Efficient Sensitivity/Uncertainty Analysis Using the Combined Stochastic Response Surface Method and Automated Differentiation: Application to Environmental and Biological Systems

Estimation of uncertainties associated with model predictions is an important component of the application of environmental and biological models. "Traditional" methods for propagating uncertainty, such as standard Monte Carlo and Latin Hypercube Sampling, however, often require performing a prohibitive number of model simulations, especially for complex, computationally intensive models. Here, a computationally efficient method for uncertainty propagation, the Stochastic Response Surface Method (SRSM) is coupled with another method, the Automatic Differentiation of FORTRAN (ADIFOR). The SRSM is based on series expansions of model inputs and outputs in terms of a set of "well-behaved" standard random variables. The ADIFOR method is used to transform the model code into one that calculates the derivatives of the model outputs with respect to inputs or transformed inputs. The calculated model outputs and the derivatives at a set of sample points are used to approximate the unknown coefficients in the series expansions of outputs. A framework for the coupling of the SRSM and ADIFOR is developed and presented here. Two case studies are presented, involving (1) a physiologically based pharmacokinetic model for perchloroethylene for humans, and (2) an atmospheric photochemical model, the Reactive Plume Model. The results obtained agree closely with those of traditional Monte Carlo and Latin hypercube sampling methods, while reducing the required number of model simulations by about two orders of magnitude.     

Integration of Stochastic Effects and Data Uncertainties into the Design of Process Equipment

Stochastic effects and data uncertainties are present in any engineering calculation. Their impact may be particularly important if they concern the design of process equipment. A calculation model for the dynamic behavior of a heat exchanger and procedures to deal with the related uncertainties are presented. Their propagation through the calculation by means of a Monte Carlo approach is shown. The temperature at the heat exchanger outlet and the step response of a sudden variation in the heat exchanger inlet temperature are simulated and evaluated by way of example. It is demonstrated that the inclusion of stochastic effects and uncertainties provides a more reliable basis for design decisions and hence reduces the probability of errors.     

关于杂合遗传算法的研究

基于遗传算法的杂合系统是将遗传算法引入已有的系统算法、启发式优化策略以及领域知识获取与优化等问题时,所产生的一种新型的综合性算法结构设计策略。本文对遗传算法与神经网络、遗传算法与模糊逻辑、遗传算法与专家系统的杂合等问题进行了系统性的研究与评述。     

随机网络瓶颈容量扩张相关机会规划模型

文章研究的问题为,在不确定环境中,怎样去增加网络中一组边的容量到一个指定的容量,以至于网络瓶颈扩张的费用不超过给定的总费用上限的概率尽可能的大.本文假定每一条边的单位扩张费用Wi是一个随机的变量,它服从一定的概率分布.带有随机单位扩张费用W的网络瓶颈容量扩张问题可以根据一些规则,列出它的相关机会规划模型的通用表达式.随后,本文将网络瓶颈容量算法、随机模拟方法和遗传算法合成在一起,设计出该问题的混合智能通用算法.最后,给出数值算例.     

Understanding Uncertainty

There is more information we don't know than we do know for making most critical decisions involving risks. Our focus must be on understanding and effectively dealing with what we don't know. As a first step in achieving this focus, a classification of the types of uncertainties that must be addressed and the sources of these types of uncertainties is presented. The purpose is to provide a framework for discussion about addressing uncertainty, particularly in risk analyses.
Both uncertainty and variability of information are addressed using four main classes:

• 1) 

  Metrical uncertainty and variability in measurement,
• 2) 

  Structural uncertainty due to complexity, including models and their validation,
• 3) 

  Temporal uncertainty in future and past states
• 4) 

  Translational uncertainty in explaining uncertain results.

The factors that contribute uncertainty and error to these classes are identified, and their interrelationships indicated. Both subjective and objective aspects are addressed.     

基于随机Petri网的生产提前期牛鞭效应测度研究

利用随机Petri网结合三角模糊参数,对产品生产的三工艺阶段生产周期的波动进行测定,得出前工艺阶段生产周期的波动造成后工艺阶段生产周期更大的波动,且波动逐级传递。证实了生产提前期也具有类似供应链中的牛鞭效应的现象,对不确定因素导致生产周期波动的测度提供了一种新的思路和方法。     

随机组合风险的风险溢价

随机组合风险在保险索赔理论、金融及经济管理等领域有广泛的应用,数学上采用随机和来刻画随机组合风险。风险溢价在金融经济学及保险经济学的理论中都是很重要的概念,它不仅与风险的大小有关,还与当事人对风险的态度有关,从理论上看就是与当事人的效用函数有关。本文研究在期望效用理论下随机组合风险的风险溢价问题,探讨了由组合数(如索赔次数)的不确定性所引起的风险溢价,给出了几种不同效用函数下随机组合风险的风险溢价的计算公式,并特别针对随机Poisson组合及随机Poisson-Geometric组合给出了其风险溢价的计算公式及性质。     

