Method for determining the elevation of the free surface of an area within a body of water

Abstract

Method for determining the free surface elevation (FSE) of an area of ​​a body of water: 1) A training database of image pairs (W,R) is created, each pair consisting of an FSE image (W) and a radar return image (R), the two images in the same pair corresponding to the same area and to the same or nearly the same time point. 2) Spatial characteristics of said area are added to each image pair (W,R), including the position relative to the radar and the principal wave direction(s). 3) Deep neural networks are trained on this database, using these spatial characteristics to specialize the neural networks and to obtain an FSE reconstruction model. 4) Real return images are acquired by radar. 5) This model is applied to the real return radar images to obtain the FSE. (Shortcut figure: Fig. 6)

Description

Title of the invention: Method for determining the elevation of the free surface of an area of ​​a body of water 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, floating or not.

[0002] To characterize waves within a body of water (e.g., a sea, an ocean, a lake), time series of free surface elevation are used. This free surface elevation gives the water depth (and therefore the wave height), relative to the situation where the surface is undisturbed (e.g., a flat sea), at any point on the water surface. Measuring free surface elevation is a widespread problem, addressing several challenges. One of the primary challenges is the detailed characterization (at the scale of individual waves) of the sea state, which is most often characterized by descriptions of the statistical distribution of individual wave heights, such as the spectrum, the significant wave height, and the mean period.These descriptors are commonly used for navigation tracking, monitoring offshore operations, energy production platform surveillance, and site monitoring for marine energy development. Having a free surface elevation measurement allows not only for more precise statistical characterizations but also for short-term predictions (from a few seconds to a few minutes) of 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 could be dangerous for a given operation (such as the transfer of personnel on board a wind turbine or a vessel) or, conversely, a period of calm that would allow the operation to be carried out.Another challenge of wave and swell predictions made from free surface elevation is the control of floating systems (particularly by means of predictive control): for example, to ensure the stabilization of a ship, to ensure the compensation of a movement, for example the compensation of heaving (which can be interesting for a floating hydrocarbon production platform), to ensure the real-time control of floating wind turbines or wave energy systems (particularly with the aim of maximizing the energy produced and / or reducing the fatigue of the components of such systems). Previous technique

[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 resulting characteristic of waves or swell at only one measurement point, for example by means of an instrumented buoy, which does not allow an indication of the elevation of the free surface at every point of a body 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 was primarily for 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 radar waves and small surface undulations caused by the wind. The backscattering of 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 approximately 5 km range, depending on the installation height of the radar antenna and the sea state), with good spatial resolution (on the order of 5 m in distance and 1° in azimuth) and sufficient temporal resolution (one image every 1 to 3 seconds) to track waves individually.

[0006] More precisely, the principle of wave measurement by radar is as follows: the electromagnetic waves emitted by the radar interact, according to Bragg's law, with the ripples (variations in height) on the water's surface, whose wavelength is on 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 ranging from ten to several hundred meters) via a set of mechanisms that are not yet fully understood. The radar images therefore exhibit patterns that resemble waves, and from which the latter can theoretically be reconstructed, with appropriate processing.

[0007] Radar images can provide sea state estimates, that is, 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 wave-by-wave reconstruction of the free surface elevation (FSE), like a three-dimensional film of the sea surface. Such a wave-by-wave reconstruction, with the vast range and resolution of radar, lends itself to a wide range of applications. In particular, it is ideal for monitoring purposes in the field of marine renewable energies and paves the way for prediction. real-time wave tracking, or tracking of ship movement, 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 wave-related factors complicate this modulation, in particular shading effects (when certain areas of the sea surface are geometrically hidden by waves closer to the radar) or the presence of micro-breaking waves.In addition to these wave-induced modulations, other factors alter the wave signal, in particular the amplification function of the signal received by the radar, the presence of shimmering noise, or meteorological factors such as rain or sea spray, which can generate backscattering.

[0009] To circumvent this problem, wave reconstruction from radar images generally relies on the "standard method" which is described in particular in the following documents: Young, I.R., 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 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.

[0010] This method does not require an explicit model for the formation (and inversion) of radar images: in this approach, the radar field of view is divided into rectangular areas, within 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 gravitational 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 is calibrated in amplitude to obtain sea state images with the correct energy.As we can see, the standard method avoids relying on detailed knowledge of image formation mechanisms, but instead relies on a considerable number of empirical parameters, such as filtering parameters, modulation transfer function parameters, and amplitude calibration parameters. Optimizing or verifying these parameters can... rely on the use of additional sensors, such as instrumented buoys, a ship's inertial navigation system, laser remote sensing (LiDAR sensor) or a microseismic wave sensor on the shore.

[0011] Another avenue for improving the standard method involves using coherent radars, which also detect the Doppler signal due to surface movement. Indeed, 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 feature.

[0012] The standard method is simply linear filtering. However, the relationship between surface elevation and sea clutter is highly non-linear. The performance achievable with the standard method is therefore inherently limited. Finally, this filtering is performed after the fact, which limits its real-time applicability. It would be preferable to perform a frame-by-frame inversion of the sea clutter, which would pave the way for real-time application.

[0013] Furthermore, sea clutter is highly inhomogeneous, depending on the area of ​​the radar field of view considered. Close to the radar, sea clutter is primarily modulated by the radial slope of the free surface elevation, while far from the radar, the occlusion (or masking) of troughs and small waves by larger waves in front dominates image formation. Moreover, sea clutter patterns are very pronounced along the main wave propagation axis, but much less so along the axis perpendicular to it. Thus, a free surface elevation (SLE) reconstruction method that takes into account the location within the radar field of view is desirable.

