A wave field reconstruction method

Abstract

The application discloses a wave field reconstruction method, which comprises the following steps: firstly, obtaining a standardized space-time data set, the data set containing effective wave height, average wave period and wave direction; then, constructing a low-rank joint wave feature subspace according to the data set; after obtaining sparse observation data and constructing an observation matrix and an observation vector based on the observation data, performing sparse regression on each variable of the data set based on the feature subspace, the matrix and the vector, obtaining a preliminary spatial distribution result of each variable, then performing Gaussian weighted fusion smoothing according to the distribution result, obtaining a preliminary reconstruction result, then determining the dynamic weight of each variable based on the reconstruction result, and optimizing the preliminary reconstruction result according to the weight, obtaining a target reconstruction result. The embodiment of the application can effectively reconstruct a high-resolution wave field under limited observation conditions, improve the reconstruction accuracy, simplify the calculation process, adapt to complex data scenarios, and quickly output high-quality results.

Description

TECHNICAL FIELD

[0001] Embodiments of the present application relate to, but are not limited to, the field of wave field reconstruction, and in particular to a wave field reconstruction method. BACKGROUND

[0002] In related technologies, due to factors such as deployment cost of observation equipment and complexity of marine environment, wave observation data is often sparsely distributed. How to achieve high-precision reconstruction of complete wave field under sparse observation conditions has become a core problem restricting the reliability of marine engineering evaluation and the improvement of marine disaster warning capability.

[0003] The existing technology mainly has three paths: one is a numerical model method, which solves wave dynamics equations through WAM, WWIII, SWAN and other spectrum models, considers the interaction of wave and flow radiation stress based on the principle of energy conservation, and can stably simulate various wave evolution, but requires high parameters of complex source terms and consumes more computing resources, which is difficult to adapt to real-time reconstruction; the second is a data-driven method, which uses the nonlinear fitting and feature extraction capabilities of deep learning, and some schemes integrate physical priors to deal with data missing, but rely on massive data and high-performance equipment, and the calculation time is long, and when the data is insufficient or noisy, it is easy to overfit / underfit, and there are practical difficulties in parameter optimization and training data selection; the third is a satellite remote sensing method, which integrates high-resolution numerical models and multi-source satellite data, and uses variational assimilation framework to optimize the spatiotemporal distribution of marine elements, which has good accuracy in sparsely observed areas and can capture cyclonic wave distribution, but is limited by satellite resolution, sampling frequency and environmental interference, and the adaptability of real-time reconstruction still needs to be improved. SUMMARY

[0004] The following is a summary of the subject matter detailed in the description. This summary is not intended to limit the scope of the claims.

[0005] The embodiments of the present application provide a wave field reconstruction method, which can reconstruct high-resolution wave field, improve accuracy to meet the needs of marine engineering and disaster warning, simplify calculation, adapt to complex scenarios, and quickly output high-quality results, providing reliable support for data-driven wave inversion and prediction.

[0006] The embodiment of the application provides a wave field reconstruction method, the method comprises the following steps: obtaining a standardized space-time data set, the data set containing effective wave height, average wave period and wave direction; constructing a low-rank joint wave feature subspace according to the standardized space-time data set; obtaining sparse observation data, and constructing an observation matrix and an observation vector based on the sparse observation data; based on the low-rank joint wave feature subspace, the observation matrix and the observation vector, performing sparse regression on each variable of the standardized space-time data set to obtain a preliminary spatial distribution result of each variable; obtaining a preliminary reconstruction result by Gaussian weighted fusion smoothing according to the preliminary spatial distribution result of each variable; determining the dynamic weight of each variable based on the preliminary reconstruction result, and optimizing the preliminary reconstruction result according to the dynamic weight to obtain a target reconstruction result.

[0007] In an embodiment of the application, the step of obtaining a standardized space-time data set comprises: obtaining wind field data and topographic bathymetric data of a target simulation area, simulating a wave field of a target sea area by using a sea wave numerical model based on the wind field data and the topographic bathymetric data, and extracting effective simulation wave height, average wave simulation period and wave direction simulation data in a target region from the wave field of the target sea area; performing error comparison according to the effective simulation wave height, the average wave simulation period, the wave direction simulation data and wave reference data to obtain target simulation data; and performing standardization, normalization and singular value decomposition noise reduction processing on the target simulation data to obtain a standardized space-time data set.

[0008] In an embodiment of the application, the low-rank joint wave feature subspace is constructed according to the standardized space-time data set, comprising: embedding the effective wave height, the average wave period and the wave direction in the standardized space-time data set into a three-dimensional tensor to obtain a time-consistent three-dimensional tensor sequence; wherein the three-dimensional tensor dimension comprises a time step, a spatial point and a parameter channel, and the parameter channel corresponds to three groups of wave parameters; performing low-rank decomposition on the three-dimensional tensor to extract a time mode, a spatial mode and a parameter correlation mode corresponding to the time step, the spatial point and the parameter channel dimension; and obtaining a low-rank joint wave feature subspace based on the extracted time mode, spatial mode and parameter correlation mode.

[0009] In an embodiment of the application, the step of obtaining sparse observation data comprises: determining a unified spatial rank adapted to different sea states by Bayesian optimization based on the low-rank joint wave feature subspace; determining a target sensor layout by iteratively optimizing the position and number of sensors through a genetic algorithm based on the low-rank features corresponding to the unified spatial rank; and obtaining sparse observation data by data collection in a target sea area according to the target sensor layout.

[0010] In an embodiment of the present application, the constructing the observation matrix and the observation vector based on the sparse observation data comprises: based on the sparse observation data, combining the total space grid number of the standardized space-time data set and the target sensor layout, a sparse observation matrix is constructed; the sparse observation data is sorted according to the significant wave height, the average wave period and the wave direction respectively, and an observation vector is constructed based on the sorted sparse observation data.

