Probabilistic verification of a biodiesel production system using statistical model checking

Biochemical system designers are increasingly using formal modelling, simulation, and verification methods to improve the understanding of complex systems. Probabilistic models can incorporate realistic stochastic dynamics, but creating and analysing probabilistic models in a formal way is challenging. In this work, we present a stochastic model of biodiesel production that incorporates an inexpensive test of fuel quality, and we validate the model using statistical model checking, which can be used to evaluate simple or complex temporal properties efficiently. We also describe probabilistic simulation and analysis techniques for stochastic hybrid system (SHS) models to demonstrate the properties of our model. We introduce a variety of properties for various configurations of the reactor as well as results of testing our model against the properties.     

A thermostatted kinetic theory model for a hybrid multisource system with storage

This paper deals with the modeling of a hybrid energy multisource network composed by a non-renewable energy source and a renewable energy source. The mathematical model is derived within the framework of the thermostatted kinetic theory where the external force field coupled to the thermostat term mimics the construction of the energy storage. The parameters of the mathematical model are set in order to promote the use of the renewable energy source thus improving the quality of the provided energy. A computational analysis is performed to show the emerging phenomena that the model is able to capture. Specifically the computational analysis is mainly addressed to a sensitivity analysis on the switching-source parameters and the transition-energy parameters. Moreover the construction of the energy storage is analyzed by performing a sensitivity analysis on the magnitude of the external force field. Discussions and future research perspectives are postponed to the last section of the paper.     

A new method for probabilistic assessments in power systems,combining monte carlo and stochastic‐algebraic methods

This article discusses a new methodology, which combines two efficient methods known as Monte Carlo (MC) and Stochastic‐algebraic (SA) methods for stochastic analyses and probabilistic assessments in electric power systems. The main idea is to use the advantages of each former method to cover the blind spots of the other. This new method is more efficient and more accurate than SA method and also faster than MC method while is less dependent of the sampling process. In this article, the proposed method and two other ones are used to obtain the probability density function of different variables in a power system. Different examples are studied to show the effectiveness of the hybrid method. The results of the proposed method are compared to the ones obtained using the MC and SA methods. © 2014 Wiley Periodicals, Inc. Complexity 21: 100–110, 2015     

概率约束最优化问题

概率约束最优化问题是随机规划的一类重要问题,在金融、管理和工程计划等领域有广泛的应用. 概率约束优化问题近年来受到了广泛的关注和重视,在应用建模、理论和方法等方面取得了不少重要的进展. 这里主要概述和总结处理概率约束的主要方法和思想,包括凸内逼近方法、情景逼近方法、DC方法和整数规划方法等,并对概率约束最优化的研究前景进行讨论.     

A new probabilistic fuzzy model: Fuzzification–Maximization (FM) approach

Over the past few decades, fuzzy logic systems have been used for nonlinear modeling and approximation in many fields ranging from engineering to science. In this paper, a new fuzzy model is developed from the probabilistic and statistical point of view. The proposed model decomposes the input–output characteristics into noise-free part and probabilistic noise part and identifies them simultaneously. The noise-free model recovers the nominal input–output characteristics of the target system and the noise model gives approximation to the probabilistic nature of the added noise. To identify the two submodels simultaneously, we propose the Fuzzification–Maximization (FM). Finally, some simulations are conducted and the effectiveness of the proposed method is demonstrated through the comparison with the previous methods.     

Sustainable energy futures: Methodological challenges in combining scenarios and participatory multi-criteria analysis

