CN112819249A - Tidal current harmonic analysis and calculation method based on sailing ADCP observation ocean current data - Google Patents

Tidal current harmonic analysis and calculation method based on sailing ADCP observation ocean current data Download PDF

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CN112819249A
CN112819249A CN202110215997.2A CN202110215997A CN112819249A CN 112819249 A CN112819249 A CN 112819249A CN 202110215997 A CN202110215997 A CN 202110215997A CN 112819249 A CN112819249 A CN 112819249A
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马云龙
朱小华
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Abstract

The invention discloses a power flow harmonic analysis and calculation method based on sailing ADCP observation ocean current data, which comprises the following steps: s1, preparing for navigation observation; s2, carrying out navigation observation; s3, correcting the misalignment angle of the observation data of the navigation ADCP; s4, eliminating error data; s5, processing blind area data; and S6, harmonic analysis and calculation. S1 includes the steps of: selecting an object sea area for flow analysis, downloading long-term tide level or water level data near the object sea area, performing harmonic analysis on the data, and selecting main tide separating information; and determining the dominant type of the object sea area, and the full-time tide type and the half-time tide type according to the harmonic analysis result of the water level data long-time sequence. The invention provides a method for observing tidal current of an ADCP (advanced digital content control protocol) during navigation aiming at short data observation time; by improving the trend harmony analysis method, the error in the demodulation can be well controlled, so that the error is closer to the actual result.

Description

Tidal current harmonic analysis and calculation method based on sailing ADCP observation ocean current data
Technical Field
The invention relates to a power flow harmonic analysis and calculation method, in particular to a power flow harmonic analysis and calculation method based on sailing ADCP observation ocean current data.
Background
The Qiongzhou strait is one of three straits (qinzhou, Taiwan and Bohai sea) near the sea in China, is between the Leizhou peninsula and the southern island in the south of the sea in Guangdong province, has a northwest export connected with the northeast of the south sea, and is an important channel for connecting the northwest of the south sea and the northwest of the north sea. The average width, length and average water depth of the strait are approximately 25km, 70km and 70m respectively, with water depths exceeding 100m at most. The Johnson strait is an important traffic main between the southern province and the continent, and is also an exchange channel for seawater between the north and north gulf of the south sea, and the current in the straits plays an important role in circulation on both sides of the straits. Quantifying tidal current transport through the strait is therefore critical to understand shelf circulation in the north of the south sea and cyclonic circulation in the north bay.
Although historical observation can roughly indicate the structural characteristics of the tidal current space, the net flow of the strait estimated by synchronous hydrological data does not exist so far under the influence of factors such as scarce observation data, uncertain observation positions and the like. In order to obtain the synchronous tidal current data across the strait, a series of anchor system current meters and single-point ADCP are arranged on the bottom layer or subsurface layer of the strait, or reciprocating sailing ADCP observation is carried out. However, since the johnson channel is an important traffic major, the busy transportation and fishery activities of the channel bring great difficulty to the arrangement of the anchor system array, and the fishing net in the channel also seriously hinders the observation data quality of the underway ADCP.
In the past, classical harmonic analysis methods are mostly used for trend research, and the classical harmonic analysis methods are based on the condition that the time series of the analyzed data is long enough and the data error is small. However, in practical situations, due to the influences of factors such as weather and navigation channels, data observation time is often forced to be interrupted, the complete phase of the tide is not completely covered, and observation data has certain random errors, so that solution errors obtained by a classical harmonic analysis method are large and deviate from actual results.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a power flow harmonic analysis and calculation method based on sailing ADCP observation ocean current data.
The specific technical scheme is as follows:
a power flow harmonic analysis and calculation method based on sailing ADCP observation ocean current data comprises the following steps:
s1, preparing for navigation observation;
s2, carrying out navigation observation;
s3, correcting the misalignment angle of the observation data of the navigation ADCP;
s4, eliminating error data;
s5, processing blind area data;
and S6, harmonic analysis and calculation.
The S1 includes the steps of:
selecting an object sea area for flow analysis, downloading long-term tide level or water level data near the object sea area, performing harmonic analysis on the data, and selecting main tide separating information;
determining the dominant type of the object sea area and the types of the full-time tide and the half-time tide according to the harmonic analysis result of the water level data long-time sequence;
designing start-stop observation time of the ADCP section, performing phase projection calculation, requiring projection of all section tide division periods to cover the whole phase of the main tide division, projecting each section observation time in the full tide period and the half tide period, and determining that the scheme is feasible if the observation time covers the full tide period and the half tide period.
The S2 includes the steps of: an 80-ton wooden fishing boat is used, the ADCP is installed on the front side of a boat body far away from an engine, the boat speed is kept at 3-5n/s, the cross section flow speed data is obtained according to the design time, the starting points of all the cross sections coincide, and the measuring line keeps a straight line.
The S3 includes the steps of:
three Cartesian coordinate systems are utilized, namely NOE, XOY and X 'OY', NOE is a geographical coordinate system, N and E respectively represent north and east of geography, and due to the existence of geomagnetic declination, the true ship direction (head line and tail line OY) can be deviated; in the process of ADCP installation, the direction of ADCP and keel line (ship head-tail connecting line) at the bottom of ship can generate smaller angle deviation beta to form X 'OY' coordinate system, namely ADCP flow measurement coordinate system, in the actual calculation, the sum of two angles alpha and beta can be obtained, namely misalignment angle gamma is alpha + beta, and in X 'OY' and NOE coordinate systemFlow velocity obtained in-line, ADCP bottom tracking mode
Figure BDA0002953813370000021
And flow rate obtained in GPS mode
Figure BDA0002953813370000022
Can be obtained by the following formula:
Figure BDA0002953813370000023
Figure BDA0002953813370000024
Figure BDA0002953813370000025
is the flow rate relative to the ADCP in the X 'OY' coordinate system,
Figure BDA0002953813370000026
and
Figure BDA0002953813370000027
the ship speed in the X 'OY' and NOE coordinate systems respectively, and the absolute flow speed error epsilon in the NOE coordinate system of the two modesADCPAnd εGPSCan be expressed as the formula:
Figure BDA0002953813370000028
Figure BDA0002953813370000029
when gamma is 0, the absolute flow rates of the two modes have no error, but because the geomagnetic deviation angle exists, gamma is not equal to 0, the flow rates of the two modes have errors, and the accuracy of the ship speed is checked after the misalignment angle is corrected.
