00 5.77 4,180 6,738

2018.06.29 00:00 5.50 4,297 3,681

를 추정하기 위한 방법으로 최소제곱법을 활용한다. 최소제곱법이란 아래의 수학식 2의 오차항

제곱의 합을 최소로 만드는 회귀계수를 찾는 방법이다. After generating multiple regression models with various input variable combinations, regression coefficients for each regression model

Least square method is used to estimate. Least squares error term in Equation 2 below

This is a method to find the regression coefficient that makes the sum of squares to the minimum.

각각에 대해 편미분하면 아래 수학식 3과 같다.To minimize Equation 2 above

The partial differential for each is as shown in Equation 3 below.

는 위 수학식 3을 0으로 만드는 값에서 발생하므로 위 수학식 3을 0으로 하는

를 각각

라 하면 아래 수학식 4와 같은 정규방정식을 얻을 수 있다.To minimize Equation 3 above

Since it occurs at the value that makes Equation 3 above 0,

Each

Then, the regular equation as in Equation 4 below can be obtained.

If the regular equation of Equation 4 above is developed, it is the same as Equation 5 below, but the subsequent development is convenient by using a matrix.

If the input variables, dependent variables, regression coefficients and errors of Equation 5 above are expressed as matrices, they are as shown in Equation 6.

Equation 1 can be expressed by Equation 7 below, and Equation 5, which is a regular expression of Equation 4, can be expressed by Equation 8 below.

의 역행렬

를 곱하면 회귀계수들은 수학식 9와 같이 추정할 수 있다.On both sides of equation (8)

Inverse matrix

Multiply by and the regression coefficients can be estimated as in Equation 9.

에 대한 예측값

는 수학식 10이다.Dependent variable

Predicted value for

Is Equation 10.

와

의 차이인 잔차

는

이다.Also,

Wow

Difference, the residual

The

to be.

By performing this process, it is possible to establish a plurality of regression models by estimating a regression coefficient for each of the plurality of regression models having various input variable combinations. After establishing multiple regression models according to all possible regression methods, the best regression model is selected based on the adjusted coefficient of determination. The process of selecting a regression model will be described below.

When using the least squares method to estimate the regression coefficient, there are some characteristics related to the residuals. First, the equations 11, 12, and 13 can be obtained from the regular equation of equation (4).

와 종속변수 평균

와의 편차를 아래 수학식 14와 같이 둘로 나눈다. Using the characteristics of these residuals that occur when the least-squares method is applied, it is possible to calculate the explanatory power for the dependent variable of the regression model, that is, the coefficient of determination that can measure the degree. First, dependent variable

And dependent variable mean

Divide the deviation between and two as shown in Equation 14 below.

를 총편차라하고,

는 잔차로서 회귀모형에 의해 설명되지 않는 편차이며

는 회귀모형에 의해 설명되는 편차이다. 양변을 제곱하고 모든 i에 대한 합을 구하면 수학식 15가 된다.here

Is the total deviation,

Is the residual, which is a deviation that is not explained by the regression model

Is the deviation described by the regression model. Equation 15 is obtained by squaring both sides and summing all i.

The last term on the right in Equation 15 is the same as Equation 16, and it can be seen that Equation 11 and 13 become 0.

Therefore, the sum of squares of the total deviation is decomposed into two sums

이고 종속변수의 총변동 중 모형에 의하여 설명되는 부분의 비율을 의미한다. 결정계수는 입력변수가 추가되면 항상 증가하는 성질을 갖고 있어 결정계수를 그대로 판단기준으로 사용하는 경우 과적합한 모형이 선정될 수 있으므로 입력변수의 개수를 반영할 수 있는 조정된 결정계수가 자주 이용된다.In Equation 17, each term is called total sum of squares (SST), sum of squares due to residual errors (SSE), and sum of squares due to regression (SSR), and the coefficient of determination (R ² ) is

Is the ratio of the portion of the total variation of the dependent variable explained by the model. Since the coefficient of determination always increases when an input variable is added, an appropriate model can be selected when the coefficient of determination is used as a judgment criterion, so the adjusted coefficient of determination that reflects the number of input variables is often used. .

는 입력변수의 수 k가 적고 결정계수

가 높을수록 좋은 성질이 있으므로 모든 가능한 회귀시 조정된 결정계수를 지표로 삼아 모형의 정도와 간결성을 동시에 고려할 수 있다. In Equation 18 above, the adjusted coefficient of determination

The number of input variables k is small and the coefficient of determination

The higher the value, the better the property, so it is possible to consider the degree and simplicity of the model at the same time by using the adjusted coefficient of determination as an indicator in all possible regressions.

For example, in the morning model, the coefficient of determination adjusted according to the number of input variables is 0.5087→0.6367→0.8157→0.8324→0.8331→0.8351→0.8353→0.8354→0.8353→0.8353→0.8352, which is the largest with 0.8354 when the number of input variables is 8. However, when the number of input variables increases, there is a problem of increasing complexity in establishing and using a model in real time. In this embodiment, a regression model can be selected when the degree of increase of the adjusted coefficient of determination decreases to 20% or less of the level of the previous increase based on the increase in the number of input variables based on the change of the adjusted coefficient of determination. For example, in the present embodiment, if the input variable increases from 1 to 2, the adjusted coefficient of determination increases by 0.1280, and when the input variable increases from 2 to 3, the adjusted coefficient of determination increases by 0.1790, and the input variable If is increased from 3 to 4, the adjusted crystal coefficient increases by 0.0167. Therefore, a regression model with 3 input variables, which is when the adjusted crystal coefficient increase rate decreases to 20% or less of the previous increase, can be selected. If a regression model with three input variables is selected, Equation 19 is given.

: 15시 압력,

: 8시 압력,

: 10시~19시 최저수요,

: 36~48시 최대수요,

: 평균이 0이고 분산이

: 인 정규분포

을 따르는 오차항이며 e-15는 10^-15, e-04는 10^-4를 의미하고 조정된 결정계수는 0.8157이다. 위에서 산출한 회귀계수들은 본 발명의 일실시예를 설명하기 위하여 예시적으로 상태정보를 이용하여 산출한 것이다.

: 15 o'clock pressure,

: 8 o'clock pressure,

: Minimum demand from 10:00 to 19:00,

: 36~48 o'clock demand,

: Mean is 0 and variance is

: Normal distribution

Is an error term, e-15 means 10 ^-15 , e-04 means 10 ^-4 and the adjusted coefficient of determination is 0.8157. The regression coefficients calculated above are calculated by using state information as an example to describe an embodiment of the present invention.

By performing such a process, one regression model may be selected from a plurality of regression models having various combinations of input variables (S211). After selecting the regression model, a model diagnosis step (S212) is performed to diagnose whether the hypothesis assumed is established to establish the selected regression model. The model diagnosis step (S212) will be described below.

If it is possible to collect an infinite number of samples from the same population, various statistics such as the regression coefficient calculated by each sample will also be infinite, and these statistics have a probability distribution, which is called a sample distribution.

It is impossible to obtain an infinite number of samples from the same population to obtain a sample distribution, but if you use some assumptions about the regression model and the basic characteristics of the matrix operation, you can know the characteristics of the sample distribution with just one sample.

