Stochastic Response and Stability Analysis of Two-Point Mooring System

The stochastic response and stability of a two-point mooring system are investigated for random sea state represented by the P-M sea spectrum. The two point mooring system is modeled as a SDOF system having only stiffness nonlinearity; drag nonlinearity is represented by an equivalent linear damping. Since no parametric excitation exists and only the linear damping is assumed to be present in the system, only a local stability analysis is sufficient for the system. This is performed using a perturbation technique and the Infante’s method. The analysis requires the mean square response of the system, which may be obtained in various ways. In the present study, the method using van-der-Pol transformation and F-P-K equation is used to obtain the probability density function of the response under the random wave forces. From the moment of the probability density function, the mean square response is obtained. Stability of the system is represented by an inequality condition expressed as a function of some important parameters. A two point mooring system is analysed as an illustrative example for a water depth of 141.5 m and a sea state represented by PM spectrum with 16 m significant height. It is shown that for certain combinations of parameter values, stability of two point mooring system may not be achieved.

First Ocean Going Ships With Springing and Whipping Included in the Ship Design

It is well known that ships vibrate due to waves. The wave induced vibrations of the hull girder are referred to as springing (resonance) and whipping (transient vibration from impacts). These vibrations contribute to the fatigue damage of fatigue sensitive details. An Ore Carrier of 400 000 dwt is currently being built by DSME, and at time of delivery, it will be the world’s largest bulk (ore) carrier. The scantlings of large ships must be carefully designed with respect to global loading, and when extending the design beyond experience, it is also wise to consider all aspects that may affect operation and the life time costs. The vessel will also enter a long term contract and is therefore to be evaluated for 30 year Brazil-China operation. In order to minimize the risk of fatigue damage, the vessel is designed according to DNV’s class notation CSA-2 requiring direct calculations of the loading and strength. Further it has been requested to include the effect of springing and whipping in the design. Reliable numerical tools for assessing the additional fatigue effect of vibrations are non-existing. DNV has, however, developed an empirical guidance on how the additional effect may be taken into account based on previous development projects related to the effect of vibrations on large ore carriers Due to the size and route of operation of the new design, it has, however, been required by the owner to carry out model tests in both ballast and cargo condition in order to quantify the contribution from vibration. The results from this project have been used for verification and further calibration of DNV’s existing empirical guidance. A test program has been designed for the purpose of evaluating the consequence in head seas for the Brazil to China trade. Full scale measurements from previous development projects of ore carriers and model tests have been utilized to convert the current model tests results into estimated full scale results for the 400 000 dwt vessels. It is further important to carefully consider how the vibrations are to be included in the design verification, and to develop a procedure for taking into account the vibrations which results in reasonable scantlings based on in-service experience with similar designs and trades. This procedure has been developed, and a structural verification has been carried out for the design. The final outcome of the model test was in line with previous experience and in overall agreement with DNV’s empirical guidance, showing a significant contribution from vibrations to the fatigue damage. The springing/whipping vibrations more than doubled the fatigue damage compared to fatigue evaluation of the isolated wave induced loading. The cargo condition vibrated relatively more than experienced on smaller vessels. Various sources to establish the wave conditions for the Brazil to China ore trade were used, and the different sources resulted in significant differences in the predicted fatigue life of the design.

Statistical Analysis on the Extreme Events of Big Waves Under Wave Climate Change Around Taiwan Waters

This study aimed to analyze the statistical characteristics of wave heights, wave energy and wave steepness, in order to investigate the wave climate changes around Taiwan Waters, especially for extreme events of big waves. The operational observation of Taiwan sea waves was initiated by the Central Weather Bureau in 1998; however, due to insufficient data length and low data space coverage, the data are unable to serve as references for long-term wave climate change research. Hence, this study adopted the SWAN (Simulation of Wave in Nearshore) Numerical Wave Hindcasting Method, which is a common method used in many studies, to hindcast the history of a wave field. The re-analysis on wind field data of the last 60 years (1948∼2008), published by the National Centers for Environmental Prediction (NCEP), was employed to make the wind field grid consistent with the hindcast wave field grid. Moreover, the Typhoon Wind Field Grid Down Scaling technique proposed by Winter & Chiou (2007) was applied to interpolate a U10 analysis field that better fits an actual typhoon wind field. The hindcast wave data were compared and validated with directional spectra, which were observed by the meteorological/oceanographic data buoys set up by the Central Weather Bureau and Water Resources Agency since 1997. Longdong, Hualien and Hsinchu Stations were chosen to represent the wave characteristics of sea areas around the island of Taiwan. According to observation data, model parameters were adjusted so that the hindcast results could be closer to observed data in Taiwan sea areas.