[0011] In an embodiment of the present application, the observation vector comprises a significant wave height observation vector, an average wave period observation vector and a wave direction observation vector; the sparse regression of each variable of the standardized space-time data set based on the low-rank joint wave feature subspace, the observation matrix and the observation vector to obtain the preliminary spatial distribution result of each variable comprises: based on the low-rank joint wave feature subspace, a first low-rank tensor basis corresponding to the significant wave height, a second low-rank tensor basis corresponding to the average wave period and a third low-rank tensor basis corresponding to the wave direction are determined; the first low-rank tensor basis, the second low-rank tensor basis and the third low-rank tensor basis are used for iterative calculation according to the observation matrix, the significant wave height observation vector, the average wave period observation vector, the wave direction observation vector, the first low-rank tensor basis, the second low-rank tensor basis and the third low-rank tensor basis respectively, to obtain a significant wave height sparse coefficient, an average wave period sparse coefficient and a wave direction sparse coefficient; the sparse regression of each variable of the standardized space-time data set is performed based on the significant wave height sparse coefficient, the average wave period sparse coefficient and the wave direction sparse coefficient, to obtain the preliminary spatial distribution result of each variable.

[0012] In an embodiment of the present application, before the sparse regression of each variable of the standardized space-time data set, the method further comprises: performing a sine-cosine component optimization processing on the wave direction in the preliminary spatial distribution result, and obtaining an optimized wave direction distribution result through an inverse cosine synthesis.

[0013] In an embodiment of the present application, the preliminary reconstruction result is obtained through a Gaussian weighted fusion smoothing according to the preliminary spatial distribution result of each variable, which comprises: taking the preliminary spatial distribution result of each variable as the to-be-smoothed data; setting a sliding window with a length of 5, and selecting the to-be-smoothed data of each current time and the to-be-smoothed data of each of the two times before and after the current time to form a window data set in a time-by-time sliding manner; assigning a weight to the window data set based on a Gaussian distribution, and performing a weighted average calculation on the to-be-smoothed data in the window data set according to the weight to obtain the preliminary reconstruction result.

[0014] In an embodiment of the present application, the dynamic weight of each variable is determined based on the preliminary reconstruction result, and the preliminary reconstruction result is optimized according to the dynamic weight to obtain a target reconstruction result, including: performing principal component analysis on the effective wave height, the average wave period and the wave direction in the preliminary reconstruction result, extracting the absolute load value of each variable in the first principal component at each time, and taking the normalized absolute load value as the dynamic weight of each variable; calculating the relative reconstruction error of each variable in the preliminary reconstruction result, and obtaining a multi-variable weighted comprehensive error according to the dynamic weight and the relative reconstruction error of the variable; and optimizing the preliminary reconstruction result of each variable according to the multi-variable weighted comprehensive error to obtain a target reconstruction result.

[0015] In an embodiment of the present application, the wave direction in the preliminary spatial distribution result is processed by sine-cosine component optimization, and the optimized wave direction distribution result is obtained by inverse cosine synthesis, including: converting the preliminary spatial distribution result of the wave direction into sine components and cosine components; based on the wave direction low-rank tensor base corresponding to the low-rank joint wave feature subspace, performing sparse regression optimization on the sine components and the cosine components respectively to obtain optimized sine components and cosine components; and according to the optimized sine components and cosine components, the optimized wave direction distribution result is calculated by an inverse tangent function.

[0016] The wave field reconstruction method provided in the embodiments of the present application first acquires a standardized space-time data set, which contains effective wave height, average wave period and wave direction, and then constructs a low-rank joint wave feature subspace according to the standardized space-time data set. After acquiring sparse observation data and constructing an observation matrix and an observation vector based on the sparse observation data, the variables of the standardized space-time data set are subjected to sparse regression based on the low-rank joint wave feature subspace, the observation matrix and the observation vector, to obtain preliminary spatial distribution results of the variables, and then the preliminary reconstruction result is obtained by Gaussian weighted fusion smoothing according to the preliminary spatial distribution results of the variables. Then, the dynamic weight of each variable is determined based on the preliminary reconstruction result, and the preliminary reconstruction result is optimized according to the dynamic weight to obtain a target reconstruction result. In the embodiments of the present application, the low-rank joint wave feature subspace is constructed based on the standardized space-time data set containing effective wave height, average wave period and wave direction under the condition of limited observation, and each variable is subjected to sparse regression by combining the observation matrix and vector constructed based on the sparse observation data, and then the Gaussian weighted fusion smoothing and dynamic weight optimization are performed, which can not only effectively reconstruct the high-resolution wave field and improve the reconstruction accuracy to meet the needs of marine engineering and disaster warning, but also simplify the calculation process, adapt to complex data scenarios, and quickly output high-quality results, thereby providing reliable support for data-driven wave inversion and prediction. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1is a flow chart of a wave field reconstruction method provided by an embodiment of the present application;

[0018] Figure 2 is a flow chart of a wave field reconstruction method provided by an embodiment of the present application Figure 1 is a specific flow chart of step 110 in the method;

[0019] Figure 3 is a physical modeling flow chart for generating a standardized spatiotemporal dataset provided by an embodiment of the present application;

[0020] Figure 4 is a specific flow chart of step 120 in the method; Figure 1

[0021] Figure 5 is a specific flow chart of step 140 in the method; Figure 1

[0022] Figure 6 is a specific flow chart of step 150 in the method; Figure 1

[0023] Figure 7 is a specific flow chart of step 150 in the method; DETAILED DESCRIPTION

[0024] In order to make the purposes, technical solutions and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0025] It should be noted that although a logical order is shown in the flow chart, in some cases, the steps shown or described can be performed in an order different from that in the flow chart. The terms "first", "second", etc. in the specification and claims and the above drawings are used to distinguish similar objects, and do not necessarily describe a specific order or sequence. It should be understood that the structures, proportions, sizes, etc. shown in the drawings of the present specification are only used to cooperate with the content disclosed in the specification, so as to be understood and read by those skilled in the art, and do not limit the defined conditions under which the present application can be implemented, and therefore do not have technical significance. Any modification of the structure, change of the proportional relationship or adjustment of the size, without affecting the effect and purpose that can be achieved by the present application, should still fall within the scope of the technical content disclosed by the present application. At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" used in the present specification are only for the convenience of clear description, and are not used to limit the scope of the present application, and the change or adjustment of the relative relationship, without substantially changing the technical content, is also regarded as the scope of the present application.​​​

[0026] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to be limiting of this application.

