Sway Motion Research Articles

Iteratively weighted dynamic modeling of four degrees of freedom motion for marine surface vehicles for k-step ahead prediction

Estimating surge, sway, roll, and yaw motions in marine vehicles are essential for many different reasons, such as maneuvering, dynamic positioning, control, and safety. In this article, an iterative-weighted model is presented for predicting marine vehicle's motions. Surge, sway, roll, and yaw speeds are used as input/output pairs, rudder and throttle references are also used as inputs. By using these input-output relations as training data, an iteratively weighted modeling algorithm is developed. The iteratively weighted model is then used for k-step ahead prediction for different maneuvering scenarios in calm waters. Estimation results are validated with varying scenarios of maneuvering to show the generalization of iteratively progressed model results. The presented work aims to bring a different perspective from a practical use viewpoint of a dynamic model of the platform without knowing the structure of the model, where only needed information are the excitation inputs and required outputs. Therefore, the presented approach has the flexibility to define input and output variables so that it can be configured for the desired application and has the potential to be extended on purpose, increasing the precision and reliability of surface/underwater vehicle's control as well as unmanned vehicles.

Wind tunnel study on the wake characteristics of a wind turbine model subjected to surge and sway motions

An experimental study was performed in a uniform incoming flow wind tunnel to investigate the effect of surge and sway motions on the wake characteristics of a wind turbine model. The platform surge and sway motions can be simulated at prescribed amplitudes and frequencies through a translation stage mounted on the base of the turbine model. The flow fields of near, intermediate, and far wakes of the turbine model were characterized by a particle image velocimetry system. Results show that the mean velocity profiles during the whole surging and swaying process of the downwind wakes were almost unchanged with that of a base-fixed turbine; however, the maximum mean velocity differences appeared near the blade tips for both motions compared with the base-fixed cases. Little difference was found between the mean velocity profiles of the turbine model while moving in different directions, for both the surge and sway motions. Later, the characteristics of instantaneous velocity profiles were investigated, and the lateral offset of the instantaneous velocity profiles for the swaying turbine at the two ends of the sway motion was observed. The offset distance was very close to sway amplitudes within the near wake, and it gradually decreased until it disappeared as the downstream distance increases. This work may provide an instrumental guide in the further research on the wake of floating offshore wind turbines.

Numerical Researches of Rectangular Barge in Variable Bathymetry Based on Boussinesq‐Step Method

Wave responses of the rectangular barge in variable bathymetry are investigated by combining the Boussinesq‐type equations and the step method. The highly accurate Boussinesq‐type equations in terms of velocity potential are adopted for simulating the evolution of waves along the inclined beach. Hydrodynamic coefficients of a rectangular barge floating on the inclined bottom are calculated by the step method in the frequency domain. Based on the impulse response function method, the motions of the barge can be predicted in the time domain. The Haskind relation is used to reform the wave exciting forces, and the mean offset in the sway motion is also given based on the mean drift force. The wave responses of the barge at different locations along the inclined beach are measured in the experiments. Compared with experimental results, the solutions of the Boussinesq‐step method present an overall good agreement.

선박의 이/접안 데이터 분석을 통한 자동 이/접안 시 횡방향속도 참조모형 개발에 관한 연구

Crabbing motion is a pure sway motion with only sway velocity. The ship’s crabbing motion is essential for an ideal berthing/unberthing process. The unberthing situation proceeds in sequential order such as crabbing motion section, pivoting section, and outer port section. For the berthing situation, the sequence has a reverse order: the inner port section, pivoting section, and crabbing motion section. In this paper, the berthing/unberthing data of the reference ship, Pukyong National University research ship“NARA”, was analyzed to develop a sway velocity reference model. Several constraints were defined to derive the crabbing motion section during berthing/unberthing. The sway velocity reference model for the auto-berthing/unberthing was developed using the estimated sway velocity. A reproduction simulation of the ship was performed to compare the designed reference model and the reference ship data.

