Hall effect sensor-based flow monitoring device and method

Abstract

Hall Effect sensor-based flow monitoring device and method for monitoring and assessment of coastal and river velocities, particularly, for measuring velocities and directions of near-bed currents and water levels. The device provides instantaneous measurements under real-world conditions and is equipped with communication capabilities for near real-time data transfer. Validation was performed in real world under steady and unsteady flow conditions. Within the device measurement range, a root-mean-square error (RMSE) below 0.1 m / s for time-averaged flow measurements was shown.

Description

[0001]Hall Effect Sensor-Based Flow Monitoring Device and Method Technical field The invention belongs to the field of flow monitoring device and method for monitoring and assessment of coastal and river velocities, particularly, for measuring velocities and directions of near-bed currents and water levels. Background art Measuring flow velocity in the field conditions plays a significant role in many scientific and industry applications, for example, in hydrological studies, sediment transport investigations, the determination of aquatic habitats in rivers, estuaries, and coastal waters, and flood warning systems. Near-bed velocity estimates are key metrics in sediment transport and river habitat studies. Popular in situ field measurement devices for flow velocity are propeller velocity flowmeters, acoustic Doppler velocimeters (ADVs), and acoustic Doppler current profilers (ADCPs). There have been efforts to develop remote-sensing methods, from the use of radars for estimating surface velocities to satellite imagery for river discharge estimation. However, such methods have either good temporal resolution or good spatial resolution, not both. The acoustic measuring devices (ADV and ADCP) have a good temporal resolution of 50Hz, whereas the spatial resolution depends on the number of devices. Due to the high cost, in general, not many of these devices are used together, especially over long periods of time and in extreme environments where the chances of recovering the instruments go down. Satellite models, for example, Planet Labs satelite SkySat, have good spatial resolution (about 0.5m ). However, the temporal resolution of SkySat is 4–5 days. Further problems arise when measuring near-seabed or near-surface velocity, as local wake features affect the measurements near the bed and air entertainment, secondary currents, and velocity tip effect influence near-surface measurements. In addition, remote-sensing methods are restricted to estimating water surface velocity, it is shown that to obtain reliable average velocities in a flow affected by natural turbulence and instrument noise, a sampling duration of 90 and 150s is found to be sufficient for ADV and ADCP, respectively. For long-term behavior and large-scale spectral analysis, when many sources of flow variability are present, a longer sampling duration is needed. This means that for reliable estimation of near-surface velocities, ADV and ADCP temporal resolution also decreases. Despite the challenges, for many applications, continuous instantaneous flow measurements are extremely important. Sediment motion depends on momentary flow features, flow type characterization, and feature detection in flows (e.g., ship detection) and requires high temporal resolution, studying stresses on submerged structural elements benefit from long-term continuous monitoring. Therefore, there is a need for cost-effective methods to provide continuous, reliable, and distributed data on the near- bed velocities. Motivated by the changing hydrological conditions imposed by the climate crisis and the need for near-bed continuous measurements, a method for in situ observations of flow velocity was proposed by Ristolainen et al. in US10215601. A bimodal flow sensing device using accelerometers was designed and used to automatically classify river hydromorphology, and new methods for near-bed velocity measurement were developed. Unfortunately, the device had several drawbacks: it had a limited flow velocity range, it could only estimate the average mean flow velocity, and it was not capable of real-time data output. The lower end of the measurement range was too high for many near-bed applications, allowing only measurements in constantly fast flows. Additionally, no measurements were possible in wave-driven coastal applications, with regularly changing flow direction and only local storage was possible, allowing data processing and output only after the recovery of the devices. Disclosure of the invention To address these and other limitations, a novel design of the flow monitoring device, from now on called Hydromast, comprising a Hall effect sensor together with a cloud- based communication setup is designed, granting near real-time (latency couple of seconds) data transfer and observations by the user. Hydromast uses magnetic field sensing at the base to instantaneously detect the exact tilt and direction of the sensing element. This allows simpler and faster estimation of flow velocity and additionally allows to measure the direction of the flow. The length of the sensing element is adjustable, allowing for varying the velocity measurement range for each application. Moreover, the new design allows for instantaneous flow estimates and opens up a new application range of unsteady flow measurements in rapidly changing environments. The device has been validated in various flow fields together with a baseline measurement for determining the behavior, robustness, and durability in real-life environments and demonstrating possible applications. This leads to an accurate, robust, and cost-efficient way to measure continuous near-bed current velocity. Brief description of illustrations Fig 1 is the overview of the Hydromast, (a) Hydromast exploded view. (b) Assembled hydromast with axes x , y , and z , mast tilt angle θ and direction , as well as mast length L and diameter D. Fig.2 illustrates the schematic response of lightly damped cylinder in crossflow, known in the art. Fig.3 is a communication framework overview. Fig 4. Hydromast tilt angle calibration. Output magnitude ^^^^^^^^for varying tilt angle ^^with the linear fit. Measurements shown for 8 different directions from ^^ = 0 to ^^ =315. Fig.5. Setup for the in-flow velocity calibration in a river. (a) Side view and (b) front view with the ADV and Hydromast (HM300) placement. (c) Assembled setup in the field. Fig.6. Velocity calibrations of 200- and 300-mm masts. (a) Dominant frequency-based