Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay

The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.

Multi-hazard joint probability distribution model for wind speed,wind direction and rain intensity

Multiple disasters such as strong wind and torrential rain pose great threats to civil infrastructures.However,most existing studies ignored the dependence structure between them,as well as the effect of wind direction.From the dimension of the engineering sector,this paper introduces the vine copula to model the joint probability distribution(JPD)of wind speed,wind direction and rain intensity based on the field data in Yangjiang,China during 1971–2020.First,the profiles of wind and rain in the studied area are statistically analyzed,and the original rainfall amounts are converted into short-term rain intensity.Then,the marginal distributions of individual variables and their pairwise dependence structures are built,followed by the development of the trivariate joint distribution model.The results show that the constructed vine copula-based model can well characterize the dependence structure between wind speed,wind direction and rain intensity.Meanwhile,the JPD characteristics of wind speed and rain intensity show significant variations depending on wind direction,thus the effect of wind direction cannot be neglected.The proposed JPD model will be conducive for reasonable and precise performance assessment of structures subjected to multiple hazards of wind and rain actions.

Sand particle lift-off velocity measurements and numerical simulation of mass flux distributions in a wind tunnel

Lift-off velocity of saltating sand particles in wind-blown sand located at 1.0 mm above the sand bed surface was measured using a phase Doppler particle analyzer in a wind tunnel. The results show that the probability distribution of lift-off velocity can be expressed as a lognormal function, while that of lift-off angle follows an exponential function. The probability distribution of lift-off angle conditioned for each lift-off velocity also follows an exponential function, with a slope that becomes steeper with increasing lift-off velocity. This implies that the probability distribution of lift-off velocity is strongly dependent on the lift-off angle. However, these lift-off parameters are generally treated as an independent joint probability distribution in the literature. Numerical simulations were carried out to investigate the effects of conditional versus independent joint probability distributions on the vertical sand mass flux distribution. The simulation results derived from the conditional joint probability distribution agree much better with experimental data than those from the independent ones. Thus, it is better to describe the lift-off velocity of saltating sand particles using the conditional joint probability distribution. These results improve our understanding of saltation processes in wind-blown sand.

Estimating Design Loads with Environmental Contour Approach Using Copulas for an Offshore Jacket Platform

Jacket-type offshore platforms are widely used for oil, gas field, and energy development in shallow water. The design of a jacket structure is highly dependent on target environmental variables. This study focuses on a strategy to estimate design loads for offshore jacket structures based on an environmental contour approach. In addition to the popular conditional distribution model, various classes of bivariate copulas are adopted to construct joint distributions of environmental variables. Analytical formulations of environmental contours based on various models are presented and discussed in this study. The design loads are examined by dynamic response analysis of jacket platform. Results suggest that the conditional model is not recommended for use in estimating design loads in sampling locations due to poor fitting results. Independent copula produces conservative design loads and the extreme response obtained using the conditional model are smaller than those determined by copulas. The suitability of a model for contour construction varies with the origin of wave data. This study provides a reference for the design load estimation of jacket structures and offers an alternative procedure to determine the design criteria for offshore structures.

Uncertainty analysis of correlated non-normal geotechnical parameters using Gaussian copula

Determining the joint probability distribution of correlated non-normal geotechnical parameters based on incomplete statistical data is a challenging problem.This paper proposes a Gaussian copula-based method for modelling the joint probability distribution of bivariate uncertain data.First,the concepts of Pearson and Kendall correlation coefficients are presented,and the copula theory is briefly introduced.Thereafter,a Pearson method and a Kendall method are developed to determine the copula parameter underlying Gaussian copula.Second,these two methods are compared in computational efficiency,applicability,and capability of fitting data.Finally,four load-test datasets of load-displacement curves of piles are used to illustrate the proposed method.The results indicate that the proposed Gaussian copula-based method can not only characterize the correlation between geotechnical parameters,but also construct the joint probability distribution function of correlated non-normal geotechnical parameters in a more general way.It can serve as a general tool to construct the joint probability distribution of correlated geotechnical parameters based on incomplete data.The Gaussian copula using the Kendall method is superior to that using the Pearson method,which should be recommended for modelling and simulating the joint probability distribution of correlated geotechnical parameters.There exists a strong negative correlation between the two parameters underlying load-displacement curves.Neglecting such correlation will not capture the scatter in the measured load-displacement curves.These results substantially extend the application of the copula theory to multivariate simulation in geotechnical engineering.

Down/up crossing properties of weighted Markov collision processes

This paper concentrates on considering the down/up crossing property of weighted Markov collision processes. The joint probability generating function of down crossing and up crossing numbers of weighted Markov collision processes until its extinction are obtained by constructing and studying a related multi-dimensional Markov chain. Hence, the joint probability distribution of down crossing and up crossing numbers and the mean numbers are obtained.

Real-time Follow-up Head Tracking in Dynamic Complex Environments

In the modes of both object motion and camera motion,an enhanced Camshift algorithm,which is based on suppressing similar color features of background and on joint color probability density distribution image,is proposed to real-time track head in dynamic complex environment.The system consists of face detection module,head tracking module and camera control module.When tracking fails,a self-recovery mechanism is introduced.At first the Adaboost face detector based on Haar-like features is implemented to find frontal faces,the false positive is filtered according to the skin color criterion,and the true face is used to initialize the tracking module.In hue saturation value(HSV) colorspace,the hue-saturation(H-S) histogram of face skin and the saturation-value(S-V) histogram of hair are built to produce the joint color probability density distribution image,and this is intended to realize the head tracking with arbitrary pose.During tracking,region of interest(ROI) is introduced,and the color probability density distribution of a specified background area outside the ROI is learned,similar color features in the head are suppressed according to the learning result.The background suppression step is intended to resolve the problem that the tracker maybe fails when the head is distracted by backgrounds having similar colors with the head.A closed loop control model based on speed regulation is applied to drive an active camera to center the head.Once tracking drift or failure is detected,the system stops tracking and returns to the face detection module.Our experimental results show that the presented system is well suitable for tracking head with arbitrary pose in dynamic complex environments,also the active camera can track moving head smoothly and stably.The system is computationally efficient and can run in real-time completely.