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stochastic framework for modeling the linear apparent behavior of complex materials:Application to random porous materials with interphases

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Acta Mechanica Sinica 2013年第6期29卷 773-782页

作者： j.Guilleminot T.T.Le C.Soize Universit Paris-Est Laboratoire Modlisation et Simulation Multi EchelleMSME UMR8208 CNRS5 Bd Descartes77454 Marne la ValleFrance

This paper is concerned with the modeling of randomness in multiscale analysis of heterogeneous materials. More specifically, a framework dedicated to the stochastic modeling of random properties is first introduced. A probabilistic model for matrix-valued second-order random fields with symmetry propertries, recently proposed in the literature, is further reviewed. Algorithms adapted to the Monte Carlo simulation of the proposed representation are also provided. The derivations and calibration procedure are finally exemplified through the modeling of the apparent properties associated with an elastic porous microstructure containing stochastic interphases.

关键词： Apparent properties MaxEnt Probabilistic model

Extending the Relational Model to Deal withProbabilistic Data

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j.urnal of Computer Science & Technology 2000年第3期15卷 230-240页

作者：马宗民 ZHANG W.j.MA W.Y CityUniversityofHongKong KowloonHongKongP.R.China

According to the soundness and completeness of information in databases, the expressive form and the semantics of incomplete information are discussed in this paper. On the basis of the discussion, the current studies on incomplete data in relational databases are reviewed. In order to represent stochastic uncertainty in most general sense in the real world, probabilistic data are introduced into relational databases. An extended relational data model is presented to express and manipulate probabilistic data and the operations in relational algebra based on the extended model are defined in this paper.

关键词： incomplete information uncertain information extended relational model probabilistic data relational algebra

The stochastic Regression Analysis as a Tool in Ecotoxicological QSAR Studies

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Biomedical and Environmental Sciences 1989年第4期2卷 385-393页

作者： j.DEVILLERS D.ZAKARYA M.CHASTRETTE j.C.DORE CTIS Laboratoire

Correspondence factor analysis(CFA)was used in conj.nction with linear regression analysis to examine the structure-activity relationships of 50 benzene derivatives tested on Pimephales *** nine molecular descriptors(numbers of C,H,O,N,Br,Cl,NO_2,OH,and NH_2 included in the molecules),CFA made it possible to define five new independent variables which were introduced in a stepwise regression analysis procedure to describe the acute toxicity(96-h LC_(50))of the aromatic *** model log 1/C=-0.727F_1+1.248F_3+4.052(r=0.918; s=0.270)is more relevant to describe the ecotoxicological behavior of the studied compounds on the fathead minnow than that obtained with principal components(log 1/C=0.151 PC_1 -0.271 PC_2+4.124;r=0.737;s=0.460).The heuristic potency of this particular statistical analysis,which is called stochastic regression analysis,is discussed in detail.1989 Academic Press,Inc.

关键词： QSAR The stochastic Regression Analysis as a Tool in Ecotoxicological QSAR Studies

Energy-aware deployment of dense heterogeneous cellular networks with QoS constraints

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Science China(Information Sciences) 2017年第4期60卷 148-165页

作者： Qimei CUI Zhiyan CUI Wei ZHENG Riku j.NTTI Weiliang XIE National Engineering Laboratory for Mobile Network Security Beijing University of Posts and Telecommunications Department of Communications and Networking Aalto University China Telecom Corporation Limited

The base station(BS) configuration is a key factor to improve energy efficiency(EE). In this paper,we focus on designing the network deployment parameters(i.e., BS densities) for biased K-tier heterogeneous cellular network(HCN) with quality of service(Qo S) provisioning. Using appropriate approximations, we derive the closed-form expressions of optimal BS density across all tiers to minimize the area power consumption(APC) by applying the stochastic geometry theory, while satisfying the users’ Qo S requirements. These results are used to obtain some new insights into the EE performance of biased HCN deployment. With the aid of this approach, the best type of BSs to be deployed or switched off for energy saving purposes can be identified from the perspectives of BS transmission power. More precisely, if the BS transmission power ratio between an arbitrary pair of tiers of K-tier HCN, e.g., the small cell BS and macro BS tiers, is higher than a threshold which is a function of path loss exponent, bias factor and power consumption, the small cell BSs are *** opposite situation takes place otherwise. Furthermore, it is also shown that, compared to the unbiased HCN scenario, significant energy savings are possible by appropriately biasing the HCN and optimizing the BS density, subj.ct to the Qo S constraints among all tiers.