[0027] Wave information is an important basis for ocean research and engineering application. High-quality wave field evolution is not only the key to ensuring the safe operation of marine engineering, but also an important support for improving disaster warning level, optimizing disaster prevention and mitigation decision-making, and emergency response capability. In practical applications, due to the deployment cost of observation equipment, complex marine environment and other factors, wave observation data is often sparsely distributed. How to achieve high-precision reconstruction of complete wave field under sparse observation conditions has become a core problem restricting the reliability of marine engineering evaluation and the improvement of marine disaster warning capability. Around this problem, existing technologies mainly develop along three paths:

[0028] First, the numerical model method solves the wave dynamics equation through the wave analysis and prediction model (WAM), the third generation wave numerical prediction model (WWIII), the nearshore wave numerical model (SWAN) and other spectral models. Based on the principle of energy conservation balance, the interaction of radiation stress between wave and flow is considered, which can stably simulate the wave evolution under various conditions. However, this method requires high parameters of complex source terms and a large amount of computing resources, making it difficult to adapt to real-time reconstruction scenarios. Second, the data-driven method uses the nonlinear fitting and feature extraction capabilities of deep learning. Some schemes construct a joint optimization framework by fusing physical priors to deal with data missing. However, this method relies on massive experimental data and high-performance equipment, and the calculation time is long. When the data is insufficient and the noise is large, overfitting or underfitting may occur. The processing of abnormal data and the generalization ability are poor. At the same time, there are still practical difficulties in the optimal combination selection of a large number of adjustable parameters and the selection of training data. Third, the satellite remote sensing method fuses high-resolution numerical models and multi-source satellite observation data, and uses the variational assimilation framework to optimize the spatiotemporal distribution of marine elements. The reconstruction accuracy is good in the sparsely observed area, and the spatial distribution characteristics of the wave under the cyclone can also be captured. However, due to the limitations of satellite resolution, sampling frequency and environmental interference, the adaptability of real-time reconstruction still needs to be improved.

[0029] In view of this, the embodiment of the present application provides a wave field reconstruction method, first, a standardized spatiotemporal dataset is obtained, the dataset contains significant wave height, mean wave period and wave direction, then a low-rank joint wave feature subspace is constructed according to the standardized spatiotemporal dataset. After obtaining sparse observation data and constructing an observation matrix and an observation vector based on the sparse observation data, based on the low-rank joint wave feature subspace, the observation matrix and the observation vector, sparse regression is performed on each variable of the standardized spatiotemporal dataset to obtain a preliminary spatial distribution result of each variable, then according to the preliminary spatial distribution result of each variable, a Gaussian weighted fusion smoothing is performed to obtain a preliminary reconstruction result, then based on the preliminary reconstruction result, dynamic weights of each variable are determined, and the preliminary reconstruction result is optimized according to the dynamic weights to obtain a target reconstruction result. In the embodiment of the present application, under the condition of limited observation, a low-rank joint wave feature subspace is constructed based on the standardized spatiotemporal dataset containing significant wave height, mean wave period and wave direction, and sparse regression is performed on each variable by combining the observation matrix and vector constructed by the sparse observation data, and then Gaussian weighted fusion smoothing and dynamic weight optimization are performed, which can not only effectively reconstruct a high-resolution wave field and improve the reconstruction accuracy to meet the needs of marine engineering and disaster warning, but also simplify the calculation process, adapt to complex data scenarios, and quickly output high-quality results, providing reliable support for data-driven wave inversion and prediction.

[0030] The embodiments of the present application will be further described below with reference to the accompanying drawings.

[0031] Reference Figure 1 , Figure 1 is a flowchart of the wave field reconstruction method provided by the embodiment of the present application. The flowchart can specifically include but is not limited to steps 110 to 160.

[0032] Step 110: obtaining a standardized spatiotemporal dataset, the dataset contains significant wave height, mean wave period and wave direction;

[0033] Step 120: constructing a low-rank joint wave feature subspace according to the standardized spatiotemporal dataset;

[0034] Step 130: obtaining sparse observation data, and constructing an observation matrix and an observation vector based on the sparse observation data;

[0035] Step 140: based on the low-rank joint wave feature subspace, the observation matrix and the observation vector, sparse regression is performed on each variable of the standardized spatiotemporal dataset to obtain a preliminary spatial distribution result of each variable;

[0036] Step 150: according to the preliminary spatial distribution result of each variable, a Gaussian weighted fusion smoothing is performed to obtain a preliminary reconstruction result;

[0037] Step 160: determining the dynamic weight of each variable based on the preliminary reconstruction result, and optimizing the preliminary reconstruction result according to the dynamic weight to obtain a target reconstruction result.

[0038] The steps 110 to 160 are described in detail below.

[0039] In a feasible embodiment, the step 110 aims to collect and organize wave data containing significant wave height Hsig, mean wave period Tm01 and wave direction Dir, and perform standardization processing such as space-time alignment and dimension unification on the data to form a standardized space-time data set with a specified format and directly usable for subsequent analysis. The data set is a wave parameter set covering time and space dimensions and having a unified data format.

[0040] In a feasible embodiment, in the step 120, based on the obtained standardized space-time data set, a low-rank joint wave feature subspace can be constructed through feature extraction and dimension reduction processing. The low-rank joint wave feature subspace is a feature space that can reflect the internal correlation of the significant wave height, mean wave period and wave direction and has a low dimension.

[0041] In a feasible embodiment, in the step 130, the sparse observation data refers to wave observation point data with a scattered spatial distribution; the observation matrix is a matrix used for calculation and describing the correspondence between observation positions and data; and the observation vector is a vector composed of sparse observation values. The observation matrix and the observation vector can be constructed based on the observation positions and observation values of the sparse observation data.

[0042] In a feasible embodiment, in the step 140, based on the low-rank joint wave feature subspace, the observation matrix and the observation vector obtained in the step 130, sparse regression calculation is performed on each variable in the significant wave height, mean wave period and wave direction in the standardized space-time data set, that is, a regression method for inversely deducing the overall distribution of a variable based on sparse observation data, so that the preliminary spatial distribution result of each variable can be obtained.