velocity Vf calibration. (b) Tilt-based velocity Vθ calibration. Calibration fit shown as a solid line, theoretical velocity limits Vf min and Vf max are shown as a dotted line. Fig 7 Setup for steady flow validation tests in a river. (a) Side view and (b) front view with the ADV and Hydromast (HM300 and HM200) placement. (c) Assembled setup in the field. Fig.8. Steady flow short-term validation data for frequency-based velocity estimate Vf . (a) 300-mm mast and (b) 200-mm mast. Filled symbols denote the data in range and empty symbols out of range. SD ranges from ADV measurements are shaded in gray. The blue box indicates the theoretical measurement range. Fig.9. Steady flow short-term validation data for tilt-based velocity estimate Vθ (a) 300- mm mast and (b) 200-mm mast. Filled symbols denote the data in range and empty symbols out of range. SD ranges from ADV measurements are shaded in gray. The blue box indicates the theoretical measurement range. Fig.10. Flow direction ϕ¯ validation data. The direction measurements were done in varying flow conditions slow (up to 0.22 m / s), medium (up to 0.61 m / s), and fast (up to 0.85 m / s). Fig.11. Steady flow long-term validation data in Vääna river. Results averaged over 30 min. (a) Frequency and tilt-based velocity estimates. (b) Flow direction . (c) Water level height. Fig.12. Setup for unsteady flow validation tests in the sea. (a) Side view and (b) front view with the ADV and Hydromast placement. (c) Assembled setup in the field. Fig.13. Unsteady flow tilt-based velocity validation test Pikakari beach, 4th May 2023, 300-mm mast. Fig.14. Unsteady flow validation tests, Vääna beach, 18th May 2023. (a) Tilt-based velocity, 300-mm mast. (b) Tilt-based velocity, 200-mm mast. (c) Direction ϕ, 200- and 300-mm mast. Examples of carrying out the invention The Hydromast is inspired by the neuromast, a major unit of functionality of the biological lateral line. A neuromast, being a mechanoreceptive organ of fish, is responsible for the sensing of mechanical changes in the surrounding flow field. The Hydromast consists of (comprises) a rigid mast that is fixed to a base with a flexible membrane, thus resembling an upscaled version of a neuromast. The bulk flow velocity over the mast generates vortex-induced vibrations (VIVs) of the mast which dominate over the random forcing due to turbulent flow conditions. Known devices comprise mast and the mast motion is recorded with a micromechanical inertial measuring unit (IMU). The invention comprises 3-D Hall effect sensor, such as TLV493D-A1B6 by Infineon Technologies AG to track the mast movement. The Hall effect sensor, located in the base, detects the strength of the magnetic field from a magnet, such as 5×5 mm neodymium cylindrical magnet installed at the base of the mast inside the flexible membrane. A main benefit of magnetic field sensing is the instantaneous position estimation of the mast for instantaneous tilt angle and direction measurements. Also, the contactless sensing of magnetic fields improves the robustness of the device, as no cables are connected to and affect the vibrating mast. This also simplifies and reduces the cost of manufacturing. Similarly to known art, the device can be equipped with an external IMU, such as MinIMU-9 by Pololu Corporation, to detect the installation angle and device base movements in unsupervised installations onto sea bed. The device comprises a base, e.g., a CNC-machined polyoxymethylene (POM) base, a flexible membrane, and a mast. Preferably, the mast is a hollow polycarbonate (PC) tube, closed at both ends and mounted to a flexible membrane, made of, e.g., silicone, e.g., Elite Double 22, by Zhermak SpA. The air inside the mast makes it positively buoyant and a higher natural frequency fN compared to a water-filled mast. The air-filled mast is more sensitive to the flow and is therefore the preferred setup. The mast is covered with a thin layer of copper (e.g., around 0.06mm) to minimize biofouling during longer deployment periods. The standard diameter of the mast D is around 15mm , but the dimensions can easily be altered for specific applications. The length of the mast L can be varied depending on the needed measurement range. A housing of the base incorporates PCBs of the microcontroller, such as Adafruit Feather with Atmel ATSAMD21 Cortex M0 processor, power, serial communication, and pressure sensor. An absolute pressure sensor, such as 86-030A-R by TE Connectivity records the water height with the pressure port integrated into the POM casing (with a range of 0–2 bar). The device can be connected directly over an RS485 serial connection to a PC or to a communication module with a raw data sampling rate of 50Hz . The power consumption of the device is approximately 0.15W at 5V supply voltage. The design of the device is shown in Fig.1(a). The Hydromast measures the mast location in the x -, y -, and z -direction using magnetic field, with Hall sensor outputs X , Y , and Z (in mT) accordingly. The coordinate system of the mast is shown in Fig.1(b). The magnitude is linearly correlated to the tilt angle θ of the device, whereas the components X and Y correlate to the mast location in the xy -plane and indicate the direction of the flow, noted as ^⃐^ . Two different methods of flow velocity estimation can be introduced: 1) velocity estimate Vf based on the dominant frequencies fd of the mast vibration (time- averaged estimate) and 2) velocity estimate Vθ based on the tilt θ of the mast (instantaneous estimate). Fluid-body forces govern the interactions between the mast due to VIV. Each Hydromast has its own natural frequency ^^^^, that is the frequency the mast oscillates with when disturbed and no forcing (i.e., flow) is present. When a cylindrical rod is put in a cross- flow, it generates vortices with a vortex shedding frequency ^^0. The first velocity estimation method of the Hydromast is based on the vibrations of the elastically supported rigid mast as a VIV resonator. In known device, the design of the device was tuned so that the lightly damped cylinder would oscillate with frequency ^^ as close as possible to the vortex shedding frequency ^^0. It was shown that the time-averaged velocity can be estimated using the mean frequency spectral amplitude after taking the Fast Fourier Transform (FFT) of the mast vibrations. When the cylinder vortex sheddingfrequency is close to the natural frequency ^^0 ≈ ^^^^, an important lock-in phenomenonoccurs: ^^0 / ^^^^ = 1. In such cases, the shedding becomes controlled by the naturalfrequency, even if small fluctuations in the flow velocity occur. This and other