Method for determining the elevation of the free surface of a body of water using radar and a drone

Abstract

The present invention relates to a method for determining the free surface elevation (FSE) of a body of water. The method employs a measurement using radar (MRA) and a localized measurement using a drone (MDR) equipped with a sensor, in order to calibrate (CAL) a free surface elevation reconstruction model (MOD) for the area under consideration. This calibrated model (MOD CAL) is then applied to real-time radar measurements (MRA) to determine the free surface elevation (FSE). Figure 1 to be published

Description

Title of the invention: Method for determining the elevation of the free surface of a body of water using radar and a drone Technical field

[0001] The present invention relates to the field of wave characterization, in particular for the monitoring, operation and control of a system subjected to waves, whether floating or not.

[0002] In order to characterize waves within a body of water (for example: a sea, an ocean, a lake), we use in particular time series of elevation of the free surface of the water. This elevation of the free surface gives the water height (therefore the wave height), relative to the situation where the surface is not disturbed (flat sea, for example), at any point of the water surface. The measurement of the elevation of the free surface is a widespread problem, in order to respond to several challenges. One of the first challenges is the fine characterization (at the scale of individual waves) of the state of the sea, which is most often characterized by descriptions of the statistical distribution of the heights of individual waves, such as the spectrum, the significant height and the average period.These descriptors are commonly used for navigation monitoring, offshore operations monitoring, energy production platform monitoring, and site monitoring for the exploitation of marine energies. Having a free surface elevation measurement not only allows for more precise statistical characterizations, but also for short-term predictions (from a few seconds to a few minutes) of the wave height and the resulting movements of a floating system. These predictions make it possible, for example, to detect the arrival of a wave train that is potentially dangerous for a given operation (for example, the transfer of personnel on board a wind turbine or a boat) or, on the contrary, a period of calm, which would allow the operation in question to be carried out.Another challenge of wave and swell predictions made from the free surface elevation is the control of floating systems (in particular by means of predictive control): for example, to ensure the stabilization of a vessel, to ensure the compensation of a movement, for example heave compensation (which can be interesting for a floating hydrocarbon production platform), to ensure the real-time control of floating wind turbines or wave energy systems (in particular with the aim of maximizing the energy produced and / or to reduce the fatigue of the components of such systems). Prior art

[0003] Several technologies have been developed to measure and determine the elevation of the free surface.

[0004] Some of these solutions make it possible to measure a characteristic resulting from the waves or the swell at only one measurement point, for example by means of an instrumented buoy, which does not make it possible to have an indication of the elevation of the free surface at any point in a zone of water.

[0005] Maritime radars, for example X-band radars, which are found on all large ships and many offshore installations, are a particularly interesting technology for measuring waves at a distance, although their initial use is rather navigation and collision avoidance. The images produced by maritime radars detect not only targets or obstacles such as ships and coastlines, but also reflections from the sea surface, known as "sea clutter", caused by the interaction between the radar waves and small ripples in the surface caused by the wind. The backscatter from this rough surface reveals the underlying shape of the waves.With appropriate processing, it is in principle possible to carry out wave measurements over a wide field of view (up to about 5 km range, depending on the installation height of the radar antenna and the sea state), with good spatial resolution (of the order of 5 m in distance and 1° in azimuth) and sufficient temporal resolution (one image every 1 to 3 seconds) to track individual waves.

[0006] More precisely, the principle of wave measurement by radar is as follows: the electromagnetic waves emitted by the radar interact, by virtue of Bragg's law, with the ripples (variations in height) of the water surface, whose wavelength is of the order of centimeters (like those of the radar waves). This results in a backscattered signal, the sea clutter or sea echo, which returns to the radar receiver, and whose intensity is modulated by the waves (which can have a length of between ten and several hundred meters) via a set of mechanisms that are not yet all well understood. Radar images therefore present patterns that resemble waves, and from which these can theoretically be reconstructed, with appropriate processing.

[0007] Radar images can provide sea state estimates, i.e. statistical information on wave height and energy content according to frequency and direction. But they should also allow us to go much further, with a true reconstruction of the free surface elevation (FSE) "wave by wave", like a three-dimensional movie of the sea surface. Such a wave-by-wave reconstruction, with the vast range and resolution of radar, lends itself to very numerous applications. It is particularly ideal for monitoring purposes in the field of marine renewable energies, and opens the way to real-time prediction of waves, or the movement of a vessel, over horizons of several minutes, thus improving the feasibility and safety of a large number of operations at sea.

[0008] However, despite their promising prospects, radars only provide a very indirect measurement of waves, via images, or intensity signals, of sea clutter. The intensity of sea clutter is modulated by the orbital velocity of the fluid at the surface and the angle of incidence of the radar beam on the sea surface, which can be linearly related to the free surface elevation that one seeks to measure. Other factors related to waves complicate this modulation, in particular shadowing effects (when certain areas of the sea surface are geometrically hidden by waves closer to the radar) or the presence of micro-breaking.In addition to these wave-induced modulations, there are other factors that alter the wave signal, in particular the amplification function of the signal received by the radar, the presence of speckle noise, or even meteorological factors such as rain or sea spray, which can generate backscattering.

[0009] To circumvent this problem, the reconstruction of waves from radar images generally relies on the “standard method” which is described in particular in the following documents:

[0010] Young, IR, Rosenthal, W., & Ziemer, F. (1985). A three-dimensional analysis of marine radar images for the determination of ocean wave directionality and surface currents. Journal of Geophysical Research: Oceans, 9O(C1), 1049-1059.