[0014] In order to overcome the limitations of the standard method, the following work focuses on the inversion of sea clutter image by image, using deep learning methods, making it possible to solve highly non-linear problems: - Ehlers, Svenja; Klein, Marco; Heinlein, Alexander; Wedler, Mathies; Desmars, Nicolas; Hoffmann, Norbert; Stender, Merten (2023) Machine learning for phase-resolved reconstruction of nonlinear ocean wave surface elevations from sparse remote sensing data. In: Ocean Engineering, vol. 288, p. 116059. DOI: 10.1016 / j.oceaneng.2 023.116059. -Zhao, Mingxu; Zheng, Yaokun; Lin, Zhiliang (2023) Sea surface reconstruction from marine radar images using deep convolutional neural networks. In: Journal of Ocean Engineering and Science, vol. 8, no. 6, p. 647-661. DOI: 10.1016 / j.joes.2023.09.002.

[0015] However, neither of these two works adjusts the inversion model according to the location within the radar's field of view. Furthermore, the first of these two references only performs an inversion along a radial cross-section of a radar's field of view, and not on a surface.

[0016] Furthermore, the method described in French patent FR3108152 (corresponding to patent applications WO2021 / 180502 and US 2023 / 0167796) employs one or more sensors (e.g., a radar, a LiDAR, an accelerometer, a displacement sensor, a pressure sensor, etc.) that measure the free surface elevation of the wave or the resulting characteristics at one or more points and derive predictions of the wave or resulting wave characteristics by means of transfer functions. This method allows for a good prediction of a wave resultant but does not allow for determining the free surface elevation at any point in an area from a radar signal.

[0017] The present invention aims to develop an improved method for determining the free surface elevation of a body of water using radar. In particular, it seeks to overcome the drawbacks of prior solutions by taking into account the spatial variability of sea clutter within the radar's field of view. Summary of the invention

[0018] The invention relates firstly to a method for determining the free surface elevation (FSE) of an area of ​​a body of water, such that, according to said method, 1) - at least one training database is constituted of a plurality of image pairs (W,R), each pair consisting of a first image (W) of free surface elevation (FSE) and a second radar return image (R), the two images of the same pair corresponding to the same area of ​​the surface of the body of water and to an identical or close instant in time, said images (W) and (R) being real or simulated 2) - to each pair of images (W,R) are added spatial characteristics of said area of ​​the surface of the body of water corresponding to this pair, spatial characteristics including at least the position relative to the radar and to the principal direction(s) of the waves, said spatial characteristics being directly known during the acquisition of the images, or being deduced from the analysis of the images themselves, or provided by an external source. 3) - at least one deep neural network, in particular of the convolutional type, or "transformer" or Fourier neural operator, is trained on at least said training database, using said spatial features to specialize said deep neural network(s), and to obtain a reconstruction model of the elevation free surface (ESL) 4) - Real return images are acquired by radar 5) - we apply said reconstruction model to said real radar return images acquired to obtain the free surface elevation (FSE).

[0019] For the purposes of the invention, "near" time means a different time but offset by an instant less than the rotation period of a radar, in particular by an instant less than three seconds.

[0020] Advantageously, the first image (W) of each image pair (W,R) can be obtained by discretizing three-dimensional time series of free surface elevation (FSE) generated by a numerical wave field simulation code, and the second image (R) of each image pair (W,R) by discretizing radar returns generated by a numerical radar simulation code.

[0021] The first images (W) of each image pair (W,R) may originate from actual free surface elevation (FSE) measurements over at least a portion of the area covered by the radar. They may be obtained in particular with at least a remote sensor of the LiDAR type (an acronym for "Light Detection And Ranging," designating a remote measurement technique based on the analysis of the properties of a light beam reflected back to its emitter) or a stereoscopic camera system or an array of measurement buoys. The second radar return images (R) may originate from actual measurements taken by at least one radar, including an X-band or S-band maritime radar.

[0022] The training database may include a first database of pairs of (W,R) surface elevation and radar return images (R), all of which are simulated, and a second database of pairs of (W,R) surface elevation and radar return images, all of which are real, the relative weight of said two databases possibly being able to be adjusted.

[0023] Said spatial characteristics may include a distance to an origin, said origin corresponding in particular to the position of the radar, and an angular orientation, in particular an azimuth.

[0024] The or at least one of the deep neural networks may be an encoder-decoder network, for example of U-Net architecture.

[0025] To obtain the free surface elevation (ESL) reconstruction model, the following procedure can be used: - Each image pair (W,R) is divided into n distinct zones, based on spatial characteristics, n being greater than or equal to 2, and in particular being equal to 4 - n deep neural networks are used, each deep neural network being specialized on a dedicated zone of the image pair, - Each neural network is trained on its dedicated image pair area (W,R).

[0026] In this case, we can divide the said image pairs (W,R) into n zones as a function of the azimuth and the distance to the radar.

[0027] To obtain said reconstruction model, one can proceed as follows: - at least one first guide image (Rgl) is formed for each radar return image (R) of the training base by means of a radar distance map, and the deep neural network is trained by means of said surface elevation image (W) and said at least first guide image (Rgl) associated.

[0028] In this case, at least one second guide image (Rg2) can be formed by means of an angular orientation map, and the deep neural network is trained also by means of said associated second guide image (Rg2).

