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Comments on "Generalized Box-Muller Method for Generating q-Gaussian Random Deviates"

IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第10期67卷 6785-6789页

作者： Nelson, Kenric P. Thistleton, William J. Photrek LLC Watertown MA 02472 USA SUNY Polytech Inst Utica NY 13502 USA

The generalized Box-Muller algorithm provides a methodology for generating q-Gaussian random variates, which generalizes the Gaussian (q = 1). The parameter -infinity < q <= 3 is related to the shape of the tail decay;q < 1 for compact-support including parabola (q = 0);1 < q <= 3 for heavy-tail including Cauchy (q = 2). This addendum clarifies the transformation q' = 3q-1/q+1 within the algorithm is due to a difference in the dimensions d of the generalized logarithm and the generalized distribution. The transformation is clarified by the decomposition of q = 1 + 2 kappa/1+d kappa, where the shape parameter -1 < kappa <= infinity quantifies the magnitude of the deformation from exponential. A simpler specification for the generalized Box-Muller algorithm is provided using the shape of the tail decay.

关键词： Random variables probability and statistics information theory complex systems nonlinear Pareto

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Uncertainty, sensitivity analysis and optimization of a reservoir geological model

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MARINE GEORESOURCES & GEOTECHNOLOGY 2021年第2期39卷 129-139页

作者： Hu Yong He Wenxiang Zhou Yanli Guo Bincheng Gao Zhaopu Yangtze Univ Coll Resources & Environm Wuhan Hubei Peoples R China PetroChina Explorat & Dev Res Inst Beijing Peoples R China SINOPEC North China Co Explorat & Dev Res Inst Zhengzhou Henan Peoples R China

Geological models are mainly obtained via interpolation of simulations using geostatistical algorithms, and the simulation results are highly uncertain. In this paper, several factors that have great influences on model results are analyzed. Through an analysis of the sensitive uncertain factors, it is found that the uncertainty of the lithofacies model has the greatest influence on the geological model, and the variogram has the second greatest influence. Therefore, ensuring the rationality of lithologic model can effectively reduce the uncertainty of the model. It is found that using seismic impedance as constraints can effectively improve the accuracy of the lithofacies model, and one can use the seismic impedance to obtain a reasonable variogram (effectively overcoming the shortage of well data), thus reducing the uncertainty of the model. Although the stochastic simulation technology used in geological modeling can yield many simulation results, only a limited number of models can be applied in practical work. In this paper, a probabilistic analysis method is proposed to optimize the model, which can provide a reference for business decision-making and risk assessment of oil and gas companies. Reserve uncertainty analysis in the exploration stage can determine the most probable reserve of the reservoir through the probabilistic characteristics of the reserve so as to determine the next exploration target. In the development stage, probabilistic analyses of the porosity, remaining oil saturation and other parameters related to oil field production can maximize the development of remaining oil. The idea of model optimization based on sensitivity analysis of model uncertainties proposed in this paper can effectively reduce the uncertainty of the model, improve the accuracy of the geological model and meet the needs of different research stages and levels.

关键词： Reserves business decisions risk assessment stochastic simulation uncertainty sensitivity analysis probability and statistics optimization of model

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Increasing distributed generation hosting capacity in distribution systems via optimal coordination of electric vehicle aggregators

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IET GENERATION TRANSMISSION & DISTRIBUTION 2021年第2期15卷 359-370页

作者： Quijano, Darwin A. Melgar-Dominguez, Ozy D. Sabillon, Carlos Venkatesh, Bala Padilha-Feltrin, Antonio Sao Paulo State Univ UNESP Elect Engn Dept BR-15385000 Ilha Solteira SP Brazil Ryerson Univ Ctr Urban Energy Toronto ON Canada

