Non-linear curved surface fitting method of water level flow relation based on riverway non-uniform flow water surface curve solution

Abstract

The invention belongs to the field of water conservancy and hydropower engineering, discloses a non-linear curved surface fitting method for a water level and flow relation based on river channel non-uniform flow water surface curve solution, and solves the problems that when a tested river reach is influenced by a variable backwater factor, a water level and flow relation alignment scheme adopted in the prior art is poor in practicability and high in accuracy. And the requirements of high precision and high adaptability of water level flow relation alignment are difficult to meet. According to the method, section water level and flow data are collected, theoretical formula derivation is carried out, and on the basis that a targeted water level and flow relation function form is determined, a water level and flow relation function analytical expression is solved through non-linear curved surface function fitting. The method has a strong hydraulic theoretical basis, allows the water level and the flow to be distributed in multiple forms, and can accurately describe nonlinear and diversified complex structures between the water level and the flow.

Description

Technical Field

[0001] The invention belongs to the field of water conservancy and hydropower engineering, and in particular relates to a nonlinear surface fitting method for a water level-discharge relationship based on solving a water surface curve of a non-uniform flow in a river channel. Background Art

[0002] Line determination is the analytical work of establishing the relationship line between two or more measured hydrological element values. In the compilation of flow data, the most critical part is to develop the water level flow relationship curve. The water level flow relationship is the correlation established between the measured flow of a section in a river channel and its corresponding water level. It is of great significance for scientific research, hydropower and water conservancy project design, water resources management, flood control and drought relief, etc.

[0003] When the tested river section is affected by the variable backwater factor, the relationship between the water level and the flow is not a single-valued function relationship, and the relationship points between the two are scattered and difficult to accurately determine the line. At present, when affected by variable backwater, the commonly used methods for determining the line of the water level and flow relationship are mainly the drop index method and the continuous time series method. Among them, the solution of the drop index needs to be completed by trial and error, the calculation is cumbersome and time-consuming, and this method is affected by factors such as the representativeness of the drop and the complexity of the water surface line, and its application has certain limitations. The principle of the continuous time series method is based on the continuity of water flow, requires many and accurate measuring points, and has time limitations. This method requires the ability to control the turning point of the flow relationship change. If the number of measurements is not enough to cover the turning point, it cannot accurately reflect the actual water level and flow relationship, especially when the flow changes greatly.

[0004] Therefore, when specific conditions are not met, the drop index method and the continuous time series method are of poor practicality and cannot meet the requirements of high precision and strong adaptability in determining the relationship between water level and flow. Summary of the invention

[0005] The technical problem to be solved by the present invention is to propose a nonlinear surface fitting method for the water level-flow relationship based on the solution of the water surface curve of the non-uniform flow in the river channel, so as to solve the problem that when the test river section is affected by the variable backwater factor, the water level-flow relationship alignment scheme used in the prior art has poor practicality and is difficult to meet the high-precision and strong adaptability requirements of the water level-flow relationship alignment.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] A nonlinear surface fitting method for the water level-discharge relationship based on the solution of the water surface curve of the non-uniform flow in the river channel comprises the following steps:

[0008] S1. Collect the measured water level, flow rate, and section data of the flow test section and the measured water level and section data of the downstream calculation section;

[0009] S2. According to the quantitative calculation method of the water surface curve of the non-uniform flow in the river channel, the hydraulic theory formula is derived, the targeted nonlinear function is constructed, and the function parameter form is estimated;

[0010] S3, according to the constructed targeted nonlinear function and parameter form, the measured water level and flow data in step S1 are iteratively fitted using a nonlinear surface function to solve the nonlinear function of the water level-flow relationship and obtain an analytical expression of the nonlinear function of the water level-flow relationship;

[0011] S4. Based on the nonlinear function analytical expression of the water level-flow relationship, calculate the goodness of fit and deduce the water level-flow relationship curve and its random uncertainty.

[0012] Furthermore, in step S2, the targeted nonlinear function constructed is:

[0013] Q=F(Z 上 , Z 下 );

[0014] Among them, Z 上 =Z 上0 +h 上 , Z 下 =Z 下0 +h 下 , Q is the flow rate of the test section, Z 上 is the water level of the test section, Z 上0 is the depth elevation of the test section, h 上 To control the water depth of the test section, Z 下 Calculate the water level of the downstream section, Z 下0 h is the elevation of the downstream section, 下 Control the water depth for the downstream calculation section.