[0029] The method for determining the free surface elevation (FSE) of an area of ​​a body of water according to the invention can implement the following steps: A1) a first image database (W) is constructed, obtained from three-dimensional time series of free surface elevation, in particular the elevation (z), the position in Cartesian (x,y) or polar (r, ¢) coordinates, and the time (t), generated by a wave field simulation code corresponding to different sea states; A2) a second image database, called return images (R), is constructed, obtained from radar returns generated by a radar simulation code using the time series generated by the wave field simulation code, parameterized according to environmental conditions, in particular wind speed and direction and the presence of precipitation. A3) we construct a training set comprising a first set of images from the first database (W) constructed in step A1) and a first set of corresponding return images from the second database (R) constructed in step A2) by integrating the environmental conditions used in step A2), so as to obtain image pairs (W,R) each consisting of a first image (W) of surface elevation and a second radar return image (R), the two images of the same pair corresponding to the same area of ​​the surface of the body of water and to an identical or close instant in time, A4) To each pair of images (W,R) in the training database, the spatial characteristics of the area of ​​the water surface corresponding to that pair are added, said spatial characteristics including a distance to an origin, said origin corresponding in particular to the position of the radar, and an orientation, in particular in azimuth, with respect to the principal direction(s) of the waves A5) a free surface elevation reconstruction model is built from the training database obtained in step A3) and the spatial features specified in step A4), by training at least one deep neural network of the convolutional or "transformer" type, in particular of the U-net type or a transformer architecture adapted to vision, or even a Fourier neural operator, the said network(s) being specialized with the spatial characteristics obtained in step A4) A6) real images are acquired using at least one radar, in particular maritime, to which their spatial characteristics defined in step A4 are added A7) the free surface elevation is determined by applying the free surface elevation reconstruction model obtained in step A5) at least to the real images acquired with the radar in step A6) with their spatial characteristics.

[0030] Preferably, in step A1) of constructing the first image database, the images are generated with scanning parameters comprising a distance (range) discretization Ar, an azimuth angle discretization Aÿ in a polar coordinate system centered around the radar, and a temporal discretization 60, where Nr is the rotation speed of the radar in rpm.

[0031] Preferably, in step A2) of constructing the second return image database, the radar simulation code is parameterized according to environmental conditions chosen from at least: the presence or absence of wind, wind speed, wind direction, the presence or absence of precipitation such as rain, precipitation intensity, the presence or absence of fog, temperature and sea state.

[0032] Advantageously, in step A2) of constructing the second return image database, each image can be generated with spatial discretizations Ar and A0 and temporal discretizations Af according to the same digitization parameters as those used in step Al) of constructing the first image database.

[0033] Advantageously, in step A5) of constructing the free surface elevation reconstruction model, said model can be validated with a validation database composed of a second set of images from the first database constructed in step A11) and a second set of corresponding return images from the second database constructed in step A2), said sets being different from those used for training.

[0034] Advantageously, in step A6) of acquiring real images using at least one maritime radar, said images can be recorded, and, in step A7) of determining the free surface elevation (FSE), a means of communication, in particular a computer means, can be used to access said recorded radar images.

[0035] Steps A1) to A5) can be carried out at least without connection to a communication network, such as an intranet or internet.

[0036] Step A7) can be performed without a connection to a communication network, using actual radar images acquired in step A6) and pre-recorded. Alternatively, steps A6) and A7) can be performed via a connection to a communication network, with acquisition and recording of radar images in step A6) and use of said radar images in step A7) as they are recorded.

[0037] The method according to the invention can also implement the following additional steps carried out between steps A5 and A6: B0) Free surface elevation (FSE) measurements are taken over at least a portion of the area covered by the radar, particularly a maritime radar, simulated in step A11, in particular using a stereoscopic camera system, a LIDAR, or an array of measuring buoys. B1) We construct a database of images obtained by digitizing the actual wave measurements obtained in step B0). B2) We construct a database of images obtained from the actual return signals obtained with a maritime radar, synchronized in time with the image database constructed in step B1). B3) a real training database is constructed from a set of ESL free surface state measurement images from the database obtained in step B1) and a set of real radar return images from the database obtained in step B2), in the form of image pairs, B4) To each pair of images from step B3) associating real ESL free surface elevation measurements and real radar returns, the spatial characteristics of the corresponding area of ​​the water surface are added, in particular in terms of distance and direction relative to the principal wave direction(s). B5) The free surface elevation reconstruction model built in step A5) is made more robust from the real training database built in step B3) and the spatial characteristics determined in step B4), using machine learning or deep learning methods, on areas concordant between real measurements and real radar returns.

[0038] (By "more robust" we understand that when applying this reconstruction algorithm to real radar data, the free surface elevation (FSE) reconstruction errors are less than those that would have been obtained with the algorithm trained only on simulated data). B6) real images are acquired using at least one radar, in particular maritime B7) Step A7) is replaced by step B7) by applying the improved free surface elevation reconstruction model obtained in step B5) at least to the real images acquired with the radar in step B6).

[0039] To carry out step B5), we can use the real data from step B3) directly with the simulated data from step A3) and perform learning from scratch in the same way as in step A5), or we can use a so-called "transfer learning" approach, in which the network pre-trained in step A5) is fitted on the real data built in step B4).

[0040] Steps B0) to B5) can be carried out at least offline, without connection to a communication network, after having carried out steps A1) to A5).

[0041] The invention also 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: - the elevation of the free surface of said body of water is determined by means of the free surface elevation determination method as described above; and - said wave-driven system is supervised, operated, or controlled as a function of the free surface elevation of said body of water thus determined.

[0042] The invention also relates to a computer, server or calculator configured to implement the free surface elevation determination method as described above.