SHIP MANOEUVRING PREDICTION BASED ON NUMERICAL TOWING TANK TECHNIQUE

A practical procedure is proposed in this paper to predict ship manoeuvrability. A three degrees of freedom MMG (Japanese Manoeuvring Mathematical Modelling Group)-type model is established to simulate rudder manoeuver. Propeller thrust and rudder loads are calculated by empirical formulas, whereas the hull forces as well as moment are determined with hydrodynamic derivatives which are derived from CFD (Computational Fluid Dynamics) computations. An own developed RANS (Reynolds-Averaged Naiver-Stokes) solver on the base of OpenFOAM is applied to simulate a range of PMM (Planar Motion Mechanism) tests and Fourier analyses of the computed results are carried out to obtain the required derivatives. In order to demonstrate the effectivity of the whole procedure and the RANS computations, the US (United States) combatant DTMB 5415 is taken as a sample for an application. Forced motions of surge, sway, yaw and yaw with drift for the bare hull with bilge keels are simulated. Thereafter, simulations of standard rudder manoeuvers, i.e. turning and zigzag, are performed by applying the computed derivatives. The results are compared with available measured data. It has been shown that the present procedure together with the RANS method can be used to evaluate the manoeuvrability of a ship since general good agreements between the simulated results and measured data are achieved.

NUMERICAL MODELLING AND ASSESSMENT OF THE UGEN FLOATING WAVE ENERGY CONVERTER

The paper presents a linear hydrodynamic model for the UGEN wave energy converter, an analysis of the dynamics of the system and the predicted ability to extract energy from the waves. The UGEN (floating device with a U tank for GENeration of electricity from waves) consists of an asymmetric floater with a large internal U tank filled with water, where the energy is extracted from the relative motion between the water inside the tank and the rolling of the floater. The floater rolling mode of motion is the main stimulator of the motion of the water in the tank, however the sway and heave motions are also coupled therefore the system has motion.

CALCULATION OF THE HYDRODYNAMIC INTERACTION BETWEEN TWO ENCOUNTERING BODIES IN COUPLING MULTI-FREEDOM MOTIONS

ellipsoids are taken as an example. By coupling the motion equations of the two bodies and the fluid flow equations, the interaction forces and moments are calculated, and the tracks are predicted. The numerical results for the model fixed motion (only free to surge) at constant speed are compared with those published in literature for the validation of the method proposed in this paper, and good agreement is found. On this basis, more complicated multi-degree of freedom motions in surge, sway and yaw directions induced by the interaction effects are simulated. By systematically comparing and analyzing the numerical results obtained at different speeds, lateral distances and body sizes, the influences of speed and lateral distance and body size The sway and yaw motion will be induced additionally due to the interaction effects when two encountering bodies sail in close proximity, which may lead to the collision accident. In the present study, two on the hydrodynamic forces are elucidated.

A unified ship manoeuvring model with a nonlinear model predictive controller for path following in regular waves

In this paper, a nonlinear model predictive controller for path following of a surface vessel in the presence of regular waves is studied. A model predictive controller is developed for a 3DoF unified manoeuvring model of the KVLCC2 crude oil tanker. The surge, sway and yaw motions of the ship are influenced by the second order wave drift forces and moments calculated based on a potential flow solver. Propeller thrust, rudder and hydrodynamic forces and moments are computed using empirical formulas available in the literature. For path following purposes, waypoints are assigned in head and beam wave conditions and a line of sight algorithm computes the reference heading angle. The rudder control is exerted by a nonlinear model predictive controller and the effectiveness of the controller is studied. The performance of the nonlinear model predictive controller is compared against that of a basic PID controller.

Experimental study on the wave energy harvesting performance of a small suspension catamaran exploiting the maximum power point tracking approach