가 상수행렬이고

는 확률벡터일 때 기댓값

와 분산

에 대해서 아래 수학식 20이 성립한다는 것이다.The basic characteristics of the matrix are

Is a constant matrix

Is expected value when probability vector

And dispersion

Equation 20 below is established.

이라는 가정을 하면 아래 수학식 21의 전개를 통해

는 표본에 따라 달라지더라도 표본에 따라 다른

들의 평균값은 결국 미지의 고정된 모수값

와 같아짐을 알 수 있고 이러한 성질을 불편성이라고 한다.In Equation 9, the input variable is a fixed value and the mean of the error term is 0, that is,

Assuming that is through the development of Equation 21 below

Although it depends on the sample, it depends on the sample.

The average value of the is ultimately an unknown fixed parameter value

You can see that it is equal to and this property is called discomfort.

의 분산은

으로 일정한 등분산이며 입력변수는 고정값이라 가정하면

의 표본분포의 분산에 대해 추정 할 수 있다. 먼저, 서로 다른 오차항끼리 독립일 경우 확률변수의 기본특성에 의해 공분산은 수학식 22와 같고,Also, the different error terms are independent, and the error term for all i

The dispersion of

Is constant constant variance and input variable is fixed value

You can estimate the variance of the sample distribution. First, when different error terms are independent, the covariance is equal to Equation 22 by the basic characteristics of random variables.

The variance is equal to Equation 23 by the equal variance assumption.

Assuming that the input variable is a fixed value, Equation (24) holds

가 성립한다. 이 때

는 대각행렬로서 행과 열의 수가 같으며 행과 열이 같은 대각원소는 1이고 그 외의 원소는 0인 행렬이다. Equation 25 below

Is established. At this time

Is a diagonal matrix, which has the same number of rows and columns, a diagonal element with the same row and column, and 0 for all other elements.

표본분포의 분산은 수학식 26 과 같다.therefore

The variance of the sample distribution is given by Equation 26.

는 모회귀모형 오차항의 분산으로 실제로는 알 수 없으므로, 수학식 27과 같이

를 통해 추정하고 이는

에 대한 불편추정량임이 알려져 있다.

Is actually unknown due to the variance of the error term of the parent regression model.

Estimated through

It is known that this is an estimate of discomfort for.

의 j행 j열의 원소를 로 정의하면

표본분포 분산의 추정값은

이다.therefore

If you define the elements of j rows and j columns of

The estimate of the variance of the sample distribution is

to be.

In addition to the above assumptions, assuming that the error term follows a normal distribution, it is possible to estimate the form of the sample distribution of various statistics, and through this, it is possible to perform a confidence interval estimation and hypothesis test for various statistics.

의 표본분포는 자유도

인

분포를 따른다고 알려져 있다. Statistics of the following equation (28)

The degree of freedom is

sign

It is said to follow the distribution.

가 발생할

범위는

이므로 통계량

에 수학식 28을 대입하여 전개하면

의 신뢰구간을 수학식 29와 같이 산출할 수 있다.

Cause

The range

Statistic

Substituting Equation 28 into and expanding

The confidence interval of can be calculated as in Equation 29.

를 포함하는 빈도는

라는 것이다.The meaning of Equation 29 above is that if you collect an infinite number of samples and obtain the above range for each sample, the width and position of the range vary depending on the sample, but these ranges are unknown parameters.

The frequency that includes

It is called.

The statistical hypothesis test sets the null hypothesis H ₀ and the alternative hypothesis H ₁ and grasps which hypothesis is appropriate, and accepts the null hypothesis without choosing an alternative hypothesis until there is clear evidence. An important hypothesis test for the linear regression coefficient is to test whether there is a linear relationship between the input variable and the dependent variable, that is, the j-th regression coefficient is significantly different from 0.

Assuming that the null hypothesis is correct, the statistical t ₀ in the following equation 31 follows the probability distribution t _nk-1 .

The estimated values, standard deviation, and t ₀ values for the regression coefficient of the morning model are shown in Table 2 below.

Regression coefficient Estimate Standard Deviation t ₀ Significant probability

1.87E-15 1.21E-02 0 One

6.85E-01 1.40E-02 49.05 <2e-16

-1.80E+00 4.29E-02 -41.89 <2e-16

1.93E+00 4.23E-02 45.65 <2e-16

의 회귀계수

의

값은 49.05로서 귀무가설

이 옳다고 가정할 경우

분포에서 49.05값이 발생할 확률, 즉 유의확률은 2e-16으로 0에 가까우므로 귀무가설을 기각할 수 있고

는 0과 유의미하게 다른 회귀계수라고 결론 내릴 수 있다. 통상 가설검정이 양측검정인지 단측검정인지에 따라 유의확률이 0.025~0.05보다 작으면 귀무가설을 기각한다.Input variable

Regression coefficient

of

The value is 49.05.

Assuming this is right

The probability of a 49.05 value in the distribution, that is, the probability of significance is 2e-16, which is close to 0, so we can reject the null hypothesis.

It can be concluded that is a regression coefficient that is significantly different from zero. Normally, the null hypothesis is rejected if the probability of significance is less than 0.025 to 0.05, depending on whether the hypothesis test is a two-sided test or a one-sided test.

의 다중공선성 측정은 다음 수학식 32의 분산팽창인자를 활용한다Even if all the assumptions previously applied are established and the model is concise through the adjusted coefficient of determination, if there is a linear relationship between the input variables, multicollinearity occurs in which the variance of the regression coefficient increases. In this case, when applying a new sample, the predictive power can be greatly reduced. Regression coefficient

To measure the multicollinearity of, use the variance expansion factor of Equation 32 below.

는 입력변수

를 기타 입력변수로 회귀분석하여 얻은 결정계수이다.

가 1이면 다중공선성이 없는 직교상태로 보고, 5~10 이상이면 다중공선성이 발생하는 것으로 본다. At this time,

Is an input variable

Is the coefficient of determination obtained by regression analysis with other input variables.

If is 1, it is regarded as an orthogonal state without multicollinearity, and if it is 5~10, it is considered that multicollinearity occurs.

: 1.334,

: 12.563,

: 12.236으로

: 10시~19시 최저수요 와

: 36~48시 최대수요 입력변수간에 선형관계가 있다. 이를 완화하기 위해 두 변수는 모형에서 제외하고 두 변수를 조합한 새로운 변수

를 모형에 포함하면 오전구간의 제1 회귀모형은 수학식 33과 같다.The distributed expansion factor of the morning model

: 1.334,

: 12.563,

: 12.236

: Minimum demand from 10:00 to 19:00

: 36~48 hours There is a linear relationship between the maximum demand input variables. To alleviate this, the two variables are excluded from the model and a new variable combining the two variables.

If is included in the model, the first regression model of the morning section is shown in Equation 33.

: 1.003,

: 1.003으로 다중공선성이 제거되었고 조정된 결정계수는 0.8187로 약간 향상되었다. Dispersion expansion factor

: 1.003,

: The multicollinearity was removed to 1.003, and the adjusted crystal coefficient was slightly improved to 0.8187.

In order to establish a regression model as described above, and to prove the inconvenience of regression coefficients, calculate variance and confidence intervals, and test hypotheses, it is necessary to analyze whether the previously applied assumptions actually hold.