[0043] The invention also relates to a computer program product downloadable from a communication network and / or recorded on a medium readable by a computer, a server or a calculator and / or executable by a processor, comprising program code instructions for implementing the free surface elevation determination method as described above, when said program is executed on a computer, a server or a calculator.

[0044] The invention also relates to a computer-readable storage medium, server or calculator, storing instructions which, when executed by a computer, server or calculator, imply that the computer, server or calculator implements the free surface elevation determination method as described above.

[0045] The invention therefore makes it possible to reconstruct wave fields from radar images using deep neural networks, for example convolutional neural networks, which are specialized by direction and distance: the main direction(s) of the wave are determined on the basis of the raw radar signals (images), then deep neural networks (or other model from machine or deep learning) are applied, specialized according to the directions resulting from the previous analysis and the distance between the measurement made by the radar and the radar itself.

[0046] In fact, since deep neural networks provide a prediction that is intrinsically translationally invariant, information indicating how far from the origin the data is located, as well as its orientation, allows to improve prediction quality: the integration of this type of spatial information, which is not explicitly contained in the data, into the training of neural networks had never been proposed until now.

[0047] In summary, the invention thus determines, in real time, the free surface elevation at any point within a body of water, accurately and simply, from images of the body of water provided by a radar. To this end, the invention implements a training campaign to be carried out, in particular, offline. This training campaign is performed using data from a radar simulator, specifically synthetic (simulated) free surface elevations and synthetic (simulated) radar returns calculated by said simulator. It makes it possible to build a free surface elevation reconstruction model from radar images, based on deep neural networks (or another machine learning or deep learning method), networks which are preferably specialized or guided by the direction and distance of the radar return (echo or sea clutter).

[0048] The invention proposes to integrate information allowing to indicate at what distance from the origin the data is located, as well as its orientation, into the training of neural networks.

[0049] Several implementations / variants of the invention are possible, including – using at least n (n > 2) deep neural networks on as many different areas of the image, or - by using a single neural network, modified from the standard formulation, by guiding it from spatial maps informing it of the distance to the radar position and / or the direction (or directions) of wave propagation, or - by combining the two approaches (several spatially guided neural networks).

[0050] Other features and advantages of the method and system according to the invention will become apparent from the following description of non-limiting examples of embodiment, with reference to the figures attached and described below. List of figures

[0051] [Fig.1] Fig. 1 is an example of a radar image obtained by an X-band radar system on board a ship. [Fig.2] Figure [Fig. 2] is an image obtained from a simulated wave field. [Fig.3] [Fig.3] is an image obtained from simulated radar returns. [Fig.4a] The [Fig.4a] is a cross-section of a radar image for an azimuth of 10°. [Fig.4b] The [Fig.4a] is a cross-section of a radar image for an azimuth of 90°. [Fig. 5] Figure 5 illustrates the relationship between V waves and R radar images. [Fig.6] Figure [Fig. 6] represents a synoptic diagram of free surface elevation reconstruction by a deep neural network RN. [Fig.7] Figure 7 is an application of the invention with four different neural networks, RN1 to RN4, specialized according to azimuth range and range (distance). [Fig. 8a] The [Fig.8a] is a reconstruction representation obtained with a single deep neural network (here a convolutional U-Net type network). [Fig.8b] Figure 8b is a reconstruction obtained with four deep neural networks (here, U-Net convolutional networks) specialized by area of ​​the image. [Fig. 9] Figure [Fig.9] represents in block diagram form the process of the invention according to a first embodiment. [Fig.10] Figure 10 represents in block diagram form the process of the invention according to a second embodiment. [Fig.11] Figure

[11] represents radar images and guides, with the initial radar image (in polar representation) at the top left, with the corresponding guide on the right (distance function, intensity from black to white indicating short to high distances respectively), and at the bottom the radar image in Cartesian representation on the left, and the corresponding guide on the right.

[0052] The references retain the same meaning from one figure to another. Description of the implementation methods

[0053] The invention relates to a method for determining the free surface elevation of an area within a body of water. Recall that the free surface elevation is the water height at a point within a body of water relative to the water surface at rest (i.e., undisturbed). Thus, the free surface elevation reflects the height of waves or swell. A body of water can 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, particularly for monitoring, The 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 a measurement zone of the radar implemented in the method.

[0054] Fig. 5 illustrates the relationship between the waves V and the radar images R which correspond to the sea clutter Fm, the reconstruction model H according to the invention aimed at obtaining image sequences or a 3D film of the sea surface from a sequence of radar images.

[0055] The method for determining the free surface elevation of an area of ​​a body of water according to the invention can in particular be implemented by computer and can be used for monitoring, operation, or control of a system subjected to waves within said body of water.

[0056] The process according to the invention has, in particular, two non-limiting embodiments. The first mode is shown schematically in [Fig.9], and the second mode in [Fig.10]. The references in both figures have the following meanings: A: Wave field simulation B: Radar return simulation C: Construction of the free surface elevation image database D: Construction of the radar return image database E: Construction of the training database E': Enlargement of the training database F: Acquisition of radar images from a real radar G: Recognition of the spatial characteristics of images H: Construction of a free surface elevation reconstruction model H': Improvement of the free surface elevation reconstruction model I: Determination of the free surface elevation J: Acquisition of direct free surface elevation measurements over at least part of the radar coverage area K: Construction of the database of directly measured free surface elevation images 1: Discretization parameters derived from the radar's digitization characteristics 2: 3D time series of free surface elevation 4: Simulated radar return images 5: Simulated environmental conditions 6: Image pairs (simulated) 6': duos of (real) images 7: Image duos, conditions 8: Images of actual radar returns 9: Spatial characteristics 10: Reconstruction Model 10': Improved reconstruction model 11: Actual environmental conditions

[0057] In X-band maritime radar systems, the signals corresponding to radar backscatter, after post-processing, are sent to a screen as the radar beam rotates. Most modern radars allow these signals to be digitized and recorded, making them accessible. Generally, the backscatter signals recorded during an antenna rotation are grouped into a single image, a kind of "snapshot" of the sea clutter.

