Search Results (120)

To address the challenges of high complexity in modeling the correlation of multi-dimensional stochastic variables and the difficulty of solving long-term scheduling models in continuous action spaces in multi-energy complementary systems, this paper proposes a long-term optimization scheduling method based on Deep Deterministic Policy Gradient (DDPG). First, an improved C-Vine Copula model is used to construct the multi-dimensional joint probability distribution of water, wind, and solar energy, and Latin Hypercube Sampling (LHS) is employed to generate a large number of water–wind–solar coupling scenarios, effectively reducing the model’s complexity. Then, a long-term optimization scheduling model is established with the goal of maximizing the absorption of clean energy, and it is converted into a Markov Decision Process (MDP). Next, the DDPG algorithm is employed with a noise dynamic adjustment mechanism to optimize the policy in continuous action spaces, yielding the optimal long-term scheduling strategy for the water–wind–solar multi-energy complementary system. Finally, using a water–wind–solar integrated energy base as a case study, comparative analysis demonstrates that the proposed method can improve the renewable energy absorption capacity and the system’s power generation efficiency by accurately quantifying the uncertainties of water, wind, and solar energy and precisely controlling the continuous action space during the scheduling process. Full article

Ensuring the security of agricultural systems is essential for achieving national food security and sustainable development. Given that agricultural systems are inherently complex and composed of coupled subsystems—such as water, land, and energy—a comprehensive and multidimensional assessment of system security is necessary. This study focuses on Northeast China, a major food-producing region, and introduces the concept of agricultural system coupling security, defined as the integrated performance of an agricultural system in terms of resource adequacy, internal coordination, and adaptive resilience under external stress. To operationalize this concept, a coupling security evaluation framework is constructed based on three key dimensions: reliability (Rel), coordination (Cor), and resilience (Res). An Agricultural System Coupling Security Index (AS-CSI) is developed using the entropy weight method, the Criteria Importance Through Intercriteria Correlation (CRITIC) method, and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, while obstacle factor diagnosis is employed to identify key constraints. Furthermore, bivariate and trivariate Copula models are used to estimate joint risk probabilities. The results show that from 2001 to 2022, the AS-CSI in Northeast China increased from 0.38 to 0.62, indicating a transition from insecurity to relative security. Among the provinces, Jilin exhibited the highest CSI due to balanced performance across all Rel-Cor-Res dimensions, while Liaoning experienced lower Rel, hindering its overall security level. Five indicators, including area under soil erosion control, reservoir storage capacity per capita, pesticide application amount, rural electricity consumption per capita, and proportion of agricultural water use, were identified as critical threats to regional agricultural system security. Copula-based risk analysis revealed that the probability of Rel–Cor reaching the relatively secure threshold (0.8) was the highest at 0.7643, and the probabilities for Rel–Res and Cor–Res to reach the same threshold were lower, at 0.7164 and 0.7318, respectively. The probability of Rel–Cor-Res reaching the relatively secure threshold (0.8) exceeds 0.54, with Jilin exhibiting the highest probability at 0.5538. This study provides valuable insights for transitioning from static assessments to dynamic risk identification and offers a scientific basis for enhancing regional sustainability and economic resilience in agricultural systems. Full article

New copula families are constructed based on orthogonality in $L^2(0,1)$. Subclasses of idempotent copulas with square integrable densities are derived. It is shown that these copulas generate exchangeable Markov chains that behave as independent and identically distributed random variables conditionally on the initial variable. We prove that the extracted family of copulas is the only set of symmetric idempotent copulas with square integrable densities. We extend these copula families to asymmetric copulas with square integrable densities having special dependence properties. One of our extensions includes the Farlie–Gumbel–Morgenstern (FGM) copula family. The mixing properties of Markov chains generated by these copulas are established. The Spearman’s correlation coefficient ${\rho }_S$ is provided for each of these copula families. Some graphs are also provided to illustrate the properties of the copula densities. Full article

