TUHH Open Research (TORE)https://tore.tuhh.deTORE captures, stores, indexes, preserves, and distributes digital research material.Mon, 05 Jun 2023 07:33:59 GMT2023-06-05T07:33:59Z50111Theoretical estimation of roll acceleration in beam seas using PDF line integral methodhttp://hdl.handle.net/11420/7539Title: Theoretical estimation of roll acceleration in beam seas using PDF line integral method
Authors: Maki, Atsuo; Dostal, Leo; Maruyama, Yuuki; Sakai, Masahiro; Sugimoto, Kei; Fukumoto, Yusuke; Umeda, Naoya
Abstract: The prevention of excessive roll acceleration is one of the fundamental requirements of an oceangoing vessel at sea. In this paper, aiming at this requirement, we propose a new theoretical method for calculating roll angular acceleration, called “PDF line integral method.”. This paper presents the derivation of this method and a numerical comparison with Monte Carlo simulation (MCS) results; also, its validity is shown. Although the utilized GZ curve (restoring curve) exhibits strong asymmetricity, the proposed method can provide for such a condition. With only the information of roll and roll rate joint probability density function (PDF), this method can approximately calculate the roll angular acceleration, which is a high-order differential property. In addition, a relatively good agreement is achieved between the theory and MCS results.
Wed, 01 Sep 2021 00:00:00 GMThttp://hdl.handle.net/11420/75392021-09-01T00:00:00ZTheoretical estimation of joint probability density function of roll angle and angular acceleration in beam seas using PDF line integral methodhttp://hdl.handle.net/11420/12099Title: Theoretical estimation of joint probability density function of roll angle and angular acceleration in beam seas using PDF line integral method
Authors: Maki, Atsuo; Dostal, Leo; Maruyama, Yuuki; Sasa, Kenji; Sakai, Masahiro; Sugimoto, Kei; Fukumoto, Yusuke; Umeda, Naoya
Abstract: So far, we have developed a calculation method for roll angular acceleration and its derivative, which is a jerk. In this study, using the probability density function (PDF) line integral method and the joint PDF (JPDF) of roll angle and angular rate, we obtain a theoretical method for the evaluation of the two properties. In particular, the estimation method of acceleration is considered crucial, as the angular acceleration is directly related to inertial forces or moments of onboard objects. Moreover, to consider the strength of container stacks, as well as the lashing strength of cargo and track on board, a separate evaluation of roll angle and roll angular acceleration is insufficient. Further, although the new-generation intact stability criteria for excessive acceleration have been discussed by the International Maritime Organization, the evaluation of JPDF of roll angle and roll angular acceleration could contribute to the efficient evaluation of the safety of crews on board. Meanwhile, no JPDF of roll angle or angular acceleration has been calculated for an arbitrary nonlinear system so far, and there is no doubt that it is a challenging problem. In this study, by applying and extending the idea of the PDF line integral method, we proposed a method for evaluating the JPDF of roll angle and angular acceleration.
Tue, 01 Mar 2022 00:00:00 GMThttp://hdl.handle.net/11420/120992022-03-01T00:00:00ZTheoretical determination of roll angular jerk of ships in irregular beam seas using PDF line integral methodhttp://hdl.handle.net/11420/10942Title: Theoretical determination of roll angular jerk of ships in irregular beam seas using PDF line integral method
Authors: Maki, Atsuo; Dostal, Leo; Maruyama, Yuuki; Sakai, Masahiro; Sugimoto, Kei; Fukumoto, Yusuke
Abstract: The time derivative of acceleration is called a jerk, which is an important property to evaluate ride comfort in elevators, cars, and so on. Likewise, evaluation of motion sickness or ride comfort on a vessel could be achieved by this jerk property in the future. In this paper, we utilize the PDF Line Integral Method (PLIM), which was newly contrived in our previous research, for calculating not only roll angular acceleration but also roll angular jerk. The derivation of this theory, as well as numerical comparison with Monte Carlo simulation (MCS) results, are presented. Although the utilized restoring curve (GZ curve) exhibits strong asymmetricity, the proposed method successfully calculates roll angular jerk for such a condition. Since roll angular jerk is a high-order differential property, the biggest advantage of PLIM is that it only requires the information of roll and roll rate joint probability density function (PDF) to provide the PDF of jerk.
