Characteristics Of Probability Density Functions Research Articles

Fluctuation characteristics of probability density function and first-passage dynamic reliability of slope systems under seismic excitations

Dynamic reliability based on the full time-history domain analysis is an important result of slope dynamic analysis when random factors are considered and also a useful tool to consider the strong coupling effect of seismic ground motions and nonlinear characteristics of rock and soil parameters. However, the effect of failure time associated with the first passage event in the time history process is seldom considered. To effectively evaluate earthquake-induced geological disasters, a probabilistic simulation method of slope stochastic dynamic reliability considering the randomness of seismic ground motions and the failure time is proposed. Clough and Penzien power spectrum model is used to simulate the non-stationary and random physical properties of seismic ground motions. Stochastic dynamic reliability analysis based on a coupling method of finite element method and limit equilibrium method (FEM-LEM) is performed considering the triggering mechanism of slope failure, integrated with Monte Carlo Simulation (MCS) and first-passage theory to obtain probability density functions (PDFs) of factor of safety (FOS) and displacement indicators, and their fluctuation characteristics with time and different peak ground acceleration (PGA) levels. The results showed that dynamic reliability of slope in the whole seismic history may be overestimated when first passage event is not considered in the evaluation of slope nonlinear dynamic time-history stability. PDFs of FOS had a significantly non-Gaussian, and even skewed distribution during slope nonlinear failure process. Normal distribution hypothesis may be unreasonable when calculating dynamic reliability of FOS index and should be used carefully for slope system under strong seismic loading. Finally, slope stochastic dynamic reliability time-history curves based on first-passage event was obtained within safety domain to provide new perspective for the performance-based seismic design of slope engineering under different seismic fortification levels and needs.

Determination of the Probability Density Function of the Mixture Signal and Additive Noise under Influence of Multiplicative Noise

Issues related to effect of multiplicative (modulating) (otherwise amplitude distortions) and additive noises on processed signal are considered. Analysis of statistical characteristics of probability density function (PDF) of instantaneous signal values against background of modulating interference is carried out. Expressions of the joint PDF envelope, phase and instantaneous signal values are obtained, for the case of only phase distortions, as well as the case when fluctuations in amplitude and phase are independent of each other. It is noted that in the second case, with the independence of phase and amplitude distortions, the PDF of the signal, first of all, is determined by the PDF of its instantaneous values and practically does not depend on the PDF of the signal phase. Expressions are obtained for the PDF useful signal and the most common PDF envelope when affecting the signal with modulating noise for deep phase distortions and for its uniform distribution over the interval (0, 2π). In addition, for the case of some functional relationship of phase and amplitude fluctuations, the expression for PDF instantaneous signal values is defined. The presence of such a functional connection allows calculating the PDF of the signal through the statistical characteristics of its envelope. It is obtained that PDF of mixture of signal and additive noise contains arbitrary distribution of phase and amplitude, as well as arbitrary law of distribution of envelope of processed signal. It is obtained that weight coefficients are determined by derivative of characteristic function of amplitude distortion in case when PDFs of said mixture are distributed according to normal law and functional connection exists between amplitude and phase distortions.

Real-Time Compact Environment Representation for UAV Navigation.

Recently, unmanned aerial vehicles (UAVs) have attracted much attention due to their on-demand deployment, high mobility, and low cost. For UAVs navigating in an unknown environment, efficient environment representation is needed due to the storage limitation of the UAVs. Nonetheless, building an accurate and compact environment representation model is highly non-trivial because of the unknown shape of the obstacles and the time-consuming operations such as finding and eliminating the environmental details. To overcome these challenges, a novel vertical strip extraction algorithm is proposed to analyze the probability density function characteristics of the normalized disparity value and segment the obstacles through an adaptive size sliding window. In addition, a plane adjustment algorithm is proposed to represent the obstacle surfaces as polygonal prism profiles while minimizing the redundant obstacle information. By combining these two proposed algorithms, the depth sensor data can be converted into the multi-layer polygonal prism models in real time. Besides, a drone platform equipped with a depth sensor is developed to build the compact environment representation models in the real world. Experimental results demonstrate that the proposed scheme achieves better performance in terms of precision and storage as compared to the baseline.