To address the impacts of source load temporal–spatial uncertainties on distribution network planning considering the global transition towards sustainable energy systems with high-penetration photovoltaic (PV) integration, this paper proposes a source–network–storage coordinated stochastic planning method. A temporal–spatial correlation probability model for PV output and load demand is constructed based on Copula theory. Scenario generation and efficient reduction are achieved through Monte Carlo sampling and K-means clustering, extracting representative daily scenarios that preserve the temporal–spatial characteristics. A coordinated planning model targeting the minimization of comprehensive costs is established to holistically optimize PV deployment, energy storage system (ESS) configuration, and network expansion schemes. Simulations on typical distribution network systems demonstrate that the proposed method, by integrating temporal–spatial correlation modeling and multi-element collaborative decision-making, significantly improves PV accommodation capacity and reduces planning costs while improving the overall economic efficiency of distribution network planning. This study provides a robust technical pathway for developing economically viable and resilient distribution networks capable of integrating large-scale renewable energy, thereby contributing to the decarbonization of the power sector and advancing the goals of sustainable energy development. Full article

The large-scale integration of renewable energy and the use of high-energy-consuming equipment in agricultural parks have a great influence on the security of rural distribution networks. To ensure reliable power delivery for residential and agricultural activities and sustainable management of distributed energy resources, this paper develops a distributed generation-supported interactive optimization framework coordinating distribution networks and agricultural parks. Specifically, a wind–photovoltaic scenario generation method based on Copula functions is first proposed to characterize the uncertainties of renewable generation. Based on the generated scenario, a bi-level interactive optimization framework consisting of a distribution network and agricultural park is constructed. At the upper level, the distribution network operators ensure the security of the distribution network by reconfiguration, coordinated distributed resource dispatch, and dynamic price compensation mechanisms to guide the agricultural park’s electricity consumption strategy. At the lower level, the agricultural park users maximize their economic benefits by adjusting controllable loads in response to price compensation incentives. Additionally, an improved particle swarm optimization combined with a Gurobi solver is proposed to obtain equilibrium by iterative solving. The simulation analysis demonstrates that the proposed method can reduce the operation costs of the distribution network and improve the satisfaction of users in agricultural parks. Full article

The classical exponential model, despite its flexibility, fails to describe data with non-constant failure or between-event dependency. To overcome this limitation, two new bivariate lifetime distributions are introduced in this paper. The Farlie–Gumbel–Morgenstern (FGM)-based and Ali–Mikhail–Haq (AMH)-based modified Fréchet–exponential (MFE) models, by embedding the flexible MEF margin in the FGM and AMH copulas. The resulting distributions accommodate a wide range of positive or negative dependence while retaining analytical traceability. Closed-form expressions for the joint and marginal density, survival, hazard, and reliability functions are derived, together with product moments and moment-generating functions. Unknown parameters are estimated through the maximum likelihood estimation (MLE) and inference functions for margins (IFM) methods, with asymptotic confidence intervals provided for these parameters. An extensive Monte Carlo simulation quantifies the bias, mean squared error, and interval coverage, indicating that IFM retains efficiency while reducing computational complexity for moderate sample sizes. The models are validated using two real datasets, from the medical sector regarding the infection recurrence times of 30 kidney patients undergoing peritoneal dialysis, and from the economic sector regarding the growth of the gross domestic product (GDP). Overall, the proposed copula-linked MFE distributions provide a powerful and economical framework for survival analysis, reliability, and economic studies. Full article

