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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]

In a high proportion of wind–photovoltaic–hydro hybrid power systems, fluctuation and dispersion make it difficult to accurately quantify the output characteristics. Therefore, in this study, a cloud model and copula correlation coefficient matrix were constructed for a hybrid power generation system based on the output data. Multiple backward cloud transformation based on the sampling-with-replacement method was proposed to calculate the improved entropy and hyperentropy to analyze the fluctuation range and dispersion degree quantitatively. A similarity index was proposed to evaluate the similarity between wind power, PV power, and hydropower. A suitable copula function was selected, and the Kendall and Spearman coefficients show the correlation relationships of the hybrid systems. The temporal and spatial characteristics of the hybrid systems were analyzed based on the two models. A typical example in Qinghai proved the effectiveness and applicability of the method. The results show that the correlation between photovoltaic power and hydropower is better and that, in summer, hydropower can be used to adjust the output of renewable energy. [ABSTRACT FROM AUTHOR]

This paper investigated reliability modeling for systems subject to dependent competing risks considering that variation of the failure threshold is not considered in most studies on competing failure reliability. Firstly, the variation of degradation quantity under shocks was analyzed, and the variation of the threshold was considered on this basis. Secondly, the cumulative degradation under the influence of the random shock process was analyzed. The attractive property of Copula functions is symmetry. Then, a linear Wiener process model was applied to model performance degradation failure, and a multi-performance degradation correlated-competition model based on a Copula function was constructed, which considered the correlated competition between multi-performance degradation failures. Lastly, a micromotor system was used to analyze the applicability of the proposed model for bivariate instances, demonstrating the rationality and effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

In medicals sciences and reliability engineering, the failure of individuals or units (I/Us) occurs due to independent causes of failure. In general, the symmetry between dependent and independent causes of failure is essential to the nature of the problem at hand. In this study, we considered the accelerated dependent competing risks model when the lifetime of I/Us was modeled using a generalized half-logistic distribution. The data were obtained with respect to constant stress accelerated life tests (ALTs) with a type-II progressive censoring scheme. The dependence structure was formulated using the copula approach (symmetric Archimedean copula). The model parameters were estimated with the maximum likelihood method; only two dependent causes of failure and bivariate Pareto copula functions were proposed. The approximate confidence intervals were constructed using both the asymptotic normality distribution of MLEs and bootstrap techniques. Additionally, an estimator of the reliability of the system under a normal stress level was constructed. The results from the estimation methods were tested by performing a Monte Carlo simulation study. Finally, an analysis of data sets from two stress levels was performed for illustrative purposes. [ABSTRACT FROM AUTHOR]

To provide the theoretical basis for the engineering application of metakaolin as aluminum-rich pozzolanic ash materials, the promoting effect of metakaolin on the macro- and micro-mechanical properties of composite cement-based composite materials was explored under high-temperature steam and standard curing conditions. Analysis techniques, which involved thermogravimetric and nanoindentation coupled with scanning electron microscopy–energy dispersive X-ray spectroscopy, were used. To analyze the experimental data, the ACI empirical formula and the copula function were used. The correlation among the hydration degree of the MK-cement cementation system, the Al/Si of the C-(A)-S-H phase, and the nanomechanical properties of the C-(A)-S-H gel phase was investigated. According to prior research, the macroscopic mechanical properties and the substitution rate of the MK-cement composite cementitious system can be improved under high-temperature curing conditions in a short period, in which the optimum substitution rate of metakaolin is 20%. The ACI empirical formula was used to demonstrate the functional relationship between the metakaolin replacement rate, curing time, and compressive strength. The MK-cement cementation system can eliminate the defect phase, reduce the CH phase content, and then increase the C-(A)-S-H gel phase content and bulk density. The micro-mechanical properties of the C-(A)-S-H gel phase rises due to its phase content and Al/Si ratio. Furthermore, the copula function verifies the dependence of the nanomechanical properties of C-(A)-S-H gel and Al/Si. [ABSTRACT FROM AUTHOR]