[0043] In a feasible embodiment, in the step 150, for the preliminary spatial distribution result of each variable, a Gaussian weighted fusion smoothing method is adopted, that is, a Gaussian function is used to perform weighted fusion and smoothing processing on the distribution results of different variables, so that local data fluctuations can be eliminated, and the preliminary reconstruction result of the entire wave field can be obtained.

[0044] In a feasible embodiment, in the step 160, based on the preliminary reconstruction result, the dynamic weight of each variable is first determined. The weight is a variable weight that is adaptively adjusted according to the spatial distribution characteristics of the wave field. Then, the preliminary reconstruction result is optimized and corrected using the dynamic weight, and finally a high-precision target wave field reconstruction result can be obtained.

[0045] In an implementable embodiment, the wave field of the target sea area can be simulated based on the SWAN model and combined with data processing to obtain a standardized spatiotemporal data set. As shown in Figure 2 The process of obtaining the standardized spatiotemporal data set in step 110 can include but is not limited to steps 210 to 230.

[0046] Step 210: Obtain wind field data and topographic bathymetric data of the target simulation area, simulate the wave field of the target sea area based on the wind field data and the topographic bathymetric data using a numerical wave model, and extract effective simulated wave height, average wave simulation period and wave direction simulation data in the target area from the wave field of the target sea area;

[0047] Step 220: Perform error comparison according to the effective simulated wave height, average wave simulation period, wave direction simulation data and wave reference data, and filter to obtain target simulation data;

[0048] Step 230: Standardize, normalize and singular value decomposition noise reduction processing are performed on the target simulation data to obtain a standardized spatiotemporal data set.

[0049] In an implementable embodiment, in step 210, the wind field data and topographic bathymetric data of the target simulation area are first collected, and the two types of data are used as input conditions to simulate and calculate the wave field of the target sea area using a numerical wave model (i.e., the SWAN model). After the simulation is completed, three core wave parameters, i.e., effective simulated wave height, average wave simulation period and wave direction simulation data in the target area, are extracted from the output wave field results of the target sea area.

[0050] In an implementable embodiment, in step 220, wave reference data is introduced as a reference standard, and the effective simulated wave height, average wave simulation period and wave direction simulation data extracted in step 210 are compared with the wave reference data for error analysis. According to the preset error threshold, wave data that meets the accuracy requirement is selected as the target simulation data.

[0051] In an implementable embodiment, in step 230, the selected target simulation data is processed in sequence: first, the data format and dimension are standardized, then the data value range is compressed by normalization, and finally, the interference noise in the data is removed by singular value decomposition noise reduction, and finally a standardized spatiotemporal data set that can be directly used for subsequent analysis is formed.

[0052] Referring to Figure 3 , Figure 3 is a physical modeling flowchart provided by the embodiment of the present application for generating a standardized spatiotemporal data set. The flowchart embodies a data closed-loop process based on SWAN physical priori. The process and Figure 2The illustrated step flow corresponds, including: first, collect ERA5 reanalysis wind field data as dynamic input, obtain ETOPO1 terrain bathymetry file as underlying surface boundary condition; based on the research needs to edit the research area grid file, clear the spatial range and grid resolution of simulation, at the same time set the time span, time step and the type of wave parameters to be output of simulation; Configure SWAN model control file, on the premise of keeping the external conditions such as wind field, terrain consistent, set multiple different physical source combinations (such as different parameter configurations of wave breaking, bottom friction and other source terms) and correspond to independent calculation output path respectively; Call SWAN wave model to drive the simulation calculation of each physical source combination, after the simulation is completed, from the running result file of each combination, extract three types of core wave field information of significant wave height Hsig, mean period Tm01 and wave direction Dir in the target simulation area. Next, take ERA5 reanalysis wave data as the wave reference data, calculate the error of each physical source combination extracted wave parameter and reference data at each space-time point; According to the error calculation result, compare and select the physical source combination with the smallest overall error as the optimal simulation scheme; Then, for the wave parameter data set simulated by the optimal physical source combination, first fill in the missing data, delete duplicate records and eliminate redundant invalid data; After data cleaning, standardization processing, normalization processing and singular value decomposition noise reduction processing are carried out in turn, forming the regular wave data results.

[0053] In a feasible embodiment, as shown in Figure 4 The execution process of step 120 for constructing a low-rank joint wave feature subspace from the standardized spatiotemporal data set can include, but is not limited to, steps 410 to 430.

[0054] Step 410: embed the significant wave height, mean wave period and wave direction in the standardized spatiotemporal data set into a three-dimensional tensor, obtaining a time-consistent three-dimensional tensor sequence; wherein the three-dimensional tensor dimensions include time steps, spatial points and parameter channels, and the parameter channels correspond to three groups of wave parameters;

[0055] Step 420: perform low-rank decomposition on the three-dimensional tensor to extract time patterns, spatial patterns and parameter correlation patterns corresponding to the time steps, spatial points and parameter channels dimensions;

[0056] Step 430: obtain a low-rank joint wave feature subspace based on the extracted time patterns, spatial patterns and parameter correlation patterns.

[0057] In an embodiment, in step 410, a uniform data embedding method is used to integrate the three types of parameters, i.e., significant wave height, mean wave period and wave direction, into a three-dimensional tensor for the standardized spatio-temporal data set. After integration, a time-consistent three-dimensional tensor sequence is formed, which contains three dimensions: time step corresponding to the time sequence node of the data, spatial point corresponding to the spatial observation position of the data, and parameter channel corresponding to the three groups of wave parameters, i.e., significant wave height, mean wave period and wave direction, thereby realizing the regularized representation of multi-dimensional wave data.

[0058] In an embodiment, in step 420, a low-rank decomposition operation can be performed on the obtained three-dimensional tensor by using Tucker tensor low-rank decomposition (Tucker decomposition), and the feature modes corresponding to each dimension of the tensor are extracted through the decomposition process. Among them, the time mode reflects the regular characteristics of the change of the wave parameters with time, the spatial mode reflects the associated characteristics of the wave parameters in the spatial distribution, and the parameter associated mode represents the inherent coupling relationship among the significant wave height, mean wave period and wave direction.