resonance points of a lightly damped cylinder are related to the bulk flow by reduced velocity ^^ is the velocity of the bulk flow and ^^ the diameter of the cylinder. For frequency based velocity estimate ^^^^, a relation based on the Strouhalnumber can be introduced, ^^^^ = ^^0^^ / ^^. For the Hydromast, the relation betweendominant frequency ^^^^(^^^^^^^^) and flow speed can be expressed as where ^^0is a constant taking into account the end-effects (of the mast tip) and other artifacts of the specific device setup. For a stationary smooth circular cylinder for Reynolds numbers ranging from 103to 105, the Strouhal number of vortex shedding is^^^^ ≈ 0.2. Using ^^^^ = 0.2 reduces Equation 2 to , where only ^^0needs to be empirically determined. In known device, a 100 mm long neutrally buoyant mast was used, which provided a working range from 0.5 m / s to 1.4 m / s. The invented device has extend working range, especially at the lower limit. This is achieved by choosing the mast with a correct natural frequency, based on the needed measurement range. Response to the cross-flow of a lightly damped circular cylinder is known. If a cylinder is free to vibrate in any direction perpendicular to its axis, many modes of vortex shedding can occur. The most important excitation occurs from resonance when vibration frequency ^^ becomes equal to natural vortex frequency ^^^^, where the vibration amplitude drastically increases and lock-in atthe high amplitude vibrations is observed. This response mode starts around ^^ / ^^^^ ≈ 1and can at most last down to ^^ / ^^^^ = 1 / 3, in the range of reduced velocity of 5 < ^^^^ <15, as schematically shown in Fig.2. This is also the range where the Hydromast vibrations occur and flow velocity can thus be determined, defining the measurement range for the Hydromast. Minimum and maximum velocities are found as ^^^^^^^^^^ = 5^^^^^^ , (3)and ^^^^^^^^^^ = 15^^^^^^ , (4)where ^^^^is the natural frequency in water. For the second velocity estimate, ^^^^, the exact position of the mast in time is determined using the Hall effect sensor outputs. This allows measuring tilt angle ^^, nearly instantaneous flow speed ^^^^as a function of ^^, and flow direction ^⃐^ . The tilt angle is assumed to be in a linear correlation with the Hall sensor measurements, and can becalculated as ^^ = ^^1^^^^^^^^ + ^^2, where ^^1 and ^^2 are empirically detected calibrationconstants. Mast tilt angle ^^ is linearly dependent on the magnitude of the magnetic field and therefore velocity is correlated to ^^^^^^^^as ^^^^ = ^^1^^^^^^^^ + ^^2, (5)where constants ^^1and ^^2are found through calibration. Magnitude itself is used here, instead of ^^ to avoid introducing unnecessary extra uncertainty, as ^^ itself is also determined using calibration fit. It is important to note that this instantaneous velocity measurement based on mast tilt ^^^^is independent from the frequency-based measurement ^^^^and can therefore be used as separate measurement quantity. The flow direction ^⃐^ can be found directly using Hall effect sensor outputs ^^ and ^^ asinstantaneous mast direction ^^ = atan2(^^, −^^) which represents the mast location. Tofind the flow direction, an average over several vibrations must be calculated, taking the median value over some time, denoted with ^⃐^ . In addition to flow measurements, the Hydromast can also be used to measure the water level changes. The device is equipped with a pressure sensor enabling continuous measurement of the water level above. Communications The Hydromast further comprises communication capabilities, enabling near real-time flow monitoring and device failure detection. These enhancements have expanded the range of potential applications for the device. To achieve this, a sensor hub based on Raspberry Pi3 is utilized (Beaglebone and other ARM-based single-board computers can be used). Fig.3 shows an overview of the communication framework. The sensor hub stores data locally and transmits it to a cloud storage, such as Amazon Cloud IoT Core using suitable protocol, such as MQTT protocol. In addition, the sensor hub can receive configuration updates from MQTT, specifically the connected mast types and calibration constants. Infrastructure as code (IaC), specifically AWS Cloud Development Kit (CDK), is employed for configuring and managing AWS services, which allows consistent configurations and stronger security. The source code for both self-developed components and IaC is maintained in GIT repositories. Python 3.9 and ReactJS are used for programming the self-developed components, including the web interface. The sensor hubs operate on self-developed application in Docker container running on BalenaOS, and their management is facilitated through BalenaCloud servers. For communication with the Amazon Cloud, various options are available, including GSM network, LoRaWAN radio connection, and Ethernet communication. The proposed networking framework makes the Hydromast deployment both secure and scalable but also efficiently manageable from the sensors fleet’s point of view. Calibration and characterization To demonstrate the behavior and characteristics of the device, characterisation was first performed in lab, after which the field tests were done for calibrating the device. Natural frequencies and measurement range For simple measurement range estimation, the mast’s natural frequency dependence on the length was characterized. Natural frequencies in water and in air for masts with varying length and mass were measured. The relation between ^^ and ^^^^in water wasrepresented by a power fit ^^^^ ∼ ^^^^, where ^^ is a constant, whereas the ratio of natural frequencies was found to be ^^^^^^^^^^ / ^^^^^^^^^^^^^^≈ 1.4. The natural frequencies and corresponding sensor measurement limits ^^^^^^^^^^ and ^^^^^^^^^^ are shown in Table I. Using these estimated ranges, the mast length can be chosen based on the measurement range needed in each specific application. For an extended measurement range, a setup with multiple Hydromasts can also be used, so that depending on the flow velocity, data from correct device is acquired. It was chosen to continue with a positively buoyant mast due to its higher natural frequencies and faster response to the flow changes, to better capture unsteady flow phenomena. It must be noted that the tension restraint force to counteract buoyancy is larger for longer masts (due to larger volume) which can also change the performance characteristics. For validation purposes, two masts were chosen: HM300 with ^^=300 mm and HM200 with ^^=200 mm length, both highlighted in Table 1. These two masts