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To improve the adaptability for renewable energy sources (RES), a multitime scale optimal dispatch method, which considers the multiple correlations of RES, is proposed in the active distribution network (ADN). The proposed method includes a multiple correlation model of RES and a scheduling framework. The multiple correlation model of RES is formulated by t Copula function, Sklar's theorem, and conditional distribution of multivariate t distribution. The multiple correlation model can estimate the forecast error of the future period according to the historical data and the latest prediction. The scheduling framework further employs the revised forecast to coordinate the fast/slow-response regulation resources in the ADN under three timescales. In the day-ahead stage, the operation state of slow-response resources is optimized and determined. In the intraday stage, the output of the fast-response resource, which is transferred to the real-time stage as reference trajectory, is optimized based on the short-term prediction. In the real-time stage, the stochastic model predictive control is adopted to adjust the output of fast-response resources based on ultra-short-term prediction and reference trajectory. Case analyses indicate that the proposed method can effectively reduce the voltage fluctuation, promote the utilization of demand-side resources, and improve the system economic performance by introducing the multiple correlation model. [ABSTRACT FROM AUTHOR]

Estimation of distribution algorithm (EDA) is an efficient population-based stochastic search technique. Since it was proposed, many attempts have been made to improve its performance in the context of nonlinear continuous optimization. However, the success of EDA depends on the accuracy of modeling, the effectiveness of sampling, and the ability of exploration. An effective EDA often needs to take some measures to adjust the model and to guide sampling. In this article, we propose a novel EDA which applies the idea of Kalman filtering to revise the modeling data and a learning strategy to improve sampling. The filtering scheme modifies the modeling data set using an estimation error matrix based on historic solution data. During the sampling process, the learning strategy determines the region to sample next based on the sampling outcomes so far, instead of completely random sampling. The proposed EDA also employs a multivariate probabilistic model based on copula function and can quickly reach the promising area in which the optimal solution is likely to be located. A collection of general benchmark functions are used to test the performance of the proposed algorithm. Computational experiments show that the EDA is effective. Note to Practitioners—In many process industries, there exist black-box operation optimization problems and large-scale nonlinear optimization problems with variable coupling. For these problems, it is difficult to establish mechanism models between input and output. However, real-time data can be measured from the system through sensors. We can utilize this process information to optimize the system so as to attain the desired objective. In this article, we propose a novel estimation of distribution algorithm (EDA) which applies a filtering scheme to revise the modeling data and a learning strategy to improve sampling, which can solve the problems with the characteristics of nonlinearity, variable coupling, and large scale. Computational experiments show that the EDA is effective. In the future, the proposed algorithm can be applied to some practical optimization problems such as operation optimization in blast furnace, which is considered as a continuous production process with variable coupling. The algorithm has the potential to help optimizing the process control parameters. [ABSTRACT FROM AUTHOR]

We consider the problem of fusing probability scores from a set of classifiers to estimate a final fused probability score. Our interest is in scenarios where the classifiers are statistically dependent. To that end, we propose a new classifier fusion approach that is data driven and founded on the statistical theory of copulas. Numerical results with both simulated and real data show that our copula based classifier fusion approach produces better probability scores than individual classifiers and outperforms existing probability score fusion approaches. [ABSTRACT FROM AUTHOR]

The uncertain nature of wind power causes difficulties in power system operation scheduling. Probabilistic descriptions of the uncertainty have been studied for decades. However, probabilistic forecasts designed for the regional multiple wind farms are few. Although the traditional methods for the single wind farm can still be used, they have the limitations in capturing the spatial correlations among wind farms, and they are less robust when multivariate observations are not so complete. To improve the forecast quality in this case, we combine the multivariate distribution modeling and probabilistic forecasts in this paper. An advanced model—the regular vine copula, which can describe the wind farms’ dependence structure precisely and flexibly with various bivariate copulas as blocks, is used in this paper. Enough simulation data can be generated from the model, which can be easily used to form the conditional forecast distributions under multiple forecast conditions. A case of 10 wind farms in East China has been used to compare the proposed method with its competitors. The results showed the method's advantages of providing reliable and sharp forecast intervals, especially in the case with limited observations available. [ABSTRACT FROM PUBLISHER]