[0059] In an embodiment, in step 430, the extracted time mode, spatial mode and parameter associated mode are taken as core feature elements, and a low-rank joint wave feature subspace can be constructed through feature fusion. The subspace can condense the key wave feature information in the three-dimensional tensor, while retaining the joint association characteristics among time, space and parameters, thereby providing a feature basis for subsequent wave field reconstruction.

[0060] In an implementable embodiment, the step of obtaining sparse observation data in step 130 includes: first, determining a unified spatial rank adapting to different sea conditions through Bayesian optimization based on the low-rank joint wave feature subspace; then, determining the target sensor layout by iteratively optimizing the positions and number of sensors based on the low-rank features corresponding to the unified spatial rank; and then, obtaining sparse observation data by data collection in the target sea area according to the target sensor layout. Specifically: first, based on the constructed low-rank joint wave feature subspace, representative time periods covering different sea conditions are selected, and the spatial rank of each time period is optimized by the Bayesian optimization method, and finally the unified spatial rank adapting to multiple sea conditions is determined; then, taking the low-rank features corresponding to the unified spatial rank as the optimization basis, the genetic algorithm is used to iteratively optimize the layout position and number of sensors, specifically, taking the minimization of the wave field reconstruction error as the goal, combining with the device deployment cost constraint, through multiple rounds of iteration, the target sensor layout and the corresponding number balancing the economy and observation efficiency are screened out; then, the observation equipment is deployed in the target sea area according to the target sensor layout and data collection is performed to obtain sparse observation data. It is worth noting that experiments show that the unified spatial rank set determined by Bayesian optimization in the representative period has good adaptability, and the optimization results based on the genetic algorithm show obvious characteristics: as the number of sensors increases, the wave field reconstruction error shows a marginal decreasing trend, and the sensor layout is more intensive in the nearshore shallow water area and relatively balanced in the deep sea area, which meets the wave observation needs of different sea areas.

[0061] In an implementable embodiment, the process of constructing the observation matrix and the observation vector based on the sparse observation data includes: based on the sparse observation data, combining the total number of space grids of the standardized spatiotemporal data set and the target sensor layout, a sparse observation matrix is constructed; and the sparse observation data is sorted according to the significant wave height, the mean wave period, and the wave direction, respectively, and the observation vector is constructed based on the sorted sparse observation data. Specifically, when constructing the sparse observation matrix, the total number of space grids covered by the standardized spatiotemporal data set is taken as the matrix dimension reference, the space grid positions corresponding to each sensor are determined according to the target sensor layout, only the row and column corresponding to the sensor layout position are given effective observation weight in the matrix, and the rest of the non-observation positions are given zero value, forming a sparse observation matrix that only retains the observation point information, which can clearly map the correspondence between the observation data and the total space grid. When constructing the observation vector, the data is sorted for three types of parameters: significant wave height, mean wave period, and wave direction. Specifically, the sparse observation values of each parameter at different sensor positions and different time steps can be arranged in a predetermined order (such as time sequence, space grid number sequence) to form a one-dimensional observation vector for each parameter, ensuring that the observation vector can accurately reflect the sparse observation results of a single wave parameter, providing an input basis for subsequent sparse regression calculations of each variable.

[0062] In an embodiment, the observation vectors include an effective wave height observation vector, an average wave period observation vector, and a wave direction observation vector. For each variable of the normalized spatiotemporal dataset, sparse regression can be performed based on the corresponding low-rank tensor basis using an orthogonal matching pursuit algorithm (OMP) to reconstruct a preliminary complete spatial distribution. Figure 5 As shown in FIG. 5, the execution process of step 140 can include, but is not limited to, steps 510-530.

[0063] Step 510: Based on the low-rank joint wave feature subspace, determine a first low-rank tensor basis corresponding to the effective wave height, a second low-rank tensor basis corresponding to the average wave period, and a third low-rank tensor basis corresponding to the wave direction.

[0064] Step 520: According to the observation matrix, the effective wave height observation vector, the average wave period observation vector, the wave direction observation vector, the first low-rank tensor basis, the second low-rank tensor basis, and the third low-rank tensor basis, respectively, perform iterative calculation to obtain the effective wave height sparse coefficient, the average wave period sparse coefficient, and the wave direction sparse coefficient.

[0065] Step 530: Based on the effective wave height sparse coefficient, the average wave period sparse coefficient, and the wave direction sparse coefficient, perform sparse regression on each variable of the normalized spatiotemporal dataset to obtain a preliminary spatial distribution result of each variable.

[0066] In an embodiment, in step 510, from the constructed low-rank joint wave feature subspace, the corresponding low-rank tensor basis can be extracted according to the variable type. Among them, the first low-rank tensor basis corresponds to the effective wave height, the second low-rank tensor basis corresponds to the average wave period, and the third low-rank tensor basis corresponds to the wave direction, which provides a feature basis support for sparse regression of each variable.

[0067] In an embodiment, in step 520, calculation is performed for the three types of variables of effective wave height, average wave period, and wave direction. The observation matrix and the observation vector corresponding to each variable, and the low-rank tensor basis are input, and the orthogonal matching pursuit algorithm (OMP) is used for iterative optimization, and the effective wave height sparse coefficient, the average wave period sparse coefficient, and the wave direction sparse coefficient can be obtained in turn, realizing sparse representation of the variable features.

[0068] In an embodiment, in step 530, the obtained sparse coefficients of each variable are combined with the corresponding low-rank tensor basis to perform sparse regression calculation on the effective wave height, the average wave period, and the wave direction in the normalized spatiotemporal dataset. The distribution of each variable in the full space can be deduced, and finally the preliminary spatial distribution result of each variable is obtained.

[0069] In an embodiment, for the periodic wave direction, to avoid discontinuity caused by angle jump, before sparse regression is performed on each variable of the normalized spatiotemporal data set, the wave direction in the preliminary spatial distribution result can be subjected to sine and cosine component optimization processing, and the optimized wave direction distribution result can be obtained by inverse cosine synthesis.

