Search Results (732)

Fatigue load modeling is crucial for optimizing and assessing the lifespan of floating wind turbines. This study addresses the complex characteristics of fatigue loads on floating wind turbines under the combined effects of wind and waves. We propose a fatigue load modeling approach based on Vine copula theory and machine learning. Firstly, we establish an optimal joint probability distribution model using Vine copula theory for the four-dimensional random variables (wind speed, wave height, wave period, and wind direction), with model fit assessed using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Root Mean Square Error (RMSE). Secondly, representative wind and wave load conditions are determined using Monte Carlo sampling based on the established joint probability distribution model. Thirdly, fatigue load simulations are performed using the high-fidelity simulator OpenFAST to compute Damage Equivalent Load (DEL) values for critical components (blade root and tower base). Finally, utilizing measured wind and wave data from the Lianyungang Ocean Observatory in the East China Sea, simulation tests are conducted. We apply five commonly used machine learning models (Kriging, MLP, SVR, BNN, and RF) to develop DEL models for blade root and tower base. The results indicate that the RF model exhibits the smallest prediction error, not exceeding 3.9%, and demonstrates high accuracy, particularly in predicting flapwise fatigue loads at the blade root, achieving prediction accuracies of up to 99.97%. These findings underscore the effectiveness of our approach in accurately predicting fatigue loads under real-world conditions, which is essential for enhancing the reliability and efficiency of floating wind turbines. Full article

Distributed photovoltaic (PV) output exhibits strong stochasticity and weak adjustability. After being integrated with the network, its interaction with stochastic loads increases the difficulty of assessing the distribution network’s static voltage stability (SVS). In response to this issue, this article presents a probabilistic assessment method for SVS in a distribution network with distributed PV that considers the bilateral uncertainties and correlations on the source and load sides. The probabilistic models for the uncertain variables are established, with the correlation between stochastic variables described using the Copula function. The three-point estimate method (3PEM) based on the Nataf transformation is used to generate correlated samples. Continuous power flow (CPF) calculations are then performed on these samples to obtain the system’s critical voltage stability state. The distribution curves of critical voltage and load margin index (LMI) are fitted using Cornish-Fisher series. Finally, the utility function is introduced to establish the degree of risk of voltage instability under different scenarios, and the SVS assessment of the distribution network is completed. The IEEE 33-node distribution system is utilized to test the method presented, and the results across various scenarios highlight the method’s effectiveness. Full article

Environmental uncertainties present a significant challenge in the design of onboard photovoltaic hybrid power systems (PV-HPS), a pivotal decarbonization technology garnering widespread attention in the shipping industry. Neglecting environmental uncertainties associated with photovoltaic (PV) output and hull resistance can lead to suboptimal solutions. To address this issue, this paper proposes a stochastic optimization method for PV-HPS, aiming to minimize greenhouse gas (GHG) emissions and lifecycle costs. Copula functions are employed to establish joint distributions of uncertainties in solar irradiance, ambient temperature, significant wave height, and wave period. Monte Carlo simulation, the bi-bin method, and the multi-objective particle swarm optimization (MOPSO) algorithm are utilized for scenario generation, scenario reduction, and design space exploration. The efficacy of the proposed method is demonstrated through a case study involving an unmanned ship. Additionally, deterministic optimization and two partial stochastic optimizations are conducted to underscore the importance of simultaneously considering environmental uncertainties related to power sources and hull resistance. The results affirm the proposed approach’s capability to reduce GHG emissions and lifecycle costs. A sensitivity analysis of bin number is performed to investigate the tradeoff between optimality and computation time. Full article

China is the largest soybean importer and consumer in the world. Soybean oil is the most-consumed vegetable oil in China, while soybean meal is the most important protein feed raw material in China, which affects the costs of animal husbandry. Volatility in the international soybean market would generate risk spillovers to China’s soybean industrial chain. This paper analyzed the channel of risk spillover from the international soybean market to China’s soybean industry chain and the asymmetry of the risk spillover. The degree of risk spillover from the international soybean market to the Chinese soybean industry chain was measured by the Copula–CoVaR model. The moderating role of inventory and demand in asymmetric risk spillovers was analyzed by quantile regression. We draw the following conclusions: First, the international soybean market impacts China’s soybean industry chain through soybeans rather than soybean meal and oil. The price fluctuation of China soybean market is obviously lower than that of the international soybean market. Second, there are apparent asymmetric risk spillovers from the international soybean market to China’s soybean industry chain, especially the soybean meal market. Third, increasing the Chinese soybean inventory and growing demand could effectively prevent the downside risk spillover from international markets to China’s soybean market. This also explains the asymmetry of risk spillovers. The research enriches the research perspective on food security, and the analysis of risk spillover mechanisms provides a scientific basis for relevant companies to develop risk-management strategies. Full article

