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Administrative strategies to cope with drought are steadily changing, from emergency procedures to day-to-day monitoring. More consideration must be paid to long-term and preventive drought control measures in the future. This paper discusses the risk of hydrological drought in the Yellow River Basin. The standardized runoff index (SRI) was used to characterize hydrological drought, and the run theory was used to identify drought states and quantify drought characteristic variables. Based on the drought severity and duration, a drought development plan was proposed and a three-dimensional copula function was constructed to obtain the joint distribution function of three-dimensional drought characteristic variables. A drought risk assessment system based on the loss × probability risk theory was constructed to explore the spatial and temporal characteristics of hydrological drought risk in the Yellow River Basin. Finally, according to the risk assessment results, the risk level was divided into low, medium and high risk, and a Bayesian network was used to explore the probability of hydrological drought. The main results are as follows: (1) From 1960 to 2018, the severity of hydrological drought in the Yellow River Basin increased, the duration lengthened, and the development speed accelerated. (2) The hydrological drought risk in the Yellow River Basin showed an overall upward trend, with the fastest increase in the HJ region of 0.041/10a. The highest annual average drought risk in the TDG region is 0.598. (3) The spatial transmission of hydrological drought risk is divided into three types: constant, enhanced and mitigation types, of which the constant type is the most common. The transmission probabilities of low, medium and high risk of hydrological drought from the HYK region to the low, medium and high risk of hydrological drought in the LJ region are 0.68, 0.66 and 0.78, respectively. [ABSTRACT FROM AUTHOR]

This study proposes a target-oriented method to study travelers' route choice behavior under travel time variability, and discusses the resulted equilibrium flow patterns. Both travel time reliability and travel time unreliability are considered in this new method, and accordingly, there are two targets. The first one is target for travel time to ensure travel time reliability, and based on this target, another one is target for excess delay to mitigate travel time unreliability. In this model, travel time and excess delay (i.e., the random vector) are stochastically correlated with each other, which is modeled with the copula function based on Sklar's Theorem, and the exact form of the copula is obtained by the proved comonotonicity relationship of this random vector. The target interaction, i.e., the complementarity relationship, is also modeled based on the utility functions, the meaning of which is that travelers have the will to make more targets achieved so as to obtain more utility. Furthermore, with this model, this paper formulates the user equilibrium as a variational inequality problem to study the long-term effect of the route choice behavior, and solves it with the method of successive average. Finally, numerical testings on the traffic network are conducted to show the convergence of the solution algorithm, and to illustrate the impact of targets on the equilibrium results. Results show that the flow change can be five times more than that with less risk-averse travelers. [ABSTRACT FROM AUTHOR]

In this paper, a functionality unit named as meta-action unit (MAU) is proposed to correlate the system function with the part actions and assess reliability of mechanical system. Firstly, the function of system is decomposed into multiple MAUs by function-movement-action (FMA). Then, the lifetime of MAU is fitted by Weibull distribution, and its parameters are estimated by support vector regression (SVR). In addition, taking the distributions of MAU as marginal distributions, the lifetime distribution of mechanical system is constructed by copula function to assess system reliability, and its parameters are estimated using the maximum likelihood estimator (MLE). Further, the reliability assessment accuracy based on MAU is compared with that from traditional method based on mechanical part failure modes. Finally, the reliability assessment of the indexing turntable (IT) is performed as an example to illustrate the feasibility and reasonability of the proposed method. [ABSTRACT FROM AUTHOR]

The intermittent nature of solar energy poses significant challenges to the integration of photovoltaic (PV) power generation into the electrical grid. Consequently, the precise forecasting of PV power output becomes essential for efficient real-time power system dispatch. To meet this demand, this paper proposes a deep learning model, the CA-Transformer, specifically designed for PV power output prediction. To overcome the shortcomings of traditional correlation coefficient methods in dealing with nonlinear relationships, this study utilizes the Copula function. This approach allows for a more flexible and accurate determination of correlations within time series data, enabling the selection of features that exhibit a high degree of correlation with PV power output. Given the unique data characteristics of PV power output, the proposed model employs a 1D-CNN model to identify local patterns and trends within the time series data. Simultaneously, it implements a cosine similarity attention mechanism to detect long-range dependencies within the time series. It then leverages a parallel structure of a 1D-CNN and a cosine similarity attention mechanism to capture patterns across varying time scales and integrate them. In order to show the effectiveness of the model proposed in this study, its prediction results were compared with those of other models (LSTM and Transformer). The experimental results demonstrate that our model outperforms in terms of PV power output prediction, thereby offering a robust tool for the intelligent management of PV power generation. [ABSTRACT FROM AUTHOR]

