RB-DEM Modeling and Simulation of Non-Persisting Rough Open Joints Based on the IFS-Enhanced Method

When the geological environment of rock masses is disturbed,numerous non-persisting open joints can appear within it.It is crucial to investigate the effect of open joints on the mechanical properties of rock mass.However,it has been challenging to generate realistic open joints in traditional experimental tests and numerical simulations.This paper presents a novel solution to solve the problem.By utilizing the stochastic distribution of joints and an enhanced-fractal interpolation system(IFS)method,rough curves with any orientation can be generated.The Douglas-Peucker algorithm is then applied to simplify these curves by removing unnecessary points while preserving their fundamental shape.Subsequently,open joints are created by connecting points that move to both sides of rough curves based on the aperture distribution.Mesh modeling is performed to construct the final mesh model.Finally,the RB-DEM method is applied to transform the mesh model into a discrete element model containing geometric information about these open joints.Furthermore,this study explores the impacts of rough open joint orientation,aperture,and number on rock fracture mechanics.This method provides a realistic and effective approach for modeling and simulating these non-persisting open joints.

Ruin Probability and Joint Distributions of Some Actuarial Random Vectors in the Compound Pascal Model

The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U（T - 1）, ｜U（T）｜ and inf U（n） （i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery） and the distributions of some actuarial random vectors.

Joint and supremum distributions in the compound binomial model with Markovian environment

In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.

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.

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.

Joint modelling of location and scale parameters of the skew-normal distribution

Joint location and scale models of the skew-normal distribution provide useful ex- tension for joint mean and variance models of the normal distribution when the data set under consideration involves asymmetric outcomes. This paper focuses on the maximum likelihood estimation of joint location and scale models of the skew-normal distribution. The proposed procedure can simultaneously estimate parameters in the location model and the scale model. Simulation studies and a real example are used to illustrate the proposed methodologies.

Parametric message passing-based relative navigation in joint tactical information distribution system

Relative navigation is a key feature in the joint tactical information distribution system（JTIDS）.A parametric message passing algorithm based on factor graph is proposed to perform relative navigation in JTIDS.First of all,the joint posterior distribution of all the terminals＇ positions is represented by factor graph.Because of the nonlinearity between the positions and time-of-arrival（TOA） measurement,messages cannot be obtained in closed forms by directly using the sum-product algorithm on factor graph.To this end,the Euclidean norm is approximated by Taylor expansion.Then,all the messages on the factor graph can be derived in Gaussian forms,which enables the terminals to transmit means and covariances.Finally,the impact of major error sources on the navigation performance are evaluated by Monte Carlo simulations,e.g.,range measurement noise,priors of position uncertainty and velocity noise.Results show that the proposed algorithm outperforms the extended Kalman filter and cooperative extended Kalman filter in both static and mobile scenarios of the JTIDS.

Modified Joint Distribution of Wave Heights and Periods

The modified versions of the linear theoretical model of Longuet-Higgins （1983） are derived in this work and also compared with the laboratory experiments carried out in MAR1NTEK. The main feature of modifications is to replace the mean frequency in the formulation with the peak frequency of the wave spectrum. These two alternative forms of joint distributions are checked in three typical random sea states characterized by the initial wave steepness. In order to further explore the properties ＆these models, the associated marginal distributions of wave heights and wave periods are also researched with the observed statistics and some encouraging results are obtained.

Long-Term Joint Distribution of One-Tenth Large (or Significant) Wave Height with Average Period

In this paper, by using the wave data from a few oceanographic observation stations in the coastal zone of the Yellow Sea, the East China Sea and the South China Sea, the long-term joint distribution of the one-tenth large (or significant) wave height with average period is studied. The statistical data demonstrate that the long- term distribution of the one- tenth wave height or average period fits the log-normal distribution, thus the joint distribution also fits the two-dimensional log-normal distribution. Then the conditional probability distribution of the average period is derived, and the range as well as the mode of the average wave period corresponding to a certain return period of wave height can be calculated easily.

Joint Distribution of Wave Periods and Rate of Change of Wave Surface Elevation

The rate of change of wave surface elevation is of much importance in ocean engineering, especially for the determination of the limitation of wave breaking. This paper gives a kind of joint distribution of wave periods and the rate of change of wave surface elevation by means of calculation of the two-order to four-order moment of the frequency spectrum based on the linear wave theory. For the first time, the distribution density function of wave periods determined by peaks is provided, and the conclusion is drawn that the rate of change of wave surface elevation obeys the Rayleigh distribution.

On the long-term joint distribution of characteristic wave height and period and its application

By analysing the scatter diagrams of characteristic the wave height H and the period T on the basis of instrumental data from various ocean wave stations, we found that the conditional expectation and standard deviation of wave period for a given wave height can be better predicted by using the equations of normal linear regression rather than by those based on the log- normal law. The latter was implied in Ochi' s bivariate log-normal model(Ochi. 1978) for the long-term joint distribution of H and T. With the expectation and standard deviation predicted by the normal linear regression equations and applying proper types of distribution, we have obtained the conditional distribution of T for given H. Then combining this conditional P(T / H) with long-term marginal distribution of the wave height P(H) we establish a new parameterized model for the long-term joint distribution P(H,T). As an example of the application of the new model we give a method for estimating wave period associated with an extreme wave height.

