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A stochastic equation for predicting tensile fractures in ductile polymer solids

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2018年 490卷 1076-1086页

作者： Nitta, Koh-hei Li, Chun-yao Kanazawa Univ Inst Sci & Engn Kakuma Campus Kanazawa Ishikawa 9201192 Japan

The statistical fracture behavior of isotactic polypropylene solids under different tensile speeds at room temperature was investigated. Tensile tests were performed more than one hundred times at different tensile speeds, and the statistical data, such as the time to break, the ultimate stress, and the tensile toughness were examined as a function of crosshead speed. All probability distribution curves of fracture time, ultimate stress, and tensile toughness followed Gaussian statistics approximately. With increasing tensile speed, the fracture time tended to decrease and the mean ultimate strength increased, whereas the toughness was independent of the tensile speed. We found an analogy in the mathematical mechanism between the ductile fracture of polymer solids and particle Brownian diffusion. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Fracture Polymeric material Mechanical response probability and statistics

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INTERCEPT TIME AND ITS PREDICTION

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IEE PROCEEDINGS-F RADAR AND SIGNAL PROCESSING 1985年第4期132卷 215-222页

作者： SELF, AG SMITH, BG SMITH ASSOCIATES CONSULTING SYST ENGINEERS LTD COBHAM KT11 3DPSURREYENGLAND ROYAL SIGNALS & RADAR ESTAB GREAT MALVERN WR14 3PSWORCSENGLAND

Intercept time is a key factor in the performance of electronic warfare (EW) surveillance and reconnaissance equipments. Interception relates to the probability of time coincidence of two or more parametric windows; scanning antennas, sweeping or stepping receivers and frequency-agile emitters give examples of such windows, where alignment or coincidence is required before detection can occur. Formulas summarised in the paper give a representative basis to the calculation of intercept time statistics, as well as allowing the duration of an intercept to be evaluated. Predicted results from computer modelling indicate that these new formulas give a much better representation of the intercept problem than that given in previous studies.

关键词： time coincidence probability intercept time statistics parametric windows computer aided analysis computer modeling radar theory stepping receivers frequency-agile emitters statistics telecommunications computing Electronic warfare electronic warfare scanning antennas Radionavigation and direction finding Communications computing radionavigation EW statistical analysis probability and statistics intercept time Radar theory sweeping receivers

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PROBABILISTIC EVALUATION OF TRANSIENT STABILITY IN A MULTIMACHINE POWER-SYSTEM

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PROCEEDINGS OF THE INSTITUTION OF ELECTRICAL ENGINEERS-LONDON 1979年第4期126卷 321-326页

作者： BILLINTON, R KURUGANTY, PRS Power System Research Group University of Saskatchewan Saskatoon Canada

There has been continuous development of better techniques for assessing transient instability in a power system. It has also been recognised that there is a need for additional indices of transient stability which more completely reflect all the factors that influence system stability. The bulk of the work in this area is based on deterministic models. The probabilistic nature of the basic factors which affect transient-stability performance of a power system has been demonstrated in recent papers.1,4This paper illustrates the inclusion of probabilistic considerations in transient-stability analysis of a practical power system by application to a multimachine configuration. A relatively simple multimachine system is used to demonstrate the technique of considering the probabilities associated with the type, location and clearance of faults. The approach in this paper is not restricted by the simplifying assumptions made in Reference 4. Reliability levels for different fault types and fault locations are evaluated, and the effect of variation of selected system parameters on the overall reliability of the system is investigated.

关键词： probability transient stability Reliability statistics transient response multimachine configuration system parameters probabilistic considerations Power system management, operation and economics stability reliability probability and statistics Maintenance and reliability power system power systems fault

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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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Quantifying the extent of crushing in granular materials: A probability-based predictive method

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2007年第10期55卷 2142-2156页

作者： Marketos, G. Bolton, M. D. Univ Cambridge Dept Engn Soil Mech Grp Cambridge CB2 1TN England

Grain crushing is one of the micromechanisms that governs the stress-strain behaviour of a granular material, and also its permeability by altering the grain size distribution. It is therefore advantageous to be able to predict the point of onset of crushing and to quantify the subsequent evolution of crushing. This paper uses the data of Discrete Element Method (DEM) simulations to inform a statistical model of granular crushing. Distributions of normalised contact forces are first obtained. If the statistical distribution of the crushing strength of the grains is then known, the onset of crushing within an assembly of grains should be predictable. Two different cases, one in which grain strength was statistically independent of grain size and one showing an arbitrary trend, were used to compare with DEM results and so confirm the validity of the statistical method. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： particle crushing granular material probability and statistics discrete element method force distribution

