Reconstruction of probabilistic S-N curves under fatigue life following lognormal distribution with given confidence

When the historic probabilistic S-N curves are given under special survival probability and confidence levels and there is no possible to re-test, fatigue reliability analysis at other levels can not be done except for the special levels. Therefore, the wide applied curves are expected. Monte Carlo reconstruction methods of the test data and the curves are investigated under fatigue life following lognormal distribution. To overcome the non-conservative assessment of existent man-made enlarging the sample size up to thousands, a simulation policy is employed to address the true production where the sample size is controlled less than 20 for material specimens, 10 for structural component specimens and the errors matching the statistical parameters are less than 5 percent. Availability and feasibility of the present methods have been indicated by the reconstruction practice of the test data and curves for 60Si2Mn high strength spring steel of railway industry.

Estimating probability curves of rock variables using orthogonal polynomials and sample moments

A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.

WEIGHTED LEAST SQUARE METHOD FOR S-N CURVE FITTING

An S-N curve fitting approach is proposed based on the weighted least square method, and the weights are inversely proportional to the length of mean confidence intervals of experimental data sets. The assumption coincides with the physical characteristics of the fatigue life scatter. Two examples demonstrate the method. It is shown that the method has better accuracy and reasonableness compared with the usual least square method.

Analysis Approach to Durability Based on Material Initial Fatigue Quality and S-N Curve

Based on probabilistic fracture mechanics approach, a new concept of material initial fatigue quality （MIFQ） is developed. Then, the relation between S-N curve and crack propagation curve is studied. From the study, a new durability analysis method is presented. In this method, S-N curve is used to determine crack growth rate under constant amplitude loading and evaluate the effects of different factors on durability and then the structural durability is analyzed. The tests and analyses indicate that this method has lower dependence on testing, and higher accuracy, reliability and generality and is convenient for application.

Combine S-N curve and fracture mechanics for fatigue life analysis of welded structures

Based on the evolution of fatigue cracks in welded structures,the fatigue life of welded structures was defined as the sum of the crack initiation life Ni and the crack propagation life Np.Correspondingly,a fatigue-life analysis method combining S-N curves and fracture mechanics theory was proposed.The equivalent structural stress method and the lower 99%boundary of the master S-N curve were used to evaluate Ni,and cracks at the end of the initiation stage were considered as semi-elliptical surface cracks.Moreover,Paris equation and the stress intensity factor range of the cracks were used to evaluate Np.Furthermore,the fatigue test results obtained from the running girder of cranes were used as a reference for comparison and verification of the results.The results revealed that the equivalent structural stress is a good indicator for the crack initiation behavior of complex welded structures.In addition,the predicted fatigue life corresponded closely to the testing life.

Regionalization of Rainfall Intensity-Duration-Frequency (IDF) Curves in Botswana

A regional analysis of design storms, defined as the expected rainfall intensity for given storm duration and return period, is conducted to determine storm Rainfall Intensity-Duration-Frequency (IDF) relationships. The ultimate purpose was to determine IDF curves for homogeneous regions identified in Botswana. Three homogeneous regions were identified based on topographic and rainfall characteristics which were constructed with the K-Means Clustering algorithm. Using the mean annual rainfall and the 24 hr annual maximum rainfall as an indicator of rainfall intensity for each homogeneous region, IDF curves and maps of rainfall intensities of 1 to 24 hr and above durations were produced. The Gamma and Lognormal probability distribution functions were able to provide estimates of rainfall depths for low and medium return periods (up to 100 years) in any location in each homogeneous region of Botswana.

