WO2022262500A1 - 一种基于steof-lstm的海洋环境要素预测方法 - Google Patents

一种基于steof-lstm的海洋环境要素预测方法 Download PDF

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WO2022262500A1
WO2022262500A1 PCT/CN2022/093025 CN2022093025W WO2022262500A1 WO 2022262500 A1 WO2022262500 A1 WO 2022262500A1 CN 2022093025 W CN2022093025 W CN 2022093025W WO 2022262500 A1 WO2022262500 A1 WO 2022262500A1
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time
space
marine
scale
prediction
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赵玉新
郝日栩
周迪
陈力恒
邓雄
张秋阳
杨德全
赵廷
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哈尔滨工程大学
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  • the invention belongs to the technical field of prediction of marine dynamic environment elements, and in particular relates to a prediction method of marine environment elements based on STEOF-LSTM.
  • Ocean forecasting mainly includes two modes: numerical forecasting and statistical forecasting.
  • numerical forecasting is the main means of marine environment forecasting at the present stage, it has disadvantages such as large amount of computation, strong sensitivity to initial conditions, and limited by timeliness. Therefore, there is an urgent need for a forecasting method that has less computational complexity than numerical forecasting and is not limited by timeliness to achieve rapid and accurate forecasting of marine dynamic environment elements.
  • Statistical forecasting method is one of the important means in marine forecasting.
  • the sample data When the sample data is large enough, it can establish a data-driven forecasting model without considering the physical laws of the research object. Therefore, statistical forecasting methods do not have problems such as physical limit limitations of numerical forecasting methods.
  • research on numerical forecasting by major institutions around the world has matured, but the extended period and medium- and long-term forecasts cannot be completed using traditional numerical forecasting methods, but statistical forecasting methods need to be considered. Therefore, it is very necessary to study the methods of marine statistical analysis and forecasting, and it also plays an extremely important role in the accurate forecasting of the marine environment and the timely grasp of marine information.
  • the application of deep learning to the forecasting research of marine time-space series data is to combine the new generation technology with the forecasting application of marine phenomena, break the bottleneck of traditional marine model forecasting technology and the limitation of cognitive level, and expand the application of key technologies such as artificial intelligence in the marine environment. It also plays an extremely important role in the accurate forecasting of my country's marine environment and the timely grasp of marine information.
  • Deep learning has good application effects and broad application prospects in the field of ocean forecasting, especially in the forecasting of complex ocean time-space sequences; compared with dynamic ocean model forecasting and traditional statistical forecasting methods, deep learning, as a data-driven model, can objectively mine complex
  • the potential relationship between spatio-temporal data brings new opportunities for intelligent analysis and mining of marine big data. Therefore, the application of deep learning to the prediction research of marine time-space series data is to combine new technologies with the application of marine phenomenon prediction, break the bottleneck of traditional marine model prediction technology and the limitation of cognitive level, and accurately forecast the marine environment and marine information. Timely mastery is extremely important.
  • the purpose of the present invention is to provide a method for predicting marine environment elements based on STEOF-LSTM.
  • Step 1 Based on the reanalysis data of the sea area to be analyzed and predicted, the stochastic dynamic analysis method and the empirical orthogonal function method are used to analyze and study the multi-scale temporal and spatial variation characteristics and law;
  • T(t) is a trend item, which is obtained through linear regression analysis
  • P(t) is a periodic item, including seasonal, monthly, annual, and inter-annual variation characteristics and laws, and the empirical analysis of the time series after detrending Orthogonal function decomposition analysis calculates the main spatial distribution mode and time period change, so as to obtain the periodic change characteristics of the dynamic elements of the marine environment
  • R(t) is the remaining random item, which is obtained by filtering
  • Step 2 Aiming at the monthly and daily small-scale time information obtained by the stochastic dynamic analysis method, the STEOF model corresponding to the time scale is used for mid- and long-term spatio-temporal analysis and prediction, and small-scale prediction results are obtained;
  • Step 2.1 For a certain marine dynamic environment element, the corresponding time-space sample matrix X of the daily marine dynamic environment element over the years is:
  • N the number of spatial grid points
  • T the number of time series
  • M the number of annual samples
  • Step 2.2 Carry out spatial-temporal empirical orthogonal decomposition on the space-time sample matrix X, obtain the eigenvalues of the matrix and the eigenvectors corresponding to each eigenvalue, calculate the total proportion of each eigenvalue in turn, and arrange the eigenvalues and eigenvectors in order , the obtained eigenvector is a time series of spatial modalities, which contains both spatial information and temporal information, and this eigenvector is called the space-time basis;
  • the eigenvector V M ⁇ M gets:
  • ⁇ is the diagonal square matrix corresponding to the eigenvalues, ⁇ 1 >...> ⁇ m >...> ⁇ M , and ⁇ m ⁇ 0;
  • Step 2.3 Project the space-time mode onto the matrix X to obtain its corresponding principal component, namely:
  • the principal component is the space-time coefficient corresponding to each space-time feature vector.
  • the space-time coefficient PC M ⁇ (N ⁇ T) is an M ⁇ (N ⁇ T)-dimensional matrix, and each row of data in PC M ⁇ (N ⁇ T) is the space-time coefficient corresponding to each space-time mode.
  • the first space-time mode The space-time coefficient of the state corresponds to the first row of the space-time coefficient PC M ⁇ (N ⁇ T) , and so on.
  • Step 2.4 Use space-time observations and space-time basis to predict space-time series
  • O space-time observation
  • t the forecast start time
  • n the number of spatial grid points
  • l the number of observations
  • the space-time basis H is divided into two parts: one part is the fitted space-time basis H f with the same period as the space-time observation, and the other part is the predicted space-time basis H p ;
  • t represents the start time of prediction
  • l represents the number of observations
  • p is the number of prediction time steps
  • M is the number of space-time bases
  • the fitting coefficient is the projection of the space-time observation on each space-time basis, and describes the similarity between a set of observations and the space-time basis:
  • Predict the future value of the space-time sequence by reconstructing the fitting coefficient and predicting the space-time base, and use the space-time empirical orthogonal decomposition method combined with the least squares method to predict the space-time sequence.
  • the prediction model is as follows Show:
  • Y represents the spatio-temporal prediction result
  • Step 3 Use the LSTM model to analyze and predict the interdecadal and interannual large-scale time information obtained by the stochastic dynamic analysis method, and obtain large-scale prediction results;
  • the LSTM model includes an input gate, an output gate, a forget gate and a memory unit; the LSTM model training process adopts the BPTT algorithm, which is divided into 4 steps: calculating the output value of the LSTM cell; reversely calculating the error term of each LSTM cell, Including two backpropagation directions of time and network level; according to the corresponding error term, calculate the gradient of each weight; apply gradient-based optimization algorithm to update the weight;
  • the forget gate reads the information of the previous state h t-1 and the current input state x t , and outputs a value between 0 and 1 to each cell state C t-1 , the number in C t-1 through the Sigmoid layer Decide what information to discard from the cell state, 1 means “completely retained", 0 means "completely discarded”;
  • i, f, c, o are input gate, forgetting gate, cell state and output gate respectively;
  • W and b are corresponding weight coefficients and bias items respectively;
  • ⁇ and tanh are Sigmoid and hyperbolic tangent activation functions respectively;
  • Step 4 Reconstruct the small-scale prediction results of the spatial-temporal empirical orthogonal function modulus and the large-scale prediction results of the long-short-term memory neural network to obtain the prediction results of analyzing and predicting the ocean dynamic environment elements in the sea area;
  • the present invention excavates the law of marine dynamic environment elements through time-domain multi-scale analysis and deep learning methods, and constructs a statistical prediction model for marine dynamic environment elements to realize marine dynamic environment elements.
  • the invention overcomes the timeliness limitation problem of the traditional marine numerical model forecasting method, can effectively make up for the shortcoming of the traditional numerical forecasting method due to the timeliness limitation of meteorological driving, and the shortcoming of the forecasting timeliness of the marine dynamic environment elements, and the occupancy of computing resources is relatively small. few. It has greatly improved the mid- and long-term prediction capabilities of marine dynamic environmental elements, and provided technical support for solving the technical problem of large-scale and long-period marine dynamic environmental element forecasting after the failure of marine numerical prediction products. And has strong scientific significance and application value.
  • Fig. 1 is a frame diagram of the present invention.
  • Fig. 2 is a result diagram of empirical orthogonal decomposition of ocean multi-element space-time in the present invention.
  • Fig. 3 is an overall flow chart of the present invention.
  • Figure 4(a) is a map of the true value of SST for 90 days.
  • Fig. 4(b) is a graph of the forecast result for 90 days after adopting the present invention.
  • Figure 4(c) is the forecast result graph of 90 days after using the STEOF method.
  • the present invention relates to the prediction technology of marine dynamic environment elements, and especially designs a medium- and long-term marine dynamic environment element based on the combination of Spatiotemporal Empirical Orthogonal Function (STEOF) and Long Short-Term Memory (LSTM).