[0011] Nieto Borge, J., Rodriguez, G. R., Hessner, K., & Gonzalez, P. I. (2004). Inversion of marine radar images for surface wave analysis. Journal of Atmospheric and Oceanic Technology, 21(8), 1291-1300.

[0012] This method does without an explicit model for the formation (and inversion) of radar images: in this approach, the radar field of view is divided into rectangular zones, in which a three-dimensional Fourier transform of the signal is applied. The wave-related components of the signal are then identified and filtered using the dispersion relation for gravity waves, which relates frequency to wavelength. The components thus obtained are then considered to be linearly related to the components of the free surface elevation signal. Finally, the reconstructed signal remains to be calibrated in amplitude, to obtain images of the sea state with the correct energy. As can be seen, the standard method avoids the need for detailed knowledge of image formation mechanisms, but relies on a considerable number of empirical parameters, such as the parameters filtering, modulation transfer function parameters, and amplitude calibration parameters. Optimization or verification of these parameters can be based on the use of additional sensors, such as instrumented buoys, a ship's inertial unit, laser remote sensing (LiDAR sensor), or a microseismic wave sensor on the shore. Another option is to use coherent radars, which also detect the Doppler signal due to surface motion. Indeed, the Doppler velocity can, in principle, be used to reconstruct the free surface elevation without going through the calibration step via a modulation transfer function; however, to obtain stable Doppler signals, the radar must observe the same points over a relatively long period, which makes the proposed measurement procedures quite complex.Furthermore, the vast majority of current maritime radars do not have this characteristic. The use of complementary measurements is therefore necessary, or at least recommended, to achieve an accurate reconstruction of the wave field from radar measurements.

[0013] Furthermore, the method described in patent application FR3108152 (WO2021 / 180502) implements one or more sensors (for example a radar, a LiDAR, an accelerometer, a displacement sensor, a pressure sensor, etc.) measuring the free surface elevation of the swell or the resulting characteristics at one or more points and deduces predictions of the swell or resulting characteristics of the swell by means of transfer functions. This method allows a good prediction of a resultant of the swell but does not allow the free surface elevation to be determined at any point in an area from a radar signal. Summary of the invention

[0014] The aim of the invention is to determine, in real time, the free surface elevation at any point in a body of water area, in a precise and simple manner. For this purpose, the invention relates to a method for determining a free surface elevation of a body of water area. The method implements a (distributed) measurement by means of a radar, and a localized measurement by means of a drone equipped with a sensor, in order to calibrate a reconstruction model of the free surface elevation in the area considered. Then, this calibrated model is applied to real-time radar measurements to determine the free surface elevation. The drone allows a precise localized measurement, which makes it possible to calibrate the model with a precise value, which makes the model more precise.In addition, the drone can carry out measurements in areas that are not or are difficult to access by radar (for example, depending on weather conditions or due to shadows or objects on the body of water). In addition, piloting the drone allows the position of the measurement points to be varied (the measurement points are not fixed): it is therefore possible to adapt the calibration according to the . conditions encountered.

[0015] The invention also relates to a system for determining a free surface elevation, and one or more methods for monitoring, operating or controlling a system subjected to waves implementing such a method.

[0016] The invention relates to a method for determining an elevation of the free surface of an area of ​​a body of water by means of a radar and at least one drone equipped with at least one sensor for remotely measuring the elevation of the free surface. For this method, the following steps are implemented: a. A reconstruction model of the elevation of the free surface is constructed, said model links a signal from said radar to the elevation of the free surface; b. A signal representative of the elevation of the free surface of said water area is measured by means of said radar; c. Said at least one drone is piloted to carry out at least one localized measurement at a measurement point of the area of ​​the body of water by means of said sensor equipping said at least one drone; d. Calibrating said free surface elevation reconstruction model using said at least one localized measurement; and e. Said calibrated free surface elevation reconstruction model is applied to a representative free surface signal measured by said radar to determine the free surface elevation of the water body area.

[0017] According to one embodiment, said at least one measurement point is defined as a function of said signal measured by said radar.

[0018] Advantageously, at least one meteorological condition is acquired, and said free surface elevation reconstruction model is a function of said at least one meteorological condition, preferably said at least one meteorological condition is chosen from wind speed, wind direction, precipitation, temperature and sea state.

[0019] According to one aspect, said sensor equipping said at least one drone is chosen from a LiDAR sensor, a thermal camera, an optical camera, a vertical beam radar.

[0020] According to one implementation, said free surface elevation reconstruction model is constructed using a modulation transfer function, an assimilation method, a machine learning method or a deep learning method.

[0021] According to one embodiment option, the steps of piloting said at least one drone and of offline calibration are carried out, and said calibrated free surface elevation reconstruction model is applied to a signal measured by the online radar.

[0022] According to an embodiment option, the steps of controlling said at least one least one drone and online calibration, to calibrate said free surface elevation reconstruction model continuously.

[0023] Advantageously, the elevation of the free surface is determined in real time.

[0024] Furthermore, the invention relates to a system for determining the free surface elevation of an area of ​​a body of water which comprises at least one radar, at least one drone equipped with at least one sensor for measuring the elevation of the free surface remotely, a system for piloting said at least one drone and computer means for implementing the method for determining the free surface elevation according to one of the preceding characteristics.

