Research On Slow Drift Extreme Response And Stability Of Ocean Structures In Random Seas

The values in the tail region of the response probability density curve of ocean structures under random loading are called extreme responses. One kind of problem often met in design is how one can accurately predict ocean structures'slow drift surge extreme responses. If the extreme rolling response of an ocean structure exceeds a critical value, the structure will lose its stability and capsize. The above mentioned extreme response and capsizing behavior can be called the extreme behavior of an ocean structure. This dissertation uses several different methods to analyze the extreme behavior of an ocean structure.To study the slow drift extreme response and the capsizing behavior of ocean structures, dynamic analysis is required on the ocean structures. When performing dynamic analysis on these structures, the added mass, damping, restoring force and wave excitation of unit wave amplitude can all be calculated by some mature commercial software. With these information the nonlinear random differential equation of motion of the ocean structure can be established. The main work of this dissertation is to study the effective methods for solving these nonlinear random differential equations of motion.When performing dynamic analysis on ocean structures, the method of numerical simulation is often used by the people, i. e. to perform numerical integration on the ocean structure's differential equation of motion, and then statistically processing the aquired response time histories. The principle for doing this is very simple and clear, and the execution is also very convenient. Meanwhile, the predicted response values in the large scope of the central part of the probability density curve are also very accurate by this means. The above advantages of numerical simulation make some researchers use it also for analyzing the extreme behavior of ocean structures. This dissertation makes counter thinking on this. Firstly, this research considers concurrently the problem of the simulation efficiency and the problem of the precision of the predicted extreme response. An example of a compliant offshore structure is used to demonstrate that the slow drift extreme responses of the ocean structure predicted by numerical simulation are not very accurate. To improve the accuracy of the predicted slow drift extreme responses, some people will consider to increase the simulation numbers. Using an example, this research first demonstrates that:when a specific level of accuracy of the slow drift extreme responses is reached, increasing the number of simulations will no longer work anymore,and the accuracy of the slow drift extreme responses is not to the satisfaction to the people. To overcome the limitation of this kind of brute force simulation, it is therefore necessary for us to study using other methods for predicting the slow drift extreme responses of ocean structures under random excitations. This dissertation also quantitatively studies of the performance of analyzing the stability behavior of ocean structures (ships) by numerical simulation. It is found that the efficiency is very low when thoroughly investigating the ship rolling initial conditions'phase space via numerical simulation, i.e. the efficiency is very low when studying the ship capsizing transient behavior via numerical simulation. This dissertation also studies the performance of numerical simulation for analyzing the ship capsizing behavior when the exciting frequency and amplitude are varied and the motion initial conditions are fixed. It is found that the efficiency is very low when using numerical simulation for studying the ship capsizing behavior in the control parameter space. Summarizing the above analysis results shows that the numerical simulations results are generally inconclusive on the ocean structures'stability behavior unless the motion initial conditions and the ocean structure system's control parameter space are thoroughly studied. Therefore, it is necessary for us to study using other methods in order to rationally analyze the stability of ocean structures.Next, this dissertation studies the performance of the path integral solution method for analyzing the slow drift extreme responses of ocean structures under random excitations. When using the path integral solution method to solve the nonlinear random differential equation of motion of an ocean structure, the Fokker-Plank-Kolmogorov equation governing the response probability density of the ocean structure is first derived from the original equation of motion. Then the Fokker-Plank-Kolmogorov equation is numerically solved to obtain the response joint probability densities of the ocean structure. Thereafter, the response displacement marginal probability densities of the ocean structure are obtained.The path integral solution method is established upon the Markov diffusion process theory and the numerical interpolation scheme. Therefore, we first systematically studies the Markov diffusion process theory. Comparison study and analysis are also conducted on various kinds of numerical interpolation schemes for doing path integration. Emphasis is put on studying a kind of high efficiency numerical interpolation scheme-the Gauss-Legendre interpolation scheme. The problems solved by the path integral solution based on Gauss-Legendre interpolation scheme are limited to weakly nonlinear cases. The author of the dissertation successfully solve a strongly nonlinear random oscillation problem by the path integral solution based on Gauss-Legendre interpolation scheme. It is found that the accuracy of the predicted extreme responses is very high even when the nonlinearity