[0058] Figure 1 represents such an example of a radar image obtained by an X-band radar system on board a ship. In terms of image processing, the problem of reconstructing the wave surface elevation consists of recovering, from a radar image R, an "instantaneous" image of the sea clutter, an image of the wave field W, an "instantaneous" image of the free surface elevation in the area covered by the radar.

[0059] A first embodiment of the invention will be described with reference to [Fig. 9]: starting from discretization parameters derived from the digitization characteristics of a radar 1, by simulating wave fields A, image series 2 of 3D time series of simulated free surface elevation are obtained, and, from these image series, and taking into account simulated environmental conditions 5, radar returns B are simulated: associated simulated radar return images 4 are obtained. A database of free surface elevation images C and a database of radar return images D are then constructed.By combining the two databases C and D and incorporating simulated environmental conditions 5, a training database E is constructed, comprising image pairs 6 (preferably at least 3 pairs) associating simulated images with their simulated radar returns and the environmental conditions 7 corresponding to the image pairs. A spatial feature recognition 9 of the images is performed, which is used to construct H a free surface elevation reconstruction model 10, which, with the acquisition F of radar images from a real radar leading to the acquisition of real radar return images 8, will allow the determination I of the free surface elevation taking into account the real environmental conditions 11.

[0060] A second embodiment of the invention will be described with reference to [Fig. 10]. This second embodiment improves the results obtained by expanding the training database with real images as follows: We acquire J direct measurements of free surface elevation over at least part of the area covered by the radar. We digitize the images 12 of these direct free surface elevation measurements to construct K a database of directly measured free surface elevation images. In addition, we acquire F real radar images 8 from a real radar F, and we construct D' a database of real radar return images synchronized with the direct measurements. The resulting pairs of real images 6' are used to expand, E', the initial training database E obtained according to the previous embodiment (see [Fig. 9]).

[0061] From the image pairs 6 and 6' and the corresponding environmental conditions 7, the spatial characteristics of the images 9 are recognized G, which allows the free surface elevation reconstruction model 10' to be improved H', in order, as in the previous embodiment, to acquire F real radar images 8 from a real radar, and to obtain the determination of the free surface elevation from the improved model 10' and the real return images 8, under real environmental conditions 11.

[0062] The free surface elevation determination system applying the method according to the invention may include means of communication between different devices. Advantageously, the free surface elevation determined by the system can normally be shared on a computer communication bus, in particular a computer communication bus connected to a system exploiting this measurement in real time or not (for example, a system for monitoring, operating or controlling a system subjected to waves).

[0063] Furthermore, the invention relates to a method for monitoring (supervising), operating, or controlling (commanding), preferably an operating or controlling method, a system subjected to waves (such as a floating or non-floating platform, a ship, or a wave energy converter, for example), wherein the following steps are carried out: 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 / embodyments or combinations of variants / embodyments described above; and b. The system subjected to waves is controlled according to the determined elevation of the free surface.

[0064] 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.

[0065] According to one embodiment of the invention, the monitoring, operating or control method may include a (phase-advanced) prediction step of the elevation of the free surface of the water body area by means of the determined free surface elevation, and the control is carried out based on the prediction of the free surface elevation so as to anticipate the control at the future predicted free surface elevation, before its arrival on the system to be monitored, operated or controlled.

[0066] 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.

[0067] The monitoring, operation or control step may in particular consist of: - navigating a vessel in an area where the free surface elevation is minimal, so that the vessel can avoid severe sea conditions such as large waves - the stabilization of a floating platform or a ship depending on the free surface elevation, - the 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 as a function of the free surface elevation.

[0068] This could involve controlling an electrical machine equipping a wave energy converter system to optimize the power produced according to the wave height,

[0069] It can also involve controlling the angle of orientation of the blades, and / or the nacelle of a wind turbine according to the waves and swell.

[0070] The monitoring, operation or control step may also consist of carrying out an operation at sea when the free surface elevation is minimal, for example: - the rescue of a shipwrecked person from a ship, - the retrieval of an object from the surface of the water by a ship, - the installation of a marine or underwater object from a ship or platform (for example, an oil pipeline), - a takeoff or landing of an aircraft on an aircraft carrier, etc. - a transfer of personnel from a ship or platform (for example, maintenance of an offshore wind turbine) Examples

[0071] The characteristics and advantages of the method according to the invention will become clearer upon reading the application examples below. Example 1

[0072] Consider a radar image R and the free surface elevation image W of a corresponding wave field. These two images, composed of pixels, have the same width and the same height.

[0073] Figure 2 shows an image W generated with a wave field simulation code for a given sea state, characterized by a mean period and significant wave height and a directional spectrum. It represents a snapshot of the sea surface within a circle with a radius of 2000 m centered around the radar, extracted from the generated elevation time series, which has a duration at least as long as one radar rotation (2 seconds in this case). In the image, which is 1024 x 1024 pixels, the horizontal axis represents the azimuth 0, ranging from 0 to 360°, and the vertical axis represents the radar distance r, ranging from 48 to 2000 meters. Each pixel of the image represents the free surface elevation, normalized to have the same order of magnitude as the intensity in the radar image. On the x-axis, the figure represents the angle # in degrees, on the y-axis on the left the span in meters and on the right the normalized free surface elevation.