A novel design of a suspension catamaran, named Wave Harmonizer Type 6 (WHzer-6), is proposed and developed. The cabin is suspended upon two displacement hulls by four compression springs and suspension linkages. Owing to the newly designed pantograph and Watt’s link, the heave, pitch, and roll motions of the cabin can be separated from the twin-hull. Meanwhile, the relative surge, yaw, and sway motions between the cabin and twin-hull are suppressed. Four sets of modified rack & pinion gears and four brushed DC motor/generators (M/Gs) are utilized to transmit the forces between the cabin and twin-hull at four control locations, respectively. When the twin-hull is excited by incident waves, the induced relative vertical motions between the cabin and twin-hull are converted into rotary motion of the rotor of the M/Gs, consequently producing electrical currents. An indirect maximum power point tracking (MPPT) algorithm is developed to maximize wave energy extraction. The maximum power points (MPPs) are sought using a hill-climbing method in a quarter-ship simulation program and verified by bench tests. Then a series of towing tank experiments is carried out in regular head and beam waves, respectively. The power production, the wave energy capture width ratio (CWR), and the corresponding motion responses of the ship are investigated and analyzed. The peak power production and the peak CWR are 0.63W and 47.4%, respectively, at the wave encounter frequency of 8.89rad/s, the wave amplitude of 0.02m, and the forward speed of 1.5m/s in head waves.

Identification of hydrodynamic coefficients of AUV in the presence of measurement biases

This paper mainly presents the parameter identification method developed from a Least Square Estimation (LSE) algorithm to estimate hydrodynamic coefficients of Autonomous Underwater Vehicle (AUV) in the presence of measurement biases. LSE based parameter determination method is developed to obtain unbiased estimated values of hydrodynamic coefficients of AUV from biased Inertial Navigation System (INS) measurements. The proposed parameter identification method consists of two phases: in the first phase, high precision INS and its auxiliary instrument including compass, pressure depth sensor, and Doppler Velocity Log (DVL) are designed as Integrated Navigational System coupled with Complementary Kalman Filter (CKF) to determine hydrodynamic coefficients of AUV by removing the INS measurement biases; in the second phase, LSE based parameter identification method is applied to the model in the first phase for obtaining unbiased estimated values of hydrodynamic coefficients of AUV. In this paper, a method for identifying the yaw and sway motion dynamic parameters of an AUV is given. Various maneuvering scenarios are verified to assess the parameter identification method employed. The simulation results indicate that using the CKF based Integrated Navigation System together with unbiased measurement conversion could produce better results for estimating the hydrodynamic coefficients of AUV.

Robust Parameter Estimation of an Empirical Manoeuvring Model Using Free-Running Model Tests

The work presents the identification and validation of the hydrodynamic coefficients for the surge, sway, and yaw motion. This is performed in two ways: using simulated data and free-running test data. The identification and validation with the simulation data are carried out using a 25° turning test and a 20°−20° zigzag manoeuvring test. For the free-running test data, two zigzag manoeuvres are used: 30°−30° zigzag for identification and 20°−20° zigzag for validation. A nonlinear manoeuvring model is proposed based on the standard Euler equations, and the hydrodynamic coefficients are computed using empirical equations. To obtain robust results, the truncated singular value decomposition is employed to diminish the multicollinearity and the parameter uncertainties due to noise. The validation is carried out by comparing the result of the measured values with the predictions obtained using the manoeuvring models. Finally, a sensitivity analysis for the simulation data is performed to understand the influence of the parameters in the manoeuvres.

Hydrodynamic Coefficients of a Floater Near a Partially Reflecting Seawall in the Presence of an Array of Caisson Blocks

Abstract In the present study, surface gravity wave scattering and radiation by a freely floating rectangular buoy placed near a partially reflecting seawall and in the presence of an array of caisson blocks are analyzed. Various hydrodynamic parameters related to the wave scattering and radiation, such as the added mass and radiation damping coefficients, correspond to sway, heave, and roll motions of the floating buoy, horizontal force, vertical force, and moment acting on the floating structure, and horizontal wave force acting on the partially reflecting seawall, are studied for a variety of wave and structural parameters. The study reveals that the resonating pattern in various hydrodynamic coefficients occurs for moderate values of the wavenumber. Furthermore, when the distance between the floater and the sidewall is an integral time of half wavelength, the resonating behavior in the sway, heave, and roll added masses, and associated damping coefficients appears, and the aforementioned hydrodynamic coefficients change rapidly around this zone. These resonance phenomena can be diminished significantly with appropriate positioning of the floater with respect to the sidewall and in the presence of partially reflecting seawall.