This paper presents new classes of strong fuzzy negations, fuzzy implications and Copulas. It begins by presenting two theorems with function classes involving the construction of strong fuzzy negations. These classes are based on a well-known equilibrium point theorem. After that, a construction of fuzzy implication is presented, which is not based on any negation. Finally, moving on to the area concerning copulas, we present proof about the third property of copulas. To conclude, we will present two original constructions of copulas. All the above constructions are motivated by a specific formula. For some specific conditions of the variables x, y and other conditions for the function f(x), the formula presented produces strict and strong fuzzy negations, fuzzy implications and copulas. Full article

For multivariate non-Gaussian involving copulas, likelihood inference is dominated by the data in the middle, and fitted models might not be very good for joint tail inference, such as assessing the strength of tail dependence. When preliminary data and likelihood analysis suggest asymmetric tail dependence, a method is proposed to improve extreme value inferences based on the joint lower and upper tails. A prior that uses previous information on tail dependence can be used in combination with the likelihood. With the combination of the prior and the likelihood (which in practice has some degree of misspecification) to obtain a tilted log-likelihood, inferences with suitably transformed parameters can be based on Bayesian computing methods or with numerical optimization of the tilted log-likelihood to obtain the posterior mode and Hessian at this mode. Full article

Understanding the propagation characteristics and driving factors from meteorological drought to hydrological drought is essential for alleviating drought and for early warning systems regarding drought. This study focused on the Weihe River basin (WRB) and its two subregions (the Jinghe River (JRB) and the middle reaches of the Weihe River (MWRB)), utilizing the Standardized Precipitation Index (SPI) and Standardized Runoff Index (SRI) to characterize meteorological and hydrological drought, respectively. Based on Copula theory and conditional probability, a quantification model for the propagation time (PT) of meteorological–hydrological drought was constructed. The dynamic characteristics of PT on annual and seasonal scales were explored. Additionally, the influences of different seasonal meteorological factors and underlying surface factors on the dynamic changes in PT were analyzed. The main conclusions were as follows: (1) The PT of meteorological–hydrological drought was characterized by faster propagation during the hot months (June–September) and slower propagation during the cold months (December to March of the following year); (2) Under the same level of hydrological drought, as the level of meteorological drought increases, the PT of the drought shortens. The propagation thresholds of meteorological to hydrological drought in the WRB, the JRB, and the MWRB are −0.69, −0.81, and −0.78, respectively. (3) In the dynamic changes in PT, the WRB showed a non-significant decrease; however, both the JRB and the MWRB exhibited a significant increase in PT across different drought levels. (4) The influence of the water and heat status during spring, summer, and winter on PT was more pronounced, while in autumn, the impact of the basin’s water storage and discharge status was more significant in the JRB and the MWRB. Full article

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. Full article

We propose the “Marshall–Olkin Bivariate Weibull Model with Modified Singularity MOBW-$\mu$”, which focuses on bivariate distributions essential for reliability and survival analyses. Distributions such as the Marshall–Olkin bivariate exponential (MOBE) and the Marshall–Olkin bivariate Weibull (MOBW) are discussed. The MOBW-$\mu$ model is introduced, which incorporates a lag parameter $\mu$ in the singular part, and probabilistic properties such as the joint survival function, marginal density functions, and the bivariate hazard rate function are explored. In addition, aspects such as the correlation structure and survival copulation are addressed and we show that the correlation of the MOBW-$\mu$ is always lower than that of its copula, regardless of the parameters. The latter result implies that the MOBW-$\mu$ does not have the Lancaster’s phenomenon that explains that any nonlinear transformation of variables decreases the correlation in absolute value. The article concludes by presenting a robust theoretical framework applicable to various disciplines. Full article

The generation of synthetic data holds significant promise for augmenting limited datasets while avoiding privacy issues, facilitating research, and enhancing machine learning models’ robustness. Generative Adversarial Networks (GANs) stand out as promising tools, employing two neural networks—generator and discriminator—to produce synthetic data that mirrors real data distributions. This study evaluates GAN variants (CTGAN, CopulaGAN), a variational autoencoder, and copulas on diverse real datasets of different complexity encompassing numerical and categorical attributes. The results highlight CTGAN’s sensitivity to training parameters and TVAE’s robustness across datasets. Scalability challenges persist, with GANs demanding substantial computational resources. TVAE stands out for its high utility across all datasets, even for high-dimensional data, though it incurs higher privacy risks, which is indicative of the curse of dimensionality. While no single model universally excels, understanding the trade-offs and leveraging model strengths can significantly enhance synthetic data generation (SDG). Future research should focus on adaptive learning mechanisms, scalability enhancements, and standardized evaluation metrics to advance SDG methods effectively. Addressing these challenges will foster broader adoption and application of synthetic data. Full article

