Voltage stability analysis considering the uncertainties of dynamic load parameters

Many uncertainties exist in power systems and they will affect the stability analysis results. Voltage stability considering uncertainty in load parameters will be discussed. With the assumption that parameter variation is normal distribution, the probabilistic characteristics of eigenvalues under the uncertainties of dynamic load parameters can be obtained. Distribution of the critical eigenvalue will determine the stability probability of a power system. The stability margin can be inferred from the probabilistic critical load level, which is the maximal load level where system is `probabilistically` stable. Case studies on three test systems illustrate that the stability margin will be reduced with load uncertainty. The proposed probabilistic results are validated using deterministic method of Monte Carlo on multi 10`000 sample studies.     

An approximate sensitivity analysis of results from complex computer models in the presence of epistemic and aleatory uncertainties

This paper focuses on sensitivity analysis of results from computer models in which both epistemic and aleatory uncertainties are present. Sensitivity is defined in the sense of “uncertainty importance” in order to identify and to rank the principal sources of epistemic uncertainty. A natural and consistent way to arrive at sensitivity results in such cases would be a two-dimensional or double-loop nested Monte Carlo sampling strategy in which the epistemic parameters are sampled in the outer loop and the aleatory variables are sampled in the nested inner loop. However, the computational effort of this procedure may be prohibitive for complex and time-demanding codes. This paper therefore suggests an approximate method for sensitivity analysis based on particular one-dimensional or single-loop sampling procedures, which require substantially less computational effort. From the results of such sampling one can obtain approximate estimates of several standard uncertainty importance measures for the aleatory probability distributions and related probabilistic quantities of the model outcomes of interest. The reliability of the approximate sensitivity results depends on the effect of all epistemic uncertainties on the total joint epistemic and aleatory uncertainty of the outcome. The magnitude of this effect can be expressed quantitatively and estimated from the same single-loop samples. The higher it is the more accurate the approximate sensitivity results will be. A case study, which shows that the results from the proposed approximate method are comparable to those obtained with the full two-dimensional approach, is provided.     

自适应蒙特卡洛法评定全站仪测距不确定度

全站仪测距精度的校准需要在标准基线场上进行,由于野外环境不可控和气象条件波动剧烈,因此判断全站仪的测量结果的可靠程度具有重要意义。为了解决全站仪测距不确定度评定模型的非线性和输入量强相关等问题,本文首先采用了自适应蒙特卡洛法进行不确定度评定,然后与GUM的不确定度评定结果进行对比,当测距距离为1 176 m时,自适应蒙特卡洛法评定的不确定度结果为2.2 mm,GUM为2.6 mm,结果显示两种不确定度评定方法的测量结果均在合理预期之内,且自适应蒙特卡洛法评定的不确定度置信区间更窄。自适应蒙特卡洛法结合了大量数据样本和自适应优化仿真次数的优势,不仅对全站仪测距过程中的各项误差源引入的不确定度分量评估更为全面,而且在保证了全站仪测距不确定度评定结果准确的同时,相比于蒙特卡洛法节约了70%的样本数量。     

基于参数识别的结构损伤概率诊断方法

为解决观测噪声等不确定性因素影响下确定性损伤识别方法的损伤误判问题,提出了结构损伤识别的概率可靠度法。通过正则化修正改善参数识别问题的不适定性,利用数据摄动和蒙特卡罗法研究观测噪声对参数识别结果的影响并获得各待识别参数的统计特征,在此基础上基于概率统计理论推导了损伤概率的计算公式。根据损伤识别试验验证了方法的有效性和准确性,分析并比较了概率可靠度法和确定性方法的损伤识别结果。试验研究表明,损伤识别的概率可靠度法能够显著改善传统确定性损伤识别方法的损伤误判问题。     

Uncertainty quantification in dynamic system risk assessment: a new approach with randomness and fuzzy theory

Quantifying uncertainty during risk analysis has become an important part of effective decision-making and health risk assessment. However, most risk assessment studies struggle with uncertainty analysis and yet uncertainty with respect to model parameter values is of primary importance. Capturing uncertainty in risk assessment is vital in order to perform a sound risk analysis. In this paper, an approach to uncertainty analysis based on the fuzzy set theory and the Monte Carlo simulation is proposed. The question then arises as to how these two modes of representation of uncertainty can be combined for the purpose of estimating risk. The proposed method is applied to a propylene oxide polymerisation reactor. It takes into account both stochastic and epistemic uncertainties in the risk calculation. This study explores areas where random and fuzzy logic models may be applied to improve risk assessment in industrial plants with a dynamic system (change over time). It discusses the methodology and the process involved when using random and fuzzy logic systems for risk management.     