Tuning for robust and optimal dynamic positioning control in BlueROV2

A tuning approach for the robust and optimal dynamic positioning control of BlueROV2 subjected to currents with varying speeds and headings is presented. A 2D planar dynamic model of BlueROV2 is developed in Matlab/Simulink and used for the study. The surge, sway and yaw motions are controlled by individual PID controllers. An extensive sensitivity study is carried out on a total of nine cases with different current speeds, current headings, and measurement noise levels. The results show that tuning a model solely using step responses from a linearized model might not produce optimal results. Further it is important to verify the system responses in time domain after tuning. Finally, it is observed that re-tuning the controllers for each simulation case may lead to better performance. However, it is also shown that the base case controller gains are sufficiently robust and lead to good performances for the other simulation cases.

Monitoring Tree Sway as an Indicator of Interception Dynamics Before, During, and Following a Storm

AbstractUnderstanding the role of trees in attenuating the timing and magnitude of effective precipitation reaching the land surface requires improved monitoring of interception dynamics. We developed a new field monitoring approach to leverage continuous monitoring of tree sway motion in quantifying continuous, dynamic time series of canopy water storage during storms. Using this approach, we additionally observed a hysteretic interception response in tree canopies, which indicates that interpreting interception processes through tree sway signals requires the consideration of changing water (i.e., mass) distribution during and following storms. These findings suggest that continuously monitoring tree sway motions offers a new technique to quantify interception processes. This advancement in whole tree interception may help improve our understanding of how interception affects ecosystem water availability/productivity and runoff dynamics that are important for both natural ecosystems and stormwater management in cities.

통합보존식 해석과 HCIB 법을 이용한 슬로싱 탱크 내부 갇힌 공기에 의한 압력 진동 모사

The code developed using a pressure-based method for unified conservation laws of incompressible/compressible fluids is expanded to handle moving or deforming body boundaries using the hybrid Cartesian/immersed boundary method. An instantaneous pressure field is calculated from a pressure Poisson equation for the whole fluid domain, including the compressible gas region. The polytropic gas is assumed for the compressible fluid so that the energy equation is decoupled. Immersed boundary nodes are identified based on edges crossing body boundaries. The velocity vector is reconstructed at the immersed boundary node using an interpolation along the assigned local normal line. The developed code is validated by comparing the time histories of pressure and wave elevation for sloshing in a rectangular and a membrane-type tank. The validated code is applied to simulate air cushion effects in a rectangular tank under sway motion. Time variations of pressure fields are analyzed in detail as the air pocket pulsates. It is shown that the contraction and expansion of the air pocket dominate the pressure loads on the wall of the tank. The present results are in good agreement with other experimental and computational results for the amplitude and the decay of the pressure oscillations measured at the pressure gauges.

Experimental investigation on the power and thrust characteristics of a wind turbine model subjected to surge and sway motions

In the present study, wind tunnel experiments were performed to investigate the power and thrust characteristics of a wind turbine model subjected to a variety of surge and sway motions. The turbine model was mounted on a translational stage to simulate the surge and sway motions at prescribed amplitudes and frequencies. The power output and rotor thrust were measured in each sets of the motion frequencies and amplitudes, respectively; and the measurements were also performed in a base-fixed turbine for comparison. Results show that the surge and sway motions with various amplitudes and frequencies all have slight impact on the mean power output and mean rotor thrust of a wind turbine. However, the rotor thrust fluctuations of the surging turbine, not only appeared significantly higher than those of the swaying turbine and base-fixed turbine at the same sets of amplitudes and frequencies, but also increased with the surge frequency and surge amplitude. Moreover, for both the surging and swaying turbine, the rotor thrust fluctuated with the same period as the surge and sway motions, respectively; and the power spectral density of the rotor thrust both exhibited a peak at the motion frequency and its odd multiple frequencies.