[0025] Furthermore, the invention relates to a method for monitoring, operating, or controlling a system subjected to waves within a body of water, in which the following steps are implemented: a. The elevation of the free surface of said body of water is determined by means of the method for determining the free surface elevation according to one of the preceding characteristics; and b. Said wave system is supervised, operated, or controlled based on the elevation of the free surface of said determined body of water.

[0026] Other characteristics and advantages of the method and system according to the invention will appear on reading the following description of non-limiting examples of embodiments, with reference to the figures appended and described below. List of figures

[0027] [Fig.l]

[0028] [Fig.l] illustrates the steps of the method for determining a free surface elevation according to a first embodiment of the invention.

[0029] [Fig.2]

[0030] [Fig.2] illustrates the steps of the method for determining a free surface elevation according to a second embodiment of the invention.

[0031] [Fig.3]

[0032] [Fig. 3] illustrates the steps of the method for determining a free surface elevation according to a third embodiment of the invention.

[0033] [Fig.4]

[0034] [Fig.4] illustrates the steps of the method for determining a free surface elevation according to a first implementation of the third embodiment of the invention.

[0035] [Fig.5]

[0036] [Fig.5] illustrates the steps of the method for determining a free surface elevation according to a second implementation of the third embodiment of the invention.

[0037] [Fig.6]

[0038] [Fig.6] illustrates an elevation of the reference free surface, and a signal obtained by a radar, for a simulated illustrative example.

[0039] [Fig.7]

[0040] [Fig.7] illustrates a free surface elevation reconstructed from a radar sensor using a method according to the prior art and a reference free surface elevation, for the example of [Fig.6].

[0041] [Fig. 8]

[0042] [Fig.8] illustrates, at several angles and several distances, the modulus and phase of the modulation transfer function determined by applying the method according to the prior art to the example of Figures 6 and 7.

[0043] [Fig.9]

[0044] [Fig.9] illustrates, at several angles and several distances, the height of the free surface elevation as a function of time, determined by several methods, for an example application. Description of the embodiments

[0045] The invention relates to a method for determining the free surface elevation of an area of ​​a body of water. It is recalled that the free surface elevation is the height of water at a point of a body of water relative to the water surface which would have no variation in height (which would not be disturbed in any way). Thus, the free surface elevation reflects the height of the waves or the swell. A body of water may be a sea, an ocean, a lake, a river, etc. The area considered by the method according to the invention is an area of ​​interest, in particular for the monitoring, operation or control of a system subjected to waves. The extent of this area of ​​interest may depend on the system subjected to waves. Alternatively, the extent of this area of ​​interest may correspond to the measurement area of ​​the radar implemented in the method.

[0046] The method according to the invention implements at least one radar and at least one drone equipped with at least one sensor for remote measurement of the elevation of the free surface.

[0047] For this method, the following steps are implemented:

[0048] 1) Construction of a free surface elevation reconstruction model

[0049] 2) Indirect measurement of waves by radar

[0050] 3) Drone piloting and localized measurement

[0051] 4) Calibration of the free surface elevation reconstruction model

[0052] 5) Determination of the free surface elevation

[0053] Steps 1 and 3 to 5 can be implemented by computer means, including a computer, a server, or a calculator. The computing resources include at least one processor and at least one computer memory. Step 1 can be performed once only before, during, or after steps 2 and 3. The steps will be detailed in the rest of the description.

[0054] According to one embodiment of the invention, the determination of the elevation of the free surface of the water area can be implemented in real time. Thus, if necessary, a system subjected to waves can be monitored, operated or controlled in real time. For this embodiment, a radar measurement step is carried out in real time. "In real time" means that the measurement is available as soon as it is taken.

[0055] [Fig.l] illustrates, schematically and in a non-limiting manner, the steps of the method according to a first embodiment of the invention. First, a free surface elevation reconstruction model MOD is constructed. Then a measurement is carried out using the MRA radar. Then, a localized free surface elevation measurement is piloted and carried out using an MDR drone. The MRA radar and MDR drone measurements are used to calibrate CAL the free surface elevation reconstruction model MOD. A calibrated free surface elevation reconstruction model MOD CAL is thus formed. This calibrated model MOD CAL is applied to an MRA radar measurement to determine a free surface elevation ESL.

[0056] According to one embodiment, the drone can be piloted at least at one measurement point defined as a function of the radar measurement. For example, as a function of an area where the radar measurement is imprecise, for example due to the presence of a shadow, a structure, etc. Additionally or alternatively, a measurement point can be determined in different areas of the area of ​​interest to try to compensate for variations in the radar measurement depending on the direction and distance.

[0057] [Fig. 2] illustrates, schematically and in a non-limiting manner, the steps of the method according to such a second embodiment of the invention. The steps identical to the first embodiment of [Fig. 1] are not re-described. The method comprises a step of PIL piloting of the drone according to the MRA radar measurement. This step of piloting the PIL drone makes it possible to obtain the measurement by the sensor of the MDR drone at at least one measurement point.

[0058] According to one implementation, the method may comprise a step of acquiring at least one meteorological condition (preferably with several meteorological conditions). For example, the meteorological condition(s) may be chosen from wind speed, wind direction, precipitation, temperature, sea state, etc. Then, the at least one measurement point may be determined as a function of the meteorological condition(s). Thus, it is possible make a localized free surface elevation measurement at a point where the radar measurement is affected by the meteorological condition(s).

