Ship motion forecasting method based on EMD-LSTM-LSSVR model

Abstract

The invention belongs to the technical field of ship and ocean engineering, and particularly relates to a ship motion forecasting method based on an EMD-LSTM-LSSVR model, and the method comprises the steps: extracting a motion time sequence of a ship part, and expanding the two ends of the motion time sequence; using empirical mode decomposition to decompose the motion time sequence into a plurality of intrinsic mode function signals and a residual signal; inputting the first intrinsic mode function signal into an LSTM network for training and prediction; respectively inputting each residual intrinsic mode function signal and each residual signal into different SVR models for training and prediction; and the prediction result of each IMF signal and the prediction result of the residual signal are summed to obtain an estimated value of the original motion sequence. According to the method, the advantages of EMD, LSTM and SVR (LSSVR) are combined, prediction is performed by decomposing a time sequence and selecting a proper model, and prediction results are integrated, so that accurate prediction of ship motion is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of ship and ocean engineering, and particularly relates to a ship motion prediction method based on an EMD-LSTM-LSSVR model. Background Art

[0002] A ship is affected by factors such as wind, waves, and currents in the marine environment, and will generate six-degree-of-freedom motions (rolling, pitching, yawing, swaying, surging, and heaving), which will affect the performance of offshore equipment and the safety of related operations. Short-term prediction of ship motion can maintain the smoothness of the personnel passage between on-board equipment and marine structures through active compensation. On the other hand, it can provide a reference for decision-making to prevent accidents. Therefore, short-term prediction of ship motion is particularly important.

[0003] Duan Wenyang et al. proposed a hybrid AR-EMD-SVR model for short-term prediction of nonlinear and non-stationary ship motions. This model combines SVR and AR-EMD technologies, and the latter uses an AR model in endpoint extension. The ship motion time series obtained through a towing tank is compared with a linear AR model, a nonlinear SVR model, and a hybrid EMD-AR model. The prediction results show that the AR-EMD technology successfully overcomes the non-stationarity of the SVR model, and the prediction performance of the AR-EMD-SVR model is better than that of other models. Chinese invention patent CN113378387A discloses a ship motion prediction method based on an improved EMD-AR model, which solves the mode mixing problem of traditional EMD and improves the accuracy of IMF by adding and removing white noise to the time series and performing empirical mode decomposition. The invention uses an SVR model to extend the envelope of the ship motion time series, reasonably calculates the envelope of the first and last extreme points, and suppresses the endpoint effect of traditional EMD. Guo Xiaoxian et al. developed a machine learning model based on LSTM to predict the heaving and surging motions of a semi-submersible platform. The training and test data are from model tests. After the motion data is input into the LSTM unit, it passes through multiple fully connected layers to finally obtain the prediction result. If wave data is used as an aid, the prediction can be up to 46.5 seconds at most, and the accuracy is close to 90%. After using an augmented noise data set, the model can effectively handle a noise level of 0.8. The model shows good ship motion prediction ability. From relevant domestic and foreign research, in order to enable the prediction method to handle non-stationary time series, introducing EMD is a mature solution. Therefore, most researchers focus on improving the details of the EMD method to make it faster or have less negative effects. A well-trained deep learning prediction method can also handle non-stationary time series, but the required training time is huge, and it will be very inflexible if it is temporarily necessary to predict the motion of other ships.

[0004] After research, most of the existing ship motion prediction methods rely on the linear AR method. However, since the AR method is based on linear assumptions, its fitting ability for strongly non-linear sequences is poor. Especially in severe sea conditions, it is difficult to provide accurate prediction results. The current motion prediction methods mainly focus on the motion time history of three degrees of freedom (heave, roll, and pitch) in the vertical plane, while ignoring the motion of three degrees of freedom in the horizontal plane. These motions in the horizontal plane have weak periodicity and are not affected by the ship's own restoring force, making it easy to exhibit non-stationarity, and traditional prediction methods are difficult to effectively handle these non-stationary motions. Existing methods usually borrow model parameter selection criteria in statistics such as the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC), but these criteria do not fully consider the characteristics of ship motion prediction, so they may not be applicable to specific prediction situations. Existing methods also lack a balance between model performance and computational cost. Summary of the Invention

[0005] The present invention solves the problem that most of the existing ship motion prediction methods rely on the linear AR method and ignore the motion of three degrees of freedom in the horizontal plane, resulting in inaccurate prediction results, and provides a ship motion prediction method based on the EMD-LSTM-LSSVR model.

