Complex event recognition (CER) applications exhibit various types of uncertainty, ranging from incomplete and erroneous data streams to imperfect complex event patterns. We review CER techniques ...that handle, to some extent, uncertainty. We examine techniques based on automata, probabilistic graphical models, and first-order logic, which are the most common ones, and approaches based on Petri nets and grammars, which are less frequently used. Several limitations are identified with respect to the employed languages, their probabilistic models, and their performance, as compared to the purely deterministic cases. Based on those limitations, we highlight promising directions for future work.
As a direct consequence of power systems restructuring on one hand and unprecedented renewable energy utilization on the other, the uncertainties of power systems are getting more and more attention. ...This fact intensifies the difficulty of decision making in the power system context; therefore, the uncertainty analysis of the system performance seems necessary. Generally, uncertainties in any engineering system study can be represented probabilistically or possibilistically. When sufficient historical data of the system variables is not available, a probability density function (PDF) might not be defined, they must be represented in another manner i.e. using possibilistic theory. When some of the system uncertain variables are probabilistic and some are possibilistic, neither the conventional pure probabilistic nor pure possibilistic methods can be implemented. Hence, a combined solution is needed. This paper gives a complete review on uncertainty modeling approaches for power system studies making sense about the strengths and weakness of these methods. This work may be used in order to select the most appropriate method for each application.
Scenario generation is an important step in the operation and planning of power systems with high renewable penetrations. In this work, we proposed a data-driven approach for scenario generation ...using generative adversarial networks, which is based on two interconnected deep neural networks. Compared with existing methods based on probabilistic models that are often hard to scale or sample from, our method is data-driven, and captures renewable energy production patterns in both temporal and spatial dimensions for a large number of correlated resources. For validation, we use wind and solar times-series data from NREL integration data sets. We demonstrate that the proposed method is able to generate realistic wind and photovoltaic power profiles with full diversity of behaviors. We also illustrate how to generate scenarios based on different conditions of interest by using labeled data during training. For example, scenarios can be conditioned on weather events (e.g., high wind day, intense ramp events, or large forecasts errors) or time of the year (e.g., solar generation for a day in July). Because of the feedforward nature of the neural networks, scenarios can be generated extremely efficiently without sophisticated sampling techniques.
Starting with the category of probabilistic approach groups, we show that the category of approach groups can be embedded into the category of probabilistic approach groups as a bicoreflective ...subcategory; further, considering a category of probabilistic topological convergence groups, we show that the category of probabilistic topological convergence groups is isomorphic to the category of probabilistic approach groups under so-called triangle function ?: ?+ ? ?+ ?? ?+, where ?+ is the set of all distance distribution functions that plays a central role for probabilistic metric spaces. Moreover, if we allow this triangle function ? to be sup-continuous, then we can show that the category of probabilistic metric groups can be embedded into the category of probabilistic approach groups as a coreflective subcategory. Furthermore, we demonstrate that every T1 probabilistic topological convergence group satisfying so-called (PM) axiom is probabilistic metrizable. Finally, among others, introducing a category of probabilistic approach transformation groups, we show that the category of probabilistic topological convergence transformation groups is isomorphic to the category of probabilistic approach transformation groups; this solves an open problem that proposed in one of our earlier papers. Moreover, we prove that the category of probabilistic metric transformation groups is isomorphic to the category of probabilistic metric probabilistic convergence transformation groups.
As the binary sensing model is a coarse approximation of reality, the probabilistic sensing model has been proposed as a more realistic model for characterizing the sensing region. A point is covered ...by sensor networks under the probabilistic sensing model if the joint sensing probability from multiple sensors is larger than a predefined threshold ε. Existing work has focused on probabilistic point coverage since it is extremely difficult to verify the coverage of a full continuous area (i.e., probabilistic area coverage). In this paper, we tackle such a challenging problem. We first study the sensing probabilities of two points with a distance of d and obtain the fundamental mathematical relationship between them. If the sensing probability of one point is larger than a certain value, the other is covered. Based on such a finding, we transform probabilistic area coverage into probabilistic point coverage, which greatly reduces the problem dimension. Then, we design the ε-full area coverage optimization (FCO) algorithm to select a subset of sensors to provide probabilistic area coverage dynamically so that the network lifetime can be prolonged as much as possible. We also theoretically derive the approximation ratio obtained by FCO to that by the optimal one. Finally, through extensive simulations, we demonstrate that FCO outperforms the state-of-the-art solutions significantly.