Assessing the risk of extreme events in a spatial domain, such as hurricanes, floods, and droughts, presents a unique significance in practice. Unfortunately, the existing extreme-value statistical models are typically not feasible for practical large-scale problems. Graphical models, on the other hand, are capable of handling sizable number of variables, but have yet to be explored in the realm of extreme-value analysis. To bridge the gap, an extreme-value graphical model is introduced in this paper, i.e., an ensemble-of-trees of pairwise copulas (ETPC). In the proposed graphical model, extreme-value marginal distributions are stitched together by means of a pairwise copulas, which in turn are the building blocks of the ensemble of trees. Novel linear-complexity stochastic gradient-based algorithms are then developed for learning the ETPC model and inferring missing data. As a result, the ETPC model is applicable to extreme-value problems with thousands of variables. It can be proven that, under mild conditions, the ETPC model exhibits the favorable property of tail-dependence between an arbitrary pair of sites (variables); consequently, the model is able to reliably capture statistical dependence between extreme values at different sites. Experimental results for both synthetic and real data demonstrate the advantages of the ETPC model in modeling fitting, imputation, and computational efficiency. [ABSTRACT FROM AUTHOR]

Soil moisture retrievals, delivered as a CATDS (Centre Aval de Traitement des Données SMOS) Level-3 product of the Soil Moisture and Ocean Salinity (SMOS) mission, form an important information source, particularly for updating land surface models. However, the coarse resolution of the SMOS product requires additional treatment if it is to be used in applications at higher resolutions. Furthermore, the remotely sensed soilmoisture often does not reflect the climatology of the soil moisture predictions, and the bias between model predictions and observations needs to be removed. In this paper, a statistical framework is presented that allows for the downscaling of the coarse-scale SMOS soil moisture product to a finer resolution. This framework describes the interscale relationship between SMOS observations and model-predicted soil moisture values, in this case, using the variable infiltration capacity (VIC) model, using a copula. Through conditioning, the copula to a SMOS observation, a probability distribution function is obtained that reflects the expected distribution function of VIC soilmoisture for the given SMOS observation. This distribution function is then used in a cumulative distribution function matching procedure to obtain an unbiased fine-scale soil moisture map that can be assimilated into VIC. The methodology is applied to SMOS observations over the Upper Mississippi River basin. Although the focus in this paper is on data assimilation apcations, the framework developed could also be used for other purposes where downscaling of coarse-scale observations is required. [ABSTRACT FROM AUTHOR]

We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models. [ABSTRACT FROM AUTHOR]

In this paper, we consider a binary decentralized detection problem where the local sensor observations are quantized before their transmission to the fusion center. Sensor observations, and hence their quantized versions, may be heterogeneous as well as statistically dependent. A composite binary hypothesis testing problem is formulated, and a copula-based generalized likelihood ratio test (GLRT) based fusion rule is derived given that the local sensors are uniform multilevel quantizers. An alternative computationally efficient fusion rule is also designed which involves injecting a deliberate random disturbance to the local sensor decisions before fusion. Although the introduction of external noise causes a reduction in the received signal-to-noise ratio (SNR), it is shown that the proposed approach can result in a detection performance comparable to the GLRT detector without external noise, especially when the number of quantization levels is large. [ABSTRACT FROM PUBLISHER]

The problem of location estimation of a source of random signals using a network of sensors is considered. A novel maximum-likelihood estimation (MLE) based approach using copula functions is proposed. The measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution. Using the theory of copulas, the joint parametric density of sensor observations (joint likelihood) is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations. The problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias. An example involving source localization of a Poisson source is presented to illustrate the proposed approach and demonstrate its performance. [ABSTRACT FROM AUTHOR]

Realistic assessments of the reliability of networked systems, series and parallel systems being special cases, require that we account for interdependence between the component life-lengths. The key to doing this is the specification and use of a suitable probability model in two or more dimensions. Consequently, several multivariate probabilistic models have been proposed in the literature. Many of these models have marginal distributions that are exponential; the ones by Gumbel, and by Marshall and Olkin being some of the earliest and the best known. The purpose of this paper is two fold: The first purpose is to articulate the nature of dependence encapsulated by such models, using a perspective which is best appreciated by a user. Specifically, we anchor on the bivariate case, and focus attention on the conditional mean as a measure of dependence. The second purpose, motivated by the first, is to introduce a new family of multivariate distributions with exponential marginals, whose conditional mean fills a void in the general forms of the conditional means of the available models. The method of "copulas" is used to generate this new family of distributions. Attention is focused on the case of exponential marginals, because the notion of "hazard potentials" enables us to use multivariate distributions with exponential marginals as a seed for generating multivariate distributions with marginals other than the exponential. [ABSTRACT FROM AUTHOR]