Spurious Waves During Generation of Multi-Chromatic Waves in the Wave Tank in Shallow Water

Accurate generation of the primary waves and the reproduction of the group-induced second-order low and high frequency waves have been considered essential for physical i.e. model test in the laboratory. In the laboratory when multi-chromatic primary waves are generated the required bounded waves will be generated naturally at the difference frequencies. In addition to that several unwanted free waves are also generated. The free waves, having the same frequencies of the bounded waves are reproduced due to mismatch of the boundary conditions at the wave paddle. The other two types of free waves are due to the wave paddle displacement and the local disturbances. We carried out physical experiments to identify the second order spurious waves in shallow water in the Offshore Engineering Basin (OEB) at the Institute for Ocean Technology (IOT) of National Research Council (NRC) Canada. In the basin water depths in the range of 0.4m to 0.6m are used for the experiments. The peak wave periods also have varied from 1.133s to 2.145s. In the experiments multi-chromatic waves are used. The drive signals of the wave-makers are generated using first-order and second-order wave generation techniques. Total 14 wave probes are used to capture the data in the wave tank. A NRC-IOT code is used to isolate the primary waves, the bounded waves and the unwanted free waves from the measured data at each wave probe. The measured data are analyzed in this paper to illustrate the differences in the waves generated by two different generation techniques.

Prediction of Water Wave Breaking Height and Depth Using ANFIS

Wave height as well as water depth at the breaking point are two basic parameters which are necessary for studying coastal processes. In this paper, the application of Fuzzy Inference System (FIS) and Adaptive Neuro-Fuzzy Inference System (ANFIS) and semi-empirical models are investigated. The data sets used in this study are published laboratory data obtained from regular wave breaking on plane, impermeable slopes collected from 22 sources. Results indicate that the developed ANFIS model provides more accurate and reliable estimation of breaking wave height, compared to semi-empirical equations. However, some of semi-empirical equations provide better predictions of water depth at the breaking point compared to the ANFIS model.

An Experimental Investigation Assessing the Validity of Quasi-Static Calculations for an Oscillating Hydrofoil

Inspired by animals, flapping wing propulsion has been of interest since the early 1900s. Flapping hydrofoil propulsion has been attempted by designers of human powered watercraft because of the novelty and the apparent high theoretical efficiency, but with limited success. The earliest human powered hydrofoil, the Wasserlaufer, was invented by Julius Schuck in 1953. The first really successful human powered hydrofoil, the Trampofoil, was invented by Alexander Sahlin in 1998. While these craft function adequately the design data for flapping hydrofoils is inadequate or not available. This paper describes an experimental program and initial results for the required data. To design a vehicle with a lifting and thrusting oscillating hydrofoil the force that the hydrofoil will exert on the vehicle through its entire oscillating cycle must ideally be known. The force profiles could be estimated via quasi-static calculations based on steady flow lift and drag coefficients, but these often do not cover the full 360 degree range that can be required and there is doubt that the steady flow coefficients properly represent the dynamic situation of an oscillating hydrofoil. Hence a valuable process would be one that could determine dynamic drag and lift coefficient loops as function of the Strouhal number, heaving and pitching profiles. To work toward the collection of this information, experimental data is being recorded in a towing tank with an oscillating NACA4415 hydrofoil over a range of Strouhal numbers and types of oscillating profiles. While there are still some limitations to the experimental equipment preliminary experimental results show the limitations of using quasi-static calculations and go some way to providing the design data for the hydrofoil section tested. We conclude that quasi-static calculations based on the gliding coefficient curve for for an oscillating hydrofoil are only valid for very small Strouhal numbers (St≪0.05). We have shown that as the Strouhal number increases, the error in such calculations increases very rapidly. We also note that the lift coefficient of the hydrofoil has a strong dependence on the angle of attack and is not affected by the gliding stall.

A Low-Cost, High Rate Motion Software Sensor System Based on Novel Data Fusion for Unmanned Surface Vehicle Navigation and Oceanographic Instrumentation Motion Correction