4 is a residual diagram of the morning interval of the first regression model according to an embodiment of the present invention, FIG. 5 is a residual diagram of the afternoon interval of the first regression model according to an embodiment of the present invention, and FIG. 6 is It is a residual diagram of the dawn section of the first regression model according to an embodiment.

First, the assumption that the independence, equivariance, normality, and mean of the error term is 0 can be confirmed through the distribution of residuals, which is the difference between the measured value and the predicted value. In the figure showing the residuals in the order of observation, if there is no pattern, the assumption of independence of the error term is established.If the width of the residuals in the predicted versus residual plot is similar across all regions, it is assumed that the variance of the error term is true. I think normality holds. Also, in the three plots, if the residual mean is close to 0, the assumption that the error term mean is 0 holds.

In the case of the assumption that the input values are fixed, even if the input variables are random variables, they are independent of each other, and if the probability distribution does not depend on the variance of the regression coefficients and error terms, it is known that all the processes developed above are established. As a result of the analysis, it can be seen that there is not much difficulty in applying the independence of errors, equivariance, and normality assumptions as shown in FIGS. If the hypothesis assumed in the model diagnosis step (S212) does not hold, or if multicollinearity exists, and the combination of variables cannot be overcome, then the model is returned to the model selection step (S211) except for the corresponding model. Models can be selected. After performing the model diagnosis (S212), a predictive power test step (S213) for evaluating the accuracy of the value predicted by the regression model is performed. The prediction power test step (S213) will be described below.

The predictive power test separates the state information into training data and test data, establishes a regression model through the above-described process using the training data, and inputs the input variables of the test data into the established regression model, and This is the process of testing the predictive power of the regression model by comparing the actual dependent variable values of the test data. The state information used to establish the first regression model is divided into training data and test data, and the predictive power is checked by comparing it with the mean square error of 0.1825 in the training data for model establishment (2015.1.1 ~ 2017.6.30). The difference between the mean square error of 0.1778 in the test data (2017.7.1 ~ 2018.6.30) is not large, so it can be evaluated as having sufficient predictive power.

If the first regression model establishment step (S210) is applied to the morning, afternoon, and dawn sections through the above-described process, the first regression model can be established for each section.

The first regression model in the morning (08:00~15:00) section is as shown in Equation 34.

: 15시 압력,

: 8시 압력 ,

: 10시~19시 최저수요 / 36~48시 최대수요,

: 평균이 0이고 분산이

인 정규분포

을 따르는 오차항이다. 분산팽창인자는

: 1.003 이고 회귀계수 관련 통계량은 아래 표 3과 같다.

: 15 o'clock pressure,

: 8 o'clock pressure,

: Minimum demand from 10:00 to 19:00 / Maximum demand from 36 to 48,

: Mean is 0 and variance is

Phosphorus Normal Distribution

Is the error term that follows. Dispersion expansion factor

: 1.003 and the statistics related to the regression coefficient are shown in Table 3 below.

Regression coefficient Estimate Standard Deviation t value Significant probability

2.09E-15 1.20E-02 0 One

6.85E-01 1.20E-02 56.98 <2e-16

-5.57E-01 1.20E-02 -46.4 <2e-16

The coefficient of determination is 0.819 for all data, 0.822 for training data, and the mean square error is 0.1810 for all data and 0.1778 for training data.

The first regression model in the afternoon (15:00~21:00) section is as shown in Equation 35.

: 21시 압력,

: 15시 압력,

: 0시 압력-8시 압력,

:6~12시 최대수요 - 12~24시 최대수요,

: 평균이 0이고 분산이

인 정규분포

을 따르는 오차항이다. 분산팽창인자는

: 1.043,

: 1.023,

: 1.059이고 회귀계수 관련 통계량은 아래 표 4와 같다.

: 21 o'clock pressure,

: 15 o'clock pressure,

: 0 hour pressure-8 hour pressure,

: Maximum demand from 6 to 12-Maximum demand from 12 to 24,

: Mean is 0 and variance is

Phosphorus Normal Distribution

Is the error term that follows. Dispersion expansion factor

: 1.043,

: 1.023,

: 1.059 and the statistics related to the regression coefficient are shown in Table 4 below.

Regression coefficient Estimate Standard Deviation t value Significant probability

3.00E-16 9.86E-03 0 One

8.81E-01 1.01E-02 87.521 <2e-16

1.88E-01 9.97E-03 18.888 <2e-16

8.84E-02 1.02E-02 8.715 <2e-16

The determination coefficient is 0.879 for all data, 0.888 for training data, and the mean square error is 0.1207 for all data, 0.1154 for training data, and 0.1383 for test data.

The first regression model in the early morning (21:00~06:00) section is as shown in Equation 36.

: 30시 압력,

: 21시 압력,

: 10~19시 최저수요,

: 24~30시 최저수요 / 30~36시 최대수요,

: 8시 압력,

: 평균이 0이고 분산이

인 정규분포

을 따르는 오차항이다. 분산팽창인자는

: 1.630,

: 1.624,

: 1.366,

: 1.826이고 회귀계수 관련 통계량은 아래 표 5와 같다.

: 30 o'clock pressure,

: 21 o'clock pressure,

: Minimum demand from 10 to 19:00,

: Minimum demand from 24 to 30 / maximum demand from 30 to 36,

: 8 o'clock pressure,

: Mean is 0 and variance is

Phosphorus Normal Distribution

Is the error term that follows. Dispersion expansion factor

: 1.630,

: 1.624,

: 1.366,

: 1.826 and statistics related to the regression coefficient are shown in Table 5 below.

Regression coefficient Estimate Standard Deviation t value Significant probability

-0.00073 0.018787 -0.039 0.969168

0.675628 0.017423 38.779 <2.2e-16

0.394126 0.01902 20.722 <2.2e-16

-0.46968 0.017626 -26.647 <2.2e-16

0.057794 0.015757 3.668 0.000255

The coefficient of determination is 0.670 for all data, 0.701 for training data, and the mean square error is 0.2635 for all data, 0.2596 for training data, and 0.2898 for test data.

To describe the second regression model establishment step (S220), the amount of gas supplied to the gas piping network is referred to as a gas inflow amount, and the amount of gas drawn out of the gas piping network is referred to as a gas extraction amount. The change in the gas filling amount is a value obtained by subtracting the gas drawing amount from the gas drawing amount.

In the second regression model establishment step (S220), a regression model having a change in average pressure for each time period included in the state information as an input variable and a change in gas filling amount as a dependent variable may be established. Since the second regression model predicts a change in the gas filling amount required to achieve the average pressure at a specific time point predicted by the first regression model, it is possible to predict how much the gas input amount should be set. Since the average pressure and the gas filling amount provide a reliable tendency to various gas piping network 10 changes, the input variable can be set to the average pressure without using all possible regression methods in establishing the second regression model.

In order to calculate the total amount of gas discharge required to adjust the average pressure, normalize the two variables using the main pipe (Pm) network gas filling change during a certain period as a dependent variable, and the average pressure change during a specific period as an input variable, and then standardize the regression model. Establish. For example, the second regression model using the change in the average pressure of the main pipe (Pm) for 6 hours as an input variable and the change in the filling amount of the gas pipe network (10) for 6 hours as a dependent variable can be established as in Equation 37 below. Can.

