Ship rolling motion real-time forecasting system based on EMD-PSO-RBFNN

Abstract

The invention belongs to the technical field of ship motion forecasting, and discloses a ship rolling motion real-time forecasting system based on EMD-PSO-RBFNN, and the system comprises the steps: collecting the historical data of the ship rolling motion, and decomposing a historical data signal into a plurality of IMFs and a residual term through EMD; the features of the ship rolling motion characteristics are extracted from the IMF and the residual terms obtained through decomposition to serve as input of an RBFNN model, the actual rolling angle serves as output, and RBFNN model training is carried out; optimizing parameters of the RBFNN model by using a PSO (Particle Swarm Optimization) algorithm to obtain an EMD-PSO-RBFNN model; and the forecasting performance of the EMD-PSO-RBFNN model is evaluated. According to the ship rolling motion real-time forecasting system based on the EMD-PSO-RBFNN, the nonlinearity of an original sequence is effectively reduced, the forecasting performance of the model is improved, and rolling motion forecasting of the ship is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of ship motion prediction, and particularly to a real-time ship roll motion prediction system based on EMD-PSO-RBFNN. Background Art

[0002] As an important waterborne transportation vehicle, the safety and efficiency of ships during sea voyages have always been the focus in the marine field. Due to the complexity of the marine environment, the ship roll motion is a complex process with characteristics such as nonlinearity, time-variation, and uncertainty, making it difficult to establish an accurate deterministic model. Severe roll motion seriously affects navigation safety. Especially in adverse sea conditions, the roll motion may cause the ship to capsize, resulting in huge economic losses. Therefore, it is crucial to perform real-time and accurate prediction of the ship roll motion to ensure navigation safety and operation efficiency.

[0003] Currently, ship motion state prediction mainly falls into two modes: hydrodynamics and non-hydrodynamics. Since the dynamic characteristics of ships change with the navigation state and external environment, it is extremely difficult to establish and solve the mathematical model of ship roll motion based on hydrodynamics. On the other hand, in the case where the specific ship state equation is not clear, a prediction model is constructed using historical data of ship motion through time series analysis methods, which shows high accuracy and reliability when dealing with stable time series data that conforms to the normal distribution law.

[0004] However, most measured ship motion data is often unstable and highly random, and non-stationary time series have a great impact on the prediction accuracy of ship roll motion. Empirical Mode Decomposition (EMD) is a data-driven time series analysis method mainly used to process nonlinear and non-stationary signals, which can effectively reduce data redundancy. The subsequences obtained by EMD decomposition have more obvious intrinsic characteristics compared to the original sequence, facilitating the analysis, identification, and prediction of complex time series.

[0005] Therefore, the present invention proposes a real-time ship roll motion prediction system based on EMD-PSO-RBFNN. Summary of the Invention

[0006] The purpose of the present invention is to provide a real-time ship roll motion prediction system based on EMD-PSO-RBFNN. The ship roll motion data is decomposed into multiple modal components by using EMD, effectively reducing the nonlinearity of the original sequence; PSO is used to optimize the center and width parameters of RBFNN, improving the prediction performance of the model, and the PSO-RBFNN model is used to perform individual prediction on each subsequence; the prediction results of each subsequence are reconstructed to achieve the final ship roll motion prediction.

[0007] To achieve the above object, the present invention provides a real-time prediction system for ship rolling motion based on EMD-PSO-RBFNN, including:

[0008] Step S1: Collect historical data of ship rolling motion, and use empirical mode decomposition (EMD) to decompose the historical data signal into multiple modal components IMF and a residual term;

[0009] Step S2: Extract features of the ship rolling motion characteristics from the decomposed modal components IMF and the residual term, use them as the input of the radial basis function neural network (RBFNN) model, and use the actual rolling angle as the output to train the radial basis function neural network (RBFNN) model;

[0010] Step S3: Use the particle swarm optimization (PSO) algorithm to optimize the parameters of the radial basis function neural network (RBFNN) model to obtain the EMD-PSO-RBFNN model;

[0011] Step S4: Evaluate the prediction performance of the EMD-PSO-RBFNN model.

