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After a transmission line is covered by ice in winter, ice-shedding and vibration occurs under special meteorological and external dynamic conditions, which leads to intense transmission line shaking. Transmission line ice-shedding and vibration often cause line flashover trips and outages. In January 2018, three 500 kV transmission lines, namely, the 500 kV Guanli line, the 500 kV Dushan line, and the 500 kV Guanqiao line, tripped and cut off due to ice-shedding and vibration in Anhui province, seriously threatening the safe operation of a large power grid. Current studies mainly focus on analyzing the influence factors and characteristics of line ice-shedding and investigating suppression measures, but they only analyze the correlation between each influencing factor and icing or shedding, and do not consider the coupling effects between multiple factors. In this paper, the key influencing factors and the probability distribution of transmission line ice-shedding were analyzed, and a multiple-factor coupling fault probability calculation model of line ice-shedding based on Copula function was proposed. The fault probability was calculated directly by considering multiple influence factors at the same time, which effectively overcame the error caused by multi-factor transformation in fuzzy membership degree and other methods. It provided an important decision-making basis for preventing and controlling transmission line ice-shedding faults. [ABSTRACT FROM AUTHOR]

Flash floods cause great harm to people's lives and property safety. Rainfall is one of the main causes of flash floods in small watersheds. The uncertainty of rainfall events results in inconsistency between the traditional single rainfall pattern and the actual rainfall process, which poses a great challenge for the early warning and forecasting of flash floods. To carry out the effective flash flood early warning and forecasting, this paper proposes a novel rainfall pattern by coupling total rainfall and peak rainfall intensity based on copula functions, i.e., the rainfall pattern of risk probability combination (RPRPC). On this basis, the Hydrologic Engineering Center-Hydrologic Modeling System (HEC-HMS) hydrological model is used to simulate the rainfall-runoff process, the trial algorithm is used to calculate the critical rainfall (CR), and the optimistic-general-pessimistic (O–G-P) early warning mode considering the decision maker's risk preference is proposed. The small watershed of Xinxian in Henan province, China, is taken as a case study for calculation. The results show that the RPRPC is feasible and closer to the actual rainfall process than the traditional rainfall pattern, Frank copula function is the best for determining the joint distribution function of total rainfall and peak rainfall intensity, and the HEC-HMS model can be applied to small watersheds in hilly areas. Additionally, both RPRPC and antecedent soil moisture condition (ASMC) have influence on CR, and the variation of RPRPC will change the influence of ASMC on CR. Finally, the effectiveness of O–G-P early warning mode is verified. [ABSTRACT FROM AUTHOR]

[Display omitted] • A hydrological model coupled with reservoir module was developed for runoff projection. • Future runoff will increase in the mainstream and northern tributaries. • The duration and severity of hydrological droughts will decrease. • The probability of concurrent hydrological droughts will decrease. • Hydrological droughts occur in the downstream or mainstream with high probability when hydrological droughts occur in its upstream or tributaries. Hydrological droughts have caused greater damage due to climate change and rapid socio-economic development. Exploring future hydrological drought variations is imperative for drought defense and infrastructure construction. This study aims to investigate future changes in hydrological droughts across the Yangtze River Basin during 2025 ∼ 2100. The Distributed Time-Variant Gain Model coupled with the Standard Operation Policy module (DTVGM-SOP) was employed to project future runoff driven by the bias-corrected Coupled Model Intercomparison Project Phase 6 (CMIP6) data. Subsequently, future spatial–temporal changes in the characteristics of hydrological droughts were analyzed based on the Standardized Runoff Index (SRI). Lastly, future changes in the probability of concurrent hydrological droughts were evaluated using the bivariate copula functions. Results show that: (1) The DTVGM-SOP model can satisfactorily simulate monthly streamflow with a high Nash-Sutcliff Efficiency (NSE) of 0.75 ∼ 0.92. Future annual maximum discharge and annual average discharge in the mainstream and the northern tributaries are expected to increase by 3.34%∼58.19% and 3.11%∼32.66% respectively, while annual maximum discharge in the southern tributaries decreases by 0.54%∼20.09%. (2) The future annual and seasonal hydrological drought frequency is expected to decrease in most regions, while the frequency in spring increases in the Qinghai Tibet Plateau. The duration and severity of future hydrological droughts are expected to decrease by 9.52%∼78.69% and 5.13%∼81.36% in the whole basin except the source area and the Yalong River Basin. (3) Future concurrent hydrological droughts will be mitigated with decreasing frequency. The probability of concurrent hydrological droughts is expected to decrease by 46.15%∼96.47%, while future changes in the conditional probability of the mainstream are diverse in different concurrent scenarios with a range of −93.41%∼40.09%. The findings are helpful to improve the understanding of future hydrological drought variations in the Yangtze River Basin and provide essential information for damage reduction. [ABSTRACT FROM AUTHOR]

