KR100888628B1 - Two dimensional dispersion coefficient observation method by combining stream-tube concept and routing procedure - Google Patents

Abstract

The present invention relates to a method for observing a two-dimensional pollution dispersion coefficient combining a related concept and a tracking procedure, wherein (a) an arbitrary longitudinal dispersion coefficient, a transverse dispersion coefficient set as an initial value, and a measured concentration distribution of an upstream end are used as input data. Calculating a concentration distribution 1 of a downstream end satisfying a predetermined equation and calculating an error 1 between the calculated concentration distribution 1 of the downstream end and the measured concentration distribution of the downstream end at the same point; (b) Longitudinal variance so that the error 2 ... error n between the concentration distribution of the downstream end calculated from the error 1 calculated in step (a) and the measured downstream distribution at the same point can be continuously reduced. Continuously calculating coefficients and lateral dispersion coefficients with constant directionality and continuously calculating concentration distributions 2 ... downstream concentrations n corresponding to the equations of step (a) and satisfying the equation of step (a), And (c) an error n + 1 between the downstream concentration concentration n + 1 calculated by adjusting the longitudinal dispersion coefficient and the lateral dispersion coefficient with constant directionality and the measured downstream concentration concentration at the same point is inversely different from the error n. Increases the flow rate and streams that have a significant impact on the pollution spread of the stream, including the step of setting the longitudinal and lateral dispersion coefficients as observations to stop the calculation and to calculate the error n when the error is minimized. Disqualification of This paper suggests a method for observing variance coefficients including eclipticity.

Related Concepts, Tracking Procedure, 2D, Pollution Dispersion Coefficient, Lateral Dispersion Coefficient, Specimen Dispersion Factor

Description

Two dimensional dispersion coefficient observation method by combining stream-tube concept and routing procedure

1 is a conceptual diagram of variance coefficient observation through a tracking procedure according to the present invention.

2 is a schematic diagram of a river section to which the dispersion coefficient observation method according to the present invention is applied.

The present invention relates to a method for observing a two-dimensional pollution dispersion coefficient combining a related concept and a tracking procedure. The present invention relates to a longitudinal dispersion coefficient and a lateral dispersion coefficient which are necessary parameters when analyzing the behavior of pollutants introduced into a stream in a two-dimensional manner. It is about how to observe.

Conventionally, as the observation technique for tracking contaminants introduced into the stream in the form of point sources, the most representative method among the observation techniques is the moment method. This method is a method of observing the lateral dispersion coefficient using the principle that the rate of change in the longitudinal secondary moment of the concentration distribution is proportional to the lateral dispersion coefficient. The moment method is a method in which the lateral dispersion coefficient can be obtained by disregarding the longitudinal dispersion when the pollutants are continuously introduced into the stream. However, the moment method has a limitation in that the longitudinal dispersion can be applied when the pollutant inflow conditions dominate. In addition, secondary moments may be distorted due to irregularities in rivers and flows, and this effect has a weakness in that dispersion coefficients are not properly observed.

In addition, the conventional stream-tube concept is a model that can consider the flow and stream irregularities, the stream's sinuosity by representing the flow in the stream as a flow concept.

In addition, the routing procedure used in the prior art has a method of predicting the flood wave in the downstream stage by using the upstream flood wave as input data.

The present invention is to provide a method for observing the dispersion coefficient even in a situation in which the source is momentarily injected while solving the weakness of the moment method that can be applied only in the situation where the source is continuously injected into the stream, the present invention described above The objective is to provide a method for observing dispersion coefficients including flow and stream irregularities that have a significant impact on the spread of pollution by incorporating related concepts into tracking procedures.

In addition, in the present invention, a method of observing a dispersion coefficient by applying the above-described tracking procedure to predict the concentration distribution of the downstream stage by using the concentration distribution of the upstream stage as input data and comparing the predicted concentration distribution with the measured concentration distribution of the downstream stage. The purpose is to present another purpose.

By following such a tracking procedure, the second moment distortion calculation process, which is a weak point of the conventional moment method, can be avoided, so that a more accurate dispersion coefficient can be observed. In addition, following the tracking procedure, the dispersion coefficient is inverted by directly comparing the concentration versus the concentration, so that both the longitudinal and lateral dispersion coefficients can be observed simultaneously.