Tue, 01 Mar 2022 00:00:00 GMThttp://hdl.handle.net/11420/109422022-03-01T00:00:00ZEnhanced estimation method and approximation method of the PDF of roll angular acceleration and jerk in beam seashttp://hdl.handle.net/11420/13741Title: Enhanced estimation method and approximation method of the PDF of roll angular acceleration and jerk in beam seas
Authors: Maki, Atsuo; Dostal, Leo; Maruyama, Yuuki; Sasa, Kenji; Sakai, Masahiro; Umeda, Naoya
Abstract: So far, the authors have established the theoretical estimation method of the Probability Density Function (PDF) of roll angular acceleration and jerk with the use of PLIM (PDF Line Integral Method), and estimations of the PDF of these properties were successfully achieved. PLIM, on the other hand, necessitates numerical integration along the complex shaped integral path. The integral path, in particular, becomes challenging in the calculation of the jerk property. However, if the restoring term is only represented by a linear component, then explicit expressions of PDF of roll angular acceleration can be obtained using the nonlinearization technique. It is noteworthy that the form of the nonlinear damping component does not constrain the applicability. This paper aims to show the derivation of the theoretical result and comparison with Monte Carlo Simulation (MCS) results. Furthermore, using the current form of the acceleration PDF, the PDF of roll angular jerk was obtained. The variance of roll angular rate determines the PDF form of the acceleration, which is the method's main advantage.
Tue, 15 Nov 2022 00:00:00 GMThttp://hdl.handle.net/11420/137412022-11-15T00:00:00ZTheoretical determination of asymmetric rolling amplitude in irregular beam seashttp://hdl.handle.net/11420/10940Title: Theoretical determination of asymmetric rolling amplitude in irregular beam seas
Authors: Maki, Atsuo; Dostal, Leo; Maruyama, Yuuki; Sakai, Masahiro; Katayama, Toru; Sugimoto, Kei; Fukumoto, Yusuke; Umeda, Naoya
Abstract: A methodology for predicting the probability density function of roll motion for irregular beam seas is developed in the author’s previous research. In this paper, two methods for the prediction of the probability density function (PDF) of the rolling amplitude are examined. One of these methods is an approach based on a non-Gaussian PDF with the use of the equivalent linearization and the moment method, which has been used by Maki in the field of naval architecture. In the framework of this method, the instantaneous joint PDF of the roll and roll rate can be calculated. Thereby, the transformation from the joint PDF to the PDF of the total energy H is necessary. In this paper, the transformation from the joint PDF of instantaneous roll and rate to the PDF of H was conducted. The other method is the energy-based stochastic averaging method, whereby the PDF of the total energy H is determined from which the roll amplitude is calculated. It is noteworthy that the proposed theory aims to predict the PDF of the amplitude of the vessel due to wind or flooding. For such conditions, the restoring curve (GZ curve) has asymmetricity. To take into account this asymmetricity, a new theory for the transform of the PDF of the total energy H to the PDFof amplitude is proposed. The obtained theoretical results show almost complete agreement, and both of the two theoretical methods i.e., the energy-based stochastic averaging method and the non-Gaussian PDF method with the use of the equivalent linearization and moment method, show equivalent prediction performance even in the asymmetric condition.
