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The paper analyzes the nonlinear damping torque and nonlinear restoring moment and establishes the nonlinear motion equation of ship rolling under random sea. The Runge-Kutta method is used in the time domain to solve the equation, and to simulate the time history of random wave excitation ship rolling and free decay process. This paper used the ship attitude inertial measurement system and its algorithm technology to construct the ship rolling angle from the acceleration measuring signals and to simulate the angle acceleration measurement signal. To study on test conditions of these parameters and the method to improve the accuracy of parameters, the effect of acceleration measurement noise on angle reconstruction accuracy is studied. Under SNR 20, reconstructed angle RMSE is 0.0019 rad. Studies show that the inertial measurement system and algorithm can effectively reconstruct ship rolling angle from the acceleration measurement signal, and the algorithm has the ability to suppress measurement noise.

The important research topic of shipping industry is stability and seakeeping problem, because of interference wave will lead to roll, pitch, yaw, heave, surge and sway motion. To get the angular displacement parameters is the basis of ship roll reduction control. Nayfeh, A.H. and Khdeir, A.A. [

Based on engineering demand, the ship displacement (linear displacement and angular displacement) measurement is widely concerned. The ninth reference is studied on ship motion inertial measurement and reconstruction technology for the displacement, providing essential ship maneuvering, dynamic positioning, and active anti rolling displacement motion parameters. In this paper, ship rolling model is established, and the simulation of ship rolling motion on the random sea, the building of ships attitude strapdown inertial measurement system and its algorithm, the simulation of ship rolling angle acceleration measurement signal in the reconstruction of rolling angular displacement, the method also can be used in acceleration of ship heaving and displacement measuring signal reconstruction line.

Model of random sea waves can be divided into 2-D irregular wave model and 3-D irregular short crested wave model of random sea waves. This paper uses 2-D irregular wave, simulation of ship in random waves on the roll motion. Firstly the obliquity of wave model is established, and simulation of wave obliquity. In this paper, the comparison between 2-D irregular wave model and the 3-D irregular wave model is not the key point.

The ship is sailing in the waves, the waves of disturbance torque is mainly related to the slope of wave surface. The slope of wave surface can be regarded as zero mean stationary random process; the waves in the slope of wave surface between the fixed points can define by the slope of wave surface spectrum

where w is the circular frequency;

where g is the acceleration of gravity.

By the type of wave obliquity model 2 to build random waves must determine the wave spectrum. The ship wave spectrums have a relationship with the actual environmental conditions. At present, the most application wave spectrum density are Pierson-Moscowitz spectral spectrum (PM) [

where

When average water depth is 20 m in Bohai sea area, the long crested random ocean wave angle by simulation in different sea conditions,

Due to the unpredicted rough wave, ship rolling, pitching, yawing angle displacement and swaying, surging, heaving linear displacement motion will occur in the navigation. The rolling is most likely to occur and the amplitude is large, when the ship rolling damping is small, then the performance of ship rolling is an important index to judge the performance of a ship. Affected by the structural characteristics and wave disturbance, the ship rolling model is nonlinear. When the rolling angle is small, usually the ship’s rolling model is linearization. The purpose of this paper is through the measurement of acceleration (measurable) to reconstruct the displacement, ignoring the ship pitching, yawing motion and sway, surge, heave motion on the coupling effect of ship rolling, establishing the nonlinear ship rolling model. In the two-dimensional long crested random waves, the ship rolling motion equation is every moment in the ship rolling direction balanced results; motion equation of the ship is

where

moment,

where D is vessel displacement, B is vessel width,

When the rolling angle is large rolling damping moment is nonlinear, at present there are mainly two forms. Froude puts forward the linear damping plus square damping and Hadarra [

Changes of restoring moment are more complex, because there are the ship rolling, pitching, heaving, wave front rise higher and the impact of the change over time, which can be expressed as

where GZ is the recovery of arm function of ship,

where GM is the initial stability of the vessel, gm(t) is pitching, heaving, wavefront increased stability due to the high initial term changes,

where

where h is transverse stability;

The above formula with both sides divided by

where

Taking a fishing boat used in the literature 10 for example [

Take the harmonic frequency step size

Length overall L/m | Moulded breadth B/m | Moulded depth H/m | Draught T/m | Displacement D/t |
---|---|---|---|---|

30.70 | 6.90 | 4.96 | 2.67 | 195 |

Total mass moment of inertia | Initial stability GM/m | Initial natural frequency of the roll | Damping coefficient | Restoring moment coefficient | |||
---|---|---|---|---|---|---|---|

1078 | 0.962 | 1.32 | 0.0208 | 0.0165 | 2.0327 | -0.7430 | 0.0643 |

6.3˚, the standard deviation of the roll angle will reach 2.2059˚, when the significant wave height is 4 m, the maximum roll angle of up to 22.4˚, the standard deviation of the roll angle will reach 8.1990˚, because the simulation of wave frequency is consistent with the ship rolling natural frequency.