[0074] The image R, shown in Figure 3, is obtained from radar returns generated by a radar simulation code using time series generated by the wave field simulation code, parameterized according to different environmental conditions (presence or absence of wind, rain, fog, etc.). Each image is generated with the same spatial discretizations Ar and A^ as the wave field image (same units represented on the x and y axes as in [Fig. 2], with the intensity of the radar return on the right).

[0075] If we analyze the R image, we observe that the characteristics of the radar return are quite different along the direction of wave propagation (which corresponds to azimuths of 90° - 100° and 270° - 280°, in this example) compared, in particular, to the perpendicular direction. They also differ depending on the distance of the radar, between the lower and upper parts of the image.

[0076] These differences can also be visualized by the cross-sections at different azimuths of the radar image shown in figures 4a (cross-section at an azimuth of 10°) and 4b (cross-section at an azimuth of 90°): we see differences between what can be called the close range, up to 1000 m, and the far range beyond 1000 m, but also between the two cross-sections, especially in the far range.

[0077] A training set is created from pairs of images (R, W) corresponding to the same situation. A minimum of three pairs of images is required to constitute this training set. However, it is preferable for the set to contain more duos to obtain a model capable of reconstructing the free surface elevation of the swell in several scenarios.

[0078] During the learning phase, a deep neural network of the "transformer" type or of the convolutional type can be used, for example, a U-Net encoder-decoder network, which is the non-limiting example chosen for the examples, preferably with a set of weights to be optimized S (In a known way, each neural network is associated with a set of parameters (weights) to be optimized).

[0079] During this phase, a radar image R is given as input to the convolutional neural network, and the latter calculates a result image W. This output is compared to the expected wave field image W by a loss function L. This loss function is, for example, a measure of structural similarity index (see Wang et al. 2004: Zhou Wang, AC Bovik, HR Sheikh, and EP Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600-612, 2004).

[0080] The result of L is used to update the set of weights & of the network G by a stochastic gradient backpropagation method and thus obtain optimal weight values

[0081] For example, a possible optimization method is described by Adam in the publication Diederik & Ba, 2015 (Diederik, PK, & Ba, J. (2015). Adam: A method for stochastic optimization. CoRR, abs / 1412.6980), with 50 epochs: the set of image pairs in the training set is seen 50 times by the network, with a learning rate of 3.104.

[0082] Formally:

[0083] argminJE(2î)[L(W, f^R)) ] ] [°°841 L(W.W') -1-SSM(W,

[0085] with 11 mean, variance, = O.Olet G = 0.03.

[0086] This free surface elevation reconstruction process by a convolutional neural network is schematically represented in Figure 6, which is a synoptic of the free surface elevation reconstruction process by a deep neural network RN such as a U-Net: it shows the image W processed by the radar model RM, to obtain the radar return R, then the use of a neural network such as U-Net to obtain the result image W.

[0087] It is observed that if several standard convolutional neural networks are used, training them on different areas of the image pair, rather than just one, much better results are obtained.

[0088] In this example, we consider four convolutional neural networks specialized according to azimuth range and range (distance) range: - Network No. 1 RN1 ([Fig.7]) learns on the close range, up to 1000 m, and on the in-wave azimuth range, i.e. two 90° intervals centered around the main wave direction (-95°) and its complement at 360° (-275°). - Network No. 2 RN2 learns on the close range, up to 1000 m, and on the off-wave azimuth range, i.e. two 90° intervals centered around the directions perpendicular to the main wave direction (~5° and -185°). - Network No. 3 RN3 learns on the far range, beyond 1000 m, and on the in-wave azimuth range. - Network No. 4 RN4 learns on the far range ("far range") and on the off-wave azimuth range ("off-wave").

[0089] These four neural networks RN1 to RN4 are represented in [Fig.7]: they are thus specialized in the image which is divided into four zones, both according to the azimuth range and according to the range (distance).

[0090] This choice of four neural networks is of course an example, the invention being able to apply to a lower or higher number of neural networks, depending on the number of areas that one wants to distinguish in the image.

[0091] Figures 8a and 8b represent reconstruction results (with the same units on the abscissa and ordinate axes as for Figures 2 and 3): - with a single neural network (standard U-Net): [Fig.8a] - and with 4 neural networks (U-Nets) specialized by area of ​​the image: [Fig. 8b]

[0092] The metric used is the local correlation between Wet and W in both cases: values ​​close to 1 indicate a strong similarity between the images, area by area. A clearly better reconstruction is obtained with the specialized U-Nets, particularly in the "off-wave" azimuth ranges. Example 2

[0093] In this example, the standard convolutional neural network (U-Net type) is modified by guiding it using a distance map that provides information about the distance to the radar position. This information, which is not initially present in the data, can be constructed from a distance map, i.e., an image of the same size as the radar image, indicating the distance to the radar at each point.

[0094] Examples of these guides, in polar and Cartesian representation, are given in [Fig. 11], which represents radar images and guides, with the initial radar image (in polar representation) at the top and the corresponding guide on the right (distance function, intensity from black to white indicating distances). low to high respectively), and below the radar image in Cartesian representation on the left, and the corresponding guide on the right.

[0095] The information corresponding to the orientation can be constructed in the same way. Training and prediction from the network is carried out using this / these guide(s).