The steps for checking the accuracy of the ship speed are as follows:
the ADCP bottom tracking ship speed is based on the existing set conditions, the flow rate error is less than 2cm/s, the GPS data is smoothed according to the 10 minute (about 5km) interval, and the ship speed is calculated by the following formula:
Figure BDA0002953813370000031
wherein
Figure BDA0002953813370000032
GPS boat speed at ith minute, ti-5And ti+5Respectively the GPS data for five minutes before and after the ith minute,
Figure BDA0002953813370000033
is the displacement in two moments.
The S4 includes the steps of:
taking the standard deviation STD of the ship direction as the standard for removing the error value, the calculation formula is as follows:
Figure BDA0002953813370000034
Hifor the ith minute of ship-wise Heading,
Figure BDA0002953813370000035
the average ship direction is N minutes, wherein N is equal to 10 minutes (the distance is about 5km), when STD is larger than 1.3, the ship direction deflection in corresponding time is larger, the error of observed data is larger, the ship speed of the section is removed, the section of data is supplemented by linear interpolation of the flow velocity of adjacent boundaries in later analysis, the flow velocity is smoothed through a window with the width of 200m and the depth of 4m, and the influence of small scale change is removed.
The S5 includes the steps of:
in a complete observation section, the blind areas of the ADCP comprise a top blind area, two side blind areas and a bottom blind area, the two side blind areas are respectively positioned on a left bank and a right bank, the side blind areas on the two sides can be ignored according to the terrain of an observation area, and only the top blind area and the bottom blind area are processed; the depth of the top dead zone is equal to the sum of the depth of the water entering the energy converter of the instrument, the depth of the instrument dead zone and the lag distance, the depth of the bottom dead zone is equal to the thickness of the side lobe layer, data loss of the top dead zone and the bottom dead zone is completed through extrapolation, the actually observed flow rate data is projected to a public end face for subsequent data analysis, and the projected data is averaged to a calculation grid with the resolution ratio of 200mx2m according to the distance.
The S6 includes the steps of:
carrying out harmonic analysis by using a classical power flow harmonic analysis method; carrying out harmonic analysis by using an improved power flow harmonic analysis method; and comparing the harmonic analysis results of the classical power flow harmonic analysis method and the improved power flow harmonic analysis method.
The classical power flow harmonic analysis method comprises the following steps:
selecting main tide, supposing that m tide is selected, supposing that the observed ocean current consists of residual current and tide, and writing an expression:
Figure BDA0002953813370000036
v is the observed current velocity, v0Is the residual flow velocity, m is the number of main partial tides, HjIs the harmonic constant of the partial tide, σiIs the angular frequency of the partial tide, t is the observation time, t is an integer, decimal or indeterminate value, the starting time of the data acquisition is the time origin, thetajIs the initial phase, the expression can also be written as:
Figure BDA0002953813370000041
xj＝Hjcosθj，yj＝Hjsinθjif t is equal to t1，t2…tnObserving at any moment, actually observing the ocean current as v1，v2...vnThen the following can be established from n partiesThe equation set formed by the equation:
v1＝v0+(cosσ1t1)x1+(sinσ1t1)y1…+(cosσjt1)xj+(sinσjt1)yj…+(cosσmt1)xm+(sinσmt1)ym
v2＝v0+(cosσ1t2)x1+(sinσ1t2)y1…+(cosσjt2)xj+(sinσjt2)yj…+(cosσmt2)xm+(sinσmt2)ym
vn＝v0+(cosσ1tn)x1+(sinσ1tn)y1…+(cosσjtn)xj+(sinσjtn)yj…+(cosσmtn)xm+(sinσmtn)ym
the sigma of each partial tide is a fixed value, the equation set formed by the n equations is a linear equation set containing 2m +1 unknowns, and the tide harmonic analysis is to obtain a solution v from the linear equation set0，xj，yjIs then based on
Figure BDA0002953813370000042
θj＝arctg(yj/xj) Obtaining the amplitude and phase corresponding to each tide; and finally, calculating an intersection point factor and an intersection point correction value at the initial moment according to the astronomical factors, and obtaining the Greenwich mean phase or other harmonic constants.
N experimental observation data are set, namely n equation sets can be formed; when the number of the partial tides is m, each partial tide contains xj，yjTwo harmonic constants, plus a residual stream v02m +1 unknowns to be solved, the equation set is a typical singular equation set, and the equation set is written into twoForm of matrix multiplication:
Figure BDA0002953813370000043
the formula is abbreviated as y ═ Ex, y is n observed flow velocities, E is a coefficient matrix of n × (2m +1), and x is 2m +1 solutions to be solved; multiplying both ends of the equation by the inverse E of the coefficient matrix-1y＝E-1Ex, then solve x ═ E-1y, and minimizes the residual y-Ex, which is the least squares solution of the system of equations.