Copyright of Pearl River is the property of Pearl River Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Traditional methods for diagnosing dam health often rely on single point measurements, which require assumptions about the distributions of these measurements. These approaches fail to integrate multiple measured values for joint diagnosis and overlook the true distribution of the measured values, leading to potential misdiagnosis. This paper proposes a dam health diagnosis method based on kernel density estimation (KDE) and copula functions to address these limitations. The method incorporates a measurement analysis flow that extends from a single point to multiple points and establishes criteria for dam health diagnosis. In addition, this paper proposes to select the optimal copula function based on the Akaike information criterion (AIC). An engineering example is presented to demonstrate the proposed method's effectiveness in diagnosing a dam's health without assuming a specific measurement distribution function. This research contributes to the field of engineering safety management by enabling comprehensive dam health diagnosis from local dam states to the entire dam structure. [ABSTRACT FROM AUTHOR]

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 recent years, with the intensification of global warming, extreme weather has become more frequent, intensifying the uncertainty of new energy output and load power, and seriously affecting the safe operation of power systems. Scene generation is an effective method to solve the uncertainty problem of stochastic planning of integrated systems of new energy generation. Therefore, this paper proposes a scenario generation and scenario reduction model of photovoltaic (PV) output and electric vehicle (EV) load power under extreme weather based on the copula function. Firstly, the non-parametric kernel density estimation method is used to fit a large number of sample data. The kernel density estimation expressions of PV and EV powers under extreme weather conditions are obtained and the corresponding goodness of fit tests are carried out. Then, a variety of joint distribution models based on the copula function are established to judge the goodness of fit of each model, and the optimal copula function is selected as the joint probability distribution function by combining the Kendall and Spearman correlation coefficients of each model. Finally, the optimal copula joint probability distribution is used to generate PV and EV power scenarios. The data of extremely hot weather in a certain province were selected for an example analysis. The results show that the output scenario obtained conforms to the correlation under this extreme weather, and has higher accuracy in reflecting the actual PV output and load power in this province under this extreme weather, which can provide a reference for reliability analyses of power systems and power grid planning. [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]

Copyright of Science Technology & Engineering is the property of Chinese Society of Technology Economics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The scenario of renewable energy generation significantly affects the probabilistic distribution system analysis. To reflect the probabilistic characteristics of actual data, this paper proposed a scenario generation method that can reflect the spatiotemporal characteristics of wind power generation and the probabilistic characteristics of forecast errors. The scenario generation method consists of a process of sampling random numbers and a process of inverse sampling using the cumulative distribution function. In sampling random numbers, random numbers that mimic the spatiotemporal correlation of power generation were generated using the copula function. Furthermore, the cumulative distribution functions of forecast errors according to power generation bins were used, thereby reflecting the probabilistic characteristics of forecast errors. The wind power generation scenarios in Jeju Island, generated by the proposed method, were analyzed through various indices that can assess accuracy. As a result, it was confirmed that by using the proposed scenario generation method, scenarios similar to actual data can be generated, which in turn allows for preparation of situations with a high probability of occurrence within the distribution system. [ABSTRACT FROM AUTHOR]

The lack of effective failure correlation analysis is one main reason for the gap between the reliability models and the actual complex systems with mixed static and dynamic characteristics. Takagi and Sugeno (T-S) dynamic fault tree is one powerful tool to analyze the static and dynamic failure logic relationship but it assumes the failure probability of the event is independent. Therefore, this paper proposes a multi-dimensional T-S dynamic fault tree analysis method involving failure correlation. The method integrates the failure probability distribution function of basic events with multi-factors and the multi-dimensional copula function, and the important measure of this method is also deduced. The reliability model expression for systems with failure correlations, both in series and in parallel, is discussed and verified. Compare the proposed method with the assumption that the probability of a failure event is independent. This method solves the problem of a large error when ignoring the failure correlation between parts and the degree of the correlation between variables can be characterized. The reliability analysis can be conducted on complex systems affected both by multi-factors and failure correlations. The proposed method is applied to the reliability analysis of a hydraulic height adjustment system and the correctness and superiority of the method are verified. [ABSTRACT FROM AUTHOR]