[0096] In practice: - A guide image G is constructed based on the problem to be solved. Here, it involves constructing an image the same size as the radar image, indicating the radar distance at each point. Another guide image could also be one providing an angular indication. - The input data is converted into a pair of images—a radar image and a distance map—and fed to the convolutional neural network. It would also be possible to use three or more guide images. Formally:

[0097] g=

[0098] fCJ)(R) =fe(R,G)

[0099] Applied to wave height estimation, on a training dataset of only 5 image pairs, the following improvements were obtained, both in the initial data representation (polar representation) and in the Cartesian representation. Table 1 below compares the estimation using a standard or guided U-net, in polar or Cartesian representation. The closer the SSIM score is to 1, the greater the similarity.

[0100] To quantify the results, the network estimates are compared to the expected results by a structural similarity index measure [Wang et al. 2004].

[0101] [Tables 1] Cartesian Polar Representation U-net Guided U-net Guided U-net SSIM Score 0.8608 0.8639 0.7504 0.8279

[0102] These data show that with a U-Net type network, good similarity is already achieved, and that with a guided U-Net network, the results are even better (SSIM scores even closer to 1). It should be noted that SSIM is an acronym for the English expression "Structural Similarity Index Measure".

[0103] In conclusion, the invention is therefore very effective, and offers different levels of performance depending on the embodiment chosen.

[0104] It is emphasized that while the examples use U-Net neural networks for illustrative purposes, the invention applies analogously to other types of deep neural networks, particularly those called "transformers" (in an architecture " "transformer" adapted to the vision), notably such as those described in the publication: Tianyang Lin, Yuxin Wang, Xiangyang Liu, Xipeng Qiu, A survey of transformers, AI Open, Volume 3, 2022, Pages 111-132, ISSN 2666-6510. (https: / / doi.org / 10.1016Zj.aiopen.2022.10.001).

[0105] It also applies analogously to at least one Fourier neural operator, notably as described in the publication Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). “Fourier neural operator for parametric partial differentia”1 equations. arXiv preprint arXiv:2010.08895.

[0106] It is also emphasized that the method according to the invention comprises various steps, which can be implemented using computer-based means, in particular a computer, a server, or a calculator. These steps can be carried out online (using computer-based means connected via computer communication, such as the internet / intranet) or offline: thus, in particular, the acquisition of real images can be done online or offline (by pre-recording and making them accessible).

Claims

1. Demands A method for determining the elevation of the free surface area (ESL) of an area within a body of water, characterized in that, according to said method, 1) - at least one training database (E) is constituted of a plurality of pairs (6) of images (W,R), each pair consisting of a first image (W) of the free surface elevation ESL and a second radar return image (R), the two images of the same pair corresponding to the same area of ​​the surface of the body of water and to an identical or close instant in time, said images (W) and (R) being real or simulated 2) - to each pair of images (W,R) are added spatial characteristics of said area of ​​the surface of the body of water corresponding to that pair, said spatial characteristics (9) including at least the position relative to the radar and to the principal wave direction(s), said spatial characteristics being directly known during the acquisition of the images, or being deduced from the analysis of the images themselves, or provided by an external source, 3) - at least one deep neural network, in particular of the convolutional type, or of the "transformer" type or a Fourier neural operator, is trained on at least said training database (E,E'), using said spatial features (9) to specialize said deep neural network(s), and to obtain a model (H) of reconstruction of the elevation of the free surface ESL in the following way: - Each pair of images (W,R) is divided into n distinct zones, based on spatial characteristics, where n is greater than or equal to 2, and in particular equal to 4 - we use n deep neural networks (RN1, RN2, RN3, RN4), each deep neural network being specialized on a dedicated area of ​​duo (6) of images (W,R), - Each neural network is trained on its dedicated image pair area (W,R). 4) - real return images (8) are acquired by radar 5) - we apply said reconstruction model (H,H') to said real return images (8) of radar acquired to obtain the free surface elevation ESL (I).

2. A method according to the preceding claim, characterized in that the first image (W) of each pair (6) of images (W,R) is obtained by discretizing three-dimensional time series (2) of free surface elevation ESL generated by a numerical wave field simulation code (A), and the second image (R) of each pair of images (W,R) is obtained by discretizing radar returns generated by a numerical radar simulation code (B).

3. A method according to any one of the preceding claims, characterized in that the first images (W) of each pair (6) of images (W,R) are derived from actual ESL free surface elevation measurements, in particular carried out with at least one remote LiDAR-type sensor or stereoscopic camera system or set of measuring buoys, over at least a part of the area covered by the radar, and in that the second radar return images (R) are derived from actual measurements carried out by at least one radar, in particular an X-band or S-band maritime radar.

4. A method according to any one of the preceding claims, characterized in that the training database (E,E') comprises a first database of image pairs (W,R) of surface elevation and radar return images (R), all of which are simulated images, and a second database of image pairs (W,R) of surface elevation and radar return images, all of which are real images, the relative weight of said two databases optionally being able to be adjusted.

5. A method according to any one of the preceding claims, characterized in that said spatial characteristics (9) comprise a distance to an origin, said origin corresponding in particular to the position of the radar, and an angular orientation, in particular an azimuth.

6. A method according to any one of the preceding claims, characterized in that the or at least one of the deep neural networks (RN1, RN2, RN3, RN4) is an encoder-decoder network, for example of U-Net architecture.

7. A method according to any one of the preceding claims, characterized in that said pairs (6) of images (W,R) are divided into n zones as a function of azimuth and distance to radar.