The improved power flow harmonic analysis method comprises the following steps:
when observed data cannot be completely represented by a fixed value and the sum of various harmonic constants, a signal becomes an observation error value in harmonic analysis, and a solution is obtained by controlling the minimum residual | y-Ex |, a larger observation error influences the accuracy of the solution, so that a classical harmonic analysis method introduces an unknown error r into the solution x, writes y ═ Ex into y ═ Ex + r, introduces a damped least square method (targeted least squares) to obtain the optimal solution, firstly introduces a parameter alpha for controlling the residual error, and establishes the following objective function J:
J＝(y-Ex)T(y-Ex)+α2xxT
expectation of solution when objective function is minimum
Figure BDA0002953813370000051
Comprises the following steps:
Figure BDA0002953813370000052
performing SVD (singular value decomposition) on the matrix E:
Figure BDA0002953813370000053
Figure BDA0002953813370000054
Figure BDA0002953813370000055
λi，Ui，Vithe ith singular value, the left singular vector, the right singular vector and the solution vector of the matrix E are respectively
Figure BDA0002953813370000056
Can be expressed as:
Figure BDA0002953813370000057
the solution to be solved is already expressed as a cluster of solution of sigma control, when the optimal solution is selected, the residual error is not controlled to be smaller and better, but a balance quantity of the solution and the residual error is selected, namely the optimal value of the factor alpha is determined, the optimal value of the alpha can be intuitively obtained by an L curve method developed by Hansen and O' least, the optimal solution of the designated factor alpha of the L curve method is the maximum curvature point on the curve, and the maximum curvature point is drawn in a coordinate system
Figure BDA0002953813370000058
And xi (alpha) are the squares of the residual and the solution respectively,
Figure BDA0002953813370000059
ξ(α)＝||x(α)||
the curvature is defined as:
Figure BDA00029538133700000510
selecting a solution corresponding to the alpha value at the maximum curvature position
Figure BDA00029538133700000511
That is, the best solution is solved as the estimated value, and the solution thereof needs to be evaluated indefinitely without determinationThe property P can be written as:
Figure BDA00029538133700000512
wherein R isnn＝rrT＝(y-Ex)(y-Ex)T
E is a coefficient matrix, alpha is an optimal weight factor, I is an identity matrix, R is a residual error, R is a coefficient matrixnnIs the square of the residual.
The harmonic analysis result comparing the classical power flow harmonic analysis method with the improved power flow harmonic analysis method comprises the following steps:
selecting 33 sections of the strait for sailing ADCP to observe ocean current data for analysis and verification, wherein the direction of the observation sections comprises southwest-northeast and northwest-southeast, a water level meter is distributed at the bottom of the north end of the strait, and the sampling frequency of the water level meter is 10 minutes;
a set of simulation experiments are carried out by using water level data in the observation period of the strait, and the water level data after 1 hour of smoothing treatment is substituted for classical harmonic analysis to obtain 5 main tide divisions (K)1，O1，M2，S2MSF), then selecting 33 water level data synchronous with ADCP observation for harmonic analysis, finally comparing the resolved amplitude and phase with the standard harmonic constant;
in order to simulate the actual situation, random errors are added into 33 water level counting data, the root mean square of the 33 random errors is equal to a given value Pi, 30 experiments are repeated for the random error Pi given each time, 30 groups of random error values are correspondingly generated, 30 experiments are respectively carried out on a classical power flow harmonic analysis method and an improved power flow harmonic analysis method according to the same method for adding the random errors, the harmonic constant of each partial tide can be obtained for each experiment, the deviation between the harmonic constant of each partial tide and a standard harmonic constant of two algorithms is respectively calculated and is called RMS, and the RMS formula is defined as:
Figure BDA0002953813370000061
n is the number of simulation experiments, 30 is selected here, AMAnd deltaMThe tide amplitude and Greenwich mean phase, A, solved for both analytical methodsTAnd deltaTFor standard amplitude and phase, 5 RMS of the principal tides can be obtained for each given Pi value, so that by gradually increasing the value of the random error Pi, the degree of response of the classical tidal flow harmonic analysis method and the improved tidal flow harmonic analysis method to Pi can be verified.
The invention has the beneficial effects that:
(1) aiming at short data observation time, a sailing ADCP tide observation method is provided;
(2) by improving the power flow harmonic analysis method, errors in the demodulation can be well controlled.
Drawings
FIG. 1 is a flow chart of a flow harmony analysis and calculation method based on sailing ADCP observation ocean current data according to the present invention;
FIG. 2 is a schematic diagram of step S1 in preparation for navigation observation according to the present invention;
FIG. 3 is a schematic representation of three Cartesian coordinate systems in an embodiment of the invention;
FIG. 4 is a difference value of the absolute values of the ship speeds in the vertical section direction in the two modes of the step S3 according to the embodiment of the present invention;
FIG. 5 is an exemplary boat speed vector diagram of step S4 in accordance with an embodiment of the present invention;
FIG. 6 is a schematic diagram of the blind area of ADCP in the embodiment of the present invention;
FIG. 7 is a diagram illustrating the L-curve and the K-curve in step S6 according to the present invention;
FIG. 8 is a graphical representation of the trend of RMS and RMSD with Pi values obtained by two harmonic analysis methods in an embodiment of the present invention;
fig. 9 is a schematic diagram of a comparison between a harmonic analysis result of a classical power flow harmonic analysis method and an improved power flow harmonic analysis method and a disclosed result in the embodiment of the present invention.
Detailed Description
The following examples are illustrative and are not to be construed as limiting the invention.