[0059] [Fig. 3] illustrates, schematically and in a non-limiting manner, the steps of the method according to such a third embodiment of the invention. The steps identical to the first embodiment of [Fig. 1] and to the second embodiment of [Fig. 2] are not re-described. The method comprises a step of acquiring at least one CDM meteorological condition. The acquired meteorological condition is used in the step of piloting the PIL drone and in the construction of the MOD wave elevation reconstruction model.

[0060] According to a first implementation of the invention, the calibration step can be done offline. In other words, the calibration step is performed only once, then the calibrated model is used online in real time. Thus, a complex model and calibration can be used to obtain a complete model for reconstructing the free surface elevation, this complete model being capable of being applied online in real time. For this implementation of the invention, the drone measurement, radar measurement and calibration steps are performed offline. And online, another online radar measurement is performed and the calibrated model is applied online to this online radar measurement.

[0061] [Fig. 4] illustrates, schematically and in a non-limiting manner, the steps of the method according to such an implementation. [Fig. 4] illustrates this implementation for the third embodiment of [Fig. 3]. However, this implementation can also be applied to the embodiments of Figures 1 and 2. The steps described in relation to the previous figures are not re-described. For this implementation, certain steps are carried out offline HL, and certain steps are carried out online EL. The offline radar measurement used for the calibration is denoted MRAh, and the online radar measurement used for the determination of the free surface elevation is denoted MRAe. Thus, offline HL, the radar measurement MRAh, the acquisition of meteorological conditions CDM, the piloting of the at least one drone PIL, the measurement by sensor of the drone MDR, the construction of the surface elevation reconstruction model MOD and the calibration CAL are carried out.In EL line, the MRAe online radar measurement is carried out and the calibrated surface elevation reconstruction model MOD CAL is applied to the MRAe online radar measurement.

[0062] According to a second implementation of the invention, the calibration step can be implemented online, continuously. In other words, the free surface elevation reconstruction model is continuously calibrated with new drone measurements. Thus, the free surface elevation reconstruction model is adapted in real time with new localized measurements, which makes it possible to obtain an accurate model at any time and at any point in the area of ​​interest. For this implementation, all steps are carried out online in real time.

[0063] [Fig. 5] illustrates, schematically and in a non-limiting manner, the steps of the method according to such an implementation. [Fig. 5] illustrates this implementation for the third embodiment of [Fig. 3]. However, this implementation can also be applied to the embodiments of Figures 1 and 2. The steps described in relation to the previous figures are not re-described. For this implementation, all the steps are carried out online EL: the radar measurement MRA is carried out, the acquisition of meteorological conditions CDM, the piloting of the at least one drone PIL, the measurement by sensor of the drone MDR, the construction of the reconstruction model of the surface elevation MOD the calibration CAL, and the calibrated surface elevation reconstruction model MOD CAL is applied. For this implementation, the piloting PIL can take into account a return from the calibrated model MOD CAL to determine at least one of the localized measurements.

[0064] 1) Construction of a free surface elevation reconstruction model

[0065] In this step, a free surface elevation reconstruction model is constructed. Such a free surface elevation reconstruction model links a measurement signal from a radar to a free surface elevation. In other words, the free surface elevation reconstruction model has as input a measurement signal from a radar and has as output a free surface elevation at any point in a body of water area. For the calibration of this model in step 4, the model may depend on at least one parameter, which is adjusted during calibration. Alternatively, the model may depend on at least one weighting, which is adjusted during calibration.

[0066] According to one embodiment of the invention, the free surface elevation reconstruction model can be constructed using a modulation transfer function, denoted MTF (or FTM). The construction of such a model does not require a large number of measurements. The following document describes an example of such a model:

[0067] Chen, Z., Zhang, B., He, Y. et al. (2015). A new modulation transfer function for ocean wave spectra retrieval from X-band marine radar imagery. Chin. J. Ocean. Limnol. 33, 1132-1141 (2015)

[0068] According to one embodiment of the invention, the free surface elevation reconstruction model can be constructed by data assimilation, i.e. by minimizing a cost function defined as the difference between the radar measurements and the predictions of a linear or non-linear wave evolution model over a time interval which is called the assimilation interval. An example of this approach is given in the following document:

[0069] Aragh, Sina & Nwogu, Okey & Lyzenga, David. (2008). Improved Estimation of Ocean Wave Fields from Marine Radars Using Data Assimilation Techniques. Pro-