Cuffless continuous blood pressure (BP) monitoring is essential for personal health management. However, its accuracy is challenged by the diversity and heterogeneity of physiological data sources. We propose a multi-source feature selection framework based on Markov blanket theory and the concept of causal invariance. We extracted 218 BP-related photoplethysmography (PPG) features from three heterogeneous datasets (differing in subject population, acquisition devices, and methods) and constructed a causal feature set using the Multi-Dataset Stable Feature Selection via Ensemble Markov Blanket (MDSFS-EMB) algorithm. BP estimation was then performed using four machine learning models. The MDSFS-EMB algorithm integrated PPFS and HITON-MB, enabling adaptability to different data scales and distribution scenarios. It employed Gaussian Copula Mutual Information, which was robust to outliers and capable of modeling nonlinear relationships. To validate the effectiveness of the selected feature set, we conducted experiments using an independent external validation dataset and explored the impact of data segmentation strategies on model prediction outcomes. The results demonstrated that the MDSFS-EMB algorithm has advantages in feature selection efficiency, prediction accuracy, and generalization capability. This study innovatively explores the causal relationships between PPG features and BP across multiple data sources, providing a clinically applicable approach for cuffless BP estimation. Full article

The volatility and uncertainty of wind power output pose significant challenges to the safe and stable operation of power systems. To enhance the economic efficiency and reliability of day-ahead scheduling in wind farms, this paper proposes a day-ahead planning and scheduling method for wind/storage systems based on multi-scenario generation and Conditional Value-at-Risk (CVaR). First, based on the statistical characteristics of historical wind power forecasting errors, a kernel density estimation method is used to fit the error distribution. A Copula-based correlation model is then constructed to generate multi-scenario wind power output sequences that account for spatial correlation, from which representative scenarios are selected via K-means clustering. An objective function is subsequently formulated, incorporating electricity sales revenue, energy storage operation and maintenance cost, initial state-of-charge (SOC) cost, peak–valley arbitrage income, and penalties for schedule deviations. The initial SOC of the storage system is introduced as a decision variable to enable flexible and efficient coordinated scheduling of the wind/storage system. The storage system is implemented using a 1500 kWh/700 kW lithium iron phosphate (LiFePO₄) battery to enhance operational flexibility and reliability. To mitigate severe profit fluctuations under extreme scenarios, the model incorporates a CVaR-based risk constraint, thereby enhancing the reliability of the day-ahead plan. Finally, simulation experiments under various initial SOC levels and confidence levels are conducted to validate the effectiveness of the proposed method in improving economic performance and risk management capability. Full article

As global warming progresses, quantifying drought thresholds for crop yield losses is crucial for food security and sustainable agriculture. Based on the CNN-LSTM model and Copula function, this study constructs a conditional probability framework for yield losses under future climate change. It analyzes the relationship between the Standardized Precipitation–Evapotranspiration Index (SPEI) and winter wheat yield, assesses the vulnerability of winter wheat in various regions to drought stress, and quantifies the drought thresholds under climate change. The results showed that (1) SPEI in Zhoukou, Sanmenxia, and Nanyang was significantly correlated with yield; (2) the drought vulnerability of southern and eastern was higher than that of center, western, and northern in the past (2000–2023) and future (2024–2047); (3) there were significant differences in drought thresholds. The yield loss of winter wheat below 30, 50, and 70 percentiles in southern and eastern (past/future) were −1.86/−2.47, −0.85/−1.39, and 0.60/0.35 (Xinyang); −1.45/−2.16, −0.75/−1.34, −0.17/−0.43 (Nanyang); −1.47/−2.24, −0.97/−1.61, 0.69/0.28 (Zhoukou); −2.18/−2.86, −1.80/−2.36, −0.75/−1.08 (Kaifeng), indicating that the drought threshold will reduce in the future. This is mainly due to the different climate and soil conditions in different regions of Henan Province. In the context of future climate change, droughts will be more frequent. Hence, the research results provide a valuable reference for the efficient utilization of agricultural water resources and the prevention and control of drought risk under climate change in the future. Full article

