scholarly journals Stochastic Dynamic Response Analysis of the 3D Slopes of Rockfill Dams Based on the Coupling Randomness of Strength Parameters and Seismic Ground Motion

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3256
Author(s):  
Rui Pang ◽  
Laifu Song
Keyword(s):  
Slope Stability ◽  
Ground Motion ◽  
Joint Probability ◽  
Copula Function ◽  
Distribution Model ◽  
Joint Probability Distribution ◽  
Strength Parameters ◽  
Distribution Models ◽  
Dynamic Reliability ◽  
Seismic Ground Motion

Because rockfill strength and seismic ground motion are dominant factors affecting the slope stability of rockfill dams, it is very important to accurately characterize the distribution of rockfill strength parameters, develop a stochastic ground motion model suitable for rockfill dam engineering, and effectively couple strength parameters and seismic ground motion to precisely evaluate the dynamic reliability of the three-dimensional (3D) slope stability of rockfill dams. In this study, a joint probability distribution model for rockfill strength based on the copula function and a stochastic ground motion model based on the improved Clough-Penzien spectral model were built; the strength parameters and the seismic ground motion were coupled using the GF-discrepancy method, a method for the analysis of dynamic reliability of the 3D slope stability of rockfill dams was proposed based on the generalized probability density evolution method (GPDEM), and the effectiveness of the proposed method was verified. Moreover, the effect of different joint distribution models on the dynamic reliability of the slope stability of rockfill dams was revealed, the effect of the copula function type on the dynamic reliability of the slope stability was analysed, and the differences in the dynamic reliability of the slope stability under parameter randomness, seismic ground motion randomness, and coupling randomness of parameters and seismic ground motion were systematically determined. The results were as follows: the traditional joint distribution models ignored related nonnormal distribution characteristics of rockfill strength parameters, which led to excessively low calculated failure probabilities and overestimations of the reliability of the slope stability; in practice, we found that the optimal copula function should be selected to build the joint probability distribution model, and seismic ground motion randomness must be addressed in addition to parameter randomness.

scholarly journals Copula-Based Method for Estimating the Minimum Void Ratio Parameters of Tailings Deposits

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Hao Li ◽  
Yichuan Tang ◽  
Shibo Li ◽  
Jianquan Ma ◽  
Xiaojie Zhao
Keyword(s):  
Probability Distribution ◽  
Fine Particle ◽  
Void Ratio ◽  
Joint Probability ◽  
Copula Function ◽  
Distribution Model ◽  
Joint Probability Distribution ◽  
Particle Content ◽  
Edge Distribution ◽  
Guarantee Rate

The pore ratio is an important parameter affecting the stability and safety of tailings reservoirs; however, the relationship between the pore ratio and physical properties of tailings sand has not been researched in-depth. In this paper, using the tailings from a tungsten mine in southern Shaanxi as a case study, the correlation between the minimum void ratio and related parameters is analyzed, based on laboratory test data, and the optimal marginal distribution function of the parameters is determined. The Gumbel-Hougard copula function that best describes the correlation between parameters is identified, and it is used to establish the joint probability distribution model of the three parameters, and the guarantee rate α is introduced to estimate and analyze the minimum void ratio. The results show that the optimal edge distribution of the fine particle content and specific gravity follows a truncated normal distribution, and the optimal edge distribution of the minimum void ratio follows a logarithmic normal distribution. According to AIC criterion, the Gumbel-Hougard copula is the best three-dimensional copula function to fit the minimum void ratio and related parameters. When the guarantee rate α is 0.485, the joint probability distribution model achieves optimal performance in terms of estimating the minimum void ratio. The maximum error of the estimation is 1.99%, which is verified through data, and the estimation meets the requirements for practical engineering. The method proposed in this paper uses the existing measured data to establish a joint probability distribution model and combines the collected fine particle content and specific gravity data with the guarantee rate to estimate the minimum void ratio, providing a novel basis for the study of the physical properties of tailings.

The Probabilistic Method of Failure Analysis to Transmission Facilities under Ice Storms

2010 ◽  
Vol 37-38 ◽  
pp. 1525-1528
Author(s):  
Wen Jun Xu ◽  
Hong Ming Yang ◽  
Ming Yong Lai ◽  
Shuang Wang
Keyword(s):  
Transmission Lines ◽  
Power Transmission ◽  
Probability Distributions ◽  
Probabilistic Method ◽  
Joint Probability ◽  
Copula Function ◽  
Value Theory ◽  
Joint Probability Distribution ◽  
Ice Storms ◽  
Power Transmission Systems

Based on Extreme Value Theory (EVT), the Generalized Pareto Distributions (GPDs) of meteorological variables wind speed and freezing precipitation is simulated. Considering the dependence of them, a joint probability distribution is calculated by the Copula function. Further more, the probability distributions of ice loads and wind loads on transmission lines are analyzed, and the failure probability of broken lines and collapsed towers under ice storms is calculated. The accuracy and validity of this analytical method is demonstrated with comparison between numerical results and the historical datas of Chen Zhou power transmission systems.