together cover a range from ^^= 0.1 to 0.7 ^^ / ^^ being sufficient for many applications and they also have a wide enough range overlap to make comparisons. Table I Characteristics of Hydromasts based on mast length Mast ^^ mass ^^ Buoyancy ^^^^water ^^^^air ^^^^^^^^^^ ^^^^^^^^^^ [mm] [g] [Hz] [Hz] [m / s] [m / s] HM50 50 9.4 positive 17.3 25.0 1.30 3.90 HM100 100 13.1 positive 7.5 12.2 0.56 1.69 HM100NB* 100 20.6 neutral 6.9 9.1 0.52 1.55 HM150 150 21.9 positive 4.9 6.5 0.37 1.10 HM150NB* 150 30.3 neutral 3.7 5.0 0.27 0.82 Mast ^^ mass ^^ Buoyancy ^^^^water ^^^^air ^^^^^^^^^^ ^^^^^^^^^^ [mm] [g] [Hz] [Hz] [m / s] [m / s] HM200 200 27.5 positive 3.1 4.2 0.23 0.69 HM300 300 39.4 positive 1.7 2.2 0.13 0.39 NB denotes neutrally buoyant mast Tilt angle calibration Tilt angle θ was expected to be linearly correlated to the Hall sensor’s output magnitude ^^^^^^^^. A table-top calibration was performed, in order to determine the calibrationcoefficients. The mast was tilted at 11 different angles from 0 < ^^ < 30degree in 8different directions with 45 degree increments. The mast tilt was recorded using a Go- Pro camera and the tilt angle was calculated from the image. The angle showed a very good linear correlation with the output magnitude ^^^^^^^^, as shown in Fig.4. The calibration constants were found to be ^^1=1.2 and ^^2=1.13, with a coefficient of determination ^^2of 0.98. In-flow Velocity Calibration The Hydromast velocity calibrations need to be determined in real flow conditions, where the turbulence levels, velocity profile and set-up are similar to the planned field applications. All calibrations characterization were performed in a natural river flow. The calibrations for flow velocity were conducted in Keila river in Estonia (latitude 59.394537 N, longitude 24.294915 E) with average water level of 102 cm measured at Keila river hydrological station. Hydromast was calibrated against ADV measurements (Vectrino Profiler, Nortek, Norway) in real-world conditions. ADV was chosen as reference because it is commercially available standard device for this type of flow measurements. An overview of the calibration setup is shown in Fig.5. One Hydromast was deployed together with an ADV for reference measurements. Samples with a duration of 60 seconds were taken at 47 locations for HM300 and 29 locations for HM200. The Hydromast and ADV measurements were synchronized by using the sync signal from the ADV to trigger the recording of the Hydromast data logger (based on a Raspberry Pi 3, Raspberry Pi Foundation in association with Broadcom). For all calibration and steady flow experiments, the Hydromast data acquisition rate was 50 Hz. When calculating ^^^^, no pre-processing of the data was done, the average velocity estimate was based on the frequency spectrum of the raw data over the duration of the sample. For calibration, 60 s long samples were first recorded and by looking at the convergence it was determined that at least 20 s sample is needed for an accurate dominant frequency estimate. Based on this, the calibration and validation sample length was chosen to be 30 s. Similarly, the tilt based velocity estimates, ^^^^, were first done based on raw data. As the interest lied in the time-averaged velocities, and average ^^^^was calculated over the duration of the sample using In the calibration as well as steady flow validation experiments, the ADV data acquisition rate was 25 Hz and the ADV data processing was kept minimal. All steady flow experiments were done in real conditions and close to the surface. Hence, to reduce the noise in the averages due different natural and device caused phenomenon, the median ADV velocity was also calculated over the duration of the 30 s sample. Fig.6(a) shows the calibration data for HM300 and HM200 together with the calibration curves for the dominant frequency-based velocity estimate ^^^^. A linear fit with constant slope ^^ / ^^^^ and calibration constant ^^0is a good approximation and describes well therelation between flow velocity and mast vibration, with ^^2 = 0.87 for HM300 and ^^2 =0.96 for HM200. For calibration, all data was used, where a clear energy peak in the frequency spectrum could be determined. For HM300, peaks were detected for velocities from 0.15 to 0.50 m / s and for HM200 the range was from 0.27 to 0.70 m / s. These ranges agree well with the theoretical estimates from Table I, according to which HM300 should work from 0.13 to 0.39 m / s and HM200 from 0.23 to 0.69 m / s. These calibrations support the theoretical assumptions. This calibration shows that dominant frequency can be used for flow velocity estimation and also, if needed, several devices with different ranges can be used for extending measurement range. Another method of determining velocity is using the tilt angle ^^. Calibration data and linear fits for this method with both Hydromasts are shown in Fig.6b. Here, all calibration points are shown (averaged over 30 seconds). Both HM300 and HM200 have a linear dependence on the magnitude ^^^^^^^^, with ^^2=0.96 for HM300 and ^^2=0.96 for HM200. The lowest speeds, at which the velocity can be measured, are 0.15 and 0.22 m / s for HM300 and HM200 respectively, being similar to the lowest limit where ^^^^can be used. HM200 has a higher slope, making it more sensitive to velocity changes, whereas HM300 has a slightly lower sensitivity. The tension restraint force to counteract buoyancy is almost double for HM300 mast compared to HM200 and this seems to make the longer mast HM300 less sensitive to tilt due to flow velocity. This lower sensitivity constitutes a close to a five times bigger measurement range for the HM300, with new range spanning from 0.15 m / s up to nearly 1 m / s. This is a large increase in range of the velocity measurement for HM300 compared to the working range for ^^^^(which was up to 0.39 m / s), expanding the applicability of the Hydromast significantly. Hence, the tilt provides an accurate estimate for flow velocity with extra benefit of having a wider measurement range compared to the frequency based estimate for HM300. It can be useful to check with ^^^^the validity of the ^^^^calibration, if devices with new membranes are used. To have independent measurements with the Hydromast, it is important for the device to detect when the measurements are in the working range, and recognize and remove outputs when the Hydromast is out of range providing unreliable data. For ^^^^this ’out of range’ criterion is defined by setting a minimum limit for spectral amplitude level at dominant frequency, so that only distinct high energy peaks are detected. For the