[0006] The technical solution claimed by the present invention is as follows:

[0007] A ship motion prediction method based on the EMD-LSTM-LSSVR model, comprising the following steps;

[0008] S1: Data preprocessing: Extract a partial ship motion time series and extend both ends of the motion time series; the motion time series refers to a string of continuous equally spaced time points and their corresponding motion response values; the motion response values are the six-degree-of-freedom motion data of the ship;

[0009] S2: Decomposition of the motion time series: Use empirical mode decomposition to decompose the motion time series obtained in S1 into multiple intrinsic mode function signals and a residual signal;

[0010] S3: Model selection and assignment: Perform min-max normalization on the wave elevation time series and the first intrinsic mode function signal obtained in S2 to obtain a two-dimensional matrix containing the first intrinsic mode function signal and the wave elevation time series, and input the two-dimensional matrix into the LSTM network for training and prediction; at the same time, input each of the remaining intrinsic mode function signals and the residual signal obtained in S2 into different SVR models for training and prediction;

[0011] S4: Integration of prediction results: Obtain the predicted value of the original motion sequence by summing the prediction results of each IMF signal and the residual signal.

[0012] In the above method, the input X of the LSTM network in S3 L is defined as:

[0013]

[0014] where: i represents the time series of the IMF1 signal, and the IMF1 signal represents the first intrinsic mode function signal; w represents the wave elevation time series; X L represents the matrix of the t nth row and the 2nd column; n c represents the current discrete time step; n t represents the time step, that is, the length of the input in time; n p is the prediction step, that is, the future time step of the model prediction output.

[0015] In the above method, the SVR model in S3 includes the LSSVR model.

[0016] In the above method, the training sets of the LSTM network and the LSSVR model are constructed through different sliding data windows; the training set of the LSTM network extracts the first intrinsic mode function signal through the corresponding sliding data window, and at the same time uses the wave elevation time series as the input vector; the sizes, update and prediction rules of the different sliding data windows are different.

[0017] In the above method, the specific rules and steps for updating and predicting the different sliding data windows are as follows:

[0018] Step 1: Use the 200-second and 1000-second long motion time series before t0 - T pre as the training set windows of LSSVR and LSTM respectively;

[0019] Step 2: Obtain the predicted value at time t0, and add the motion measurement value at time t0 - T pre +Δt to the new training set of LSSVR, that is, its sliding data window will be updated and trained after each prediction;

[0020] Step 3: Update the new target prediction time to t0 + Δt, and train with the new sliding data window, and obtain the predicted value until the target time is updated to t0 + 500Δt. At this time, the training set window of the LSTM network moves backward by 200 seconds, and the LSTM training set is updated once;

[0021] Step 4: Repeat the above operations along the time until all test set data have been predicted;

[0022] In the above Steps 1 - 4, t0 represents the time point where the first prediction result is located; T preis the prediction time length, and Δt is the sampling period.

[0023] In the above method, in S1, an autoregressive model is used to extend the endpoints of the motion time series. Specifically: at both ends of the sliding data window, it is extended by prediction to the nearest extreme point, and the extended data is used as the input for empirical mode decomposition, where: the Levinson-Durbin iterative algorithm is used to solve the parameters in the autoregressive model, and the BIC criterion is used for the order determination of the autoregressive model.

