二阶二次矩法在船舶结构可靠性分析中的应用

二阶二次矩法在船舶结构可靠性分析中的应用桂洪斌，郭昌捷（大连理工大学船舶工程学院，大连１１６０２４）关键词船舶；结构可靠性／二阶二次矩法分类号Ｕ６６１．４２以概率论为基础的结构可靠性分析与设计理论，虽然诞生较晚，但发展迅速，新的理论和方法不断产生，...

疲劳安全与寿命可靠性评估二次三阶矩方法

提出了疲劳安全与寿命可靠性评估的二次三阶矩方法，并且给出了常用随机变量的三阶矩计算方法，由于采用三参数威布尔分布拟合，可以较好描述各种分布形态的随机变量，与传统的一次二阶矩方法比较，该文提出的方法计算精度高，适应性强．

结合无功二次精确矩法的混沌社会情感优化算法的多目标无功优化

针对配电网无功优化的特点,提出一种新的方法。首先,采用无功二次精确矩法确定无功补偿点;然后建立以有功网损最小、电压偏差最小及静态电压稳定裕度最大的多目标无功优化模型,用模糊方法将多目标优化问题转化为单目标问题,并以最大、一般和最小3种运行方式模拟配电网的实际运行;接着在社会情感优化算法上引入情感强度定律,模拟人类情感变化以提高寻优精度;同时引入混沌扰动机制,来增强种群多样性以提高全局搜索能力;最后对IEEE 33节点配电网系统进行仿真分析,结果表明该优化方法可以有效地降低网损与提高电压质量。

钢筋混凝土梁—板结构可靠度计算方法研究

本文主要针对预制钢筋混凝土梁—现浇板复合结构的结构可靠度进行分析,采用美国混凝土学会ACI-318对一个简支梁—板结构进行了配筋设计与验算,并根据极限状态方程,分别采用一阶二次矩法及Rackwitz-Fiessler法计算了该结构的结构可靠度指标,最后使用蒙特卡洛模拟对计算结果进行了验证。计算结果表明,上述三种方法均能有效的计算结构可靠度指标,并且很好地描述该结构的可靠性能;该结构的性能主要由抗弯能力控制,在本结构中箍筋主要起到抵抗水平剪力及防止混凝土开裂的作用。

岩土工程简化可靠度设计方法——修正分位数法

现阶段多数规范推荐的半概率设计方法分项系数法与传统容许应力设计法具有相似的设计过程,易于被岩土工程师接受。然而,当实际岩土体参数统计量及分布类型等与分项系数设计法校准过程所采用的不一致时,分项系数法的设计结果往往会产生较大偏差。分位数设计法与分项系数法设计过程相似,且能够解决分项系数法设计偏差较大的问题。遗憾的是,该方法需要事先通过大量可靠度分析建立岩土结构物设计参数与有效随机维度间的回归函数,该过程不仅计算量较大而且十分繁琐,不利于工期紧迫条件下的快速可靠度设计。为此,提出了基于修正分位数法的岩土工程简化可靠度设计方法。首先介绍了原始有效随机维度–分位数设计法(ERD-QVM)和分位一阶二次矩可靠度分析方法,在此基础上提出了基于简单迭代算法的修正分位数法。最后以桩基础设计和方形基础设计为例阐明了所提方法的有效性。结果表明:修正分位数法为工期紧迫的岩土结构物可靠度设计提供了一种有效分析工具。修正分位数法不仅能够有效地避免原始ERD-QVM需要建立关于设计参数回归函数的问题,极大地降低原始ERD-QVM的计算量,而且能够得到合理的岩土结构物设计结果。修正分位数法设计结果更保守,原始ERD-QVM可能产生偏危险的设计,这对岩土结构物稳定性非常不利。两种设计方法具有相似的设计稳健性。

含多裂纹结构的断裂可靠性分析

基于随机有限元法和可靠性设计理论,建立了一种含多裂纹结构的断裂可靠性分析模型。首先,根据最小二乘法则建立应力强度因子的表达式,然后将影响结构断裂的不确定因素视为随机变量,通过一阶二次矩法和随机有限元法求出每条裂纹的可靠度指标,最后将含多裂纹结构看作一个由所有裂纹组成的串联系统,求出各裂纹之间的相关系数,并得出多裂纹结构失效概率的Ditlevsen界限值。数值算例表明,本方法具有较强的适用性。