The second regression model of Equation 37 above means that in order to increase or decrease the average pressure by 1, the gas filling amount supplied to the gas piping network 10 must be increased or decreased by 0.9983 for a specific period. It can be achieved by making it as high as 0.9983. The goodness of fit is 0.997, and the input and dependent variables are physically related and have sufficient accuracy to be used in practice. Therefore, model diagnosis and predictive power test can be omitted.

Through the above process, a first regression model and a second regression model may be established (S210 and S220). Next, in the information providing step (S300), using the first regression model and the second regression model, short-term operation information necessary for the operation of the gas piping network 10 may be provided (S300a).

In the information providing step, in providing the short-term operation information (S300a), in the first regression model, the conversion information providing step of standardizing and providing items selected as the input variable so that the degree of the effect of the input variable on the dependent variable is compared (S310) ), and in order to achieve the average pressure (S320) predicted by the first regression model at a specific time point, the supply information provision step (S330) for predicting and providing a change in the expected gas inflow amount using the second regression model It can contain.

In the conversion information providing step (S310 ), the input variables selected in the first regression model may be standardized and provided. Since the input variables are different physical quantities and have different scale values, it is difficult to intuitively recognize the effect of each of the input variables on the average pressure of the main pipe Pm, which is a dependent variable. Therefore, by standardizing the input variables selected in the first regression model and providing them to the manager, when the manager adjusts the input variables, the influence on the average pressure can be intuitively recognized, thereby helping the manager to make convenient decisions. have.

Also, an average pressure prediction step (S320) may be performed based on the first regression model. Using the first regression model, the average pressure at the end of each section that divides the day can be estimated. For example, the average pressure of the main pipe (Pm) at 8 o'clock at the start of the morning section (08:00 to 15:00) and at 15:00 at the end can be predicted. That is, the morning section manager can be provided with an average pressure forecast at 15:00, which is the end of the morning section when starting work. Equally, the afternoon section manager can be provided with an average pressure forecast at 21 o'clock at the end of the afternoon section when starting work.

Next, in the supply information providing step (S330), in order to achieve the average pressure predicted by the first regression model at a specific time point, the predicted gas filling amount change using the second regression model can be predicted and provided to the manager. . Since the average pressure at the end of the section was predicted in the above-described average pressure prediction step, the second gas flow model can be used to predict the required gas inlet amount (expected gas filling amount change + gas withdrawal amount) to achieve the average pressure at the end of the section. have. For example, the amount of gas input required to achieve the main pipe (Pm) average pressure predicted value at 15 o'clock at the end of the morning section (from 8 am to 15 o'clock) can be predicted at the start of the morning section, so the manager needs the gas input. It is possible to control the gas piping network 10 so that the gas is supplied by the amount.

Next, a process (S200b) of establishing a long-term regression model in the model establishment step (S200) after the state information collection step (S100) will be described.

7 is a flowchart illustrating detailed steps of a method for providing operation information of a gas piping network 10 according to an embodiment of the present invention.

Gas direct import operators may be individuals or corporations other than the operating entity operating the gas piping network 10. Gas direct import operators can withdraw gas from the gas piping network 10 within the withdrawal contract capacity range (t/h), and withdraw the gas within the withdrawal contract capacity (t/h) range. Fin) to inject gas into the gas piping network (10).

However, there is a problem in that the amount of gas to be drawn in is greater than the capacity of the piping, and thus, the gas input needs to be restricted. This problem is due to the fact that gas outlets of gas direct import operators are distributed throughout the country, but gas injection points are concentrated in Boryeong, one of the gas inlets, leading to bottlenecks at Boryeong base connection points. to be.

When a gas direct import operator draws less gas than the gas is drawn out, it is called a draw-in limit, and the operating entity of the gas pipeline network (ie, an operator who supplies gas to the gas pipeline network, for example, Korea Gas Corporation) Gas rental is generated from the company to the direct gas supplier. Therefore, as a direct gas importer draws less gas, additional gas must be drawn in later. This is called gas return. In the present specification, the days when gas intake restrictions and returns occur are referred to as gas intake restriction dates and gas additional ingestion dates, respectively.

In order for gas direct import operators to enter into a gas intake contract using Boryeong base, it is expected to provide a gas intake facility (Fin, for example, Boryeong base) with an increase in pressure in the intake area, and accordingly the gas intake restriction date and the additional gas availability date. In addition, relevant departments and related organizations should review whether the gas inflow contract is manageable. However, the above-mentioned short-term regression model cannot predict the local pressure increase in the gas inlet facility area, gas inlet restriction, and the period during which gas can be added. In order to solve this problem, the method for providing operation information of the gas piping network 10 according to an embodiment of the present invention reliably predicts operation information such as a gas entry restriction date and a gas additional entry possible date through 3 to 5 regression models. Can provide.

In describing the 3rd to 5th regression models, the capacity of the pipe is the same as the amount of gas input, and is the amount at which the gas can be drawn at the maximum within the allowable pressure range of the pipe at the connection point (Fin) of the gas supply facility. Also, the expected amount of gas inflow is the same as the expected amount of gas withdrawal.

In the future, the gas intake facility (Fin)'s gas intake restriction date and the possible additional gas intake date can be estimated by comparing the expected gas intake capacity of the gas intake facility (Fin) with the expected capacity of the pipe. If the expected amount of gas inflow from Boryeong Station on any day is greater than the expected capacity of the pipe (capable of entering), it can be expected to be the gas inflow limiting date, which must limit the gas inflow by the difference, and the expected intake amount is less than the expected capacity By the difference, it can be expected that it is a possible gas inflow date that can additionally draw gas.

Therefore, in order to predict the gas intake restriction date and the possible gas intake date, it is necessary to first establish a predicted model of gas intake and the capacity of the pipe network. At this time, the expected amount of withdrawal is the same as the expected amount of withdrawal, and the estimated amount of withdrawal is the amount of the withdrawal contract determined by the contract multiplied by the expected facility utilization rate. Therefore, it is useful to establish the facility utilization rate model instead of the expected amount of gas input, so that the estimated value of each model can be calculated by multiplying the output value of the model by the withdrawal contract capacity. The facility utilization rate refers to the ratio of actual gas withdrawal to the withdrawal contract capacity.

Both facility utilization rate and piping capacity are affected by gas demand, and gas demand is affected by temperature. Therefore, by establishing a temperature-demand model, a demand-capacity model, and a demand-facility utilization model, you can estimate various statistics such as the limit of gas inflow by period, the date of additional gas intake, and the amount of inflow available by using average temperature by period. It is possible to estimate various values necessary for making a decision necessary for operating the gas pipeline network 10 or the capacity of the gas pipeline network 10 between the direct-introducing operator and the operating entity of the gas pipeline network 10.

As shown in FIG. 7, the model establishment step (S200b) according to an embodiment of the present invention uses the temperature as an input variable and Bayes to establish a third regression model for predicting the annual demand of the gas piping network 10. The third regression model establishment step (S230) of estimating the regression coefficient using theorem to establish the third regression model, and the gas to establish the fourth regression model predicting the capacity of the gas supply point of the gas piping network 10 The fourth regression model establishment step (S240) of establishing the fourth regression model by estimating the regression coefficient using Bayes' theorem as the input variable and the fifth regression model predicting the annual facility utilization rate of gas direct import operators In order to establish, a fifth regression model establishment step (S250) of establishing a fifth regression model by using gas demand as an input variable and estimating a regression coefficient using Bayes' theorem may be included.