[0015] Furthermore, in step S4, the goodness of fit R 2 The calculation is as follows:

[0016]

[0017] in, Solve for the flow rate fit value, Solve for the average value of the measured flow rate;

[0018] The random uncertainty X' Q =2S e , where S e is the standard deviation of the measured points.

[0019] Furthermore, the method further comprises the steps of:

[0020] S5, loop through steps S3-S4, and when the convergence degree, goodness of fit, and uncertainty coefficient of the water level-flow relationship curve meet the requirements, the obtained Q=F(Z 上 , Z 下 ) is the final fitting result.

[0021] The beneficial effects of the present invention are:

[0022] (1) The present invention adopts a targeting function derived from a hydraulic theory formula. With the help of the strong nonlinear expression ability of the nonlinear surface fitting function, it can be expressed with higher precision through the measured points, avoiding the difficulty in selecting the targeting function. At the same time, it allows the relationship between water level and flow to present a variety of distribution forms. The smooth characteristics of the nonlinear surface function itself can better avoid the mutation problem, making the water level-flow relationship curve smooth and continuous.

[0023] (2) Compared with the conventional water level-flow relationship curve alignment method, the present invention adopts computer fitting solution capability, has fast calculation speed and accurate results, can update the water level-flow relationship of measured data in real time, and provide a clear analytical expression of the water level-flow relationship curve. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 is a flow chart of a nonlinear surface fitting method in an embodiment of the present invention;

[0025] Figure 2 This is the current measured water level and flow relationship diagram of the Xiluodu hydrological station from 2020 to 2023;

[0026] Figure 3 It is a nonlinear surface fitting graph obtained by performing nonlinear surface fitting on the water level-flow relationship of the Xiluodu hydrological station from 2020 to 2023 using the solution of the present invention. DETAILED DESCRIPTION

[0027] Nonlinear surface fitting can better adapt to and process complex data patterns by using nonlinear function forms and complex model structures, providing higher flexibility, being able to fit data points of nonlinear relationships more accurately, and providing higher fitting effects. Therefore, the present invention aims to provide a nonlinear surface fitting method for the water level-discharge relationship based on the solution of the water surface curve of the non-uniform flow in the river channel, using a target function derived from a hydraulic theory formula, and with the help of the strong nonlinear expression ability of the nonlinear surface fitting function, it can be expressed with higher precision through the measured points, avoiding the difficulty in selecting the target function, and at the same time, the smooth characteristics of the nonlinear surface fitting function itself can better avoid local mutation problems, further improving the reliability and practicality of the method. This can solve the problem that when the test river section is affected by the variable backwater factor, the water level-discharge relationship alignment scheme used in the prior art has poor practicality and is difficult to meet the high precision and strong adaptability requirements of the water level-discharge relationship alignment.

[0028] Example

[0029] Taking the nonlinear surface fitting of the water level-discharge relationship of the Xiluodu hydrological station as an example, the nonlinear surface fitting method for the water level-discharge relationship based on the solution of the water surface curve of the non-uniform flow in the river provided in this embodiment is shown in Figure 1 , which comprises the following steps:

[0030] S1. Collect the measured water level, flow rate, and section data of the flow test section and the measured water level and section data of the downstream calculation section;

[0031] In this step, the measured water level, flow and cross-section data of the section are selected from the monitoring section data of the Xiluodu Hydropower Station dedicated hydrological station and its downstream variable backwater from 2020 to 2023, both of which are trapezoidal cross-section shapes.

[0032] Xiluodu Hydrological Station is the outflow control station of Xiluodu Hydropower Station, with a catchment area of ​​454,400km 2 The test section of the station is affected by the backwater support of the downstream Xiangjiaba Hydropower Station reservoir, and the water level and flow relationship is complex. For the current measured water level and flow relationship diagram of the Xiluodu Hydrological Station from 2020 to 2023, please refer to Figure 2 ,It can be seen that after being affected by backwater, the water level-flow relationship points are scattered and it is difficult to establish a relationship.

