Search Results (11)

The representativeness of long-term wind data at a site remains a challenge, as it is essential for resource analysis, production adjustment in operating plants, and the simulation of hybridised plants. A representative one-year hourly time series, known as a Wind Reference Year (WRY), is required, yet the availability of long-term real data is rare, making the estimation of WRY from reanalysis data and shorter measurement campaigns a common approach. In this study, Gaussian Mixture Copula Models (GMCM) and five regression models were applied and compared. The GMCM was trained using 15 years of reanalysis data to generate simulations, and subsequently, regression-based Measure–Correlate–Predict (MCP) methods were applied to adapt the simulated reference year to site-specific conditions. Finally, the Hungarian algorithm was used to reorder the simulated data series, aligning it with a typical wind pattern and producing the WRY dataset. The results were validated against 15 years of real measurements and benchmarked against a heuristic method based on long-term similarity of main wind parameters and the commercial tool Windographer. The findings demonstrate the potential of the proposed method, showing improvements over existing techniques and providing a robust approach to constructing representative WRY datasets. Full article

This study proposes Bayesian estimation of multivariate regular vine (R-vine) copula models with generalized autoregressive conditional heteroskedasticity (GARCH) margins modeled by Gaussian-mixture distributions. The Bayesian estimation approach includes Markov chain Monte Carlo and variational Bayes with data augmentation. Although R-vines typically involve computationally intensive procedures limiting their practical use, we address this challenge through parallel computing techniques. To demonstrate our approach, we employ thirteen bivariate copula families within an R-vine pair-copula construction, applied to a large number of marginal distributions. The margins are modeled as exponential-type GARCH processes with intertemporal capital asset pricing specifications, using a mixture of Gaussian and generalized Pareto distributions. Results from an empirical study involving 100 financial returns confirm the effectiveness of our approach. Full article

Ultra-high-performance concrete (UHPC) mixtures exhibit tightly coupled ingredient–property relations and heterogeneous reporting, which complicate the data-driven prediction of compressive and flexural strength. We present an end-to-end framework that (i) harmonizes mixture records, (ii) completes numeric features using a dependence-preserving Gaussian copula routine, and (iii) standardizes/encodes predictors with training-only fits. The feature space focuses on domain ratios and concise interactions (water–binder, superplasticizer–binder, total fiber, water–binder, superplasticizer–binder, and fiber normalized by water–binder). A physics-informed multi-task neural network (PINN) is trained in log space with Smooth-L1 supervision and learned per-task noise scales for uncertainty-weighted balancing, while soft monotonicity penalties are applied to input gradients so that predicted strength is non-increasing in water–binder (both targets) and, when available, non-decreasing in fiber content for flexural response. In parallel, histogram-based gradient boosting is fitted per target; a convex combination is then selected on the validation slice and fixed for testing. On the held-out sets, the blended model attains an MAE/RMSE/R² of 10.86 MPa/14.68 MPa/0.848 MPa for compressive strength and 2.78 MPa/3.67 MPa/0.841 MPa for flexural peak, improving over the best single family by 0.5 RMSE (compressive) and 0.16 RMSE (flexural), with corresponding R² gains of 0.01–0.02. Residual-versus-prediction diagnostics and predicted–actual overlays indicate aligned trends and reduced heteroscedastic tail errors. Full article

We introduce a distributional CNN-LSTM framework for probabilistic multivariate modeling and heterogeneous treatment effect (HTE) estimation. The model jointly captures complex dependencies among multiple outcomes and enables precise estimation of individual-level conditional average treatment effects (CATEs). In simulation studies with multivariate Gaussian mixtures, the CNN-LSTM demonstrates robust density estimation and strong CATE recovery, particularly as mixture complexity increases, while classical methods such as Kernel Density Estimation (KDE) and Gaussian Copulas may achieve higher log-likelihood or coverage in simpler scenarios. On real-world datasets, including Iris and Criteo Uplift, the CNN-LSTM achieves the lowest CATE RMSE, confirming its practical utility for individualized prediction, although KDE and Gaussian Copula approaches may perform better on global likelihood or coverage metrics. These results indicate that the CNN-LSTM can be trained efficiently on moderate-sized datasets while maintaining stable predictive performance. Overall, the framework is particularly valuable in applications requiring accurate individual-level effect estimation and handling of multimodal heterogeneity—such as personalized medicine, economic policy evaluation, and environmental risk assessment—with its primary strength being superior CATE recovery under complex outcome distributions, even when likelihood-based metrics favor simpler baselines. Full article