[0012] Preferably, in step S1, let R be a specific time series, and the calculation steps of the empirical mode decomposition (EMD) are as follows:

[0013] Step S121: Identify all local extreme points in the signal, and use the local maximum and local minimum values to generate the upper envelope U R and the lower envelope L R respectively by interpolation;

[0014] Step S122: Calculate the local mean function m(t) and the new signal d(t) as follows:

[0015]

[0016] d(t) = x(t) - m(t) (2);

[0017] where x(t) is the original signal;

[0018] Step S123: Before d(t) is transformed into the modal component IMF, this process will be carried out according to the following criteria:

[0019]

[0020] where T represents the signal length and j represents the number of iterative calculations; usually, the ζ value is set between 0.2 and 0.3;

[0021] Step S124. Continue to iterate steps S121 - S123 until all intrinsic mode functions and residual signals are obtained, as follows:

[0022] R = IMF 1 + IMF 2 + … + IMF j + … + IMF n + r(4);

[0023] where EMD decomposes the R series into a set of modal components IMF and a residual series r.

[0024] Preferably, in step S2, extract the characteristics of the ship's rolling motion from the decomposed modal components IMF and the residual term as the input of the radial basis function neural network RBFNN model, and the actual rolling angle as the output, and perform the training of the radial basis function neural network RBFNN model. The specific process is as follows:

[0025] Step S21. Use the Gaussian function as the radial basis function, as follows:

[0026]

[0027] where c represents the center of the neuron, σ represents the expansion parameter of the network, and x is the input data point;

[0028] Step S22. During the training process, use the Levenberg - Marquardt backpropagation algorithm to update the weights W of the neural network, as follows:

[0029] ΔW = -(J T J + γI) -1 J T e(6);

[0030] e i = Y i - y i (7);

[0031]

[0032] where ΔW is the change in weights; J is the Jacobian matrix; γ is the adjustment parameter; I is the identity matrix; y is the true value; e is the prediction error; E(W,B) represents the error function; B is the bias; O i is the actual output; o i is the predicted output of the radial basis function neural network RBFNN model;

[0033] Step S23. Use the weights obtained during the training process and the design matrix of the test data to predict the output of the test set, as follows:

[0034]

[0035] Among them, W is the weight obtained during the training process; φ test is the design matrix of the test data; is the predicted output of the test set.

[0036] Preferably, in step S3, the particle swarm optimization (PSO) algorithm is used to optimize the parameters of the radial basis function neural network (RBFNN) model. Let the position parameter of the nth particle be represented by a d-dimensional vector, and the particle velocity and position are updated as follows:

[0037]

[0038] l n,k (t + 1) = l n,k (t) + v n,k (t + 1)(12);

[0039] Among them, ω is the inertia weight; v n,k (t) and l n,k (t) are the velocity and position of the nth particle in the kth dimension at the tth iteration; is the historical best position of the particle individual at this time; is the global best position of the entire particle swarm at this time; c 1 is the self-learning factor; c 2 is the social learning factor; r 1 , r 2 is a random value between [0, 1].

[0040] Preferably, in step S4, the mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), normalized root mean square error (NRMSE), mean absolute percentage error (MAPE), and coefficient of determination R 2 , are used to evaluate the prediction performance of the EMD - PSO - RBFNN model.

[0041] Preferably, the calculation expressions of each evaluation index are as follows:

[0042]

[0043] Among them, y i is the actual value at time i; is the predicted value at time i; n is the number of predicted data; is the average value of the data.

[0044] Therefore, the present invention adopts the above-mentioned real-time prediction system for ship roll motion based on EMD-PSO-RBFNN, uses EMD to decompose the ship roll motion data into multiple modal components, effectively reducing the nonlinearity of the original sequence; uses PSO to optimize the center and width parameters of RBFNN, improves the prediction performance of the model, and uses the PSO-RBFNN model to predict each subsequence separately; and reconstructs the prediction results of each subsequence to achieve the final ship roll motion prediction.