[0033] S2. According to the quantitative calculation method of the water surface curve of the non-uniform flow in the river channel, the hydraulic theory formula is derived, the targeted nonlinear function is constructed, and the function parameter form is estimated;

[0034] In this step, according to the measured cross-sectional data collected in step S1, the hydraulic theory formula is derived according to the quantitative calculation method of the water surface curve of the river non-uniform flow, and the targeted nonlinear function Q = F (Z 上 , Z下 ), and estimate the function parameter form. Among them, Z 上 =Z 上0 +h 上 , Z 下 =Z 下0 +h 下 , Q is the flow rate of the test section, Z is the water level of the test section, Z 上0 is the depth elevation of the test section, h 上 To control the water depth of the test section, Z 下 Calculate the water level of the downstream section, Z 下0 h is the elevation of the downstream section, 下 Control the water depth for the downstream calculation section.

[0035] According to the energy equation of non-uniform flow in open channel, the hydraulic theory formula is derived. The specific process is as follows:

[0036] The basic formula of the energy equation for non-uniform flow in an open channel is:

[0037]

[0038] In formula (1): h i Control water depth for the section; v i is the cross-sectional flow velocity; g is the gravitational acceleration; Δl is the length of the flow segment; is the average hydraulic gradient of the flow section.

[0039] According to Xie Cai's formula:

[0040] In formula (2): v is the average flow velocity of the section (m / s); R is the hydraulic radius (m); J is the hydraulic slope of the flow section.

[0041] From formula (1) and formula (2), we can get:

[0042]

[0043] Combining formulas (1) to (5), we can derive the expression of flow rate Q:

[0044]

[0045] In formula (6), h1 is the controlled water depth of the Xiluodu special hydrological station section; h2 is the controlled water depth of the monitoring section at the downstream variable backwater; i is the bottom slope; g is the gravitational acceleration; and A is the cross-sectional area of ​​the water flow.

[0046] According to the characteristics of the trapezoidal water-passing section, there are:

[0047] A=(b+m*h)*h (7)

[0048]

[0049] In formulas (7) and (8), m is the slope coefficient; h is the controlled water depth of the section; and b is the slope coefficient.

[0050] The relationship between water depth and water level in the section:

[0051] Z 上 =Z 上0 +h1 (9)

[0052] Z 下 =Z 下0 +h2 (10)

[0053] In formula (9) and (10): Z 上 is the water level of the test section, Z 上0 To test the depth elevation of the section, Z 下 Calculate the water level of the downstream section, Z 下0 Calculate the elevation of the cross-section deep well for the downstream.

[0054] For the determined test section and downstream calculation section, the slope coefficient, side slope coefficient, bottom slope and other related parameters are all constants.

[0055] Combining formulas (6) to (10), we can simplify and derive the flow function expression Q = F (Z 上 , Z 下 ), which indicates that the relationship between variables is more complicated and does not satisfy the superposition principle and proportional relationship of linear functions.

[0056] S3, according to the constructed targeted nonlinear function and parameter form, the measured water level and flow data in step S1 are iteratively fitted using a nonlinear surface function to solve the nonlinear function of the water level-flow relationship and obtain an analytical expression of the nonlinear function of the water level-flow relationship;

[0057] In this step, according to the target function and parameter form derived in step S2, the measured water level and flow data collected in step S1 are iteratively fitted using a nonlinear surface function to solve the nonlinear function of the water level-flow relationship, and obtain Q = F (Z 上 , Z 下 ) is an analytical expression for .

[0058] S4. Calculate the goodness of fit based on the nonlinear function analytical expression of the water level-discharge relationship, and deduce the water level-discharge relationship curve and its random uncertainty;

[0059] In this step, the goodness of fit is calculated in, Solve for the flow rate fit value, Solve for the average value of the measured flow. Calculate the random uncertainty X' of the water level flow relationship curveQ =2S e , where S e is the standard deviation of the measured points.

[0060] By looping through the above steps S3-S4, when the iterative fitting converges, the goodness of fit, and the uncertainty coefficient of the water level-discharge relationship curve meet the requirements, the obtained Q=F(Z 上 , Z 下 ) is the analytical expression we are looking for.

[0061] The above scheme was used to fit the water level-flow relationship of the Xiluodu Hydrological Station from 2020 to 2023, and the fitting results were statistically analyzed in terms of goodness of fit, mean absolute error, mean relative error, and random uncertainty. The statistical results are shown in Table 1 below.