Climate change impacts many aspects of life and requires innovative thinking on various issues. The electricity sector is affected in several ways, including changes in the production components and consumption patterns. One of the most important issues for Independent System Operators, a state-controlled organization responsible for ensuring the reliability, availability, and quality of electricity delivery in the country, is the response to climate change. This is reflected in the appropriate design of production units to cope with the increase in demand due to extreme heat and cold events and the development of models aimed at predicting the probability of such events. In our work, we address this challenge by proposing a novel probability model for peak demand as a function of wet temperature (henceforth simply temperature), which is a weighting of temperature and humidity. We study the relationship between peak demand and temperature using a new Archimedean copula family, shown to be effective for this purpose. This family, the Clayton generalized Gamma, is a multi-parameter copula function that comprises several members. Two new measures of fit, an economic measure and a conditional coverage measure, were introduced to select the most appropriate family member based on the empirical data of daily peak demand and minimum temperature in the winter. The Clayton Gamma copula showed the lowest cost measure and the best conditional coverage and was, therefore, proven to be the most appropriate member of the family. [ABSTRACT FROM AUTHOR]

In power system planning, the growth of renewable energy generation leads to several challenges including system reliability due to its intermittency and uncertainty. To quantify the relatively reliable capacity of this generation, capacity credit is usually adopted for long-term power system planning. This paper proposes an evaluation of the capacity credit of renewable energy generation using stochastic models for resource availability. Six renewable energy generation types including wind, solar PV, small hydro, biomass, biogas, and waste were considered. The proposed models are based on the stochastic process using the Wiener process and other probability distribution functions to explain the randomness of the intermittency. Moreover, for solar PV—the generation of which depends on two key random variables, namely irradiance and temperature—a copula function is used to model their joint probabilistic behavior. These proposed models are used to simulate power outputs of renewable energy generations and then determine the capacity credit which is defined as the capacity of conventional generation that can maintain a similar level of system reliability. The proposed method is tested with Thailand's power system and the results show that the capacity credit depends on the time of day and the size of installed capacity of the considered renewable energy generation. [ABSTRACT FROM AUTHOR]

The traditional DGA (Dissolved Gas Analysis) diagnosis method does not consider the dependence between fault characteristic gases and uses the relationship between gas ratio coding and fault type to make the decision. As a tool of the dependence mechanism between variables, a copula function can effectively analyze the correlation between variables when it cannot determine whether the linear correlation coefficient can correctly measure the correlation between variable relationships. In this paper, the edge variable of a copula function is selected from the fault characteristic gas of a transformer, and the distribution type of the edge variable is fitted at the same time. Then, Bayesian estimation with the Gaussian residual likelihood function is used to fit the parameters of a copula function and a copula function is selected to describe the optimal dependence of the fault characteristic gas of transformer. The relationship between a copula function and the state of transformer is studied. The results show that the copula function boundary with hydrocarbon gas as edge variable can divide the transformer as healthy or defective state. When the cumulative distribution probability (CDF) value of the dissolved gas in the oil in the copula function is close to 0.8, the fluctuation of its gas concentration leads to a sharp change in the probability. Therefore, the analysis of dissolved gas in oil based on a copula function can be used as a powerful technical solution for oil-immersed power transformer fault diagnosis. [ABSTRACT FROM AUTHOR]

The instability of seabed slope sediments is the main factor influencing the safety of marine resource development. Therefore, to ensure the safe operation of submarine pipelines under complex and uncertain seabed rock and soil conditions, a reliability model was developed to elucidate the trend of impact-related pipeline damage due to submarine slides. Then, a risk assessment of the damage process of submarine slides impacting pipelines was conducted, which is of great significance for the in-depth safety assessment of pipelines impacted by submarine slides. Based on the copula function, a joint probability distribution model considering the correlation among risk variables was established for rational correlation characterization. A probability analysis method of impact-related pipeline damage attributed to submarine slides based on the copula function was proposed. The Monte Carlo simulation (MCS) method was employed to simulate the random uncertainty in limited observation values and accurately determine the reliability of safe pipeline operation under the action of submarine slides. The conclusions were as follows: (1) Based on the copula function, a joint probability distribution model of risk variables with any marginal distribution function and related structure could be developed. (2) The copula function could reasonably characterize relevant nonnormal distribution characteristics of risk variables and could simulate samples conforming to the distribution pattern of the risk variables. (3) The failure probability calculated with the traditional independent normal distribution model was very low, which could result in a notable overestimation of the reliability of submarine pipelines. [ABSTRACT FROM AUTHOR]