This work presents a novel strategy, designed from the distribution system operator viewpoint, aimed at estimating the hosting capacity in electric distribution systems when controllable plug-in electric vehicles are in place. The strategy seeks to determine the maximum wind-based distributed generation penetration by coordinating, on a forecast basis, the dispatch of electric vehicle aggregators, the operation of voltage regulation devices, and the active and reactive distributed generation power injections. Different from previous works, the proposed approach leverages controllable features of electric vehicles taking into account technical electric vehicle characteristics, driving behaviour of electric vehicle owners, and electric vehicle energy requirements to accomplish their primary purpose. The presented strategy is formulated as a two-stage stochastic mixed-integer linear programming problem. The first stage maximises the distributed generation installed capacity, while the second stage minimises the energy losses during the planning horizon. probability density functions are used to describe the uncertainties associated with renewable distributed generation, conventional demand, and electric vehicle driving patterns. Obtained results show that controlling the power dispatched to electric vehicle aggregators can increase the distributed generation hosting capacity by up to 15% (given a 40% electric vehicle penetration), when compared to an uncontrolled electric vehicle approach.

关键词： probability electric vehicle energy requirements two-stage stochastic mixed-integer linear programming problem electric vehicles Control of electric power systems Power system planning and layout voltage control electric distribution systems linear programming Optimisation techniques renewable distributed generation power injections renewable energy sources distributed power generation integer programming Transportation planning horizon plug-in electric vehicles power generation control power generation planning Voltage control battery powered vehicles power distribution planning Distribution networks probability and statistics Distributed power generation electric vehicle driving patterns probability density functions power distribution control stochastic processes voltage regulation devices distributed generation hosting capacity distribution system operator viewpoint Other topics in statistics electric vehicle aggregators

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Neural Sequence Transformation

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COMPUTER GRAPHICS FORUM 2021年第7期40卷 131-140页

作者： Mukherjee, Sabyasachi Mukherjee, Sayan Hua, Binh-Son Umetani, Nobuyuki Meister, Daniel Univ Tokyo Tokyo Japan Univ Illinois Chicago IL 60680 USA Blueqat Co Ltd Tokyo Japan VinAI Res Hanoi Vietnam VinUniversity Hanoi Vietnam

Monte Carlo integration is a technique for numerically estimating a definite integral by stochastically sampling its integrand. These samples can be averaged to make an improved estimate, and the progressive estimates form a sequence that converges to the integral value on the limit. Unfortunately, the sequence of Monte Carlo estimates converges at a rate of O(root n), where n denotes the sample count, effectively slowing down as more samples are drawn. To overcome this, we can apply sequence transformation, which transforms one converging sequence into another with the goal of accelerating the rate of convergence. However, analytically finding such a transformation for Monte Carlo estimates can be challenging, due to both the stochastic nature of the sequence, and the complexity of the integrand. In this paper, we propose to leverage neural networks to learn sequence transformations that improve the convergence of the progressive estimates of Monte Carlo integration. We demonstrate the effectiveness of our method on several canonical 1D integration problems as well as applications in light transport simulation.

关键词： CCS Concepts • Mathematics of computing → Numerical analysis probability and statistics • Computing methodologies → Machine learning algorithms Ray tracing

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Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems

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MATERIALS 2023年第7期16卷 2817页

作者： Grzybowski, Andrzej Z. Domanski, Zbigniew Derda, Tomasz Czestochowa Tech Univ Dept Math PL-42201 Czestochowa Poland

When random-strength components work as an interconnected parallel system, then its carrying capacity is random as well. In a case where such a multicomponent system is a subject of the stepwise-growing workload, some of its components fail and their loads are taken over by the ones that are intact. When the loading process is continued, the additional loads trigger consecutive failures that degrade the system, eventually leading to a complete failure. If the goal of the system is to carry as much load as possible, then the loading process should be continued, but no longer than until the loading capacity of the whole system is reached. On the other hand, with every additional load step, a failure of the system becomes more probable, as the carrying capacity is random and known solely through its probability distribution. In such cases, the decision on when to cease the loading process is not obvious. We introduce and analyse a minimal model of failure spreading in an array of progressively loaded pillars controlled by a decision-maker who stops the process when a required load is attained. We show how to construct an optimal stopping rule. Under some additional assumptions regarding the adopted loss function, it is argued that the optimal stopping rule is of the threshold type and it significantly depends on the shape of the load-step probability distribution.