On using residual risk to assess the cost effectiveness and health protectiveness of remedy selection at superfund sites

This article examines the importance of determining residual risk and its impact on remedy selection at Superfund Sites. Within this examination, risks are assessed using probabilistic models that incorporate the uncertainty and variability of the input parameters, and utilize parameter distributions based on current and applicable site-specific data. Monte Carlo methods are used to propagate these uncertainties and variabilities through the risk calculations resulting in a distribution for the estimate of both risk and residual risk. Such an approach permits an informed decision based on a broad information base which involves considering the entire uncertainty distribution of risk rather than a point estimate for each exposure scenario. Using the probabilistic risk estimates, with current and applicable site-specific data, alternative decisions regarding cleanup are obtained for two Superfund Sites.     

A Probabilistic Method to Predict Fatigue Crack Initiation

A probabilistic method to predict macrocrack initiation due to fatigue damage is presented in this paper. Acoustic non-linearity is used to quantify pre-macrocrack initiation damage. This data is then used in a probabilistic analysis of fatigue damage. The probabilistic fatigue damage analysis consists of a suitably chosen damage evolution equation to model accumulated damage coupled with a procedure to calculate the probability of macrocrack initiation. The probability of macrocrack initiation is evaluated using the Monte Carlo Method with Importance Sampling. Numerical results for the probabilistic assessment of fatigue damage for a sample problem are presented and compared with experimental results.     

基于频响函数综合的浮筏隔振系统误差传递分析

采用基于频响函数综合的子结构方法对浮筏隔振系统进行建模分析和误差传递分析。针对测试频响函数的一些常见误差,如测试噪声对频响函数幅值和相位的污染,同一子结构的频响函数不满足互易性,原点频响函数的虚部小于零等,分析其在综合时由于误差传递和放大效应对综合结果的影响。并采用矩方法对误差传递进行定量分析,将矩方法的结果和采用Monte Carlo方法的结果进行对比,结果表明矩方法具有较高的效率和精度。     

Probabilistic fracture mechanics by Galerkin meshless methods – part II: reliability analysis

 This is the second in a series of two papers generated from a study on probabilistic meshless analysis of cracks. In this paper, a stochastic meshless method is presented for probabilistic fracture-mechanics analysis of linear-elastic cracked structures. The method involves an element-free Galerkin method for calculating fracture response characteristics; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using a virtual crack extension technique described in the companion paper [1]. Numerical examples based on mode-I and mixed-mode problems are presented to illustrate the proposed method. The results show that the predicted probability of fracture initiation based on the proposed formulation of the sensitivity of fracture parameter is accurate in comparison with the Monte Carlo simulation results. Since all gradients are calculated analytically, reliability analysis of cracks can be performed efficiently using meshless methods. Received 20 February 2001 / Accepted 19 December 2001     

基于正弦激励的压电加速度计模型参数辨识

针对压电加速度计常规校准无法完全满足实际机械动态量测量要求的问题,采用基于加速度计模型参数校准的方法。参数未知的线性二阶微分方程用来表示加速度计动态特性,利用绝对法振动校准加速度计频率响应数据,采用最小二乘算法确定了未知的参数的值,同时利用蒙特卡罗法确定了参数值的不确定度。最后对加速度计进行了瞬态冲击加速度校准,计算辨识所得模型在相同冲击激励下的预测输出。结果表明:瞬态冲击加速度校准与计算辨识模型结果相差不超过1%。     

多源不确定性条件下气动弹性系统颤振可靠性分析方法

传统的气动弹性系统颤振分析模型大多是在确定性参数条件下建立的,当系统中存在不确定因素时,按确定性方法设计的气动弹性系统存在颤振失效风险.以概率和非概率区间模型为基础,建立了单源不确定性条件下颤振可靠性分析模型;在此基础上,针对含随机和区间多源不确定参数的气动弹性系统颤振可靠性分析问题,提出一种基于分步求解策略的新型混合...     

城市燃气管网三维度抗震韧性定量评估方法

为了量化评估城市燃气管网系统的抗震韧性,并充分考虑地震动输入,管网连通性能评估,以及修复过程三个方面的不确定性,该文提出了技术维度、组织维度、社会维度下的燃气管网抗震韧性定量评估流程.衔接地震动预测方程(GMPE)输入,基于蒙特卡罗模拟对燃气管网连通性进行计算.通过随机模拟修复资源分配求得燃气管网在每次模拟破坏工况下的...     