[0024] In the above method, the LSTM network is configured to only output the last time step of the sequence; the hidden layer of the LSTM network contains 128 units, and a fully connected neural network layer is connected after this layer; the Mini Batch size is set to one-twentieth of the training set, the maximum number of iterations is 600, the early stopping option is enabled, and the corresponding validation patience parameter is 30; the optimizer uses the Adam algorithm, the initial learning rate is set to 0.005, and it decays at a rate of one-fifth every 200 iterations.

[0025] In the above method, the time step parameter in the LSTM network is determined using the instantaneous autocorrelation function, and the instantaneous autocorrelation function introduces a spherical wave function to correct the lag time error caused by the non-stationarity of the time series in the calculation of the autocorrelation function.

[0026] In the above method, according to the calculated instantaneous autocorrelation function, the following formula is used to determine the final time step k:

[0027] |ρ xx (τ0)|≤ε

[0028]

[0029] where: Δt represents the sampling interval of the time series; ρ xx represents the instantaneous autocorrelation function; ε represents a reference value of 0.36; τ0 is the time lag value.

[0030] In the above method, the instantaneous autocorrelation function corrected based on the spherical wave function is used to determine the time step of the LSTM network, and the time step of the LSTM is dynamically adjusted during the prediction process.

[0031] Beneficial effects:

[0032] The present invention provides a ship motion prediction method based on an EMD-LSTM-LSSVR model, which extracts a partial motion time series of a ship and extends both ends of the motion time series to reduce the "boundary effect" caused by the time series boundary, that is, the inaccurate prediction that may be caused by insufficient data at the beginning and end of the sequence; the motion time series refers to a string of continuous equally spaced time points and their corresponding motion response values, and the motion response value is the six-degree-of-freedom motion data of the ship. The present invention can be implemented separately for the motion of each degree of freedom to obtain the motion prediction values on different degrees of freedom, and solves the problem that the existing ship motion prediction methods ignore the motion of the three degrees of freedom in the horizontal plane, resulting in inaccurate prediction results; the empirical mode decomposition is used to decompose the motion time series into multiple intrinsic mode function signals and a residual signal, and the first intrinsic mode function signal (IMF1) obtained by the decomposition is combined with the wave elevation time series as an auxiliary feature quantity and input into the LSTM network for training and prediction, which improves the prediction accuracy of the LSTM network. At the same time, the remaining intrinsic mode function signals and residual signals are respectively trained and predicted by the SVR model. Due to the problems of high-frequency characteristics and mode mixing, the IMF1 generated by the empirical mode decomposition (EMD) sometimes cannot be well modeled by the SVR. After investigation and research, it is found that the IMF1 calculated by the EMD under different data windows before and after has high consistency. Therefore, the LSTM network is introduced to predict the IMF1. The LSTM network can effectively predict the rapid fluctuations of the signal. At the same time, because the signal has high consistency before and after, the number of times of repeating training to update the network parameters is reduced, and the calculation cost is effectively controlled. The method provided by the present invention combines the advantages of EMD, LSTM and SVR, realizes the accurate prediction of ship motion by decomposing the time series, selecting a suitable model for prediction, and integrating the prediction results, and solves the problem that most of the existing ship motion prediction methods rely on the linear AR method, resulting in inaccurate prediction results.

[0033] The time step parameter in the LSTM network is determined using the instantaneous autocorrelation function. Compared with the autocorrelation function calculated directly from long-term measurement values, the instantaneous autocorrelation function introduces the prolate spheroidal wave function (PSWF) to correct the lag time error caused by the non-stationarity of the time series in the calculation of the autocorrelation function, and can better reflect the current sequence characteristics.