The state information for establishing the third, fourth, and fifth regression models may use daily gas demand, daily facility utilization rate, daily capacity, and the like. As exemplarily illustrated in Table 6, daily demand utilized demand for the past year, and the expected amount of gas inflow from the gas intake facility (Fin) is the contract amount of withdrawal (t/h) × facility utilization. Was utilized. The capacity was obtained by conducting a simulation experiment using the pipe network analysis program (Synergi Gas).

Pause Demand (ton/day) Facility utilization rate Carrying capacity (t/h) 2017.6.28 88,957 0.847 557

2018.6.27 97,847 0.801 577

In the steps of establishing the third regression model (S230), establishing the fourth regression model (S240), and establishing the fifth regression model (S250), in establishing the regression model, it is possible to reflect the heteroscedasticity, irregularity of the error term and subjectivity of the analyst. Use Bayes' theorem. Since the facility utilization rate has a value from 0 to 1, it is appropriate to assume that the error term follows the beta distribution rather than the normal distribution. In the case of capacity, the standard deviation of the error term linearly increases or decreases depending on the input variable. Bayes' theorem is used to properly reflect this. In addition, since the uncertainty is large for the next 5 to 10 years, the period for which the forecast of the available gas and the expiration date is required is large, so using Bayes' theorem, the analyst's judgment based on the experience of gas system operation as well as data through observation and simulation Can reflect the uncertainty in the statistics to be estimated.

In addition, in the third regression model establishment step (S230) and the fifth regression model establishment step (S250), sections are divided into weekdays, Saturdays, and Sundays (including holidays), and regression models are established for each section, respectively. In the establishment phase (S240), a section is divided into a summer season (April to October) and a winter season (November to March) in which the operation method of the gas piping network 10 changes, and a regression model can be established for each section.

The third, fourth, and fifth regression model establishment steps (S230, S240, and S250) may include establishment of a likelihood function (S201), pre-distribution grant (S202), and post-distribution calculation (S203), respectively.

First, in the process of establishing the likelihood function (S201), the likelihood function of the third regression model (at temperature-demand) and the fourth regression model (demand-acceptance) is set to a normal distribution, and the fifth regression model (demand-facility utilization rate) In the case of ), the utilization rate takes a value from 0 to 1, so it can be set as a beta distribution. Also, the average of each distribution is set to the 2nd to 3rd orthogonal polynomial regression model of the input variable, and the standard deviation follows the simple linear model for the input variable, but can be set to have a value greater than 0.

Next, in the process of assigning the prior distribution (S202), the prior distribution for the regression coefficient of the polynomial regression model is assumed to be a normal distribution, and the mean and standard deviation of the prior distribution are calculated by applying the least squares method to the orthogonal polynomial regression model. Apply the value of 100 times the standard deviation and the estimated value of one regression coefficient. In the case of the simple linear model, the data are divided into 15-20 groups in the order of input variable size, and a linear model is established with the average of the input variables of each group as the input variable and the standard deviation of the group as the response variable.

Next, in the process of estimating the posterior distribution (S203), Bayes' theorem aims to calculate the posterior distribution through a pre-distribution, likelihood function, and peripheral distribution. Since the direct calculation of the peripheral distribution is difficult, the Markov chain in the present invention The posterior distribution is estimated using the Monte Carlo method.

Hereinafter, a process of establishing a regression model using Bayes' theorem will be described in more detail.

Bayes' theorem can be derived from the definition of conditional probability in Equation 38 below. The conditional probability is the probability that another event H will occur under the condition that an event D has occurred.

는 사건 D가 발생할 확률이고

는 사건 H와 D가 동시에 발생할 확률이다. 또한 반대로

이므로

이 성립하고 이를 위의 식에 대입하면 아래 수학식 39의 베이즈 정리를 얻을 수 있다.

Is the probability that event D will occur

Is the probability that events H and D will occur simultaneously. Also on the contrary

Because of

By establishing this and substituting it into the above equation, the Bayes theorem of Equation 39 below can be obtained.

D usually means observation data, and H means the hypothesis to be estimated or tested or the regression coefficient of the model.

로서 사후분포(posterior distribution)라 하고 관측자료를 고려했을 때, 회귀계수 H가 가질 수 있는 각각의 값에 대해 부여된 확신의 정도, 즉 확률분포를 의미한다.

는 사전분포(prior distribution)로서 자료를 고려하기 전에 회귀계수 H가 가질 수 있는 각각의 값에 대한 확신의 정도 또는 확률분포이다.

는 가능도함수(likelyhood function)로서 회귀계수 H가 사실이라 가정할 때 D를 관측할 확률이다.

는 주변부분포(marginal distribution)으로 모든 H에 대해 D가 발생할 확률로서 상수값을 갖는다. The final thing we want to get through Bayes' theorem

It is called the posterior distribution, and when considering the observation data, it means the degree of confidence given to each value of the regression coefficient H, that is, the probability distribution.

Is the degree of confidence or probability distribution for each value that the regression coefficient H can have before considering the data as a prior distribution.

Is the likelihood function, which is the probability of observing D assuming that the regression coefficient H is true.

Is the marginal distribution, and has a constant value as the probability that D will occur for all Hs.

For example, in the fourth regression model establishment stage, when trying to establish a model of pipe capacity (y) according to gas demand (x) as shown in Equation 40 below,

를 따른다고 가정하고 가능도 함수에는 위 모형을 대입하면 균일분포와 정규분포의 정의를 통해 사전분포는 다음 수학식 41과 같이(S202), 가능도함수는 다음 수학식 42와 같이(S201) 계산할 수 있다.To estimate the regression coefficients using Bayes' theorem, you must calculate the prior distribution, likelihood function, and marginal distribution. If all the regression coefficients have a prior distribution, they are independent of each other and all are uniformly distributed.

Assuming that the following model is substituted for the likelihood function, the pre-distribution can be calculated as in Equation 41 (S202), and the likelihood function can be calculated as in Equation 42 (S201) by defining the uniform distribution and the normal distribution. have.

In order to directly calculate the marginal distribution, the integral must be calculated for all regression coefficients to be estimated as shown in Equation 43 below, which is generally known to be very difficult.

Therefore, a method of obtaining a posterior distribution is required even indirectly without directly calculating the peripheral distribution. The representative method is Markov Chain Monte Carlo (MCMC) (S203).

가 취하는 값을 상태(state)라고 하고, 상태들의 전체모임을 상태공간(state space)라 한다. 만일 아래 수학식 44와 같이

은 오로직

에만 의존하고

에 의존하지 않을 때 이 성질을 마코프 성질이라 하고 이런 성질을 갖는 확률과정을 마코프과정이라 하며 상태공간이 이산형인 마코프과정을 마코프 사슬(Markov chain)이라 부른다.The Markov Process means a stochastic process with Markov Property. At this time, in the probability process

The value it takes is called a state, and the entire gathering of states is called a state space. If Equation 44 below

Silver only

Rely only on

When not dependent on, this property is called the Markov property, the probability process having this property is called the Markov process, and the Markov process in which the state space is discrete is called the Markov chain.