[0045] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flow chart of ship rolling motion prediction in an embodiment of the present invention;

[0047] Figure 2 Schematic diagram of the "Yukun" wheel in an embodiment of the present invention;

[0048] Figure 3 This is a diagram showing the change in the ship's roll angle during the Z-shaped test of the "Yukun" ship in an embodiment of the present invention;

[0049] Figure 4 is a decomposition diagram of a ship roll angle time series based on EMD in an embodiment of the present invention;

[0050] Figure 5 is the prediction result of the PSO-RBFNN for the subsequence in the embodiment of the present invention;

[0051] Figure 6 is a comparison diagram of the roll angle prediction of the EMD-PSO-RBFNN and PSO-RBFNN models in an embodiment of the present invention;

[0052] Figure 7 is a comparison diagram of prediction errors of EMD-PSO-RBFNN and PSO-RBFNN models in an embodiment of the present invention;

[0053] Figure 8 1 is a comparison chart of the prediction results of different models in the embodiment of the present invention; wherein, (a) is the prediction results of PSO-ANN, PSO-BP and PSO-SVM; (b) is the prediction results of EMD-PSO-ANN, EMD-PSO-BP and EMD-PSO-SVM;

[0054] Figure 9 It is the visualization result of the prediction error of each model in the embodiment of the present invention. DETAILED DESCRIPTION

[0055] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0056] A real-time prediction system for ship rolling motion based on EMD-PSO-RBFNN. First, the ship rolling motion data is decomposed into multiple modal components (IMFs) by using empirical mode decomposition (EMD); then, PSO is used to optimize the center and width parameters of RBFNN, and the PSO-RBFNN model is used to predict each subsequence separately; finally, the prediction results of each subsequence are reconstructed to achieve the final prediction of ship rolling motion.

[0057] Among them, as Figure 1 shown, the specific implementation process of a real-time prediction system for ship rolling motion based on EMD-PSO-RBFNN is as follows:

[0058] Step S1, data preprocessing.

[0059] Step S11, collect historical data of ship rolling motion, specifically including the rolling angle of the time series.

[0060] Step S12, use empirical mode decomposition (EMD) to decompose the original signal into multiple IMFs and a residual term.

[0061] Empirical mode decomposition (EMD) is a data-driven multi-scale signal processing method that can adaptively decompose non-stationary and non-linear signals into the sum of zero-mean amplitude modulation and frequency modulation components. EMD does not require prior assumptions about the nature of the signal, but decomposes according to the time-scale characteristics of the signal. It has now been widely used in the fields of ocean, atmosphere, earth and astronomical observation analysis, mainly for signal denoising, detrending, feature extraction, compression and recognition, etc.

[0062] Compared with traditional decomposition methods (such as wavelet transform), EMD can automatically decompose the original time series data into multiple independent intrinsic mode functions (IMFs) and a residual, avoiding the problem of manually adjusting to generate the most appropriate number of subsequences. Among them, R represents a specific time series, and the calculation steps of EMD are as follows:

[0063] Step S121, identify all local extreme points in the signal, and use these local maxima and local minima to generate the upper envelope U R and the lower envelope L R ;

[0064] Step S122, calculate the local mean function m(t) and the new signal d(t) as follows:

[0065]

[0066] d(t) = x(t) - m(t) (2);

[0067] Among them, x(t) is the original signal;

[0068] Step S123: Before d(t) is transformed into an IMF, this process will be carried out according to the following criteria:

[0069]

[0070] Among them, T represents the signal length, and j represents the number of iterative calculations. Usually, the ζ value is set between 0.2 and 0.3.

[0071] Step S124: Continue to iterate steps S121 - S123 until all intrinsic mode functions and residual signals are obtained, that is, EMD decomposes the R series into a set of IMFs and a residual series r, as follows:

[0072] R = IMF 1 + IMF 2 + … + IMF j + … + IMF n + r (4);

[0073] Step S2: Extract the characteristics of the ship's rolling motion from the decomposed modal components IMFs and the residual terms as the input of the radial basis function neural network RBFNN model, and the actual rolling angle as the output, and perform the training of the radial basis function neural network RBFNN model.

[0074] The radial basis function neural network (RBFNN) is a three-layer feedforward neural network with radial basis functions as the hidden layer functions. Due to the simplicity of its structure and strong adaptability to local input features, it shows excellent performance in many fields such as financial forecasting, environmental monitoring, and medical diagnosis. Especially in the prediction of time series data, RBFNN can effectively capture time dependence and nonlinear relationships, thus providing accurate prediction results.