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Bayesian assessment of site-specific performance of geotechnical design charts with unknown model uncertainty

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS 2017年第5期41卷 781-800页

作者： Wang, Y. Zhao, T. City Univ Hong Kong Dept Architecture & Civil Engn Tat Chee Ave Kowloon Hong Kong Peoples R China

Soil properties are indispensable input parameters in geotechnical design and analysis. In engineering practice, particularly for projects with relatively small or medium sizes, soil properties are often not measured directly, but estimated from geotechnical design charts using results of some commonly used laboratory or in situ tests. For example, effective friction angle phi' of soil is frequently estimated using standard penetration test (SPT) N values and design charts relating SPT N values to phi'. Note that directly measured phi' data are generally not available when (and probably why) the use of design charts is needed. Because design charts are usually developed from past observation data, on either empirical or semi-theoretical basis, uncertainty is unavoidably involved in the design charts. This situation leads to two important questions in engineering practice: (1) how good or reliable are the soil properties estimated in a specific site when using the design charts? (or how to measure the performance of the design charts in a specific site?);and (2) how to incorporate rationally the model uncertainty when estimating soil properties using the design charts? This paper aims to address these two questions by developing a Bayesian statistical approach. In this paper, the second question is firstly addressed (i.e., soil properties are probabilistically characterized by rationally incorporating the model uncertainty in the design chart). Then, based on the characterization results obtained, an index is proposed to evaluate the site-specific performance of design charts (i.e., to address the first question). Equations are derived for the proposed approach, and the proposed approach is illustrated using both real and simulated SPT data. (C) 2016 John Wiley & Sons, Ltd.

关键词： design charts probability and statistics Bayesian method model uncertainty soil properties

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A Sparse Regression Method for Group-Wise Feature Selection with False Discovery Rate Control

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2018年第4期15卷 1066-1078页

作者： Gossmann, Alexej Cao, Shaolong Brzyski, Damian Zhao, Lan-Juan Deng, Hong-Wen Wang, Yu-Ping Tulane Univ Bioinnovat PhD Program New Orleans LA 70118 USA Tulane Univ Ctr Bioinformat & Genom New Orleans LA 70118 USA Univ Texas MD Anderson Canc Ctr Dept Bioinformat & Computat Biol Houston TX 77004 USA Indiana Univ Dept Epidemiol & Biostat Bloomington IN USA Jagiellonian Univ Inst Math PL-31007 Krakow Poland Tulane Univ Dept Global Biostat & Data Sci New Orleans LA 70118 USA Tulane Univ Dept Biomed Engn New Orleans LA 70118 USA

The method of Sorted L-One Penalized Estimation, or SLOPE, is a sparse regression method recently introduced by Bogdan et. al. [1]. It can be used to identify significant predictor variables in a linear model that may have more unknown parameters than observations. When the correlations between predictor variables are small, the SLOPE method is shown to successfully control the false discovery rate (the expected proportion of the irrelevant among all selected predictors) at a user specified level. However, the requirement for nearly uncorrelated predictors is too restrictive for genomic data, as demonstrated in our recent study [2] by an application of SLOPE to realistic simulated DNA sequence data. A possible solution is to divide the predictor variables into nearly uncorrelated groups, and to modify the procedure to select entire groups with an overall significant group effect, rather than individual predictors. Following this motivation, we extend SLOPE in the spirit of Group LASSO to Group SLOPE, a method that can handle group structures between the predictor variables, which are ubiquitous in real genomic data. Our theoretical results show that Group SLOPE controls the group-wise false discovery rate (gFDR), when groups are orthogonal to each other. For use in non-orthogonal settings, we propose two types of Monte Carlo based heuristics, which lead to gFDR control with Group SLOPE in simulations based on real SNP data. As an illustration of the merits of this method, an application of Group SLOPE to a dataset from the Framingham Heart Study results in the identification of some known DNA sequence regions associated with bone health, as well as some new candidate regions.