Droughts have such essential features as long duration,large scope of influence,and spatio-temporal continuity,and a single variable or double variables were mostly considered in previous studies. By identifying arid patches and judging the continuity between two adjacent droughts based on the given threshold,a spatio-temporally continuous 3D identification method has been proposed for drought events,measuring a drought event in terms of 5 characteristic variables of duration,area,severity,intensity,and central location;the duration-area-severity frequency analysis method based on Copula function has been proposed. Taking Southwest China as an example,SPI drought indices are used to identify the drought events that lasted 3 months or longer in recent 52 years,which totaled 78. Among them,the most serious event from Aug. 2009 to Jun. 2010 has a recurrence period of 94 years. The comparison between the probability distribution function and the Copula function indicates that the 3 characteristic variables of duration,area and severity shall be simultaneously considered upon frequency analysis of drought events. [ABSTRACT FROM AUTHOR]

We build copula function-based joint distribution models for the annual maximum flood peaks of the Yangtze River and Poyang Lake, to analyze the coincidence probabilities, using scenarios that combine with the impoundment of three Gorges, define influencing indexes and relative contribution rates on flood coincidence at varying frequencies. The study shows the probabilities for coincidence of floods with 1000, 100, and 10-year return periods in both Yangtze main stem and Poyang Lake are respectively 0.02, 0.19 and 2.87%, with higher coincidence probabilities for shorter return periods; when 1000-year flood occurs in the Yangtze, the probabilities for Poyang Lake to encounter flood of the 1000, 100, or 10-year magnitude are higher than 16.08, 42.48 or 74.77% respectively; Poyang-Yangtze flood coincidence is affected by operation of the hydraulic engineering. The lowering of flood peaks caused by the Three Gorges impoundment and regulation of the lake have respectively reduced the probabilities of Poyang-Yangtze flood coincidence by about 7.0 and 1.97%, with average relative contribution rates − 33.82 and − 17.1%; influenced by hydrological projects in Poyang basin, variations in Poyang’s inflow flood have displayed an average contribution rate of 20.4% for the negative effect on extreme (P < 5% or P > 90%) flood coincidence, while having a positive contribution rate of 38.2% on floods of other return periods. The results can help increase our understanding of flood coincidence, and support flood control efforts in Poyang Lake; its analytical approach may also be useful to other applications of copula functions. [ABSTRACT FROM AUTHOR]

There is complicated correlations in mechanical system. By using the advantages of copula function to solve the related issues, this paper proposes the mechanical system reliability model based on copula function. And makes a detailed research for the serial and parallel mechanical system model and gets their reliability function respectively. Finally, the application research is carried out for serial mechanical system reliability model to prove its validity by example. Using Copula theory to make mechanical system reliability modeling and its expectation, studying the distribution of the random variables (marginal distribution) of the mechanical product' life and associated structure of variables separately, can reduce the difficulty of multivariate probabilistic modeling and analysis to make the modeling and analysis process more clearly. [ABSTRACT FROM AUTHOR]

