概率论中几种概率模型方法总结

概率论中几种常用的概率模型是古典概型、几何概型、贝努里概型.本文对概率论中几种概率模型方法进行了总结.

解数学题的概率模型方法

解数学题的概率模型方法全景华用“初等概率”的概念解决一些初等数学问题的方法，我们称之为“概率模型方法”。它是解决数学问题的一种有效途径。下面通过例题说明这种方法的应用。１．证明代数恒等式例１若ａ、ｂ、ｃ均为界于０和１间的实数，则ａ＋ｂ＋ｃ－ａｂ－ｂｃ...

考虑隐性故障的继电保护系统可靠性分析及评估

为了更好地评估继电保护系统的可靠性,搭建了考虑隐性故障和系统运行状态变化时单一保护系统的可靠性模型。而后基于所搭建的可靠性模型,计算得到了随潮流变化时隐性故障率的变化情况和隐性故障修复率对继电保护系统正常运行的影响,并给出了基于概率模型的方法对超高压线路继电保护系统的可靠性进行评估。基于概率模型的方法是对马尔可夫状态空间模型方法的一种简化,适合工程应用,为完善继电保护系统的可靠性评估提供了可行的数学方法。算例验证了所提方法的正确性。

Reliability analysis of laminated composite under compression and shear loads

Carrying on a series of compression and shear tests by a large number of specimens, reliabilities of T300/QY8911 laminated composite were studied when dispersibility models were described. The results show that the stress is linearly dependent on the strain and the damage modes of specimens are brittle fracture for both kinds of tests. Dispersibility models of compression and shear strength are expressed as Re-N（415.39, 6 586.36） and Rs-ln（5.071 8, 0.155 3）, respectively. When normal and lognormal distributions were used to describe the dispersibility models of compression and shear strength, and the compression or shear load follows the normal distribution, the almost same failure probability can be obtained from different reliability analysis methods.

Nash Model Parameter Uncertainty Analysis by AM-MCMC Based on BFS and Probabilistic Flood Forecasting

A hydrologic model consists of several parameters which are usually calibrated based on observed hy-drologic processes. Due to the uncertainty of the hydrologic processes, model parameters are also uncertain, which further leads to the uncertainty of forecast results of a hydrologic model. Working with the Bayesian Forecasting System (BFS), Markov Chain Monte Carlo simulation based Adaptive Metropolis method (AM-MCMC) was used to study parameter uncertainty of Nash model, while the probabilistic flood forecasting was made with the simu-lated samples of parameters of Nash model. The results of a case study shows that the AM-MCMC based on BFS proposed in this paper is suitable to obtain the posterior distribution of the parameters of Nash model according to the known information of the parameters. The use of Nash model and AM-MCMC based on BFS was able to make the probabilistic flood forecast as well as to find the mean and variance of flood discharge, which may be useful to estimate the risk of flood control decision.

Non-deterministic fatigue life analysis using convex set models

The non-probabilistic approach to fatigue life analysis was studied using the convex models-interval, ellipsoidal and multiconvex models. The lower and upper bounds of the fatigue life were obtained by using the second-order Taylor series and Lagrange multiplier method. The solving process for derivatives of the implicit life function was presented. Moreover, a median ellipsoidal model was proposed which can take into account the sample blind zone and almost impossibility of concurrence of some small probability events. The Monte Carlo method for multi-convex model was presented, an important alternative when the analytical method does not work. A project example was given. The feasibility and rationality of the presented approach were verified. It is also revealed that the proposed method is conservative compared to the traditional probabilistic method, but it is a useful complement when it is difficult to obtain the accurate probability densities of parameters.

Impacts and uncertainty analysis of elevated temperature and CO_2 concentration on wheat biomass

Impacts of climatic change on agriculture and adaptation are of key concern of scientific research. However, vast uncertainties exist among global climates model output, emission scenarios, scale transformation and crop model parameterization. In order to reduce these uncertainties, we integrate output results of four IPCC emission scenarios of A1 FI, A2, B1 and B2, and five global climatic patterns of HadCM3, PCM, CGCM2, CSIRO2 and ECHAM4 in this study. Based on 20 databases of future climatic change scenarios from the Climatic Research Unit （CRU） , the scenario data of the climatic daily median values are generated on research sites with the global mean temperature increase of 1℃（GMT＋ID）, 2℃（GMT＋2D） and 3℃（GMT＋3D）. The impact of CO2 fertilization effect on wheat biomass for GMT＋I D, GMT＋2D and GMT＋3D in China＇s wheat-producing areas is studied in the process model, CERES-Wheat and probabilistic forecasting method. The research results show the CO2 fertilization effect can compensate reduction of wheat biomass with warming temperature in a strong compensating effect. Under the CO2 fertilization effect, the rain-fed and irrigated wheat biomasses increase respectively, and the increment of biomass goes up with temperature rising. The rain-fed wheat biomass increase is greater than the irrigated wheat biomass. Without consideration of CO2 fertilization effect, both irrigated and rain-fed wheat biomasses reduce, and there is a higher probability for the irrigated wheat biomass than that of the rain-fed wheat biomass.

A random medium model for simulation of concrete failure

A random medium model is developed to describe damage and failure of concrete.In the first place,to simulate the evolving cracks in a mesoscale,the concrete is randomly discretized as irregular finite elements.Moreover,the cohesive elements are inserted into the adjacency of finite elements as the possible cracking paths.The spatial variation of the material properties is considered using a 2-D random field,and the stochastic harmonic function method is adopted to simulate the sample of the fracture energy random field in the analysis.Then,the simulations of concrete specimens are given to describe the different failure modes of concrete under tension.Finally,based on the simulating results,the probability density distributions of the stress-strain curves are solved by the probability density evolution methods.Thus,the accuracy and efficiency of the proposed model are verified in both the sample level and collection level.

Hierarchical topic modeling with nested hierarchical Dirichlet process

This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonpara-metric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as well as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more fine-grained topic rela-tionships compared to the hierarchical latent Dirichlet allocation model.