Comparison of Optimum Spline-Based Probability Density Functions to Parametric Distributions for the Wind Speed Data in Terms of Annual Energy Production

The common approach to wind energy feasibility studies is to use Weibull distribution for wind speed data to estimate the annual energy production (AEP). However, if the wind speed data has more than one mode in the probability density, the conventional distributions including Weibull fail to fit the wind speed data. This highly affects the technical and economic assessment of a wind energy project by causing crucial errors. This paper presents a novel way to define the probability density for wind speed data using splines. The splines are determined as a solution of constrained optimization problems. The constraints are the characteristics of probability density functions. The proposed method is implemented for different wind speed distributions including multimodal data and compared with Weibull, Weibull and Weibull and Beta Exponentiated Power Lindley (BEPL) distributions. It is also compared with two other nonparametric distributions. The results show that the spline-based probability density functions produce a minimum fitting error for all the analyzed cases. The AEP calculated based on this method is considered to have high fidelity, which will decrease the investment risk.

Characteristics of Wind Loads Acting on Complex Long-Span Roof Structure

The Shenzhen New Railway Station (SNRS) has roof dimensions of 450 m long and 408 m wide. This paper presents the results of wind loads acting on the large-span roof structure. In the wind tunnel test, wind-induced pressures including mean and fluctuating components were measured from the roof of a 1:200 scale SNRS model under suburban boundary layer wind flow configuration in a boundary layer wind tunnel of HD-2 at Hunan University. Based on the data obtained simultaneously from the wind tunnel tests, the distributions of the mean and fluctuating wind pressure coefficients and the characteristics of probability density functions of wind pressures of typical pressure taps were analyzed in detailed. The outcomes of the experimental study indicate that: (1) The maximum mean negative wind pressure coefficients on the roof occur at the windward leading edge region, where the maximum fluctuating wind pressure coefficients occur also in this region; (2) There are some differences of the maximum mean negative wind pressure coefficients and RMS wind pressure coefficients under conditions with different number of trains inside the station, but such effects on the overall pressure distributions on the whole roof are negligible; (3) There are clearly negative skewed distributions for some pressure taps at the windward leading roof edge and much longer negative tails are observed, which follow Non-Gaussian distributions. The results presented in this paper are expected to be of considerable interest and of use to researchers and professionals involved in designing complex long-span roof structures.

Pitting Corrosion Propagation Analysis of Reinforcement in RC Bridge Beams Considering Uncertain Information

The prediction of pitting corrosion-induced structural performance degradation is limited by the inspection means and experimental data. Incomplete information and tempral and spatial uncertainties of corrosion are integrated to develop the time-dependent pit depth model. The reinforcement corrosion is divided into two stages in this model. The approach is illustrated by a removed concrete bridge. The evolutionary characteristic of probability density function of the pit depth is analyzed, and the probabilistic distribution pattern and distribution parameters are also obtained. Besides, The sensitivity of input parameters on the pitting model are also discussed. The results show that under appropriate conditions of concrete strength (>25MPa), increase the same percentage of concrete strength is more sensitive to the pit depth than improvement the same percentage of concrete cover thickness. The effects of continuous improvement of concrete strength or increase the thickness on corrosion depth gradually decreases. The proposed procedure can be used to evaluation of existing reinforced concrete bridge.