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] ceedings of the International Offshore and Polar Engineering Conference. In this case, the parameters of the free surface elevation reconstruction model adjusted during calibration are the parameters of the assimilation method. According to one embodiment of the invention, the free surface elevation reconstruction model can be constructed by a machine learning method or by a deep learning method. The construction of such a model does not require a priori knowledge of the physical phenomena.For this embodiment, the following steps can be implemented: - a learning base is constructed, which comprises radar measurement signals and measurements of the free surface elevation, alternatively or cumulatively, the learning base can comprise simulated radar measurement signals, and / or simulated free surface elevation measurements (this type of simulated measurements is called "synthetic" measurements) and - a free surface elevation reconstruction model is constructed by means of a machine learning method trained on the constructed learning base, the free surface elevation reconstruction model associating a free surface elevation with a radar measurement signal. Machine learning can be a supervised or unsupervised method, such as a neural network, random forest, support vector machine, etc. For example, if the model is built using a neural network, then the calibration step may consist of changing some weights of the neural network. Alternatively, the construction of the surface elevation reconstruction model can be implemented by any analogous method. Advantageously, the construction of the surface elevation reconstruction model can depend on weather conditions. Thus, the model can take these weather conditions into account to improve the model's accuracy. For example, for machine learning construction, the learning base can additionally include weather conditions. 2) Indirect measurement of waves by radar In this step, a signal representative of the free surface elevation of the water area is measured using a radar. In other words, a measurement is made using the radar of the water area. The radar provides an indirect measurement of the free surface elevation over a measurement surface (which may correspond to the area of ​​interest). An indirect measurement is a measurement that is correlated to the free surface elevation of the swell in a complex manner and requires a reconstruction procedure to be usable. This is particularly the case for the intensity of the radar signal, which is affected by modulations induced by the waves (speed orbital to the surface, angle of incidence of the radar beam, shadowing effects, micro-breaks, etc.), and by the radar itself (amplification function of the received signal, speckle noise), etc. The radar measurement signal is the normalized intensity of the signal backscattered by the sea, preferably with as little processing as possible. This signal can normally be available, in digitized form, at the output of the latest generation navigation radars. For this configuration, a digitizing device can be provided to be able to exploit the analog signal sent to a radar screen. The radar can be considered as an indirect measurement in two dimensions of the free surface elevation. Thus, the radar can provide a time series in two dimensions of the free surface elevation.

[0076] According to one embodiment, the radar may be an X-band radar. The X-band is a segment of the microwave region of the electromagnetic spectrum, with a frequency range of 8 to 12 GHz and a wavelength of approximately 3 cm. An X-band radar allows for measurement availability as soon as it is taken. In addition, such a radar allows for a wide field of view (up to approximately 5 km range, depending on the installation height of the radar antenna and the sea state), with good spatial resolution (for example, of the order of 5 m in distance and 1° in azimuth) and good temporal resolution (for example, one image every 1 to 3 seconds) to follow the swell “wave by wave”. Alternatively, the radar may be a radar with bands close to the X-band (Ku band, in particular, or S band), with better temporal and / or spatial resolutions, or any similar technology.

[0077] According to one aspect, the radar may be a coastal radar or a radar equipping a floating system, for example a radar equipping a ship, a floating platform, or a radar equipping a fixed platform.

[0078] For the method according to the invention, a radar measurement is carried out in real time, for the application of the calibrated model. In addition, a radar measurement is carried out for the calibration of the model. This radar measurement for the calibration can be carried out offline or online depending on the implementation envisaged (see embodiments of figures 4 and 5 described above). 3) Drone piloting and localized measurement

[0079] During this step, the at least one drone is piloted to carry out a localized measurement of the free surface elevation using the sensor equipping the at least one drone. The localized measurement is carried out at a measurement point in the area of ​​the body of water. Thus, at least one georeferenced measurement of the free surface elevation is carried out for the calibration of the reconstruction model.

[0080] According to one aspect of the invention, the drone is flying and comprises at least one sensor for remote measurement of the free surface elevation. The sensor may preferably be a sensor for direct measurement of the free surface elevation. The term "measurement direct", a directly usable measurement of the elevation of the free surface of waves or swell, provided by a sensor that is calibrated once and for all and is completely autonomous thereafter. On the contrary, a radar as used in step 2 provides an indirect measurement. Thus, we can consider that the drone makes a direct one-dimensional measurement of the free surface elevation (measurement point).

[0081] According to exemplary embodiments, the sensor equipping the drone can be chosen from a LiDAR sensor (laser remote sensing), a thermal camera, an optical camera, a vertical beam radar, or any similar sensor.

[0082] According to one embodiment, the position of each measurement point can be determined, with the aim of improving the free surface elevation reconstruction model. The determination of the position of each measurement point can advantageously be automatic. The position of each measurement point can depend on the measured radar signal, to determine at least one measurement point for which the radar measurement is not precise, for example due to a shadow, an object, the presence of micro-breaking, or other. For the embodiment for which at least one meteorological condition is acquired, the position of each measurement point can be determined as a function of the meteorological condition.

[0083] For this embodiment, the drone is piloted so that it is positioned vertically above the measurement point, so that it adopts a stationary flight there, while a remote measurement of the elevation of the free surface is carried out, by means of at least one sensor fitted to the drone.

[0084] According to one implementation of the invention, the drone can be piloted at several altitudes relative to the level of the water surface, in order to improve the accuracy of the localized measurement.

[0085] According to one aspect, the method can implement a plurality of measurements located at a plurality of measurement points, by means of the sensor of a drone, or by means of a plurality of drones equipped with sensors. Advantageously, a portion of the plurality of measurement points can be aligned, so as to carry out measurements in a determined direction. Preferably, the measurement points within an alignment can be regularly spaced. Advantageously, the measurement points can be distributed over several alignments.

[0086] For the implementation for which the calibration is carried out offline, this step of piloting the drone and localized measurement can be implemented offline, only once. Thus, the use of the drone is limited in time, and once the calibration is completed, the drone can be applied to another process.

[0087] For the implementation for which the calibration is carried out online, this step of piloting the drone and localized measurement can be implemented continuously and online. Thus, the model can constantly be calibrated, which provides greater precision. bearing of the calibrated model.

[0088] In order to determine the free surface elevation from the sensor equipping the drone, a calibration of the measurement of the sensor equipping the drone can be carried out beforehand. The calibration methodology of the wave measurement system on board the drone depends on the technology of the measurement sensor.

