A sounding correction method based on an adaptive river cross-section model

Abstract

The present invention provides a sounding correction method based on an adaptive river cross-section model. By taking the derivative of the mathematical function model, the slope at any position of the cross-section can be deduced. According to the mathematical geometric model of the beam angle effect, the water depth correction of the measurement beam angle effect of the river cross-section is realized, and a data set for processing the cross-section water depth data is obtained. Finally, tide level correction is performed through the tide level data set to obtain a data set of cross-section results. Practice has proved that this method establishes a precise mathematical model to simulate and express the river cross-section, truly restores the river morphology according to the law of the beam angle effect of the sounding instrument, improves the sounding accuracy to a certain extent, has good economic and social benefits, and is suitable for popularization and use.

Description

Technical Field

[0001] The present invention relates to the technical field of bathymetric survey applications in marine surveying and mapping, and particularly to a sounding correction method based on an adaptive river cross-section model. Background Art

[0002] Work such as the analysis of the storage capacity curve and sediment deposition analysis of large reservoirs mainly relies on the river cross-section. Currently, single-beam or multi-beam measurement methods are generally used in the field to collect river cross-section data. However, there are many difficulties in precise sounding in steep and deep rivers, and the beam angle effect is a rather difficult problem. Since the sounding beam emitted by the sounder has a beam opening angle, the greater the water depth of the river and the steeper the slope of the water bottom, the lower the absolute sounding accuracy. By analyzing the principle of the beam angle effect, it is found that the comprehensive slope information and water depth information of the water bottom are the key factors affecting the beam angle effect. Based on the above analysis of the beam angle effect, through the analysis and verification of measured data, a method of using ideas such as piecewise functions and high-order polynomial fitting to adaptively simulate the cross-section shape to obtain the cross-section slope is proposed to solve the problem of beam angle effect correction. Summary of the Invention

[0003] The purpose of the present invention is to provide a sounding correction method based on an adaptive river cross-section model to address the sounding impact caused by the beam angle effect in view of the deficiencies of the above-mentioned prior art.

[0004] To achieve the above purpose, the present invention adopts the following technical solutions:

[0005] The present invention provides a sounding correction method based on an adaptive river cross-section model, including the following steps:

[0006] S1. Use the strongest echo of the instrument-measured water depth echo data to proofread the water depth data, perform SVP gradient correction for the thermocline, tide level correction, and calculate the starting distance of the cross-section to obtain the preprocessed set D of cross-section water depth data S , and obtain the preprocessed set D of cross-section results n ;

[0007] S2. Establish a polynomial regression mathematical model for the preprocessed set D of cross-section results n ;

[0008] S3. According to the difference between the polynomial regression mathematical model and the actual river cross-section shape, perform adaptive interval fitting on the river cross-section to obtain an adaptive mathematical model of the river cross-section;

[0009] S4. Take the derivative of the adaptive mathematical model of the river cross-section to derive the slope at any position of the cross-section;

[0010] S5. Correct the self - adaptive mathematical model of the river channel cross - section according to the established beam - angle effect to achieve the correction of the water depth measured by the depth sounder of the river channel cross - section, and obtain the processed data set D of the cross - section water depth S′ ;

[0011] S6. Perform tide level correction through the tide level data set C(L i ) to obtain the result data set D of the cross - section N .

[0012] Furthermore, in the above - mentioned S1, the pre - processed result data set D of the cross - section n is:

[0013] D n =[(L1, H1), (L2, H2), L(L n , H n )];

[0014] wherein, L n is the starting distance of the n - th river channel cross - section point; H n is the river bottom elevation of the n - th river channel cross - section point;

[0015] The pre - processed data set D of the cross - section water depth S is:

[0016] D S =[(L1, S1), (L2, S2), L(L n , S n )];

[0017] wherein, S n is the water depth data value of the n - th river channel cross - section point.