Online learning has become increasingly prevalent in real-world applications, where data streams often comprise heterogeneous feature types—both nominal and numerical—and labels may not arrive synchronously with features. However, most existing online learning methods assume homogeneous data types and synchronous arrival of features and labels. In practice, data streams are typically heterogeneous and exhibit asynchronous label feedback, making these methods insufficient. To address these challenges, we propose a novel algorithm, termed Online Asynchronous Learning over Streaming Nominal Data (OALN), which maps heterogeneous data into a continuous latent space and leverages a model pool alongside a hint mechanism to effectively manage asynchronous labels. Specifically, OALN is grounded in three core principles: (1) It utilizes a Gaussian mixture copula in the latent space to preserve class structure and numerical relationships, thereby addressing the encoding and relational learning challenges posed by mixed feature types. (2) It performs adaptive imputation through conditional covariance matrices to seamlessly handle random missing values and feature drift, while incrementally updating copula parameters to accommodate dynamic changes in the feature space. (3) It incorporates a model pool and hint mechanism to efficiently process asynchronous label feedback. We evaluate OALN on twelve real-world datasets; the average cumulative error rates are 23.31% and 28.28% under the missing rates of 10% and 50%, respectively, and the average AUC scores are 0.7895 and 0.7433, which are the best results among the compared algorithms. And both theoretical analyses and extensive empirical studies confirm the effectiveness of the proposed method. Full article

To investigate an appropriate wind load design for buildings considering dynamic air density changes, classical extreme value and copula theories were utilized. Using wind speed, air temperature, and air pressure data from 123 meteorological stations in Shandong Province from 2004 to 2017, a joint probability distribution model was established for extreme wind speed and air density. The basic wind pressure was calculated for various conditional return periods. The results indicated that the Gumbel and Gaussian mixture model distributions performed well in extreme wind speed and air density fitting, respectively. The joint extreme wind speed and air density distribution exhibited a distinct bimodal pattern. The higher the wind speed was, the greater the air density for the same return conditional period. For the 10-year return period, the air density surpassed the standard air density, exceeding 1.30 kg/m³. The basic wind pressures under the different conditional return periods were more than 10% greater than those calculated from standard codes. Applying the air density based on the conditional return period in engineering design could enhance structural safety regionally. Full article

This study uses a hybrid model of the exponential generalised auto-regressive conditional heteroscedasticity (eGARCH)-extreme value theory (EVT)-Gumbel copula model to investigate the dependence structure between Bitcoin and the South African Rand, and quantify the portfolio risk of an equally weighted portfolio. The Gumbel copula, an extreme value copula, is preferred due to its versatile ability to capture various tail dependence structures. To model marginals, firstly, the eGARCH(1, 1) model is fitted to the growth rate data. Secondly, a mixture model featuring the generalised Pareto distribution (GPD) and the Gaussian kernel is fitted to the standardised residuals from an eGARCH(1, 1) model. The GPD is fitted to the tails while the Gaussian kernel is used in the central parts of the data set. The Gumbel copula parameter is estimated to be $\alpha =1.007$, implying that the two currencies are independent. At 90%, 95%, and 99% levels of confidence, the portfolio’s diversification effects (DE) quantities using value at risk (VaR) and expected shortfall (ES) show that there is evidence of a reduction in losses (diversification benefits) in the portfolio compared to the risk of the simple sum of single assets. These results can be used by fund managers, risk practitioners, and investors to decide on diversification strategies that reduce their risk exposure. Full article