斜拉桥索塔的可靠性分析

本文采用一阶二次矩法对斜拉桥索塔进行了可靠性分析，主要讨论塔架横桥向屈曲利顺桥向强度破坏两种失效模式，并以著名的法国Ｂｒｏｔｏｎｎｅ桥为例给出数值计算结果，同时对有关随机变量作参数分析，讨论其对塔架可靠度的影响。

腐蚀疲劳作用下的船舶极限强度可靠性分析

由于腐蚀和疲劳的综合作用,船舶舯横剖面模数随时间减少,造成船体结构承载能力降低。本文通过对腐蚀和疲劳作用的定量分析,提出一种船体结构可靠性的计算方法。建立随时间变化的腐蚀、疲劳及剖面模数的模型,并通过一阶二次矩法计算船体瞬时可靠性,得出了船舶全寿命期内舯横剖面的剖面模数、可靠性指标随时间的变化曲线。

地震作用下基础隔震框剪结构竖向连续倒塌可靠度分析

在引入隔震支座地震损伤模型的基础上,运用整体可靠度理论对基础隔震框剪结构进行竖向连续倒塌可靠度分析。首先,利用隔震支座的地震损伤模型,得到罕遇地震作用下最易失效的隔震支座;然后,在考虑损伤结构不确定性参数的基础上,利用竖向随机动力增量分析(IDA)方法,得到损伤结构竖向连续倒塌荷载系数;以荷载系数为整体性能指标,进行易损性分析;利用基于最大熵原理的二次四阶矩法,计算损伤结构发生倒塌的概率,最后,以一基础隔震框剪结构为例,利用该方法计算损伤结构竖向连续倒塌的可靠度指标及失效概率。研究表明,该方法可直观地得到结构抗竖向连续倒塌的能力,为评估结构在地震作用下产生损伤提供量化依据。

宽发光截面半导体激光器的光束质量研究

本文通过二阶矩法,分析了二维增益调制对于宽发光截面半导体激光器(BAL)的光束质量改善效果。光束质量是激光器工业应用中需要考虑的重要因素。BAL可以提供更大的输出功率,但其光束质量较常规半导体激光器差。本文测量了经过二维增益调制后的BAL。结果与未经过调制的BAL进行了比较。结果表明,经过二维增益调制后的BAL具有较高的阈值和较低的斜率效率,光束质量提高了20%。

Reliability analysis of earth slopes using hybrid chaotic particle swarm optimization

A numerical procedure for reliability analysis of earth slope based on advanced first-order second-moment method is presented,while soil properties and pore water pressure may be considered as random variables.The factor of safety and performance function is formulated utilizing a new approach of the Morgenstern and Price method.To evaluate the minimum reliability index defined by Hasofer and Lind and corresponding critical probabilistic slip surface,a hybrid algorithm combining chaotic particle swarm optimization and harmony search algorithm called CPSOHS is presented.The comparison of the results of the presented method,standard particle swarm optimization,and selected other methods employed in previous studies demonstrates the superior successful functioning of the new method by evaluating lower values of reliability index and factor of safety.Moreover,the presented procedure is applied for sensitivity analysis and the obtained results show the influence of soil strength parameters and probability distribution types of random variables on the reliability index of slopes.

A modified method to calculate reliability index using maximum entropy principle

Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.

Time-variant reliability analysis of three-dimensional slopes based on Support Vector Machine method

In the reliability analysis of slope, the performance functions derived from the most available stability analysis procedures of slopes are usually implicit and cannot be solved by first-order second-moment approach. A new reliability analysis approach was presented based on three-dimensional Morgenstem-Price method to investigate three-dimensional effect of landslide in stability analyses. To obtain the reliability index, Support Vector Machine （SVM） was applied to approximate the performance function. The time-consuming of this approach is only 0.028% of that using Monte-Carlo method at the same computation accuracy. Also, the influence of time effect of shearing strength parameters of slope soils on the long-term reliability of three-dimensional slopes was investigated by this new approach. It is found that the reliability index of the slope would decrease by 52.54% and the failure probability would increase from 0.000 705% to 1.966%. In the end, the impact of variation coefficients of c andfon reliability index of slopes was taken into discussion and the changing trend was observed.