[0018] Furthermore, in the above - mentioned S2, assuming that there is a linear relationship between H n and L i , i , then the mathematical model is:

[0019]

[0020] wherein, L i is the starting distance of the i - th river channel cross - section point; H i is the river bottom elevation of the i - th river channel cross - section point; b0, b1, b2, b3,... b k-1 , b k are the fitting coefficients of the mathematical model; L i , is the unary k - th order polynomial of the mathematical model;

[0021] Then the polynomial regression mathematical model

[0022]

[0023] wherein, is the regression estimated value of H i ; a0, a1, a2, a3, … a k-1 , a k are the regression estimated values of the model b0, b1, b2, b3, … b k-1 , b k ;

[0024] Let

[0025]

[0026] wherein, ε is the sum of squared residuals;

[0027] Make ε take partial derivatives with respect to a0, a1, … a k respectively, and make each partial derivative value be 0:

[0028]

[0029] Use Cramer's rule to solve the values of each coefficient:

[0030]

[0031]

[0032] wherein, m is the m-th column of the coefficient determinant P.

[0033] Furthermore, the specific value of 3 is:

[0034] The k-th order fitting expression of the river channel cross-section adaptive mathematical model G(L i ) in the interval [L1, L n is:

[0035]

[0036] wherein, is the polynomial fitting coefficient of the piecewise fitting equation G(L i ), j is the adaptive j-segment mathematical model, is the value in the interval [L1, L n , and

[0037]

[0038] Further, in S4, the derivative of the adaptive mathematical model of the river channel cross-section is taken to derive the slope G′(L at any position of the river channel cross-section under the sounding measurement i ):

[0039]

[0040] Then the slope P(L at any position of the river channel cross-section i ):

[0041] P(L i ) = arctanG′(L i ).

[0042] Further, in S5, when in the adaptive mathematical model of the river channel cross-section, the slope P(L of the cross-section i ) is not greater than the true slope P(L of the terrain i ) 真 , the established correction model is:

[0043]

[0044] The processed set D of cross-section water depth data obtained S′ :

[0045] D S′ = [(L1, s(L1)), (L2, s(L2)), … (L n , s(L n ))].

[0046] Further, in S6, the tide level data set C(L i ) is:

[0047] C(L i ) = [(L1, C1), (L2, C2), … (L n , C n )];

[0048] where C1, C2, C n are the tide levels at L1, L2, L n respectively;

[0049] Then H′ i = C i - s(L i ), and H′ i is the final river bottom elevation;

[0050] The final cross-section data set D after correction is obtained N :

[0051] D N = [(L1, H′1), (L2, H′2), … (Ln ,H′ n )]。

[0052] The beneficial effects of the present invention are as follows: By performing water temperature thermocline correction, starting distance calculation, and tide level correction on the calibrated water depth values, a preprocessed set of cross-section results and a preprocessed set of cross-section water depth data are obtained. For the preprocessed set of cross-section results, a polynomial regression mathematical model is established. According to the difference between the above mathematical model and the actual river channel morphology, the river channel cross-section is adaptively fitted in intervals to obtain an adaptive mathematical model of the river channel cross-section. By taking the derivative of this mathematical function model, the slope at any position of the cross-section can be deduced. According to the mathematical geometric model of the beam angle effect, the water depth correction of the single-beam measurement beam angle effect of the river channel cross-section is realized to obtain a processed set of cross-section water depth data. Finally, tide level correction is performed through the tide level data set to obtain a data set of cross-section results.