Propagation of Uncertainty in Risk Assessments: The Need to Distinguish Between Uncertainty Due to Lack of Knowledge and Uncertainty Due to Variability

In quantitative uncertainty analysis, it is essential to define rigorously the endpoint or target of the assessment. Two distinctly different approaches using Monte Carlo methods are discussed: (1) the end point is a fixed but unknown value (e.g., the maximally exposed individual, the average individual, or a specific individual) or (2) the end point is an unknown distribution of values (e.g., the variability of exposures among unspecified individuals in the population). In the first case, values are sampled at random from distributions representing various "degrees of belief" about the unknown "fixed" values of the parameters to produce a distribution of model results. The distribution of model results represents a subjective confidence statement about the true but unknown assessment end point. The important input parameters are those that contribute most to the spread in the distribution of the model results. In the second case, Monte Carlo calculations are performed in two dimensions producing numerous alternative representations of the true but unknown distribution. These alternative distributions permit subject confidence statements to be made from two perspectives: (1) for the individual exposure occurring at a specified fractile of the distribution or (2) for the fractile of the distribution associated with a specified level of individual exposure. The relative importance of input parameters will depend on the fractile or exposure level of interest. The quantification of uncertainty for the simulation of a true but unknown distribution of values represents the state-of-the-art in assessment modeling.     

考虑决策者心理行为的混合型随机多属性决策方法

针对混合型随机多属性决策问题,提出一种考虑决策者心理行为的决策分析方法。在该方法中,首先将具有离散型随机变量、灰色型随机变量和语言型变量形式的属性值规范化到区间内;然后将决策者给出的针对不同时期的属性期望视为参照点,并通过计算方案属性值与参照点的距离构建方案的益损矩阵;进一步地,依据累计前景理论,计算方案在不同属性上的收益和损失价值,并在此基础上,通过集结不同属性和不同时期的方案前景值确定各方案的综合前景值,进而依据得到的综合前景值确定方案排序结果。最后,通过一个算例说明了该方法的有效性和可行性。     

具有模糊预约时间的VRP混合遗传算法

在对具有模糊预约时间的多对多货物收发情况下的车辆路径问题进行简单描述的基础上,构建了该问题的多目标数学规划模型,提出了解决该问题的一种基于插入启发式算法、并用修正的推—碰—掷过程进行改进的混合遗传算法,最后,给出了该问题的一个计算实例,并与改进的Solomon插入启发式算法进行了比较.     

Integrating Uncertainty and Interindividual Variability in Environmental Risk Assessment

An integrated, quantitative approach to incorporating both uncertainty and interindividual variability into risk prediction models is described. Individual risk R is treated as a variable distributed in both an uncertainty dimension and a variability dimension, whereas population risk I (the number of additional cases caused by R) is purely uncertain. I is shown to follow a compound Poisson-binomial distribution, which in low-level risk contexts can often be approximated well by a corresponding compound Poisson distribution. The proposed analytic framework is illustrated with an application to cancer risk assessment for a California population exposed to 1,2-dibromo-3-chloropropane from ground water.     

基于前景理论的多阶段随机多准则决策方法

研究一种基于动态参考点的多阶段随机多准则决策方法。考虑多阶段决策过程中决策者的风险偏好,建立了基于前景理论的多阶段随机多准则决策分析框架,提出了一种基于阶段发展特征的动态参考点设置方法;构建准则权重的目标规划模型,结合阶段参考点动态变化的特征测算各阶段备选方案的综合前景值;设计方案综合前景值的范围估算模型,以反映决策风险对评价结果的影响;案例研究验证了上述方法的可行性和实际效果。     

公司价值的随机优化模型

本文研究了净现金流为随机过程情况下的企业价值,并建立了企业价值的随机优化模型。探讨了在一定的风险水平和其它相关约束条件下,确定企业的资本结构、企业债务的承担能力等,使得公司价值最大化,并应用于实际项目中。     

考虑不确定性影响的银行服务质量评价

本文研究了不确定性对服务质量评价的影响,建立了服务质量评价的均值—方差模型,并进行了实证分析和检验。这一模型被应用来对我国主要商业银行的服务质量和顾客满意度进行排序分析,其结果显示银行服务质量的提高应该从服务的平均水平和一致性两个方面来努力。     

Percentiles of the Product of Uncertainty Factors for Establishing Probabilistic Reference Doses

