Flow measurement method and device

By using 77GHz millimeter-wave radar and digital beamforming technology, the system achieves rapid switching between narrow-beam water level and wide-beam flow velocity, solving the problem that traditional flow measurement equipment is susceptible to environmental influences, improving measurement accuracy and equipment integration, and making it suitable for stable monitoring of irrigation canals.

CN121783276APending Publication Date: 2026-04-03MAS TECH (SHENZHEN) CO LTD
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-01-20
Publication Date
2026-04-03

AI Technical Summary

Technical Problem

Traditional flow measurement equipment is susceptible to siltation, floating debris entanglement, and water corrosion, resulting in decreased measurement accuracy. Furthermore, the separate installation of water level and flow velocity measurement equipment increases the size and weight of the equipment, and the time lag in data synchronization affects measurement accuracy.

Method used

Employing 77GHz millimeter-wave radar and digital beamforming technology, the system enables rapid switching between narrow-beam water level measurement and wide-beam flow velocity measurement via an antenna array. Combined with fast Fourier transform and Doppler frequency shift calculation, it calculates water level, flow velocity, and flow rate data.

Benefits of technology

It achieves high-precision non-contact flow measurement, reduces equipment size and weight, and improves measurement accuracy and reliability, making it suitable for long-term stable monitoring in open water flow environments.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention relates to the technical field of measurement, and discloses a flow measurement method and device.The method comprises the steps that an antenna array is configured to be in the mode that narrow wave beams vertically and downwards transmit frequency modulation continuous waves, fast Fourier transform is conducted on water surface echo difference frequency signals, and the space height distance is obtained; calculating according to the installation height and the air height distance to obtain water level data; switching the antenna array into a wide wave beam, transmitting continuous waves in a pitch angle scanning range, and performing vector calculation on water surface echo Doppler frequency shift to obtain flow velocity data; according to the water level data and the geometric parameters of the channel section, the area of the overflowing section is calculated, according to the flow velocity data and the area of the overflowing section, accumulated flow data is calculated, and by means of the method, the size and weight of equipment are reduced, and installation difficulty and maintenance cost are reduced; the non-contact measurement mode avoids pollution and damage risks caused by contact between the sensor and the water body, and is suitable for long-term stable monitoring of open water flow environments such as irrigation district channels and the like.
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Description

Technical Field

[0001] This invention relates to the field of measurement technology, and in particular to a flow measurement method and apparatus. Background Technology

[0002] Traditional flow measurement technology requires the installation of sensors in the water body. During long-term operation, these sensors are susceptible to siltation, entanglement of floating debris, and water corrosion, leading to decreased measurement accuracy, frequent equipment maintenance, and the risk of being destroyed during floods. Water level measurement radar and flow velocity measurement radar need to be installed and powered independently, which not only increases the size and weight of the equipment and the difficulty of installation and commissioning, but also causes a time difference in data synchronization between the two sets of equipment. When the water level changes rapidly, it will cause errors in flow calculation and affect the accuracy of measurement. Summary of the Invention

[0003] This invention provides a flow measurement method and device. The invention reduces the size and weight of the equipment, lowers the installation difficulty and maintenance cost, and the non-contact measurement method avoids the risk of pollution and damage caused by the sensor coming into contact with the water body. It is suitable for long-term stable monitoring of open water flow environments such as irrigation canals.

[0004] In a first aspect, the present invention provides a flow measurement method, the flow measurement method comprising: The antenna array is configured to transmit frequency-modulated continuous waves vertically downwards with a narrow beam. The difference frequency signal of the water surface echo is subjected to fast Fourier transform to obtain the air altitude range. The water level data is obtained by calculating the distance between the installation height and the aforementioned air height; The antenna array is switched to a wide beam and a continuous wave is emitted within the elevation angle scanning range. Vector calculation is performed on the Doppler frequency shift of the water surface echo to obtain the flow velocity data. The cross-sectional area of ​​the flow passage is calculated based on the water level data and the channel cross-sectional geometric parameters, and the cumulative flow rate is calculated based on the flow velocity data and the cross-sectional area of ​​the flow passage.

[0005] In conjunction with the first aspect, in a first implementation of the first aspect of the present invention, the flow measurement method further includes: A frequency-modulated continuous wave is generated by a radar signal generator and simultaneously fed into multiple transmitting units of the antenna array via a power distribution network. For the water level measurement mode, the phase delay and amplitude weighting coefficient of each transmitting unit are calculated so that each transmitting unit forms a narrow beam pointing vertically downward, and the first beamforming parameters are obtained. The vertical phase gradient is adjusted for the flow velocity measurement mode so that each transmitting unit forms a wide beam and scans within the elevation angle scanning range to obtain the second beamforming parameters; The first beamforming parameter and the second beamforming parameter are respectively loaded into the phase shifter and amplitude controller corresponding to each transmitting unit.

[0006] In conjunction with the first aspect, in a second implementation of the first aspect of the present invention, the antenna array is configured to transmit frequency-modulated continuous waves vertically downwards with a narrow beam, and a fast Fourier transform is performed on the water surface echo difference frequency signal to obtain the air altitude range, including: The water surface echo signal collected by the receiving antenna array is phase-corrected and amplitude-weighted by a digital beamforming receiving network, and the signals from multiple receiving units are coherently combined to obtain the composite echo signal. The synthesized echo signal and the local oscillator signal are mixed in a mixer to obtain a difference frequency signal. The difference frequency signal is then subjected to a fast Fourier transform to detect the spectral peak and extract the peak frequency. The single-measurement altitude distance is calculated based on the peak frequency, speed of light, sweep period, and sweep bandwidth, and the average of multiple single-measurement altitude distances is calculated to obtain the altitude distance.

[0007] In conjunction with the first aspect, in a third implementation of the first aspect of the present invention, the single-measurement altitude distance is calculated based on the peak frequency, speed of light, sweep period, and sweep bandwidth, and the average of multiple single-measurement altitude distances is calculated to obtain the altitude distance, including: The product of the peak frequency, speed of light, and sweep period is divided by twice the sweep bandwidth to obtain the single measurement altitude distance. The single-measurement altitude distance is acquired multiple times within a preset time period, and the average value of the multiple single-measurement altitude distances is calculated to obtain the altitude distance.