Many survival data analyses aim to assess the effect of different risk factors on survival time. In some studies, the survival times are correlated, and the dependence between survival times is related to their spatial locations. Identifying and considering the dependence structure of data is essential in survival modeling. The copula functions are helpful tools for incorporating data dependencies. So, one may use these functions for modelling spatial survival data. This paper presents a model for spatial survival data by the Gumbel-Hougaard copula function. A two-stage estimator using a composite likelihood function is used to estimate regression and dependence parameters. A simulation study investigates the performance of the model. Finally, the proposed model is applied to model a set of COVID-19 data. [ABSTRACT FROM AUTHOR]

In many practical situations, more than one failure mechanism may contribute to product failure. Many studies assume independence between the different competing risks of failure. Nevertheless, the assumption of independence is not always justified in various practical applications. When the competing risks are assumed dependent, it is important to identify models that describe their dependence structure. Copulas are considered a powerful tool to model such dependence structures. This paper addresses the problem of developing Bayesian life test acceptance criteria through two-sample prediction of future observations based on another independent Weibull progressively Type-II censored sample with binomial random removals. It is assumed that unit failure occurs due to only one of two competing risks. Dependence among the competing risks of failure is modeled using Archimedean copulas with nonconjugate prior distributions. A Metropolis–Hastings Markov chain Monte Carlo algorithm is implemented to derive the prediction intervals that define the proposed acceptance criteria. The derived acceptance criteria enable manufacturers to conform to the required quality specifications and help their clients to properly set their quality expectations. A real data example is provided to illustrate the proposed life test acceptance criteria. [ABSTRACT FROM AUTHOR]

From large-scale aerospace systems to household appliances and other systems in daily life, the application of parallel systems is involved. A parallel system is a typical structural dependence multi-component system, in addition to a series system and hybrid system. This paper takes a parallel system as the research object and minimizes the expected cost rate or maximizes the availability by determining the optimal two-dimensional age replacement interval. The structural dependence of the components is described by the copula function, and the system life model is established. Based on the system life model, the two-dimensional age replacement expected cost rate model and availability model are proposed. In case analysis, the simulated annealing algorithm (SAA), genetic algorithm (GA) and particle swarm optimization (PSO) algorithm are used to find the optimal warranty scheme for the engine fuel fine filter. SAA can converge faster and find a warranty scheme that makes the warranty cost rate lower or the availability higher. Compared with one-dimensional age replacement, two-dimensional age replacement strategy has more advantages in saving warranty costs and improving system availability. Finally, rationalization suggestions are put forward for managers to make maintenance decisions through comparative analysis and sensitivity analysis. [ABSTRACT FROM AUTHOR]

As an essential mechanical component, a rolling bearing can exhibit multiple failure modes that may occur independently or in correlation with one another. A reliability analysis method that meticulously accounts for the interdependencies among various bearing failure modes is presented in this paper. The examination of wear and fatigue failure mechanisms in rolling bearings is carried out using the Physics of Failure (PoF) approach. By considering the influence of uncertain variables, the limit state functions for individual failure modes are formulated through the application of stress‐strength interference theory. In the context of wear failure, the limit state function is derived using working clearance as the characteristic quantity. On the other hand, the limit state function for fatigue failure is constructed with a focus on fatigue damage accumulation. The Copula function is used to characterize the relationship between wear failure and fatigue failure, and a reliability calculation model for rolling bearings is developed, considering the correlation between these failure modes. Ultimately, the proposed method is utilized to assess the reliability of bearings under two different sets of test conditions. The feasibility of this method is confirmed through test data, demonstrating its effectiveness in predicting bearing reliability. Through the application of this method, engineers can optimize bearing size parameters, select appropriate initial clearances, and enhance the reliability design of bearing. [ABSTRACT FROM AUTHOR]

In order to use the high ability of the artificial neural network (ANN) in data fitting, this paper introduces an ANN in stochastic process to describe the mean function for degradation modeling. Due to the fact that the existing method cannot handle the bivariate dependent degradation conditions, a bivariate dependent degradation model based on Copula function and ANN‐supported stochastic processes is proposed. Considering the random effects caused by individual difference, it is assumed that the unknown parameters in the stochastic processes and Copula functions are randomly distributed. Based on the maximum likelihood and moment estimation methods, a related statistical inference method for ANN training and parameter estimation is developed to use the bivariate dependent degradation model. An actual fatigue crack dataset is used to demonstrate the validity of the proposed method. The obtained results show that the dependent relationship between two degradation indicators should not be neglected, and it can be efficiently handled by the proposed method. Furthermore, the proposed degradation model can provide reliability and degradation intervals with enough precision due to the fact that it considers the random effects caused by individual difference. [ABSTRACT FROM AUTHOR]