And then we discuss the factors influence the ship rolling, including external excitation and sensitivity analysis of empirical parameters.

The results of the significant wave height are shown in

^{2}, the ship rolling variance is maximal, and then it decreases with the increase of the total mass moment of inertia, because the total mass moment of inertia influences the natural frequency of ship rolling.

_{1}. We notice that b_{1} will have a significant impact on the ship rolling. When b_{1} is 0.017, the ship rolling standard deviation is maximal, and then it is essentially unchanged.

The results of b_{3} are shown in _{3}. In the center of 0.0165, the value of 30% range is approximate linear variation, so the estimated value of this parameter should be very careful, then I studied the relationship between the changes b_{3} and the mean wave period with the ship rolling. From _{3} has the similar trend.

_{1} on the ship rolling. When k_{1} is 1.65, the ship rolling standard deviation is maximal, and then it decreases with the increase of k_{1}. k_{1} represents the water displacement of ships and ship the metacentric height, the wavefront of the elevated lead to metacentric height changes, then influence the ship rolling.

The results of k_{3} are shown in _{3}. And when k_{3} reaches −0.75, the ship rolling standard deviation is maximal. Then, it decreases with the increase of k_{3}.

_{5} on the ship rolling. Firstly the ship rolling gradually increases with the increase of k_{5}. When k_{5} reaches 0.07, the ship rolling standard deviation is maximal, and then it decreases with the increase of k_{5}.

In summary, from the simulation results, the moment of inertia have great influence on ship rolling, in order to get the precise value of the moment of inertia, we must modified calculation moment of inertia based on the actual shipment, In addition to b1, other parameters have significant effects on rolling, therefore, to study on test conditions of these parameters and the method to improve the accuracy of parameters.

In order to get the ship attitude angle and acceleration parameters, sensor placement scheme as shown in

The second-order integration filter is the key to design acceleration reconstruction displacement method [

The designing method of second order integral filter is included digital filtering method and frequency domain integral method, the ninth literature studied that the design methods of FIR filter, then filter parameters are obtained.

In the random wave excitation for ship rolling motion, when removed wave interference moment, the ship rolling into the free state. Random wave feature wave height is 1m; the mean wave period is the 4.76 s MPM spectrum, course angle is

The rolling angle equation of the second derivative is to get ship’s roll angle acceleration information. Ship rolling angular acceleration frequency is 0.23 hz, FIR filter target frequency is

In the wave excitation of 0 - 300 s and free rolling 300 s - 600 s, there were no significant difference between the FIR reconstruction of angular displacement and dynamic simulation of angular displacement in amplitude and phase, as shown in ^{−2}. In the excitation wave rolling, reconstruction of angular displacement of RMSE in with measurement noise for 0.0019 rad, in the absence of measurement noise for 0.0012 rad. Research shows that design of FIR filter can effectively reconstruct displacement from the acceleration signal, and has the strong ability of noise suppression [

Roll form | Angular acceleration (rad∙s^{−2}) | FIR filter reconstruction angular displacement (rad) | ||
---|---|---|---|---|

No measurement noise | Contain the measurement noise | No measurement noise | Contain the measurement noise | |

Random waves excitation ship rolling | 0 | 0.0134 | 0.0012 | 0.0019 |

Free rolling | 0 | 0.0133 | 0.0004 | 0.0015 |

The ship displacement measurement is the key link to ship attitude control, dynamic positioning, offshore construction operation, etc. The paper analyzes nonlinear damping torque and nonlinear restoring moment and establishes the nonlinear motion equation of ship rolling under random sea. The Runge-Kutta method is used in the time domain to solve the equation, and to simulate the time history of random wave excitation ship rolling and free decay process. To simulate the angle acceleration measurement signal, the paper uses the ship attitude inertial measurement system and its algorithm technology to construct the ship rolling angle from the acceleration measuring signals. From the simulation results, the moment of inertia has great influence on ship rolling. In order to get the precise value of the moment of inertia, we must modify calculation moment of inertia based on the actual shipment. Studies show that the inertial measurement system and algorithm can effectively reconstruct ship rolling angle from the acceleration measurement signal, and the algorithm has the ability to suppress measurement noise.

Jianhui Lu,Chunlei Zhang,Shaonan Chen,Yunxia Wu, (2015) Ship Nonlinear Rolling and Roll Angle Reconstruction Based on FIR. Open Access Library Journal,02,1-10. doi: 10.4236/oalib.1102171