In other words, Markov's nature is that, given past and present information, the conditional distribution of the future depends only on the current information and is independent of past information.” In addition, the probability of change from state i to state j above is referred to as transition probability, and is defined separately from Equation 45 below according to the period required for the state change.

에서 1단계 후에 상태 j로 변화될 확률을 원소로 나타낸 아래 수학식 46의 행렬 P를 추이확률행렬(transition probability matrix)이라고 한다. State i

The matrix P of Equation (46) below, which represents the probability that it will change to state j after step 1 in an element, is called a transition probability matrix.

If the state i can change from state j to vice versa, and vice versa, then the two states are said to be communicative, and the Markov chains in which all states are reachable are called irreducible. In addition, if the probability of eventually returning to state i again during the Markov chain probability process starting from state i is 1, it is said to be recurrent.

의 확률로 j에 도달할 기회를 갖기 때문에 결국 j를 유한번의 시간내에 방문하게 된다. 이를 통해 마코프 체인이 약분불가, 즉 모든 상태가 서로도달가능할 때, 이 중 한 상태가 재귀적이면 결국 모든 상태가 재귀적이 됨을 알 수 있다.If the state i is recursive and can reach j, the probability that the Markov chain starting at i will reach j is 1. This means that if i is recursive, the Markov chain continues to visit i over time and every time

Since we have a chance to reach j with probability of, we eventually visit j within a finite number of times. Through this, it can be seen that when the Markov chain is weak, that is, when all states can reach each other, if one of these states is recursive, eventually all states become recursive.

이라고 하면 극한의 시간에서 마코프 사슬이 j상태에 머무르는 비율(Long run proportion)

를 불변확률분포(invariant probability distribution)라 부르고 초기상태에 관계없이

이다.The average time it takes for the Markov chain to be weak and recursive, to leave j and back to j

Is the rate at which the Markov chain stays in the j state at extreme times (Long run proportion)

Is called the invariant probability distribution and regardless of the initial state

to be.

이라하고, j에서 출발하여 j까지 돌아오는데 걸리는 추가시간을

라고 하며 또 다시 j에서 출발하여 j까지 돌아오는데 걸리는 추가시간을

라고 한다면 장기적으로 j를 n번 방문하는데 소요된 시간은

이다. 이때

은

에 소요된 유한의 시간이고,

는

에 소요된 유한의 시간들로 평균은

이며, 결국

는 j를 방문한 횟수 n을, n번 방문하는데 걸린시간

로 나눈 값이므로 다음 수학식 47과 같이 장기적으로

이 성립함을 알 수 있다.The reasons for the above relationship are as follows. The time for the Markov chain to start at any initial state i and return to j

And the extra time it takes to depart from j and return to j

The additional time it takes to depart from j and return to j

In the long run, the time taken to visit j n times is

to be. At this time

silver

Is the finite time spent on,

The

The finite time spent on the average

And eventually

Is the number of times n visited j, the time taken to visit n times

Since it is divided by, the following equation (47)

You can see that this is true.

즉,

이면 양의 재귀(positive recurrent)상태라 하고

즉,

이면 영의 재귀상태(null recurrent)라 하며 다음의 정리가 성립한다.At this time,

In other words,

It is called positive recurrent state.

In other words,

It is called null recurrent and the following theorem holds.

이고, i와 j가 서로도달 가능하므로

인 n이 있다. 0보다 큰 두 수를 곱하면 0보다 크므로

이다.

는 마코프 사슬이 장기적으로 상태 i에서 n번의 시간후에 상태 j에 도달할 비율이므로 마코프 사슬이 장기적으로 상태 j에 머물 비율보다 클 수 없다. 즉, 아래 수학식 48이 성립하므로 상태 j역시 양의 재귀적이다.In the Markov chain, state i is positive recursion and j is positive recursion if it can reach each other. Because state i is positive recursion

And i and j can reach each other.

There is n. Multiplying two numbers greater than zero is greater than zero, so

to be.

Is the rate at which the Markov chain will reach state j after n to n times in the long term, and therefore cannot be greater than the rate at which the Markov chain will remain at state j in the long term. That is, since the following equation (48) holds, the state j is also positively recursive.

Through this, it can be seen that if the Markov chain is weak and one of them is positively recursive, eventually all states become positively recursive.

는 장기적으로 상태 i에서 상태 j로 변화할 비율이므로 아래 수학식 49와 같이 모든 i에 대해서

를 각각 더해준다면 이는 장기적으로 마코프 사슬이 상태 j에 머무를 비율이 된다.Also,

Is the ratio that changes from state i to state j in the long run, so for all i as shown in Equation 49 below,

If each is added, this is the rate at which the Markov chain will stay in state j in the long run.

는 다음 수학식 50의 방정식을 만족하는 유일한 해로 알려져 있다.If the Markov chain is weak and recursive, a positive probability distribution

Is known as the only solution that satisfies the equation (50).

는

임을 알 수 있다.Using the above result, the equation in Equation 51 below is satisfied.

The

You can see that

This is because when the above two expressions are added to all i, the following Equation 52 is established to form the same as Equation 50 above.

의 총합은 1이므로 아래의 수학식 53과 같은 추이행렬 P를 구성할 수 있다면 상기 수학식 51에 의해 이 마코프 사슬이 장기적으로 상태 i에 머무는 비율이 곧 사후확률분포

이다.Post distribution to obtain through Bayes' theorem

Since the sum of is 1, if the transition matrix P as shown in Equation 53 below can be constructed, the rate at which this Markov chain stays in the state i in the long term by Equation 51 is the posterior probability distribution.

to be.

의 확률로 수락되므로 상기 수학식 53은 아래 수학식 54와 같다.One of methods for constructing a transition matrix that can satisfy Equation 53 is the Metropolis-Hastings algorithm. First, we construct the Markov trend matrix Q which is not weak. This is called the proposed distribution because it proposes to change state i to state j with the probability of q _ij . This offer

Since it is accepted as a probability of Equation 53, Equation 54 is as follows.

를 다음 수학식 55와 같이 정의한다면 수학식 54는 아래와 같이 항상 성립함을 알 수 있다.

If is defined as the following Equation 55, it can be seen that Equation 54 always holds as shown below.

이면,

이고 따라서 수학식 54는 성립한다. if

If it is,

Therefore, Equation 54 is established.

이면,

이므로 역시 수학식 54가 성립한다.Contrary

If it is,

Therefore, Equation 54 holds.

는 약분되어 없어지므로 실제

계산은 다음 수학식 56과 같이 사전확률

과 가능도함수

만을 활용한다.Peripheral distribution in trend probability calculation

Is weak and disappears.

Calculation is as follows:

And likelihood function

Use only.

와 같이 추정하고자 하는 확률변수가 여러개인 경우 효율적 마코프사슬을 구성하는 것이 중요하다. 예를 들어 마코프 사슬이 10,000회가 진행되는 동안, 대부분의 경우 제안분포가 거절되면 확률변수가 가질 수 있는 다양한 범위와 확률을 충분히 탐색할 수 없기 때문이다. 따라서 거절될 수 없는 제안분포를 생성하는 방법을 많이 쓰는데 이를 깁스 샘플링이라 한다.if

As described above, it is important to construct an efficient Markov chain when there are multiple random variables to be estimated. This is because, for example, while the Markov chain is 10,000 times in progress, in most cases, if the proposed distribution is rejected, the various ranges and probability that the random variable can have cannot be sufficiently explored. Therefore, many methods are used to generate a proposal distribution that cannot be rejected. This is called Gibbs sampling.