[0008] In conjunction with the first aspect, in the fourth implementation of the first aspect of the present invention, the water level data is obtained by calculating the distance between the installation height and the air height, including: Read the installation height measured and stored by a level during equipment installation from the system parameter memory; The difference between the installation height and the air height is calculated to obtain the vertical distance from the radar installation position to the water surface, and the vertical distance from the radar installation position to the water surface is used as the water level data.

[0009] In conjunction with the first aspect, in a fifth implementation of the first aspect of the present invention, the antenna array is switched to a wide beam and a continuous wave is transmitted within the elevation angle scanning range. Vector calculation is performed on the Doppler frequency shift of the water surface echo to obtain flow velocity data, including: After loading the second beamforming parameters, the beam center elevation angle is calculated based on the installation height and the distance of the flow velocity irradiation area. The elevation scan is performed within the scanning range above and below the beam center elevation angle according to the preset step angle. At each pitch angle, the water surface echo signal is received and mixed with the transmitted signal to obtain a Doppler intermediate frequency signal, and the actual flow velocity corresponding to the pitch angle is calculated based on the Doppler intermediate frequency signal. The flow velocity data is obtained by weighted averaging the actual flow velocities corresponding to each pitch angle.

[0010] In conjunction with the first aspect, in the sixth implementation of the first aspect of the present invention, the Doppler intermediate frequency signal is obtained by mixing the received water surface echo signal with the transmitted signal at each pitch angle, and the actual flow velocity corresponding to the pitch angle is calculated based on the Doppler intermediate frequency signal, including: At each elevation angle, the water surface echo signal collected by the receiving antenna array is mixed with the transmitted signal in a mixer to obtain the Doppler intermediate frequency signal; A fast Fourier transform is performed on the Doppler intermediate frequency signal, the spectral peak is detected and the Doppler frequency shift value is extracted, and the Doppler frequency shift value is multiplied by the speed of light and then divided by twice the carrier frequency to obtain the radial flow velocity corresponding to the pitch angle. The radial velocity is divided by the cosine of the pitch angle and then vectorized to obtain the actual velocity corresponding to the pitch angle.

[0011] In conjunction with the first aspect, in the seventh implementation of the first aspect of the present invention, the cross-sectional area of ​​the flow passage is calculated based on the water level data and the channel cross-sectional geometric parameters, and the cumulative flow rate is calculated based on the flow velocity data and the cross-sectional area of ​​the flow passage, including: Read the pre-stored channel cross-section geometric parameters from the system parameter memory. The channel cross-section geometric parameters include the channel bottom width, side slope gradient, and channel type. When the channel type is a trapezoidal channel, the cross-sectional area is obtained by adding the product of the channel bottom width, the slope gradient, and the water level data, and then multiplying the product by the water level data. When the channel type is a rectangular channel, the cross-sectional area is obtained by multiplying the channel bottom width and the water level data. When the channel type is a circular pipe, the cross-sectional area is calculated based on the relationship between the water level data and the pipe diameter. The instantaneous flow rate is obtained by multiplying the flow velocity data by the cross-sectional area of ​​the flow passage, and the instantaneous flow rate is then integrated over time to obtain the cumulative flow rate data.

[0012] In conjunction with the first aspect, in the eighth implementation of the first aspect of the present invention, the flow velocity data is multiplied by the cross-sectional area of ​​the flow passage to obtain the instantaneous flow rate, and the instantaneous flow rate is integrated over time to obtain the cumulative flow rate data, including: The actual flow velocity corresponding to each pitch angle is multiplied by the corresponding cross-sectional area of ​​the flow path and the cosine value of the pitch angle, and then summed. The sum is then divided by the cross-sectional area of ​​the flow path to obtain the average flow velocity of the cross-section. The average flow velocity of the cross-section is multiplied by the cross-sectional area of ​​the flow path to obtain the instantaneous flow rate. Multiple instantaneous flow rates are acquired, and each instantaneous flow rate is multiplied by a preset sampling period and then summed to obtain cumulative flow data.

[0013] In a second aspect, the present invention provides a flow measurement device, the flow measurement device comprising: The transmitting module is used to configure the antenna array to transmit frequency-modulated continuous waves vertically downwards in a narrow beam, and to perform a fast Fourier transform on the water surface echo difference frequency signal to obtain the air altitude distance. The calculation module is used to calculate the water level data based on the installation height and the distance between the installation height and the air height. The vector solution module is used to switch the antenna array to a wide beam and transmit continuous waves within the elevation angle scanning range, and to perform vector solution on the Doppler frequency shift of the water surface echo to obtain flow velocity data; The flow accumulation module is used to calculate the cross-sectional area of ​​the flow passage based on the water level data and the channel cross-sectional geometric parameters, and to calculate the cumulative flow data based on the flow velocity data and the cross-sectional area of ​​the flow passage.

[0014] The technical solution provided by this invention utilizes the short-wavelength characteristics of 77GHz millimeter-wave radar, combined with digital beamforming technology to achieve flexible beam direction control on a single-board antenna array, resolving the technical contradiction between measurement accuracy and equipment integration in traditional radar flowmeters. By configuring the phase and amplitude of each transmitting unit through phase shifters and amplitude controllers, rapid switching between an 8° narrow-beam water level measurement mode and a 10° wide-beam 27° elevation scan flow velocity measurement mode can be completed within milliseconds, achieving quasi-synchronous high-precision measurement of water level and flow velocity. The water level measurement accuracy reaches ±5 mm with a blind zone of less than 20 cm, and the flow velocity measurement accuracy reaches ±1% of full scale. The digital beamforming receiving network achieves coherent synthesis of signals from multiple receiving units through phase correction and amplitude weighting, effectively suppressing clutter interference from canal banks and floating objects, improving the signal-to-noise ratio and measurement reliability. Doppler frequency shift data is collected point-by-point within the elevation scan range and vector calculation is performed to obtain the vertical distribution information of the water surface velocity. The average cross-sectional velocity is calculated through layered weighted averaging, improving the accuracy of flow calculation. The single-board antenna integrated design reduces the size and weight of the equipment, lowers the difficulty of installation and maintenance costs, and the non-contact measurement method avoids the risk of pollution and damage caused by the sensor coming into contact with the water body. It is suitable for long-term stable monitoring in open water flow environments such as irrigation canals.