As shown in fig. 1, a method for analyzing and calculating power flow harmony based on observation of ocean current data by an aviation ADCP includes the following steps:
s1, preparing for navigation observation;
selecting an object sea area for flow analysis, downloading long-term tide level or water level data near the object sea area, performing harmonic analysis on the data, and selecting main tide separating information;
determining the dominant type of the object sea area and the types of the full-time tide and the half-time tide according to the harmonic analysis result of the water level data long-time sequence;
designing start-stop observation time of the ADCP sections, carrying out phase projection calculation, requiring projections of all section tide division periods to cover the whole phase of the main tide division, projecting each section observation time in the full tide and half tide periods as shown in figure 2 (a water level data near the strait in the figure; b navigation ADCP timetable; c and d are projections of the navigation ADCP observation time in the full tide and half tide periods respectively, the upper digit represents the navigation section number and is sorted according to the observation time), so that the observation time covers the full tide and half tide periods, and the scheme is determined to be feasible.
S2, carrying out navigation observation;
a wooden fishing boat is used which has a minimum disturbance to the magnetic compass direction of the instrument and weighs about 80 tons. The ADCP is installed on the front side of the ship body far away from the engine, and the ship speed is kept between 3 and 5 m/s. And acquiring the flow velocity data of the sections according to the design time, wherein the starting points of the sections are required to coincide as much as possible, and the measuring lines keep straight lines.
S3, correcting the misalignment angle of the observation data of the navigation ADCP;
by using three cartesian coordinate systems, as shown in fig. 3, NOE, XOY, X 'OY', NOE being a geographic coordinate system, N and E representing north and east of the geography, respectively, the true ship direction (the head and tail lines OY of the ship) may be deviated due to the existence of the geomagnetic declination; thus, an included angle alpha is formed between the XOY coordinate system taking the real ship direction as a reference and the NOE geographic coordinate system, and the XOY coordinate system is installed on the ADCPIn the process, a small angle deviation beta occurs between the direction of the ADCP and a keel line (an end-to-end connecting line) at the bottom of the ship to form an X 'OY' coordinate system, namely an ADCP flow measurement coordinate system, in the actual calculation, the sum of two angles alpha and beta can be obtained, namely a misalignment angle gamma is alpha + beta, and in the X 'OY' and NOE coordinate systems, the flow velocity obtained in an ADCP bottom tracking mode is
Figure BDA0002953813370000081
And flow rate obtained in GPS mode
Figure BDA0002953813370000082
Can be obtained by the following formula:
Figure BDA0002953813370000083
Figure BDA0002953813370000084
Figure BDA0002953813370000085
is the flow rate relative to the ADCP in the X 'OY' coordinate system,
Figure BDA0002953813370000086
and
Figure BDA0002953813370000087
the ship speed in the X 'OY' and NOE coordinate systems respectively, and the absolute flow speed error epsilon in the NOE coordinate system of the two modesADCPAnd εGPSCan be expressed as the formula:
Figure BDA0002953813370000088
Figure BDA0002953813370000089
when gamma is equal to 0, there is no error in the absolute flow rates of the two modes, but due to the existence of the magnetic declination angle, gamma is not equal to 0, for example, the magnetic declination angle alpha is approximately equal to 3 degrees (gamma is approximately equal to alpha) in the north sea area of south China sea, and when the ship speed is equal to 0
Figure BDA00029538133700000810
Flow rate of flow
Figure BDA00029538133700000811
When is equal toADCP＝0.1cm s-1，εGPS＝36cm s-1. It can be seen that there is some error in both modes of flow rate, and the error in the GPS mode is larger, so it is important to estimate and correct the misalignment angle.
The steps for checking the accuracy of the ship speed are as follows:
the ADCP bottom tracking ship speed is based on the existing set conditions, the flow rate error is less than 2cm/s, the GPS data is smoothed according to the 10 minute (about 5km) interval, and the ship speed is calculated by the following formula:
Figure BDA00029538133700000812
wherein
Figure BDA00029538133700000813
GPS boat speed at ith minute, ti-5And ti+5Respectively the GPS data for five minutes before and after the ith minute,
Figure BDA00029538133700000814
is the displacement in two moments. FIG. 4 (the two dotted lines are. + -. 5cm/s, respectively) shows the difference between the absolute values of the ship speeds in the vertical section direction in the two modes
Figure BDA00029538133700000815
Δ V is controlled to be substantially 5cm s-1Within.
S4, eliminating error data;
during high-speed ship or hydrological investigation, the ship direction change can cause the measured ship speed error to be large, and thus the flow measurement accuracy of the ADCP is affected, so that the error value caused by the change must be removed. Taking the standard deviation STD of the ship direction as the standard for removing the error value, the calculation formula is as follows:
Figure BDA00029538133700000816
Hifor the ith minute of ship-wise Heading,
Figure BDA00029538133700000817
for an average ship direction of N minutes, where N is equal to 10 minutes (distance about 5km), fig. 5 is an exemplary ship speed vector diagram (blue and red vectors represent bottom-tracked ship speed and GPS ship speed of a bottom-tracked dead section, respectively, (a) is an STD time series of ship directions, (b) is a ship speed vector without error removal and (c) is a ship speed vector diagram with error removal), comparing graphs (a) and (b) shows that when STD > 1.3, the ship direction deflection is greater and the observation data error is greater for the corresponding time, removing the ship speed, as shown in (c). In the later analysis, the data of the section is compensated through linear interpolation of the flow velocity of the adjacent boundary, the flow velocity is smoothed through a window with the width of 200m and the depth of 4m, and the influence of small scale change is removed.