To address the enhanced coupling characteristics in reactive power partitioning of power grids with high-penetration renewable energy integration, this paper proposes an optimized reactive power partitioning method that integrates dynamic source–load correlation characteristics and regional coupling degree evaluation. Conventional static electrical distance-based partitioning methods struggle to adapt to dynamic coupling effects caused by renewable energy output fluctuations, leading to degraded partition decoupling performance. This study innovatively constructs a Copula function-based joint probability distribution model for source–load correlation. By employing non-parametric estimation and undetermined coefficient methods to solve marginal distribution parameters, and utilizing the K-means clustering algorithm to generate typical scenario sets, a comprehensive source–load coupling evaluation framework is established, incorporating the renewable energy output proportion and time-varying correlation index. For electrical distance calculation, a generalized construction method for extended sensitivity matrices is proposed, featuring dynamic weight adjustment through regional coupling degree correction factors. Simulation results demonstrate that in practical case studies, compared with traditional partitioning schemes, the proposed method reduces the regional coupling degree metric by 4.216% and enhances the regional reactive power imbalance index suppression by 11.082%, validating its effectiveness in achieving reactive power local balance and reactive power partitioning. This research breaks through the theoretical limitations of static partitioning and provides theoretical support for dynamic zonal control in modern power systems with high renewable penetration. Full article

To enhance the accuracy and real-time capability of estimated in-block time (EIBT) predictions at airports, this study proposes a two-stage integrated prediction method. By extending the prediction time window for arrival times, this method systematically models and analyzes the integrated arrival time, thereby achieving precise EIBT predictions. This study divides the arrival process into the approach flight stage and the taxi-in stage, constructing predictive models for each and identifying key influencing factors. Additionally, copula entropy is employed to optimize feature selection. Based on operational data from Shanghai Pudong International Airport, a LightGBM-based prediction model was developed and validated across multiple datasets. The results demonstrate that the two-stage integrated forecasting method significantly outperforms single-stage modeling, with the best model achieving a prediction accuracy of 87.11% within a ±5 min error margin. Furthermore, this study validates the effectiveness of copula entropy in enhancing model prediction performance. This research provides theoretical support and practical references for improving the real-time predictive capabilities of airport collaborative decision-making systems, as well as a technical pathway for integrated air-surface management research at multi-runway airports. Full article

Climate change and urbanization are increasingly threatening urban environments through pluvial flooding, prompting the widespread use of coupled hydrological–hydrodynamic models. These models provide accurate urban flood simulations and forecasting capabilities, and they can analyze the benefits of low-impact development stormwater control measures in surface-flooding processes. However, most studies have primarily focused on analyzing the stormwater control effects for specific flood events, lacking an analytical framework that accounts for uncertainty. This research proposes a framework for evaluating uncertainty in urban pluvial-flood stormwater control, combining urban-scale simulation, stormwater control modeling, and uncertainty analysis, while constructing nonlinear dependencies between the features reflecting the surface-flood-control benefits. Based on uncertainty analysis and copula methods, this research aims to support sustainable urban planning and provide a sustainable decision-making approach for urban stormwater management. The results show that the uncertainty assessment method based on generalized likelihood uncertainty is effective. By comparing the posterior joint distribution with the prior joint distribution, for different governance performance metrics, the joint, synergistic, conditional, and combined governance effects all exhibit consistent trends as the metrics change. The current research presents an innovative method for simulating and analyzing stormwater control benefits at the urban scale, providing valuable insights for urban sustainable development and flood mitigation strategies. Full article