는 사후분포

를 따른다고 할 때, 깁스샘플링은 우선

중 임의의 수를 선택한다. 선택한 수가 i라 하면 이후 확률변수 X를 다음 수학식 57과 같이 생성한다.Probability vector

Is post-distribution

When you follow, Gibbs sampling is first

Choose any number. If the selected number is i, then random variable X is generated as shown in Equation 57 below.

를 제외한 나머지 확률변수들은 현재상태로 고정한 상태에서의 조건부 확률을 통해

를 현상태

에서 다음상태

로 옮길 것을 제안한다. 즉, 현재상태가

일 때, 제안분포는

를 다음상태로 제안한다. 이상의 깁스 샘플러에 의한 제안분포는 다음 수학식 58과 같이 쓸 수 있다.In other words,

The rest of the random variables, except for

The status quo

In the next state

Suggest to move to. In other words, the current state

When the distribution is

Propose to the next state. The proposed distribution by the Gibbs sampler can be written as in Equation 58 below.

에 수학식 58을 대입하면 아래 수학식 59와 같으므로 언제나 제안을 수락한다.So the probability of accepting this offer

Substituting equation (58) into equation (59) below always accepts the offer.

In order to estimate the posterior distribution of the regression coefficient of the fourth regression model (demand-acceptance) in the winter season (November to March) by applying the above, the likelihood function is first set as in Equation 60 below (S201): .

,

,

를 직교화하여 사용하였다. 이는 다항회귀모형에서 발생할 수 있는 계산의 불안정성과 다중공선성을 해결하기 위함이다. 만일 입력변수 원값을 사용하면 마코프 사슬 몬테카를로 과정중 계산오류가 발생할 수 있고, 이를 해결하기 위해 입력변수를 표준화하여도 다중공선성은 남아 있어 회귀계수 사후분포가 여러 개의 피크값을 갖는 경우가 발생하여 추정값의 불확실성이 커진다. At this time, in the actual calculation, the input variable using the poly function of software r

,

,

Was orthogonalized. This is to solve the computational instability and multicollinearity that can occur in the polynomial regression model. If the original value of the input variable is used, a calculation error may occur during the process of Markov chain Monte Carlo, and the multicollinearity remains even if the input variable is normalized to solve this, and the posterior distribution of the regression coefficient has multiple peak values. Uncertainty increases.

The dictionary distribution for each regression coefficient is set as Equation 61 below as a normal distribution independent of each other (S202).

,

에 대한 대략적인 값을 부여하기 위해 가능도함수를 최소제곱법으로 추정하면 아래 표 7과 같고,

에는

추정값을

에는

표준편차의 100배를 한 값을 부여한다.

,

In order to give an approximate value for, the likelihood function is estimated by the least square method, as shown in Table 7 below,

In

Estimate

In

Assign a value that is 100 times the standard deviation.

Regression coefficient Estimate Standard Deviation t value Significant probability

8.55E-17 2.85E-02 0 One

1.03E+01 3.48E-01 29.466 <2e-16

4.88E+00 3.48E-01 13.992 <2e-16

-1.11E+00 3.48E-01 -3.197 0.0017

,

에 적절한 값을 부여하기 위해 입력변수를 크기순으로 15그룹으로 나누고 그룹별 입력변수의 평균을 입력변수로 하고 그룹별 표준편차를 반응변수로 하여 단순선형회귀 모형을 수립하고 이를 최소제곱법을 구하면 아래 표 8과 같고,

에는

추정값을

에는

표준편차의 100배를 한 값을 부여한다.

,

To give an appropriate value to the data, divide the input variable into 15 groups in size order, set the simple linear regression model with the average of the input variables for each group as the input variable, and the standard deviation for each group as the response variable. Table 8 below,

In

Estimate

In

Assign a value that is 100 times the standard deviation.

Regression coefficient Estimate Standard Deviation t value Significant probability

0.36132 0.03838 9.415 3.61E-07

1.68752 0.51537 3.274 0.00604

Thereafter, the Markov chain Monte Carlo method was implemented, but the first 5,000 times were used as burn-in periods, and then the posterior distribution of each regression variable was estimated through 30,000 samplings (S203).

Generates random numbers using the extracted 3rd regression model (at temperature-demand), 4th regression model (demand-capacity), and the 5th regression model (demand-facility utilization ratio). Calculate various statistics required.

According to the above-described process, the likelihood functions of the third regression model (at temperature-demand) and the fourth regression model (demand-acceptance) are set as in Equation 62 below, and the prior distribution for each regression coefficient is Equation 63 below: As shown in the figure, a normal distribution independent of each other is given.

은 정규분포,

,

는 제3 회귀모형(기온-수요)에서는 기온과 수요, 제4 회귀모형(수요-수용력)에서는 수요와 수용력을 의미하고

는 모두 직교화하여 사용한다. At this time,

Is the normal distribution,

,

Means temperature and demand in the third regression model (at temperature-demand), and demand and capacity in the fourth regression model (demand-acceptance).

All orthogonally used.

In addition, the likelihood function of the fifth regression model (demand-facility utilization rate) is set as in Equation 64 below, and the prior distribution for each regression coefficient is given an independent normal distribution as in Equation 65 below.

는 베타분포이고

는 가능도 함수의 평균으로

이며

는 가능도 함수의 표준편차로

이다.

Is the beta distribution

Is the average of the likelihood functions

Is

Is the standard deviation of the likelihood function

to be.

8 is a view showing an estimation of a regression coefficient of a fourth regression model in a summer section according to an embodiment of the present invention.

를 추정하는 과정은 도 8과 같다. 제5 회귀모형(수요-시설이용률)의 회귀모형은 가스 직도입 사업자의 영업비밀에 속하는 것으로 구체적인 모형은 미기재한다.In the case of the Monte Carlo chain in Markov, 5,000 burn-in runs were performed, and then 30,000 samples were generated to estimate the regression coefficient. The regression coefficients are obtained from the posterior distribution rather than from a single value. The standardized response variable is used to perform Markov chain Monte Carlo, and the average of the posterior distributions of the regression coefficients of the 3rd regression model (at temperature-demand) and the 4th regression model (demand-acceptance) is shown in Table 7 below. Regression coefficient of the 4th regression model (demand-acceptance) of the section from April to November)

The process of estimating is as shown in FIG. 8. The regression model of the fifth regression model (demand-facility utilization rate) belongs to the trade secret of gas direct import operators, and a specific model is not listed.