[0015] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0016] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of one embodiment of the flow measurement method in this invention; Figure 2 This is a schematic diagram of one embodiment of the flow measurement device in this invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] The terms "comprising" and "having," and any variations thereof, used in the embodiments of this invention are intended to cover non-exclusive inclusion. For example, a process, method, apparatus, product, or device that includes a series of steps or units is not limited to the steps or units listed, but may optionally include other steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0020] To facilitate understanding of this embodiment, a flow measurement method disclosed in this invention will first be described in detail. For example... Figure 1 As shown, this method includes the following steps: 101. Configure the antenna array to transmit frequency-modulated continuous waves vertically downwards with a narrow beam, and perform a fast Fourier transform on the water surface echo difference frequency signal to obtain the air height distance. Specifically, by configuring the radar transmitting module, the antenna array forms a vertical downlink narrow beam pattern with an 8° beam angle, and periodically transmits a 77GHz frequency-modulated continuous wave signal to the water surface below with a preset sweep bandwidth and sweep period. When the radar wave encounters the water surface, it is reflected, and the reflected echo is synchronously collected by multiple receiving units of the receiving antenna array. The collected signal is then subjected to phase correction and amplitude weighting operations through a digital beamforming receiving network. The data from each receiving unit are coherently superimposed to form a unidirectional synthetic echo signal, effectively suppressing clutter interference from canal bank boundaries or floating objects and improving the echo signal-to-noise ratio. The synthetic echo signal and the local oscillator signal undergo frequency conversion in a mixer to generate a difference frequency signal whose frequency components are proportional to the target distance. After analog-to-digital conversion, the difference frequency signal is processed by a digital signal processing module using a fast Fourier transform to construct a spectral image of the echo energy distribution in the frequency domain. The amplitude peaks in the spectral image are extracted and their corresponding frequency values ​​are located to obtain the main peak frequency of the echo. Based on the peak frequency, combined with the preset sweep period, sweep bandwidth, and speed of light constant, the altitude ranging formula R = (c × f) is used. 峰值 × T 扫频 The air height distance for a single measurement is calculated using (2 × B). Several water level distance measurement processes are executed consecutively within a short period of time, and outlier removal and mean filtering are performed on the air height distances obtained from each measurement. The average value of the calculated multiple measurements is used as the effective air height distance output for the current measurement cycle.

[0021] 102. Calculate the water level data based on the installation height and the distance between the installation height and the above-mentioned height. Specifically, based on the parameter management module, the preset installation height value is read from the equipment's parameter memory. This installation height is measured by installation engineers using a high-precision level during initial installation and written to a designated address in the memory via a configuration program for long-term storage as a calibration benchmark. The difference between the installation height (used as a static reference value) and the real-time measured air distance is calculated. Subtracting the currently measured air distance from the installation height yields the vertical distance between the radar installation location and the water surface. Since the installation height represents the fixed vertical distance of the radar antenna array relative to a known reference point on the channel bottom or bank, while the air distance represents the real-time distance from the radar's transmitting surface to the water surface, the difference constitutes the instantaneous water depth value below the radar, i.e., the current vertical water level height relative to the reference point.

[0022] 103. Switch the antenna array to a wide beam and transmit continuous waves within the elevation angle scanning range, perform vector calculation on the Doppler frequency shift of the water surface echo, and obtain the flow velocity data; Specifically, the digital beamforming control module loads a pre-stored second beamforming parameter matrix into the antenna array control unit. This second beamforming parameter matrix defines the wide-beam excitation mode at a 10° beam angle and its phase control rules in the elevation direction. After loading, based on the installation height parameters written during initial installation and the geometric relationship of the flow velocity measurement illumination area, the horizontal distance from the radar position to the water surface flow velocity observation area is calculated using the conversion formula L≈0.577H. The beam elevation center angle is then calculated as the current center elevation direction of the flow velocity measurement beam. The system performs constant-step scanning of the elevation angle around the central elevation angle, moving upwards and downwards to both sides within a total range of 27°. The scanning step angle is set to 0.1° based on the system resolution. The dwell time for each angle varies from 10 to 50 milliseconds. At each dwell angle, the antenna array transmits a 77 GHz continuous wave towards the water surface and receives its echo signal. The received echo signal is frequency-mixed with the local oscillator signal in a mixer to generate a Doppler intermediate frequency (IF) signal containing information about the water surface flow velocity. The Doppler IF signal is then converted from analog to digital by an ADC and input to a signal processor for spectrum analysis. The dominant frequency component is extracted to calculate the Doppler frequency shift corresponding to the current elevation angle. Based on the known radar carrier frequency and the speed of light constant, the Doppler frequency shift is converted into the radial velocity at that angle. Combined with the cosine value of the elevation angle, vector projection is performed to calculate the true flow velocity, i.e., V. k =f k × c / (2 × f0× cosθ k ). Among them, V k f represents the actual flow velocity at the pitch angle θk. k The pitch angle represents the Doppler shift frequency, c represents the speed of electromagnetic waves in a vacuum (i.e., the speed of light), f0 represents the radar's transmission carrier frequency (77 GHz here), and cosθ k The value is the cosine of the pitch angle. Weights are assigned to the actual flow velocity data at each of the 270 pitch angles obtained from the entire scan. The weight value is positively correlated with the signal-to-noise ratio of the echo signal corresponding to each angle, reflecting the reliability of the data measured at that angle. A weighted average algorithm is then used to synthesize these flow velocity values ​​to obtain representative flow velocity data.

[0023] 104. Calculate the cross-sectional area of ​​the flow passage based on the water level data and the channel cross-sectional geometric parameters, and calculate the cumulative flow data based on the flow velocity data and the cross-sectional area of ​​the flow passage.