The present invention to achieve the above object,

(a) Any longitudinal dispersion coefficient, lateral dispersion coefficient and the measured upstream stage concentration distribution set as initial values are used as input data to calculate the concentration distribution 1 of the downstream stage that satisfies a certain equation, and the calculated downstream stage Calculating an error 1 between the concentration distribution 1 of and the concentration distribution of the downstream downstream end measured at the same point;

(b) Longitudinal variance so that the error 2 ... error n between the concentration distribution of the downstream end calculated from the error 1 calculated in step (a) and the measured downstream distribution at the same point can be continuously reduced. Continuously calculating coefficients and lateral dispersion coefficients with constant directionality and continuously calculating concentration distributions 2 ... downstream concentrations n corresponding to the equations of step (a) and satisfying the equation of step (a), And

(c) The error n + 1 between the concentration distribution n + 1 at the downstream end and the measured concentration distribution at the downstream point at the same point calculated by adjusting the longitudinal and lateral dispersion coefficients with constant directionality is inversely compared to the error n. Stops the calculation if it increases, and sets the longitudinal and lateral dispersion coefficients as observations so that the error n at which the error is minimized is measured. It is characterized by providing a method for observing pollution dispersion coefficients.

Hereinafter, with reference to the accompanying drawings with respect to the present invention will be described in detail with respect to the two-dimensional contamination dispersion coefficient observation method combining the concept and the tracking procedure of the present invention.

The present invention proposes a new dispersion coefficient observation formula combining the related concept and the tracking procedure, and observes the dispersion coefficient based on the concentration data obtained from the actual natural river according to the proposed observation procedure.

First, we derive the dispersion coefficient observation formula combining the related concepts and the tracking procedure.

The two-dimensional transfer-dispersion equation introducing the related concept is as follows. In other words,

Where C is the concentration, λ is the time, D _L is the longitudinal dispersion coefficient, ξ is the longitudinal distance, η is the dimensionless nougat flow rate, and S _T is the tube dispersion coefficient.

In Equation 1, S _T has a relationship with the lateral dispersion coefficient as in the following equation.

Where Ψ is the cross-sectional shape coefficient, H is the average depth, U is the average flow rate, Q is the flow rate, and D _T is the lateral dispersion coefficient.

And when the initial function form of the pollutant introduced into the stream is f (ξ, η), the solution of the equation (1) is as follows.

Substituting the concentration distribution of the upstream stage instead of f (ξ, η) and converting the concentration distribution over time at a fixed point, the concentration distribution of the downstream stage is calculated by the following equation.

와

는 상류단 및 하류단 각각의 지점에서 취득한 농도분포의 도심에 해당하는 시간이다.Where C (ξ ₂ , η, λ) is the concentration distribution when the dimensionless nominal flow rate η and time is λ at the downstream ξ ₂ point, and C (ξ ₁ , η, λ) is the upstream end ξ ₁ Concentration distribution when dimensionless nougat flow at point η and time is λ,

Wow

Is the time corresponding to the downtown of the concentration distribution obtained at each of the upstream and downstream ends.

Thus, Equation 4 is an observation equation of the dispersion coefficient proposed in the present invention.

The application procedure of the equation according to the present invention is as follows.

That is, arbitrary longitudinal dispersion coefficients and lateral dispersion coefficients are set to initial values, and the concentration distribution (C (ξ ₁ , η, λ)) of the upstream stage is substituted into Equation 4, and the downstream end concentration distribution (C (ξ ₂ , η, λ)) is calculated and calculated. Here, if the conventional research results are used as the initial values of the longitudinal dispersion coefficient and the lateral dispersion coefficient, the observations of the longitudinal dispersion coefficient and the lateral dispersion coefficient of the present invention do not greatly deviate from the conventional research results, so that the calculation time may be shortened. Can be. In other words, it is preferable that the longitudinal dispersion coefficient be Fischer (1979) and the horizontal dispersion coefficient be the initial value of Elder (1959).