is very strong. Next, the slow drift extreme responses of an ocean structure under random excitations are analyzed via path integral solution method in this dissertation . For comparison, we adopt the same ocean structure example once analyzed via numerical simulation , i. e. the slow drift surge motion of a compliant offshore structure. First, we compare the accuracy of the path integral solutions and the numerical simulation solutions in the special case that the system equation has analytical solutions. We compare the ocean structure's slow drift displacement extreme response marginal probability density values predicted via 5100 rounds numerical simulations and 25 rounds path integral solutions. It is found that the accuracy of the results of the slow drift extreme responses of the ocean structure predicted by the path integral solution method is much higher than those predicted by the numerical simulation. The efficiency for predicting the slow drift extreme responses of the structure by the path integral solution method is higher than that of the numerical simulation. Next, in the general case that the structure system equation has no analytical solutions, we obtain accurate prediction of the slow drift extreme responses of the compliant offshore structure via the path integral solution method. We find that another advantage of path integral solution is that the ocean structure's slow drift extreme response exceeding probabilities can be obtained as a by-product. Also almost no extra computer running time is needed for doing this.When using the path integral solution method for solving the slow drift extreme responses of an ocean structure, the initial probability density of the slow drift response of the ocean structure is decided by the researcher. Whether a good choice is made has great influence on the running time of the path integration. To find an optimal way for selecting the initial probability density in order to further improve the efficiency of the path integral method, this dissertation proposes a compound path integral solution method. The idea of the compound path integral solution is to estimate a rough initial probability density using small number of numerical simulations and the 3 sigma rules of normal distribution. The initial probability density obtained by this means will be very similar as the final result. Then the obtained initial probability density is inserted to the source code of the path integral solution method. The number of numerical path integrations will be reduced via this means. We compare the accuracy of the compound path integral solutions and original path integral solutions in the special case that the system equation has analytical solutions. The accuracy and efficiency of the compound path integral solution method is validated. Next, in the general case that the structure system equation has no analytical solutions, we calculate the slow drift extreme responses of a moored floating cylinder. This research demonstrates that the path integral solution method together with suitable commercial hydrodynamic software can provide a powerful tool for naval architects and ocean engineers for predicting the extreme responses of slow drift oscillations of moored ocean structures under random excitations.This dissertation finally studies the performance of the existing Melnikov method for analyzing the stability behavior of ocean structures (ships) under random excitations. Instead of directly solving the rolling motion differential equation of a ship, the Melnikov method concentrates on studying the qualitative behavior of the system ( or more precisely, the changes in qualitatively different behaviors.). In the research we utilize the Melnikov method that has been validated by others for analyzing the dynamic stability of a barge. To do so we first calculate the hydrodynamic force coefficients in the ship's rolling differential equation. Next, we non-dimensionalize the hydrodynamic force coefficients, and calculate the nonlinear damping needed for overcoming the critical wave exciting moment using the existing Melnikov formulas . We find that the critical rolling exciting moment and the ship's damping are connected via the Melnikov criteria formula. This makes it possible for the designer to adjust the ship's damping value according to the critical rolling exciting moment value, e.g.. to increase the dimensions of the bilge keel, or to change other main parameters of the ship. This aspect is particularly important in the initial design phase of the design circle. After comparing the efficiency of the numerical simulation for studying the ship's capsizing behavior in the control parameter space, we find that Melnikov analysis is efficient and conclusive, and has advantages over numerical simulation. Next, we use the Melnikov method to analyze the capsizing behavior of a biased ship. Given a bias value, we utilize the stochastic Melnikov mean square value analysis to obtain the critical wave exciting moment values corresponding to various damping values. We also compare the efficiency of using numerical simulation to thoroughly study the ship's rolling initial conditions'phase space. It is found that the efficiency of using the Melnikov method for analyzing the biased ship's capsizing behavior in the ship initial design phase is high. Summarizing the research results, we believe that together with suitable commercial hydrodynamic software the Melnikov method can be used as a highly efficient auxiliary tool for analyzing the dynamic stability of ship.Some Mathematica software packages have been developed by the author during the research project. In the final stage of this research we give some further research directions in this field.