Fault propagation behaviour analysis is the basis of fault diagnosis and health maintenance. Traditional fault propagation studies are mostly based on a priori knowledge of a causality model combined with rule-based reasoning, disregarding the limitations of experience and the dynamic characteristics of the system that cause deviations in the identification of critical fault sources. Thus, this paper proposes a dynamic analysis method for fault propagation behaviour of machining centres that combines fault propagation mechanisms with model structure characteristics. This paper uses the design structure matrix (DSM) to establish the fault propagation hierarchy structure model. Considering the correlation of fault time, the fault probability function of a component is obtained and the fault influence degree of nodes are calculated. By introducing the Copula and Coupling degree functions, the fault influence degree of the edges between the same level and different levels are calculated, respectively. This paper constructs a fault propagation intensity model by integrating the edge betweenness and uses it as an index to analyze real-time fault propagation behaviour. Finally, a certain type of machining centre is taken as an example for specific application. This study can provide as a reference for the fault maintenance and reliability growth of a machining centre. [ABSTRACT FROM AUTHOR]

Studying the impact of mainshock–aftershock sequences on dam reliability is crucial for effective disaster prevention measures. With this purpose in mind, a new method for stochastic dynamic response analyses and reliability assessments of dams during seismic sequences has been proposed. Firstly, a simulation method of stochastic seismic sequences is described, considering the dependence between mainshock and aftershock based on Copula function. Then, a novel practical framework for stochastic dynamic analysis is established, combined with the improved point selection strategy and the direct probability integration method (DPIM). The DPIM is employed on a nonlinear system with one degree of freedom and compared with Monte Carlo simulation (MCS). The findings reveal that the method boasts exceptional precision and efficiency. Finally, the seismic performance of a practical dam was evaluated based on the above method, which not only accurately estimates the response probability distribution and dynamic reliability of the dam, but also greatly reduces the required calculations. Furthermore, the impact of aftershocks on dam seismic performance is initially evaluated through a probability approach in this research. It is found that seismic sequences will significantly increase the probability of earth dam failure compared with sequences of only mainshocks. In addition, the influence of aftershocks on reliability will further increase when the limit state is more stringent. Specifically, the novel analysis method proposed in this paper provides more abundant and objective evaluation indices, providing a dynamic reliability assessment for dams that is more effective than traditional evaluation methods. [ABSTRACT FROM AUTHOR]

An important aspect of the multidimensional perception of poverty phenomenon is the dependence among the underlying indicators. However, the commonly applied approaches to multidimensional poverty assessment do not capture this interdependence. In this paper we propose a new multidimensional poverty index accounting for the dependence and innovate over the weighting approach. The weighting method proposed here incorporates the copula-based rank dependence among well-being dimensions and contains necessary normative parameters. In particular, the latter includes the elasticity of substitution among dimensions and the belief-adjusting parameter, which specifies the direction of relation between the dependence and the weights. The results of poverty evaluation in the selected European countries suggest that multidimensional poverty is driven not only by the individual shortfalls, but also by the degree of interdependence among well-being indicators. Moreover, multidimensional poverty is relatively higher, if dimensional weights are in direct proportion to the dependence compared to the cases of inverse relation and equal weighting. Considering the novel weighting approach, this paper contributes to the literature on composite indicators by suggesting a channel to enclose the dependence structure in the multidimensional poverty index. [ABSTRACT FROM AUTHOR]

The traditional design flood estimation method assumes that the flood peak and the flood volume are at the same frequency, without considering the correlation between the two flood characteristics. Furthermore, when the design flood region composition under a specific return period is estimated, although the traditional method is from the most unfavorable point of view, it is impossible to quantitatively describe the correlation between the floods in each subarea. Therefore, in this paper, Copula function is used to deduce the design flood peak and flood volume at different frequencies which consider the combined effects of flood peak and flood volume, and then obtains the design flood process at different frequencies. The marginal distribution of flood components in each area is established and the most suitable Copula function between components in each area and design section is preferred which consider the spatial correlation between each flood zone and Huayuankou section, and then explore the most likely design flood region composition. It shows that the design results obtained by considering the correlation between flood elements in this study are slightly higher than those deduced by traditional methods under the same return period. The method in this paper can qualitatively and quantitatively describe the design flood region composition in the study area so as to obtain the design flood results that consider both the correlation of flood characteristics and spatial correlation at the same time, which are more objective and more consistent with the actual situation of design flood region composition in the basin. [ABSTRACT FROM AUTHOR]