Wind turbine components’ failure prognosis allows wind farm owners to apply predictive maintenance techniques to their fleets. Determining the health status of a turbine’s component typically requires verifying many variables that should be monitored simultaneously. The scope of this study is the selection of the more relevant variables and the generation of a health status indicator (Failure Index) to be considered as a decision criterion in Operation and Maintenance activities. The proposed methodology is based on Gaussian Mixture Copula Models (GMCMs) combined with a smoothing method (Cubic spline smoothing) to define a component’s health index based on the previous behavior and relationships between the considered variables. The GMCM allows for determining the component’s status in a multivariate environment, providing the selected variables’ joint probability and obtaining an easy-to-track univariate health status indicator. When the health of a component is degrading, anomalous behavior becomes apparent in certain Supervisory Control and Data Acquisition (SCADA) signals. By monitoring these SCADA signals using this indicator, the proposed anomaly detection method could capture the deviations from the healthy working state. The resulting indicator shows whether any failure is likely to occur in a wind turbine component and would aid in a preventive intervention scheduling. Full article

The univariate alpha power exponential (APE) distribution has several appealing characteristics. It behaves similarly to Weibull, Gamma, and generalized exponential distributions with two parameters. In this paper, we consider different bivariate mixture models starting with two independent univariate APE models, and, in the latter case, starting from two dependent APE models. Several useful structural properties of such a mixture model (under the assumption of two independent APE distribution) are discussed. Bivariate APE (BAPE), in short, modelled under the dependent set up are also discussed in the context of a copula-based construction. Inferential aspects under the classical and under the Bayesian paradigm are considered to estimate the model parameters, and a simulation study is conducted for this purpose. For illustrative purposes, a well-known motor data is re-analyzed to exhibit the flexibility of the proposed bivariate mixture model. Full article

In the short-term operation of the power generation of cascade reservoirs, uncertainty factors such as inflow forecast errors could cause various types of risks. The inflow to a downstream reservoir is not only affected by inflow forecast errors from upstream reservoirs but also the forecast errors associated with inflow to the stream segment between the reservoirs, such as from a tributary. The inflow forecast errors of different forecast periods may also be correlated. To address this multivariate problem, the inflow forecast error variables were jointly fitted in this study using the Gaussian mixture model (GMM) and a t-Copula function based on the analysis of the error distribution characteristics in different forecast periods. Therefore, a stochastic model that coupled with the GMM and t-Copula to calculate inflow forecast errors in multiple forecast periods was established. Furthermore, according to the simulation results of the stochastic model and the predicted runoff series, a set of simulated runoff processes were obtained. Then they were combined with the existing power generation plan to carry out the risk analysis for short-term operation of the power generation in a cascade reservoir. The approach was evaluated using the Jinguan cascade hydropower system within the Yalong River basin as a case study. For this case study, the risk analysis for short-term operation of the power generation was analyzed based on stochastic simulation of the inflow forecast errors; the results show the feasibility and effectiveness of the proposed methods. Full article

Extreme precipitation can seriously affect the ecological environment, agriculture, human safety, and property resilience. A full-scale and scientific assessment in extreme precipitation characteristics is necessary for water resources management and providing decision-making support to mitigate the potential losses brought by extreme precipitation. In the present study, a multidimensional risk assessment framework is developed to investigate the spatial–temporal changes in different extreme precipitation indicators. The Gaussian mixture model (GMM) is applied to fit the distribution for each indicator and carry out single index risk assessment. The joint probabilistic features of multiple extreme indicators can be explored through coupling the GMM distributions into copulas. In addition, the moving window approach and the Mann–Kendall test are integrated to examine non-stationary risks (evaluated by “AND”, “OR”, and Kendall return periods) of multidimensional indicators along with their changing trends and significance. The proposed assessment framework is applied to the Loess Plateau, China. Four extreme precipitation indicators are characterized: the amount (P95), the number of days (D95), the intensity (I95), and the proportion (R95) of extreme precipitation. The spatial–temporal changes of these indicators and their multidimensional combinations (including six two-dimensional and three three-dimensional combinations) are fully identified and quantitatively evaluated. Full article