Hydromast analysis, two dominant frequency peaks are detected in the spectrum (due to the 8-shaped movement of the mast) and the second one, at higher frequency, representing the cross-flow vibrations, is chosen to be the estimate. This criterion depends on the length of the Hydromast and is determined based on the calibration data. For tilt angle based estimate ^^^^the ’out of range’ criterion is simply the minimum and maximum values for the magnitude ^^^^^^^^, also determined based on the calibration results. Validation The validation of the Hydromast velocity estimations was performed in three stages. First, validation was performed in steady flow conditions in a river, with many 30 s measurements. In the second stage, two devices were installed for a long period in steady flow in a river, to show long-term data and validate communication capabilities. This flow is steady in short-term but has variations over longer time. Finally, the validation was performed in unsteady flow conditions on the coastline to demonstrate and validate the capability of the Hydromast measuring unsteady flows. Steady flow, short-term tests The short-term validation tests were performed on the same site as used for calibration but at different flow conditions. Measurements were taken in many locations in the river to show the performance of the device with the same setup at many different flow speeds. Measurement points were chosen to take into account the working ranges of the Hydromasts and steady flow conditions. A setup with two Hydromasts, HM300 and HM200, together with the ADV (Vectrino Profiler) was assembled as shown in Fig.7. The validation was performed at the same location as the calibration experiments, with a higher water level (112 cm measured at Keila water level station) which allowed finding locations with a wide range of flow velocities. A total of 139 samples were collected for velocities from 0.01 to 1.05 m / s. The results of the velocity estimations based on the mast vibrations are shown in Fig.8(a) and (b) for HM300 and HM200 respectively. ADV measurement serves as our reference velocity. It must be noted that also these measurements have uncertainty and to visualize that, the ADV measurements are shown with standard deviation (SD) (shaded in grey), which can be considered as the uncertainty of the reference measurement. Points, which according to ADV have high turbulence intensity (TI) levels, above 40%, are indicated with pink in the figures. Comparison of the ^^^^from the longer HM300 with ADV is shown in Fig.8(a). Hydromast data agrees well with the reference ADV, having root-mean-square-error (RMSE) of 0.065 m / s and all velocities detected lay within the estimated measurement range, between ^^^^^^^^^^ and ^^^^^^^^^^, indicated as a shaded box in the figure. In this case the majority of the data detected lies within the theoretical measurement range, supporting the theoretical model. The used criteria of minimum energy level at dominant frequency works well for peak detection, only showing data that is within the theoretical range. Turbulent measurements have a slightly higher variation but overall there is also a good agreement to the reference measurement, showing that no significant change in data quality is introduced. In Fig.8(b) the Hydromast HM200 data is shown for ^^^^. The measurements agree well with the ADV within the estimated measurement range. Above 0.6 m / s dominant frequencies are still detected but seem to drift away from the reference value. Thischange is probably due to a mode shift in vibration occurring near ^^^^ = 15. It was seenthat above this value also tilt does not change anymore, the vibration is somewhat altered and does not represent velocity changes well, even though peaks in the energy spectrum are still present. As there was no good indicator found in the spectra to filter the ’out of range’ data, ^^^^could be used as an indicator of the velocity range, so that if ^^^^is out of its measurement range, no output of ^^^^is provided. Points with this criteria applied are indicated in Fig.8(b) as empty symbols. For all the data, the RMSE value is 0.113 m / s, whereas the data with ^^^^based criteria (filled symbols) has RMSE 0.03 m / s. Alternatively, an empirical calibration fit could be used on the data, which follows the higher end frequencies better and accounts for that mode change. But with this approach there is the downside that each membrane needs an extended calibration in similar flow conditions as the application. Tilt based velocities from HM300 are shown in Fig.9(a). Below 0.15 m / s, which is the lower theoretical measurement limit, the measurements have a constant value and are not usable (empty symbols indicate ’out of range’ data). There is an agreement between ADV and Hydromast from 0.15 m / s up to even 1.0 m / s, with RMSE of 0.047 m / s excluding turbulent and out of range points (RMSE is 0.093 m / s including all points). The measurement range is higher than the one achieved in calibration, but seems that the lower sensitivity to flow velocity allows much wider measurement range. This demonstrates that the HM300 can be used on its own for a wide range of velocity measurements from 0.1 to 1.0 m / s, compared to ^^^^measurement range being only one third of it. Only some of the high turbulence data at higher velocities is not following the trend, therefore care needs to be taken at very turbulent conditions at high flow speeds (higher than ^^^^range). Fig.9(b) shows results for tilt based ^^^^for HM200. At low velocities the ’out of range’ data is again constant as for the other mast (hollow symbols). Above that there is an excelent agreement between ADV and Hydromast measurements between 0.3 m / s and 0.7 m / s, where in-range data is marked with filled symbols and having RMSE of 0.03 m / s. Above that the HM200 has reached its maximum tilt angle and does not capture flow velocities above 0.7 m / s. Out of range data based on magnitude limits is shown with empty symbols and it can be seen that this criterion works well for these velocities, filtering out data which does not represent correct velocities. For HM200, the working range of ^^^^is the same as the theoretical range of ^^^^in Table I. Overall, both velocity estimates agree well with the reference measurements. Some of the high turbulent data do not follow general trends, but there seems not to be any systematic impact. In high turbulence conditions and high speeds the data has lower accuracy and could overestimate the flow speed, whereas at lower speeds high turbulence intensity does not seem to affect the results. A set of