Currently, it is still a challenge to study the degradation mechanisms of the space traveling wave tube amplifier (TWTA) with no failure and small sample tests. Given that the Copula functions are used to describe the correlation of multiple performance characteristics, this paper develops a bivariate hybrid stochastic degradation model to evaluate the in-orbit reliability of TWTA. Firstly, based on the impact analysis of the life of TWTA, helix current and anode voltage are selected as the performance degradation parameters. Secondly, stochastic processes with random effects based on the one-dimensional Wiener process and Gamma process are applied to describe the degradation of TWTA's helix current and anode voltage, respectively, and the corresponding marginal distribution function is obtained. Then, the Copula function is utilized to describe the correlation between two different performance parameters of TWTA. Meanwhile, this paper also proposed a two-step method to estimate the reliability level of TWTA based on its in-orbit telemetry data through a two-step method, which contains a Markov Chain Monte Carlo (MCMC) algorithm and a maximum likelihood estimation (MLE) algorithm. Besides, the Bayes-Bootstrap sampling method is also used to improve the evaluation accuracy to overcome the defect of an in-orbit small sample of TWTA. Finally, a TWTA degradation case with a set of telemetry data is carried out, and the results show that the method proposed in this paper is more applicable and more accurate than other methods. [ABSTRACT FROM AUTHOR]

Statistical tools are crucial for a variety of hydrological applications, whether to model processes and enhance understanding and knowledge or to design infrastructure systems. Given the rapid evolution of statistical methods and the need for a solid theoretical foundation for their correct application, a multidisciplinary community STAtistics in HYdrology Working Group (STAHY-WG) aggregated under the International Association of Hydrological Sciences (IAHS) umbrella to contribute to this research field. Now, more than 15 years since its inception, this paper summarizes the main achievements of this productive community collaboration in four (of many) branches of statistical hydrology: extreme value analysis, multivariate analysis, time series analysis, and regionalization. The aim is to provide an overview of recent developments, offer practical suggestions (e.g. software packages), and outline future challenges to support scientists and practitioners in their endeavours within the realm of statistical hydrology studies. [ABSTRACT FROM AUTHOR]

Multiple dangerous sites often coexist in complex structures like aircraft turbine rotors, and its failure-correlated reliability evaluation usually occurs the thorny problems of high-efficacy computing and correlation quantification. In this paper, a novel unified reliability evaluation framework is proposed: to meet the high-efficacy computing demand of multi-site reliability evaluation, a new optimized Kriging surrogate-based improved importance sampling (OKS-IIS) method is first presented; furthermore, to quantify the failure correlation relationships among multiple dangerous sites, a novel failure correlation analysis (FCA) strategy is further developed. A typical reliability evaluation of high-pressure turbine rotor with multiple dangerous sites is selected, to validate the effectiveness of the proposed framework. Methods comparison show that the OKS-IIS method can improve computing efficiency while keeping computing accuracy, and the FCA strategy can accurately quantify the multi-site failure correlation. The current efforts would shed a light on the complex reliability evaluation problems involving failure correlation. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Irrigation & Drainage is the property of Journal of Irrigation & Drainage Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of China Rural Water & Hydropower is the property of China Rural Water & Hydropower Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An important alternative distribution to the Weibull, generalized exponential and gamma distributions that is used in survival analysis is the Nadarajah-Haghighi exponential distribution. Similar to the Weibull, generalized exponential and gamma distributions, the Nadarajah-Haghighi exponential distribution is an extension of the well known exponential distribution. In this paper, a copula function commonly used to model very weak linear dependence was used to introduced a bivariate Nadarajah-Haghighi distribution. The joint survival function, joint probability density function and joint cumulative distribution were given in closed form. Bayesian method of estimation was used to estimate the model parameters considering the presence of right censoring and covariates. Posterior summaries of interest were obtained via standard Markov Monte Carlo (MCMC) technique. Two real data sets were used to illustrate the importance and flexibility of the bivariate model in comparison with some competing models. It was observed that, the bivariate Nadarajah-Haghighi distribution provides a better flt than bivariate exponential, bivariate Weibull, bivariate generalized exponential and bivariate modified Weibull distributions. [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]

Determining the operation scenarios of renewable energies is important for power system dispatching. This paper proposes a renewable scenario generation method based on the hybrid genetic algorithm with variable chromosome length (HGAVCL). The discrete wavelet transform (DWT) is used to divide the original data into linear and fluctuant parts according to the length of time scales. The HGAVCL is designed to optimally divide the linear part into different time sections. Additionally, each time section is described by the autoregressive integrated moving average (ARIMA) model. With the consideration of temporal correlation, the Copula joint probability density function is established to model the fluctuant part. Based on the attained ARIMA model and joint probability density function, a number of data are generated by the Monte Carlo method, and the time autocorrelation, average offset rate, and climbing similarity indexes are established to assess the data quality of generated scenarios. A case study is conducted to verify the effectiveness of the proposed approach. The calculated time autocorrelation, average offset rate, and climbing similarity are 0.0515, 0.0396, and 0.9035, respectively, which shows the superior performance of the proposed approach. [ABSTRACT FROM AUTHOR]