[0075] Step S21: Use the Gaussian function as the radial basis function, as follows:

[0076]

[0077] Among them, c represents the center of the neuron, σ represents the expansion parameter of the network, and x is the input data point.

[0078] Step S22: In the neural network, the Levenberg - Marquard (L - M) backpropagation algorithm is a commonly used training method and also a widely used optimization algorithm. It does not require manual specification of the learning rate and will adaptively adjust the step size.

[0079] The L-M backpropagation algorithm is used to update the weights W of the neural network during training as follows:

[0080] ΔW = -(J T J + γI) -1 J T e (6);

[0081] e i = Y i - y i (7);

[0082]

[0083] where ΔW is the change in weights; J is the Jacobian matrix, which can be calculated by Equation (9); γ is the adjustment parameter; I is the identity matrix; y is the true value, e is the prediction error; E(W, B) represents the error function, B is the bias; O i is the actual output, o i is the predicted output of the RBFNN model.

[0084] Step S23: Use the weights W obtained during training and the design matrix φ of the test data test to predict the output of the test set , as follows:

[0085]

[0086] Step S3: Use the particle swarm optimization (PSO) algorithm to optimize the parameters of the radial basis function neural network (RBFNN) model to obtain the EMD-PSO-RBFNN model.

[0087] Particle swarm optimization (PSO) is a population-based optimization algorithm. Its core idea is to find the optimal solution through information exchange and cooperation among particles. In the basic PSO algorithm, assume that the position parameter of the nth particle is represented by a d-dimensional vector. Update the particle velocity and position as follows:

[0088]

[0089] l n,k (t + 1) = l n,k (t) + v n,k (t + 1) (12);

[0090] where ω is the inertia weight; v n,k (t) and l n,k (t) are the velocity and position of the nth particle in the kth dimension at the tth iteration; is the historical best position of the particle individual at this time; is the global optimal position of the entire particle swarm at this time; c 1 is the self-learning factor; c 2 is the social learning factor; r 1 , r 2 is a random value between [0, 1].

[0091] In the present invention, the parameter settings of the particle swarm optimization PSO algorithm are as follows:

[0092] The number of particles is 16, c 1 and c 2 is equal to 1.5, ω is equal to 0.5, and the maximum number of iterations is 100.

[0093] Step S4, evaluate the prediction performance of the EMD-PSO-RBFNN model.

[0094] The mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), normalized root-mean-square error (NRMSE), mean absolute percentage error (MAPE), and coefficient of determination (R 2 ) are used to comprehensively evaluate the prediction performance of the EMD-PSO-RBFNN model. The smaller the values of MAE, MSE, RMSE, NRMSE, and MAPE, the smaller the prediction error of the model. R 2 is closer to 1, the higher the prediction accuracy of the model.

[0095] The calculation expressions of each evaluation index are as follows:

[0096]

[0097] Among them, y i is the actual value at time i; is the predicted value at time i; n is the number of predicted data; is the average value of the data.

[0098] In practical applications, based on the above system for real-time prediction, the data of the ship's rolling motion is collected in real time through sensors; the EMD-PSO-RBFNN model is used to predict the newly collected data to obtain the future rolling angle.

[0099] Embodiment

[0100] Due to the complexity of the ocean environment, the ship's motion state presents dynamic time-varying characteristics, making the prediction of ship rolling motion extremely challenging. This is mainly due to the complexity and variability of the ocean environment and the difficulty in detecting ship dynamics in time series. Ship dynamics are often obscured by the overall trend or fluctuation of the time series, while multiple influencing factors such as wind and waves appear in the time series with different frequencies and characteristics, increasing the difficulty of identification and prediction.

[0101] In order to solve this problem, the present invention proposes a real-time prediction system for ship roll motion based on EMD-PSO-RBFNN, which combines the advantages of EMD, PSO and RBFNN. EMD decomposition is used to reduce data redundancy and obtain the representation of significant non-coupled coefficients of the original time series, thereby generating effective long-term forecasts. Although the time series is decomposed into sub-signals with different frequencies, they are still nonlinear in nature, so PSO-RBFNN is used to train and predict the sub-sequences, and the neural network is used to represent the nonlinearity in the sub-sequences; RBFNN gives the model adaptability and nonlinear representation capabilities; PSO optimizes the width parameters of RBFNN while searching for the best center position of RBFNN to improve the prediction performance of the model. Finally, the prediction of ship motion is achieved by reconstructing the prediction results of the modal components.