关键词： array of pillars failure multicomponent system optimal stopping rule probability and statistics strength

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Resilience assessment of mobile emergency generator-assisted distribution networks: A stochastic geometry approach

Journal of Economy and Technology

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Journal of Economy and Technology 2023年 1卷 48-74页

作者： Chenhao Ren Rong-Peng Liu Wenqian Yin Qinfei Long Yunhe Hou Department of Electrical and Electronic Engineering The University of Hong Kong Hong Kong SAR China Department of Electrical and Computer Engineering McGill University Montreal QC H3A 0G4 Canada

Escalation of extreme weather events represents substantial threat to power system infrastructure. Mobile emergency generators (MEGs) can form part of a flexible restoration strategy against such destructive events. However, with continued expansion of distribution networks, quantification of the impact of MEGs has become increasingly challenging owing to extreme-weather-event-induced uncertainties. In this paper, we propose a stochastic geometry-based method for assessing the impact of MEG deployment on distribution networks affected by extreme weather events through investigation of structural features. First, we propose a distance measure to represent the electrical connection between power grid components. Subsequently, we adopt the point process and Voronoi tessellation to describe the spatial distribution of power grid components and the service coverage provided by MEGs under different scenarios. Then, we propose a set of assessment metrics to evaluate the survivability of power grid components and the resilience of the entire distribution network under extreme weather events. Finally, we derive accurate analytical expressions for the distance distribution and resilience metrics, such as coverage probability and load shedding, enabling us to explore the relationship between MEG deployment decisions, structural features, and power grid resilience. The proposed method enables analytic assessment of the impact of MEG deployment on the resilience of distribution networks, and provides beneficial insights to help formulate efficient measures for enhancing resilience. Case studies demonstrated that the proposed method is accurate and efficient in dealing with network analysis and assessment problems for distribution networks under massive potential failure scenarios.

关键词： Power grid structure Stochastic geometry Poisson process Mobile emergency generator Resilience assessment Power system resilience probability and statistics

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Day-ahead and intra-day wind power forecasting based on feedback error correction

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IET RENEWABLE POWER GENERATION 2021年第13期15卷 2840-2848页

作者： Gupta, Akshita Kumar, Arun Boopathi, Kadhirvel Indian Inst Technol Roorkee Hydro & Renewable Energy Dept Roorkee 247667 Uttarakhand India Indian Inst Technol Roorkee Hydro & Renewable Energy Dept Roorkee Uttarakhand India Natl Inst Wind Energy NIWE Res & Dev Resource Data Analyt & Forecasting & Solar Radiat Chennai Tamil Nadu India

The major hindrance in the development of large-scale grid integration of wind energy into the power system is the production of intermittent and variable power. A largescale integration requires a forecasting mechanism to support the power system operators while operating the grids. This study forecasts the day-ahead and intra-day wind power using the wavelet decomposition, followed by the autoregressive integrated moving average. The forecasting has been attempted on two datasets, actual and error wind power. The forecasting using the wavelet decomposition employs the discrete wavelets consisting of 16 wavelets, grouped into 5 families. The optimum length of the past data used for the model formulation has also been examined for the various scenarios. The forecasting results have been compared based on various performance metrics. The results of the forecasted values have been compared with the reference ARIMA model to see the effectiveness of the proposed wavelet-ARIMA model. The results indicate that the feedback mechanism used in the error dataset have improved the forecasting efficiency over the use of actual data in both the day-ahead and intra-day forecasting. Also, it has been observed that some of the wavelet families outperformed the other families in terms of accuracy and speed.

关键词： wavelet decomposition probability and statistics wind power plants power system operators feedback error correction autoregressive moving average processes feedback mechanism Power system planning and layout Wind power plants intra-day wind power forecasting large-scale grid integration load forecasting power grids forecasting theory variable power actual error wind power forecasting mechanism wind power autoregressive integrated moving average ARIMA model wind energy

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Hierarchical scaling model for size effect on tensile strength of polycrystalline rock

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2023年 247卷

作者： Wang, Zhi-Yang Li, Ying-Wei Wu, Zhi-Jun Wuhan Univ Sch Civil Engn Wuhan 430072 Hubei Peoples R China

Here, we proposed an analytical model for quantifying the intriguing size-dependent tensile strength of polycrystalline rock, i.e. first ascending then descending with the increase of specimen size. The meso-structure of polycrystalline rock was firstly degraded to a hierarchical arrangement of regularly cuboid mineral grains. The tensile strength distribution of mineral grain interface (GI) is modeled by Weibull distribution, and the stress state near the failed GI is analytically calculated. Then a probabilistic analysis of the failure evolution in hierarchical mineral grain sets (sets of sets) was performed by considering the meso crack initiation at the GI to their propagation at macro scale, so that the tensile strength distribution and the meso crack accumulation in the rock specimen can be derived. The consistency between the model predictions and experimental results demonstrates the proposed model is valid. In addition, the results revel that the size effect trend, ascending or descending, is determined by the dispersion degree of structure strength distribution.