S5, processing blind area data;
as shown in fig. 6, in a complete observation cross section, the ADCP blind areas include a top blind area, two side blind areas, and a bottom blind area, the two side blind areas are respectively located on the left and right banks, the side blind areas on both sides can be ignored according to the terrain of the observation area, and only the top blind area and the bottom blind area are processed; the depth of the top dead zone is equal to the sum of the depth of the water entering the transducer of the instrument, the depth of the dead zone of the instrument and the lag distance, (300kHz ADCP top dead zone is about 3m (sensor depth 1m + dead zone depth 0.14m + layer thickness 2m), the depth of the bottom dead zone is generally equal to the thickness of the side lobe layer, the thickness of the bottom dead zone is about 4m (H x (20 degrees out of 1-cos20 degrees is ADCP wave velocity angle, H is water depth, and typical water depth is about 70m) caused by the interference of a submarine interface to sound waves, the depth of the bottom dead zone is equal to the thickness of the side lobe layer, the data loss of the top dead zone and the bottom dead zone is completed through extrapolation, the actually observed flow rate data is projected to a public end face for subsequent data analysis, and the projected data is averaged into a calculation grid with the resolution of 200m x2m according to.
And S6, harmonic analysis and calculation.
Carrying out harmonic analysis by using a classical power flow harmonic analysis method; carrying out harmonic analysis by using an improved power flow harmonic analysis method; and comparing the harmonic analysis results of the classical power flow harmonic analysis method and the improved power flow harmonic analysis method.
The classical power flow harmonic analysis method comprises the following steps:
selecting main tide, supposing that m tide is selected, supposing that the observed ocean current consists of residual current and tide, and writing an expression:
Figure BDA0002953813370000091
v is the observed current velocity, v0Is the residual flow velocity, m is the number of main partial tides, HjIs the harmonic constant of the partial tide, σiIs the angular frequency of the partial tide, t is the observation time, t is an integer, decimal or indeterminate value, the starting time of the data acquisition is the time origin, thetajIs the initial phase, the expression can also be written as:
Figure BDA0002953813370000092
xj＝Hjcosθj，yj＝Hjsinθjif t is equal to t1，t2…tnObserving at any moment, actually observing the ocean current as v1，v2…vnThen, a system of n equations can be established as follows:
v1＝v0+(cosσ1t1)x1+(sinσ1t1)y1…+(cosσjt1)xj+(sinσjt1)yj…+(cosσmt1)xm+(sinσmt1)ym
v2＝v0+(cosσ1t2)x1+(sinσ1t2)y1…+(cosσjt2)xj+(sinσjt2)yj…+(cosσmt2)xm+(sinσmt2)yn
vn＝v0+(cosσ1tn)x1+(sinσ1tn)y1…+(cosσjtn)xj+(sinσjtn)yj…+(cosσmtn)xm+(sinσmtn)ym
the sigma of each partial tide is a fixed value, the equation set formed by the n equations is a linear equation set containing 2m +1 unknowns, and the tide harmonic analysis is to obtain a solution v from the linear equation set0，xj，yjIs then based on
Figure BDA0002953813370000101
θj＝arctg(yj/xj) Obtaining the amplitude and phase corresponding to each tide; and finally, calculating an intersection point factor and an intersection point correction value at the initial moment according to the astronomical factors, and obtaining the Greenwich mean phase or other harmonic constants.
N experimental observation data are set, namely n equation sets can be formed; when the number of the partial tides is m, each partial tide contains xj，yjTwo harmonic constants, plus a residual stream v0And 2m +1 unknowns are to be solved, the equation set is a typical singular equation set, and the equation set is written into a form of multiplying two matrixes:
Figure BDA0002953813370000102
the formula is abbreviated as y as Ex, y is n observed flow ratesE is a coefficient matrix of n x (2m +1), and x is 2m +1 solutions to be solved; multiplying both ends of the equation by the inverse E of the coefficient matrix-1y＝E-1Ex, then solve x ═ E-1y, and minimizes the residual y-Ex, which is the least squares solution of the system of equations.
The improved power flow harmonic analysis method comprises the following steps:
when observed data cannot be completely represented by a fixed value and the sum of various harmonic constants, a signal becomes an observation error value in harmonic analysis, and a solution is obtained by controlling the minimum residual | y-Ex |, a larger observation error influences the accuracy of the solution, so that a classical harmonic analysis method introduces an unknown error r into the solution x, writes y ═ Ex into y ═ Ex + r, introduces a damped least square method (targeted least squares) to obtain the optimal solution, firstly introduces a parameter alpha for controlling the residual error, and establishes the following objective function J:
J＝(y-Ex)T(y-Ex)+α2xxT
expectation of solution when objective function is minimum
Figure BDA0002953813370000103
Comprises the following steps:
Figure BDA0002953813370000104
performing SVD (singular value decomposition) on the matrix E:
Figure BDA0002953813370000111
Figure BDA0002953813370000112
Figure BDA0002953813370000113
λi，Ui，Vithe ith singular value, the left singular vector, the right singular vector and the solution vector of the matrix E are respectively
Figure BDA0002953813370000114
Can be expressed as:
Figure BDA0002953813370000115
the solution to be solved is already expressed as a cluster of solution of sigma control, when the optimal solution is selected, the residual error is not controlled to be smaller and better, but a balance quantity of the solution and the residual error is selected, namely the optimal value of the factor alpha is determined, the optimal value of the alpha can be intuitively obtained by an L curve method developed by Hansen and O' least, the optimal solution of the designated factor alpha of the L curve method is the maximum curvature point on the curve, and the maximum curvature point is drawn in a coordinate system
Figure BDA0002953813370000116
And ξ (α) are the squares of the residual and the solution, respectively, as shown in FIG. 7 (L-curve on the left, K-curve on the right, "+" being the point of maximum curvature)
Figure BDA0002953813370000117
ξ(α)＝||x(α)||
The curvature is defined as:
Figure BDA0002953813370000118
from the L-curve, it can be seen that the solution vector is inversely proportional to the square of the residual, so that a smaller residual results in a larger error of the solution, which is not consistent with the actual situation, and we select the solution corresponding to the α value (+ position) where the curvature is maximum
Figure BDA0002953813370000119
That is, the solution is the best solution, and is the estimated value, and the solution needs to be evaluated indefinitely, and the uncertainty P can be written as:
Figure BDA00029538133700001110
wherein R isnn＝rrT＝(y-Ex)(y-Ex)T
E is a coefficient matrix, alpha is an optimal weight factor, I is an identity matrix, R is a residual error, R is a coefficient matrixnnIs the square of the residual.