[0070] In an embodiment, the implementation process of the optimized wave direction distribution result includes: based on the wave direction low-rank tensor basis corresponding to the low-rank joint wave feature subspace, performing sparse regression optimization on the sine component and the cosine component respectively to obtain the optimized sine component and the optimized cosine component; and based on the optimized sine component and the optimized cosine component, calculating the optimized wave direction distribution result by the arctangent function.

[0071] In an embodiment, as shown in FIG. 6, the execution process of step 150 can include, but is not limited to, steps 610-630. Figure 6

[0072] Step 610: taking the preliminary spatial distribution result of each variable as the to-be-smoothed data;

[0073] Step 620: setting a sliding window with a length of 5, and selecting the to-be-smoothed data of each current time and two adjacent times before and after the current time in a time-by-time sliding manner to form a window data set;

[0074] Step 630: assigning weights to the window data set based on Gaussian distribution, and performing weighted average calculation on the to-be-smoothed data in the window data set according to the weights to obtain a preliminary reconstruction result.

[0075] In an embodiment, steps 610-630 are a complete process of Gaussian weighted fusion smoothing, which is used to perform time dimension smoothing on the preliminary spatial distribution result of each variable to weaken local fluctuations. First, step 610 is performed to determine the effective wave height, the average wave period, and the wave direction variable preliminary spatial distribution result obtained by sparse regression as the to-be-smoothed data; then, step 620 is performed to set a sliding window with a length of 5, and to select the to-be-smoothed data of each current time and two adjacent times before and after the current time in a time-by-time sliding manner along the time axis to form a window data set; finally, step 630 is implemented to assign weights to each time data in the window data set according to Gaussian distribution. The current time data has the highest weight, and the weight gradually decreases with the increase of time distance. Then, the to-be-smoothed data in the window data set is subjected to weighted average calculation according to the weight, and finally the smoothed preliminary reconstruction result is obtained.

[0076] ​In a feasible embodiment, in the process of obtaining the preliminary reconstruction result by Gaussian weighted fusion smoothing according to the preliminary spatial distribution result of each variable, in order to weaken the jitter and jump of the time-by-time reconstruction data and ensure the time sequence continuity and physical consistency of the wave field, the following specific operations are performed:

[0077] A sliding window with a length of 5 is set, the current time is taken as the center, and the preliminary spatial distribution data of the current time and the two adjacent times before and after the current time are selected to form a window data set; Gaussian weights are assigned to the data of each time in the window data set, and the weight calculation formula is:

[0078]

[0079] wherein i represents the time offset of the data in the window relative to the current time (i=0 corresponds to the current time). Based on the weight, the data of each time in the window data set is weighted and calculated to obtain the smoothing result of the current time:

[0080]

[0081] When processing the time close to the end point of the sequence (the window cannot cover the two times before and after the current time), the data of the time that can be covered is selected by using a truncated window, the weights of the truncated window are re-normalized, and then the weighted calculation is performed to ensure that the smoothing result of the end point time is continuous and reasonable.

[0082] In a feasible embodiment, the execution process of step 160 includes: first, performing principal component analysis on the significant wave height, the mean wave period and the wave direction in the preliminary reconstruction result, extracting the absolute loading value corresponding to each variable in the first principal component of each time, and taking the normalized absolute loading value as the dynamic weight of each variable; then, calculating the relative reconstruction error of each variable in the preliminary reconstruction result, and obtaining the multi-variable weighted comprehensive error according to the dynamic weight and the relative reconstruction error of the variable; then, optimizing the preliminary reconstruction result of each variable according to the multi-variable weighted comprehensive error to obtain the target reconstruction result.

[0083] Specifically, first, principal component analysis is performed on the significant wave height (Hsig), the mean wave period (Tm01) and the wave direction (Dir) in the preliminary reconstruction result, the absolute loading value corresponding to each variable in the first principal component of each time is extracted, and the normalized absolute loading value is taken as the dynamic weight (denoted as , , ) of each variable; then, the relative reconstruction error (denoted as , , ) of each variable in the preliminary reconstruction result is calculated, and the multi-variable weighted comprehensive error is obtained according to the dynamic weight by the formula The integrated multivariate weighted comprehensive error is obtained; then, the preliminary reconstruction result of each variable is optimized according to the multivariate weighted comprehensive error, and the target reconstruction result is obtained. The core logic of using principal component analysis to determine the dynamic weight is: the absolute load value of the first principal component directly reflects the contribution degree of each variable to the overall characteristics of the wave field, and under normal circumstances, the higher the load value, the higher the proportion of the corresponding variable in the wave field information at that moment, and the influence weight of the reconstruction result is also correspondingly higher. Through this normalization based on the load value, the weight is dynamically adjusted over time (instead of using a fixed value), which is more in line with the dynamic change characteristics of the wave field, and the weight needs to meet the basic constraints. In the above multivariate weighted comprehensive error formula, 、 、 correspond to the dynamic weights of the significant wave height, the mean wave period and the wave direction respectively, 、 、 are the relative reconstruction errors of each variable. Through the formula, the single variable error can be integrated into a comprehensive error reflecting the overall reconstruction accuracy, which can avoid the one-sidedness of single variable error evaluation.

[0084] In a feasible embodiment, in the process of optimizing each time period spatial rank and determining a unified spatial rank adapting to various sea conditions by the Bayesian optimization method, the setting of the unified spatial rank is related to the multivariate weighted comprehensive error. The core purpose of determining the unified spatial rank by Bayesian optimization is to select a unified low rank combination for the longitude and latitude two spatial modes on the representative time period ( , ), which guarantees the wave field reconstruction accuracy and also considers the calculation efficiency, and the low rank combination is followed in the subsequent full time period reconstruction process.