Application of response surface method for contact fatigue reliability analysis of spur gear with consideration of EHL

In order to consider the effects of elastohydrodynamic lubrication(EHL) on contact fatigue reliability of spur gear, an accurate and efficient method that combines with response surface method(RSM) and first order second moment method(FOSM) was developed for estimating the contact fatigue reliability of spur gear under EHL. The mechanical model of contact stress analysis of spur gear under EHL was established, in which the oil film pressure was mapped into hertz contact zone. Considering the randomness of EHL, material properties and fatigue strength correction factors, the proposed method was used to analyze the contact fatigue reliability of spur gear under EHL. Compared with the results of 1.5×105 by traditional Monte-Carlo, the difference between the two failure probability results calculated by the above mentioned methods is 2.2×10-4, the relative error of the failure probability results is 26.8%, and time-consuming only accounts for 0.14% of the traditional Monte-Carlo method(MCM). Sensitivity analysis results are in very good agreement with practical cognition. Analysis results show that the proposed method is precise and efficient, and could correctly reflect the influence of EHL on contact fatigue reliability of spur gear.

Reflection spectra of fiber Bragg gratings in quadratic strain field

We theoretically analyze the reflection spectra of the fiber Bragg gratings in the quadratic strain field,and resolve the numerical value with transfer matrix method.When the value of pressure is changed,we can obtain diverse reflection spectra of the fiber Bragg gratings,which is in good accordance with the experimental results.

Resistance Partial Factor and Reliability of Cast Ball-and-Socket Support Joint

Considering the uncertainty of material performance, geometric characteristic and analysis method, the analysis of statistical parameters of the resistance of cast ball-and-socket support joints and the reliability analysis are carried out by JC method （improved first-order second-moment method） based on the relevant experimental data. Results show that the resistance partial factor of the joint increases with the increase of the reliability index. The resis- tance partial factors are suggested corresponding to the reliability index under different load combinations. Moreover, the suggested resistance partial factor is adopted in reliability design, and it is found that the reliability index of the joint is larger than the target reliability index. The optimal load combination is the one in which live load plays an im- portant control role. Finally, based on the suggested resistance partial factors, the reliability analysis of cast bail-and- socket support ioints of a proiect is conducted.

基于Kruskal和Floyd算法的馈线新增负荷接入方法

规划人员一般采用简单的方法对配电网网架进行扩展,以应对配电网有新增负荷节点出现的情况,这可能导致电压质量达不到要求或配电网运行不经济等问题。提出一种基于Kruskal和Floyd算法配电网新增负荷的接入方法,该方法计及了新增负荷前配电系统的无功配置情况。通过Kruskal算法得到配电网网架初始结构,以满足供电半径为目标,运用Floyd算法得到新增负荷接入线路的次短路径,当电压不满足要求时,采用无功二次精确矩法确定无功补偿点的位置和补偿容量,以保证系统的电压质量,并进一步降低线损。对算例进行数字仿真,仿真结果验证了该方法的可行性和实用性。

基于可靠度理论的桥梁涡激振动概率性评价

涡激共振是大跨度桥梁在低风速下容易发生的一种风致振动,涉及的不确定因素众多,利用可靠度理论对这类风致振动进行安全估算是大跨度桥梁风振研究的趋势。探讨了桥梁涡振的三种失效模式,包括基于涡振风速的失效模式、基于涡振振幅的失效模式和基于前两种失效模式交集的涡振刚度失效模式,基于此,以某座大跨度桥梁为例,应用二次四阶矩法计算了基于涡振振幅的失效概率,并与二次二阶矩法的计算结果进行了比较,用Monte Carlo模拟法(MC)进行了验证,发现基于二次四阶矩法的可靠度分析相对于二次二阶矩法具有较高的精度。然后,基于二次四阶矩法的计算结果得到了桥梁涡振刚度失效的概率,研究表明:单独考虑桥梁涡振发生风速或涡振振幅的失效概率偏于保守,应结合起来考虑。