Scour Development Around Submarine Pipelines due to Current Based on the Maximum Entropy Theory

This paper presents the results from laboratory experiments and theoretical analysis to investigate the development of scour around submarine pipeline under steady current conditions. Experiments show that the scour process takes place in two stages: the initial rapid scour and the subsequent gradual scour development stage. An empirical formula for calculating the equilibrium scour depth(the maximum scour depth) is developed by using the regression method. This formula together with the maximum entropy theory can be applied to establish a formula to predict the scour process for given water depth, diameter of pipeline and flow velocity. Good agreement between the predicted and measured scour depth is obtained.

Prediction of extreme wind velocity at the site of the Runyang Suspension Bridge

This paper presents a distribution free method for predicting the extreme wind velocity from wind monitoring data at the site of the Runyang Suspension Bridge (RSB), China using the maximum entropy theory. The maximum entropy theory is a rational approach for choosing the most unbiased probability distribution from a small sample, which is consistent with available data and contains a minimum of spurious information. In this paper, the theory is used for estimating a joint probability density function considering the combined action of wind speed and direction based on statistical analysis of wind monitoring data at the site of the RSB. The joint probability distribution model is further used to estimate the extreme wind velocity at the deck level of the RSB. The results of the analysis reveal that the probability density function of the maximum entropy method achieves a result that fits well with the monitoring data. Hypothesis testing shows that the distributions of the wind velocity data collected during the past three years do not obey the Gumbel distribution. Finally, our comparison shows that the wind predictions of the maximum entropy method are higher than that of the Gumbel distribution, but much lower than the design wind speed.

A moment-based stochastic edge-based smoothed finite element method for electromagnetic forming process

In this paper, a novel stochastic method named as the moment-based stochastic edge-based finite element method(MSES-FEM)is proposed to deal with the uncertain electromagnetic problems. First, electromagnetic and mechanical field are formulated by smoothed Galerkin Weak Form under edge-based smoothed finite element method(ES-FEM) scheme. The moment analysis is then applied to obtain the first four moments of the responses and to observe the effects of each random variable on electromagnetic field responses. The maximum entropy theory is employed to calculate the probability density functions(PDFs) of the responses. A quasi-static electromagnetic problem and a practical electromagnetic forming problem(EMF) are performed. The proposed method successfully solves stochastic electromagnetic forming analysis under the uncertain parameters. Numerical results obtained by the proposed MSES-FEM are quite satisfactory with the ones by the Monte Carlo simulation(MCS).