[0024] Specifically, the parameter configuration module reads the preset channel cross-section geometric parameters from the internal memory. The geometric parameters include the channel bottom width B, the slope m, and the channel type T. The channel bottom width B represents the horizontal width of the bottom of the channel, the slope m represents the horizontal extension distance of the slope corresponding to each unit of vertical height, and the channel type T is an enumeration type that identifies the channel cross-section as one of the three shapes: trapezoidal, rectangular, or circular. Based on the real-time water level data H provided by the water level measurement module, and combined with the channel type T, the corresponding cross-sectional area calculation strategy is executed: When T is identified as a trapezoidal channel, the slope gradient m is multiplied by the water level H to obtain the slope extension width mH, which is then added to the channel bottom width B and multiplied by the water level H. The calculation formula is A = (B + mH) × H, where A represents the flow cross-sectional area. When T is identified as a rectangular channel, the slope gradient m is considered to be 0, and the channel bottom width B is directly multiplied by the water level H, i.e., A = B × H. When T is identified as a circular pipe, the flow cross-sectional area A corresponding to the current water level is calculated according to the geometric relationship between the water level data H and the preset pipe diameter D, based on the arc area formula. The arc area calculation needs to consider the position of the water level H relative to the pipe radius R = D / 2. The central angle, chord length, and arc height are obtained through geometric inversion, thereby obtaining the effective area A of the partial circle. Based on the cross-sectional area A, and combined with the weighted average flow velocity V provided by the radar flow velocity module, multiplying V by A yields the instantaneous flow rate Q at the current moment, i.e., Q = V × A, where Q is the volume of water passing through the cross-section of the measuring point per unit time, in cubic meters per second. Flow rate sampling is performed at time intervals Δt, and the instantaneous flow rate Q(t) within each sampling period is calculated. i Perform numerical integration, and calculate the formula as V. 总 = Σ[Q(t i ) × Δt], where V 总 Σ represents the cumulative flow, Σ indicates the summation across all time slices, and Δt is the sampling period length. i Let V be the time point of the i-th sampling. The cumulative flow data V... 总 The water level H, cross-sectional area A, and instantaneous flow rate Q are stored in the local memory and reported to the remote monitoring platform in real time through RS485 or 4G communication interface, thereby realizing continuous recording and remote visual monitoring of hydrological data.

[0025] In one specific embodiment, the flow measurement method further includes: A frequency-modulated continuous wave is generated by a radar signal generator and simultaneously fed into multiple transmitting units of the antenna array via a power distribution network. For the water level measurement mode, the phase delay and amplitude weighting coefficient of each transmitting unit are calculated so that each transmitting unit forms a narrow beam pointing vertically downward, and the first beamforming parameters are obtained. The vertical phase gradient is adjusted for the flow velocity measurement mode so that each transmitting unit forms a wide beam and scans within the elevation angle scanning range to obtain the second beamforming parameters; The first beamforming parameter and the second beamforming parameter are respectively loaded into the phase shifter and amplitude controller corresponding to each transmitting unit.

[0026] Specifically, the radar signal source module initiates the FMCW signal synthesis process. The frequency-modulated continuous wave (FMCH) is a linear frequency-modulated signal with a center frequency of 77 GHz and an adjustable bandwidth, employing a sawtooth wave sweep mode. The signal is uniformly distributed via the power distribution network of the RF front-end and then simultaneously fed into multiple transmitting units in the antenna array. Each transmitting unit is connected to a programmable phase shifter and amplitude controller to achieve digital synthesis of the array beam in different spatial directions. For the water level measurement mode, a highly directional and low-blind-zone vertical downbeam is required. Therefore, the beam control unit calculates the required phase delay φ for each transmitting unit based on the array geometry and target pointing angle. 1k and amplitude weighting coefficient α 1k , where φ 1k Let α be the phase offset of the k-th transmitting unit in the water level measurement mode. 1k The excitation amplitude is determined. By constructing phase control weights with equal amplitude and phase or slight windowing, the main lobe of the beam is precisely pointed vertically to the water surface to form a concentrated energy radiation region with an 8° beam angle, resulting in the first beamforming parameter matrix. This matrix contains the control vectors of all transmitting units. To support the wide-angle scanning requirements in the flow velocity measurement mode, the phase gradient of the antenna array is recalculated in the elevation direction to achieve radiation coverage with a 10° beam angle and a 27° scanning range. A set of phase delay parameters φ, which vary with the angle, is set according to the target elevation angle θ scanning sequence. 2k (θ) and magnitude weight α 2k (θ), where φ 2k (θ) represents the phase delay that needs to be applied to the k-th element at a specific pitch angle θ, α 2k (θ) represents its amplitude weighting value. This parameter set is organized into a second beamforming parameter set, corresponding to the beam control sequence within the entire elevation scanning angle domain. The first and second beamforming parameters are written into the phase shifter and amplitude controller corresponding to each transmission channel, respectively. The first beamforming parameter is used for fixed pointing excitation loading during the water level measurement cycle, while the second beamforming parameter is dynamically loaded in a scanning manner during the flow velocity measurement phase. Combined with the time scheduling strategy controlled by the digital signal processing module, the radar array beam can be quickly switched between the two working modes of water level and flow velocity, thereby completing high-precision non-contact measurement.

[0027] In one specific embodiment, the antenna array is configured to transmit frequency-modulated continuous waves vertically downwards with a narrow beam. A fast Fourier transform is performed on the water surface echo difference frequency signal to obtain the air-to-ground distance, including: The water surface echo signal collected by the receiving antenna array is phase-corrected and amplitude-weighted by a digital beamforming receiving network, and the signals from multiple receiving units are coherently combined to obtain the composite echo signal. The synthesized echo signal and the local oscillator signal are mixed in a mixer to obtain a difference frequency signal. The difference frequency signal is then subjected to a fast Fourier transform to detect the spectral peak and extract the peak frequency. The single-measurement altitude distance is calculated based on the peak frequency, speed of light, sweep period, and sweep bandwidth, and the average of multiple single-measurement altitude distances is calculated to obtain the altitude distance.