  • STEM Spatiotemporal Empirical Orthogonal Function
  • LSTM Long Short-Term Memory
  • STEOF-LSTM hybrid model Statistical forecasting method, called STEOF-LSTM hybrid model.
  • the present invention is mainly applied to the analysis and forecasting of marine dynamic environment elements during the voyage period of ships, underwater/surface unmanned submersibles, offshore engineering and other platforms. Monthly mid- to long-term analysis and forecast.
  • the purpose of the present invention is to meet the needs of multi-platform marine environment protection such as ships, underwater/surface unmanned submersibles, offshore engineering, etc., through the study of space-time big data mining that adapts to the characteristics of multi-source, heterogeneous, and multi-modal data in the ocean
  • the method of analysis and forecasting and forecasting proposes a medium- and long-term analysis and forecasting method for marine dynamic environment elements based on artificial intelligence methods. This method can effectively make up for the shortcoming of the traditional numerical forecasting method due to the short forecasting time of the ocean dynamic environment elements due to the limitation of the meteorological driving time.
  • Utilizing the method for analyzing and forecasting marine dynamic environment elements of the present invention can realize statistical analysis and forecasting of marine dynamic environment elements with a timeliness of three months, in order to solve the large-scale and long-period marine dynamic environment elements after the failure of marine numerical forecast products Forecasting and prediction, a technical problem, provides technical support and has strong scientific significance and application value.
  • the present invention is based on large-scale and long-term ocean reanalysis data, by studying multi-scale spatio-temporal characteristics, and comprehensively considering the impact correlation, it adopts random dynamic analysis method and empirical orthogonal function method to analyze the time-space sequence of marine dynamic environment elements.
  • the extraction of time and space features based on the long-term short-term memory network and the time-space empirical orthogonal function, conducts multi-scale analysis and prediction of the space-time characteristics of the marine dynamic environment elements, so as to realize the long-term and large-scale space-time prediction of the marine dynamic environment elements.
  • the invention overcomes the timeliness limitation problem of the traditional marine numerical model forecasting method, greatly improves the mid- and long-term forecasting ability of marine dynamic environment elements, and solves the large-scale and long-period marine dynamic environment element forecast prediction after the failure of marine numerical forecast products This technical problem provides technical support.
  • a method for predicting marine environmental elements based on STEOF-LSTM comprising the following steps:
  • Step 1 Based on the reanalysis data of the sea area to be analyzed and predicted, the stochastic dynamic analysis method and the empirical orthogonal function method are used to analyze and study the multi-scale temporal and spatial variation characteristics and
  • the multi-scale analysis method is as follows:
  • the global marine dynamic environment elements are regarded as a long-term dynamic sequence, and the stochastic dynamic analysis method is mainly used to analyze its annual, monthly, daily changes, trends, and periodic characteristics.
  • Stochastic dynamic analysis method Affected by climate, man-made, and other disturbance factors, marine dynamic environmental elements can show certain trends, periodicity, and randomness, and this type of time series is called a stationary random time series.
  • the analysis of such time series is mainly to decompose them into four types of fluctuations: Trend, Seasonal, Cycle, and Rand for dynamic approximate analysis.
  • the time series decomposition of marine dynamic environment elements can be obtained as follows:
  • T(t) is a trend item
  • P(t) is a periodic item
  • R(t) is a residual random item.
  • the periodic item contains seasonal, monthly, interannual, and interdecadal variation characteristics and laws.
  • the linear trend item in the decomposition is calculated by unary linear regression analysis; the periodic item analysis is empirically orthogonal to the time series after detrending
  • the function decomposition analysis calculates the main spatial distribution mode and time period change, so as to obtain the period change characteristics of the dynamic elements of the marine environment; the final residual item is obtained by filtering.
  • Step 2 For the monthly and daily small-scale time information obtained by the stochastic dynamic analysis method, use the time-scale empirical orthogonal function model of the corresponding time scale to conduct medium- and long-term spatiotemporal analysis and prediction, and obtain small-scale prediction results.
  • the present invention adopts spatiotemporal empirical orthogonal function (Spatiotemporal Empirical Orthogonal Function, STEOF) to integrate the time series information within the interannual signal into the vector of spatial arrangement.
  • the method of the spatiotemporal empirical orthogonal function is as follows: for a certain marine dynamic environment Elements, corresponding to the spatial-temporal sample matrix X of the daily ocean dynamic environment elements in the space to be analyzed:
  • X represents the time-space sample matrix of daily marine dynamic environment elements over the years
  • n represents the number of spatial grid points
  • t represents the number of time series
  • m represents the number of annual samples.
  • the eigenvector is the time series of the spatial mode, which contains both spatial information and time information, and this eigenvector is called the space-time basis.
  • the Jacobi iterative method is usually used to solve the eigenvalues and eigenvectors of the covariance matrix of the space-time sample matrix X, when the rank of the matrix is large, the calculation amount of the Jacobi iterative method is very large.
  • the number of space-time grid points N ⁇ T is much larger than the number of periods M, so space-time transformation is required to reduce the amount of calculation.
  • the eigenvector V M ⁇ M gets:
  • ⁇ is the diagonal square matrix corresponding to the eigenvalues, that is:
  • ⁇ 1 >...> ⁇ m >...> ⁇ M , and ⁇ 0.
  • each column of eigenvector values has a non-zero eigenvalue corresponding to it one by one.
  • This operation is called space-time empirical orthogonal decomposition.
  • the eigenvectors obtained by the empirical orthogonal decomposition of space-time are the time series of spatial modes, which contain both spatial and temporal information, which we call the space-time basis.
  • Each spatiotemporal basis represents the evolution of spatial patterns over time. Therefore, the spatio-temporal empirical orthogonal decomposition method extracts the main features of temporal variation of spatial patterns based on historical data.
  • the principal components are the spatiotemporal coefficients corresponding to each spatiotemporal feature vector.
  • the space-time coefficient PC M ⁇ (N ⁇ T) is an M ⁇ (N ⁇ T)-dimensional matrix, and each row of data in PC M ⁇ (N ⁇ T) is the space-time coefficient corresponding to each space-time mode.
  • the first space-time mode The space-time coefficient of the state corresponds to the first row of the space-time coefficient PC M ⁇ (N ⁇ T) , and so on.
  • the forecast problem of marine dynamic environment elements in the area to be analyzed is transformed from a time extrapolation problem to a problem of finding similar processes from historical time series changes.
  • a set of space-time basis is established by using the decomposition results of multiple space-time series, and space-time observations and space-time basis are used to predict space-time series.
  • O space-time observation
  • t the start time of prediction
  • n the number of spatial grid points
  • l the number of observations.
  • the space-time basis H is divided into two parts: one is the fitted space-time basis H f with the same period as the space-time observation, and the other is the predicted space-time basis H p .
  • t represents the prediction start time
  • N represents the number of spatial grid points
  • l represents the number of observations
  • p is the number of prediction time steps
  • M is the number of space-time bases.
  • the eigenvectors of the space-time matrix are orthogonal to each other, that is, the space-time basis is linearly independent.
  • least squares estimation is the optimal fitting method. Solve the fitted coefficients and the fitted space-time basis for space-time observations using a least-squares estimation method.
  • the fit coefficients are the projections of the space-time observations onto each space-time basis, describing the similarity between a set of observations and the space-time basis:
  • S represents the fitting coefficient, as follows:
  • m represents the mth mode.
  • Each space-time base can be regarded as a description of the changing law of a space-time sequence. Therefore, when the law of the space-time sequence in the fitting stage can be described by the space-time basis, the change of the space-time sequence in the prediction stage will also conform to the same law. Accordingly, the future value of the space-time series is predicted by reconstructing the fitting coefficients and predicting the space-time basis. Therefore, the space-time sequence is predicted by combining the space-time empirical orthogonal decomposition method with the least squares method to predict the space-time sequence.
  • the prediction model is shown in the following formula:
  • Y represents the result of spatio-temporal prediction
  • N represents the number of spatial grid points
  • t represents the start time of prediction
  • p represents the number of time steps of prediction.
  • Step 3 The long-short-term memory neural network method is used to analyze and predict the inter-decadal and inter-annual large-scale time information obtained by the stochastic dynamic analysis method, and obtain large-scale prediction results.
  • Long Short Term Memory networks LSTMs
  • LSTMs a special RNN network
  • LSTM consists of an input gate, an output gate, and a forgetting gate. It is composed of a memory unit and its specific structure is shown in Figure 2.
  • the data flow inside the LSTM in which the forget gate reads the information of the previous state h t-1 and the current input state x t , and outputs a value between 0 and 1 to each cell state C t-1 through the Sigmoid layer,
  • the number in C t-1 determines what information is discarded from the cell state, 1 represents "completely retained", 0 represents "completely discarded”; then we decide what new information will be updated and placed in the cell through the input gate layer
  • first input h t-1 and x t into the Sigmoid function to determine the value to be updated then create a candidate value vector C t through the tanh layer, then multiply the old state by f t to determine the information we need to forget, and add The product of the above it and C t generates a new candidate value .