The harmonic analysis result comparing the classical power flow harmonic analysis method with the improved power flow harmonic analysis method comprises the following steps:
selecting 33 sections of the strait for sailing ADCP to observe ocean current data for analysis and verification, wherein the direction of the observation sections comprises southwest-northeast and northwest-southeast, a water level meter is distributed at the bottom of the north end of the strait, and the sampling frequency of the water level meter is 10 minutes;
a set of simulation experiments are carried out by using water level data in the observation period of the strait, and the water level data after 1 hour of smoothing treatment is substituted for classical harmonic analysis to obtain 5 main tide divisions (k)1，O1，M2，S2MSF), the amplitude and phase values, namely the standard harmonic constant, the result parameters are shown in the following table 1, 33 water level data synchronous with ADCP observation are selected for harmonic analysis, and finally the difference of the two algorithms under the condition of insufficient sampling can be checked by comparing the solved amplitude and phase values with the standard harmonic constant.
TABLE 1 Water level indicator reconciliation analysis results
Figure BDA0002953813370000121
Indicates the main partial tide
Because the accuracy of the anchored water level counting data is high, but the navigation ADCP data is influenced by undersampling and line measurement in the actual situation, certain errors exist in the data, the errors can influence the resolution accuracy to simulate the actual situation, random errors are added into 33 water level counting data, the root mean square of 33 random errors is equal to a given value Pi, 30 times of experiments are repeated for each given random error Pi, 30 groups of random error values can be correspondingly generated, 30 times of experiments are respectively carried out on a classical power flow harmonic analysis method and an improved power flow harmonic analysis method according to the method of adding the random errors in the same way, the harmonic constant of each tide can be obtained in each experiment, the deviation between the harmonic constant of each tide and the standard harmonic constant of two algorithms is calculated, the deviation is called RMS, and the RMS formula is defined as:
Figure BDA0002953813370000122
n is the number of simulation experiments, 30 is selected here, AMAnd deltaMThe tide amplitude and Greenwich mean phase, A, solved for both analytical methodsTAnd deltaTFor standard amplitude and phase, 5 RMS of the principal tides can be obtained for each given Pi value, so that by gradually increasing the value of the random error Pi, the degree of response of the classical tidal flow harmonic analysis method and the improved tidal flow harmonic analysis method to Pi can be verified.
FIG. 8 shows the trend of RMS and RMSD with Pi for two harmonic analysis methods, and FIG. 8-b shows that 5 RMS values increase with increasing Pi, but the RMS of the classical harmonic analysis method () increases more rapidly, while the improved harmonic analysis method (+) RMS controls better and increases more slowly.
FIG. 8-a is the trend of residuals of two algorithms as a function of Pi values. The classical power flow harmonic analysis method is best solved by minimizing the residual error control, but the residual error of the improved power flow harmonic analysis method is compared with the improved power flow harmonic analysis method, two values are very close to each other, the improved power flow harmonic analysis method also controls the residual error to be very small, and the difference between the two values is about 4% of the residual error of the classical power flow harmonic analysis method. The above situations all illustrate that the improved power flow harmonic analysis method does not obtain the best solution by using the loss observation value.
Through the simulation experiment, the fact that the solution precision of the improved harmonic analysis method is obviously superior to that of the classical harmonic analysis method under the conditions of insufficient sampling and random errors in observation can be obviously seen. Therefore, the improved tidal current harmony analysis method is mainly adopted to analyze the tidal current data of the johnson strait.
Similarly, the trend analysis is respectively carried out on the sailing ADCP data by utilizing a classical trend harmony analysis method and an improved trend harmony analysis method, and compared with the published results, as shown in fig. 9, it is obvious that the results of the classical trend harmony analysis method are both vertically-averaged elliptical distribution of the surface layer 40m flow velocity and quite disordered vertical distribution, the difference from the published results is large, and the errors of the major axis, the minor axis, the major axis angle and the phase of the full-time tide (half-time tide) ellipse of the two observation results are far larger than the results of the improved trend harmony analysis method. Comparing the results of the two analysis methods, the result calculated based on the improved trend harmony analysis method is more reliable and well matched with the published research result.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.

Claims (10)

1. A power flow harmonic analysis and calculation method based on sailing ADCP observation ocean current data is characterized by comprising the following steps:
s1, preparing for navigation observation;
s2, carrying out navigation observation;
s3, correcting the misalignment angle of the observation data of the navigation ADCP;
s4, eliminating error data;
s5, processing blind area data;
and S6, harmonic analysis and calculation.
2. The method for calculating power flow harmony analysis based on underway ADCP observation ocean current data of claim 1, wherein the S1 comprises the steps of:
selecting an object sea area for flow analysis, downloading long-term tide level or water level data near the object sea area, performing harmonic analysis on the data, and selecting main tide separating information;
determining the dominant type of the object sea area and the types of the full-time tide and the half-time tide according to the harmonic analysis result of the water level data long-time sequence;
designing start-stop observation time of the ADCP section, performing phase projection calculation, requiring projection of all section tide division periods to cover the whole phase of the main tide division, projecting each section observation time in the full tide period and the half tide period, and determining that the scheme is feasible if the observation time covers the full tide period and the half tide period.
