A new look at the response surface method for reliability analysis using chaos theory

To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.     

Probabilistic evaluation of seismic performance of 3‐story 3D one‐ and two‐way steel moment‐frame structures

This paper presents the results of a probabilistic evaluation of the seismic performance of 3D steel moment‐frame structures. Two types of framing system are considered: one‐way frames typical of construction in the United States and two‐way frames typical of construction in Japan. For each framing system, four types of beam–column connections are considered: pre‐Northridge welded‐flange bolted‐web, post‐Northridge welded‐flange welded‐web, reduced‐beam‐section, and bolted‐flange‐plate connections. A suite of earthquake ground motions is used to compute the annual probability of exceedence (APE) for a series of drift demand levels and for member plastic‐rotation capacity. Results are compared for the different framing systems and connection details. It is found that the two‐way frames, which have a larger initial stiffness and strength than the one‐way frames for the same beam and column volumes, have a smaller APE for small drift demands for which members exhibit no or minimal yielding, but have a larger APE for large drift demands for which members exhibit large plastic rotations. However, the one‐way frames, which typically comprise a few seismic frames with large‐sized members that have relatively small rotation capacities, may have a larger APE for member failure. The probabilistic approach presented in this study may be used to determine the most appropriate frame configuration to meet an owner's performance objectives. Copyright © 2008 John Wiley & Sons, Ltd.     

Performance‐based optimum seismic design of reinforced concrete structures

A fully automated design methodology based on nonlinear response history analysis is proposed for the optimum seismic design of reinforced concrete (RC) structures. The conventional trial‐and‐error process is replaced by a structural optimization algorithm that serves as a search engine capable of locating the most efficient design in terms of cost and performance. Two variations of the proposed design methodology are introduced. The first approach treats the optimum design problem in a deterministic manner, while in the second variation the optimum design is sought in the framework of a reliability‐based optimization problem. The reliability‐based approach seems to be a more rational procedure since more meaningful design criteria that correlate better with the performance‐based design concept can be adopted. Thus, the practice of using the mean annual frequency of a limit‐state being exceeded to assess the candidate designs is compared with the use of deterministic criteria. Both formulations take into consideration the structural response for a number of limit‐states, from serviceability to collapse prevention. The proposed design procedure is specifically tailored to the design of RC structures, where a preliminary design step of generating tables of concrete sections is introduced. In order to handle the large size of the tables, the concept of multi‐database cascade optimization is implemented. The final design has to comply with the provisions of European design codes. The proposed methodology allows for a significant reduction of the direct construction cost combined with improved control of the seismic performance under earthquake loading. Copyright © 2008 John Wiley & Sons, Ltd.     

多高层建筑结构层间位移和层剪力的动力可靠度计算

在虚拟激励法的基础上推导了多高层建筑结构剪切层模型在地震作用下层间相对位移和层地震剪力的自功率谱密度函数的解析表达,通过数值积分获得层间相对位移和层地震剪力的各阶谱矩和标准差,基于随机动力响应过程跨越安全界限次数为泊松过程和两态马尔可夫过程的假设,计算了层间相对位移和层地震剪力的动力可靠度,并用Matlab语言编制了动力可靠度的计算程序.算例表明该方法是高效的和有效的.     

基于改进遗传算法的边坡可靠度分析

采用基于概率的可靠性分析方法来分析边坡的稳定性,以克服目前大多数分析方法以确定性安全系数为评判标准的弊端。对于每次搜索中给定的滑移面,结合拉格朗日乘子法提出边坡可靠度的计算模型;采用遗传算法搜索关键滑移面,提出边坡的适应度函数。为克服标准遗传算法在进化过程中无法调节全局搜索和局部搜索速度、且可能陷入次优解的缺陷,改进了子代中最佳个体的确定方法,来并以相邻两代的群体多样性特征值增量为导向,动态调节交叉概率和变异概率,以保持群体的多样性和搜索的有效性。实例分析结果表明,本文方法可以提高遗传算法的搜索能力和收敛速度,保证解全局最优;该法适用于边坡稳定可靠度分析,且前处理简单;在遗传操作前预优化可靠指标计算模型能大大减少遗传算法中的计算量,节约机时。     

某天然气储配站场地边坡处治可靠性评价

在分析某天然气储配站场地环境地质条件的基础上,对其开挖形成的高边坡采用喷锚及格构锚固措施进行处治;采用重庆市地方规范规定的极限平衡法及数值模拟分析两种方法对边坡处治后的可靠性进行综合评价,结果表明治理工程实施后边坡稳定安全系数达到规范规定,设计锚杆无破坏现象,有效处治的边坡能满足天然气储配站场地环境的安全要求     

地下水位随机性影响下的边坡可靠性分析

在边坡稳定性评价模型中可将地下水的水压力总分为静水压力和动水压力。建立考虑水压力的剩余推力法边坡稳定性力学分析模型。推导了利用已知两点地下水位求解其间任一点地下水位和含水层厚度的求解公式。将地下水位和滑面的抗剪强度指标作为随机变量,利用已有数据求其分布特征,提出基于Monte-Carlo法与剩余推力法的边坡可靠性分析方法,并对某公路边坡进行可靠性分析。计算结果表明地下水位的变化与边坡失效概率的变化成正相关关系。在地下水位变化较大的7、8、9月,将地下水位作为随机变量计算得到的边坡失效概率为60%左右,而将地下水位作为确定量计算的边坡失效概率为10%~30%;在地下水位变化不大的其它月份,二者差别不大,但前者总大于后者。     

立式储油罐地震作用下的抗提离可靠度分析

储油罐在水平地震作用下会出现罐底提离而导致储油罐发生提离破坏,影响储油罐的可靠性。为了研究立式储油罐在地震作用下的抗提离可靠度情况,文中总结建立了在储油罐抗提离可靠度分析中涉及的随机变量的概率模型,运用可靠性分析的JC法对不同工况下的储油罐进行了抗提离可靠度计算,得出了储油罐在地震作用下的提离破坏规律。通过计算实例可以看出,对大型储油罐在地震作用下的抗提离可靠度分析是切实可行的。     

Influence of model type,bias and input parameter variability on reliability analysis for simple limit states in soil–structure interaction problems

ABSTRACT

A general closed-form solution for the true probability of failure of a simple limit state function with one load term and one resistance term is derived. The formulation considers contributions due to model type, uncertainty in method bias values, bias dependencies, uncertainty in estimates of nominal values for correlated and uncorrelated load and resistance terms, and average margin of safety expressed as the operational factor of safety. Example calculations are presented using different load and resistance models for the pullout internal stability limit state of steel strip reinforced soil walls together with matching bias data reported in the literature.