Global sensitivity analysis (GSA) plays an important role in uncertainty analysis and quantification. Conventional GSA for structures requires tackling two main challenges: (1) the incomplete probability information of inputs and (2) the effects caused by the static/dynamic correlation of random variables or stochastic processes. In this paper, two kinds of novel copula-based methods for variance-based GSA are proposed to address these challenges. Based on the known samples, the proposed methods can choose the optimal copula function to construct the joint distribution of inputs, and compute the global sensitivity indices combined with Monte Carlo (MC) simulation. Time-variant copula function is used to generate the samples of time series which are both auto-correlated and cross-correlated, and the proposed methods are extended to develop time-variant GSA of dynamic structures with correlated random variables and stochastic processes. Four engineering examples are given to illustrate the good applicability and capability of the proposed methods for the dependent model functions under incomplete probability information. [ABSTRACT FROM AUTHOR]

The capability of a distributed renewable generator (DRG) in providing load low-voltage ride-through (LVRT) is examined. The harnessed renewable power, load demand, and the occurrences of low-voltage incidents are treated as random variables. The probability of successful load LVRT is assessed through the use of a copula function to quantify the stochastic dependency between the load and the renewable power. The analysis is then applied to the case of a series-connected photovoltaic DRG incorporated with capacitor energy storage, wherein the focus is to establish the analytical relationship between the probability of successful load LVRT and the rated power/energy capacities of the DRG capacitor. Determination of the optimal capacities of the DRG capacitor is achieved through maximization of the expected economic benefits obtained from the renewable energy harness and load LVRT minus the cost of the DRG capacitor. [ABSTRACT FROM AUTHOR]

Evidence theory contains powerful features for uncertainty analysis and can be effectively employed to address the epistemic uncertainty, which is attributed to a lack of information in complex engineering problems. This paper presents an evidence theory model based on the copula function and the related structural reliability analysis method. It is an effective tool for uncertainty modeling and reliability analysis with dependent evidence variables. In the evidence theory model, a canonical maximum likelihood (CML) method was adopted to estimate the correlation parameter, and the Akaike information criterion (AIC) was utilized to select a reasonable Archimedean copula function and whereby construct the joint basic probability assignment (BPA) for the multidimensional evidence variables. Based on the joint BPA function, a procedure for reliability analysis was formulated to compute the reliability interval on the structure with evidence uncertainty. Four numerical examples were provided to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In the present work, climate change impacts on three spring (March-June) flood characteristics, i.e. peak, volume and duration, for 21 northeast Canadian basins are evaluated, based on Canadian regional climate model (CRCM) simulations. Conventional univariate frequency analysis for each flood characteristic and copula based bivariate frequency analysis for mutually correlated pairs of flood characteristics (i.e. peak-volume, peak-duration and volume-duration) are carried out. While univariate analysis is focused on return levels of selected return periods (5-, 20- and 50-year), the bivariate analysis is focused on the joint occurrence probabilities P1 and P2 of the three pairs of flood characteristics, where P1 is the probability of any one characteristic in a pair exceeding its threshold and P2 is the probability of both characteristics in a pair exceeding their respective thresholds at the same time. The performance of CRCM is assessed by comparing ERA40 (the European Centre for Medium-Range Weather Forecasts 40-year reanalysis) driven CRCM simulated flood statistics and univariate and bivariate frequency analysis results for the current 1970-1999 period with those observed at selected 16 gauging stations for the same time period. The Generalized Extreme Value distribution is selected as the marginal distribution for flood characteristics and the Clayton copula for developing bivariate distribution functions. The CRCM performs well in simulating mean, standard deviation, and 5-, 20- and 50-year return levels of flood characteristics. The joint occurrence probabilities are also simulated well by the CRCM. A five-member ensemble of the CRCM simulated streamflow for the current (1970-1999) and future (2041-2070) periods, driven by five different members of a Canadian Global Climate Model ensemble, are used in the assessment of projected changes, where future simulations correspond to A2 scenario. The results of projected changes, in general, indicate increases in the marginal values, i.e. return levels of flood characteristics, and the joint occurrence probabilities P1 and P2. It is found that the future marginal values of flood characteristics and P1 and P2 values corresponding to longer return periods will be affected more by anthropogenic climate change than those corresponding to shorter return periods but the former ones are subjected to higher uncertainties. [ABSTRACT FROM AUTHOR]