Computer program of nonlinear, curved regression for ‘probacent’-probability equation in biomedicine

On the basis of experimental observations on animals, applications to clinical data on patients and theoretical statistical reasoning, the author developed a com-puter-assisted general mathematical model of the ‘probacent’-probability equation, Equation (1) and death rate (mortality probability) equation, Equation (2) derivable from Equation (1) that may be applica-ble as a general approximation method to make use-ful predictions of probable outcomes in a variety of biomedical phenomena [1-4]. Equations (1) and (2) contain a constant, γ and c, respectively. In the pre-vious studies, the author used the least maximum- difference principle to determine these constants that were expected to best fit reported data, minimizing the deviation. In this study, the author uses the method of computer-assisted least sum of squares to determine the constants, γ and c in constructing the ‘probacent’-related formulas best fitting the NCHS- reported data on survival probabilities and death rates in the US total adult population for 2001. The results of this study reveal that the method of com-puter-assisted mathematical analysis with the least sum of squares seems to be simple, more accurate, convenient and preferable than the previously used least maximum-difference principle, and better fit-ting the NCHS-reported data on survival probabili-ties and death rates in the US total adult population. The computer program of curved regression for the ‘probacent’-probability and death rate equations may be helpful in research in biomedicine.

一种基于P-S-N的可靠性高精确度数值求解方法

根据应力-强度干涉分布理论和可靠性设计方法,建立基于P-S-N(可靠性-应力-寿命)的可靠度计算数学模型,并利用概率分布密度曲线干涉区间积分、复合梯形法则和辛普生法则来实现可靠度的高精确度数值化求解,通过编写计算机程序算法得以实现。算例表明,与传统的可靠性计算方法相比,系统可靠性的计算精确度得到显著提高,研究成果具有工程应用背景。

螺旋埋弧焊接X70钢管焊缝金属P-S-N曲线的建立

通过对螺旋埋弧焊接X70钢管焊缝金属进行疲劳试验,得到了不同应力幅和应力比下的疲劳寿命数据,对疲劳寿命的概率分布进行了分析;依据当量疲劳寿命公式,获得疲劳抗力系数和当量疲劳极限,并对其概率分布进行分析,进而建立了焊缝金属的P-S-N曲线,给出了指定存活率下的疲劳寿命曲线。结果表明:焊缝金属的疲劳寿命服从对数正态分布,疲劳抗力系数服从对数正态分布,以当量应力表示的疲劳极限服从正态分布。

一种修正金属材料S-N曲线的新方法探讨

为了准确估算机械结构的疲劳寿命,基于非概率集合理论,提出了修正金属材料S-N曲线的新方法,与经验公式方法和实验概率统计方法相比,新方法客服了概率统计方法需要预先知道大量统计数据的缺点,且计算量小。并利用典型的数值算例进行了计算,结果表明利用新方法修正材料S-N曲线快速,准确。

Development of damage probability matrices based on Greek earthquake damage data

A comprehensive study is presented for empirical seismic vulnerability assessment of typical structural types, representative of the building stock of Southern Europe, based on a large set of damage statistics. The observational database was obtained from post-earthquake surveys carried out in the area struck by the September 7, 1999 Athens earthquake. After analysis of the collected observational data, a unified damage database has been created which comprises 180,945 damaged buildings from/after the near-field area of the earthquake. The damaged buildings are classified in specific structural types, according to the materials, seismic codes and construction techniques in Southern Europe. The seismic demand is described in terms of both the regional macroseismic intensity and the ratio αg/ao, where αg is the maximum peak ground acceleration （PGA） of the earthquake event and ao is the unique value PGA that characterizes each municipality shown on the Greek hazard map. The relative and cumulative frequencies of the different damage states for each structural type and each intensity level are computed in terms of damage ratio. Damage probability matrices （DPMs） and vulnerability curves are obtained for specific structural types. A comparison analysis is fulfilled between the produced and the existing vulnerability models.