This paper analyses the combined use of scenario building and participatory multi-criteria analysis (PMCA) in the context of renewable energy from a methodological point of view. Scenarios have been applied increasingly in decision-making about long-term consequences by projecting different possible pathways into the future. Scenario analysis accounts for a higher degree of complexity inherent in systems than the study of individual projects or technologies. MCA is a widely used appraisal method, which assesses options on the basis of a multi-dimensional criteria framework and calculates rankings of options. In our study, five renewable energy scenarios for Austria for 2020 were appraised against 17 sustainability criteria. A similar process was undertaken on the local level, where four renewable energy scenarios were developed and evaluated against 15 criteria. On both levels, the scenario development consisted of two stages: first an exploratory stage with stakeholder engagement and second a modelling stage with forecasting-type scenarios. Thus, the scenarios consist of a narrative part (storyline) and a modeled quantitative part. The preferences of national and local energy stakeholders were included in the form of criteria weights derived from interviews and participatory group processes, respectively. Especially in the case of renewable energy promotion in Austria, the paper systematically analyses the potentials and limitations of the methodology (1) for capturing the complexity of decision-making about the long-term consequences of changes in socio-economic and biophysical systems and (2) for appraising energy futures. The paper concludes that assessing scenarios with PMCA is resource intense, but this methodology captures successfully the context of technology deployment and allows decision-making based on a robust and democratic process, which addresses uncertainties, acknowledges multiple legitimate perspectives and encourages social learning.     

The probability approach to numerical solution of nonlinear parabolic equations

A number of new layer methods for solving semilinear parabolic equations and reaction‐diffusion systems is derived by using probabilistic representations of their solutions. These methods exploit the ideas of weak sense numerical integration of stochastic differential equations. In spite of the probabilistic nature these methods are nevertheless deterministic. A convergence theorem is proved. Some numerical tests are presented. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 490–522, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10020     

A selective view of stochastic inference and modeling problems in nanoscale biophysics

Advances in nanotechnology enable scientists for the first time to study biological processes on a nanoscale molecule-by-molecule basis. They also raise challenges and opportunities for statisticians and applied probabilists. To exemplify the stochastic inference and modeling problems in the field, this paper discusses a few selected cases, ranging from likelihood inference, Bayesian data augmentation, and semi- and non-parametric inference of nanometric biochemical systems to the utilization of stochastic integro-differential equations and stochastic networks to model single-molecule biophysical processes. We discuss the statistical and probabilistic issues as well as the biophysical motivation and physical meaning behind the problems, emphasizing the analysis and modeling of real experimental data. This work was supported by the United States National Science Fundation Career Award (Grant No. DMS-0449204)     

Optimization via simulation: A review

We review techniques for optimizing stochastic discrete-event systems via simulation. We discuss both the discrete parameter case and the continuous parameter case, but concentrate on the latter which has dominated most of the recent research in the area. For the discrete parameter case, we focus on the techniques for optimization from a finite set: multiple-comparison procedures and ranking-and-selection procedures. For the continuous parameter case, we focus on gradient-based methods, including perturbation analysis, the likelihood ratio method, and frequency domain experimentation. For illustrative purposes, we compare and contrast the implementation of the techniques for some simple discrete-event systems such as the (s, S) inventory system and theGI/G/1 queue. Finally, we speculate on future directions for the field, particularly in the context of the rapid advances being made in parallel computing.     

SmartFarm – Data based optimization for optimal energy management

In the project SmartFarm we develop a method that automatically decides which renewable energies are profitable to use at the farm for the next hours. To this means optimization methods are used on various levels. Initially, all necessary data is measured on a demonstration object. This data forms the basis for data based learning methods for the modelling of the consumers (e.g. milk cooling), the producers (e.g. solar plant) and the energy storage systems (e.g. battery storage device). In this paper we will focus on the data based models of the producers and energy storage systems. Optimization methods are used to identify optimal parameters for a general ansatz function, which is derived from a Taylor approximation. We develop all models with real data of the demonstration object and verify them with this data as well. Numerical results and the further course of action will be discussed in the paper. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Graphical Explanation in Belief Networks

Abstract

Belief networks provide an important bridge between statistical modeling and expert systems. This article presents methods for visualizing probabilistic “evidence flows” in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in expert systems, we present a hierarchy of explanations, ranging from simple colorings to detailed displays. Our approach complements parallel work on textual explanations in belief networks. Graphical-Belief, Mathsoft Inc.'s belief network software, implements the methods.     

Modelling of uncertainty in discrete dynamical systems

Dynamic systems that are not Gaussian, stationary and linear are difficult to model by full probabilistic analysis. Sufficient information for practical application can often be obtained by second moment analysis, described in the paper. Alternatively, second moment analysis can be performed using point distributions. Two new methods in this class, one exact for linear systems and one approximate, are described. Examples show the application and illustrate the accuracy.     