3. The method for calculating power flow harmony analysis based on underway ADCP observation ocean current data of claim 1, wherein the S2 comprises the steps of: an 80-ton wooden fishing boat is used, the ADCP is installed on the front side of a boat body far away from an engine, the boat speed is kept at 3-5m/s, the cross section flow speed data is obtained according to the design time, the starting points of all the cross sections coincide, and the measuring line keeps a straight line.
4. The method for calculating power flow harmony analysis based on underway ADCP observation ocean current data of claim 1, wherein the S3 comprises the steps of:
three Cartesian coordinate systems are utilized, namely NOE, XOY and X 'OY', NOE is a geographical coordinate system, N and E respectively represent north and east of geography, and due to the fact that geomagnetic declination exists, the true ship direction can deviate; in the actual calculation, only the sum of two angles alpha and beta, namely the misalignment angle gamma is alpha + beta, can be obtained, and the flow velocity obtained in the ADCP bottom tracking mode in the X 'OY' and NOE coordinate systems
Figure FDA0002953813360000011
And in GPS modeThe resulting flow rate
Figure FDA0002953813360000012
Can be obtained by the following formula:
Figure FDA0002953813360000013
Figure FDA0002953813360000021
Figure FDA0002953813360000022
is the flow rate relative to the ADCP in the X 'OY' coordinate system,
Figure FDA0002953813360000023
and
Figure FDA0002953813360000024
the ship speed in the X 'OY' and NOE coordinate systems respectively, and the absolute flow speed error epsilon in the NOE coordinate system of the two modesADCPAnd εGPSCan be expressed as the formula:
Figure FDA0002953813360000025
Figure FDA0002953813360000026
when gamma is 0, the absolute flow rates of the two modes have no error, but because the geomagnetic declination exists, gamma is not equal to 0, the flow rates of the two modes have errors, and the accuracy of the ship speed is checked after the misalignment angle is corrected;
the steps for checking the accuracy of the ship speed are as follows:
according to the existing set conditions, the ADCP bottom tracking ship speed is less than 2cm/s in flow rate error, the GPS data is smoothed at intervals of 10 minutes, and the ship speed is calculated by the following formula:
Figure FDA0002953813360000027
wherein
Figure FDA0002953813360000028
GPS boat speed at ith minute, ti-5And ti+5Respectively the GPS data for five minutes before and after the ith minute,
Figure FDA0002953813360000029
is the displacement in two moments.
5. The method for calculating power flow harmony analysis based on underway ADCP observation ocean current data of claim 1, wherein the S4 comprises the steps of:
taking the standard deviation STD of the ship direction as the standard for removing the error value, the calculation formula is as follows:
Figure FDA00029538133600000210
Hifor the ith minute of ship-wise Heading,
Figure FDA00029538133600000211
the average ship direction is N minutes, wherein N is equal to 10 minutes, when STD is larger than 1.3, the ship direction deflection in the corresponding time is larger, the error of observed data is larger, the ship speed of the section is removed, the section of data is compensated through linear interpolation of the flow speed of adjacent boundaries in the later analysis, the flow speed is smoothed through a window with the width of 200m and the depth of 4m, and the influence of small scale change is removed.
6. The method for calculating power flow harmony analysis based on underway ADCP observation ocean current data of claim 1, wherein the S5 comprises the steps of:
in a complete observation section, the blind areas of the ADCP comprise a top blind area, two side blind areas and a bottom blind area, the two side blind areas are respectively positioned on a left bank and a right bank, the side blind areas on the two sides can be ignored according to the terrain of an observation area, and only the top blind area and the bottom blind area are processed; the depth of the top dead zone is equal to the sum of the depth of the water entering the energy converter of the instrument, the depth of the instrument dead zone and the lag distance, the depth of the bottom dead zone is equal to the thickness of the side lobe layer, data loss of the top dead zone and the bottom dead zone is completed through extrapolation, the actually observed flow rate data is projected to a public end face for subsequent data analysis, and the projected data is averaged to a calculation grid with the resolution ratio of 200m x2m according to the distance.
7. The method for calculating power flow harmony analysis based on underway ADCP observation ocean current data of claim 1, wherein the S6 comprises the steps of:
carrying out harmonic analysis by using a classical power flow harmonic analysis method; carrying out harmonic analysis by using an improved power flow harmonic analysis method; and comparing the harmonic analysis results of the classical power flow harmonic analysis method and the improved power flow harmonic analysis method.