Monitoring agricultural drought is crucial for mitigating yield losses in winter wheat, especially in the Huang-Huai-Hai (HHH) region of China. Current drought indices often fall short in accurately representing the water supply–demand dynamics for crops, neglect irrigation practices, and overemphasize drought intensity rather than its evolution and overall impact. To address these concerns, we developed a novel transpiration drought index utilizing the Water Balance for Winter Wheat (WBWW) model. This index integrated variations in atmospheric conditions, soil moisture conditions, crop resistance, and irrigation practices to enhance the evaluation of water supply and demand dynamics. The WBWW model was initially validated against field transpiration measurements, achieving an R² of 0.7573, thereby confirming its reliability for subsequent analyses. To create a mechanistic understanding of crop water supply and demand, we adopted the reduction rate of actual and potential transpiration to identify drought events and constructed joint probability distributions of drought duration and severity using copulas. This led to the development of the Winter Wheat Drought Assessment Index (WDAI). The grade threshold for the WDAI was established based on historical drought data from the HHH region through a series of statistical threshold determination methods. Our findings showed that the WDAI successfully identified 87.36% of drought samples according to their recorded grades, with 97.13% within one grade of historical records. Comparative analyses with retained regional data and existing indices—the Crop Water Deficit Index (CWDI) and the Relative Soil Moisture Index (RSMI)—further demonstrated its effectiveness. Our study represents a robust tool for dynamic drought monitoring in the HHH region and offers critical insights into agricultural irrigation practices. Full article

This paper addresses the challenge of assessing photovoltaic (PV) hosting capacity in distribution networks while accounting for the uncertainty of PV output, a critical step toward achieving sustainable energy transitions. Traditional optimization methods for dealing with uncertainty, including robust optimization (RO) and stochastic optimization (SO), often result in overly conservative or optimistic assessments, hindering the efficient integration of renewable energy. To overcome these limitations, this paper proposes a novel distributionally robust chance-constrained (DRCC) assessment method based on Kullback–Leibler (KL) divergence. First, the time-segment adaptive bandwidth kernel density estimation (KDE) combined with Copula theory is employed to model the conditional probability density of PV forecasting errors, capturing temporal and output-dependent correlations. The KL divergence is then used to construct a fuzzy set for PV output, quantifying its uncertainty within specified confidence levels. Finally, the assessment results are derived by integrating the fuzzy set into the optimization model. Case studies demonstrate its effectiveness of the method. Key findings indicate that higher confidence levels reduce PV hosting capacities due to broader uncertainty ranges, while increased historical sample sizes enhance the accuracy of distribution estimates, thereby increasing assessed capacities. By balancing conservatism and optimism, this method enables safer and more efficient PV integration, directly supporting sustainability goals such as reducing fossil fuel dependence and lowering carbon emissions. The findings provide actionable insights for grid operators to maximize renewable energy utilization while maintaining grid stability, advancing global efforts toward sustainable energy infrastructure. Full article

This study is based on the stock returns of 11 subindustry markets in the international clean energy market from 2010 to 2024 and constructs a skewed t distribution dynamic factor copula model. The time-varying load factor is used to characterize the correlation between a single subindustry market and the entire system, and the joint probability of distress is calculated as a measure of the overall level of systemic risk. Two indicators, Systemic Vulnerability Degree and Systemic Importance Degree, are introduced to evaluate the vulnerability of a single subindustry market in systemic risk and its contribution to systemic risk. A conditional risk-spillover index is constructed to measure the risk-spillover level between subindustry markets. This method fully considers the individual differences and inherent correlations of the international clean energy market subsectors, as well as the fat tail and asymmetry of returns, thus capturing more information and more timely information. This study found that the correlation between subindustry markets changes over time, and during the crisis, the market correlation shows a significant upward trend. In the measurement of the overall level of systemic risk, the joint probability of distress can identify the changes in systemic risk in the international clean energy market. The systemic risk of the international clean energy market presents the characteristics of rapid and multiple outbreaks, and the joint default risk probability of the whole system can exceed 0.6. The outbreak of systemic risk is closely related to a series of major international events, showing a strong correlation. In addition, the systemic vulnerability analysis found that the biofuel market has the lowest systemic vulnerability, and the advanced materials market has the highest vulnerability. The energy efficiency market is considered to be the most important market in the system. The advanced materials market and renewable energy market play a dominant role in the risk contribution to other markets, while the geothermal market, solar market, and wind energy market are net risk overflow parties in the tail risk impact, and the developer market and fuel cell market are net risk receivers. This study provides a theoretical basis for systemic risk management and ensuring the stability of the international clean energy market. Full article