In hydrological practice, individual elements of the hydrological cycle are most often estimated and evaluated separately. Uncertainty in the size estimation of extrema discharges and their return period can affect the statistical assessment of the significance of floods. One example is the simultaneous occurrence and joining of extremes at the confluence of rivers. The paper dealt with the statistical evaluation of the occurrence of two independent variables and their joint probabilities of occurrence. Bivariate joint analysis is a statistical approach for the assessment of flood threats at the confluence of rivers. In our study, the annual maximum discharges monitored on four selected Slovak rivers and their tributaries represent the analyzed variables. The Archimedean class of copula functions was used as a set of mathematical tools for the determination and evaluation of the joint probability of annual maximal discharges at river confluences. The results of such analysis can contribute to a more reliable assessment of flood threats, especially in cases where extreme discharges occur simultaneously, increasing the risk of devastating effects. Finally, the designed discharges of the different return periods calculated by using the univariate approach and the bivariate approach for the gauging station below the confluence of the rivers was evaluated and compared. [ABSTRACT FROM AUTHOR]

Copyright of China Rural Water & Hydropower is the property of China Rural Water & Hydropower Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The probabilistic dependence in a multi-variate random field consists of two parts: the spatial dependence of a random quantity at different positions and the probabilistic dependence between different random variables at the same position. The classical model cannot capture the possible non-Gaussian dependence or nonlinear dependence between different random variables. To this end, in this paper, an approach by synthesizing the spatial correlation function and the multi-variate copula function (SCFVCF) is proposed. In this model, the correlation function model is adopted to quantify the spatial dependence involved in the random field of the prime variable, and the copula function model is adopted to quantify the dependence configuration between subordinate variables. The properties of such multi-variate random fields are then studied. To generate samples of such multi-variate random fields, the spectral representation method is incorporated with the conditional sampling method. As an example, to illustrate the application of SCFVCF, the random field of the constitutive parameters of concrete is adopted. The results demonstrate that the proposed method can capture the spatial dependence of compressive strength, and at the same time the dependence configuration between different parameters is consistent with the test complete compressive stress-strain curves. [ABSTRACT FROM AUTHOR]

With the rapid development of information and automation technology, the manufacturing system is evolving towards more complexity and integration. The system components will inevitably suffer from degeneration, and the impact of component-level failure on the system reliability is a valuable issue to be studied, especially when failure dependence exists among the components. Thus, it is vital to construct a system reliability evaluation mechanism that helps to characterize the healthy status of the system and facilitate wise decision making. In this paper, a reliability analysis framework for a failure-dependent system is proposed, in which copula functions with optimized parameters are used for the description of different failure correlations, and a fuzzy inference model is constructed to derive the subsystem reliability based on the component-level failure correlation. Finally, a Bayesian network is applied to infer the system reliability based on the system structure combined with the impact of failure correlation inside. Simulation results of the proposed method show that the inference results of system reliability are reasonable and effective in different cases. Compared with the copula Bayesian network method, the proposed method shows better adaptability to failure-dependent systems to varying degrees. This work can provide theoretical guidance for evaluating the reliability of manufacturing systems of different types. [ABSTRACT FROM AUTHOR]