关键词： heterogeneous cellular networks stochastic geometry energy efficiency BS density energy saving

Probabilistic description of extreme oscillations and reliability analysis in rolling motion under stochastic excitation

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中国科学:技术科学英文版 2023年第9期66卷 2586-2596页

作者： ZHAO Dan LI YongGe XU Yong LIU Qi KURTHS j.rgen School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710072China MOE Key Laboratory for Complexity Science in Aerospace Northwestern Polytechnical UniversityXi’an 710072China Potsdam Institute for Climate Impact Research Potsdam 14412Germany Department of Physics Humboldt University BerlinBerlin 12489Germany

Large-amplitude rolling motions, also regarded as extreme oscillations, are a great threat to marine navigation, which may lead to capsizing in ship motion. Therefore, it is important to quantify extreme oscillations, assess reliability of ship systems, and establish a suitable indicator to characterize extreme oscillations in ship systems. In this work, extreme events are investigated in a ship model considering a complex ocean environment, described by a single-degree-of-freedom nonlinear system with stochastic harmonic excitation and colored Gaussian noise. The stationary probability density function(PDF) of the system is derived through a probabilistic decomposition-synthesis method. Based on this, we infer the classical damage rate of the system. Furthermore, a new indicator, independent of the PDF, is proposed to quantify the damage related only to the fourth-order moment of the system and the threshold for extreme events. It is more universal and easier to determine as compared with the classical damage rate. A large damping ratio, a large noise intensity, or a short correlation time can reduce the damage rate and the value of the *** findings provide new insights and theoretical guidance to avoid extreme oscillations and assess the reliability of practical ship movements.

关键词： rolling motion colored noise extreme oscillations reliability probabilistic decomposition-synthesis method

Spatial Localization for Nonlinear Dynamical stochastic Models for Excitable Media

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Chinese Annals of Mathematics,Series B 2019年第6期40卷 891-924页

作者： Nan CHEN Andrew j.MAj.A Xin T.TONG Department of Mathematics University of Wisconsin-MadisonWI53705USA Department of Mathematics and Center for Atmosphere Ocean Science Courant Institute of Mathematical SciencesNew York UniversityNew YorkNY10012USA Center for Prototype Climate Modeling New York University AbuDhabiSaadiyat IslandAbuDhabiUAE Department of Mathematics National University of SingaporeSingapore 119076Singapore

Nonlinear dynamical stochastic models are ubiquitous in different *** statistical properties are often of great interest,but are also very challenging to *** excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized *** this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is *** mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global *** analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed *** important applications of these theoretical results are *** are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data *** examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical *** latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.

关键词： Large state dimensions Diffusion Mean field interaction Spatial averaging strategy Efficiently sampling

SYNCHRONIZATION OF MASTER-SLAVE MARKOVIAN SWITCHING COMPLEX DYNAMICAL NETWORKS WITH TIME-VARYING DELAYS IN NONLINEAR FUNCTION VIA SLIDING MODE CONTROL

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Acta Mathematica Scientia 2017年第2期37卷 368-384页

作者： M.Syed ALI j.YOGAMBIGAI 曹进德 Department of Mathematics Thiruvalluvar UniversityVellore 632115Tamil NaduIndia Department of Mathematics Southeast UniversityNanjing 210096China Department of Mathematics Faculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia

In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the traj.ctory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

关键词： Markovian switching complex dynamical networks Lyapunov-Krasovskii method sliding mode control Linear Matrix Inequality

Path integral solutions for n-dimensional stochastic differential equations underα-stable Lévy excitation

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Theoretical & Applied Mechanics Letters 2023年第2期13卷 98-112页

作者： Wanrong Zan Yong Xu j.rgen Kurths School of Mathematics Northwest UniversityXi’an710127China Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an710129China MIIT key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical UniversityXi’an710129China Potsdam Institute for Climate Impact Research Potsdam14412Germany Department of Physics Humboldt University of BerlinBerlin12489Germany

In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and ***,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic ***,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov ***,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.

关键词： Path integral method α-stable Lévy noise Monte carlo method Fokker-Planck-Kolmogorov equation

REAL CODED GENETIC ALGORITHM FOR stochastic HYDROTHERMAL GENERATION SCHEDULING

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j.urnal of Systems Science and Systems Engineering 2011年第1期20卷 87-109页

作者： j.rnail S.DHILLON j.S.DHILLON D.P.KOTHARI G.Z.S.College of Engineering and Technology Sant Longowal Institute of Engineering and Technology Vindhya Institute of Technology and Science

The intent of this paper is to schedule short-term hydrothermal system probabilistically considering stochastic operating cost curves for thermal power generation units and uncertainties in load demand and reservoir water inflows. Therefore, the stochastic multi-obj.ctive hydrothermal generation scheduling problem is formulated with explicit recognition of uncertainties in the system production cost coefficients and system load, which are treated as random variable. Fuzzy methodology has been exploited for solving a decision making problem involving multiplicity of obj.ctives and selection criterion for best compromised solution. A real-coded genetic algorithm with arithmetic-average-bound-blend crossover and wavelet mutation operator is applied to solve short-term variable-head hydrothermal scheduling problem. Initial feasible solution has been obtained by implementing the random heuristic search. The search is performed within the operating generation limits. Equality constraints that satisfy the demand during each time interval are considered by introducing a slack thermal generating unit for each time interval. Whereas the equality constraint which satisfies the consumption of available water to its full extent for the whole scheduling period is considered by introducing slack hydro generating unit for a particular time interval. Operating limit violation by slack hydro and slack thermal generating unit is taken care using exterior penalty method. The effectiveness of the proposed method is demonstrated on two sample systems.

关键词： stochastic multi-obj.ctive optimization real-coded genetic algorithm fuzzy set economicload dispatch