Macrospatial Correlation Model of Seismic Ground Motions

2005 ◽  
Vol 21 (4) ◽  
pp. 1137-1156 ◽  
Author(s):  
Min Wang ◽  
Tsuyoshi Takada
Keyword(s):  
Spatial Correlation ◽  
Ground Motion ◽  
Joint Probability ◽  
Observation Data ◽  
Residual Value ◽  
Attenuation Relationship ◽  
Correlation Model ◽  
Stochastic Field ◽  
Seismic Ground Motion ◽  
Joint Probability Density

It is very important to estimate a macrospatial correlation of seismic ground motion intensities for earthquake damage predictions, building portfolio analyses etc., whereby damage in different locations has to be taken into account simultaneously. This study focuses on spatial correlation of the residual value between an observed and a predicted ground motion intensity, which is estimated by an empirical mean attenuation relationship. The residual value is modeled in such a way that the joint probability density function (PDF) of seismic ground-motion intensity can be characterized by the spatial correlation model as well as an empirical mean attenuation relationship, assuming that it constitutes a homogeneous two-dimensional stochastic field. Using the dense observation data of earthquakes that occurred in Japan and Taiwan in recent years, the macrospatial correlation model is proposed and the assumption of homogeneity is verified in this paper.

scholarly journals The joint probability distribution of runoff and sediment and its change characteristics with multi-time scales

2014 ◽  
Vol 62 (3) ◽  
pp. 218-225 ◽  
Author(s):  
Jinping Zhang ◽  
Zhihong Ding ◽  
Jinjun You
Keyword(s):  
Probability Distribution ◽  
Time Scales ◽  
Joint Probability ◽  
Copula Function ◽  
Annual Runoff ◽  
Joint Probability Distribution ◽  
Mode Decomposition ◽  
Change Characteristics ◽  
Empirical Mode Decomposition Method ◽  
Statistical Analysis Method

Abstract River runoff and sediment transport are two related random hydrologic variables. The traditional statistical analysis method usually requires those two variables to be linearly correlated, and also have an identical marginal distribution. Therefore, it is difficult to know exactly the characteristics of the runoff and sediment in reality. For this reason, copulas are applied to construct the joint probability distribution of runoff and sediment in this article. The risk of synchronous-asynchronous encounter probability of annual rich-poor runoff and sediment is also studied. At last, the characteristics of annual runoff and sediment with multi-time scales in its joint probability distribution space are simulated by empirical mode decomposition method. The results show that the copula function can simulate the joint probability distribution of runoff and sediment of Huaxia hydrological station in Weihe River well, and that such joint probability distribution has very complex change characteristics at time scales.

Stochastic Optimal Dispatch of Power System with Multiple Wind Farms

2010 ◽  
Vol 143-144 ◽  
pp. 414-418
Author(s):  
Shuang Wang ◽  
Hong Ming Yang ◽  
Shuang Zuo ◽  
Wen Jun Xu ◽  
Bin Zhang
Keyword(s):  
Power System ◽  
Wind Power ◽  
Model Simulation ◽  
Joint Probability ◽  
Wind Farms ◽  
Sample Average Approximation ◽  
Copula Function ◽  
Joint Probability Distribution ◽  
Chance Constrained Programming ◽  
Optimal Dispatch

Wind power at different locations may has a significant degree of correlation. A copula function, in this paper, is employed to characterize the Joint Probability Distribution (JPD) of wind power from multiple wind farms considering their correlation. Based on this, an optimal dispatch model of power system with multiple wind farms is proposed based on Chance Constrained Programming (CCP) to describe the randomness of wind power. And a new method named Sample Average Approximation (SAA) is used to transform the chance constrians in CCP. Finally the Particle Swarm Optimization (PSO) is used to solve the dispatch model. Simulation results show the affectivity of this model and method, which will be highly useful for optimal dispatch of power system with multiple wind farms.

Numerical decomposition for the reliability-oriented sensitivity with dependent variables using vine copulas

2020 ◽  
pp. 1-24
Author(s):  
Pan Wang ◽  
Haihe Li ◽  
Xiaoyu Huang ◽  
Zheng Zhang ◽  
Sinan Xiao
Keyword(s):  
Kernel Function ◽  
Joint Probability ◽  
Copula Function ◽  
Numerical Approach ◽  
Joint Probability Distribution ◽  
Copula Theory ◽  
Dependent Variables ◽  
Distribution Parameters ◽  
Input Variables ◽  
Vine Copula

Abstract For the reliability-oriented sensitivity analysis with respect to the parameters of input variables, by introducing the copula function to describe the joint probability distribution with dependent input variables, the reliability-oriented sensitivity can be decomposed into independent sensitivity and dependent sensitivity, which can be used to measure the influence of distribution parameters separately. Since the parameters of multivariate copula function are difficult to be estimated and not flexible in high dimension, the bivariate copulas are preferred in practice. Then the vine copula model is employed to transform the multivariate joint probability density function (PDF) into the product of multiple bivariate copulas and marginal PDF of all variables. Based on copula theory, the computation of reliability-oriented sensitivity with dependent variables can be transformed into the computation of a kernel function for each marginal PDF and the computation of a copula kernel function for each pair-copula PDF involved in the vine factorization. A general numerical approach is proposed to compute the separate sensitivity. Then, some numerical examples and engineering applications are employed to validate the rationality of the proposed method.

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