[0085] The specific process is as follows:

[0086] (1) Representative time period sampling: randomly extract 3 groups of monthly conventional wave data and 6 hours of extreme sea condition wave data in the typhoon process, form a representative time period set covering the conventional and extreme scenarios;

[0087] (2) Parameter space setting: the search range of the low rank combination ( , ) is limited in the integer grid of ( , ) ∈ , and discrete search is performed;

[0088] (3) Objective function definition: the minimization of the multivariate PCA weighted comprehensive error E is taken as the optimization objective, wherein , 、 , the relative reconstruction error of the significant wave height Hsig, the mean period Tm01, and the wave direction Dir, respectively, , , are the dynamic weights of each variable obtained by the PCA method;

[0089] (4) Acquisition strategy selection: Gaussian process is used to fit the objective function, and the expected improvement is used as the acquisition function. The average objective function value is calculated on the representative time interval set determined in step (1) for each evaluation to guide the search direction in the next round;

[0090] (5) Unified spatial rank determination: the optimal low-rank combination (Ropt) of the wave data of each representative time interval is obtained respectively, , The empirical distribution of all optimal low-rank combinations is counted, and the mode (i.e. the highest frequency combination) in the distribution is taken as the global unified spatial rank.

[0091] In a feasible embodiment, in the process of determining the dynamic weight by principal component analysis (PCA), the basic constraint condition needs to be met when determining the weight:

[0092]

[0093] The specific value mode is: the absolute load value corresponding to each variable in the first principal component is extracted by performing principal component analysis on the preliminary reconstruction result of each time interval, and the absolute load value is normalized to obtain the dynamic weight of each variable in the corresponding time interval.

[0094] In a feasible embodiment, based on the low-rank characteristics corresponding to the unified spatial rank, the position and number of sensors are iteratively optimized by genetic algorithm to determine the target sensor layout and number, and the core is to simultaneously determine the number N of sensors and the spatial position set S under the given budget and operation constraint, and finally realize the minimization of the weighted comprehensive error E.

[0095] The fitness function of the optimization process adopts the average weighted comprehensive error in the representative time interval, that is:

[0096]

[0097] wherein, is the set of representative time intervals for evaluation, and the reconstruction process is consistent with the process of determining the unified spatial rank.

[0098] The optimization process needs to meet the following constraint conditions:

[0099] (1) Quantity constraint: the number N of sensors needs to be within the preset interval, that is, Nmin≤N≤Nmax;

[0100] (2) Geometric constraints: set the minimum distance between adjacent sensors and the land and forbidden area cannot be selected;

[0101] (3) Cost constraints: total cost ≤ budget cost.

[0102] Referring to Figure 7 , Figure 7 is the algorithm framework provided by the embodiment of the application for multivariate joint reconstruction and evaluation. First, the historical data of the significant wave height Hsig, the mean period Tm01 and the wave direction Dir are simulated by the SWAN wave model, and the wave data obtained by simulation are sequentially subjected to normalization processing and SVD denoising (i.e., singular value decomposition denoising) to form a standardized space-time data set; based on the data set, the three types of variables Hsig, Tm01 and Dir are embedded to construct a joint tensor X; the joint tensor X is subjected to Tucker tensor decomposition to extract the time mode, the space mode and the parameter correlation mode to construct a low-rank joint wave feature subspace; the sensor layout is optimized by Bayesian optimization and genetic algorithm in combination with the feature subspace, the sparse observation data are collected after the target sensor layout is determined, and then an observation matrix M and an observation vector Y are constructed; based on the low-rank joint wave feature subspace, the observation matrix M and the observation vector Y, OMP is used for sparse regression of each variable to obtain a preliminary spatial distribution result of each variable; the preliminary spatial distribution result is subjected to time smoothing by a Gaussian sliding window with a length of 5 to obtain a preliminary reconstruction result; the dynamic weight of each variable is calculated by introducing principal component analysis, and the weighted multivariate comprehensive error E is solved by formula in combination with the reconstruction error of each variable; it is judged whether the comprehensive error E meets the preset accuracy requirement, if the error is appropriate, the wave field reconstruction is completed, and if the error is not appropriate, the feature subspace is re-optimized in the Tucker tensor decomposition link until the accuracy requirement is met.

[0103] In a feasible embodiment, after obtaining the target reconstruction result, result verification and in-depth analysis can be further carried out, specifically including: first, in view of the situation that the monthly wave field reconstruction error rises in individual periods, the wave propagation path characteristics in the error rising period are analyzed in combination with the simulation results of the SWAN wave numerical model, and the error stability of the error extreme value in the period is evaluated to determine the cause of the error fluctuation; then, the abnormal time and abnormal space point are identified from the error distribution graph, and the final reconstruction wave field result is output after being verified twice with the actual observation data or the numerical simulation result; finally, two typhoon working condition periods in which the reconstruction result shows obvious differences are selected, the wave propagation path difference between the two periods is compared and analyzed, and the correlation between the difference and the target sensor spatial distribution is explored to provide reference basis for subsequent sensor layout optimization or wave field reconstruction accuracy improvement.

[0104] In a feasible embodiment, to verify the reconstruction performance of the method, a comparative experiment with a typical neural network model is also carried out, specifically: two types of models, convolutional neural network and long short-term memory network, are selected as benchmark comparison models, and under two typical working conditions of swells and typhoons, the time series prediction results and tensor reconstruction values of wave multivariate are compared and analyzed. The experimental data is constructed by using the SWAN simulation data of the whole year of 2023 to build the training and verification data set, among which the swell working condition (from 22:00 on November 11, 2023 to 22:00 on November 15) and the typhoon working condition (from 16:00 on August 31, 2023 to 16:00 on September 4) are set as the model verification stage, and the rest of the time data is used for model training and testing.

[0105] In the comparative experiment, the three types of models all take the significant wave height Hsig, the mean period Tm01, the wave direction Dir, and the wind speed components (u, v) and the wind direction as input features, and predict the wave variable values at the next moment through multivariate regression; and the same training parameter configuration is adopted, including the maximum iteration number (MaxEpochs = 500), the initial learning rate (InitialLearnRate = 0.0005), the L2 regularization coefficient (0.005), and the Dropout ratio (0.3), to ensure the consistency of the comparison conditions.

[0106] According to the results of the three types of models under the swell and typhoon working conditions, the method can reconstruct the full-field wave elements with high precision without training, especially in the case of data sparsity and sea state change, and its reconstruction accuracy and stability are better than the convolutional neural network and the long short-term memory network which rely on a large amount of data learning, fully embodying the advantages of the method in practical application.