문제를 더 간단히 하기 위해 매개변수 중 a=1로 고정시키면 결정해야 할 매개변수는 b만 남게 되고, 매개변수 b를 2로 가정하면 y= x+2가 되어 직선 A가 되며, 직선 A는 육안으로도 확인할 수 있듯이 측정치의 점들과 많은 차이가 있어 계산치(회귀식)와 측정치 간의 오차는 크다고 할 수 있다.
다음으로, 다시 b를 줄여서 1로 가정하면 y= x+1이 되어 직선 B가 되고, 직선 B는 측정치의 점들과 잘 일치하여 오차가 적다고 할 수 있으며, 다시 b를 줄여 0으로 가정하면 y= x가 되어 직선 C가 되는데 직선 C는 계산치(회귀식)와 측정치 간의 오차가 다시 커지게 되어, 매개변수 b=1일때가 오차가 최소라고 할 수 있다.
따라서, 위와 같은 방법으로 본 발명에서는 우선 종분산계수를 고정시키고 횡분산계수를 조정하여 하류단의 산출 농도분포와 측정 농도분포 간의 오차가 최소가 되는 순간에서의 횡분산계수를 관측치로 설정하고, 다시 설정된 횡분산계수 관측치를 고정하고 종분산계수를 조정하여 하류단의 산출 농도분포와 측정 농도분포 간의 오차가 최소가 되는 순간에서의 종분산계수를 관측치로 설정하게 되는데, 이러한 방법은 축차대입법(iteration)을 이용한 비선형 다중회귀법에서는 통상적인 방법이어서 더 이상의 구체적인 과정은 생략하도록 하겠다.
본 발명에서처럼 회귀식의 방정식이 비선형이 되면 계산은 매우 복잡해지고 이런 비선형 문제를 풀기 위한 방법이 Gauss-Newton방법이고, 이상의 과정을 컴퓨터로 수행하기 위해 프로그램 언어를 통해 직접 알고리즘을 코딩한 프로그램이나 Gauss-Newton방법이 내장된 기존의 Matlab(이하 '프로그램'이라 함.)을 활용하게 된다.
따라서, 본 발명에서 종분산계수와 횡분산계수의 관측치를 컴퓨터에서 설정하는 과정을 살펴보면,
우선, 초기값으로 설정된 임의의 종분산계수와 횡분산계수 및 측정된 상류단의 농도분포가 입력자료로 입력장치에 의해 메인 메모리에 입력되고, 컴퓨터의 중앙처리장치가 상기 입력자료들과 수학식 4가 포함된 메인 메모리 내의 프로그램을 이용해 수학식 4를 만족하는 초기값 하류단의 농도분포1을 산출하고 그 산출된 하류단의 농도분포1과 동일 지점에서의 측정된 하류단의 농도분포 간의 초기값 오차1을 산정하여 저장하고,
다음으로, 중앙처리장치가 Gauss-Newton법이 내장된 메인 메모리 내의 프로그램을 이용하여, 상기에서 산정된 오차1보다 산출된 하류단의 농도분포와 동일 지점에서의 측정된 하류단의 농도분포 간의 오차2...오차n을 계속적으로 감소시킬 수 있도록 종분산계수와 횡분산계수를 일정한 방향성을 가지고 반복적으로 조정하여 그에 대응하고 수학식 4를 만족하는 하류단의 농도분포2...하류단의 농도분포n을 계속적으로 산출하되, 컴퓨터의 중앙처리장치는 오차가 계속적으로 감소하는 방향으로 종분산계수와 횡분산계수를 일정한 간격을 가지면서 자동적으로 반복하여 증가 또는 감소되게 하며,
그 다음으로, 종분산계수와 횡분산계수를 일정한 방향성을 가지고 조정하여 산출된 하류단의 농도분포n+1과 동일 지점에서의 측정된 하류단의 농도분포 간의 오차n+1이 오차n 보다 역으로 증가하면 중앙처리장치는 계산을 중지하고, 오차가 최소가 되는 순간인 오차n이 산정되도록 하는 종분산계수와 횡분산계수를 관측치로 저장하게 되는 것이다. 상기에서 반복되는 계산과정은 통상의 회귀분석에서 사용되는 방법이라 할 것이다.Then, the longitudinal dispersion coefficient and the lateral dispersion coefficient are adjusted so that the calculated concentration distribution of the downstream stage matches the measured concentration distribution of the downstream stage. In addition, the optimum longitudinal dispersion coefficient and the lateral dispersion coefficient are set as observations so that the calculated concentration distribution and the measured concentration distribution are optimally matched.
That is, the longitudinal dispersion coefficient and the lateral dispersion coefficient are determined through conventional regression analysis to minimize the error between the calculated concentration distribution of the downstream end and the concentration distribution of the downstream end measured at the same point. Using the Gauss-Newton method, one of the nonlinear multiple regression methods, the longitudinal and lateral dispersion coefficients are minimized to minimize the mean squared error between the calculated concentration distribution and the measured concentration distribution in the lower width at the downstream ξ ₂ point. It is preferable to adjust by iteration, and at this time, the instantaneous longitudinal dispersion coefficient and the lateral dispersion coefficient are set as observations when the average value of the error squares has a minimum value.
Here, the Gauss-Newton method, which is one of the nonlinear multiple regression methods used for determining the 'minimum' from the minimum value of the mean square of the error square (hereinafter referred to as 'error'), is similar to the linear regression method. Explain the principles of linear regression and present common ways of judging 'minimum'.
First, we want to match the linear equation y = ax + b well with some measurement (points in Table 2), as shown in the graph below, where the parameters are the slope a and the intercept b. Longitudinal and lateral dispersion coefficients.)