Background/Objectives: The forced social isolation implemented to prevent the spread of the COVID-19 virus was accompanied by a worsening of mental health, an increase in insomnia symptoms, and the emergence of ‘skin hunger’—an increased longing for personal touch. This study aimed to enhance our understanding of the interconnection between sleep, mental health, and the need for physical (NPC) and real-life social contact (NRL-SC). Methods: A total of 2827 adults participated in an online survey during the second COVID-19 lockdown. A Bayesian Gaussian copula graphical model (BGCGM) and a Bayesian-directed acyclic graph (DAG) were estimated, and mixed ANOVAs were carried out. Results: NPC with non-family members (t(2091) = 12.55, p < 0.001, d = 0.27) and relational lifestyle satisfaction (t(2089) = 13.62, p < 0.001, d = 0.30) were lower during the second lockdown than before the pandemic. In our BGCGM, there were weak positive edges between the need for PC and RL-SC on one hand and sleep and mental health on the other. Conclusions: During the second lockdown, people craved less physical contact with non-family members and were less satisfied with their relational lifestyle than before the pandemic. Individuals with a greater need for PC and RL-SC reported poorer mental health (i.e., worry, depression, and mental fatigue). Full article

Financial markets are increasingly interlinked. Therefore, this study explores the complex relationships between the Tadawul All Share Index (TASI), West Texas Intermediate (WTI) crude oil prices, and Bitcoin (BTC) returns, which are pivotal to informed investment and risk-management decisions. Using copula-based models, this study identified Student’s t copula as the most appropriate one for encapsulating the dependencies between TASI and BTC and between TASI and WTI prices, highlighting significant tail dependencies. For the BTC–WTI relationship, the Frank copula was found to have the best fit, indicating nonlinear correlation without tail dependence. The predictive power of the identified copulas were compared to that of Long Short-Term Memory (LSTM) networks. The LSTM models demonstrated markedly lower Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Scaled Error (MASE) across all assets, indicating higher predictive accuracy. The empirical findings of this research provide valuable insights for financial market participants and contribute to the literature on asset relationship modeling. By revealing the most effective copulas for different asset pairs and establishing the robust forecasting capabilities of LSTM networks, this paper sets the stage for future investigations of the predictive modeling of financial time-series data. The study highlights the potential of integrating machine-learning techniques with traditional econometric models to improve investment strategies and risk-management practices. Full article

This article proposes a novel methodology for estimating metallurgical copper recovery, a critical feature in mining project evaluations. The complexity of modeling this nonadditive variable using geostatistical methods due to low sampling density, strong heterotopic relationships with other measurements, and nonlinearity is highlighted. As an alternative, a copula-based conditional quantile regression method is proposed, which does not rely on linearity or additivity assumptions and can fit any statistical distribution. The proposed methodology was evaluated using geochemical log data and metallurgical testing from a simulated block model of a porphyry copper deposit. A highly heterotopic sample was prepared for copper recovery, sampled at 10% with respect to other variables. A copula-based nonparametric dependence model was constructed from the sample data using a kernel smoothing method, followed by the application of a conditional quantile regression for the estimation of copper recovery with chalcocite content as secondary variable, which turned out to be the most related. The accuracy of the method was evaluated using the remaining 90% of the data not included in the model. The new methodology was compared to cokriging placed under the same conditions, using performance metrics RMSE, MAE, MAPE, and R². The results show that the proposed methodology reproduces the spatial variability of the secondary variable without the need for a variogram model and improves all evaluation metrics compared to the geostatistical method. Full article

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. Full article

There are many families of bivariate distributions with given marginals. Most families, such as the Farlie–Gumbel–Morgenstern (FGM) and the Ali–Mikhail–Haq (AMH), are absolutely continuous, with an ordinary probability density. In contrast, there are few families with a singular part or a positive mass on a curve. We define a general condition useful to detect the singular part of a distribution. By continuous extension of the bivariate diagonal expansion, we define and study a wide family containing these singular distributions, obtain the probability density, and find the canonical correlations and functions. The set of canonical correlations is described by a continuous function rather than a countable sequence. An application to statistical inference is given. Full article