[0107] The above description of disclosed embodiments enables one skilled in the art to make or use the application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein can be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A wave field reconstruction method, characterized in that, The method includes: Obtain a standardized spatiotemporal dataset containing significant wave height, average wave period, and wave direction; A low-rank joint wave feature subspace is constructed based on the standardized spatiotemporal dataset. Acquire sparse observation data, and construct an observation matrix and observation vector based on the sparse observation data; Based on the low-rank joint wave feature subspace, the observation matrix, and the observation vector, sparse regression is performed on each variable of the standardized spatiotemporal dataset to obtain the preliminary spatial distribution results of each variable; Based on the preliminary spatial distribution results of the variables, a preliminary reconstruction result is obtained through Gaussian weighted fusion smoothing. Based on the preliminary reconstruction results, the dynamic weights of each variable are determined, and the preliminary reconstruction results are optimized according to the dynamic weights to obtain the target reconstruction results; The steps for acquiring sparse observation data include: determining a unified spatial rank suitable for different sea conditions based on the low-rank joint wave feature subspace using Bayesian optimization; determining the target sensor layout by iteratively optimizing the position and number of sensors based on the low-rank features corresponding to the unified spatial rank using a genetic algorithm; and collecting data in the target sea area according to the target sensor layout to obtain sparse observation data. Before performing sparse regression on each variable of the standardized spatiotemporal dataset, the method further includes: optimizing the wave direction in the preliminary spatial distribution result by sine and cosine components, and obtaining the optimized wave direction distribution result by inverse cosine synthesis; The process involves optimizing the wave direction in the preliminary spatial distribution result using sine and cosine components, and obtaining the optimized wave direction distribution result through inverse cosine synthesis. This includes: converting the preliminary spatial distribution result of the wave direction into sine and cosine components; performing sparse regression optimization on the sine and cosine components based on the low-rank tensor basis of the wave direction corresponding to the low-rank joint wave feature subspace to obtain the optimized sine and cosine components; and calculating the optimized wave direction distribution result using the arctangent function based on the optimized sine and cosine components.

2. The method according to claim 1, characterized in that, The steps for obtaining the standardized spatiotemporal dataset include: Acquire wind field data and topographic and water depth data of the target simulation area. Based on the wind field data and the topographic and water depth data, use a wave numerical model to simulate the wave field of the target sea area, and extract effective simulated wave height, average wave simulation period and wave direction simulation data of the target area from the wave field of the target sea area. The target simulation data is obtained by comparing the error of the effective simulated wave height, the average simulated wave period, the simulated wave direction data and the wave reference data. The target simulation data is standardized, normalized, and subjected to singular value decomposition for noise reduction to obtain a standardized spatiotemporal dataset.

3. The method according to claim 1, characterized in that, The low-rank joint wave feature subspace constructed based on the standardized spatiotemporal dataset includes: The effective wave height, average wave period, and wave direction in the standardized spatiotemporal dataset are uniformly embedded into a three-dimensional tensor to obtain a time-consistent three-dimensional tensor sequence; wherein, the three-dimensional tensor dimensions include time step, spatial point, and parameter channel, and the parameter channel corresponds to three sets of wave parameters; The three-dimensional tensor is decomposed into low rank to extract the temporal pattern, spatial pattern and parameter association pattern corresponding to the time step, spatial point and parameter channel dimensions; Based on the extracted temporal pattern, spatial pattern, and parameter association pattern, a low-rank joint wave feature subspace is obtained.

4. The method according to claim 1, characterized in that, The construction of the observation matrix and observation vector based on the sparse observation data includes: Based on the sparse observation data, and combined with the number of grid cells in the full space of the standardized spatiotemporal dataset and the target sensor layout, a sparse observation matrix is ​​constructed. Sparse observation data are organized according to significant wave height, average wave period, and wave direction, and observation vectors are constructed based on the organized sparse observation data.

5. The method according to claim 1, characterized in that, The observation vectors include the significant wave height observation vector, the average wave period observation vector, and the wave direction observation vector. The preliminary spatial distribution results of each variable in the standardized spatiotemporal dataset are obtained by performing sparse regression on each variable based on the low-rank joint wave feature subspace, the observation matrix, and the observation vector, including: Based on the aforementioned low-rank joint wave feature subspace, the first low-rank tensor basis corresponding to the effective wave height, the second low-rank tensor basis corresponding to the average wave period, and the third low-rank tensor basis corresponding to the wave direction are determined. The effective wave height sparse coefficient, the average wave period sparse coefficient, and the wave direction sparse coefficient are obtained by iterative calculation based on the observation matrix, the effective wave height observation vector, the average wave period observation vector, the wave direction observation vector, the first low-rank tensor basis, the second low-rank tensor basis, and the third low-rank tensor basis, respectively. Based on the effective wave height sparsity coefficient, the average wave period sparsity coefficient, and the wave direction sparsity coefficient, sparse regression is performed on each variable of the standardized spatiotemporal dataset to obtain the preliminary spatial distribution results of each variable.

6. The method according to claim 1, characterized in that, The preliminary reconstruction result is obtained by Gaussian weighted fusion smoothing based on the preliminary spatial distribution results of the variables, including: The preliminary spatial distribution results of the variables are used as the data to be smoothed; Set a sliding window of length 5, and select the data to be smoothed at each current time and two times before and after it in a time-by-time sliding manner to form a window dataset; Weights are assigned to the window dataset based on a Gaussian distribution, and a weighted average is calculated on the data to be smoothed in the window dataset according to the weights to obtain a preliminary reconstruction result.

7. The method according to claim 1, characterized in that, The process of determining the dynamic weights of each variable based on the preliminary reconstruction results, and optimizing the preliminary reconstruction results according to the dynamic weights to obtain the target reconstruction result, includes: Principal component analysis was performed on the effective wave height, average wave period and wave direction in the preliminary reconstruction results. The absolute loading values ​​of each variable in the first principal component at each time moment were extracted and normalized as the dynamic weights of each variable. Calculate the relative reconstruction error of each variable in the preliminary reconstruction result, and obtain the multivariate weighted comprehensive error based on the dynamic weight and the relative reconstruction error of the variable; The preliminary reconstruction results of each variable are optimized based on the multivariate weighted comprehensive error to obtain the target reconstruction result.

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