虚拟增广S-N曲线样本的投射法

为解决小子样条件下结构疲劳可靠性的有效评估问题,利用正态分布和标准正态分布之间的相互转化关系,在对数疲劳寿命服从正态分布和同破坏率的前提下,建立了虚拟增广S-N曲线样本的投射法模型。通过实例验证,该投射模型估算的带可靠度的安全寿命与真实试验结果的平均误差一般在5%以内。在显著度小于等于0.05时,用F检验和t检验验证了投射样本和真实试验样本无显著性差异,表明可以用投射法得到的虚拟样本代替真实试验样本参与后期的疲劳统计分析。

Structural Stress-Fatigue Life Curve Improvement of Spot Welding Based on Quasi‑Newton Method

ΔF-N curves are usually used to predict the fatigue life of spot welding in engineering,but they are time-consuming and laborious and not universal.For the purpose of predicting the fatigue life of spot welding accurately and efficiently,tensile-shear fatigue tests were conducted to obtain the fatigue life of spot-welded specimens with different sheet thicknesses combinations.These specimens were simulated by using the finite element method,and the structural stress was theoretically calculated.In the double logarithmic coordinate system,the structural stress-fatigue life(S-N)curve of spot welding was fitted by the least-squares method,based on the quasi-Newton method.The square of the correlation coefficient of the S-N curve was taken as the optimization objective,with the correction coefficients of force,bending moment,spot welding diameter,and sheet thickness as the variables.During the optimization process,three different ways were utilized to get three optimized spot welding S-N curves,which are suitable for different situations.The results show that the fitting effect of the S-N curve is improved,the data points are more compact,and the optimization effect is significant.These S-N curves can be used to predict the fatigue life,which provide the basis for practical engineering application.

Unified Principal S-N Equation for Friction Stir Welding of 5083 and 6061 Aluminum Alloys

With the popularization of friction stir welding(FSW),5083-H321 and 6061-T6 aluminum alloy materials are widely used during the FSW process.In this study,the fatigue life of friction stir welding with two materials,i.e.,5083-H321 and 6061-T6 aluminum alloy,are studied.Fatigue tests were carried out on the base metal of these two materials as well as on the butt joints and overlapping FSW samples.The principle of the equivalent structural stress method is used to analyze the FSW test data of these two materials.The fatigue resistances of these two materials were com-pared and a unified principal S-N curve equation was fitted.Two key parameters of the unified principal S-N curve obtained by fitting,Cd is 4222.5,and h is 0.2693.A new method for an FSW fatigue life assessment was developed in this study and can be used to calculate the fatigue life of different welding forms with a single S-N curve.Two main fatigue tests of bending and tension were used to verify the unified principal S-N curve equation.The results show that the fatigue life calculated by the unified mean 50%master S-N curve parameters are the closest to the fatigue test results.The reliability,practicability,and generality of the master S-N curve fitting parameters were verified using the test data.The unified principal S-N curve acquired in this study can not only be used in aluminum alloy materials but can also be applied to other materials.

Probability Distribution of SARS-Cov-2 (COVID) Infectivity Following Onset of Symptoms: Analysis from First Principles

The phasing out of protective measures by governments and public health agencies, despite continued seriousness of the coronavirus pandemic, leaves individuals who are concerned for their health with two basic options over which they have control: 1) minimize risk of infection by being vaccinated and by wearing a face mask when appropriate, and 2) minimize risk of transmission upon infection by self-isolating. For the latter to be effective, it is essential to have an accurate sense of the probability of infectivity as a function of time following the onset of symptoms. Epidemiological considerations suggest that the period of infectivity follows a lognormal distribution. This proposition is tested empirically by construction of the lognormal probability density function and cumulative distribution function based on quantiles of infectivity reported by several independent investigations. A comprehensive examination of a prototypical ideal clinical study, based on general statistical principles (the Principle of Maximum Entropy and the Central Limit Theorem) reveals that the probability of infectivity is a lognormal random variable. Subsequent evolution of new variants may change the parameters of the distribution, which can be updated by the methods in this paper, but the form of the probability function is expected to remain lognormal as this is the most probable distribution consistent with mathematical requirements and available information.