measurements were also performed to evaluate the flow direction. For direction, no calibration is needed, as the direction ^⃐^ can be calculated directly from the Hall sensor output. For this, the full experimental setup was rotated by 45 degree increments and measurements from Hydromast and ADV were compared. This was done with both devices, at several flow speeds, to test the sensitivity at slow, medium and high velocities. The measured angles compared with the ADV reference are shown in Fig.10. Both Hydromasts show a very good direction estimate, having RMSE of 3.46 °. The variaton is bigger in places where also ADV had higher RMS, showing that there was higher variability in flow, resulting in less reliable results. Steady flow, long-term tests A long-term river test was performed in order to verify the Hydromast durability and performance, as well as demonstrate the near real-time flow monitoring. Two devices were deployed, in the same configuration as shown in Fig.7. Validation measurements were taken with an ADV (Vectrino Profiler, Nortek AS, Norway) every second day over a two week testing period. The validation test was carried out in Vääna river, Estonia (latitude:59.292888 N, longitude 24.739287 E). In this experimental setup, the devices were streaming data online. The two Hydromasts were connected to a Raspberry Pi 3 (Raspberry Pi Foundation in association with Broadcom) microcomputer running Balena OS. The device was battery and solar panel powered over the whole testing period. The live data stream monitoring over GSM network allowed to evaluate the Hydromast performance as well as detect faults in the measurements. This allowed near real-time monitoring (about 3 s latency) of river flow velocity, water level and direction. The average velocities throughout the two-week tests for both HM200 and HM300 are shown in Fig.11(a). The frequency based velocity ^^^^was estimated for 30s intervals and averaged over 30 minute periods. The tilt based ^^^^was calculated as instantaneous velocity and averaged over 30-minute periods. These tests were ran during spring entering into the dry season, hence, the river water flow velocity decreases in time. Both ^^^^and ^^^^show a steady decrease in flow velocity from 0.37 to 0.2 m / s and agree well with the ADV reference measurements taken. For tilt based ^^^^from HM300, higher variations in speed are captured compared to ^^^^. For higher speeds during first days ^^^^seems to overestimate compared to the reference velocities, but both measurements are within the ADV standard deviation range. After 4th of April, where speeds are lower, the agreement with ADV reference measurements becomes very good for both of the velocity estimates. As for HM200, ^^^^and ^^^^measure continuously during the first days and agree very well with each other and with reference ADV measurements. After 4th April 2023 flow velocity started to fall below the measurement range of the HM200 and it does not give an accurate estimate anymore. For ^^^^, ^^^^^^^^goes below minimum limit defined earlier (data marked as light grey) and for ^^^^, fewer high energy peaks are detected. In addition, flow direction was estimated for the same experiments, and the results are shown together with the ADV direction in Fig.11(b). As there was no specific device orientation reference taken at the test site, comparison with ADV was made using the first measurement point. Based on that, a constant offset of 5 ° was removed from the Hydromast data. In Fig.11(c) the depth estimates using the Hydromast are shown. Tallinn-Harku weather station data were used as the atmospheric pressure reference and manual measurements were taken for comparison during ADV measurements. Both Hydromasts behave similarly well and agree with the measurement points, all estimates varying within 10 cm range (HM200 does not follow the trend during the last two days and this is due to a failure of the pressure sensor, which was determined after the tests). Unsteady flow Several tests were conducted in the sea, near the coast, to validate the behavior of the Hydromast in unsteady waves with varying flow direction and magnitude. Measurements were done for 10 minute time periods, in order to allow long enough data sets for spectral analysis with acquisition rate of 50 Hz. A commercial ADV (Vector, Nortek AS, Norway) was used as the reference measurement device, with acquisition rate of 8 Hz. Two Hydromasts, HM200 and HM300, together with the ADV probe in between were installed on a solid frame and immersed in sea on a sandy flat surface, at about 0.9 m depth. The experimental setup of this test is shown in Fig.12. To validate the unsteady velocity estimations, measurements were taken simultaneously for the two Hydromasts and ADV. The experiments were done on two days: on 4th May 2023 in Pikakari beach, Estonia (lat:59°28’26.2"N long:24°43’27.4"E) and on 18th May 2023 at Vääna beach, Estonia (lat:59°25’29.0"N long: 24°20’19.1"E). Locations and days were chosen to test devices at different flow conditions. For both, the Hydromast and the ADV, the first velocity estimations were done on raw data. The resulting velocity estimations were then passed through a lowpass filter with cutoff frequency 2 Hz for consistency and better comparison. On the 4th of May, the conditions were very calm, the maximum velocity reached was 0.3 m / s. These velocities were below HM200 measurement range, therefore only HM300 data is analysed and shown. Figure 13 shows 5 minutes of the measurements of ADV and HM300. It can be seen that the Hydromast shows similar behavior in velocity magnitude as the reference ADV. It can clearly be seen that HM300 follows nicely the same trend as the reference measurement for higher flow speeds, demonstrating the capability of the Hydromast to estimate instantaneous flow velocities in unsteady flow. The unsteady measurements on 18th May 2023 are shown in Fig 14(a) and (b), for HM300 and HM200, respectively. In this case the velocity was within the measurement range for both devices. HM300 shows a very good correlation throughout the data, following all the ADV peaks closely, especially well seen at the zoom-in. HM200 in Fig.14(b) shows agreement with ADV at higher speeds but is cutting off the lower velocities, as it is not sensitive enough at low speeds. At speeds above the minimum theoretical range a very good correlation with the reference measurement can be observed. The root-mean-square deviation from ADV data was 0.095 m / s for HM200 and 0.101 m / s for HM300. In addition, both HM200 and HM300 were used to estimate the flow directions during the 18th May