[0089] According to a first example, if it is a scanning LiDAR, we can for example apply the methodology described in the following document:

[0090] Huang, Z., Yeh, C., Tseng, K., and Hsu, W. (2018). A UAV-RTK Lidar System for Wave and Tide Measurements in Coastal Zones. Journal of Atmospheric and Oceanic Technology 35, 8, 1557-1570,

[0091] This method is suitable for a measurement system consisting of an aerial drone, a lidar, an altitude and heading reference system (AHRS) and a real-time kinematic (RTK) global navigation satellite system (GNSS). In this case, the calibration of the drone's measurement sensor is used to obtain the parameters necessary to transform the raw LiDAR data into georeferenced free surface elevation data and can be carried out on land, using repeated measurements on two horizontal plates.

[0092] According to a second example, for a drone equipped with a measurement system using stereoscopic optical cameras, it is possible to envisage using the WASS methodology and toolbox described in the following document:

[0093] Bergamasco, F., Torsello, A., Sclavo, M., Barbariol, F., Benetazzo, A. (2017). WASS: An open-source pipeline for 3D stereo reconstruction of ocean waves, Computers and Geosciences, vol. 107, pp.28-36, 2017 DOI: 10.1016 / j.cageo.2017.07.001.

[0094] This method makes it possible to automatically recover the extrinsic parameters of the stereoscopic platform (necessary to reconstruct the free surface elevation), so that it is not necessary to perform a calibration directly on the marine site, or to perform an intrinsic calibration using a reference target (a sufficiently large object seen by the two cameras). Some adaptations may be required compared to the calibration of a purely stationary stereoscopic system (for example, if the drone is to be flown at different altitudes, a different calibration may be provided for each flight altitude).

[0095] 4) Calibration of the free surface elevation reconstruction model

[0096] In this step, the free surface elevation reconstruction model constructed in step 1 is calibrated using the localized free surface elevation measurement performed in step 3. In other words, the free surface elevation reconstruction model is adapted so that at the measurement points, the free surface elevation measurement is consistent with the output of the reconstruction model. of the free surface elevation. The calibration of the free surface elevation reconstruction model also takes into account the radar measurement made in step 2 as input to the model to obtain the model output. Thanks to this calibration, the calibrated free surface elevation reconstruction model is accurate at every point in the area of ​​interest.

[0097] As a reminder, this step can be performed once beforehand offline, or can be performed continuously online. For offline implementation, the parameters of the free surface elevation reconstruction model can be determined using a large number of localized measurements, covering a set of conditions (including weather conditions). The calibration methodology can then be performed “ex-post” (i.e. after the measurement campaign) and rely on intensive calculations. For online implementation, the free surface elevation reconstruction model can be such that its parameters can be adjusted in real time, based on direct measurements made by the drone(s).

[0098] For the embodiment for which the surface elevation reconstruction model depends on a parameter, the calibration consists of adapting this parameter, to obtain consistency between the localized free surface elevation measurement and the output of the surface elevation reconstruction model at the measurement point. In this case, the free surface elevation reconstruction model may comprise one or more parameters, and their calibration consists of finding the appropriate parameters to obtain a free surface elevation as accurate as possible from the radar measurements. The best parameters depend, in general, on the characteristics of the radar, its settings, its installation, and the characteristics of the sea state and the atmosphere in the observed area (included in the meteorological conditions).

[0099] The methodology for calibrating the free surface elevation reconstruction model depends on the free surface elevation reconstruction model considered, as well as the implementation considered (offline or online).

[0100] According to a first example, for which the reconstruction model of the free surface elevation is constructed by means of a modulation transfer function (MTF), the method described in the following document can be applied:

[0101] Chen, Z., Zhang, B., He, Y. et al. (2015). A new modulation transfer function for ocean wave spectra retrieval from X-band marine radar imagery. Chin. J. Ocean. Limnol. 33, 1132-1141 (2015)

[0102] For this method, a calibrated modulation transfer function is obtained by dividing the one-dimensional (1D) wavenumber spectrum estimated from radar measurements by the 1D wavenumber spectrum estimated from point measurements of free surface elevation made by a buoy. For the method according to the invention, the measurements obtained by the buoy are replaced by those taken by the drone, at the request of the measurement coordination system.

[0103] For other free surface elevation reconstruction model constructions, similar methods can be implemented. 5) Determination of the free surface elevation

[0104] In this step, the free surface elevation reconstruction model calibrated in step 4 is applied to the radar measurement signal from step 2 to determine the free surface elevation of the water body area. In other words, a free surface elevation is determined at any point in the area of ​​interest as an output of the calibrated free surface elevation reconstruction model, which has a radar measurement signal as input.

[0105] For this step, the radar measurement signal used is an online measurement signal. Thus, for the implementation of the offline calibration, the method implements an offline radar measurement for the calibration of the model, and an online radar measurement for the application of the calibrated model. In addition, for the implementation of the online calibration, the method implements a continuous radar measurement.

[0106] Furthermore, the invention relates to a system for determining free surface elevation. Such a system comprises: - At least one radar, - At least one drone equipped with at least one sensor for remotely measuring the free surface elevation, - A piloting system for each drone, and - IT resources (e.g. a computer, server or cal culator, which comprises at least one processor and at least one memory) for implementing the method of determining the free surface elevation according to any one of the previously described variants or any one of the combinations of previously described variants.