Tue, 01 Mar 2022 00:00:00 GMThttp://hdl.handle.net/11420/109402022-03-01T00:00:00ZPractical method for evaluating wind influence on autonomous ship operationshttp://hdl.handle.net/11420/13751Title: Practical method for evaluating wind influence on autonomous ship operations
Authors: Maki, Atsuo; Maruyama, Yuuki; Dostal, Leo; Sakai, Masahiro; Sawada, Ryohei; Sasa, Kenji; Umeda, Naoya
Abstract: The autonomous operations of marine vehicles have recently attracted significant attention. In particular, automation of harbor operations, such as autonomous docking or berthing, is a challenging target. In low-speed harbor operations, the external disturbance of wind is a non-negligible factor. Therefore, the stochastic behavior of gusty wind should be considered in numerical simulations. This study presents a practical computational scheme for generating random wind velocity fields. In the proposed method, the von Kármán’s spectrum [1] and Hino’s wind speed spectrum [2] were fitted by a degree of freedom (1DoF) filter driven by the Wiener process. The corresponding Itô’s equation had the form of the Ornstein–Uhlenbeck process. By employing the analytical solution of the Ornstein–Uhlenbeck process, the wind process was successfully generated without time series repetition. Furthermore, the wind speed and direction processes were also generated from the measured drift and diffusion terms. The spectra of these numerical results are consistent with the observed spectra.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/11420/137512022-01-01T00:00:00ZApplication of linear filter and moment equation for parametric rolling in irregular longitudinal waveshttp://hdl.handle.net/11420/13655Title: Application of linear filter and moment equation for parametric rolling in irregular longitudinal waves
Authors: Maruyama, Yuuki; Maki, Atsuo; Dostal, Leo; Umeda, Naoya
Abstract: Parametric rolling is one of the dangerous dynamic phenomena. To discuss the safety of a vessel when a dangerous phenomenon occurs, it is important to estimate the probability of certain dynamical behavior of the ship with respect to a certain threshold level. In this paper, the moment values are obtained by solving the moment equations. Since the stochastic differential equation (SDE) is needed to obtain the moment equations, the autoregressive moving average (ARMA) filter is used. The effective wave is modeled using the 6th-order ARMA filter. In addition, the parametric excitation process is modeled using a non-memory transformation obtained from the relationship between GM and wave elevation. The resulting system of equations is represented by the 8th-order Itô stochastic differential equation, which consists of a second-order SDE for the ship motion and a 6th-order SDE for the effective wave. This system has nonlinear components. Therefore, the cumulant neglect closure method is used as higher-order moments need to be truncated. Furthermore, the probability density function of roll angle is determined using moment values obtained from the SDE and the moment equation. Here, two types of the probability density function are suggested and have a good agreement.
Mon, 12 Sep 2022 00:00:00 GMThttp://hdl.handle.net/11420/136552022-09-12T00:00:00ZImproved stochastic averaging method using Hamiltonian for parametric rolling in irregular longitudinal waveshttp://hdl.handle.net/11420/9696Title: Improved stochastic averaging method using Hamiltonian for parametric rolling in irregular longitudinal waves
Authors: Maruyama, Yuuki; Maki, Atsuo; Dostal, Leo; Umeda, Naoya
Abstract: Using the stochastic averaging method, the probability density function (PDF) of roll motion for parametric rolling in irregular waves is obtained. In this paper, the stochastic averaging method using Hamiltonian proposed by Dostal is used, and the PDF of roll amplitude and Hamiltonian are derived from the equations of roll motion. In addition, the asymptotic behavior of PDF is investigated to improve the accuracy of the calculation. Furthermore, to improve the applicability of this method, the simulation-based stochastic method is proposed. Compared to the results of the stochastic averaging method proposed by Roberts and Dostal, the results using this improved method show a good agreement. The results are examined for parametric excitation using white noise as well as colored noise. Moreover, the relationship between the scale parameter and the PDF is theoretically analyzed and formulated.