호우사상의 시간적 정량화를 위한 베타분포의 적용

본 연구에서는 주어진 호우사상을 베타분포로 적절히 표현하기 위한 매개변수의 결정 방법을 제시하였다. 이를 위해 첨두에 대한 고려를 추가한 경우와 그렇지 않은 경우, 실제 우량주상도 및 첨두를 중심으로 재배열된 수정 우량주상도를 사용하는 경우 등을 고려하여 그 특성을 비교 검토하였다. 본 연구는 서울 지점의 2010년 독립 호우사상과 1961~2010년 사이의 연 최대치 독립 호우사상을 대상으로 베타분포를 적용하고, 그 결과를 분석하였다. 그 결과를 정리하면 다음과 같다. 첫째, 베타분포를 이용하여 실제 호우사상의 우량주상도 형태를 유사하게 표현하기 위해서는 첨두에 대한 추가적인 고려가 필요한 것으로 확인되었다. 둘째, 첨두를 중심으로 시간강우를 좌우 순차적으로 재배열한 수정 우량주 상도를 이용하는 경우가 실제 우량주상도를 이용하는 경우보다 실제 강우의 시간분포 특성에 보다 가까운 베타분포를 유도함을 확인하였다. This study suggested the parameter estimation method for given rainfall events to be properly expressed by the beta distribution. For this purpose, this study compared the characteristics of probability density function with the parameter proposed considering the cases with and without addition to the rainfall peak, and the cases of using the real hyetograph and the rearranged hyetograph about the rainfall peak. As an example, this study analyzed the independent rainfall events at Seoul in 2010 and the annual maximum independent rainfall events from 1961 to 2010. The results derived are as follows. First, this study confirmed the necessity of additional consideration on rainfall peak to mimic the real hyetograph of rainfall events by the beta distribution. Second, this study confirmed the case of using rearranged hyetograph about the rainfall peak derived a better beta distribution to well mimic the characteristics of real rainfall than the case using the real hyetograph.

Solution method of overtopping risk model for earth dams

Hydrologic risk analysis relies on a series of probabilistic analyses, and it is a complex problem in estimating the probability distributions of multiple independent and random variables. The goal of this study is to presents the procedure and application of a probability-based risk analysis methodology to evaluate earth dam overtopping risk that induced by concurrent flood and wind. The uncertainty arising from initial water surface level, flood, wind velocity, and dam height are discussed in this research. The improved Monte Carlo simulation and mean-value first-order second-moment method are used to solve the proposed dam overtopping risk model, respectively. The nonparametric kernel density estimation method, which can better learn the complex multimodal characteristic of probability density function than that of traditional parametric estimation method, is employed to improve the probability density function of initial water surface level. The latin hypercube sampling is introduced to generate uniform random number, which improves the efficient and stability compared with simple random sampling. Afterward, an application to the Dongwushi Reservoir in China illustrates that the dam overtopping risk computed using the improved Monte Carlo simulation is lower than that using mean-value first-order second-moment method. Furthermore, the sensitivity analysis show that initial water surface level is more sensitive to overtopping risk than wind velocity.

The Characteristics of Probability Density Function in the Log-law Region in Turbulent Boundary Layer.

The log-law of a zero pressure gradient turbulent boundary layer is obtained by analyzing the similarity of the probability density functions of the streamwise velocity fluctuation. The slope of the log law is found to be constant, independent of the Reynolds number. We used the Kullback Leibler divergence of probability density function to identify the log-law region in experimental data. The outer edge of logarithmic region does not indicate the constant value when normalized by the boundary layer thickness. Rather, it is a function of the Reynolds number, and when the Reynolds number is suffucuently high, this value approaches to 0.2.

Statistical Characteristics of Void Fraction Fluctuations and Flow Regime Identification in Vertical Gas-Liquid Two-Phase Flow

In this investigation, an objective and quantitative method is developed for the identification and classification of flow regimes in vertical gas-liquid two-phase flow. It is clarified that the features of probability density function (PDF) and the parameters of the PDF expected according to the maximum entropy principle (MEP) can be used as objective flow regime indicators and quantitative flow regime discriminators, respectively. In this experiment, the void fraction fluctuations are measured by the constant current technique. The PDFs are classified into three major types and correspond to three dominant flow patterns: bubbly, intermittent and annular. That is, a uni-modal PDF with a low void fraction corresponds to a bubbly flow pattern; a bimodal PDF corresponds to an intermittent flow pattern; and a uni-modal PDF with a high void fraction corresponds to an annular flow pattern. Furthermore, the relationship between the statistical parameters of the void fraction fluctuations (the mean value, the standard deviation, and the coefficients of skewness and kurtosis) and the flow patterns is discussed. It is shown that classification of uni-modal and bimodal PDFs can be made according to the coefficients of skewness and kurtosis.