[0107] According to one embodiment, the free surface elevation determination system may comprise means of communication between the different devices. Concerning the data link systems, communication with the drone and / or its piloting and acquisition system may be done by radio waves. Communication between the radar, the computer system and the piloting system of each drone may be done by all kinds of computer bus, including remote transmission. Preferably, the computer means implementing the calibration may be intended to be physically close to the radar, in particular for the large quantity of data to be exchanged. Advantageously, the free surface elevation determined by the system may be shared normally on a computer communication bus, in particular a computer communication bus connected to an operating system this measurement in real time or not (for example a monitoring, exploitation or control system of a system subject to waves).

[0108] Furthermore, the invention relates to a method for monitoring (supervision), operating or controlling (command), preferably an operating or controlling method, a system subjected to waves (such as a floating or non-floating platform, a ship, a wave energy system for example), in which the following steps are implemented: a. The elevation of the free surface of an area of ​​a body of water is determined by means of the free surface elevation determination method according to any one of the variants or combinations of variants described above; and b. The system subjected to waves is controlled according to the determined free surface elevation.

[0109] Thus, the method according to the invention allows monitoring, operation or control of a system subjected to waves, to increase its performance, and / or limit the fatigue of the system subjected to waves and / or to improve the feasibility and safety of a large number of operations at sea.

[0110] According to one embodiment of the invention, the monitoring, operating or controlling method may comprise a step of predicting (in advance of phase) the elevation of the free surface of the water area by means of the elevation of the determined free surface, and the control is carried out as a function of the prediction of the elevation of the free surface so as to anticipate the control at the future elevation of the predicted free surface, before its arrival on the system to be monitored, operated or controlled.

[0111] The system subjected to waves may in particular be chosen from a ship, an aircraft carrier, an energy production platform (for example an oil platform), a renewable energy production system (for example an offshore wind turbine, a wave energy system), or a device for transferring personnel or equipment at sea (gangway, crane), or any similar system.

[0112] The monitoring, operating or controlling step may in particular consist of: - Navigation of a vessel in an area where the free surface elevation is minimal, so the vessel can avoid severe maritime conditions such as large waves, - Stabilization of a floating platform or a vessel based on the free surface elevation, - Control (for example predictive control) of a renewable energy production system to maximize the energy produced or to reduce the fatigue of the production system depending on the free surface elevation: • Control of an electrical machine equipping a wave energy system to optimize the power produced depending on the height of the swell, • Control of the orientation angle of the blades and / or the nacelle of a wind turbine depending on the waves and the swell, - Carrying out an operation at sea when the free surface elevation is minimal, for example: • Rescue of a castaway from a ship, • Recovery of an object on the surface of the water from a ship, • Installation of a marine or underwater object from a ship or platform (for example, an oil pipeline), • Takeoff or landing of an aircraft on an aircraft carrier, etc. • Transfer of personnel from a ship or platform (e.g. maintenance of an offshore wind turbine) Examples

[0113] The characteristics and advantages of the method according to the invention will appear more clearly on reading the application example below.

[0114] The first example aims to demonstrate the benefit of calibration using localized measurements. For this first example, we use a free surface elevation reconstruction model using a modulation transfer function.

[0115] A reference surface elevation is simulated for a Gaussian sea with a JONSWAP type spectrum. The JONSWAP spectrum is an empirical relationship that defines the distribution of wave energy as a function of frequency in deep waters, which is particularly suitable for the seas of Northern Europe. This simulation is carried out by superimposing a large number of sinusoidal waves of different frequencies and directions, and with randomly drawn amplitudes and phases. The simulation lasts 10 minutes with a time step of 1 second. The radial slope of the surface of the free surface elevation (with respect to the radar observation direction) is also calculated. From the reference free surface elevation and its radial slope, a synthetic radar image (i.e., a simulated radar measurement) is formed using a model similar to that described in the following document:

[0116] Lyzenga, DR, & Walker, DT (2015). A simple model for marine radar images of the ocean surface. IEEE Geoscience and Remote Sensing Letters, 12(12), 2389-2392.

[0117] This model includes tilt modulation, shading, speckle noise, and logarithmic signal amplification.

[0118] [Fig.6] illustrates, schematically and in a non-limiting manner, the reference free surface elevation REF, and the radar image RAD, in a reference frame of x, y coordinates. For the reference free surface elevation REF, the gray level translates the water height. For the RAD radar image, the gray level reflects the signal measured by the radar and digitized on 8 bits (therefore between 0 and 255).

[0119] Then, the free surface elevation reconstruction model using the average modulation transfer function (method according to the prior art) is used to reconstruct the free surface elevation using the radar image.

[0120] [Fig.7] illustrates, schematically and in a non-limiting manner, the reconstructed free surface elevation REC (according to the method according to the prior art with an average modulation transfer function) and reference REF. It can be seen that the reconstruction according to the method of the prior art is not completely precise.

[0121] In this figure, three series of PM points are identified, for which the modulation transfer function is determined. These points are referenced in the (x, y) frame of reference as a function of the distance from the center C (x=0 and y=0) and an angle relative to the line y=0.