Diversity of beetle species and functional traits along gradients of deadwood suggests weak environmental filtering

Background: Gradients in local environmental characteristics may favour the abundance of species with particular traits, while other species decline, or favour species with different traits at the same time, without an increase in average species abundances. Therefore, we asked: do variations in species and traits differ along gradients of deadwood variables? Do species abundance and trait occurrence change with species richness within or between functional groups? Thus, we analysed the beetle assemblages of five forest sites located in Italy, along the Apennines mountains.Methods: From 2012 to 2018 we sampled beetles and five deadwood types in 193 plots to characterise the deadwood gradient: standing dead trees, snags, dead downed trees, coarse woody debris, and stumps. We modelled beetle species relative abundances and trophic traits occurrences against the deadwood variables using joint species distribution models.Results: Out of 462 species, only 77 showed significant responses to at least one deadwood type, with a weak mean response across species. Trophic groups showed mostly negative responses to deadwood variables. Species abundance increased with species richness among sites only for phytophagous and saproxylophagous. Trait occurrence did not increase with species richness among sites, except for phytophagous and saproxylophagous.However, trait occurrence changed significantly with species richness of several trophic groups within some sites.We found that increases in species richness do not result in decreases in species abundance of a given trophic group, but rather null or positive relationships were found suggesting low interspecific competition.Conclusions: Our findings suggest that in Mediterranean mountain forests there is still room for increasing the level of naturalness, at least for what concerns deadwood management. On one side, our findings suggest that competition for deadwood substrates is still low, on the other side they indicate that increasing deadwood volume and types to improve overall beetle richness may increase also beetle abundances.

Research on Coordinated Development and Optimization of Distribution Networks at All Levels in Distributed Power Energy Engineering

The uncertainty of distributed generation energy has dramatically challenged the coordinated development of distribution networks at all levels.This paper focuses on the multi-time-scale regulation model of distributed generation energy under normal conditions.The simulation results of the example verify the self-optimization characteristics and the effectiveness of real-time dispatching of the distribution network control technology at all levels under multiple time scales.

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.

Joint Limit Distributions of Exceedances Point Processes and Partial Sums of Gaussian Vector Sequence

In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.

Cramer-Rao bound and signal-to-noise ratio gain in distributed coherent aperture radar

This paper studies the estimation performance of the coherent processing parameter （CPP）, including time delay differences and phase synchronization errors among different apertures of the distributed coherent aperture radar （DCAR）. Firstly, three architectures of signal processing in the DCAR are introduced. Secondly, the closed-form Cramer-Rao bound （CRB） of the CPP estimation is derived and compared. Then, the closed-form CRB is verified by numerical simulations. Finally, when the next generation radar works in a fully coherent mode, the closed-form signal-to-noise ratio （SNR） gain of the three architectures is presented.

PATH INTEGRAL SOLUTION OF NONLINEAR DYNAMIC BEHAVIOR OF STRUCTURE UNDER WIND EXCITATION

A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito＇ s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted. Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.

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.

Design Tide Hydrograph with A Given Risk Threshold by A Copula-Based Multivariate Method

This paper describes the development of a T-year design tide hydrograph （DTH）. A core innovation is that the proposed technique uses the design risk threshold and copula-based conditional risk probability to analyze the optimal combination of high waters and low waters of the DTH. A brief description of the method is presented. The in situ semi-diurnal tide data at the coast of Jiangsu Province in China are analyzed. Marginal distributions for high waters and low waters of tides are examined. Furthermore, the joint distributions, condition risk probabilities and risk thresholds of high waters and low waters are presented. Results of the DTH from the proposed method are compared with those from the traditional same-multiple enlarging design approach. It is demonstrated that the proposed method is preferable.

Generative Adversarial Networks with Joint Distribution Moment Matching

Generative adversarial networks(GANs)have shown impressive power in the field of machine learning.Traditional GANs have focused on unsupervised learning tasks.In recent years,conditional GANs that can generate data with labels have been proposed in semi-supervised learning and have achieved better image quality than traditional GANs.Conditional GANs,however,generally only minimize the difference between marginal distributions of real and generated data,neglecting the difference with respect to each class of the data.To address this challenge,we propose the GAN with joint distribution moment matching(JDMM-GAN)for matching the joint distribution based on maximum mean discrepancy,which minimizes the differences of both the marginal and conditional distributions.The learning procedure is iteratively conducted by the stochastic gradient descent and back-propagation.We evaluate JDMM-GAN on several benchmark datasets,including MNIST,CIFAR-10 and the Extended Yale Face.Compared with the state-of-the-art GANs,JDMM-GAN generates more realistic images and achieves the best inception score for CIFAR-10 dataset.