Date Published: June 13, 2019
Publisher: Public Library of Science
Author(s): Xiaogang Huang, Dongge Lei, Lulu Cai, Tianhao Tang, Zhibin Wang, Lixiang Li.
In this paper, a new prediction approach is proposed for ocean vessel heave compensation based on echo state network (ESN). To improve the prediction accuracy and enhance the robustness against noise and outliers, a generalized similarity measure called correntropy is introduced into ESN training, which is referred as corr-ESN. An iterative method based on half-quadratic minimization is derived to train corr-ESN. The proposed corr-ESN is used for the heave motion prediction. The experimental results verify its effectiveness.
When operating on sea, a vessel is inevitably affected by waves, wind and ocean currents, thereby moving away from the desired position horizontally and vertically . The vertical motion of the vessel, also called heave motion, which is undesirable for offshore installations, offshore drilling and other tasks on sea because it reduces the work efficiency, causes damage to safety manufacturing system, facility and operation. To reduce this passive effects, heave compensation technologies were proposed to remove vessel’s heave motion from the load, which results in the decoupling of load motion from ship motion . Now, heave compensation is popular in underwater conveying systems for oil and gas fields, payload transfer between vessels. Heave compensation technology can be classified into two classes, namely passive heave compensation (PHC) and active heave compensation (AHC). Compared to PHC, AHC can provide higher decoupling efficiency. AHC system is a close-loop system, in which the ship’s heave motion is measured and fed back to a controller. Then, the controller drives an actuator to move in an opposite direction of the heave motion. Some research result show that a controller with heave motion prediction is helpful in creating an AHC system, which results in 100% effectiveness in heave motion decoupling . Furthermore, heave motion prediction can be used to partially correct a large phase lag within the controller structure . Hence, heave motion prediction is an important issue to AHC.
ESN is a recurrent neural network, whose structure is shown in Fig 1. An ESN consists of an input layer, a hidden layer and an output layer. The hidden layer is also called dynamic reservoir. The neural units in reservoir are sparsely connected each other. Different from other RNNs, the input weights Win, the weights between reservoir units Wx and the feedback weight Wfb are predetermined randomly without being trained, only the output weights Wout should be trained. This characteristic greatly reduces the computation complexity. The training of ESN is divided into two stages. Firstly, the training data is fed into ESN and the state of reservoir X(t) is calculated and updated as
where X(t) ∈ RN is the state of reservoir at time instant t, u(t) ∈ RL is the external input at time instant t, Wx ∈ RN×N is the reservoir weight matrix and Win ∈ RN×L is the input weight matrix. f(⋅) is the activation function, usually the tanh function is adopted. For leaky integrator ESN, the state is updated as
where α is called leaking rate. The output of ESN is computed as
where y(t) ∈ R1×M is the output of ESN at time instant t, z(t) = [XT(t) uT(t + 1)] ∈ R1×(N+L) is the concatenation of reservoir states and input vectors and Wout ∈ R(N+L)×M the output weight matrix, g(⋅) is a nonlinear mapping function. In practice, the nonlinear function g(⋅) is selected as linear function. Therefore, the output can be written as
one can get
then, the optimal output weight matrix is obtained as
In this section, the simulation studies are conducted to verify the effectiveness of the proposed method. All the algorithms are implemented in Matlab 2016b programming language and run in a ThinkPad T440 notebook computer with Intel Core™ i5-4200U processor, 8G random access memory (RAM). The heave motion data is taken from . The data is measured from a simulation platform of wave movement with an accelerometer. The sampling frequency is 100Hz. The measured data is normalized into [0, 1], which is shown in Fig 2 (The data can be referred to S1 Fig).
A correntropy based ESN is proposed to predict heave motion for the purpose of heave compensation. The proposed approach adopts correntropy instead of MSE as the error criterion for ESN training, which is called corr-ESN. An iterative training algorithm is derived using half quadratic optimization theory. Since the correntropy is insensitive to noise and outliers, the corr-ESN is more accurate than ESN for heave motion prediction. Simulation results validate the effectiveness of the proposed method.