[0102] 1. If Figure 1 As shown, this embodiment is based on the actual measured data of the "Yu Kun" ship at sea for system verification. The relevant ship type parameters of the "Yu Kun" ship are shown in Table 1.

[0103] Table 1. Relevant ship type parameters of the “Yukun” ship

[0104] Parameter Description Value LoA Length between perpendiculars 116m Lbp Length between perpendiculars 105m B Beam 18m D Depth 8.35m GT Gross tonnage 6106 V Design speed 16.9 kn T Design draft 5.4m

[0105] 2. Experimental data and preprocessing.

[0106] The data used comes from the sea trials of the training ship "Yu Kun". The schematic diagram of the "Yu Kun" is as follows: Figure 2 As shown. The ship zigzag test is a traditional maneuvering test used to evaluate the maneuverability of the ship. To verify the effectiveness of the proposed system, the experimental data of the 20° / 20° full-scale Z-shaped sea test conducted by the "Yukun" ship in the Bohai Sea under sea condition level 4 on August 8, 2009 were used. In order to verify the applicability of the proposed EMD-PSO-RBFNN model, the straight-line voyage before and after the Z-shaped test was also included, with a total of 636 sets of experimental data. The 636 roll state data samples were divided, the first 60% of the samples were used as training sets, and the last 40% of the samples were used as test sets. In the Z-shaped test, the initial speed of the ship was set to 14.7kn. The ship's roll angle during the ship's motion during the Z-shaped test changes, such as Figure 3as shown

[0107] Preprocess the roll angles obtained from the Z-shaped test at sea of the "Yukun" ship according to the proposed EMD method. EMD automatically decomposes the roll angle signal into 7 IMFs and a residue. Comparing with the original signal as Figure 3 shown, it can be seen that the non-linearity of the obtained IMFs and residue after decomposition decreases significantly, as Figure 4 shown

[0108] 3. Simulation results of ship roll motion prediction

[0109] In the simulation experiment, the data of the first 382 s and the data of the last 254 s are used as the sample space and test data respectively, that is, according to the ratio of 6:4 of the divided training set and test set, the IMFs and residue obtained by EMD decomposition are used for prediction experiments in the same proportion. The comparison diagram of the prediction of each IMF and residue by PSO-RBFNN is as Figure 5 shown

[0110] From Figure 5 it can be seen that the PSO-RBFNN model has a good prediction effect on each subsequence. Summing up each predicted subsequence can obtain the original signal, that is, the ship roll angle. In order to prove the advantage of the EMD decomposition process, the traditional PSO-RBFNN is used to make predictions using the same ship roll motion database for comparison

[0111] As Figure 6 shown, it shows the comparison of the predicted ship roll angle and the actual value (Actual) between EMD-PSO-RBFNN and PSO-RBFNN under the same conditions. From Figure 6 it can be seen that the proposed ensemble prediction method based on EMD can give a stable prediction for ship roll motion prediction, and has a higher prediction accuracy than the prediction without EMD combination Figure 6 It can be clearly seen from that the prediction deviation of PSO-RBFNN at the top of the roll angle is larger than that of EMD-PSO-RBFNN

[0112] As Figure 7 shown, it shows the comparison of the prediction error (δ) of the ship roll angle between EMD-PSO-RBFNN and PSO-RBFNN under the same conditions. It can be intuitively seen from Figure 7 that the MAE, MSE, RMSE, NRMSE and MAPE of EMD-PSO-RBFNN are much smaller than those of PSO-RBFNN. This is because of the advantage of the decomposed subsequences with small non-linearity obtained by EMD, indicating that the individual decomposed sub-signals show similar dynamics, which is convenient for representation and prediction, thus reducing the prediction error of the EMD-PSO-RBFNN model

[0113] To verify the effectiveness of the EMD-PSO-RBFNN model, models such as PSO-ANN, PSO-BP, PSO-SVM, EMD-PSO-ANN, EMD-PSO-BP, and EMD-PSO-SVM were used to simulate the ship roll motion prediction under the same conditions. The prediction results of each model and the roll angle density distribution (ρ) are as follows Figure 8 as shown.