8. A method according to any one of the preceding claims, characterized in that, to obtain said reconstruction model (H,H'), at least one first guide image Rgl is formed for each radar return image (R) of the training base (E,E') by means of a radar distance map, and the deep neural network is trained by means of said surface elevation image (W) and said at least first guide image Rgl associated with it.

9. Method according to the preceding claim, characterized in that, to obtain said reconstruction model (H,H'), at least one second guide image Rg2 is formed by means of an angular orientation map, and the deep neural network is trained also by means of said associated second guide image Rg2.

10. A method for determining the free surface elevation (FSE) of an area of ​​a body of water according to any one of the preceding claims, characterized in that the following steps are carried out: A1) a first image database (W) is constructed, obtained from three-dimensional time series (2) of free surface elevation, in particular the elevation (z), the position in Cartesian (x,y) or polar (r, β) coordinates, and the time (t), generated by a wave field simulation code (A) corresponding to different sea states; A2) a second image database, called return images (R), is constructed, obtained from radar returns generated by a radar simulation code (B) using said time series generated by the wave field simulation code, parameterized according to environmental conditions (5).in particular the wind speed and direction and the presence of precipitation A3) we construct a training set (E,E') comprising a first set of images from the first database (W) constructed in step A1) and a first set of corresponding return images from the second database (R) constructed in step A2) by integrating the environmental conditions used in step A2), so as to obtain image pairs (W,R) each consisting of a first image (W) of surface elevation and a second radar return image (R), the two images of the same pair corresponding to the same area of ​​the surface of the body of water and to an identical or close instant in time, A4) To each pair of images (W,R) in the training database (E,E'), the spatial characteristics (9) of the area of ​​the water surface corresponding to that pair are added, said spatial characteristics including a distance to an origin, said origin corresponding in particular to the position of the radar, and an orientation, in particular in azimuth, with respect to the principal direction(s) of the waves. A5) A free surface elevation reconstruction model (H,H') is constructed from the training database (E,E') obtained in step A3) and the spatial characteristics specified in step A4), by training at least one deep neural network of the convolutional or "transformer" type, in particular of the U-Net type, or Fourier neural operator, said network(s) being specialized with the spatial characteristics obtained in step A4). A6) The data is acquired real images (F) using at least one radar, including maritime radar,to which are added their spatial characteristics defined in step A4) A7) the free surface elevation ESL is determined by applying the (H,H') free surface elevation reconstruction model obtained in step A5) at least to the real images (8) acquired with the radar in step A6) with their spatial characteristics.,

11. Method according to the preceding claim, characterized in that, in step A2) of constructing the second return image database, the radar simulation code is parameterized according to environmental conditions (5) chosen from at least: the presence or absence of wind, wind speed, wind direction, the presence or absence of precipitation such as rain, precipitation intensity, the presence or absence of fog, temperature and sea state.

12. A method according to any one of claims 10 or 11, characterized in that, in step A5) of construction of the (H,H') free surface elevation reconstruction model, said model is validated with a validation database composed of a second set of images from the first database constructed in step A11) and a second set of corresponding return images from the second database constructed in step A2), said sets being different from those used for training.

13. A method according to any one of claims 10 to 12, characterized in that, in step A6) of acquiring (F) the real images (8) using at least one maritime radar, said images are recorded, and in that, in step A7) of determining the free surface elevation ESL, a means of communication, in particular a computer means, is used to access said recorded radar images.

14. A method according to any one of claims 10 to 13, characterized in that the following additional steps are also carried out (which are performed between steps A5 and A6): B0) ESL free surface elevation measurements are performed over at least part of the area covered by the radar, in particular a maritime radar, simulated in step A1a), in particular by means of a stereoscopic camera system, a LIDAR or an array of measuring buoys; B1) a database of images obtained by digitizing the actual wave measurements obtained in step B0); B2) a database of images obtained from the actual return signals obtained with a maritime radar is constructed, synchronized in time with the image database constructed in step B1a).B3) A real-world training database is constructed from a set of ESL measurement images from the database obtained in step B1) and a set of real radar return images from the database obtained in step B2), in the form of image pairs. B4) To each image pair from step B3, associating real ESL free surface elevation measurements and real radar returns, the spatial characteristics of the corresponding area of ​​the water surface are added, particularly in terms of distance and direction relative to the principal wave direction(s). B5) The free surface elevation reconstruction model constructed in step A5) from the real-world training database obtained in step B3) and the spatial characteristics determined in step B4) is made more robust, using machine learning or deep learning methods.on areas where actual measurements and radar returns are consistent, B6) actual images (8) are acquired (F) using at least one radar, particularly a maritime radar, B7) Step A7) is replaced by step B7) by applying the improved free surface elevation reconstruction model (H') obtained in step B5) at least to the real images (8) acquired with the radar in step B6).

15. A method for monitoring, operating, or controlling a wave-driven system within a body of water, wherein the following steps are carried out: - the free surface elevation of said body of water is determined by means of the free surface elevation determination method according to any one of the preceding claims; and - said wave-driven system is supervised, operated, or controlled as a function of the free surface elevation of said body of water thus determined.

16. Computer, server or calculator configured to implement the method according to any one of claims 1 to 15.

17. Product computer program downloadable from a communication network and / or stored on a medium readable by a computer, server or calculator and / or executable by a processor, comprising program code instructions for carrying out the method according to any one of claims 1 to 15, when said program is executed on a computer, server or calculator.

18. Computer-readable storage medium, server or calculator, storing instructions which, when executed by a computer, server or calculator, imply that the computer, server or calculator implements the method according to any one of claims 1 to 15.

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