  • the LSTM model training process uses the BPTT algorithm similar to the classic back propagation (Back Propagation, BP) algorithm principle, which is divided into four steps: calculate the output value of the LSTM cell according to the calculation method; reversely calculate the output value of each LSTM cell
  • the error term includes two backpropagation directions of time and network level; according to the corresponding error term, the gradient of each weight is calculated; the gradient-based optimization algorithm is applied to update the weight.
  • Step 4 Reconstruct the small-scale prediction results of the spatio-temporal empirical orthogonal function modulus and the large-scale prediction results of the long-short-term memory neural network to obtain the prediction results of analyzing and predicting the marine dynamic environment elements in the sea area.
  • the reconstruction method of the present invention is as follows: The marine environment dynamics proposed by the present invention based on stochastic dynamic analysis, spatiotemporal empirical orthogonal function (Spatiotemporal Empirical Orthogonal Function, STEOF) and long short-term memory network (Long Short-Term Memory, LSTM) The element forecasting model is called the STEOF-LSTM model.
  • This model mainly uses the stochastic dynamic analysis method to realize the multi-scale analysis and transformation of the time-space sequence data of the dynamic elements of the marine environment in the designated sea area, and obtains the large-scale and small-scale components of the time-space sequence data of the dynamic elements of the marine environment; based on STEOF, the small-scale Forecast of large-scale time information; use large-scale time information to construct LSTM neural network to realize the prediction of large-scale time information.
  • the high-frequency forecast results of STEOF and the low-frequency forecast results of the LSTM neural network are superimposed to realize the reconstruction of large-scale information and small-scale information, and obtain the final forecast results of the dynamic elements of the marine environment.
  • the beneficial effect of the present invention is that the present invention proposes a large-scale, long-term Based on the ocean reanalysis data, the law of marine dynamic environment elements is excavated through time-domain multi-scale analysis and deep learning methods, and a statistical prediction model for marine dynamic environment elements is constructed to realize the mid- and long-term spatio-temporal statistical forecasting method of ocean dynamic environment elements.
  • Ocean Numerical Model Forecasting The invention overcomes the timeliness limitation problem of the traditional marine numerical model forecasting method, can effectively make up for the shortcoming of the traditional numerical forecasting method due to the timeliness limitation of meteorological driving, and the shortcoming of the forecasting timeliness of the marine dynamic environment elements, and the occupancy of computing resources is relatively small. few. It has greatly improved the mid- and long-term prediction capabilities of marine dynamic environmental elements, and provided technical support for solving the technical problem of large-scale and long-period marine dynamic environmental element forecasting after the failure of marine numerical prediction products. And has strong scientific significance and application value.
  • the present invention proposes a small, fast and effective method for mid- and long-term analysis and prediction of marine dynamic environment elements, aiming at the marine environment guarantee requirements of multiple platforms such as ships, underwater/surface unmanned submersibles, and offshore engineering.
  • the present invention uses the method for analyzing and forecasting marine dynamic environment elements of the present invention to realize statistical analysis and forecasting of marine dynamic environment elements with a timeliness of three months, in order to solve the large-scale and long-period marine dynamic
  • the technical problem of environmental element forecasting and prediction provides technical support, and has strong scientific significance and application value.
  • the technical scheme adopted in the present invention is:
  • Step 1 Based on the reanalysis data of the sea area to be analyzed and predicted, the stochastic dynamic analysis method and the empirical orthogonal function method are used to analyze and study the multi-scale temporal and spatial variation characteristics and
  • the multi-scale analysis method is as follows:
  • the global sea surface temperature is regarded as a long-term dynamic sequence, and the stochastic dynamic analysis method is mainly used to analyze its annual, monthly, daily changes, trends, and periodic characteristics.
  • Stochastic dynamic analysis method Affected by climate, man-made, and other disturbance factors, sea surface temperature can show certain trends, periodicity, and randomness.
  • time series a stationary random time series.
  • the analysis of such time series is mainly to decompose them into four types of fluctuations: Trend, Seasonal, Cycle, and Rand for dynamic approximate analysis.
  • the time series decomposition of sea surface temperature can be obtained as follows:
  • T(t) is a trend item
  • P(t) is a periodic item
  • R(t) is a residual random item.
  • the periodic item contains seasonal, monthly, interannual, and interdecadal variation characteristics and laws.
  • the linear trend item in the decomposition is calculated by unary linear regression analysis; the periodic item analysis is empirically orthogonal to the time series after detrending
  • the function decomposition analysis calculates the main spatial distribution mode and time period change, so as to obtain the period change characteristics of the dynamic elements of the marine environment; the final residual item is obtained by filtering.
  • the results of multi-scale time analysis of sea surface temperature by stochastic dynamic analysis method in the present invention are shown in Fig. 2 .
  • Step 2 Aiming at the monthly and diurnal small-scale time information of sea surface temperature obtained by the stochastic dynamic analysis method, the medium- and long-term spatio-temporal analysis and prediction are carried out using the spatio-temporal empirical orthogonal function model corresponding to the time scale, and the small-scale prediction results are obtained.
  • the time range is from January 1, 1958 to December 31, 2016, and the space range is 99°E ⁇ 150°E, 10°S ⁇ 52°N.
  • the present invention adopts spatiotemporal empirical orthogonal function (Spatiotemporal Empirical Orthogonal Function, STEOF) to integrate the time series information within the interannual signal into the vector of spatial arrangement.
  • the method of the spatiotemporal empirical orthogonal function is as follows: for sea surface temperature Ocean dynamic environment elements, corresponding to the spatial-temporal sample matrix X of daily sea surface temperature in the space to be analyzed:
  • X represents the time-space sample matrix of daily sea surface temperature over the years
  • n represents the number of spatial grid points
  • t represents the number of time series
  • m represents the number of annual samples.
  • the eigenvector is the time series of the spatial mode, which contains both spatial information and time information, and this eigenvector is called the space-time basis.
  • the Jacobi iterative method is usually used to solve the eigenvalues and eigenvectors of the covariance matrix of the space-time sample matrix X, when the rank of the matrix is large, the calculation amount of the Jacobi iterative method is very large.
  • the number of space-time grid points N ⁇ T is much larger than the number of periods M, so space-time transformation is required to reduce the amount of calculation.
  • the eigenvector V M ⁇ M gets:
  • ⁇ is the diagonal square matrix corresponding to the eigenvalues, that is:
  • ⁇ 1 >...> ⁇ m >...> ⁇ M , and ⁇ 0.
  • each column of eigenvector values has a non-zero eigenvalue corresponding to it one by one.
  • This operation is called space-time empirical orthogonal decomposition.
  • the eigenvectors obtained by the empirical orthogonal decomposition of space-time are the time series of spatial modes, which contain both spatial information and time information, called the space-time basis.
  • Each spatiotemporal basis represents the evolution of spatial patterns over time. Therefore, the spatio-temporal empirical orthogonal decomposition method extracts the main features of temporal variation of spatial patterns based on historical data.
  • the principal components are the spatiotemporal coefficients corresponding to each spatiotemporal feature vector.
  • the space-time coefficient PC M ⁇ (N ⁇ T) is an M ⁇ (N ⁇ T)-dimensional matrix, and each row of data in PC M ⁇ (N ⁇ T) is the space-time coefficient corresponding to each space-time mode.
  • the first space-time mode The space-time coefficient of the state corresponds to the first row of the space-time coefficient PC M ⁇ (N ⁇ T) , and so on.
  • the forecast problem of marine dynamic environment elements in the area to be analyzed is transformed from a time extrapolation problem to a problem of finding similar processes from historical time series changes.
  • a set of spatio-temporal bases is established using the decomposition results of multiple spatio-temporal series, and the spatio-temporal observations and spatio-temporal bases are used to predict the spatio-temporal series.
  • O space-time observation
  • t the start time of prediction
  • n the number of spatial grid points
  • l the number of observations.
  • the space-time basis H i is divided into two parts: one is the fitted space-time basis H f with the same period as the space-time observation, and the other is the predicted space-time basis H p .
  • t represents the prediction start time
  • N represents the number of spatial grid points
  • l represents the number of observations
  • p is the number of prediction time steps
  • M is the number of space-time bases.
  • the eigenvectors of the space-time matrix are orthogonal to each other, that is, the space-time basis is linearly independent.
  • least squares estimation is the optimal fitting method. Solve the fitted coefficients and the fitted space-time basis for space-time observations using a least-squares estimation method.
  • the fit coefficients are the projections of the space-time observations onto each space-time basis, describing the similarity between a set of observations and the space-time basis:
  • S represents the fitting coefficient, as follows:
  • m represents the mth mode.
  • Each space-time base can be regarded as a description of the changing law of a space-time sequence. Therefore, when the law of the space-time sequence in the fitting stage can be described by the space-time basis, the change of the space-time sequence in the prediction stage will also conform to the same law. Accordingly, the future value of the space-time series is predicted by reconstructing the fitting coefficients and predicting the space-time basis. Therefore, the space-time sequence is predicted by combining the space-time empirical orthogonal decomposition method with the least squares method to predict the space-time sequence.