Modeling of uncertainty for flood wave propagation induced by variations in initial and boundary conditions using expectation operator on explicit numerical solutions

This study proposes a framework for uncertainty analysis by incorporating explicit numerical solutions of governing equations for flood wave propagation with the expectation operator. It aims at effectively evaluating the effect of variations in initial and boundary conditions on the estimation of flood waves. Spatiotemporal semivariogram models are employed to quantify the correlation of the variables in time and space. The 1D nonlinear kinematic wave equation for the overland flow (named EVO_NS_KWE) is applied in the model development. Model validation is made by comparison with the Monte Carlo simulation model in the calculation of statistical properties of model outputs (ie, flow depths), that is, the mean, standard deviation, and coefficient of variation. The results from the model validation show that the EVO_NS_KWE model can produce excellent approximations of the mean and less satisfactory approximations of the standard deviation and coefficient of variation compared with those obtained by using the Monte Carlo simulation model. It concludes that the uncertainties of flow depths in the domain are significantly affected by variations in the boundary condition. Future application of the EVO_NS_KWE model enables the evaluation of uncertainty in model outputs induced by the initial and boundary condition subject to uncertainty and will also provide corresponding probabilistic information for risk quantification method.     

失配误差的蒙特卡洛分析

针对极限相位法评定失配误差引入的测量不确定度普遍偏大的问题,提出了采用蒙特卡洛法对其评定的新方法。以交替比较法校准功率座为实例,研究了蒙特卡洛法评定失配误差引入的测量不确定度的具体实现方法,并将其得到的结果与极限相位法进行比较。结果表明,蒙特卡洛法更适合用于失配误差引入的测量不确定度进行评定。     

Measurement Uncertainty of Dew-Point Temperature in a Two-Pressure Humidity Generator

This article describes the measurement uncertainty evaluation of the dew-point temperature when using a two-pressure humidity generator as a reference standard. The estimation of the dew-point temperature involves the solution of a non-linear equation for which iterative solution techniques, such as the Newton?CRaphson method, are required. Previous studies have already been carried out using the GUM method and the Monte Carlo method but have not discussed the impact of the approximate numerical method used to provide the temperature estimation. One of the aims of this article is to take this approximation into account. Following the guidelines presented in the GUM Supplement 1, two alternative approaches can be developed: the forward measurement uncertainty propagation by the Monte Carlo method when using the Newton?CRaphson numerical procedure; and the inverse measurement uncertainty propagation by Bayesian inference, based on prior available information regarding the usual dispersion of values obtained by the calibration process. The measurement uncertainties obtained using these two methods can be compared with previous results. Other relevant issues concerning this research are the broad application to measurements that require hygrometric conditions obtained from two-pressure humidity generators and, also, the ability to provide a solution that can be applied to similar iterative models. The research also studied the factors influencing both the use of the Monte Carlo method (such as the seed value and the convergence parameter) and the inverse uncertainty propagation using Bayesian inference (such as the pre-assigned tolerance, prior estimate, and standard deviation) in terms of their accuracy and adequacy.     

An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

This paper presents an efficient analytical Bayesian method for reliability and system response updating without using simulations. The method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability index or confidence interval. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method are compared with traditional simulation-based methods.     

Reliability analysis of large structural systems

Brute force Monte Carlo simulation methods can, in principle, be used to calculate accurately the reliability of complicated structural systems, but the computational burden may be prohibitive. A new Monte Carlo based method for estimating system reliability that aims at reducing the computational cost is therefore proposed. It exploits the regularity of tail probabilities to set up an approximation procedure for the prediction of the far tail failure probabilities based on the estimates of the failure probabilities obtained by Monte Carlo simulation at more moderate levels. In this paper, the usefulness and accuracy of the estimation method is illustrated by application to a particular example of a structure with several thousand potentially critical limit state functions. The effect of varying the correlation of the load components is also investigated.     

Development of stochastic isogeometric analysis (SIGA) method for uncertainty in shape

In this paper, a new method is proposed that extend the classical deterministic isogeometric analysis (IGA) into a probabilistic analytical framework in order to evaluate the uncertainty in shape and aim to investigate a possible extension of IGA in the field of computational stochastic mechanics. Stochastic IGA (SIGA) method for uncertainty in shape is developed by employing the geometric characteristics of the non-uniform rational basis spline and the probability characteristics of polynomial chaos expansions (PCE). The proposed method can accurately and freely evaluate problems of uncertainty in shape caused by deformation of the structural model. Additionally, we use the intrusive formulation approach to incorporate PCE into the IGA framework, and the C++ programming language to implement this analysis procedure. To verify the validity and applicability of the proposed method, two numerical examples are presented. The validity and accuracy of the results are assessed by comparing them to the results obtained by Monte Carlo simulation based on the IGA algorithm.     

Uncertainty Calculation for Spectral-Responsivity Measurements

This paper discusses a procedure for measuring the absolute spectral responsivity of optical-fiber power meters and computation of the calibration uncertainty. The procedure reconciles measurement results associated with a monochromator-based measurement system with those obtained with laser sources coupled with optical fiber. Relative expanded uncertainties based on the methods from the Guide to the Expression of Uncertainty in Measurement and from Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement”-Propagation of Distributions using a Monte Carlo Method are derived and compared.An example is used to illustrate the procedures and calculation of uncertainties.