[0122] [Fig.8] illustrates the modulus M and the phase P of the modulation transfer function as a function of the frequency f in Hz, for these points PM of [Fig.7]. The left-hand curves correspond to an angle 01 of 60° with respect to the line y=0, the center curves correspond to an angle 02 of 30° with respect to the line y=0 and the right-hand curves correspond to an angle 03 of 0° with respect to the line y=0. The references RI to R4 designate the distance with respect to the center of the reference frame C with Rl=600m, R2=1000m, R3=1400m and R4=1800m.

[0123] It is noted that the curves vary greatly from one point to another. Consequently, the application of a method according to the prior art with an average modulation transfer function does not make it possible to precisely obtain the wave spectrum, nor, a fortiori, a precise reconstruction of the “wave to wave” free surface elevation of the area of ​​interest.

[0124] Furthermore, it can be noted that the modulation transfer function exhibits variations which are relatively regular as a function of distance and azimuth (here, for example, the slope and amplitude of the transfer function decrease with distance).

[0125] With the method according to the invention, by flying the drone at a few well-chosen distances and azimuths, and for a few minutes at each location, it is possible to calibrate the parameters of a simple model of the spatial variations of the modulation transfer function, and thus precisely exploit radar images over large areas.

[0126] For the second example, a reconstruction of the free surface elevation is carried out using local transfer functions obtained by averaging the transfer function within a radius of 100m around each point PM and it is compared to the reconstruction obtained using an average transfer function.

[0127] Then, at each of the twelve PM points defined previously in [Fig.7], we applies to the reconstructed free surface elevation (of which the REC diagram represents a representation at a given instant) the inverse of the transfer function: either the local transfer function corresponding to the area around the point considered, or the average transfer function.

[0128] [Fig.9] shows the free surface elevation time series H in m thus reconstructed as a function of time T in s, for the six points, respectively at 1000 m and 1800 m distance from the radar for angles 01, 02, 03. The series indicated by REC-L are those obtained from the local transfer functions, while those obtained by the average transfer function are indicated by REC-M. The reference time series are indicated by REF. It is noted that the amplitudes of the signals are quite different.

[0129] Table 1 indicates for the six points, respectively at R2 = 1000 and R4 = 1800 m distance from the radar for angles 01, 02, 03, the quadratic errors between the reconstructions by local transfer function (ERR-REC-L) and global (ERR-REC-M) and the reference free surface elevation.

[0130] [Tables 1] 01, R2 02, R2 03, R2 01, R4 02, R4 03, R4 ERR-REC- L 0.4763 0.5302 0.5531 0.6027 0.6666 0.6813 ERR-REC- M 0.7365 0.6572 0.6660 0.7064 0.9483 0.9640

[0131] Reconstructions by local transfer function are clearly more precise. Thus, the method according to the invention allows a determination of the elevation of the free surface compared to a method implementing a constant modulation transfer function.

Claims

Claims

1. Method for determining a free surface elevation (ESL) of an area of ​​a body of water by means of a radar and at least one drone equipped with at least one sensor for remotely measuring the elevation of the free surface, characterized in that the following steps are implemented: a. A free surface elevation reconstruction model (MOD) is constructed, said model connecting a signal from said radar to the elevation of the free surface; b. A signal representative of the elevation of the free surface of said area of ​​water is measured by means of said radar (MRA); c. Said at least one drone is piloted to carry out at least one localized measurement (MDR) at a measurement point of the area of ​​water by means of said sensor equipping said at least one drone; d. Said free surface elevation reconstruction model is calibrated (CAL) by means of said at least one localized measurement; and e.Said calibrated free surface elevation reconstruction model (MOD CAL) is applied to a representative signal of the free surface measured by said radar to determine the free surface elevation of the water body area.

2. Method according to claim 1, in which said at least one measurement point is defined as a function of said signal measured by said radar (MRA).

3. Method according to one of the preceding claims, in which at least one meteorological condition (CDM) is acquired, and said free surface elevation reconstruction model (MOD) is a function of said at least one meteorological condition (CDM), preferably said at least one meteorological condition (CDM) is chosen from wind speed, wind direction, precipitation, temperature and sea state.

4. Method according to one of the preceding claims, in which said sensor equipping said at least one drone is chosen from a sensor LiDAR, thermal camera, optical camera, vertical beam radar.

5. Method according to one of the preceding claims, in which said free surface elevation reconstruction model (MOD) is constructed by means of a modulation transfer function, an assimilation method, by a machine learning method or by a deep learning method.

6. Method according to one of the preceding claims, in which the steps of piloting (PIL) said at least one drone and of offline calibration (HL) are carried out, and said calibrated free surface elevation reconstruction model (MOD CAL) is applied to a signal measured by the online radar (MRAe).

7. Method according to one of claims 1 to 5, in which the steps of piloting said at least one drone (MDR) and of calibration (CAL) are carried out online (EL), to calibrate (CAL) said free surface elevation reconstruction model continuously.

8. Method according to one of the preceding claims, in which the elevation of the free surface (ESL) is determined in real time.

9. System for determining the free surface elevation of an area of ​​a body of water which comprises at least one radar, at least one drone equipped with at least one sensor for measuring the elevation of the free surface remotely, a system for piloting said at least one drone and computer means for implementing the method for determining the free surface elevation according to one of the preceding claims.

10. A method for monitoring, operating, or controlling a system subjected to waves within a body of water, in which the following steps are implemented: a. The free surface elevation (ESL) of said body of water is determined by means of the free surface elevation determination method according to one of claims 1 to 8; and b. Said system subjected to waves is supervised, operated, or controlled as a function of the free surface elevation of said determined body of water.

Images