[0028] Specifically, the system receives echo signals from the antenna array. The water surface echo signal is the signal reflected back after a 77GHz frequency-modulated continuous wave illuminates the water surface. The signals received by each receiving antenna element have phase and amplitude differences due to their different spatial locations. To extract the echo information from the target water surface, a digital beamforming receiving network is used to perform phase correction and amplitude weighting operations on the signals of each receiving unit. This involves applying calculated phase compensation and weighting coefficients to each receiving channel, enabling all signals to be spatially coherently synthesized in the target direction, forming a highly directional synthetic echo signal, thereby effectively suppressing clutter interference from non-target directions. The synthetic echo signal is input into a mixer and frequency-mixed with the reference signal (i.e., the local oscillator signal) output from the local oscillator to generate a difference frequency signal containing target range information. The difference frequency signal is an intermediate frequency modulated signal reflecting the change in distance between the target and the radar; its frequency is proportional to the round-trip time. After analog-to-digital conversion, the difference frequency signal is input into a digital signal processor, and a fast Fourier transform algorithm is used to transform it from the time domain to the frequency domain, obtaining a spectrum. In the frequency spectrum, the frequency corresponding to the main peak is the difference frequency corresponding to the target water surface, denoted as f. 峰值 Based on the ranging principle of linear frequency modulated radar, using the formula R = (c × f 峰值 × T 扫频 ) / (2 × B) Calculate the altitude distance of a single measurement, where R represents the distance from the radar to the water surface, c is the speed of light, and f 峰值 T is the main peak frequency of the spectrum. 扫频 Let B be the frequency sweep cycle and B be the frequency modulation bandwidth. The above process will be repeated several times within each measurement cycle. After filtering out outliers from all the R values ​​obtained from each single measurement, the mean value will be calculated to obtain the air height distance used for water level calculation.

[0029] In one specific embodiment, the single-measurement altitude distance is calculated based on the peak frequency, speed of light, sweep period, and sweep bandwidth, and the average of multiple single-measurement altitude distances is calculated to obtain the altitude distance, including: The product of the peak frequency, speed of light, and sweep period is divided by twice the sweep bandwidth to obtain the single measurement altitude distance. The single-measurement altitude distance is acquired multiple times within a preset time period, and the average value of the multiple single-measurement altitude distances is calculated to obtain the altitude distance.

[0030] Specifically, after performing Fast Fourier Transform (FFT) processing on the water surface echo signal, the main peak frequency is extracted from the spectrum, denoted as f. 峰值 , representing the frequency difference component corresponding to the current distance between the radar and the water surface. Based on the linear frequency modulated radar ranging formula, the air-altitude range calculation module is activated, and f is... 峰值 The propagation speed c of electromagnetic waves in a vacuum and the frequency modulation period T 扫频 Multiplying these three factors yields a product that reflects the physical relationship between echo time delay and frequency offset. Dividing the product by twice the FM bandwidth B, using the formula R = (c × f) 峰值 × T 扫频 The formula ) / (2 × B) calculates the single altitude measurement result at the current moment, where R represents the distance between the radar and the water surface. Within a preset time window, such as 1 second to 10 seconds, multiple distance measurement operations are performed, with the altitude distance calculated independently each time according to the formula. All R values ​​obtained within this time period are summarized, and after removing outlier samples that deviate from the median value by more than a set threshold using a mean filtering algorithm, the remaining valid data are averaged to output a stable altitude distance.

[0031] In one specific embodiment, water level data is calculated based on the installation height and the distance between the installation height and the air gap, including: Read the installation height measured and stored by a level during equipment installation from the system parameter memory; The difference between the installation height and the air height is calculated to obtain the vertical distance from the radar installation position to the water surface, and the vertical distance from the radar installation position to the water surface is used as the water level data.

[0032] Specifically, during the equipment power-on initialization phase, the configuration management module calls the corresponding installation height parameter address in the non-volatile parameter memory to read the vertical height value obtained during equipment installation using a high-precision level. This vertical height value represents the fixed vertical distance between the center point of the radar antenna surface and the channel bottom or a designated reference surface. The installation height value is precisely measured by construction personnel during the system deployment phase and written into the system's internal storage area via configuration software, where it is permanently stored as a static reference parameter for all water level calculations. Within each measurement cycle, the real-time air height distance data R obtained by the radar ranging module is used... 平均 This refers to the vertical distance from the radar antenna's transmission point to the current water surface position. The difference between the real-time air altitude value and the read installation height parameter is calculated, i.e., H = H 安装 R 平均 The calculation process, where H is the current water level, H 安装 For installation height, R 平均 This represents the currently measured air height distance. The difference calculation operation is performed in the digital signal processor with floating-point precision, taking into account the filtering correction coefficients for minor installation deviations in the equipment pitch angle or disturbances caused by water surface echo fluctuations. Multiple air height samples obtained within the same measurement period are processed by moving average before being included in the difference calculation to avoid instantaneous water level jumps caused by individual abnormal echoes. At the same time, the obtained water level H is stored in the local Flash memory and pushed to the upper-level monitoring platform or hydrological data center according to the set data reporting cycle via RS485 or 4G communication modules, realizing remote monitoring and data retention of channel hydrological dynamics.

[0033] In one specific embodiment, the antenna array is switched to a wide beam and a continuous wave is transmitted within the elevation angle scanning range. Vector calculation is performed on the Doppler frequency shift of the water surface echo to obtain flow velocity data, including: After loading the second beamforming parameters, the beam center elevation angle is calculated based on the installation height and the distance of the flow velocity irradiation area. The elevation scan is performed within the scanning range above and below the beam center elevation angle according to the preset step angle. At each pitch angle, the water surface echo signal is received and mixed with the transmitted signal to obtain a Doppler intermediate frequency signal, and the actual flow velocity corresponding to the pitch angle is calculated based on the Doppler intermediate frequency signal. The flow velocity data is obtained by weighted averaging the actual flow velocities corresponding to each pitch angle.