experiments when the flow speed was high enough to work with both masts. A short 1-minute segment of the directions is shown in Figure 14(c). The direction varies a lot as the flow near coast have short waves due to wind and swell. Direction estimations from both devices show very good agreement when compared to the ADV, having equally fast reaction to the change of the direction. The characterization and validation of the Hydromast with the Hall effect sensor has been performed. Both velocity estimates, the frequency based velocity ^^^^and the tilt based ^^^^, perform well in measuring flow velocities in various setups. For ^^^^, the functional dependency as well as the working range agree well with the described theoretical framework. Further, the longer mast HM300 resolves well lower velocities and can be easily used as an independent measurement. For the shorter mast HM200, the velocity range is wider, but an extra range criteria based on ^^^^needs to be used to detect the measurement range and allow accurate velocity estimates. However, HM200 measurements are more robust, whereas overlap for HM300 is relatively small for ^^^^and ^^^^. When calculating average flow speeds over longer periods of time using HM200, care needs to be taken interpreting the low velocity data. Around the lower limit of the measurement range frequency based estimations only occur for higher velocities for HM200 and not for lower, which can lead to biased results. One option would be using estimate from tilt as an indicator, if ^^^^is reliable, similar to what was suggested for upper velocities in the short validation tests. Further, a minimum number of samples required for the average can be implemented. As for the tilt based ^^^^, for HM300, the measurement range is three times larger than for ^^^^, allowing the device to be used in applications with high velocity variations. For HM200, range is comparable with ^^^^, giving independent and reliable velocity estimates. Using ^^^^, instantaneous velocities in changing flow conditions can be measured, allowing measurements in areas where flow direction is constantly changing, like with the waves on the coast. Here again, HM300 seems to perform better, capturing lower velocities than HM200 and both sensors seem to capture higher velocities. In unsteady flow, the ADV velocity and the Hydromast velocity showed good correlation. However, the measurements were taken in not ideal conditions for the ADV, namely the experiments were done in shallow water (i.e., ADV was both close to the bottom and near the surface). For more robust unsteady flow characterisation, additional work is needed to accurately describe the Hydromast reaction time for instantaneous measurements. Direction estimate and water column height measurements were done against reference measurements in different flows. The estimates agreed between devices as well as with the references, showing that they are reliable extra measurements that can be taken during testing. In steady river flow there was very little variation and the results just show the stability of the direction measurement in time, which agrees with ADV estimates within 5 degrees. The Hydromast has the capability of a near real-time data monitoring, when a sensor hub can be mounted above water. This is useful for long-term measurements and is also helpful for fault detection. Based on the validation data, the overall uncertainties of the measurements were estimated for the 95% confidence level, reported in Table 1. Same estimates for ADV have also been shown for comparison. As both velocity estimates have their own pros and cons, it could be considered to use the two independent velocity estimates in parallel and combine them for higher accuracy. Alternatively, for higher accuracy, calibrations can be performed before the actual tests in similar flow conditions to capture the specific behavior. High turbulence levels would provide rapid changes in velocity output and that could be an indicator that caution needs to be taken in data interpretation. Table II. Uncertainty estimates (95% confidence level). Mast ^^^^[m / s] ^^^^[m / s]^⃐^ [deg]Water level [m]HM200 0.096 0.050 12.10 0.004 HM300 0.049 0.094 12.02 0.003 ADV 0.129 0.129 36.45 N / A The Hydromast measurements are independent of the water quality and surface reflections, allowing it to be used also in locations, where acoustic methods fail. In future, more reliable pressure sensors should be used in order to avoid drifting and providing more reliable water depth data. Additional research could be done on fault detection and unwanted debris detection. Also, finding a way to estimate turbulence intensity from the Hydromast output would be a useful feature, in order to indicate high turbulence conditions. The compact design and affordable price of the Hydromast (roughly of a commercial ADV) coupled with its versatile communication capabilities, make it suitable for a wide range of applications in shallow water environments. Its low cost enables distributed sensing in various applications, including improving safety in harbors by monitoring currents, detecting ship traffic along coastlines, and evaluating bed load for sediment transportation studies. Furthermore, the distributed sensing capability allows for the application of these devices in the aquaculture industry, as well as in the field of renewable energy, for site monitoring and site evaluation. The Hall effect sensor based low-cost flow monitoring device Hydromast was characterized and validated against a commercial acoustic Doppler velocimeter and shown to perform well in various flows, with flow speeds from 0.15 to 1 m / s. With this new device, average and instantaneous flow speed along with flow direction and water depth can be measured, allowing the devices to be used in both steady and fluctuating flow conditions. Cloud communication functionalities were developed so that monitoring can be done online, allowing long term testing with live outputs and data analysis, as well as allowing fault detection. With low cost and high reliability in near- bed flow velocity estimations, the described device can be used in various flow conditions for flow velocity and direction estimation, both short as well as long-term flow monitoring, as a single device or in a larger grid with a near real-time data output to the user. This work was supported by the EU through European Social Fund project "ICT programme", H2020 project ILIAD (grant agreement No 101037643), H2020 project LAKHSMI (grant agreement No 635568.) and by the Estonian Research Council project SolidShore (grant agreement EMP480).

