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A ship motion forecasting approach based on empirical mode decomposition method hybrid deep learning network and quantum butterfly optimization algorithm

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Abstract

Ship motion (SHM) forecasting value is an important parameter for ship navigation and operation. However, due to the coupling effect of wind, wave, and current, its time series has strong nonlinear characteristics, so it is a great challenge to obtain accurate forecasting results. Therefore, considering the strong nonlinear of SHM time series, firstly, this paper decomposes the original time series into multiple intrinsic mode functions (IMF) using empirical mode decomposition (EMD) technology and then establishes a hybrid deep learning network for each IMF based on convolutional neural network (CNN) and gated recurrent unit (GRU) according to the characteristics of SHM time series. On this basis, the EMD-CNN-GRU (ECG) hybrid forecasting model of SHM is constructed by integrating a component forecasting model. Secondly, considering the difficulty of hyper-parameters selection of ECG model, this paper improves the butterfly optimization algorithm (BOA) based on quantum theory, designs the quantum coding rules of butterfly spatial position, establishes the optimization process of butterfly algorithm based on quantum coding, and then proposes the quantum butterfly optimization algorithm (QBOA). Finally, a hybrid forecasting approach integrating ECG and QBOA is proposed, namely ECG & QBOA. To evaluate the feasibility and performance of the proposed approach. A prediction experiment was carried out with the SHM data of a real ship. The results indicate that, compared with the other comparison models selected in this paper, ECG-based models have significant higher forecasting accuracy (with MAPE values of 10.86% and 12.69% in two experiments, respectively, and with significant accuracy improvement of at least 10% than other compared models), and the QBOA has obtained more appropriate hyper-parameters combination of ECG model.

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Data Availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

Ship motion (SHM):

Abbreviation of ship six degree of freedom motion

Empirical mode decomposition (EMD):

A signal decomposition technique

Intrinsic mode function (IMF):

The name of the sequence after EMD decomposition

Convolutional neural network (CNN):

A deep learning network

Gate recurrent unit (GRU):

A deep learning network

Long short-term memory (LSTM):

A deep learning network

Depth neural network (DNN):

A deep learning network

Butterfly optimization algorithm (BOA):

A parameter optimization algorithm

Quantum butterfly optimization algorithm (QBOA):

An improved BOA

EMD-CNN-GRU (ECG):

Abbreviation of EMD-CNN-GRU hybrid model

Artificial neural network (ANN):

Traditional neural network

Autoregressive moving average (ARMA):

Time series prediction model

Autoregressive integrated moving average (ARIMA):

Time series prediction model

Support vector machine (SVM):

Time series forecasting method

Mean absolute percentage error (MAPE):

Prediction and evaluation index

Root mean square error (RMSE):

Prediction and evaluation index

X(t):

Original ship motion time series

X max(t):

An upper envelope sequence composed of the maximum of X(t)

X min(t):

A lower envelope sequence composed of the minimum of X(t)

m(t):

The sequence of the average values of Xmax(t) and Xmin(t)

IMF(t):

The sequence of Intrinsic Mode Function

r n(t):

The residual sequence

x k :

xk Represents a feature map of the input tensor of the layer k, which is a one-dimensional tensor

w k :

Filters weight of layer k

b k :

Bias terms

C :

The size of filters

D :

The depth of the feature map

m :

The size of the pooling

s :

The step of pooling

\(\phi\) :

Activation function

x t :

The input sequence of GRU in the tth time step

h t :

Hidden layer output in the tth time step

\(\tilde{h}_{t}\) :

Candidate state in the tth time step

z t :

Update gate

r t :

Reset gate

W r, W z, W t and W :

Weight parameters

f :

f Stands for flavor intensity

c :

c Is sensory modal

a :

a Is the power component

I :

I Is the stimulus intensity related to the fitness value

g θ * :

g* Represents the optimal butterfly position found in the current iteration

r :

r Is a random number

P :

P Is switch probability

P r :

PR is a random number

μ and ν :

μ And v represent the probability amplitude of the basic state

x j :

xj Represents the position of the ith butterfly

x ij max :

xijMax represents the upper search limit of xij

x ij min :

xijMin represents the lower search limit of xij

θ :

θ Represents phase

∆θ :

∆θ Represents phase increment

d i :

The ith number in the time series

D i :

Normalization result of the ith number

d max :

Maximum in time series

D min :

The minimum value in time series

\(\hat{d}\) :

The predicted value of the model

f fitness :

Fitness function value of the algorithm

L t :

Model loss on training data set

L v :

Model loss on validation data set

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Acknowledgements

The work is supported by the following project grants, National Key Research and Development Program of China (2019YFB1504403); High-tech Ship Technology Project (MC-202030-H04); Heilongjiang Excellent Youth Fund Project (YQ2021E015); National Natural Science Foundation of China (No.51509056); and Ministry of Science and Technology, Taiwan (MOST 110-2410-H-161-001).

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Authors and Affiliations

  1. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, Heilongjiang, 150001, China

    Ming-Wei Li, Dong-Yang Xu & **g Geng

  2. Department of Information Management, Asia Eastern University of Science and Technology, 58, Sec. 2, Sichuan Rd., Panchiao District, New Taipei, 22064, Taiwan

    Wei-Chiang Hong

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Li, MW., Xu, DY., Geng, J. et al. A ship motion forecasting approach based on empirical mode decomposition method hybrid deep learning network and quantum butterfly optimization algorithm. Nonlinear Dyn 107, 2447–2467 (2022). https://doi.org/10.1007/s11071-021-07139-y

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