The seismic fragility of water supply networks is an important research component for lifeline engineering in earthquake-prone regions. An accurate computational model was established to rapidly and efficiently assess pipeline damage under seismic excitation. In this study, the fragility of the pipeline network is deduced based on Copula function technology and the series-parallel model. This solves the low accuracy problem caused by simplifying elbow, tee, and other nodes and ignores the correlation between connected components in the fragility calculation of the buried pipeline network. Then, the shaking table tests of the elbow pipe, tee pipe, and scale pipeline network are performed, and the prototype pipeline network's finite element comparative calculation model is also established. Then, the optimal Copula function for the pipeline network, the Gumbel Copula function, is obtained by calculating the correlation between each component's seismic demand. It was found that the seismic demand of pipe and elbow components in the sand is higher than that in the clay, while the opposite is valid for the tee component. After that, a two-parameter log-normal distribution is employed to obtain the seismic fragility of three types of components in different soil properties. It was also found that the maximum failure probability can be obtained from the elbow leakage. The fragility of the elbow pipe is greater than that of the tee pipe. The fragility of components is then applied to the fragility calculation of the scale pipeline network by a series-parallel model, and the obtained results are compared with numerical simulations. It is demonstrated that the series-parallel combination calculation-based results have a high safety reserve for the pipeline design. At present, urban municipal pipeline networks face many challenges in earthquake-prone regions, such as old pipeline infrastructure and poor seismic performance, which make their nodes and push-on joints vulnerable to damage. Based on the above social needs, this paper focuses on the accurate calculation theory of the seismic fragility of the buried water supply network. A more reasonable calculation method of the reliability of the pipeline network is established by considering the influence of the fragility of connected pipe components. This method employs the failure probability of various components to accurately calculate the fragility of the large and complex pipeline network. This study can provide basic theories for the seismic fragility of pipeline networks, the calculation of seismic connectivity, and the construction of resilient pipeline networks. In addition, the conclusions proposed in the study, such as the fragility comparison of tees and elbows and the design concept of "strong nodes", can guide the design of pipeline network nodes, which has great practical significance and social benefits. [ABSTRACT FROM AUTHOR]

Quantitatively analyze the uncertainties in turbulence models is of great meaning for research and engineering. In this paper, we develop a Bayesian uncertainty analysis framework based on copulas. The proposed framework is applied to the parametric uncertainty quantification and calibration of the shear-stress transport turbulence model for the flow over a Gaussian bump. A copula function is used to establish the correlation between variables and construct the weight function, which enables greater consideration of Bayesian inference. Prior analysis is conducted based on Sobol indices with the nonintrusive polynomial chaos method, demonstrating the important effects of κ , a 1 , and β ∗ on the flow, both for the wall force coefficients and the Reynolds shear stress. Next, the wall force coefficients and Reynolds shear stress are used as training sets to verify the effectiveness of the method. The results show that modeling the relationship based on copulas is necessary and effective, and that the weight function adaptively balances the influence of physical quantities at different inference locations. The proposed method effectively corrects the computational deviations of the corresponding physical quantities. In addition, the confidence interval for the posterior sample is increased, enhancing the likelihood of obtaining results close to the actual values. • A copula-based Bayesian uncertainty quantification framework with adaptive weight function is proposed. • Gaussian bump is a recently proposed meaningful geometry shape, attracting wide concerns, but has not been studied enough by now. • Detailed and innovative prior and posterior analysis is conducted. • The physical mechanisms of the parameters for separated flow are analyzed. [ABSTRACT FROM AUTHOR]

For solving the problem of the inevitable decline in the accuracy of cross-subject emotion recognition via Electroencephalograph (EEG) signal transfer learning due to the negative transfer of data in the source domain, this paper offers a new method to dynamically select the data suitable for transfer learning and eliminate the data that may lead to negative transfer. The method which is called cross-subject source domain selection (CSDS) consists of the next three parts. 1) First, a Frank-copula model is established according to Copula function theory to study the correlation between the source domain and the target domain, which is described by the Kendall correlation coefficient. 2) The calculation method for the Maximum Mean Discrepancy is improved to determine the distance between classes in a single source. After normalization, the Kendall correlation coefficient is superimposed, and the threshold is set to identify the source-domain data most suitable for transfer learning. 3) In the process of transfer learning, on the basis of Manifold Embedded Distribution Alignment, the Local Tangent Space Alignment method is used to provide a low-dimensional linear estimation of the local geometry of nonlinear manifolds, which maintains the local characteristics of the sample data after dimensionality reduction. Experimental results show that compared with the traditional methods, the CSDS increases the accuracy of emotion classification by approximately 2.8% and reduces the runtime by approximately 65%. [ABSTRACT FROM AUTHOR]