[0034] In summary, the method provided by the present invention combines the advantages of EMD, LSTM, and SVR (LSSVR). By decomposing the time series, selecting appropriate models for prediction, and integrating the prediction results, accurate prediction of ship motion is achieved. The sliding data window strategy is used to continuously update the training set to adapt to the dynamic changes of the time series and improve the prediction accuracy. The AR model is used to process the EMD boundary effect to reduce the prediction error caused by insufficient boundary data. The instantaneous autocorrelation function is introduced to determine the time step parameter, which can more accurately reflect the characteristics of the current sequence and improve the prediction accuracy. Description of the Drawings

[0035] Figure 1 It is a schematic flowchart of the ship motion prediction method based on the EMD-LSTM-LSSVR model in the embodiment of the present invention. Detailed Embodiments

[0036] The following further describes the specific embodiments of the present invention with reference to the drawings. It should be noted here that the description of these embodiments is for helping to understand the present invention, but does not limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0037] In this embodiment, it is default that a 1000-second ship motion time series has been obtained before using this prediction method, specifically a series of continuous equally spaced time points and their corresponding motion response values.

[0038] The present invention provides a ship motion prediction method based on the EMD-LSTM-LSSVR model, as Figure 1 shown, including the following steps:

[0039] S1: Data preprocessing: Extract the partial motion time series of the ship and extend both ends of the motion time series, that is, extend the data at the beginning and end of the motion time series to reduce the possible inaccurate subsequent prediction caused by insufficient data at the beginning and end of the motion time series; the motion time series refers to a string of continuous equally spaced time points and their corresponding motion response values; in a specific embodiment of the present invention, the autoregressive (AR) model is applied to process the EMD boundary effect, that is, at both ends of the sliding data window, it is extended by prediction to the nearest extreme point. Specifically, the sliding data window contains the latest time series. The autoregressive model can continuously predict the 1st, 2nd, 3rd, ……, nth points at the end of the time series, but the accuracy of the later prediction points is lower. For these prediction points, only the part between the first prediction point and the prediction points forming the first extreme point is taken as the final extended data. Similarly, by reversing the order of the sliding data window data, the head of the time series can be extended, and the extended data is used as the input for EMD. In a specific embodiment of the present invention, the Levinson-Durbin iterative algorithm is used to solve the parameters in the AR model, and the BIC criterion is used for the order determination of the AR model. The Levinson-Durbin algorithm, the BIC criterion, and the parameter solution method of the LSSVR model are all technologies that can be publicly consulted. The present invention has not modified this part of the technology, so it will not be elaborated.

[0040] S2: Decomposition of the motion time series: Use empirical mode decomposition (EMD) to decompose the motion time series obtained in S1 into multiple intrinsic mode function signals (IMFs) and a residual signal; among them, the first intrinsic mode function (IMF1) signal is subsequently input into a long short-term memory (LSTM) network for prediction, and each of the remaining IMF signals and the residual signal are respectively predicted by a support vector regression (SVR) model.

[0041] S3: Model selection and allocation: Perform min-max normalization on the wave elevation time series (wave time history data) and the first intrinsic mode function signal obtained in S2 to obtain a two-dimensional matrix containing the first intrinsic mode function signal and the wave elevation time series, and input the two-dimensional matrix into the LSTM network for training and prediction; at the same time, input each of the remaining intrinsic mode function signals and the residual signal in S2 into different SVR models for training and prediction; the SVR model includes the LSSVR model. The wave elevation time series is obtained by measuring the wave height at a nearby point. The wave action is the cause of the ship's motion, and statistically, the correlation coefficient between the first intrinsic mode function signal and the wave time history is the highest.

[0042] The time series of wave elevation and the IMF1 signal are processed by min-max normalization to obtain a two-dimensional matrix containing the first intrinsic mode function signal and the time series of wave elevation. The time series of wave surface elevation needs to use a part of the predicted values, and its prediction step is consistent with the prediction step of the motion.

[0043] The input X of the LSTM network L is defined as:

[0044]

[0045] where i represents the time series of the IMF i signal, w is the time series of wave elevation, and XL is an n t row 2-column matrix, and n c represents the current discrete time step, and n t represents the time step, that is, the length of the input in time, and n p is the prediction step, that is, the future time step of the model's predicted output.