[0053] This method uses mathematical models such as piecewise functions and polynomial fitting to simulate and represent the river channel cross-section. According to the law of the beam angle effect of the sounding instrument, it more realistically restores the river channel morphology, improves the sounding accuracy to a certain extent, has good economic and social benefits, and is suitable for popularization and use. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a schematic flow chart of a sounding correction method based on an adaptive river channel cross-section model;

[0055] Figure 2 is a diagram of the overall polynomial fitting mathematical model of the cross-section;

[0056] Figure 3 is one of the diagrams of the adaptive interval fitting mathematical model of the cross-section;

[0057] Figure 4 is the second diagram of the adaptive interval fitting mathematical model of the cross-section;

[0058] Figure 5 is the third diagram of the adaptive interval fitting mathematical model of the cross-section;

[0059] Figure 6 is a simulation diagram of sounding by the sounding instrument;

[0060] Figure 7 The calibration data before correction in the example is the data before the impoundment of a certain reservoir;

[0061] Figure 8 The calibration data after correction in the example is the data before the impoundment of a certain reservoir. DETAILED DESCRIPTION OF THE INVENTION

[0062] To make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0063] Please refer to Figure 1 , a sounding correction method based on an adaptive river cross-section model, comprising the following steps:

[0064] S1. Use the strongest echo of the instrument-measured water depth echo data to proofread the water depth data, perform SVP gradient correction for the thermocline, tide level correction and calculation of the starting distance of the cross-section, and preprocess the cross-section water depth data set D S , to obtain the preprocessed cross-section result set D n ;

[0065] S2. Establish a polynomial regression mathematical model for the preprocessed cross-section result set D n ;

[0066] S3. According to the difference between the polynomial regression mathematical model and the actual river channel shape, perform adaptive interval fitting on the river channel cross-section to obtain an adaptive mathematical model of the river channel cross-section;

[0067] S4. Take the derivative of the adaptive mathematical model of the river channel cross-section to derive the slope at any position of the cross-section;

[0068] S5. Correct the adaptive mathematical model of the river channel cross-section according to the established beam angle effect to realize the sounding correction of the water depth measured by the sounding instrument on the river channel cross-section, and obtain the processed cross-section water depth data set D S′ ;

[0069] S6. Perform tide level correction through the tide level data set C(L i ), to obtain the cross-section result data set D N .

[0070] In the above S1, the preprocessed cross-section result set D n is:

[0071] D n =[(L1, H1), (L2, H2), L(L n , H n )];

[0072] wherein, L n is the starting distance of the nth river channel cross-section point; H n is the river bottom elevation of the nth river channel cross-section point;

[0073] The preprocessed cross-section water depth data set D S is:

[0074] DS = [(L1, S1), (L2, S2), L(L n , S n )];

[0075] Among them, S n is the water depth data value of the nth river cross-section point.

[0076] The preprocessing set of the No. 01 cross-section data is shown in Table 1

[0077] Table 1 Preprocessing set of the No. 01 cross-section

[0078]

[0079]

[0080] Establishment of polynomial regression mathematical model:

[0081] In the said S2, assuming that there is a linear relationship between H n in the cross-section result preprocessing set D i and L i ,

[0082]

[0083] where L i is the starting distance of the ith river cross-section point; H i is the river bottom elevation of the ith river cross-section point; b0, b1, b2, b3,... b k-1 , b k are the fitting coefficients of the mathematical model; L i , is the unary k-order polynomial of the mathematical model;

[0084] Then the said polynomial regression mathematical model

[0085]

[0086] where, is the regression estimated value of H i ; a0, a1, a2, a3,... a k-1 , a k are the regression estimated values of the model b0, b1, b2, b3,... b k-1 , b k ;

[0087] Let

[0088]

[0089] Among them, ε is the sum of squared residuals;

[0090] Make ε take partial derivatives with respect to a0, a1, … a k Find the partial derivatives and set each partial derivative value to 0:

[0091]

[0092]

[0093] Use Cramer's rule to solve the values of each coefficient:

[0094]

[0095]

[0096]

[0097] Among them, m is the m-th column of the coefficient determinant P.

[0098] The 5th-order polynomial fitting mathematical model of the overall cross-section data set is shown in Figure 2 .