To make the problem simpler, if you fix a = 1 of the parameters, only b remains to be determined, assuming that parameter b is 2, y = x + 2 becomes straight line A, and the straight line A becomes naked As can be seen, there are many differences between the measured values and the error between the calculated value and the measured value.
Next, assuming that b is reduced to 1 again, y = x + 1 to make a straight line B, and the straight line B agrees well with the points of the measured value, so that the error is small. = x becomes a straight line C. The straight line C increases the error between the calculated value (regression equation) and the measured value again. When the parameter b = 1, the error is the minimum.
Therefore, in the present invention as described above, first, the longitudinal dispersion coefficient is fixed and the horizontal dispersion coefficient is adjusted to set the lateral dispersion coefficient at the instant when the error between the calculated concentration distribution and the measured concentration distribution at the downstream end becomes the minimum, and By resetting the observed lateral dispersion coefficient observation and adjusting the longitudinal dispersion coefficient, the longitudinal dispersion coefficient at the moment when the error between the calculated concentration distribution and the measured concentration distribution at the downstream end becomes minimal is determined. In the nonlinear multiple regression method using iteration, it is a conventional method, and further detailed steps will be omitted.
When the equation of the regression equation becomes nonlinear as in the present invention, the calculation is very complicated and the method for solving this nonlinear problem is the Gauss-Newton method, and a program or a Gauss coded algorithm directly through a programming language to perform the above process by a computer. -Use existing Matlab (hereinafter referred to as 'program') with Newton method.
Therefore, the process of setting the observation values of the longitudinal dispersion coefficient and the lateral dispersion coefficient in the computer in the present invention,
First, any longitudinal dispersion coefficient, lateral dispersion coefficient, and measured upstream concentration distribution set as initial values are input to the main memory by the input device as input data, and the central processing unit of the computer is Using the program in the main memory including 4, the concentration distribution 1 of the downstream downstream end satisfying Equation 4 is calculated and the initial value between the calculated downstream concentration distribution 1 and the measured downstream end distribution at the same point. Calculate and store the value error 1,
Next, the central processing unit uses a program in the main memory incorporating the Gauss-Newton method, and the error between the concentration distribution of the downstream stage and the measured downstream concentration distribution at the same point calculated from the error 1 calculated above. 2 ... To continuously reduce the error n, the longitudinal dispersion factor and the lateral dispersion coefficient are repeatedly adjusted with a constant directionality, and the concentration distribution of the downstream stage satisfying Equation 4 is satisfied. Concentration distribution n is continuously calculated, but the central processing unit of the computer automatically increases or decreases the longitudinal dispersion coefficient and the horizontal dispersion coefficient at regular intervals in a direction of decreasing errors continuously.
Next, the error n + 1 between the downstream concentration concentration n + 1 calculated by adjusting the longitudinal dispersion factor and the lateral dispersion coefficient with constant directionality and the measured downstream concentration concentration at the same point is inversely different from the error n. If it increases, the central processing unit stops the calculation and stores the longitudinal and lateral dispersion coefficients as observations so that the error n at which the error becomes the minimum is calculated. The calculation process repeated above will be referred to as a method used in a conventional regression analysis.

Conceptually, this is illustrated in FIG. 1.

The following describes an example of calculating the dispersion coefficient by applying the equation presented in the present invention.