  • the prediction model is shown in the following formula:
  • Y represents the result of spatio-temporal prediction
  • N represents the number of spatial grid points
  • t represents the start time of prediction
  • p represents the number of time steps of prediction.
  • the small-scale information of sea surface temperature time-space series can be completed for time-space prediction.
  • the present invention takes the time range as January 1, 1958 to December 31, 2016, and the space range as 99°E Taking the SST spatio-temporal series of ⁇ 150°E, 10°S ⁇ 52°N as an example, the spatiotemporal prediction of small-scale information of sea surface temperature is realized.
  • Step 3 The long-short-term memory neural network method is used to analyze and predict the inter-decadal and inter-annual large-scale time information obtained by the stochastic dynamic analysis method, and obtain large-scale prediction results.
  • LSTMs Long Short Term Memory networks
  • RNNs Long Short Term Memory networks
  • LSTM a special RNN network
  • It contains a dynamic gate mechanism.
  • LSTM consists of an input gate, an output gate, and a forgetting gate. It is composed of a memory unit and its specific structure is shown in Figure 2.
  • the present invention takes the time-space series of sea surface temperature from January 1, 1958 to December 31, 2016 as an example to predict large-scale information of sea surface temperature.
  • the data flow inside the LSTM in which the forget gate reads the information of the previous state h t-1 and the current input state x t , and outputs a value between 0 and 1 to each cell state C t-1 through the Sigmoid layer,
  • the number in C t-1 determines what information is discarded from the cell state, 1 represents "completely retained", 0 represents "completely discarded”; then we decide what new information will be updated and placed in the cell through the input gate layer
  • first input h t-1 and x t into the Sigmoid function to determine the value to be updated then create a candidate value vector C t through the tanh layer, then multiply the old state by f t to determine the information we need to forget, and add The product of the above it and C t generates a new candidate value .
  • the LSTM model training process uses the BPTT algorithm similar to the classic back propagation (Back Propagation, BP) algorithm principle, which is divided into four steps: calculate the output value of the LSTM cell according to the calculation method; reversely calculate the output value of each LSTM cell
  • the error term includes two backpropagation directions of time and network level; according to the corresponding error term, the gradient of each weight is calculated; the gradient-based optimization algorithm is applied to update the weight.
  • the long-short-term memory network method can be used to complete the prediction of large-scale information of sea surface temperature.
  • the present invention takes the time-space sequence of sea temperature from January 1, 1958 to December 31, 2016 as an example to realize the sea surface temperature. Prediction of small-scale information on surface temperature.
  • Step 4 Reconstruct the small-scale prediction results of the spatio-temporal empirical orthogonal function modulus and the large-scale prediction results of the long-short-term memory neural network to obtain the prediction results of analyzing and predicting the marine dynamic environment elements in the sea area.
  • the reconstruction method of the present invention is as follows: The marine environment dynamics proposed by the present invention based on stochastic dynamic analysis, spatiotemporal empirical orthogonal function (Spatiotemporal Empirical Orthogonal Function, STEOF) and long short-term memory network (Long Short-Term Memory, LSTM)
  • STEOF Spatial Empirical Orthogonal Function
  • LSTM Long Short-Term Memory
  • This model mainly uses the stochastic dynamic analysis method to realize the multi-scale analysis and transformation of the time-space sequence data of the dynamic elements of the marine environment in the designated sea area, and obtains the large-scale and small-scale components of the time-space sequence data of the dynamic elements of the marine environment; based on STEOF, the small-scale Forecast of large-scale time information; use large-scale time information to construct LSTM neural network to realize the prediction of large-scale time information.