Probability Distribution and Their Non-linear Relationship between Node Degree and Clustering Coefficient of Aviation Network of China Based on Complex Network

In order to reveal the complex network feature of aviation network of China,probability distribution of node degree and clustering coefficient of aviation network of China was researched according to statistics data of civil aviation of China.It was verified that node degree had power function probability distribution.Clustering coefficient of nodes with exponential function probability distribution was discovered.It was found that node degree and clustering coefficient had single peak nonlinear relationship.At the left side of the peak,there is no certain relationship between them.At the right side of the peak,clustering coefficient became smaller with the rise of node degree and there was negative exponential function relationship between them by regression analysis.

区域地质灾害易发性评价的证据权法原理与实践

在阐述证据权法概念与原理的基础上,以西北黄土高原滑坡、崩塌地质灾害高易发的兰州市区为评价区,详解基于证据权法的区域地质灾害易发性评价的技术流程,利用GIS工具,开展评价指标选取与相关性分析、证据因子权重与后验概率分析、评价模型检验、易发程度评价。分析结果显示,坡度、坡向、地层岩性、断层、绿化灌溉、土地利用类型等地质灾害影响因素之间呈无相关或弱相关性,符合相互独立的要求,组成的模型ROC曲线(接受者操作特征曲线)AUC值(曲线下面积)为0.85,具有较高的预测精度。理论与实践表明,与其他统计学方法相比,证据权法同时考虑了评价指标中存在地质灾害与不存在地质灾害2种情况,避免了当地质灾害不存在时权重偏大导致结果失真的问题。证据权法结果为地质灾害发生的绝对概率,可以作为不同区域、地区的地质灾害易发程度对比的依据。

外置耗能角钢的摇摆-自复位桥梁双柱墩地震易损性分析

为评估设置耗能角钢的摇摆-自复位桥梁双柱墩的抗震能力,本文建立该结构的有限元分析模型,分别定义和量化双柱墩不同损伤状态和损伤指标。本文从太平洋地震工程研究中心选取16条近断层地震动,基于增量动力分析,得到该结构的地震响应。基于最小二乘法,对得到的增量动力分析曲线进行对数回归分析,计算结构不同损伤状态的超越概率及易损性曲线。研究表明:当地面峰值加速度为0.1 g时,外置耗能角钢与耗能钢筋屈服的超越概率分别为34%和22%;当峰值加速度为0.4 g时,外置耗能角钢与耗能钢筋失效的超越概率分别为6%和11%,而预应力筋未屈服;当峰值加速度为1.0 g时,外置耗能角钢和耗能钢筋失效的概率分别达到85%和91%,桥墩发生倒塌的概率为46%。

二维曲线型随机变量函数概率分布的计算

利用转换法给出二维曲线型随机变量函数概率分布的求解方法,指出在特殊情形下其与一维连续型随机变量函数概率分布的关系,并举例说明了求解方法的有效性.所给结果为二维曲线型随机变量的相关研究提供了新思路,具有一定的教学参考价值.

基于三相动态谐波分析的电能表误差检测方法

在检测电能表误差时,原始信号中谐波的干扰会导致检测结果与实际情况存在较大偏差。为此,提出基于三相动态谐波分析的电能表误差检测方法。在谐波分析阶段,考虑到谐波的动态属性会导致三相信号的采样执行效果难以达到同步,构建了余弦组合窗——旁瓣最低与最速下降窗,利用其对电能表离散信号进行截取,以此避免信号能量向临近谱线泄漏,再利用离散傅里叶变换对信号进行处理,实现对谐波的提取。在误差检测阶段,以离散随机信号的概率密度函数为导向,采用最优直方图曲线拟合法对其加以分析,并结合标准情况下电能表信号的分布状态,实现对误差的计算。在测试结果中,电能表误差检测结果的偏差始终稳定在3.0%以内。