Tue, 01 Mar 2022 00:00:00 GMThttp://hdl.handle.net/11420/96962022-03-01T00:00:00ZThe improvement of stochastic averaging method to solve the ship rolling response excited by narrow-band waveshttp://hdl.handle.net/11420/15339Title: The improvement of stochastic averaging method to solve the ship rolling response excited by narrow-band waves
Authors: Liu, Yaliu; Liu, Liqin; Maki, Atsuo; Dostal, Leo; Dostal, Leo
Abstract: The stochastic averaging method of energy envelope can accurately solve the random motion response under the excitation of white noise. The noise had to fulfill the condition of strong mixing which roughly means that the process has to be broad-band. However, the sea conditions in practical engineering conditions are narrow-band spectra. Research on applicability of the stochastic averaging method of energy envelope shows that for narrow-band excitation, the damping of the system and excitation intensity should be small, and the excitation bandwidth should be large. Based on the above background, the improvement of stochastic averaging method of energy envelope under narrow-band waves is studied. The phase angle θ is introduced to characterize the relationship between kinetic energy and potential energy of the system. The drift coefficients and diffusion coefficients are averaged with respect to the period of θ. When the excitation frequency is in the lock-in field, large parametric rolling appears. The stationary probability density function (PDF) of the roll angle obtained by solving the Fokker-Planck-Kolmogorov (FPK) equation compares well with Monte Carlo simulation in the lock-in field. The improved method can relax the limitation of broad-band excitation required by stochastic averaging method. It can also consider both the nonlinear damping and nonlinear restoring force of roll motion. Therefore, the improved method is an efficient way to calculate the nonlinear roll response of ships in real sea conditions.
Tue, 01 Aug 2023 00:00:00 GMThttp://hdl.handle.net/11420/153392023-08-01T00:00:00ZFirst passage times for nonlinear ship dynamics using Gaussian random fields and effective waveshttp://hdl.handle.net/11420/15334Title: First passage times for nonlinear ship dynamics using Gaussian random fields and effective waves
Authors: Dostal, Leo; Hollm, Marten; Maki, Atsuo
Abstract: It is important to know the mean time until critical roll motion occurs in various operating and sea conditions, in order to determine and ensure the safety of ship designs and operating ships. Since typical ocean waves are irregular, the forcing and roll response of the ship is considered to be a stochastic process of colored noise type. However, the simulation of the corresponding first passage times is very time consuming. Therefore, an approach for the determination of mean first passage times of critical roll motion of ships is proposed in this paper which needs much less computation time. This approach is based on explicit formulas for the roll energy of the ship. These formulas are used to determine the mean first passage times based on integral expressions, which were previously obtained. The resulting integral expressions can be computed very fast using standard quadrature formulas. Moreover, the underlying model for ship dynamics is extended by introducing a new effective wave for short-crested sea states. This is an extension to the improved Grim's effective wave concept.
Tue, 01 Aug 2023 00:00:00 GMThttp://hdl.handle.net/11420/153342023-08-01T00:00:00ZEstimation of acceleration probability density function for parametric rolling using PLIMhttp://hdl.handle.net/11420/15353Title: Estimation of acceleration probability density function for parametric rolling using PLIM
Authors: Maruyama, Yuuki; Maki, Atsuo; Dostal, Leo; Umeda, Naoya
Abstract: As previously reported, container loss due to severe roll angles and high acceleration is still a problem for container ships. In this paper, the roll's angular acceleration is explored. First, the acceleration is divided into two components. The PDF line integral method (PLIM) is used to obtain the probability density function (PDF) of each acceleration component. We point out that it is inappropriate to obtain the joint PDF of roll angle and rate via the standard transformation from roll energy to roll angle-roll rate. Furthermore, we suggest a method for calculating the joint PDF of roll angle and effective wave elevation. Although theoretically calculating the PDF of roll angular acceleration is attempted, the theory differs from the Monte Carlo simulation (MCS) result. Therefore, it is necessary to study an alternative way to obtain a reasonable PDF of roll angular acceleration. Finally, the PDF of cargo lateral acceleration is derived, showing that the proposed theory agrees well with the MCS result. In comparison to our previous results using the PLIM method, the computation of acceleration for large roll motion is much more difficult. This leads to new challenges.
Sat, 15 Jul 2023 00:00:00 GMThttp://hdl.handle.net/11420/153532023-07-15T00:00:00Z