  • the high-frequency prediction results of STEOF and the low-frequency prediction results of LSTM neural network are superimposed to realize the reconstruction of large-scale information and small-scale information, and obtain the final prediction results of marine environmental dynamic elements.
  • the sea temperature time-space sequence with a time range of January 1, 1958 to December 31, 2016 and a space range of 99°E to 150°E and 10°S to 52°N is taken as an example, as shown in Figure 4 Figure 4(a) to Figure 4(c) show the comparison between the prediction results of different models and the true value of the depth 0m layer, in which Figure 4(a) is the true value from 1 to 90 days, and Figure 4(b) is the STEOF-LSTM The forecast results of the neural network method from 1 to 90 days, and Figure 4(c) shows the forecast results of the STEOF method from 1 to 90 days.

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Abstract

本发明属于海洋动力环境要素预测技术领域，具体涉及一种基于STEOF-LSTM的海洋环境要素预测方法。本发明基于大范围、长时间的海洋再分析数据，通过时域多尺度分析和深度学习方法挖掘海洋动力环境要素的规律，构建面向海洋动力环境要素的统计预测模型，以实现海洋动力环境要素的中长期时空统计预报。本发明可以有效弥补传统的数值预报方法由于气象驱动时效限制而导致的海洋动力环境要素预报时效较短的缺陷，且对计算资源的占用较少。大幅度提高了海洋动力环境要素的中长期预测能力，为解决海洋数值预报产品失效后的大范围、长周期海洋动力环境要素预报预测这一技术难题提供技术支撑。并具有较强的科学意义和应用价值。

Description

一种基于STEOF-LSTM的海洋环境要素预测方法 技术领域
本发明属于海洋动力环境要素预测技术领域，具体涉及一种基于STEOF-LSTM的海洋环境要素预测方法。
背景技术
海洋预报主要包含数值预报和统计预报两种模式。尽管数值预报是现阶段海洋环境预报的主要手段，但存在诸如运算量大、对初始条件敏感性强及受时效性限制等缺点。因此，迫切需要一种相比于数值预报计算量更少、不受到时效性限制的预报方法来实现海洋动力环境要素的快速准确预报。
统计预报方法作为海洋预报中的重要手段之一，当样本数据足够大的时候，其能够不考虑研究对象的物理规律而建立数据驱动的预报模型。因此，统计预报方法不存在类似数值预报方法的物理极限限制等问题。目前，全球各大机构在数值预报方面的研究已经趋于成熟，但是对于延伸期以及中长期的预报无法利用传统的数值预报方法来完成，而需要考虑采用统计预报方法来实现。因此，对于海洋统计分析预报方法的研究是十分必要的，对海洋环境的精准预报和海洋信息的及时掌握也有着极为重要的作用。
传统的海洋环境分析预报多采用人工手动分类识别、海洋模式模拟和传统统计分析等方法。人工手动分类识别方法受主观因素的影响而不能真实刻画数据中的隐含信息；海洋模式模拟存在诸如运算量大、初始条件不精确及受时效性限制等缺点；而传统统计分析对复杂的海洋过程不能通过复杂的公式和繁琐的计算获得较好的结果。且海洋时空数据多为非结构或半结构化数据，数据之间关系复杂或无关联，对传统的统计分析和海洋模式模拟提出了挑战。而深度学习，以数据为驱动，通过多层学习提取数据中的有用信息，客观挖掘数据之间的可能关系，能够提高数据处理效率和精度，为海洋大数据的智能分析挖掘带来新的契机。因此，将深度学习应用于海洋时空序列数据的预测研究，是将新一代技术与海洋现象预测应用相结合，打破传统海洋模式预测技术瓶颈与认知水平的限制，拓展人工智能等关键技术在海洋中应用的重要方法，并对我国海洋环境的精准预报和海洋信息的及时掌握也有着极为重要的作用。
深度学习在海洋预报特别是海洋复杂时空序列的预报领域具有良好的应用效果和广阔的应用前景；相比于动力学海洋模式预报和传统统计预报方法，深度学习作为数据驱动模型，能够客观挖掘复杂时空数据之间的潜在关系，为海洋大数据的智能分析挖掘带来新的契机。因此，将深度学习应用于海洋时空序列数据的预测研究，是将新技术与海洋现象预测应用相结合，打破传统海洋模式预测技术瓶颈与认知水平的限制，对海洋环境的精准预报和海洋信 息的及时掌握具有极为重要的作用。
发明内容
本发明的目的在于提供一种基于STEOF-LSTM的海洋环境要素预测方法。
本发明的目的通过如下技术方案来实现：包括以下步骤：
步骤1：基于待分析预测海域的再分析数据，利用随机动态分析法和经验正交函数方法分析研究海洋动力环境要素的年代际、年际、月、日这类多尺度时间和空间变化特征和规律；
将海洋动力环境要素对应的时间序列分解为趋势、周期、随机来进行动态近似分析：
SLH(t)＝T(t)+P(t)+R(t)
其中，T(t)为趋势项，通过一元线性回归分析计算获得；P(t)为周期项，包含季节性、月、年、年际变化特征和规律，对去趋势后的时间序列进行经验正交函数分解分析，计算出主要空间分布模态和时间周期变化，从而获得海洋环境动力要素的周期变化特征；R(t)为剩余随机项，通过滤波获得；
步骤2：针对随机动态分析法得到的月、日际的小尺度时间信息，采用对应时间尺度的STEOF模型进行中长期时空分析预测，得到小尺度的预测结果；
步骤2.1：针对某种海洋动力环境要素，其对应的历年逐日海洋动力环境要素时空样本矩阵X为：
Figure PCTCN2022093025-appb-000001
对任一时空样本矩阵X，其矩阵维度为M×(N×T)，N表示空间网格点的数量，T表示时间序列的数量，M表示年样本的数量；
步骤2.2：对时空样本矩阵X进行作时空经验正交分解，得到该矩阵的特征值和各特征值对应的特征向量，依次计算各个特征值总占比并按顺序对特征值及特征向量进行排列，得到的特征向量为空间模态的时间序列，其中既包含空间信息又包含时间信息，将这种特征向量称之为时空基底；
通过矩阵变换得到C *矩阵的特征向量后，计算出C矩阵的特征向量，令X与其转置阵的乘积如下式所示：
Figure PCTCN2022093025-appb-000002
特征向量V M×M得：
C *×V *＝V *×Λ
其中，Λ为特征值对应的对角方阵，
Figure PCTCN2022093025-appb-000003
λ 1＞…＞λ m＞…＞λ M，且λ m≥0；
任一特征向量V m如下式所示：
Figure PCTCN2022093025-appb-000004
步骤2.3：将时空模态投影到矩阵X上得到其对应的主成分，即：
PC M×(N×T)＝V T M×(N×T)×X M×(N×T)
其中，主成分是每个时空特征向量所对应的时空系数。时空系数PC M×(N×T)是M×(N×T)维的矩阵，PC M×(N×T)中每行数据就是对应每个时空模态的时空系数，第一个时空模态的时空系数对应于时空系数PC M×(N×T)的第一行，以此类推。
步骤2.4：利用时空观测和时空基础来预测时空序列；
定义时空观测值O如下式所示：
O＝[o 1,t-l…o N,t-l…o 1,t-l+i…o N,t-l+i…o 1,t…o N,t] T
其中，O表示时空观测；t表示预测开始时间；n表示空间网格点的数目；l是观测次数；
时空基H被分为两部分：一部分是与时空观测具有相同周期的拟合时空基H f，另一部分是预测时空基H p；
Figure PCTCN2022093025-appb-000005
Figure PCTCN2022093025-appb-000006
Figure PCTCN2022093025-appb-000007
其中，t表示预测开始时间；l表示观测次数；p是预测时间步数；M是时空基的个数；
使用最小二乘估计方法求解时空观测值的拟合系数和拟合时空基，拟合系数是时空观测在每个时空基上的投影，描述了一组观测与时空基之间的相似性：
O＝H f S
其中，S表示拟合系数，S＝[S 1…S m…S M]
通过重构拟合系数和预测时空基来预测时空序列的未来值，使用将时空经验正交分解方法与最小二乘法相结合时空经验正交函数预测模型的来预测时空序列，预测模型如下式所示：
Y＝H p S＝[y 1,t+1…y N,t+1…y 1,t+j…y N,t+j…y 1,t+p…y N,t+p] T
其中，Y表示时空预测结果；
步骤3：采用LSTM模型对随机动态分析法得到的年代际、年际的大尺度时间信息进行分析预测，得到大尺度预测结果；
所述的LSTM模型包括输入门、输出门、遗忘门和记忆单元；LSTM模型训练过程采用BPTT算法，分为4个步骤：计算LSTM细胞的输出值；反向计算每个LSTM细胞的误差项，包括时间和网络层级2个反向传播方向；根据相应的误差项，计算每个权重的梯度；应用基于梯度的优化算法更新权重；
遗忘门读取上一个状态h t-1和当前输入状态x t的信息，通过Sigmoid层输出一个在0到1之间的数值给每个细胞状态C t-1，C t-1中的数字决定从细胞状态中丢弃什么信息，1代表“完全保留”，0代表“完全舍弃”；
首先将h t-1与x t输入Sigmoid函数确定将要更新的值，然后通过tanh层创建候选值向量 C t，接着将旧状态与f t相乘，确定需要遗忘的信息，加上i t与C t的乘积产生新的候选值；最终，我们根据新的细胞状态来决定输出什么值，通过Sigmoid层决定输出的细胞状态，然后将细胞状态通过tanh进行处理并将其与Sigmoid的输出相乘得到这一时间的输出形式化的描述如下：
Figure PCTCN2022093025-appb-000008