[0099] The specific value of 3 is as follows:

[0100] The adaptive mathematical model G(L i ) of the river channel cross-section within the interval [L1, L n has a k-th order fitting expression as:

[0101]

[0102] Among them, is the polynomial fitting coefficient of the piecewise fitting equation G(L i ), j is the adaptive j-segment mathematical model,

[0103] is the value within the interval [L1, L n , and

[0104]

[0105] Perform 5th-order polynomial 3-segment adaptive fitting on the cross-section data set, and the fitting results are as follows:

[0106]

[0107]

[0108]

[0109]

[0110] The fitting mathematical model for the cross-section adaptive interval [-186, -146.7] is shown in Figure 3 , and the fitting mathematical model for the cross-section adaptive interval [-146.3, 103.2] is shown in Figure 4 , and the fitting mathematical model for the cross-section adaptive interval [113.6, 386.8] is shown in Figure 5 .

[0111] In the above-mentioned S4, the derivative of the cross-section adaptive mathematical model of the river channel is calculated to derive the slope G′(L at any position of the river channel cross-section under the sounding measurement i ):

[0112]

[0113] Then, the derivative of the cross-section data set adaptive mathematical model is as follows:

[0114]

[0115] Then the slope P(L at any position of the river channel cross-section i ):

[0116] P(L i ) = arctanG′(L i ).

[0117] In the above-mentioned S5, when in the cross-section adaptive mathematical model of the river channel, the slope P(L of the cross-section i ) is not greater than the true slope P(L of the terrain i ) 真 , as shown in Figure 6 , the established correction model is:

[0118]

[0119] The processed cross-section water depth data set D S′ :

[0120] D S′ = [(L1, s(L1)), (L2, s(L2)), … (L n , s(L n ))].

[0121] In the above-mentioned S6, the tidal level data set C(L i ) is:

[0122] C(L i ) = [(L1, C1), (L2, C2), … (L n, C n )];

[0123] Among them, C1, C2, C n are the tidal levels at L1, L2, L n respectively;

[0124] Then H′ i = C i - s(L i ), where H′ i is the final river bottom elevation;

[0125] The corrected final cross-section dataset D N is as follows:

[0126] D N = [(L1, H′1), (L2, H′2), … (L n , H′ n )].

[0127] The cross-section dataset of Section 01 is the final cross-section dataset D obtained based on the above water depth correction and tidal level correction N as shown in Table 2.

[0128] Table 2 Data of the cross-section result dataset of Section 01

[0129]

[0130]

[0131] Specifically, the accuracy assessment is calculated according to the formula of the mean square error of observations of the same accuracy . Due to the characteristics of underwater measurement, it is difficult to obtain the true measurement value. Generally, the land measurement accuracy is higher than the underwater measurement accuracy. Therefore, large reservoirs can use underwater fixed features, such as the sounding benchmark calibration field established before water storage, fixed flat dams, roads, or the land topography after water recession as reference data. Reservoirs without a benchmark field and natural water areas can use the data obtained by more accurate sounding equipment such as multi-beam systems for verification.

[0132] The calibration data in this example is the data before water storage of a certain reservoir. See Figure 7 before correction, and the effect after correction is shown in Figure 8 . The mean square error before correction in this example is: 1.60 m, and the mean square error after correction is: 0.31 m, and the accuracy is improved by more than 2 times.

[0133] When the present invention is in use, before measurement installation: Install the depth sounder, and use a total station, theodolite, or level with a collimation vertical wire to assist in the installation, so that the transducer of the depth sounder is vertical when the ship is stationary. Install the GNSS antenna, and use a total station, theodolite, level with a collimation vertical wire or a plumb bob to assist, so that the phase center of the GNSS antenna and the phase center of the depth sounder are in the same position vertically. Measure the draft of the transducer and determine the sound velocity of the water body. If there is a temperature gradient in the water body, the sound velocity profile data should be measured to correct the depth for the gradient.

[0134] The above-described embodiments only express the implementation manners of the present invention, and the description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention should be based on the appended claims.