Exposure guidelines for potentially toxic substances are often based on a reference dose (RfD) that is determined by dividing a no-observed-adverse-effect-level (NOAEL), lowest-observed-adverse-effect-level (LOAEL), or benchmark dose (BD) corresponding to a low level of risk, by a product of uncertainty factors. The uncertainty factors for animal to human extrapolation, variable sensitivities among humans, extrapolation from measured subchronic effects to unknown results for chronic exposures, and extrapolation from a LOAEL to a NOAEL can be thought of as random variables that vary from chemical to chemical. Selected databases are examined that provide distributions across chemicals of inter- and intraspecies effects, ratios of LOAELs to NOAELs, and differences in acute and chronic effects, to illustrate the determination of percentiles for uncertainty factors. The distributions of uncertainty factors tend to be approximately lognormally distributed. The logarithm of the product of independent uncertainty factors is approximately distributed as the sum of normally distributed variables, making it possible to estimate percentiles for the product. Hence, the size of the products of uncertainty factors can be selected to provide adequate safety for a large percentage (e.g., approximately 95%) of RfDs. For the databases used to describe the distributions of uncertainty factors, using values of 10 appear to be reasonable and conservative. For the databases examined the following simple "Rule of 3s" is suggested that exceeds the estimated 95th percentile of the product of uncertainty factors: If only a single uncertainty factor is required use 33, for any two uncertainty factors use 3 x 33 approximately 100, for any three uncertainty factors use a combined factor of 3 x 100 = 300, and if all four uncertainty factors are needed use a total factor of 3 x 300 = 900. If near the 99th percentile is desired use another factor of 3. An additional factor may be needed for inadequate data or a modifying factor for other uncertainties (e.g., different routes of exposure) not covered above.     

考虑两类赔款数据相关性的随机性准备金进展法及改进

本文创新性地提出基于成对抽数的非参数Bootstrap方法、二元正态分布和Copulas函数三种考虑已决赔款与已报案赔款相关性的随机性准备金进展法,并结合非寿险精算实务中的经典流量三角形数据,应用R软件对三种考虑相关性的随机性准备金进展法进行了完整的编程实现,并模拟得到了最终损失、未决赔款准备金和IBNR的完整的预测分布。本文提出的考虑相关性的随机性准备金进展法不但考虑了两类赔款数据之间的相关性,而且体现了不同事故年已发生已报案未决赔款准备金进展情况之间的差异。这种处理相关性的思路和方法在多元准备金评估中具有重要的应用价值。     

Uncertainty in Measurements of Dermal Absorption of Pesticides

Dermal absorption experiments form an important component in the assessment of risk from exposure to pesticides and other substances. Much dermal absorption data is gathered in rat experiments carried out using a certain standard protocol. Uncertainties in these data arise from many sources and can be quite large. For example, measurements of the systemic absorption of hexaconazole differed by more than an order of magnitude within a single experiment. Two diniconazole studies produced quite different results, due to minor differences in protocol and in chemical formulation. Limits of detection can also prevent accurate measurement when the amounts absorbed are small. These examples illustrate the need for measuring and reporting uncertainties in estimates that are based on these data. The most direct way to estimate uncertainty is to compute the sample standard deviations of replicate measurements. By pooling these estimates across dose and duration groups for which they are similar, the number of degrees of freedom is increased, and more precise confidence intervals can be obtained. In particular, the ratio of upper to lower 95% confidence limits was reduced by as much as ten-fold for hexaconazole, seven-fold for uniconazole, and nearly four-fold for propiconazole.     

企业动态能力及其功效:环境不确定性的影响

当前关于动态能力的维度及其功效还存在较大分歧,有些学者甚至认为动态能力毫无价值,应该摒弃动态能力研究.本文从战略过程视角,依据相关文献与访谈调查,将动态能力分解为组织意会能力、柔性决策能力及动态执行能力,探讨了动态能力与持续优势的关系及环境不确定性在其中的影响作用.通过对中国地区217家企业的实证研究发现,动态能力确实对持续优势有显著的正向影响,环境不确定性是动态能力的驱动因素而非调节变量,环境动态性对企业持续优势有显著的正向影响,敌对性则对持续优势有显著的负向影响.本研究的结论澄清了动态能力的价值前提,探明了环境不确定性的影响机理,对理论研究与实践操作都有一定的启发意义.     

Mixed Levels of Uncertainty in Complex Policy Models

The characterization and treatment of uncertainty poses special challenges when modeling indeterminate or complex coupled systems such as those involved in the interactions between human activity, climate and the ecosystem. Uncertainty about model structure may become as, or more important than, uncertainty about parameter values. When uncertainty grows so large that prediction or optimization no longer makes sense, it may still be possible to use the model as a behavioral test bed to examine the relative robustness of alternative observational and behavioral strategies. When models must be run into portions of their phase space that are not well understood, different submodels may become unreliable at different rates. A common example involves running a time stepped model far into the future. Several strategies can be used to deal with such situations. The probability of model failure can be reported as a function of time. Possible alternative surprises can be assigned probabilities, modeled separately, and combined. Finally, through the use of subjective judgments, one may be able to combine, and over time shift between models, moving from more detailed to progressively simpler order-of-magnitude models, and perhaps ultimately, on to simple bounding analysis.