关键词： probability and statistics correlation and regression analysis statistical computing machine learning mathematics and statistics biology and genetics

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Stochastic effects in plasticity in small volumes

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INTERNATIONAL JOURNAL OF PLASTICITY 2014年 52卷 117-132页

作者： Shao, Shuai Abdolrahim, Niaz Bahr, David F. Lin, Guang Zbib, Hussein M. Washington State Univ Sch Mech & Mat Engn Pullman WA 99164 USA Purdue Univ Sch Mat Engn W Lafayette IN 47907 USA Pacific NW Natl Lab Computat Sci & Math Div Richland WA 99352 USA

Recent studies of micro- and nano-scale metallic structures have exposed considerable statistical distribution, in addition to significant size dependencies, in the yield strength. This intrinsic statistical variation is particularly evident in the micro-compression and microtension thin film tests. This work investigates the relationship between the initial dislocation density, the heterogeneous initial spatial dislocation distribution, and the resulting localized deformation with multiscale discrete dislocation dynamics simulations. This relationship is examined separately from commonly reported external factors affecting observed strength, such as variations in specimen geometry and base support. Towards this end, we performed multiscale dislocation dynamics simulations of geometries commonly employed in micro-scale testing techniques, including micro-pillar compression, microtensile thin film, and microbulge tests. The statistical variation of yield strengths from all three simulation geometries is in agreement with experimental data from the corresponding loading techniques. We show that the onset of plasticity is stochastic in small volumes containing a small density of dislocations: a contrast to classical deterministic plasticity theory. The yield stress in these small volumes is stochastic, not deterministic, because of statistical variation of the initial dislocation content. The numerical results exhibit a localized deformation process and demonstrate a strong dependence of the yield stress on the initial dislocation density, the initial dislocation spatial distribution, and the specimen geometry size. Leveraging nucleation theory, a stochastic model for the onset of plasticity in micro- and nano-scale structures is developed based on these results. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Dislocations Beams and columns Metallic material probability and statistics Multiscale

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Cardinal interpolation

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2007年第9期29卷 1538-1545页

作者： Gustafson, Steven C. Parker, David R. Martin, Richard K. USAF Inst Technol Wright Patterson AFB OH 45433 USA USAF Res Lab Wright Patterson AFB OH 45433 USA

A Bayesian probability density for an interpolating function is developed, and its desirable properties and practical potential are demonstrated. This density has an often needed but previously unachieved property, here called cardinal interpolation, which ensures extrapolation to the density of the least-squares linear model. In particular, the mean of the cardinal interpolation density is a smooth function that intersects given (x, y) points and which extrapolates to their least-squares line, and the variance of this density is a smooth function that is zero at the point x values, that increases with distance from the nearest point x value, and that extrapolates to the well-known quadratic variance function for the least-squares line. The new cardinal interpolation density is developed for Gaussian radial basis interpolators using fully Bayesian methods that optimize interpolator smoothness. This optimization determines the basis function widths and yields an interpolating density that is non-Gaussian except for large magnitude x and which is therefore not the outcome of a Gaussian process. Further, new development shows that the salient property of extrapolation to the density of the least-squares linear model can be achieved for more general approximating (not just interpolating) functions.

关键词： Bayesian statistics interpolation modeling and prediction probability and statistics regression

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Quantifying reliability statistics for electrochemical shock of brittle materials

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2014年第1期70卷 71-83页

作者： Woodford, William H. Chiang, Yet-Ming Carter, W. Craig MIT Dept Mat Sci & Engn Cambridge MA 02139 USA

In brittle polycrystalline materials, anisotropic shape changes-such as those due to thermal expansion, composition changes, and piezoelectricity-can induce stresses severe enough to drive fracture. The stresses developed are microstructurally heterogeneous and develop in proportion to a generalized external stimulus rather than an applied load;as a consequence, traditional Weibull models do not capture the relevant scaling of failure probabilities with respect to applied stimulus or microstructural feature sizes. These limitations are surmounted by a stochastic method, called Finite Element plus Monte Carlo (FE+MC), which enables quantification of reliability statistics in brittle polycrystalline materials subjected to microstructurally heterogeneous stresses which may be driven by non-mechanical stimulii. A finite element analysis computes the stress distributions for a hypothetical defect-free virtual microstructure and a subsequent Monte Carlo analysis distributes flaws throughout the microstructure with sizes chosen from an experimental flaw size distribution. The FE+MC method is validated for uniaxial tensile loading, for which the expected Weibull distribution of failure probability is reproduced. As a demonstration of the utility of this method in a more complex stress state, we consider electrochemical shock of polycrystalline LiXCoO2 electrodes;the computed composition-dependent failure probabilities reproduce key features of experimental acoustic emission measurements not explained by previous modeling approaches. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Fracture Microstructures Anisotropic material Polycrystalline material probability and statistics

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