This paper studied the reasonable estimation of factor coefficients when the multi-factor model is used to describe the return rates of financial assets. New methods to estimate factor coefficients were proposed by examining financial implication of factor coefficients and utilizing the Copula theory. Through modeling the joint distribution of each factor and the return rate of the financial asset with the Archimedean Copula function, the new method estimated factor coefficients in two steps: the sign of the coefficient and its occurring probability were first determined by the Kendall's tam the fluctuation scale of the factor coefficient was then calculated as the ratio of the variation of the financial asset's return rate with respect to the change of each factor. Moreover, the above method was further improved by emphasizing the influence of distribution tails on the factor coefficient, which was done by introducing the tail correlation. Empirical tests were carried out with trading data from Chinese stock markets. The practicality and advantage of our new methods were demonstrated by calculating the R-square value, the mean-square deviation of the random error term, and the corresponding tail mean-square deviation of the determined multi-factor models with different factor coefficient estimation methods, as well as their application to the value-at-risk and conditional value-at-risk calculations of the portfolio. Empirical results show that the improved new method is the best, while the new method is obviously better than the traditional linear regression method. [ABSTRACT FROM AUTHOR]

Seasonal design floods which consider information on seasonal variation are very important for reservoir operation and management. The seasonal design flood method currently used in China is based on seasonal maximum (SM) samples and assumes that the seasonal design frequency is equal to the annual design frequency. Since the return period associated with annual maximum floods is taken as the standard in China, the current seasonal design flood cannot satisfy flood prevention standards. A new seasonal design flood method, which considers dates of flood occurrence and magnitudes of the peaks (runoff), was proposed and established based on copula function. The mixed von Mises distribution was selected as marginal distribution of flood occurrence dates. The Pearson Type III and exponential distributions were selected as the marginal distribution of flood magnitude for annual maximum flood series and peak-over-threshold samples, respectively. The proposed method was applied at the Geheyan Reservoir, China, and then compared with the currently used seasonal design flood methods. The case study results show that the proposed method can satisfy the flood prevention standard, and provide more information about the flood occurrence probabilities in each sub-season. The results of economic analysis show that the proposed design flood method can enhance the floodwater utilization rate and give economic benefits without lowering the annual flood protection standard. Citation Chen, L., Guo, S. L., Yan, B. W., Liu, P. & Fang, B. (2010) A new seasonal design flood method based on bivariate joint distribution of flood magnitude and date of occurrence. Hydrol. Sci. J. 55(8), 1264-1280. [ABSTRACT FROM AUTHOR]

Extreme weather conditions put heavy environmental loads on systems and may cause catastrophic failure. Classification societies such as Lloyd's Register, DNV GL and the American Bureau of Shipping recommend methods for environmental load calculations. These methods do not consider dependencies among parameters when calculating environmental loads. This paper proposes a novel methodology to consider the copula-based bivariate failure function to evaluate the dependence structure of parameters and minimize uncertainty in load calculations. It also presents a robust operational failure assessment model that considers real-time environmental parameters along with their dependencies. The proposed methodology and models are tested on a semi-submersible mobile unit (SMU). The failure probability corresponding to the wind and wave loads imposed on the SMU is calculated using a physical reliability model and Bayesian network. The copula-based bivariate failure function defines the dependence using the parameters δ , which are estimated using maximum likelihood estimation. A detailed case study illustrates the advantage of the proposed methodology. The proposed method is of vital significance to developing a safe operating envelope for offshore assets likely to face extreme weather conditions. • A novel methodology to estimate load using the copula-based bivariate failure function. • The methodology also evaluates the dependence structure and uncertainty in the load calculations. • A robust operational failure assessment model is also proposed. • This work will assist in developing a safe operating envelope for offshore assets in extreme weather conditionss. [ABSTRACT FROM AUTHOR]