8. The calculation method of power flow harmony analysis based on navigable ADCP observation ocean current data as claimed in claim 7, wherein the classical power flow harmony analysis method comprises the following steps:
selecting main tide, supposing that m tide is selected, supposing that the observed ocean current consists of residual current and tide, and writing an expression:
Figure FDA0002953813360000031
v is the observed current velocity, v0Is the residual flow velocity, m is the number of main partial tides, HjIs the harmonic constant of the partial tide, σiIs the angular frequency of the partial tide,t is observation time, t is integer, decimal or indeterminate value, the starting time of data acquisition is the time origin, thetajIs the initial phase, the expression can also be written as:
Figure FDA0002953813360000032
xj＝Hjcosθj，yj＝Hjsinθjif t is equal to t1，t2...tnObserving at any moment, actually observing the ocean current as v1，v2...vnThen, a system of n equations can be established as follows:
v1＝v0+(cosσ1t1)x1+(sinσ1t1)y1...+(cosσjt1)xj+(sinσjt1)yj...+(cosσmt1)xm+(sinσmt1)ym
v2＝v0+(cosσ1t2)x1+(sinσ1t2)y1...+(cosσjt2)xj+(sinσjt2)yj...+(cosσmt2)xm+(sinσmt2)ym
vn＝v0+(cosσ1tn)x1+(sinσ1tn)y1...+(cosσjtn)xj+(sinσjtn)yj...+(cosσmtn)xm+(sinσmtn)ym
the sigma of each partial tide is a fixed value, the equation set formed by the n equations is a linear equation set containing 2m +1 unknowns, and the tide harmonic analysis is to obtain a solution v from the linear equation set0，xj，yjIs then based on
Figure FDA0002953813360000033
θj＝arctg(yj/xj) Obtaining the amplitude and phase corresponding to each tide; finally, calculating an intersection point factor and an intersection point correction value at the initial moment according to astronomical factors, and obtaining a Greenwich mean phase or other harmonic constants;
n experimental observation data are set, namely n equation sets can be formed; when the number of the partial tides is m, each partial tide contains xj，yjTwo harmonic constants, plus a residual stream v0And 2m +1 unknowns are to be solved, the equation set is a typical singular equation set, and the equation set is written into a form of multiplying two matrixes:
Figure FDA0002953813360000041
the formula is abbreviated as y ═ Ex, y is n observed flow velocities, E is a coefficient matrix of n × (2m +1), and x is 2m +1 solutions to be solved; multiplying both ends of the equation by the inverse E of the coefficient matrix-1y＝E-1Ex, then solve x ═ E-1y, and minimizes the residual y-Ex, which is the least squares solution of the system of equations.
9. The method of claim 7, wherein the improved power flow harmonic analysis method comprises the steps of:
when observed data cannot be completely represented by the sum of a fixed value and various harmonic constants, a signal becomes an observation error value in harmonic analysis, and a solution is obtained by controlling the minimum residual error y-Ex |, a larger observation error influences the accuracy of the solution, so that an unknown error r is introduced into the solution x by a classical harmonic analysis method, y ═ Ex is written into y ═ Ex + r, the optimal solution is solved by introducing a damped least square method, firstly, a parameter alpha for controlling the residual error is introduced, and the following objective function J is established:
J＝(y-Ex)T(y-Ex)+a2xxT
expectation of solution when objective function is minimum
Figure FDA0002953813360000042
Comprises the following steps:
Figure FDA0002953813360000043
performing SVD on the matrix E:
Figure FDA0002953813360000044
Figure FDA0002953813360000045
Figure FDA0002953813360000046
λi，Ui，Vithe ith singular value, the left singular vector, the right singular vector and the solution vector of the matrix E are respectively
Figure FDA0002953813360000047
Can be expressed as:
Figure FDA0002953813360000048
the solution to be solved is already expressed as a cluster of solutions controlled by sigma, when the optimal solution is selected, the residual error is not controlled to be smaller and better, but a balance quantity which is the optimal value of the solution and the residual error is selected, namely the optimal value of the factor alpha is determined, an L curve method developed by Hansen and O' left can intuitively obtain the optimal value of alpha, the optimal solution of the factor alpha is specified by the L curve method to be the maximum curvature point on the curve, zeta (alpha), and zeta (alpha) are respectively the squares of the residual error solution,
ζ(α)＝||n(α)||，ξ(α)＝||x(α)||
the curvature is defined as:
Figure FDA0002953813360000051
selecting a solution corresponding to the alpha value at the maximum curvature position
Figure FDA0002953813360000052
That is, the solution is the best solution, and is the estimated value, and the solution needs to be evaluated indefinitely, and the uncertainty P can be written as:
Figure FDA0002953813360000053
wherein R isnn＝rrT＝(y-Ex)(y-Ex)T
E is a coefficient matrix, alpha is an optimal weight factor, I is an identity matrix, R is a residual error, R is a coefficient matrixnnIs the square of the residual.
10. The method of claim 7, wherein the comparing the blending analysis results of the classical flow blending analysis method and the improved flow blending analysis method comprises the following steps:
selecting 33 sections of the strait for sailing ADCP to observe ocean current data for analysis and verification, wherein the direction of the observation sections comprises southwest-northeast and northwest-southeast, a water level meter is distributed at the bottom of the north end of the strait, and the sampling frequency of the water level meter is 10 minutes;
carrying out a group of simulation experiments by using water level data in the observation period of the strait, substituting the water level data subjected to smoothing treatment for 1 hour for classical harmonic analysis to obtain amplitude and phase values of 5 main partial tides, namely standard harmonic constants, selecting 33 water level data synchronous with ADCP observation for harmonic analysis, and finally comparing the solved amplitude and phase values with the standard harmonic constants;
in order to simulate the actual situation, random errors are added into 33 water level counting data, the root mean square of the 33 random errors is equal to a given value Pi, 30 experiments are repeated for the random error Pi given each time, 30 groups of random error values are correspondingly generated, 30 experiments are respectively carried out on a classical power flow harmonic analysis method and an improved power flow harmonic analysis method according to the same method for adding the random errors, the harmonic constant of each partial tide can be obtained for each experiment, the deviation between the harmonic constant of each partial tide and a standard harmonic constant of two algorithms is respectively calculated and is called RMS, and the RMS formula is defined as:
Figure FDA0002953813360000061
n is the number of simulation experiments, 30 is selected here, AMAnd deltaMThe tide amplitude and Greenwich mean phase, A, solved for both analytical methodsTAnd deltaTFor standard amplitude and phase, 5 RMS main partial tides can be obtained for each given Pi value, so that the response degree of the classical power flow harmonic analysis method and the improved power flow harmonic analysis method to the Pi can be tested by gradually increasing the random error Pi value;
and finally comparing the harmonic analysis results of the classical power flow harmonic analysis method and the improved power flow harmonic analysis method with the published results.
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