There are a variety of degradation models in the literature, each with a certain effect of random variation around the mean degradation path on the time-to-failure of the device being degraded. To assess the dependence that the random variation around the mean degradation path exerts on the resulting time-to-failure, this paper presents copula functions for time-to-failure-based degradation models with respect to two well-known degradation models, namely, the multiplicative degradation model and the additive degradation model. The implied copula functions for the case of the multiplicative degradation model have explicit forms. The implied copula functions are proved to be symmetric in the case of deterministic effect of degradation on failure, but the copulas obtained when failure is affected uncertainly by degradation are asymmetric. Necessary and sufficient conditions for the implicit copula functions to be symmetric are given. [ABSTRACT FROM AUTHOR]

A new, non-parametric and binless estimator for the mutual information of a d-dimensional random vector is proposed. First of all, an equation that links the mutual information to the entropy of a suitable random vector with uniformly distributed components is deduced. When d = 2 this equation reduces to the well known connection between mutual information and entropy of the copula function associated to the original random variables. Hence, the problem of estimating the mutual information of the original random vector is reduced to the estimation of the entropy of a random vector obtained through a multidimensional transformation. The estimator we propose is a two-step method: first estimate the transformation and obtain the transformed sample, then estimate its entropy. The properties of the new estimator are discussed through simulation examples and its performances are compared to those of the best estimators in the literature. The precision of the estimator converges to values of the same order of magnitude of the best estimator tested. However, the new estimator is unbiased even for larger dimensions and smaller sample sizes, while the other tested estimators show a bias in these cases. [ABSTRACT FROM AUTHOR]

Mastering the lodging risk of planting environment is of great significance to the optimal layout of maize varieties and the breeding of lodging resistant varieties. However, the existing lodging risk models are still at the stage of single or multi-factors independent analysis, and lack of assessment for different lodging types. To address this issue, based on the mechanism of different lodging types, the Archimedean copula function was used to describe the joint probability distribution of wind speed and precipitation, and the lodging risk assessment model of maize was established. By comparing the goodness of fit, when the rank correlation coefficient of these two is positive and negative, the corresponding optimal joint probability distribution functions are the Gumbel copula and Frank copula. According to the spatial distribution of lodging risk, the area from Liaodong Bay northward to Tongyu, Jilin province in the Northeast and the North China Plain has a high frequency of lodging, in which the probability of stalk lodging is two to four times that of root lodging. Finally, we discussed how to apply the lodging risk distribution results to optimize the maize variety test sites to improve the efficiency and reliability of the existing test system. The method proposed in this paper comprehensively considers the synergistic effect of multiple factors and can provide technical support for other risk assessment. [ABSTRACT FROM AUTHOR]

Drought is one of the most severe natural disasters. However, many of its characteristic variables have complex nonlinear relationships. Therefore, it is difficult to construct effective drought assessment models. In this study, we analyzed regional drought characteristics in China to identify their relationship with changes in meridional and zonal temperature gradients. Drought duration and severity were extracted according to standardized precipitation evapotranspiration index (SPEI) drought grades. Trends in drought duration and severity were detected by the Mann-Kendall test for the period of 1979–2019; they showed that both parameters had been steadily increasing during that time. Nevertheless, the increasing trend in drought severity was particularly significant for northwest and southwest China. A composite analysis confirmed the relationships between drought characteristics and temperature gradients. The northwest areas were relatively less affected by temperature gradients, as they are landlocked, remote from the ocean, and only slightly influenced by the land–ocean thermal contrast (LOC) and the meridional temperature gradient (MTG). The impacts of LOC and MTG on drought duration and severity were positive in the southwest region of China but negative in the northeast. As there was a strong correlation between drought duration and severity, we constructed a 2D copula function model of these parameters. The Gaussian, HuslerReiss, and Frank copula functions were the most appropriate distributions for the northeast, northwest, and southwest regions, respectively. As drought processes are highly complex, the present study explored the internal connections between drought duration and severity and their responses to meteorological conditions. In this manner, an accurate method of predicting future drought events was developed. [ABSTRACT FROM AUTHOR]