A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability ...distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position and survey state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of
logic
programming languages such as Prolog, which have been considered for over 20 years.
El objetivo del presente artículo es caracterizar las habilidades de alfabetización y pensamiento probabilístico que las personas docentes de matemática, en formación inicial y en activo, utilizan ...cuando se enfrentan a problemas reales, donde interviene la incertidumbre. Para tal efecto, se siguió una metodología cualitativa, mediante un diseño de estudio de casos y el método de análisis de contenido. Como técnica para obtener información, se aplicó un instrumento de dos situaciones problemas en las cuales se solicitó respuesta a preguntas abiertas. Se realizó la selección de 55 participantes mediante un muestreo del tipo intencionado o por disposición, de los cuales 26 eran docentes en activo y 29 docentes en formación inicial. Entre los principales resultados se destacan que las personas docentes del estudio, tanto en formación inicial como en activo, no han desarrollado una competencia probabilística que transite por lo intuitivo, lo clásico y lo frecuencial, recurriendo esencialmente al significado clásico de probabilidad. Además, se evidencia un escaso desarrollo de ideas conceptuales y argumentativas que permitan comparar resultados empíricos y teóricos. En conclusión, se observa que las personas docentes seleccionadas, en formación inicial y en activo, no han desarrollado habilidades de alfabetización y pensamiento probabilístico, que posibiliten una enseñanza de la probabilidad que vaya más allá de lo algorítmico, promoviendo ambientes de aprendizaje para la alfabetización probabilística de los estudiantes en la etapa escolar.
Wind farms commonly cluster in regions rich in wind resources. Thus, correlation of wind speeds from different wind farms should not be ignored when modeling a power system with large wind energy ...penetration. This paper proposes a probabilistic optimal power flow (POPF) technique based on the quasi-Monte Carlo simulation (QMCS) considering the correlation of wind speeds using copula functions. In this paper, a copula function is used to model the dependent structure of random wind speeds and their forecast errors. QMCS is employed in the sampling procedure to reduce computation burden. The proposed method is applied in probabilistic power flow (PPF). Furthermore, the PPF is used in the POPF problem that aims at minimizing the expectation and downside risk of fuel cost simultaneously. Simulation studies are conducted on a modified IEEE 118-bus power system with wind farms integrated in two areas, and the results show that the accuracy and efficiency are improved by the proposed method.
The main idea of this work is an application of probabilistic entropy and also relative entropy in the numerical analysis of uncertainty propagation in the homogenization of some composite materials. ...The homogenization method is based on the determination of deformation energy for the representative volume elements computed with the use of some specific finite element method experiments. Uncertainty propagation concerns material and geometrical design parameters of particulate composites and is performed thanks to an application of polynomial responses; probabilistic moments of the effective tensor are computed via the iterative generalized stochastic perturbation technique and the semi‐analytical probabilistic method. Probabilistic entropy is determined according to Shannon theory, while relative entropies equations employed here follow mathematical models created by Kullback & Leibler, Jeffreys, Hellinger, and Bhattacharyya. Deterministic analyses have been performed with the use of the system ABAQUS, while all the remaining procedures have been programmed in the computer algebra system MAPLE.
With increasing wind penetration, wind power ramps (WPRs) are currently drawing great attention to balancing authorities, since these wind ramps largely affect power system operations. To help better ...manage and dispatch the wind power, this paper develops a data-driven probabilistic WPR forecasting (p-WPRF) method based on a large number of simulated scenarios. A machine learning technique is first adopted to forecast the basic wind power forecasting scenario and produce the historical forecasting errors. To accurately model the distribution of wind power forecasting errors, a generalized Gaussian mixture model is developed and the cumulative distribution function (CDF) is also analytically deduced. The inverse transform method based on the CDF is used to generate a large number of forecasting error scenarios. An optimized swinging door algorithm is adopted to extract all the WPRs from the complete set of wind power forecasting scenarios. The p-WPRF is generated based on all generated scenarios under different weather and time conditions. Numerical simulations on publicly available wind power data show that the developed p-WPRF method can predict WPRs with a high level of reliability and accuracy.
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