关键词： Rock Tensile strength Size effect Analytical model probability and statistics

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Álgebra Lineal en Ciencia de Datos

Álgebra Lineal en Ciencia de Datos

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丛书名： Wellesley-Cambridge Press

2022年

作者： Gilbert Strang

ISBN: (数字)9781611977387

ISBN: (纸本)9781611977387

Álgebra lineal y los fundamentos del aprendizaje profundo, ¡juntos por fin! Del profesor Gilbert Strang, aclamado autor de Introducción al álgebra lineal, llega Álgebra lineal en ciencia de datos, el primer libro de texto que enseña álgebra lineal junto con aprendizaje profundo y redes neuronales. Este libro de texto ameno pero riguroso contiene un curso completo de álgebra lineal y de la matemática relacionada que los estudiantes deben saber para familiarizarse con el aprendizaje a partir de los datos. Se incluyen: los cuatro subespacios fundamentales, descomposición en valores singulares, matrices especiales, técnicas de cálculo con matrices grandes, compressed sensing, probabilidad y estadística, optimización, arquitectura de redes neuronales, descenso por gradiente estocástico y retropropagación.

Audiencia

Este libro es para cualquier persona que quiera aprender cómo se reducen e interpretan los datos mediante métodos matriciales. Este es el texto del segundo curso de álgebra lineal 18.065 impartido por el profesor Strang. Las conferencias del 18.06 sobre OpenCourseWare son ampliamente conocidas y el nuevo curso parte de los cuatro subespacios fundamentales y las factorizaciones básicas de una matriz. Explica cómo funciona el aprendizaje profundo y es completamente accesible sin el primer texto.

Sobre el Autor

Gilbert Strang es profesor de matemáticas en el Instituto Tecnológico de Massachusetts y miembro honorario del Balliol College de la Universidad de Oxford. También es un autor prolífico de una docena de libros de texto y monografías de gran prestigio. Gilbert Strang se desempeñó como presidente de la Sociedad de Matemáticas Industriales y Aplicadas (SIAM) de 1999 a 2000 y presidió el Comité Nacional de Matemáticas de EE. UU. de 2003 a 2004. Ganó los premios Henrici y Su Buchin en ICIAM 2007 y la Medalla Von Neumann de la Asociación Estadounidense de Mecánica Computacional. Es SIAM Fellow y miembro de la A

关键词： linear algebra data science deep learning machine learning matrix methods neural networks probability and statistics optimization singular values least squares neural nets

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The Bayesian Causal Inference of Body Ownership Model: Use in VR and Plausible Parameter Choices

The Bayesian Causal Inference of Body Ownership Model: Use i...

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28th IEEE Conference on Virtual Reality and 3D User Interfaces (IEEE VR)

作者： Schubert, Moritz Endres, Dominik Philipps Univ Marburg Marburg Germany

ISBN: (纸本)9781665440578

Experiencing virtual body ownership is an important component of user experience in virtual reality applications with embodied avatars. A functioning model of body ownership could allow designers of such applications to predict the occurrence of body ownership illusions in users. One attempt at such a model, the Bayesian Causal Inference of Body Ownership (BCIBO) model, explains body ownership as inference about the causes of sensory signals. When sensory signals under consideration (e.g. tactile and visual signals) are attributed to a single object (e.g. a rubber hand), then this object is incorporated into the body. We investigate an unrealistic choice of parameter values in the original specification of the BCIBO model and make some suggestions for improvements.

关键词： Mathematics of computing probability and statistics Probabilistic inference problems Bayesian computation Applied computing Law, social and behavioral sciences Psychology

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