One of the major challenges in the navigation of underwater vehicles is obtaining precise and reliable positioning updates. Dead-Reckoning aided with Doppler velocity measurement has been, and remains, the most common method for underwater navigation for small vehicles. DR uses a set of navigation instruments to estimate the position of the vehicle by integrating the body-fixed velocity, accelerations, and angular rates with respect to time. Instrument error and bias lead to position error that increases exponentially with time. Thus, current DR systems require frequent position recalibrations. The Global Positioning System (GPS) provides measurements of geodetic coordinates for air and surface vehicles and it is often used to correct positioning error. However, underwater vehicles cannot use GPS for inflight navigation because GPS signals only penetrate a few centimeters past the air-sea interface. Thus, underwater vehicle navigation systems are limited to periodic position update from the GPS when they surface and extend an antenna through the air-sea interface. Standard GPS receivers are unable to provide the rate or precision required when used on a small vessel such as an Unmanned Surface Vehicle (USV). To overcome this, a low cost high rate motion measurement system for an USV with underwater and oceanographic purposes is proposed. The proposed onboard system for the USV consists of an Inertial Measurement Unit (IMU) with accelerometers and rate gyros, a GPS receiver, a flux-gate compass, a roll and tilt sensor and an ADCP. Interfacing all the sensors proved rather challenging because of their different characteristics. Some of the instruments have digital output (Compass/ADCP/GPS) while others have an analog output (IMU/tilt sensor). The proposed data fusion technique integrates the IMU, GPS receiver, flux-gate compass as well as tilt sensor and develops an embeddable software package, using real time data fusion methods, for a USV to aid in navigation and control as well as controlling an onboard Acoustic Doppler Current Profiler (ADCP). While ADCPs non-intrusively measure water flow, they suffer from the inability to distinguish between motions in the water column and self-motion. Thus, the vessel motion contamination needs to be removed to analyze the data and the system developed in this text provides the motion measurements and processing to accomplish this task.

Tsunami Attack Evaluation and Countermeasures for Moored Small Ships in a Port

There is increasing concern over the possibility of the occurrence of huge Toukai, Tonankai, and Nankai earthquakes in the Nankai Trough, located in the Pacific Ocean off Japan. It is estimated that there is a 50% probability of a tsunami being generated by an earthquake in this area over the next 30 years. A tsunami attack on the coast of Japan would not only increase the sea level, but would also create strong horizontal flows in bays and ports. In particular, along the coastal area of Osaka Bay, Japan, there are numerous small ports where pleasure ships and/or fishery boats are moored. Any small ships moored in these ports would be subject to violent motion by strong lateral flows, even if they are moored to each other. As a consequence, the mooring lines would be cut, ships would move uncontrollably, and causing damage to facilities. Thus, it is very important from the viewpoint of marine-disaster prevention to gain a better understanding of the motion of small vessels originating in tsunami flows and to develop countermeasures in the face of a tsunami attack. In this paper, basic analyses of the ship motions resulting from a tsunami attack are carried out, and possible countermeasures are investigated. First, we describe mathematical models approximating the flow of tsunami and the abrupt maneuvers of relatively small vessels while being moored. Next, numerical simulations of the lateral motion of moored ships resulting from a tsunami attack on a fishery port located in the Osaka Bay are carried out. Additionally, the possibility of relatively high tension to be generated along the mooring lines is evaluated. Finally, the results of computer simulations demonstrate that such hazardous phenomena can be addressed with appropriate countermeasures.

Statistical Analysis of a Set of Basin Waves

In a recent paper the effect of variations in calibrated wave parameters on wave crest and height distributions was analyzed (OMAE2010-20304, [1]). Theoretical distribution functions were compared to wave measurements with a variation in water depth, wave seed (group spectrum) and location of measurement for the same initial power spectrum. The wave crest distribution of the shallow water waves exceeded both second-order and Rayleigh distribution. Whereas, in intermediate water depth the measured crests followed the second order distribution. The distributions of the measured waves showed that different wave seeds result in the same wave height and crest distributions. Measured wave heights were lower closer to the wave maker. In this paper the results of the continued statistical analysis of basin waves are presented with focus on wave steepness and their influence on wave height and wave crest distributions. Furthermore, the sampling variability of the presented cases is assessed.

A Ship Flotation Control System Based on Pump-Driven Tank

Extensive development in ship motion control strategies and systems in recent decades has called for higher requirements in control system accuracy and reliability. In this paper, a ship flotation control system based on pump-driven active tank is established. A special case is discussed, where the ship is heeling under an asymmetric loading either by structural damage or asymmetric consumption of ammunition. The purpose of the control system is to keep the ship in upright floating position in waves by transferring liquid between the tanks. Kalman filter is designed to eliminate the wave disturbance, in order to identify the heeling angle caused by asymmetric loading change. The effect of wave disturbance at different wave encounter angles, wave heights, as well as ship speeds is analyzed. Tuning of filter parameters such as initial state variables, initial error covariance and noise covariance is performed to achieve better filtering performance for different parameters of waves and ship motion. To verify the control model, simulation is conducted for a 3340t ship and the simulation results are compared with the theoretical calculations. The research results show the applicability and efficiency of Kalman filter. The concept of the control system presented in the paper is helpful to improve ship stability and safety when ship upright floating condition is disturbed.