[0034] Specifically, after switching to the flow velocity measurement mode, the beam control module writes the preset second beamforming parameters into the phase shifter and amplitude controller of each transmitting unit, so that the radar waves emitted by the entire antenna array form a wide beam shape in the vertical direction, thereby covering a certain range of elevation angle scanning intervals. Combining the antenna installation height value H stored during the installation phase and the set horizontal projection distance L of the flow velocity illumination area, the beam center elevation angle θ0 = arctan(L / H) is calculated using the arctangent function. That is, the beam tilt angle required from the radar antenna to the center area of ​​the water surface flow velocity measurement, and a scanning angle range Δθ is set above and below the beam center elevation angle θ0 to form a beam from (θ0) The complete pitch scan range is from (θ0 + Δθ). The control system gradually adjusts the beam direction within the above scan range at preset angle steps δθ, adjusting one pitch angle θ at a time. k The direction emitted by the corresponding radar array is θ k The system transmits a continuous wave signal and simultaneously activates the receiving antenna array to collect the echo signal reflected from the water surface in that direction. The transmitted signal and the received echo are mixed in a local mixer to generate a Doppler intermediate frequency (IF) signal, with a frequency f0. k The velocity component V of the fluid surface along the radar line of sight k The relationship between them is: V k = (λ · f k ) / (2 · cosθ k ), where λ is the radar wavelength, f k For pitch angle θ k The received Doppler frequency shift, cosθ k Let λ be the cosine of the angle between the radar wave direction and the direction perpendicular to the water surface. In the formula, λ is a radar system design parameter, and f is... k The main peak frequency is obtained by extracting it from the intermediate frequency signal spectrum using FFT, while cosθ is... k Based on the current beam elevation angle θ k Calculated. Because V k Since it only represents the line-of-sight velocity component in that direction, a cosine correction based on geometric relationships is required at each pitch angle. At all pitch angles θ k After executing the calculation process on (k=1 to N), a set of actual flow velocities V1, V2, ..., V is obtained. n And combined with the gain distribution or weighting function W of the beam direction corresponding to each elevation angle. k Perform weighted average calculation: V 平均 =(Σ(W k · V k )) / ΣW k V 平均 This refers to the final output flow rate data, W.k The beam power weight or signal-to-noise ratio weight is the beam power weight or signal-to-noise ratio weight in the k-th pitch angle direction. The calculation result reflects the fluid velocity in the main energy direction.

[0035] In one specific embodiment, the Doppler intermediate frequency signal is obtained by mixing the received water surface echo signal with the transmitted signal at each pitch angle, and the actual flow velocity corresponding to the pitch angle is calculated based on the Doppler intermediate frequency signal, including: At each elevation angle, the water surface echo signal collected by the receiving antenna array is mixed with the transmitted signal in a mixer to obtain the Doppler intermediate frequency signal; A fast Fourier transform is performed on the Doppler intermediate frequency signal, the spectral peak is detected and the Doppler frequency shift value is extracted, and the Doppler frequency shift value is multiplied by the speed of light and then divided by twice the carrier frequency to obtain the radial flow velocity corresponding to the pitch angle. The radial velocity is divided by the cosine of the pitch angle and then vectorized to obtain the actual velocity corresponding to the pitch angle.

[0036] Specifically, during the elevation scan, the radar array is controlled to sequentially transmit continuous wave signals in various directions, and at each elevation angle θ... k In the corresponding direction, the receiving antenna array is activated to synchronously acquire the echo signal reflected from the water surface. After the echo signal is mixed with the local reference transmitted signal by a mixer, a Doppler intermediate frequency (IF) signal containing velocity information is obtained. A Fast Fourier Transform (FFT) is performed on the Doppler IF signal to extract the peak frequency f with the strongest energy in the spectrum. k This frequency is the current pitch angle θ. k The Doppler frequency shift value in the corresponding direction. Based on the classical Doppler principle, the frequency shift value f... k Converted to radial velocity component V rk The conversion formula is: V rk = (c · f k ) / (2 · f0), where c represents the speed of electromagnetic waves in air, i.e., the speed of light, f0 is the carrier frequency of the radar, and f k The extracted Doppler frequency shift value, with "2" in the denominator representing the factor that doubles the frequency change due to the round-trip propagation path. This is because there is an angle θ between the water flow direction and the radar beam direction. k The obtained V rk This is only the projection of the actual flow velocity along the radar line of sight, therefore it is combined with the elevation angle θ. k Back projection processing is performed, that is, converting the radial velocity into the actual velocity through vector geometry. This is done by dividing by the cosine of the pitch angle, cosθ. k To achieve this, the specific calculation formula is: V k = V rk / cosθ k V kThe current pitch angle θ k The actual flow velocity value corresponding to the direction, cosθ k For θ k The cosine function value obtained reflects the true horizontal velocity component of the flow.

[0037] In one specific embodiment, the flow cross-sectional area is calculated based on the water level data and channel cross-sectional geometric parameters, and the cumulative flow data is calculated based on the flow velocity data and the flow cross-sectional area, including: Read the pre-stored channel cross-section geometric parameters from the system parameter memory. The channel cross-section geometric parameters include the channel bottom width, side slope gradient, and channel type. When the channel type is a trapezoidal channel, the cross-sectional area is obtained by adding the product of the channel bottom width, the slope gradient, and the water level data, and then multiplying the product by the water level data. When the channel type is a rectangular channel, the cross-sectional area is obtained by multiplying the channel bottom width and the water level data. When the channel type is a circular pipe, the cross-sectional area is calculated based on the relationship between the water level data and the pipe diameter. The instantaneous flow rate is obtained by multiplying the flow velocity data by the cross-sectional area of ​​the flow passage, and the instantaneous flow rate is then integrated over time to obtain the cumulative flow rate data.