[0046] In a specific embodiment of the present invention, two sliding data windows are used to respectively construct the training sets of the LSTM network and the LSSVR model in the EMD-LSTM-LSSVR prediction model to provide more reasonable IMF components. Since the training speed of the LSSVR model is relatively fast, the LSSVR model is retrained and predicted using a new sliding data window at each time step. In the combined model of EMD-LSTM-LSSVR, the sizes and update rules of the sliding data windows used by the LSTM network and the LSSVR model are different because the training speed of the LSTM network is much slower than that of the LSSVR. The training set of the LSTM model extracts IMF1 through its own sliding data window and uses the time series of wave elevation as the input vector.

[0047] The specific rules and steps for updating and predicting the sliding data window are as follows:

[0048] Step 1: The 200-second and 1000-second long motion time series before t0-T pre are respectively used as the training set windows of the LSSVR and the LSTM;

[0049] Step 2: Obtain the predicted value at time t0, and add the motion measurement value at time t0-T pre +Δt to the new training set of the LSSVR, that is, its sliding data window will be updated and trained after each prediction;

[0050] Step 3: The new target prediction time is updated to t0 + Δt, and it is trained using the new sliding data window to obtain the predicted value until the target time is updated to t0 + 500Δt. At this time, the training set window of the LSTM network moves backward by 200 seconds, and the LSTM training set is updated once.

[0051] Step 4: Repeat the above operations along the time until all the test set data have been predicted.

[0052] In the above Steps 1 - 4, t0 represents the time point where the first prediction result is located; T pre is the prediction time length, and Δt is the sampling period.

[0053] The LSTM network is configured to output only the last time step of the sequence. The hidden layer of the LSTM contains 128 units, and a fully connected neural network (FCN) layer is connected after this layer. The mini - batch size is set to one - twentieth of the training set, and the maximum number of epochs is 600. To prevent overfitting, the early stop option is enabled, and the corresponding validation patience parameter is 30. The optimizer uses the Adam algorithm, the initial learning rate is set to 0.005, and it decays at a rate of one - fifth every 200 epochs.

[0054] The time step parameter in the LSTM network is determined using the instantaneous autocorrelation function, and the instantaneous autocorrelation function introduces a spherical wave function to correct the lag time error caused by the non - stationarity of the time series in the autocorrelation function calculation. The time step of the LSTM network is determined using the instantaneous autocorrelation function modified based on the spherical wave function, and the time step of the LSTM is dynamically adjusted during the prediction process.

[0055] According to the calculated instantaneous autocorrelation function, the final time step k is determined using the following formula:

[0056] |ρ xx (τ0)| ≤ ε

[0057]

[0058] where: Δt represents the sampling interval of the time series; ρ xx represents the instantaneous autocorrelation function; ε represents the reference value of 0.36; τ0 represents the time lag value.

[0059] S4: Prediction result integration: By summing the prediction results of each IMF signal and the residual signal, the predicted value of the original motion sequence is obtained.

Claims

1. A ship motion prediction method based on EMD-LSTM-LSSVR model, characterized in that: The method comprises the following steps: S1: Data preprocessing: extracting the partial motion time series of the ship and extending the two ends of the motion time series; the motion time series refers to a series of continuous equally spaced time points and their corresponding motion response values; the motion response value is the six-degree-of-freedom motion data of the ship; S2: Motion time series decomposition: Use empirical mode decomposition to decompose the motion time series obtained in S1 into multiple intrinsic mode function signals and a residual signal; S3: Model selection and allocation: Perform minimum-maximum normalization processing on the wave rise time series and the first intrinsic mode function signal obtained in S2 to obtain a two-dimensional matrix containing the first intrinsic mode function signal and the wave rise time series, and input the two-dimensional matrix into the LSTM network for training and prediction; At the same time, each remaining intrinsic mode function signal and residual signal of S2 is input into different SVR models for training and prediction; S4: Prediction result integration: The prediction results of each IMF signal and the residual signal are summed to obtain the estimated value of the original motion sequence.