Heat and drought stress, which often occur together, are the main environmental factors limiting the survival and growth of vegetation. Studies on the response of gross primary production (GPP) to extreme climate events such as heat and drought are highly significant for the identification of ecologically vulnerable regions, ecological risk assessments, and ecological environmental protection. We got 1982–2017 climatic data from the University of East Anglia Climatic Research Unit, Norwich, England, and GPP data from National Earth System Science Data Sharing Service Platform, Beijing, China. Using Theil–Sen median trend analysis and the Mann–Kendall test, we analyzed trends in temperature and the standardized precipitation/standardized precipitation evapotranspiration indices in the eight vegetation regions of China. Additionally, the response of GPP to the single and combined impacts of heat and drought were analyzed using multidimensional copula functions, and GPP reduction probabilities were estimated under different drought levels and heat intensities. The results showed that the probability of a drastic GPP reduction increases with increasing drought levels and heat intensities. The combined impacts of heat and drought on vegetation productivity is greater than the impacts of either drought or heat alone and presents a nonlinear superposition of the two extremes. The impact of heat on GPP is not evident when the drought level is high. The temperate grassland and warm temperate deciduous broad-leaved forest regions are the most sensitive regions to drought and heat in China. This study provides a scientific basis for the comprehensive evaluation of the risk of GPP reduction under the single and combined impacts of heat stress and drought stress. [ABSTRACT FROM AUTHOR]

A novel methodology for modelling time to failure of systems under a degradation process is proposed. Considering the method degradation may have influenced the failure of the system under the setup of the model several implied lifetime distributions are outlined. Hazard rate and mean residual lifetime of the model are obtained and a numerical situation is delineated to calculate their amounts. The problem of modelling the amount of degradation at the failure time is also considered. Two monotonic aging properties of the model is secured and a characterization property of the symmetric degradation models is established. [ABSTRACT FROM AUTHOR]

Many experiments require simultaneously testing many hypotheses. This is particularly relevant in the context of DNA microarray experiments, where it is common to analyze many genes to determine which of them are differentially expressed under two conditions. Another important problem in this context is how to model the dependence at the level of gene expression. In this paper, we propose a Bayesian procedure for simultaneously testing multiple hypotheses, modeling the dependence through copula functions, where all available information, both objective and subjective, can be used. The approach has the advantage that it can be used with different dependency structures. Simulated data analysis was performed to examine the performance of the proposed approach. The results show that our procedure captures the dependence appropriately classifying adequately a high percentage of true and false null hypotheses when choosing a prior distribution beta skewed to the right for the initial probability of each null hypothesis, resulting in a very powerful procedure. The procedure is also illustrated with real data. [ABSTRACT FROM AUTHOR]

Lithium-ion batteries are widely used as basic power supplies and storage units for large-scale electric drive products such as electric vehicles. Their reliability is directly related to the life and safe operation of the electric drive products. In fact, the cells have a dependent relationship with the degradation process and they affect the degradation rate of the entire battery pack, thereby affecting its reliability. At present, most research focuses on the reliability of battery packs and assumes that their cells are independent of each other, which may cause the reliability of the evaluation to deviate greatly from the actual level. In order to accurately assess the reliability of lithium-ion batteries, it is necessary to build a reliability model considering the dependency among cells for the overall degradation of lithium-ion battery packs. Therefore, in this study, based on a lithium-ion battery degradation test, the Wiener process is used to analyze the reliability of four basic configurations of lithium-ion battery packs. According to the degradation data of the battery packs, the Copula function is used to quantitatively describe the dependent relationship in the degradation process of a single battery, and the quantitative dependent relationship is combined with the reliability model to form a new reliability model. Finally, taking the battery system of Tesla S as an example, a feasible optimization method for battery pack design is provided based on the model constructed in this work. [ABSTRACT FROM AUTHOR]

Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period. [ABSTRACT FROM AUTHOR]