[0038] Specifically, the processor is invoked to initiate a read instruction to the system parameter memory, loading the channel cross-sectional geometric parameters corresponding to the measurement site. These geometric parameters include the channel bottom width B, the slope gradient n, and the channel type T. The channel bottom width B is defined as the width of the horizontal section at the bottom of the channel. The slope gradient n is defined as the ratio of the slope to the horizontal plane (i.e., the ratio of the horizontal length to the vertical height of the slope). The channel type T indicates which of the three standard cross-sections—rectangular, trapezoidal, or circular—the current channel belongs to. The calculation method for the cross-sectional area A of different cross-sectional shapes is determined based on the current water level data H. If T is a trapezoidal channel, the calculation is performed according to the trapezoidal hydraulic geometry model as follows: A = (B + n·H)·H, where the first term B + n·H represents the water surface width, which is multiplied by the water depth H to obtain the trapezoidal cross-sectional area. If T is a rectangular channel, it simplifies to A = B·H, directly multiplying the channel bottom width by the water level to obtain the rectangular cross-sectional area. If T is a circular pipe, the effective cross-sectional area A under partially filled conditions is solved by combining the arc area formula in the circular geometry model or the lookup table method with the relationship between the pipe diameter D and the water level H. The calculation involves parameters such as the sector angle, arc height, and chord length, which are solved by the lookup table method or embedded algorithm module. The collected real-time flow velocity data V is multiplied by the cross-sectional area A to obtain the instantaneous flow rate Q, i.e., Q = V·A, where V represents the average actual flow velocity of the fluid on the measurement cross-section, and A is the instantaneous cross-sectional area of ​​that cross-section. Perform an integral operation on the instantaneous flow rate Q in the time dimension, multiply the Q value in each sampling period by the corresponding time interval Δt and accumulate them to obtain the cumulative flow rate Σ(Q·Δt).

[0039] In one specific embodiment, the flow velocity data is multiplied by the cross-sectional area of ​​the flow path to obtain the instantaneous flow rate, and the instantaneous flow rate is integrated over time to obtain the cumulative flow rate data, including: The actual flow velocity corresponding to each pitch angle is multiplied by the corresponding cross-sectional area of ​​the flow path and the cosine value of the pitch angle, and then summed. The sum is then divided by the cross-sectional area of ​​the flow path to obtain the average flow velocity of the cross-section. The average flow velocity of the cross-section is multiplied by the cross-sectional area of ​​the flow path to obtain the instantaneous flow rate. Multiple instantaneous flow rates are acquired, and each instantaneous flow rate is multiplied by a preset sampling period and then summed to obtain cumulative flow data.

[0040] Specifically, based on the multi-elevation velocity measurement model, multiple elevation angles θ are obtained from the elevation scan of the antenna array. k and its corresponding actual flow velocity V k V k θ represents the true fluid velocity obtained after Doppler frequency shift calculation in the direction of the k-th pitch angle. k This represents the pitch angle corresponding to that direction. Combined with the cross-sectional area S of the current collector covered in each pitch direction... k Sk It is the geometric projected area derived from the radar beam covering different depths or locations on the channel cross-section, theoretically satisfying ∑S k = S, where S is the total flow area of ​​the entire cross-section. For each direction k, calculate its effective velocity projection along the cross-section direction, i.e., V. k ·cosθ k and compare it with the corresponding sub-section area S k Multiplying the values ​​represents the effective flow contribution per unit area in that direction. Summing over all directions yields ∑(V k ·cosθ k ·S k Divide the total projected flow rate by the total area S to obtain the average flow velocity V of the calculated cross-section. 平均 = ∑(V k ·cosθ k ·S k This allows for the weighted calculation of non-uniform velocity fields. The cross-sectional average velocity V is then calculated. 平均 Multiplying this by the total flow area S directly yields the instantaneous flow rate Q = V. 平均 •S represents the volume of water flowing through the body per unit time measured at the current moment. Continuous sampling is performed within a preset time period, for example, the instantaneous flow rate Q is collected every Δt seconds. n After accumulating N measurements, perform the following integral approximation operation: Σ(Q n The sum of Δt is the cumulative flow rate over the entire measurement period.

[0041] The flow measurement method in the embodiments of the present invention has been described above. The flow measurement device in the embodiments of the present invention is described below. Please refer to [link / reference]. Figure 2 One embodiment of the flow measurement device in this invention includes: Transmitting module 201 is used to configure the antenna array to transmit frequency-modulated continuous waves vertically downward with a narrow beam, and to perform fast Fourier transform on the water surface echo difference frequency signal to obtain the air altitude distance. Calculation module 202 is used to calculate and obtain water level data based on the installation height and the distance between the air gaps. Vector calculation module 203 is used to switch the antenna array to a wide beam and transmit continuous waves within the elevation angle scanning range, and to perform vector calculation on the Doppler frequency shift of the water surface echo to obtain flow velocity data; The flow accumulation module 204 is used to calculate the cross-sectional area of ​​the flow passage based on the water level data and the channel cross-sectional geometric parameters, and to calculate the cumulative flow data based on the flow velocity data and the cross-sectional area of ​​the flow passage.

[0042] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the above-described apparatus, devices, and units can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0043] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0044] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A flow measurement method, characterized in that, include: The antenna array is configured to transmit frequency-modulated continuous waves vertically downwards with a narrow beam. The difference frequency signal of the water surface echo is subjected to fast Fourier transform to obtain the air altitude range. The water level data is obtained by calculating the distance between the installation height and the aforementioned air height; The antenna array is switched to a wide beam and a continuous wave is emitted within the elevation angle scanning range. Vector calculation is performed on the Doppler frequency shift of the water surface echo to obtain the flow velocity data. The cross-sectional area of ​​the flow passage is calculated based on the water level data and the channel cross-sectional geometric parameters, and the cumulative flow rate is calculated based on the flow velocity data and the cross-sectional area of ​​the flow passage.

2. The flow measurement method according to claim 1, characterized in that, The flow measurement method further includes: A frequency-modulated continuous wave is generated by a radar signal generator and simultaneously fed into multiple transmitting units of the antenna array via a power distribution network. For the water level measurement mode, the phase delay and amplitude weighting coefficient of each transmitting unit are calculated so that each transmitting unit forms a narrow beam pointing vertically downward, and the first beamforming parameters are obtained. The vertical phase gradient is adjusted for the flow velocity measurement mode so that each transmitting unit forms a wide beam and scans within the elevation angle scanning range to obtain the second beamforming parameters; The first beamforming parameter and the second beamforming parameter are respectively loaded into the phase shifter and amplitude controller corresponding to each transmitting unit.