Enhancement of a leg-wheel mechanism by hydraulics toward compliantly balancing platforms for heavy duty work

This paper presents CRAWHEL, a proposed low-height leg-wheel platform for dexterous and safe construction work. The platform supports most of its weight with two large wheels in the center and crawling in a low position with four hydraulically driven legs. By actively manipulating the contact force of legs and wheels by hydraulic joint torque control, the body can respond to unexpected reaction forces and to sudden changes in terrain shape. Thereby, it maintains the position and orientation stably while generating necessary force to the work tools. This paper describes the design concept and verifies it using preliminary simulations and experiments. For this purpose, the first hardware prototype with 16 degrees of freedom, 2 m length, 660 mm height, and 145 kg weight was fabricated. Details of the hardware and the whole-body motion control method are presented herein. Numerical analysis underscores the effectiveness of leg-wheel coordinated control for the most commonly used horizontal sway motions. The experimentally obtained results demonstrate that the prototype can maintain the position and posture of the base even if the ground actually moves irregularly, or if a strong disturbance is applied.

Roll restoring coefficients of planing boats’ maneuver using 2D+t approach

Importance of maneuverability as a main feature of safety for a marine craft is broadly recognized. Mathematical modeling together with Maneuver Hydrodynamic Coefficients (MHCs) is employed for maneuverability simulation. Generally, experimental, analytical and numerical methods are employed for extraction of MHCs which 2D+t approach is recently employed. In this study, roll restoring MHCs of planing hulls are evaluated by the 2D+t approach. Running attitude of planing boats alters during any kind of maneuver due to forward speed change. This study presents a simple and applicable PMM procedure for consideration of running attitude to extract MHCs. In this procedure at a given forward speed, the planing hull is restrained to PMM apparatus in a fixed running attitude resulted from conventional resistance test at the same forward speed. This procedure is employed by 2D+t method for prismatic planing hulls in a set of forward speeds in roll condition. It has resulted three regression formulae for Y_ϕ, K_ϕ and N_ϕ as function of dead-rise angle and Froude number. The result of this study can be directly used in simulation of maneuvers via mathematical model. Moreover, this approach may be followed for other MHCs related to sway and yaw motions in future work.

Framework for reconstructing wave loads on a floating cylinder using monitored data of structural motion and wave elevation

This study develops a framework for reconstructing the wave loads on a floating cylinder by utilising the monitored data of wave elevation and structural motions, which involve surge, sway, roll, and pitch motions. The proposed method can be applied to perform wave load monitoring and data collection for offshore structures in a stochastic wave field. The derivation of the wave load reconstruction based on the potential flow theory is presented in detail. The linear reconstruction method (as the basis of the proposed method) is first established to simplify the reconstruction process. A nonlinear reconstruction method considering the second-order wave effects is introduced to improve the reconstruction accuracy for nonlinear wave loads. The concept of wave load reconstruction on a complex structure is also addressed. A case analysis is performed on a floating circular cylinder under three conditions. When the structural motions are pure translational motions or pure rotational motions, the wave loads on the cylinder can be reconstructed accurately with the transfer functions ατ,n and βτ,n. When the structural motions consist of both translational and rotational motions, the transfer functions are dependent on the structural motion pattern. Singularity points with a specific motion pattern are present, whereby the reconstruction would fail. In the cases where diffraction and radiation waves occur simultaneously, the two types of waves need to be decoupled from the monitored wave elevation, and the wave loads caused by the diffraction and radiation waves are reconstructed separately.

Path-following Control for Autonomous Navigation of Marine Vessels Considering Disturbances

Path-following control is considered as one of the most fundamental skills to realize autonomous navigation of marine vessels in the ocean. This study addresses with the path-following control for a ship in which there are environmental disturbances in the directions of the surge, sway, and yaw motions. The guiding principle and back-stepping method was utilized to solve the ship’s tracking problem on the reference path generated by a virtual ship. For path-following control, error dynamics is one of the most important skills, and it extends to the research fields of automatic collision avoidance and automatic berthing control. The algorithms for the guiding principles and error variables have been verified by numerical simulation. As a result, most error variables converged to zero values with the controller except for the yaw angle error. One of the most interesting results is that the tracking errors of path-following control between two ships are smaller than the existing safe passing distances considering interaction forces from near passing ships. Moreover, a trade-off between tracking performance and the ship’s safety should be considered for determining the proper control parameters to prevent the destructive failure of actuators such as propellers, fins, and rudders during the path-following of marine vessels.