[0062] Table 1 Statistical results of fitting results

[0063]

[0064] It can be seen that after iteration and calibration of model parameters, the average goodness of fit of the water level of the Xiluodu hydrological station, the water level at the downstream variable backwater point and the flow of the test section of the Xiluodu hydrological station reached 0.98918, and the average relative error between the measured points and the fitting values ​​was only 5.00%, indicating good fitting accuracy.

[0065] Figure 3 A nonlinear surface fitting diagram is given by using the scheme of the present invention to perform nonlinear surface fitting on the water level-flow relationship of the Xiluodu Hydrological Station from 2020 to 2023. In the figure, the X-axis is the water level of the Xiluodu Hydrological Station, the Y-axis is the water level at the downstream variable backwater, the Z-axis is the flow of the Xiluodu Hydrological Station, the black dots are the measured flow values, and the surface is the fitted water level-flow relationship curve. Figure 3 It can be seen that this scheme can more accurately describe the nonlinear and multivariate complex structure between water level and flow.

[0066] In summary, the present invention provides a nonlinear surface fitting method for the water level-flow relationship based on the solution of the water surface curve of the non-uniform flow in the river channel, collects cross-sectional water level and flow data, derives through theoretical formulas, and uses nonlinear surface function fitting to solve the analytical expression of the water level-flow relationship function on the basis of determining the form of the targeted water level-flow relationship function. The present invention has a strong hydraulic theoretical foundation, allows the water level and flow to have a multivariate distribution, and can accurately describe the nonlinear and multivariate complex structure between the water level and flow.

[0067] Finally, it should be noted that the above embodiments are only preferred implementations and are not intended to limit the present invention. It should be pointed out that for those skilled in the art, several modifications, equivalent replacements, improvements, etc. can be made without departing from the scope of the present invention and the scope of protection of the claims, and all of these should be included in the protection scope of the present invention.

Claims

1. A nonlinear surface fitting method for the relationship between water level and flow rate based on the solution of water surface curve of non-uniform flow in river channel, characterized in that: The following steps are involved: S1. Collect the measured water level, flow rate, and section data of the flow test section and the measured water level and section data of the downstream calculation section; S2. According to the quantitative calculation method of the water surface curve of the non-uniform flow in the river channel, the hydraulic theory formula is derived, the targeted nonlinear function is constructed, and the function parameter form is estimated; S3, according to the constructed targeted nonlinear function and parameter form, the measured water level and flow data in step S1 are iteratively fitted using a nonlinear surface function to solve the nonlinear function of the water level-flow relationship and obtain an analytical expression of the nonlinear function of the water level-flow relationship; S4. Based on the nonlinear function analytical expression of the water level-flow relationship, calculate the goodness of fit and deduce the water level-flow relationship curve and its random uncertainty.

2. A nonlinear surface fitting method for the relationship between water level and flow rate based on the solution of the water surface curve of the non-uniform flow in the river as claimed in claim 1, characterized in that: In step S2, the targeted nonlinear function constructed is: Q=F(Z 上 ,Z 下 ); Among them, Z 上 =Z 上0 +h 上 , Z 下 =Z 下0 +h 下 , Q is the flow rate of the test section, Z 上 is the water level of the test section, Z 上0 is the depth elevation of the test section, h 上 To control the water depth of the test section, Z 下 Calculate the water level of the downstream section, Z 下0 h is the elevation of the downstream section, 下 Control the water depth for the downstream calculation section.

3. A nonlinear surface fitting method for the relationship between water level and flow rate based on the solution of the water surface curve of the non-uniform flow in the river as claimed in claim 2, characterized in that: In step S4, the goodness of fit R 2 The calculation is as follows: in, Solve for the flow rate fit value, Solve for the average value of the measured flow rate; The random uncertainty X' Q =2S e , where S e is the standard deviation of the measured points.

4. A nonlinear surface fitting method for the relationship between water level and flow rate based on the solution of the water surface curve of the non-uniform flow in the river as claimed in claim 3, characterized in that: The method further comprises the steps of: S5, loop through steps S3-S4, and when the convergence degree, goodness of fit, and uncertainty coefficient of the water level-flow relationship curve meet the requirements, the obtained Q=F(Z 上 , Z 下 ) is the final fitting result.

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