The characteristics of the multivariate wind loads field on the roof are crucial to the wind-resistant design of low-rise buildings, which contain the correlation characteristics in space and probability characteristics in the time domain. This paper proposes a framework for constructing a Joint Probability Density Function (Joint PDF) model for a multivariate wind loads field. It provides a detailed correlation analysis for the first time. This paper employs wind pressure data collected from the roof of a low-rise building during Typhoon Muifa. It was found that the correlation becomes more robust with increasing roof pitch and the wind pressures are strongly correlated with a correlation coefficient exceeding 0.50 when the roof pitch is above 15°. The mixture distribution model is applied to the probability density function fitting procedure of wind pressure time series under typhoon climate, and the fitting effect is significantly better than other classical probability density functions. The optimal copula function is determined according to the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for estimating the Joint PDF. The results reveal that Gumbel-copula and Student-copula have the highest proportion in optimal copula functions, accounting for over 90% of the total copula functions. Then, a bivariate Joint PDF for wind pressures are established with the optimal copula function. Additionally, the comparison between measured bivariate Joint PDF and that constructed using copula functions verifies the accuracy of the proposed framework for constructing Joint PDFs. The Joint PDF of wind pressures can enhance the understanding of the stochastic characteristics of local wind load fields on roofs, and the correlation characteristics in space provide crucial references for improving the accuracy of wind load random field simulation and saving the cost of wind resistance design. • A comprehensive correlation analysis of multivariate wind load field is carried out. • The wind pressures are strongly correlated when the roof pitch exceeds 15°. • The Gumbel-copula and Student-copula have the largest percentage of optimal copula function for the wind pressures. • The type of copula function is related to the symmetry of the correlation between the upper and lower tails. • The established joint probability density function model has an excellent fitting effect. [ABSTRACT FROM AUTHOR]

A hurricane event can often produce both intense rainfall and a storm tide that can cause a major compound flooding threat to coastlines. This paper examined applications of multivariate copula‐based time series models using data observed during Hurricane Irma (2017) along the coastlines of Florida, Georgia, and South Carolina, United States. Multivariate time series models were developed using bivariate copulas wherein storm tide and rainfall data were modeled using LOWESS‐based autoregressive moving average (ARMA). n samples of observed data were then synthesized using a Monte Carlo approach in which the empirical copula and the parametric estimate of the copula were obtained to approximate two‐sided p‐values using the Rosenblatt probability integral transform method. Analysis suggested that proper selection of the underlying LOWESS‐based ARMA model was the crucial aspect for modeling compound flooding wherein Archimedean, Elliptical, and Extreme Value copulas all offered consistent flexibility in terms of dependence modeling. As a backdrop to compound flood probabilities, this research also outlined both theoretical and applied frameworks for the calculation of non‐exceedance probabilities in a multidimensional environment using classical isofrequency probability assumptions for the "AND" (a bivariate joint probability) and Survival Kendall definitions. Random realizations from storm copulas combined with multivariate non‐exceedance probability definitions ultimately showed there were periods of temporal yet cyclical high intensities that lasted 1–2 hr. Lastly, a discussion is presented on the broader application of the proposed methodology within the field of engineering design and risk management which may serve as a catalyst for the continued research in compound flooding. Plain Language Summary: When a storm tide and intense rainfall simultaneously co‐occur in coastal areas, the potential for flooding is often much greater than from either independent event. Understanding how to assess the probability of these compound events is important in planning for and managing flood risks in coastal communities. This study investigated the temporal dynamics of these two phenomena during a landfalling hurricane across the southeast United States using a multivariate copula‐based time series model. The analysis revealed that storm tide dynamics were more accurately captured in the proposed model when compared to rainfall observations, although temporal rainfall was reasonably described by the model. This study highlights the temporal multivariate probabilistic approach needed to cope with compound flood risk assessment. All outcomes outlined herein are based on the theory of multivariate copula‐based dependence models with three application sites that illustrated the proposed methods. Key Points: The likelihood of joint occurrence of storm tide and intense rainfall is calculated using bivariate copulasMultivariate non‐exceedance probability of rainfall and storm tide was higher using the Survival Kendall (SK) definition when compared to the "AND" definitionCopulas analysis combined with multivariate non‐exceedance probability showed there were periods of temporal yet cyclical high intensities [ABSTRACT FROM AUTHOR]

Measuring the risks of the carbon financial market is of great significance for investment decision-making, risk supervision, and the healthy development of the carbon trading market. Different from previous studies based on traditional VaR (value at risk), this study measures the integrated risk of China's carbon market based on the Copula-EVT (Extreme Value Theory) -VaR model which can explore the unique strength of the copula and EVT-VaR models, of which the copula model is applied to capture the dependence between the different risk factors of carbon price volatility and macroeconomic fluctuation, while the EVT-VaR is used to explore the risk value. The empirical results show that the traditional VaR that only considers a single risk factor from carbon price volatility is likely to overestimate the risk. In addition, compared with other methods that do not consider the interdependence between risk factors, using the copula function to measure the carbon market integration risk is more effective, and backtesting also confirms this conclusion. This paper provides a specific reference for carbon emission companies to participate in the carbon market. It provides a theoretical basis for the supervision of the risk management of the carbon market. [ABSTRACT FROM AUTHOR]

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