Claims

Claims 1. A hydromast type sensor device for determining fluid flow parameters, the sensor comprising: a base unit; a hydromast, comprising an oblong element, having a flexible link in one end, said oblong element fixed mechanically to said base unit with said flexible link and extending into fluid, said oblong element mechanically connected to a sensor; and a data acquisition module inside said base unit, said data acquisition module electrically connected to said sensor, wherein said data acquisition module is adapted to determine flow parameters from the measured sensor signal, wherein such flow parameters include flow speed, direction of flow, type of flow, and Reynolds number characterized in that said sensor is a tilt and direction sensor.

2. A hydromast type sensor device as in claim 1, characterized in that said tilt and direction sensor is a magnet effect sensor.

3. A hydromast type sensor device as in claim 1, characterized in that said magnet effect sensor is a 3D Hall effect sensor and said oblong element comprises a magnet at its end proximate to the base unit.

4. A sensor device as in claims 1 to 3, characterized in that said oblong element is a hollow tube with gas inside, so that the oblong element is positively buoyant.

5. A sensor device as in claims 1 to 4, characterized in that said oblong element is covered with a biofouling resistant layer.

6. A sensor device as in claim 5, characterized in that said biofouling resistant layer is a copper layer.

7. A method for determining fluid flow parameters in a reservoir, fluid body or in a pipe, wherein said method comprises: introducing into said fluid flow a hydromast type sensor device as in claims 1 to 6;determining by said data acquisition module a tilt θ and / or fd dominant frequencies of said oblong element or calculating by said data acquisition module said fluid flow parameters from said frequency spectrum.

8. The method as in claim 7, wherein said fluid flow parameters comprise flow direction, flow velocity and the type of the fluid flow.

9. The method as in claim 8, wherein said flow velocity Vf is calculated aswhere D is the diameter of the oblong member, St is the Strouhal number, fd is dominant frequencies and C0 is a constant taking into account the end-effects of the mast tip and other artifacts of the specific device setup.

10. The method as in claim 8, wherein said flow velocity V θ is calculated as where C1 and C2 are constants found through calibration and MXYZ are the magnitudes of the oblong element.

Images