Modeling aspects and numerical analysis of offshore systems

There is a strong effort to improve the efficiency of renewable energy systems in order to reduce the CO₂ emissions. This paper addresses an approach to increase the efficiency of an ocean wave energy plant with a model based predictive controller. For this controller it is necessary to have a prediction of the ocean waves and a model of the whole system. The future development of the ocean waves is predicted by an AR-model. A system identification yields the model of the energy plant. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stochastic system for generalized polytropic filtration

In this paper, we study a certain class of stochastic quasilinear parabolic equations describing a generalized polytropic elastic filtration in the framework of variable exponents Lebesgue and Sobolev spaces. We establish an existence result in the infinite dimensional framework of weak probabilistic solutions when the forcing terms do not satisfy Lipschitz conditions, and the governing equations are subjected to cylindrical Wiener processes. We use a Galerkin method, derive crucial a priori estimates for the approximate solutions, and combine profound analytic and probabilistic compactness results in order to pass to the limit. Several difficulties arise in obtaining these uniform bounds and passing to the limit since the nonlinear elliptic part of the leading operator admits nonstandard growth. Apart from adapting the above essential tools, we extend classical methods of monotonicity to the present situation.     

Solution of a stochastic Darcy equation by polynomial chaos expansion

This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. The computational complexity of this algorithm is determined by the order of the polynomial chaos expansion and the number of terms in the Karhunen–Loève expansion. We calculate various Eulerian and Lagrangian statistical characteristics of the flow by the conventional Monte Carlo and probabilistic collocation methods. Our calculations show a significant advantage of the probabilistic collocation method over the directMonte Carlo algorithm.     

A Survey of Optimization by Building and Using Probabilistic Models

This paper summarizes the research on population-based probabilistic search algorithms based on modeling promising solutions by estimating their probability distribution and using the constructed model to guide the exploration of the search space. It settles the algorithms in the field of genetic and evolutionary computation where they have been originated, and classifies them into a few classes according to the complexity of models they use. Algorithms within each class are briefly described and their strengths and weaknesses are discussed.     

Electricity price forecasting accounting for renewable energies: optimal combined forecasts

Electricity price forecasting is an interesting problem for all the agents involved in electricity market operation. For instance, every profit maximisation strategy is based on the computation of accurate one-day-ahead forecasts, which is why electricity price forecasting has been a growing field of research in recent years. In addition, the increasing concern about environmental issues has led to a high penetration of renewable energies, particularly wind. In some European countries such as Spain, Germany and Denmark, renewable energy is having a deep impact on the local power markets. In this paper, we propose an optimal model from the perspective of forecasting accuracy, and it consists of a combination of several univariate and multivariate time series methods that account for the amount of energy produced with clean energies, particularly wind and hydro, which are the most relevant renewable energy sources in the Iberian Market. This market is used to illustrate the proposed methodology, as it is one of those markets in which wind power production is more relevant in terms of its percentage of the total demand, but of course our method can be applied to any other liberalised power market. As far as our contribution is concerned, first, the methodology proposed by García-Martos et al (2007 and 2012) is generalised twofold: we allow the incorporation of wind power production and hydro reservoirs, and we do not impose the restriction of using the same model for 24?h. A computational experiment and a Design of Experiments (DOE) are performed for this purpose. Then, for those hours in which there are two or more models without statistically significant differences in terms of their forecasting accuracy, a combination of forecasts is proposed by weighting the best models (according to the DOE) and minimising the Mean Absolute Percentage Error (MAPE). The MAPE is the most popular accuracy metric for comparing electricity price forecasting models. We construct the combination of forecasts by solving several nonlinear optimisation problems that allow computation of the optimal weights for building the combination of forecasts. The results are obtained by a large computational experiment that entails calculating out-of-sample forecasts for every hour in every day in the period from January 2007 to December 2009. In addition, to reinforce the value of our methodology, we compare our results with those that appear in recent published works in the field. This comparison shows the superiority of our methodology in terms of forecasting accuracy.