其中，i、f、c、o分别是输入门、遗忘门、细胞状态和输出门；W和b分别为对应的权重系数和偏置项；σ和tanh分别为Sigmoid和双曲正切激活函数；
步骤4：将时空经验正交函数模的小尺度预报结果与长短期记忆神经网络的大尺度预测结果进行重构，得到分析预测海域海洋动力环境要素的预测结果；
利用随机动态分析方法实现对指定海域海洋环境动力要素时空序列数据的多尺度分析和变换，得到海洋环境动力要素时空序列数据的大尺度分量和小尺度分量；以STEOF为基础实现对小尺度时间信息的预报；利用大尺度时间信息构建LSTM模型实现对大尺度时间信息的预报；将STEOF的高频预报结果与LSTM神经网络低频预报结果进行叠加，以实现大尺度信息和小尺度信息的重构，得到最终海洋环境动力要素的预报结果。
本发明的有益效果在于：
本发明基于大范围、长时间的海洋再分析数据，通过时域多尺度分析和深度学习方法挖掘海洋动力环境要素的规律，构建面向海洋动力环境要素的统计预测模型，以实现海洋动力环境要素的中长期时空统计预报。本发明克服了传统海洋数值模式预报方法的时效性限制问题，可以有效弥补传统的数值预报方法由于气象驱动时效限制而导致的海洋动力环境要素预报时效较短的缺陷，且对计算资源的占用较少。大幅度提高了海洋动力环境要素的中长期预测能力，为解决海洋数值预报产品失效后的大范围、长周期海洋动力环境要素预报预测这一技术难题提供技术支撑。并具有较强的科学意义和应用价值。
附图说明
图1为本发明的框架图。
图2为本发明中海洋多要素时空经验正交分解结果图。
图3为本发明的总体流程图。
图4(a)为90天的海温真实值图。
图4(b)为采用本发明后90天的预报结果图。
图4(c)为采用STEOF方法后90天的预报结果图。
具体实施方式
下面结合附图对本发明做进一步描述。
本发明涉及海洋动力环境要素预测技术，特别设计一种基于时空经验正交函数(Spatiotemporal Empirical Orthogonal Function,STEOF)和长短期记忆网络(Long Short-Term Memory,LSTM)结合的海洋动力环境要素中长期统计预测方法，称为STEOF-LSTM混合模型。本发明主要应用于舰船、水下/水面无人潜器、海上工程等平台在出航时期的海洋动力环境要素分析预报工作，对海面高度、海温、盐度和密度等要素进行时长为三个月的中长期分析预报。
本发明的目的是为了针对舰船、水下/水面无人潜器、海上工程等多平台的海洋环境保障需求，通过研究适应海洋多源、异构、多模态数据特征的时空大数据挖掘分析和预测预报方法，提出了一种基于人工智能方法的海洋动力环境要素中长期分析预报方法。该方法可以有效弥补传统的数值预报方法由于气象驱动时效限制而导致的海洋动力环境要素预报时效较短的缺陷。利用本发明的海洋动力环境要素分析预报方法，可以实现对海洋动力环境要素做出时效性为三个月的统计分析预报，为解决海洋数值预报产品失效后的大范围、长周期海洋动力环境要素预报预测这一技术难题提供技术支撑，并具有较强的科学意义和应用价值。
本发明基于大范围、长时间的海洋再分析数据，通过研究多尺度时空特征，综合考虑影响关联关系的基础上，采用随机动态分析法和经验正交函数方法对海洋动力环境要素的时空序列进行时间及空间特征的提取，基于长短期记忆网络和时空经验正交函数对海洋动力环境要素时空特征进行多尺度的分析预测，以实现海洋动力环境要素的长时间、大范围时空预测。本发明克服了传统海洋数值模式预报方法的时效性限制问题，大幅度提高了海洋动力环境要素的中长期预测能力，为解决海洋数值预报产品失效后的大范围、长周期海洋动力环境要素预报预测这一技术难题提供技术支撑。
一种基于STEOF-LSTM的海洋环境要素预测方法，包括以下步骤：
步骤1：基于待分析预测海域的再分析数据，利用随机动态分析法和经验正交函数方法分析研究海洋动力环境要素的年代际、年际、月、日这类多尺度时间和空间变化特征和规律，所述多尺度分析方法如下：
利用长时间序列再分析数据分析研究了全球及中国周边海域海面温度、海面盐度、海面 高度和海表流场在内的各种海洋环境动力要素的多尺度时间和空间变化特征和规律，掌握了全球及中国周边海域海洋动力环境要素的年代际、年际、月、日这类不同时间尺度的变化规律和空间分布特征。
将全球海洋动力环境要素看作一个长时间动态变化的序列，主要运用随机动态分析法分析其年、月、日变化以及趋势、周期特征。
随机动态分析法。受到气候、人为、其他干扰因素的影响，海洋动力环境要素可表现出一定的趋势性、周期性和随机性，将这类时间序列称为平稳性随机时间序列。对这类时间序列进行分析主要是将它们分解为趋势(Trend)，季节(seasonal)，周期(Cycle)，随机(Rand)四种波动来进行动态近似分析。对海洋动力环境要素的时间序列分解可得：
SLH(t)＝T(t)+P(t)+R(t)
其中，T(t)为趋势项，P(t)为周期项，R(t)为剩余随机项。周期项中包含着季节性、月、年际、年代际变化特征和规律，分解中的线性趋势项通过一元线性回归分析计算获得；周期项分析则是对去趋势后的时间序列进行经验正交函数分解分析，计算出主要空间分布模态和时间周期变化，从而获得海洋环境动力要素的周期变化特征；最后的残差项通过滤波获得。
步骤2：针对随机动态分析法得到的月、日的小尺度时间信息，采用对应时间尺度的时空经验正交函数模型进行中长期时空分析预测，得到小尺度的预测结果。本发明采用时空经验正交函数(Spatiotemporal Empirical Orthogonal Function,STEOF)，将年际信号以内的时间序列信息融入到空间排列的向量中，所述时空经验正交函数方法如下：针对某种海洋动力环境要素，其对应的待分析空间历年逐日海洋动力环境要素时空样本矩阵X：
Figure PCTCN2022093025-appb-000009
式中，X表示历年逐日海洋动力环境要素时空样本矩阵，n表示空间网格点的数量，t表示时间序列的数量，m表示年样本的数量。
对任一时空样本矩阵X，其矩阵维度为M×(N×T)，对时空样本矩阵X进行奇异值分解，并得到该矩阵的特征值和各特征值对应的特征向量，依次计算各个特征值总占比并按顺序对特征值及特征向量进行排列。此时的特征向量为空间模态的时间序列，其中既包含空间信息又包含时间信息，将这种特征向量称之为时空基底。
由于求解时空样本矩阵X的协方差矩阵的特征值和特征向量通常采用Jacobi迭代方法， 当矩阵的秩较大时，Jacobi迭代方法的计算量很大。时空网格点的个数N×T远大于周期数M，因此需要进行时空变换以降低计算量。显然，C＝X·X T和C *＝X T·X具有相同的非零特征值，但它们的特征向量不同。因此，通过矩阵变换得到C *矩阵的特征向量后，计算出C矩阵的特征向量，令X与其转置阵的乘积如下式所示：
Figure PCTCN2022093025-appb-000010
特征向量V M×M得：
C *×V *＝V *×Λ         (3)
式中，Λ为特征值对应的对角方阵，即：
Figure PCTCN2022093025-appb-000011
其中，λ 1＞…＞λ m＞…＞λ M，且λ≥0。
任一特征向量V m如下式所示：
Figure PCTCN2022093025-appb-000012
式中，每一列特征向量值都有一个非0的特征值与其一一对应，这个操作称作时空经验正交分解。时空经验正交分解得到的特征向量是空间模态的时间序列，既包含空间信息又包含时间信息，我们称之为时空基。每个时空基表示空间模式随时间的变化过程。因此，时空经验正交分解方法基于历史数据提取空间模式时间变化的主要特征。
将时空模态投影到矩阵X上得到其对应的主成分，即：
PC M×(N×T)＝V T M×(N×T)×X M×(N×T)         (6)
主成分是每个时空特征向量所对应的时空系数。时空系数PC M×(N×T)是M×(N×T)维的矩阵，PC M×(N×T)中每行数据就是对应每个时空模态的时空系数，第一个时空模态的时空系数对应于时空系数PC M×(N×T)的第一行，以此类推。
利用所提出的时空经验正交函数分解方法，将待分析区域的海洋动力环境要素预报问题由时间外推问题转变为一个从历史时间序列变化中找寻相似过程的问题。利用多个时空序列 的分解结果建立了一组时空基，并利用时空观测和时空基础来预测时空序列。
定义时空观测值O i如下式所示：
O＝[o 1,t-l…o N,t-l…o 1,t-l+i…o N,t-l+i…o 1,t…o N,t] T      (7)
式中，O表示时空观测，t表示预测开始时间，n表示空间网格点的数目，l是观测次数。
时空基H被分为两部分：一部分是与时空观测具有相同周期的拟合时空基H f，另一部分是预测时空基H p。
Figure PCTCN2022093025-appb-000013
Figure PCTCN2022093025-appb-000014
Figure PCTCN2022093025-appb-000015
式中，t表示预测开始时间，N表示空间网格点的数目，l表示观测次数，p是预测时间步数，以及M是时空基的个数。
时空矩阵的特征向量彼此正交，即时空基是线性独立的。对于线性无关的基函数，最小二乘估计(LSE)是最优的拟合方法。使用最小二乘估计方法求解时空观测值的拟合系数和拟合时空基。拟合系数是时空观测在每个时空基上的投影，描述了一组观测与时空基之间的相似性：
O＝H f S             (11)
式中，S表示拟合系数，如下所示：
S＝[S 1…S m…S M]            (12)
式中，m表示第m个模态。
每个时空基都可视为一个时空序列的变化规律的描述。因此，当拟合阶段时空序列的规律可由时空基描述时，会导致预测阶段时空序列的变化也符合相同规律。据此，通过重构拟合系数和预测时空基来预测时空序列的未来值。因此，使用将时空经验正交分解方法与最小二乘法相结合时空经验正交函数预测模型的来预测时空序列，预测模型如下式所示：
Y＝H p S＝[y 1,t+1…y N,t+1…y 1,t+j…y N,t+j…y 1,t+p…y N,t+p] T   (13)
式中，Y表示时空预测结果，N表示空间网格点的数量，t表示个预测开始时间，p表示预测时间步数。
步骤3：采用长短期记忆神经网络方法对随机动态分析法得到的年代际、年际的大尺度时间信息进行分析预测，得到大尺度预测结果。长短期记忆网络(Long Short Term Memory networks，LSTMs)，一种特殊的RNN网络，该网络设计出来是为了解决长依赖问题，它包含一个动态的门机制，LSTM由输入门、输出门、遗忘门和记忆单元组成，其具体结构如图2所示。