In the present invention, the species dispersion and the lateral dispersion coefficients were observed by applying to natural rivers in order to verify and examine the above-described techniques. Applied rivers are the only two-dimensional tracer experiments in Korea, where the concentration data exist, Seomgang, Cheongmicheon, and Hongcheongang, all seven sections were applied, and the schematic diagram of the applied streams and sections is shown in FIG.

Table 1 summarizes the dispersion coefficients observed through the observation method developed in the present invention and the existing moment method.

Application section Prior art (moment method) The present invention Dimensionless lateral dispersion coefficient (D _T / HU _* ) Dimensionless lateral dispersion coefficient (D _T / HU _* ) Dimensional Dispersion Coefficient (D _L / HU _* ) S-Expt 1 0.45 0.52 26.9 S-Expt 2 0.76 0.79 22.7 S-Expt 3 0.27 0.36 25.4 C-Expt 1 0.24 0.69 31.5 H-Expt 1 0.47 0.88 26.2 H-Expt 2 0.24 0.87 20.9 H-Expt 3 0.33 0.41 13.6

In the observation results of the lateral dispersion coefficient in Table 1, the large values are found in the S-Expt 2 which is the intersection of the curves and the H-Expt 1 which is the sharp curve. On the other hand, S-Expt 3 composed of straight sections is smaller than other experimental sections. In the case of severe curvature, the unequal main flow distribution and the secondary flow increase the lateral dispersion coefficient because of the effect of increasing the lateral diffusion in the intermediate region.

In addition, since the generation and disappearance of the secondary flow in the alternating bends is more active than the single bends, the lateral dispersion coefficient in S-Expt 2 is large due to its influence. The observation method developed in the present invention reflects this effect well. On the other hand, the moment method, which is a conventional technique that cannot take into account river irregularities and velocity fields, produces small values.

In addition, although the longitudinal dispersion coefficient cannot be calculated by the moment method, the observation method in the present invention can calculate both the longitudinal dispersion coefficient and the lateral dispersion coefficient as shown in Table 1 above.

As described above, the two-dimensional pollution dispersion coefficient observation method combining the related concept and the tracking procedure of the present invention performs an observation of an appropriate dispersion coefficient when a contaminant is introduced into a stream in a point source state, thereby performing two observations in the intermediate region. It is effective to accurately grasp the diffusion phenomenon of pollutants with dimensional behavior.

In addition, the behavior analysis of the pollutants through the present invention has the effect of providing the basic information, such as the operation of the intake station, water quality prediction and alarm system development.

Claims (2)

(a) Any longitudinal dispersion coefficient, lateral dispersion coefficient, and measured upstream concentration distribution set as initial values are input to the main memory by the input device as input data, and the central processing unit is inputted to the input data and Using the program in the main memory containing the equation, the concentration distribution 1 of the downstream stage satisfying the following equation is calculated and the error 1 between the calculated downstream concentration distribution 1 and the measured downstream concentration distribution at the same point is calculated. Calculating and storing;

Where C (ξ ₂ , η, λ) is the nominal nominal flow rate η at the downstream ξ ₂ point and C (ξ ₁ , η, λ) is the upstream ξ Concentration distribution when dimensionless nominal flow rate η and time is λ at point ₁ , U is mean velocity, λ is time, D _L is longitudinal dispersion coefficient, ξ is longitudinal distance, η is dimensionless nougat flow rate, S _T Is the related variance coefficient,

Wow

Is the time corresponding to the city center of the concentration distribution obtained at each of the upstream and downstream ends.) (b) The central processing unit uses a program in the main memory incorporating the Gauss-Newton method, and at the same point as the concentration distribution at the downstream end calculated from the error 1 calculated in step (a). In order to continuously reduce the error 2 ... error n between the measured downstream concentration concentrations, the longitudinal dispersion coefficient and the lateral dispersion coefficient are repeatedly adjusted with constant directionality, and the equation of step (a) is adjusted. Continuously calculating the concentration distribution 2 at the downstream end, and the concentration distribution n at the downstream end, and (c) The error n + 1 between the concentration distribution n + 1 at the downstream end and the measured concentration distribution at the downstream point at the same point calculated by adjusting the longitudinal and lateral dispersion coefficients with constant directionality is inversely compared to the error n. When the central processing unit increases, the CPU stops the calculation and stores the longitudinal and lateral dispersion coefficients as observations so that the error n, which is the moment when the error is minimized, is stored as an observation. 2D pollution dispersion coefficient observation method combined with. delete

Images