arXiv subjects

Leo Dostal

Publications and source records attributed to Leo Dostal.

10 recordsLinked to original sources

arXiv2024

Validation of Theoretical Estimation Methods and Maximum Value Distribution Calculation for Parametric Roll Amplitude in Long-Crested Irregular Waves

Parametric rolling is a parametric excitation phenomenon caused by GM variation in waves. There are a lot of studies of the estimation the conditions, the occurrence, and the amplitude of parametric rolling. On the other hand, there are relatively few cases in which theoretical methods for estimating parametric roll amplitudes in irregular waves have been validated in tank tests. The primary objective of this study is to validate theoretical estimation methods for the parametric roll amplitude in irregular waves and improve their accuracy. First, the probability density functions (PDF) of the parametric roll amplitude obtained from the model ship motion experiment in irregular waves are compared with that obtained from theoretical estimation methods. Second, the method to improve the accuracy of estimation of the roll restoring variation in irregular waves is suggested. Third, the method to estimate the distribution of the maximum amplitude of parametric rolling in irregular waves. As a result, the PDFs of the roll amplitude obtained from the experiments differ from the results of theoretical estimation. After that, by correcting GM variation, the results of theoretical estimation are closer to the experimental results. Moreover, by the theoretical estimation method using the moment equation, the qualitative estimation for the PDF of the maximum roll amplitude is succeeded.

physics.flu-dyn↗

arXiv2023

Approximate probability density function for nonlinear surging in irregular following seas

The broaching that follows the surf-riding is a dangerous phenomenon that can lead to the capsizing of a vessel due to its violent yaw motion. Most of the previous studies on surf-riding phenomena in irregular waves have been conducted by replacing irregular waves with regular waves. In contrast, this study provides suggestions on how to directly calculate nonlinear surge motion in irregular seas. In this study, the statistical aspects of the surf-riding phenomenon are first presented. Then, under several approximations, we show how to calculate the probability density function theoretically. Although the results obtained are based on strong approximations, it is found that the nonlinear surge oscillations in irregular following seas can be explained from a qualitative point of view.

math.DS↗

arXiv2023

Experimental Study on Reinforcement Learning-based Control of an Acrobot

We present computational and experimental results on how artificial intelligence (AI) learns to control an Acrobot using reinforcement learning (RL). Thereby the experimental setup is designed as an embedded system, which is of interest for robotics and energy harvesting applications. Specifically, we study the control of angular velocity of the Acrobot, as well as control of its total energy, which is the sum of the kinetic and the potential energy. By this means the RL algorithm is designed to drive the angular velocity or the energy of the first pendulum of the Acrobot towards a desired value. With this, libration or full rotation of the unactuated pendulum of the Acrobot is achieved. Moreover, investigations of the Acrobot control are carried out, which lead to insights about the influence of the state space discretization, the episode length, the action space or the mass of the driven pendulum on the RL control. By further numerous simulations and experiments the effects of parameter variations are evaluated.

cs.RO↗

arXiv2023

Comparison of stochastic stability boundaries for parametrically forced systems with application to ship rolling motion

Numerous accidents caused by parametric rolling have been reported on container ships and pure car carriers (PCCs). A number of theoretical studies have been performed to estimate the occurrence condition of parametric rolling in both regular and irregular seas. Some studies in random wave conditions have been the approximate extension of the occurrence conditions for regular waves (e.g. Maki et al). Furthermore, several researches have been based on the stochastic process in ocean engineering (Roberts and Dostal). This study tackled the parametric rolling in irregular seas from the stability of the system's origin. It provided a novel theoretical explanation of the instability mechanism for two cases: white noise parametric excitation and colored noise parametric excitation. The authors then confirmed the usefulness of the previously provided formulae by Roberts and Dostal through numerical examples.

physics.app-ph↗

arXiv2022

Application of Linear Filter and Moment Equation for Parametric Rolling in Irregular Longitudinal Waves

Parametric rolling is one of the dangerous dynamic phenomena. In order 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 by using the 6th-order ARMA filter. In addition, the parametric excitation process is modeled by 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 by 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.

math.DS↗

arXiv2022

Stochastic Assessment of Acceleration Probability Density Function for Parametric Rolling Using Moment Method