LSTM内部的数据流，其中遗忘门读取上一个状态h t-1和当前输入状态x t的信息，通过Sigmoid层输出一个在0到1之间的数值给每个细胞状态C t-1，C t-1中的数字决定从细胞状态中丢弃什么信息，1代表“完全保留”，0代表“完全舍弃”；接着我们通过输入门层来决定什么样的新信息将被更新并且放在细胞状态中，首先将h t-1与x t输入Sigmoid函数确定将要更新的值，然后通过tanh层创建候选值向量C t，接着将旧状态与f t相乘，确定我们需要遗忘的信息，加上i t与C t的乘积产生新的候选值，最终，我们根据新的细胞状态来决定输出什么值，通过Sigmoid层决定输出的细胞状态，然后将细胞状态通过tanh进行处理并将其与Sigmoid的输出相乘得到这一时间的输出形式化的描述如下：
Figure PCTCN2022093025-appb-000016
式中，i、f、c、o分别是输入门、遗忘门、细胞状态和输出门；W和b分别为对应 的权重系数和偏置项；σ和tanh分别为Sigmoid和双曲正切激活函数。LSTM模型训练过程采用的是与经典的反向传播(Back Propagation,BP)算法原理类似的BPTT算法，分为4个步骤：按照计算方法计算LSTM细胞的输出值；反向计算每个LSTM细胞的误差项，包括时间和网络层级2个反向传播方向；根据相应的误差项，计算每个权重的梯度；应用基于梯度的优化算法更新权重。
步骤4：将时空经验正交函数模的小尺度预报结果与长短期记忆神经网络的大尺度预测结果进行重构，得到分析预测海域海洋动力环境要素的预测结果。本发明所述重构方法如下：本发明所提出的基于随机动态分析、时空经验正交函数(Spatiotemporal Empirical Orthogonal Function,STEOF)和长短期记忆网络(Long Short-Term Memory，LSTM)的海洋环境动力要素预报模型，称为STEOF-LSTM模型。该模型主要利用随机动态分析方法实现对指定海域海洋环境动力要素时空序列数据的多尺度分析和变换，得到海洋环境动力要素时空序列数据的大尺度分量和小尺度分量；以STEOF为基础实现对小尺度时间信息的预报；利用大尺度时间信息构建LSTM神经网络实现对大尺度时间信息的预报。将STEOF的高频预报结果与LSTM神经网络低频预报结果进行叠加，以实现大尺度信息和小尺度信息的重构，得到最终海洋环境动力要素的预报结果。
与现有技术相比，本发明的有益效果是：本发明针对舰船、水下/水面无人潜器、海上工程等多平台的海洋环境保障需求，提出了一种基于大范围、长时间的海洋再分析数据，通过时域多尺度分析和深度学习方法挖掘海洋动力环境要素的规律，构建面向海洋动力环境要素的统计预测模型，以实现海洋动力环境要素的中长期时空统计预报方法，对比海洋数值模式预报。本发明克服了传统海洋数值模式预报方法的时效性限制问题，可以有效弥补传统的数值预报方法由于气象驱动时效限制而导致的海洋动力环境要素预报时效较短的缺陷，且对计算资源的占用较少。大幅度提高了海洋动力环境要素的中长期预测能力，为解决海洋数值预报产品失效后的大范围、长周期海洋动力环境要素预报预测这一技术难题提供技术支撑。并具有较强的科学意义和应用价值。
实施例1：
本发明针对舰船、水下/水面无人潜器、海上工程等多平台的海洋环境保障需求，提出了一种小型、快速且有效的海洋动力环境要素中长期分析预报方法。本发明利用本发明的海洋动力环境要素分析预报方法，可以实现对海洋动力环境要素做出时效性为三个月的统计分析预报，为解决海洋数值预报产品失效后的大范围、长周期海洋动力环境要素预报预测这一技术难题提供技术支撑，并具有较强的科学意义和应用价值。本发明所采用的技术方案是：
步骤1：基于待分析预测海域的再分析数据，利用随机动态分析法和经验正交函数方法分析研究海洋动力环境要素的年代际、年际、月、日这类多尺度时间和空间变化特征和规律，所述多尺度分析方法如下：
利用1958年1月1日至2016年12月31日的长时间序列再分析数据分析研究了全球及中国周边海域海面温度、海面盐度、海面高度和海表流场在内的各种海洋环境动力要素的年代际、年际、月、日这类多尺度时间和空间变化特征和规律，掌握了全球及中国周边海域海洋动力环境要素的年代际、年际、月、日不同时间尺度的变化规律和空间分布特征。
下面以海面温度为例，介绍基于STEOF-LSTM混合模型的海洋环境要素预测方法，其他海洋动力环境要素也同样适用于该预测方法。
将全球海表温度看作一个长时间动态变化的序列，主要运用随机动态分析法分析其年、月、日变化以及趋势、周期特征。
随机动态分析法。受到气候、人为、其他干扰因素的影响，海表温度可表现出一定的趋势性、周期性和随机性，我们将这类时间序列称为平稳性随机时间序列。对这类时间序列进行分析主要是将它们分解为趋势(Trend)，季节(seasonal)，周期(Cycle)，随机(Rand)四种波动来进行动态近似分析。对海表温度的时间序列分解可得：
SLH(t)＝T(t)+P(t)+R(t)
其中，T(t)为趋势项，P(t)为周期项，R(t)为剩余随机项。周期项中包含着季节性、月、年际、年代际变化特征和规律，分解中的线性趋势项通过一元线性回归分析计算获得；周期项分析则是对去趋势后的时间序列进行经验正交函数分解分析，计算出主要空间分布模态和时间周期变化，从而获得海洋环境动力要素的周期变化特征；最后的残差项通过滤波获得。本发明中随机动态分析法的海表温度多尺度时间分析结果如图2所示。
步骤2：针对随机动态分析法得到的海表温度的月、日际的小尺度时间信息，采用对应时间尺度的时空经验正交函数模型进行中长期时空分析预测，得到小尺度的预测结果。本发明以时间范围为1958年1月1日至2016年12月31日，空间范围为99°E～150°E、10°S～52°N的海温时空序列为例，进行海表温度小尺度信息的时空预测。本发明采用时空经验正交函数(Spatiotemporal Empirical Orthogonal Function,STEOF)，将年际信号以内的时间序列信息融入到空间排列的向量中，所述时空经验正交函数方法如下：针对海表温度这种海洋动力环境要素，其对应的待分析空间历年逐日海表温度时空样本矩阵X：
Figure PCTCN2022093025-appb-000017
式中，X表示历年逐日海表温度时空样本矩阵，n表示空间网格点的数量，t表示时间序列的数量，m表示年样本的数量。
对任一时空样本矩阵X，其矩阵维度为M×(N×T)，对时空样本矩阵X进行奇异值分解，并得到该矩阵的特征值和各特征值对应的特征向量，依次计算各个特征值总占比并按顺序对特征值及特征向量进行排列。此时的特征向量为空间模态的时间序列，其中既包含空间信息又包含时间信息，将这种特征向量称之为时空基底。
由于求解时空样本矩阵X的协方差矩阵的特征值和特征向量通常采用Jacobi迭代方法，当矩阵的秩较大时，Jacobi迭代方法的计算量很大。时空网格点的个数N×T远大于周期数M，因此需要进行时空变换以降低计算量。显然，C＝X·X T和C *＝X T·X具有相同的非零特征值，但它们的特征向量不同。因此，通过矩阵变换得到C *矩阵的特征向量后，计算出C矩阵的特征向量，令X与其转置阵的乘积如下式所示：
Figure PCTCN2022093025-appb-000018
特征向量V M×M得：
C *×V *＝V *×Λ
式中，Λ为特征值对应的对角方阵，即：
Figure PCTCN2022093025-appb-000019
其中，λ 1＞…＞λ m＞…＞λ M，且λ≥0。
任一特征向量V m如下式所示：
Figure PCTCN2022093025-appb-000020
式中，每一列特征向量值都有一个非0的特征值与其一一对应，这个操作称作时空经验正交分解。时空经验正交分解得到的特征向量是空间模态的时间序列，既包含空间信息又包 含时间信息，称之为时空基。每个时空基表示空间模式随时间的变化过程。因此，时空经验正交分解方法基于历史数据提取空间模式时间变化的主要特征。
将时空模态投影到矩阵X上得到其对应的主成分，即：
PC M×(N×T)＝V T M×(N×T)×X M×(N×T)
主成分是每个时空特征向量所对应的时空系数。时空系数PC M×(N×T)是M×(N×T)维的矩阵，PC M×(N×T)中每行数据就是对应每个时空模态的时空系数，第一个时空模态的时空系数对应于时空系数PC M×(N×T)的第一行，以此类推。
利用所提出的时空经验正交函数分解方法，将待分析区域的海洋动力环境要素预报问题由时间外推问题转变为一个从历史时间序列变化中找寻相似过程的问题。利用多个时空序列的分解结果建立了一组时空基，并利用时空观测和时空基础来预测时空序列。
定义时空观测值O如下式所示：
O＝[o 1,t-l…o N,t-l…o 1,t-l+i…o N,t-l+i…o 1,t…o N,t] T
式中，O表示时空观测，t表示预测开始时间，n表示空间网格点的数目，l是观测次数。
时空基H i被分为两部分：一部分是与时空观测具有相同周期的拟合时空基H f，另一部分是预测时空基H p。
Figure PCTCN2022093025-appb-000021
Figure PCTCN2022093025-appb-000022
Figure PCTCN2022093025-appb-000023
式中，t表示预测开始时间，N表示空间网格点的数目，l表示观测次数，p是预测时间步数，以及M是时空基的个数。
时空矩阵的特征向量彼此正交，即时空基是线性独立的。对于线性无关的基函数，最小二乘估计(LSE)是最优的拟合方法。使用最小二乘估计方法求解时空观测值的拟合系数和拟合时空基。拟合系数是时空观测在每个时空基上的投影，描述了一组观测与时空基之间的相似性：
O＝H f S
式中，S表示拟合系数，如下所示：
S＝[S 1…S m…S M]
式中，m表示第m个模态。
每个时空基都可视为一个时空序列的变化规律的描述。因此，当拟合阶段时空序列的规律可由时空基描述时，会导致预测阶段时空序列的变化也符合相同规律。据此，通过重构拟合系数和预测时空基来预测时空序列的未来值。因此，使用将时空经验正交分解方法与最小二乘法相结合时空经验正交函数预测模型的来预测时空序列，预测模型如下式所示：
Y＝H p S＝[y 1,t+1…y N,t+1…y 1,t+j…y N,t+j…y 1,t+p…y N,t+p] T
式中，Y表示时空预测结果，N表示空间网格点的数量，t表示个预测开始时间，p表示预测时间步数。