Counting Temperature-demand model Demand-capacity model weekday Saturday holiday April-November December to March

0 0 0 0 0

-14.490 -6.487 -7.494 12.767 10.265

3.443 1.629 1.762 -3.313 4.962

1.954 0.711 0.592 Not applicable -0.601

0.279 -0.302 -0.391 0.441 0.354

0.280 0.309 -0.095 0.011 0.854

After establishing the third, fourth, and fifth regression models using the above-described processes (S230, S240, and S250), an information provision step is provided to provide long-term information necessary for long-term operation of the gas piping network 10. (S300b). In the information providing step (S300b), the demand is predicted by substituting the third regression model for the average temperature for the past 30 years, which can represent the long-term temperature in the future, and using the third regression model to predict the demand. The capacity and facility utilization rate can be predicted by entering the fifth regression model. In the information providing step (S300b), the capacity of the gas supply point of the gas piping network 10 predicted by using the fourth regression model and the facility utilization rate predicted by using the fifth regression model in the contract capacity of the gas direct import operator By comparing the expected amount of input calculated by multiplying, it is possible to provide long-term information by calculating a restriction date of gas input and a possible date of additional gas input.

Generates 10,000 random numbers using the posterior distribution of the 3rd regression model (at temperature-demand), the 4th regression model (demand-capacity), and the 5th regression model (demand-facility utilization) model, and uses the facility utilization rate and contract capacity By calculating the expected amount of gas inflow, and comparing the expected amount of gas inflow with the capacity, the 95% confidence interval of the period for the restriction on gas inflow and the allowable period for additional gas in the current contracted capacity is calculated to be 17 to 43 days. If you compare the gas intake and restriction dates predicted by the regression model with the actual gas intake and restriction dates, the actual gas intake restriction date from 2018.1 to 2018.9 is 20 days, so the model seems applicable. Therefore, the gas pipeline network 10 operating entity and the gas direct import operator can refer to the decision making by receiving the predicted values for the annual gas inflow and outgoing dates.

In addition, demand, facility utilization rate, and capacity can change, so if the level of change and the degree of confidence in it are expressed in advance, it is possible to analyze how the available and restricted dates of gas change accordingly. For example, if you strongly believe that the facility utilization rate will increase by 5%, the allowable and limiting days for gas entry will take 20 to 47 days. Here, a 5% increase in facility utilization rate was reflected by adding 0.05 to the section coefficient of the polynomial regression model, and the degree of strong belief was reflected by dividing the standard deviation of the prior distribution by 100 again.

If the contract capacity is multiplied by the estimated facility utilization rate and the contract capacity is repeated, the effect of the increase in contract capacity in the future is 95% confidence. It is estimated that the capacity is limited.

9 is a view showing the estimated spare capacity of each gas supply point connected to the gas pipe network 10 according to an embodiment of the present invention.

Forecast of gas acceptance margin (acceptable capacity-expected amount of intake) by period is shown in FIG. 9. In FIG. 8, the solid line in the curved form corresponds to the average free capacity, and the horizontal solid line corresponds to the free capacity 0 based on the original data, and the upper and lower point sums indicate the 95% and 5% intervals, respectively. The operational information that predicts the margin of gas acceptance will help private gas direct import operators to make decisions regarding LNG contracts and arrival times.

The above-described method for providing operation information of the gas piping network 10 according to an embodiment of the present invention predicts an appropriate average pressure of the gas piping network 10 after a few hours in the short term, and the amount of gas drawn to reach the appropriate average pressure. Since it can provide information about, it helps the administrator to manage the gas piping network 10. In addition, it is possible to predict the annual gas demand, the capacity of the pipe network, the facility utilization rate of gas direct import operators, and use it to provide information on the possible and restricted dates for gas introduction, so that the gas pipeline network 10 operators and gas direct import operators Helps to make decisions about direct gas introduction.

The gas piping network 10 operating information providing method according to an embodiment of the present invention described above may be written in computer program code and stored in a storage device, and executed by a processor to generate operating information and display devices such as a display. Through this, operation information can be provided to the administrator.

Although the present invention has been described in detail through specific examples, the present invention is specifically for describing the present invention, and the present invention is not limited to this, and by those skilled in the art within the technical spirit of the present invention. It will be apparent that the modification and improvement are possible.

All simple modifications or changes of the present invention belong to the scope of the present invention, and the specific protection scope of the present invention will be clarified by the appended claims.

10: gas pipeline network
Pm: Main piping
Ps: Assistant piping
Fout: Consumer
Fin: Gas Inlet Facility

Claims (8)

A state information collection step of collecting and converting the state information measured at a plurality of points in the gas pipeline network into a database;
A model establishment step of selecting an input variable and estimating a regression coefficient to establish a regression model based on the state information; And
And an information providing step of providing operation information necessary for the operation of the gas piping network using the regression model.
The status information
It includes at least one item of pressure, demand, maximum demand, minimum demand, gas intake amount, average pressure at the plurality of points, and temperature at a plurality of points in the gas piping network,
The model building step
A third regression model establishment step of establishing the third regression model by estimating a regression coefficient using Bayes' theorem as the temperature as an input variable and establishing a third regression model for predicting the annual demand of the gas pipeline network;
In order to establish a fourth regression model for predicting the capacity of a gas supply point of the gas piping network, a fourth regression model is established by estimating a regression coefficient using Bayes' theorem with gas demand as an input variable. Regression model establishment stage; And
In order to establish a fifth regression model that predicts annual facility utilization rate of gas direct import operators, a fifth regression model is established that establishes the fifth regression model by estimating the regression coefficient using Bayes' theorem as gas demand. Including steps,
The above steps are written in computer program code and executed by a processor. delete The method according to claim 1,
The model building step
In order to establish a first regression model for predicting the average pressure of the plurality of points at a specific time point, all possible regressions (All items) included in the state information or a combination of items that are linearly related to each other are preliminary input variables (All A first regression model establishment step of selecting an input variable from the preliminary input variables using a possible regression method and estimating a regression coefficient using a least squares method to establish the first regression model; And
In order to establish a second regression model for predicting the amount of gas input to be supplied to the gas piping network in order to achieve the average pressure at the specific time point predicted by the first regression model, the average over time included in the state information A method of providing operation information of a gas piping network, further comprising a second regression model establishment step of establishing a regression model having a pressure change as an input variable and a gas filling amount change as a dependent variable. The method according to claim 3,
The above information providing step
A conversion information providing step of standardizing and providing items selected as the input variable so that the degree of influence of the input variable on the dependent variable in the first regression model is compared; And
In order to achieve the average pressure predicted by the first regression model at the specific point in time, using the second regression model, providing supply information providing and predicting the change in the gas filling amount, providing gas pipeline network operation information Way. The method according to claim 3,
The first regression model establishment step
Predict the average pressure at a reference point that divides the section by dividing the day into at least two or more sections based on the manager's shift shift and the highest average pressure during the day, and establishing the first regression model for each section. How to provide gas pipeline network operation information. delete The method according to claim 1,
The above information providing step
Estimation of the incoming capacity calculated by multiplying the capacity of the gas supply point of the gas piping network predicted using the fourth regression model and the contract capacity of the gas direct import operator by the facility utilization rate predicted using the fifth regression model In comparison, a method for providing operation information of a gas piping network is to provide long-term information by calculating a restriction date for a gas input and a possible date for additional gas. The method according to claim 1,
The third regression model establishment step and the fifth regression model establishment step are
Sections are divided into weekdays, Saturdays, and Sundays (including holidays), and regression models are established for each section.
The fourth regression model establishment step
Gas pipeline network operation information provision method that divides sections in summer and winter and establishes regression models for each section.

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