3. The flow measurement method according to claim 2, characterized in that, The antenna array is configured to transmit frequency-modulated continuous waves vertically downwards with a narrow beam. A fast Fourier transform is performed on the difference-frequency signal of the water surface echo to obtain the air-to-ground distance, including: The water surface echo signal collected by the receiving antenna array is phase-corrected and amplitude-weighted by a digital beamforming receiving network, and the signals from multiple receiving units are coherently combined to obtain the composite echo signal. The synthesized echo signal and the local oscillator signal are mixed in a mixer to obtain a difference frequency signal. The difference frequency signal is then subjected to a fast Fourier transform to detect the spectral peak and extract the peak frequency. The single-measurement altitude distance is calculated based on the peak frequency, speed of light, sweep period, and sweep bandwidth, and the average of multiple single-measurement altitude distances is calculated to obtain the altitude distance.

4. The flow measurement method according to claim 3, characterized in that, The single-measurement altitude distance is calculated based on the peak frequency, speed of light, sweep period, and sweep bandwidth, and the average of multiple single-measurement altitude distances is calculated to obtain the altitude distance, including: The product of the peak frequency, speed of light, and sweep period is divided by twice the sweep bandwidth to obtain the single measurement altitude distance. The single-measurement altitude distance is acquired multiple times within a preset time period, and the average value of the multiple single-measurement altitude distances is calculated to obtain the altitude distance.

5. The flow measurement method according to claim 4, characterized in that, The water level data is calculated based on the installation height and the distance between the installation height and the air gap, including: Read the installation height measured and stored by a level during equipment installation from the system parameter memory; The difference between the installation height and the air height is calculated to obtain the vertical distance from the radar installation position to the water surface, and the vertical distance from the radar installation position to the water surface is used as the water level data.

6. The flow measurement method according to claim 5, characterized in that, The antenna array is switched to a wide beam and a continuous wave is transmitted within the elevation angle scanning range. Vector calculation is performed on the Doppler frequency shift of the water surface echo to obtain flow velocity data, including: After loading the second beamforming parameters, the beam center elevation angle is calculated based on the installation height and the distance of the flow velocity irradiation area. The elevation scan is performed within the scanning range above and below the beam center elevation angle according to the preset step angle. At each pitch angle, the water surface echo signal is received and mixed with the transmitted signal to obtain a Doppler intermediate frequency signal, and the actual flow velocity corresponding to the pitch angle is calculated based on the Doppler intermediate frequency signal. The flow velocity data is obtained by weighted averaging the actual flow velocities corresponding to each pitch angle.

7. The flow measurement method according to claim 6, characterized in that, At each pitch angle, the received water surface echo signal is mixed with the transmitted signal to obtain a Doppler intermediate frequency signal, and the actual flow velocity corresponding to the pitch angle is calculated based on the Doppler intermediate frequency signal, including: At each elevation angle, the water surface echo signal collected by the receiving antenna array is mixed with the transmitted signal in a mixer to obtain the Doppler intermediate frequency signal; A fast Fourier transform is performed on the Doppler intermediate frequency signal, the spectral peak is detected and the Doppler frequency shift value is extracted, and the Doppler frequency shift value is multiplied by the speed of light and then divided by twice the carrier frequency to obtain the radial flow velocity corresponding to the pitch angle. The radial velocity is divided by the cosine of the pitch angle and then vectorized to obtain the actual velocity corresponding to the pitch angle.

8. The flow measurement method according to claim 7, characterized in that, The cross-sectional area of ​​the flow passage is calculated based on the water level data and the channel cross-sectional geometric parameters, and the cumulative flow rate is calculated based on the flow velocity data and the cross-sectional area of ​​the flow passage, including: Read the pre-stored channel cross-section geometric parameters from the system parameter memory. The channel cross-section geometric parameters include the channel bottom width, side slope gradient, and channel type. When the channel type is a trapezoidal channel, the cross-sectional area is obtained by adding the product of the channel bottom width, the slope gradient, and the water level data, and then multiplying the product by the water level data. When the channel type is a rectangular channel, the cross-sectional area is obtained by multiplying the channel bottom width and the water level data. When the channel type is a circular pipe, the cross-sectional area is calculated based on the relationship between the water level data and the pipe diameter. The instantaneous flow rate is obtained by multiplying the flow velocity data by the cross-sectional area of ​​the flow passage, and the instantaneous flow rate is then integrated over time to obtain the cumulative flow rate data.

9. The flow measurement method according to claim 8, characterized in that, Multiplying the flow velocity data by the cross-sectional area of ​​the flow passage yields the instantaneous flow rate, and integrating the instantaneous flow rate over time yields the cumulative flow rate data, including: The actual flow velocity corresponding to each pitch angle is multiplied by the corresponding cross-sectional area of ​​the flow path and the cosine value of the pitch angle, and then summed. The sum is then divided by the cross-sectional area of ​​the flow path to obtain the average flow velocity of the cross-section. The average flow velocity of the cross-section is multiplied by the cross-sectional area of ​​the flow path to obtain the instantaneous flow rate. Multiple instantaneous flow rates are acquired, and each instantaneous flow rate is multiplied by a preset sampling period and then summed to obtain cumulative flow data.

10. A flow measurement device, characterized in that, For performing the flow measurement method as described in any one of claims 1-9, comprising: The transmitting module is used to configure the antenna array to transmit frequency-modulated continuous waves vertically downwards in a narrow beam, and to perform a fast Fourier transform on the water surface echo difference frequency signal to obtain the air altitude distance. The calculation module is used to calculate the water level data based on the installation height and the distance between the installation height and the air height. The vector solution module is used to switch the antenna array to a wide beam and transmit continuous waves within the elevation angle scanning range, and to perform vector solution on the Doppler frequency shift of the water surface echo to obtain flow velocity data; The flow accumulation module is used to calculate the cross-sectional area of ​​the flow passage based on the water level data and the channel cross-sectional geometric parameters, and to calculate the cumulative flow data based on the flow velocity data and the cross-sectional area of ​​the flow passage.