通过上述的时空经验正交函数方法即可完成海表温度时空序列小尺度信息进行时空预测，本发明以时间范围为1958年1月1日至2016年12月31日，空间范围为99°E～150°E、10°S～52°N的海温时空序列为例，实现了海表温度小尺度信息的时空预测。
步骤3：采用长短期记忆神经网络方法对随机动态分析法得到的年代际、年际的大尺度时间信息进行分析预测，得到大尺度预测结果。
长短期记忆网络(Long Short Term Memory networks，LSTMs)，一种特殊的RNN网络，该网络设计出来是为了解决长依赖问题，它包含一个动态的门机制，LSTM由输入门、输出门、遗忘门和记忆单元组成，其具体结构如图2所示。本发明以时间范围为1958年1月1日至2016年12月31日的海温时空序列为例，进行海表温度大尺度信息的预测。
LSTM内部的数据流，其中遗忘门读取上一个状态h t-1和当前输入状态x t的信息，通过Sigmoid层输出一个在0到1之间的数值给每个细胞状态C t-1，C t-1中的数字决定从细胞状态 中丢弃什么信息，1代表“完全保留”，0代表“完全舍弃”；接着我们通过输入门层来决定什么样的新信息将被更新并且放在细胞状态中，首先将h t-1与x t输入Sigmoid函数确定将要更新的值，然后通过tanh层创建候选值向量C t，接着将旧状态与f t相乘，确定我们需要遗忘的信息，加上i t与C t的乘积产生新的候选值，最终，我们根据新的细胞状态来决定输出什么值，通过Sigmoid层决定输出的细胞状态，然后将细胞状态通过tanh进行处理并将其与Sigmoid的输出相乘得到这一时间的输出形式化的描述如下：
Figure PCTCN2022093025-appb-000024
式中，i、f、c、o分别是输入门、遗忘门、细胞状态和输出门；W和b分别为对应的权重系数和偏置项；σ和tanh分别为Sigmoid和双曲正切激活函数。LSTM模型训练过程采用的是与经典的反向传播(Back Propagation,BP)算法原理类似的BPTT算法，分为4个步骤：按照计算方法计算LSTM细胞的输出值；反向计算每个LSTM细胞的误差项，包括时间和网络层级2个反向传播方向；根据相应的误差项，计算每个权重的梯度；应用基于梯度的优化算法更新权重。
通过上述的长短期记忆网络方法即可完成海表温度大尺度信息进行预测，本发明以时间范围为1958年1月1日至2016年12月31日的海温时空序列为例，实现了海表温度小尺度信息的预测。
步骤4：将时空经验正交函数模的小尺度预报结果与长短期记忆神经网络的大尺度预测结果进行重构，得到分析预测海域海洋动力环境要素的预测结果。本发明所述重构方法如下：本发明所提出的基于随机动态分析、时空经验正交函数(Spatiotemporal Empirical Orthogonal Function,STEOF)和长短期记忆网络(Long Short-Term Memory，LSTM)的海洋环境动力要素预报模型，称为STEOF-LSTM模型，该模型结构如图3所示。该模型主要利用随机动态分析方法实现对指定海域海洋环境动力要素时空序列数据的多尺度分析和变换，得到海洋环境动力要素时空序列数据的大尺度分量和小尺度分量；以STEOF为基础实现对小尺度时间信息的预报；利用大尺度时间信息构建LSTM神经网络实现对大尺度时间信息的预报。将STEOF的 高频预报结果与LSTM神经网络低频预报结果进行叠加，以实现大尺度信息和小尺度信息的重构，得到最终海洋环境动力要素的预报结果。
本实施例以时间范围为1958年1月1日至2016年12月31日，空间范围为99°E～150°E、10°S～52°N的海温时空序列为例，如图4(a)至图4(c)所示为深度0m层的不同模型预报结果与真值比较图，其中图4(a)为1至90天的真实值，图4(b)为STEOF-LSTM神经网络方法1至90天预报结果，图4(c)为STEOF方法1至90天预报结果。
以上所述仅为本发明的优选实施例而已，并不用于限制本发明，对于本领域的技术人员来说，本发明可以有各种更改和变化。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。

Claims (1)

  1. 一种基于STEOF-LSTM的海洋环境要素预测方法，其特征在于，包括以下步骤：
    步骤1：基于待分析预测海域的再分析数据，利用随机动态分析法和经验正交函数方法分析研究海洋动力环境要素的年代际、年际、月、日这类多尺度时间和空间变化特征和规律；
    将海洋动力环境要素对应的时间序列分解为趋势、周期、随机来进行动态近似分析：
    SLH(t)＝T(t)+P(t)+R(t)
    其中，T(t)为趋势项，通过一元线性回归分析计算获得；P(t)为周期项，包含季节性、月、年、年际变化特征和规律，对去趋势后的时间序列进行经验正交函数分解分析，计算出主要空间分布模态和时间周期变化，从而获得海洋环境动力要素的周期变化特征；R(t)为剩余随机项，通过滤波获得；
    步骤2：针对随机动态分析法得到的月、日的小尺度时间信息，采用对应时间尺度的STEOF模型进行中长期时空分析预测，得到小尺度的预测结果；
    步骤2.1：针对某种海洋动力环境要素，其对应的历年逐日海洋动力环境要素时空样本矩阵X为：
    Figure PCTCN2022093025-appb-100001
    对任一时空样本矩阵X，其矩阵维度为M×(N×T)，N表示空间网格点的数量，T表示时间序列的数量，M表示年样本的数量；
    步骤2.2：对时空样本矩阵X进行作时空经验正交分解，得到该矩阵的特征值和各特征值对应的特征向量，依次计算各个特征值总占比并按顺序对特征值及特征向量进行排列，得到的特征向量为空间模态的时间序列，其中既包含空间信息又包含时间信息，将这种特征向量称之为时空基底；
    通过矩阵变换得到C *矩阵的特征向量后，计算出C矩阵的特征向量，令X与其转置阵的乘积如下式所示：
    Figure PCTCN2022093025-appb-100002
    特征向量V M×M得：
    C *×V *＝V *×Λ
    其中，Λ为特征值对应的对角方阵，
    Figure PCTCN2022093025-appb-100003
    λ 1＞…＞λ m＞…＞λ M，且λ m≥0；
    任一特征向量V m如下式所示：
    Figure PCTCN2022093025-appb-100004
    步骤2.3：将时空模态投影到矩阵X上得到其对应的主成分，即：
    PC M×(N×T)＝V T M×(N×T)×X M×(N×T)
    其中，主成分是每个时空特征向量所对应的时空系数。时空系数PC M×(N×T)是M×(N×T)维的矩阵，PC M×(N×T)中每行数据就是对应每个时空模态的时空系数，第一个时空模态的时空系数对应于时空系数PC M×(N×T)的第一行，以此类推。
    步骤2.4：利用时空观测和时空基础来预测时空序列；
    定义时空观测值O如下式所示：
    O＝[o 1,t-l…o N,t-l…o 1,t-l+i…o N,t-l+i…o 1,t…o N,t] T
    其中，O表示时空观测；t表示预测开始时间；n表示空间网格点的数目；l是观测次数；
    时空基H i被分为两部分：一部分是与时空观测具有相同周期的拟合时空基H f，另一部分是预测时空基H p；
    Figure PCTCN2022093025-appb-100005
    Figure PCTCN2022093025-appb-100006
    Figure PCTCN2022093025-appb-100007
    其中，t表示预测开始时间；l表示观测次数；p是预测时间步数；M是时空基的个数；
    使用最小二乘估计方法求解时空观测值的拟合系数和拟合时空基，拟合系数是时空观测在每个时空基上的投影，描述了一组观测与时空基之间的相似性：
    O＝H fS
    其中，S表示拟合系数，S＝[S 1…S m…S M]
    通过重构拟合系数和预测时空基来预测时空序列的未来值，使用将时空经验正交分解方法与最小二乘法相结合时空经验正交函数预测模型的来预测时空序列，预测模型如下式所示：
    Y＝H pS＝[y 1,t+1…y N,t+1…y 1,t+j…y N,t+j…y 1,t+p…y N,t+p] T
    其中，Y表示时空预测结果；
    步骤3：采用LSTM模型对随机动态分析法得到的年代际、年际的大尺度时间信息进行分析预测，得到大尺度预测结果；
    所述的LSTM模型包括输入门、输出门、遗忘门和记忆单元；LSTM模型训练过程采用BPTT算法，分为4个步骤：计算LSTM细胞的输出值；反向计算每个LSTM细胞的误差项，包括时间和网络层级2个反向传播方向；根据相应的误差项，计算每个权重的梯度；应用基于梯度的优化算法更新权重；
    遗忘门读取上一个状态h t-1和当前输入状态x t的信息，通过Sigmoid层输出一个在0到1之间的数值给每个细胞状态C t-1，C t-1中的数字决定从细胞状态中丢弃什么信息，1代表“完全保留”，0代表“完全舍弃”；
    首先将h t-1与x t输入Sigmoid函数确定将要更新的值，然后通过tanh层创建候选值向量C t，接着将旧状态与f t相乘，确定需要遗忘的信息，加上i t与C t的乘积产生新的候选值；最终，我们根据新的细胞状态来决定输出什么值，通过Sigmoid层决定输出的细胞状态，然后将细胞状态通过tanh进行处理并将其与Sigmoid的输出相乘得到这一时间的输出形式化的描述如下：
    Figure PCTCN2022093025-appb-100008
    其中，i、f、c、o分别是输入门、遗忘门、细胞状态和输出门；W和b分别为对应的权重系数和偏置项；σ和tanh分别为Sigmoid和双曲正切激活函数；
    步骤4：将时空经验正交函数模的小尺度预报结果与长短期记忆神经网络的大尺度预测结果进行重构，得到分析预测海域海洋动力环境要素的预测结果；
    利用随机动态分析方法实现对指定海域海洋环境动力要素时空序列数据的多尺度分析和变换，得到海洋环境动力要素时空序列数据的大尺度分量和小尺度分量；以STEOF为基础实现对小尺度时间信息的预报；利用大尺度时间信息构建LSTM模型实现对大尺度时间信息的预报；将STEOF的高频预报结果与LSTM神经网络低频预报结果进行叠加，以实现大尺度信息和小尺度信息的重构，得到最终海洋环境动力要素的预报结果。
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