Container ships encounter large roll angles and high acceleration, and container loss remains a problem. This study proposes a method for calculating the probability density function~(PDF) of roll angular and cargo lateral accelerations. First, the moment values of these accelerations are derived using the linearity of expectation and the validity of this method is examined. Second, the PDF shapes of these accelerations are proposed and their coefficients are determined using the obtained moment values. Our proposed method can be used to derive the PDFs of roll angular and cargo lateral accelerations.

math.DS↗

arXiv2021

Localized stationary seismic waves predicted using a nonlinear gradient elasticity model

This paper aims at investigating the existence of localized stationary waves in the shallow subsurface whose constitutive behaviour is governed by the hyperbolic model, implying non-polynomial nonlinearity and strain-dependent shear modulus. To this end, we derive a novel equation of motion for a nonlinear gradient elasticity model, where the higher-order gradient terms capture the effect of small-scale soil heterogeneity/micro-structure. We also present a novel finite-difference scheme to solve the nonlinear equation of motion in space and time. Simulations of the propagation of arbitrary initial pulses clearly reveal the influence of the nonlinearity: strain-dependent speed in general and, as a result, sharpening of the pulses. Stationary solutions of the equation of motion are obtained by introducing the moving reference frame together with the stationarity assumption. Periodic (with and without a descending trend), as well as localized stationary waves, are found by analyzing the obtained ordinary differential equation in the phase portrait, and integrating it along the different trajectories. The localized stationary wave is in fact a kink wave and is obtained by integration along a homoclinic orbit. In general, the closer the trajectory lies to a homoclinic orbit, the sharper the edges of the corresponding periodic stationary wave and the larger its period. Finally, we find that the kink wave is in fact not a true soliton as the original shapes of two colliding kink waves are not recovered after interaction. However, it may have high amplitude and reach the surface depending on the damping mechanisms (which have not been considered). Therefore, seismic site response analyses should not a priori exclude the presence of such localized stationary waves.

physics.geo-ph↗

arXiv2020

Soliton Collision in Random Seas

Although extreme or freak waves are repeatedly measured in the oceans, their origin is largely unknown. The interaction of different water waves is seen as one reason for their emergence. One way to consider nonlinear waves in deep water is to look at solutions of the nonlinear Schrödinger equation, which plays an important role in the determination of extreme waves. One specific solution is the soliton solution. Therefore the question arises, how nonlinear waves behave as they interact or collide. Using a relaxation pseudo spectral scheme for the computation of solutions of the nonlinear Schrödinger equation, the behavior of colliding solitons is studied. Thereby, different wave amplitudes and angles of collision are considered. In addition to this, the influence of an initial perturbation by random waves is studied, which is generated using a Pierson-Moskowitz spectrum.

nlin.PS↗

arXiv2019

Study on the Behavior of Weakly Nonlinear Water Waves in the Presence of Random Wind Forcing

Specific solutions of the nonlinear Schrödinger equation, such as the Peregrine breather, are considered to be prototypes of extreme or freak waves in the oceans. An important question is, whether these solutions also exist in the presence of gusty wind. Using the method of multiple scales, a nonlinear Schrödinger equation is obtained for the case of wind forced weakly nonlinear deep water waves. Thereby, the wind forcing is modeled as a stochastic process. This leads to a stochastic nonlinear Schrödinger equation, which is calculated for different wind regimes. For the case of wind forcing which is either random in time or random in space, it is shown that breather type solutions such as the Peregrine breather occur even in strong gusty wind conditions.

nlin.PS↗

arXiv2019

First Passage Time of Nonlinear Diffusion Processes with Singular Boundary Behavior

New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from approximations of the energy or amplitude of second order nonlinear stochastic differential equations. Since the diffusion of a stochastic process vanishes at an entrance boundary, the entrance boundary is called a singular point of the stochastic process. The theorems for the moments of the first passage times are validated based on existing analytical results. In addition, the first passage times of a nonlinear stochastic differential equation, which is important for the determination of dangerous ship roll dynamics, are calculated. The proposed analytical expressions for the moments of the first passage times can be calculated very fast using standard quadrature formulas.

math.AP↗