Claims

1. A sounding correction method based on an adaptive river cross-section model, characterized in that, Including the following steps: S1. Use the strongest echo pair of the instrument-measured water depth echo data to proofread the water depth data, perform SVP gradient correction on the thermocline, tidal level correction and calculation of the starting distance of the cross-section, and obtain the preprocessing set D of the cross-section water depth data S , and obtain the preprocessing set D of the cross-section results n ; S2. Preprocess the cross-section result preprocessing set D n Establish a polynomial regression mathematical model; S3. According to the difference between the polynomial regression mathematical model and the actual river channel morphology, adaptively fit the river channel cross-section in intervals to obtain an adaptive mathematical model of the river channel cross-section; S4. Derive the slope at any position of the cross-section by differentiating the adaptive mathematical model of the river channel cross-section; S5. Establish a correction model based on the established beam angle effect Implement the depth correction of the water depth measured by the fathometer for the river channel cross-section to obtain the processed set D of cross-section water depth data S′ ; S6. Perform tide level correction through the tide level dataset C(L i ) to obtain the cross-section result dataset D N ; In S1, the cross-section result preprocessing set D n is as follows: D n = [(L1, H1), (L2, H2), L(L n , H n )]; Among them, L n is the starting distance of the nth river cross-section point; H n is the river bottom elevation of the nth river cross-section point. The preprocessed set D of cross-sectional water depth data S is as follows: D S = [(L1, S1), (L2, S2), L(L n , S n )]; Among them, S n is the water depth data value of the cross-section point of the nth river channel point; In S2, assume that in the cross-section result preprocessing set D n H i and L i , There is a linear relationship between them, and the mathematical model is: Among them, L i is the starting distance of the cross-section point of the river channel at the i-th point; H i is the river bottom elevation of the cross-section point of the river channel at the i-th point; b0, b1, b2, b3, … b k-1 and b k are the fitting coefficients of the mathematical model; L i and are the unary k-th order polynomials of the mathematical model; Then the polynomial regression mathematical model Among them, is the regression estimated value of H i ; a0, a1, a2, a3, … a k-1 , a k are the regression estimated values of coefficients b0, b1, b2, b3, … b k-1 , b k ; Let where ε is the sum of squared residuals; Let ε be differentiated with respect to a0, a1, … a k respectively, and set each partial derivative to zero: Solve the values of each coefficient using Cramer's rule: where m is the m-th column of the coefficient determinant P.

2. The sounding correction method based on an adaptive river cross-section model according to claim 1, wherein The specific content of S3 is as follows: Adaptive mathematical model of river channel cross-section G(L i ) The k-order fitting expression in the interval [L1, L n is as follows: Among them, is the piecewise fitting equation G(L i ) polynomial fitting coefficient, j is the adaptive j-segment mathematical model, is the value within the interval of [L1, L n , and 3. A sounding correction method based on an adaptive river cross-section model according to claim 2, characterized in that In S4, the derivative of the adaptive mathematical model of the river channel cross-section is obtained, and the slope G′(L i ) at any position of the river channel cross-section under the sounding measurement is derived: Then the slope P(L i ) at any position of the river channel cross-section is: P(L i ) = arctan G′(L i ).

4. A sounding correction method based on an adaptive river cross-section model according to claim 3, characterized in that In S5, when in the cross-section self-adaptive mathematical model of the river channel, the slope P(L i ) of the cross-section is not greater than the true slope P(L i ) of the terrain 真 , the correction model established is: The obtained cross-section water depth data processing set D S′ : D S′ = [(L1, s(L1)), (L2, s(L2)), …(L n , s(L n ))].

5. A sounding correction method based on an adaptive river cross-section model according to claim 4, characterized in that In S6, the tidal level dataset C(L i ) is as follows: C(L i ) = [(L1, C1), (L2, C2), … (L n , C n )]; Among them, C1, C2, and C n are the tidal levels at L1, L2, and L n respectively; Then H′ i = C i - s(L i ), where H′ i is the final river bottom elevation; Obtain the final cross-section data set D after correction N : D N = [(L1, H′1), (L2, H′2), … (L n , H′ n )].

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