[0114] As can be seen from Figure 8 (a) in, the prediction effects of PSO-SVM and PSO-BP are worse than that of PSO-ANN; while Figure 8 as can be intuitively seen from (b) in, when PSO-SVM, PSO-ANN, and PSO-BP are combined with EMD for prediction, the prediction error of EMD-PSO-BP decreases; the prediction errors of EMD-PSO-ANN and EMD-PSO-SVM increase instead, indicating that in the case of the ensemble prediction method based on EMD, the prediction effects of PSO-ANN and PSO-SVM are not so good, and PSO-BP can reduce the prediction error in the ensemble prediction method based on EMD, and the roll angle density distribution of EMD-PSO-ANN is closer to the actual value than other models, but there are still errors.

[0115] The visualization results of the relevant prediction error evaluation indicators of the EMD-PSO-RBFNN, EMD-PSO-ANN, EMD-PSO-BP, EMD-PSO-SVM, PSO-RBFNN, PSO-ANN, PSO-BP, and PSO-SVM models are as follows Figure 9 as shown; the detailed numerical comparison of the prediction errors is shown in Table 2.

[0116] Table 2 Comparison of prediction errors of each model

[0117]

[0118] It can be clearly seen from Figure 9 and Table 2 that the EMD-PSO-RBFNN model has the lowest prediction error and the best performance. Among the models without using EMD enhancement, PSO-ANN performs the best; some error indicators of PSO-SVM are slightly lower than those of PSO-ANN, but its stability and accuracy are higher; the prediction error of PSO-RBFNN is higher than that of PSO-ANN. Although the R 2 value is high, the MAPE value is large, indicating that the error and fluctuation are large; the PSO-BP model performs the worst, with high error and low R 2 value, indicating its insufficient ability to handle nonlinear and noisy data.

[0119] In the model enhanced by EMD, EMD-PSO-RBFNN performs excellently in all metrics, significantly outperforming PSO-ANN. Compared with PSO-RBFNN, the error of EMD-PSO-RBFNN is significantly reduced. Among them, MAPE is reduced by 93.87%, and the R 2 value is increased by 5.16%, indicating its extremely high prediction accuracy and reliability.

[0120] The prediction effects of other EMD-enhanced models such as EMD-PSO-BP, EMD-PSO-ANN, and EMD-PSO-SVM are not as expected. Although the error of EMD-PSO-BP is reduced, it is still not ideal; while the errors of EMD-PSO-ANN and EMD-PSO-SVM increase instead, and the R 2 value is low and MAPE is large, indicating that these models are unstable and ineffective in dealing with non-linear and non-stationary signals.

[0121] In summary, EMD-PSO-RBFNN performs outstandingly in all error metrics, significantly outperforming other models, showing obvious advantages in the complex ship roll angle prediction problem. Traditional models such as PSO-BP, PSO-ANN, and PSO-SVM perform poorly in dealing with non-linear and non-stationary signals. Even after enhancement, the performance of PSO-ANN, PSO-SVM, and PSO-BP models fails to reach the level of EMD-PSO-RBFNN, having certain limitations. Therefore, the model proposed in the present invention shows more excellent performance in ship roll motion prediction, can be used as a prediction tool for ship motion, and provides real-time, reliable, and efficient support for intelligent ship navigation.

[0122] Therefore, the present invention adopts the above-mentioned real-time ship roll motion prediction system based on EMD-PSO-RBFNN, uses EMD to decompose ship roll motion data into multiple modal components, effectively reducing the non-linearity of the original sequence; uses PSO to optimize the center and width parameters of RBFNN, improving the prediction performance of the model, and uses the PSO-RBFNN model to make individual predictions for each subsequence; reconstructs the prediction results of each subsequence to achieve the final ship roll motion prediction.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A real-time prediction system for ship rolling motion based on EMD-PSO-RBFNN, characterized in that: include: Step S1, collecting historical data of ship rolling motion, and using empirical mode decomposition (EMD) to decompose the historical data signal into multiple modal components (IMFs) and a residual term; Step S2, extracting the characteristics of the ship's rolling motion characteristics from the decomposed modal components IMF and residual terms as input to the radial basis function neural network RBFNN model, and taking the actual rolling angle as output to train the radial basis function neural network RBFNN model; Step S3, using particle swarm optimization PSO algorithm to optimize radial basis function neural network RBFNN model parameters to obtain EMD-PSO-RBFNN model; Step S4: Evaluate the prediction performance of the EMD-PSO-RBFNN model.