2. The ship motion prediction method based on the EMD-LSTM-LSSVR model according to claim 1, characterized in that: Input X of the LSTM network in S3 L is defined as: Where: i represents the time series of IMF1 signal, IMF1 signal represents the first intrinsic mode function signal; w represents the wave rise time series; X L Indicates n t The matrix of row and column 2; n c Represents the current discrete time step; n t Indicates the time step, that is, the length of the input in time; n p is the prediction step size, i.e., the future time steps for which the model predicts the output.

3. The ship motion prediction method based on the EMD-LSTM-LSSVR model according to claim 1, characterized in that: The SVR model described in S3 includes the LSSVR model.

4. The ship motion prediction method based on the EMD-LSTM-LSSVR model according to claim 3 is characterized in that: The training sets of the LSTM network and the LSSVR model are constructed through different sliding data windows; the training set of the LSTM network extracts the first intrinsic mode function signal through the corresponding sliding data window, and uses the wave rise time series as the input vector; the sizes, update and prediction rules of the different sliding data windows are different.

5. The ship motion prediction method based on the EMD-LSTM-LSSVR model according to claim 4 is characterized in that: The specific rules and steps for updating and predicting different sliding data windows are as follows: Step 1: Subtract t0-T pre The previous 200-second and 1000-second long motion time series were used as training set windows for LSSVR and LSTM, respectively; Step 2: Get the predicted value at time t0 and subtract t0-T pre The motion measurements at time +Δt are added to the new training set of LSSVR, that is, its sliding data window is updated and trained after each prediction; Step 3: The new target prediction time is updated to t0+Δt, and the new sliding data window is used for training and obtaining the prediction value until the target time is updated to t0+500Δt. At this time, the training set window of the LSTM network moves backward 200 seconds and the LSTM training set is updated once; Step 4: Repeat the above steps along the time until all test set data have been predicted; In the above steps 1 to 4, t0 represents the time point of the first prediction result; T pre is the prediction time length, and Δt is the sampling period.

6. The ship motion prediction method based on the EMD-LSTM-LSSVR model according to claim 4 is characterized in that: In S1, an autoregressive model is used to extend the endpoints of the motion time series. Specifically, the two ends of the sliding data window are extended to the nearest extreme point through prediction, and the extended data is used as the input of empirical mode decomposition, wherein: the Levinson-Durbin iterative algorithm is used to solve the parameters in the autoregressive model, and the BIC criterion is used to determine the order of the autoregressive model.

7. The ship motion prediction method based on the EMD-LSTM-LSSVR model according to claim 1, characterized in that: The LSTM network is configured to output only the last time step of the sequence; the hidden layer of the LSTM network contains 128 units, and a fully connected neural network layer is connected after this layer; the Mini Batch size is set to one twentieth of the training set, the maximum iteration round is 600, the early stopping option is enabled, and the corresponding verification patience parameter is 30; the optimizer uses the Adam algorithm, the initial learning rate is set to 0.005, and it decays at a rate of one-fifth every 200 iteration rounds.

8. The ship motion prediction method based on the EMD-LSTM-LSSVR model according to claim 7, characterized in that: The time step parameter in the LSTM network is determined using the instantaneous autocorrelation function, which introduces a spherical wave function to correct the lag time error caused by the non-stationarity of the time series in the calculation of the autocorrelation function.

9. The ship motion prediction method based on the EMD-LSTM-LSSVR model according to claim 8, characterized in that: Based on the calculated instantaneous autocorrelation function, the final time step k is determined using the following formula: |r xx (τ0)|≤ε Where: Δt represents the sampling interval of the time series; ρ xx represents the instantaneous autocorrelation function; ε represents the reference value of 0.36; τ0 represents the time lag value.

10. The ship motion prediction method based on the EMD-LSTM-LSSVR model according to claim 8, characterized in that: The instantaneous autocorrelation function based on the correction of spherical wave function is used to determine the time step of LSTM network, and the time step of LSTM is dynamically adjusted during the forecasting process.

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