2. A real-time prediction system for ship rolling motion based on EMD-PSO-RBFNN according to claim 1, characterized in that: In step S1, let R be a specific time series, and the calculation steps of the empirical mode decomposition EMD are as follows: Step S121, identify all local extreme points in the signal, and use the local maximum and local minimum to generate upper envelopes U respectively by interpolation. R and the lower envelope L R ; Step S122: Calculate the local mean function m(t) and the new signal d(t), as shown below: d(t)=x(t)-m(t)(2); Among them, x(t) is the original signal; Step S123, before d(t) is converted into modal component IMF, the process will be performed according to the following criteria: Where T represents the signal length, j represents the number of iterative calculations; the ζ value is usually set between 0.2 and 0.3; Step S124: Continue to iterate steps S121-S123 until all intrinsic mode functions and residual signals are obtained, as shown below: R=IMF1+IMF2+…+IMF j +…+IMF n +r (4); Among them, EMD decomposes the R series into a set of modal components IMF and a residual series r.

3. The real-time prediction system for ship rolling motion based on EMD-PSO-RBFNN according to claim 1 is characterized in that: In step S2, the characteristics of the ship's rolling motion characteristics are extracted from the decomposed modal components IMF and residual terms as the input of the radial basis function neural network RBFNN model, and the actual roll angle is used as the output to train the radial basis function neural network RBFNN model. The specific process is as follows: Step S21: Use a Gaussian function as a radial basis function, as shown below: Where c represents the center of the neuron, σ represents the expansion parameter of the network, and x is the input data point; Step S22: During the training process, the weight W of the neural network is updated using the Levenberg-Marquard back propagation algorithm, as shown below: ΔW=-(J T J+γI) -1 J T (6) and i =And i -and i (7); Where ΔW is the change in weight; J is the Jacobian matrix; γ is the adjustment parameter; I is the identity matrix; y is the true value; e is the prediction error; E(W,B) represents the error function; B is the bias; O i is the actual output; o i is the predicted output of the radial basis function neural network RBFNN model; Step S23: Use the weights obtained during the training process and the design matrix of the test data to predict the output of the test set, as shown below: Among them, W is the weight obtained during the training process; φ test is the design matrix for the test data; is the predicted output for the test set.

4. The real-time prediction system for ship rolling motion based on EMD-PSO-RBFNN according to claim 1 is characterized in that: In step S3, the particle swarm optimization (PSO) algorithm is used to optimize the radial basis function neural network (RBFNN) model parameters. Assuming that the position parameter of the nth particle is represented by a d-dimensional vector, the particle velocity and position are updated as follows: l n,k (t+1)=l n,k (t)+v n,k (t+1) (12); Where ω is the inertia weight; v n,k (t) and l n,k (t) is the velocity and position of the nth particle in the kth dimension at the tth iteration; This is the optimal historical position of the individual particle at this time; is the global optimal position of the entire particle swarm at this time; c1 is the self-learning factor; c2 is the social learning factor; r1, r2 are random values ​​between [0,1].

5. The real-time prediction system for ship rolling motion based on EMD-PSO-RBFNN according to claim 1 is characterized in that: In step S4, the mean absolute error MAE, mean square error MSE, root mean square error RMSE, normalized root mean square error NRMSE, mean absolute percentage error MAPE and determination coefficient R are used. 2 , to evaluate the forecasting performance of the EMD-PSO-RBFNN model.

6. A ship rolling motion real-time prediction system based on EMD-PSO-RBFNN according to claim 5, characterized in that: The calculation expressions of each evaluation index are as follows: Among them, y i is the actual value at time i; is the predicted value at time i; n is the number of predicted data; is the mean of the data.

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