Integrated system identification and reliability evaluation of stochastic building structures

System identification and reliability evaluation play a significant role in structural health monitoring to ensure the serviceability and safety of existing structures. Although the development of system identification methods has attained much attention and some degree of maturity, reliability evaluation of existing structures still remains a challenging problem especially when uncertainties in measurement data and inherent randomness, which are inevitably involved in civil structures, are considered. In this regard, this paper presents a framework for integrated system identification and reliability evaluation of stochastic building structures. Two algorithms are proposed to respectively evaluate component reliability and system reliability of stochastic building structures by combining a statistical moment-based system identification method and a probability density evolution equation-based reliability evaluation method. System identification is embedded in the procedure of reliability evaluation of a stochastic building structure. The uncertainties in both the structure and the external excitation are considered. Numerical examples show that the structural component and system reliabilities of a three-story shear building structure with three damage scenarios can be effectively evaluated by the proposed methods.     

考虑场地效应的建筑群动力可靠度PDEM评估

城市建筑群的动力可靠度评估对于区域防灾减灾具有重要意义。场地效应会导致地震动的空间变异性和土-结构相互作用效应,进而显著影响区域建筑群的非线性地震响应,而确定性区域震害模拟方法仍不足以准确反映随机建筑群动力系统的整体性态。该研究引入实测地震动场和土-结构相互作用效应,发展了建筑群系统非线性地震响应时域求解方法,并遵循概率守恒假定,建立基于概率密度演化方法(PDEM)的建筑群系统动力可靠度评估框架。以某高层框架结构建筑群为例,进行了场地效应下确定性建筑群非线性地震响应分析,进而完成了随机建筑群动力可靠度评估,并评估了场地效应对建筑群系统动力可靠度影响,得到了有益结论。     

System reliability analysis of spatial variance frames based on random field and stochastic elastic modulus reduction method

This paper presents the stochastic elastic modulus reduction method for system reliability analysis of spatial variance frames based on the perturbation stochastic finite element method (PSFEM) and the local average of a random field. The stochastic responses and reliability index of each element of a structural frame are characterized by the PSFEM and the first-order second-moment method, to properly handle the correlation structures and scale of fluctuation of random fields. A strategy of elastic modulus adjustment for the estimation of system reliability is developed to determine the range and magnitude of elastic modulus reduction, by taking the element reliability index as a governing parameter. The collapse mechanism and system reliability index of a stochastic framed structure are determined through iterative computations of the PSFEM. Compared with the failure mode approaches in traditional system reliability analysis, the proposed method avoids two major difficulties, namely the identification of significant failure modes and estimation of the joint probability of failure modes. The influences of the correlation structure and scale of fluctuation of the random field upon system reliability are investigated to demonstrate the accuracy and computational efficiency of the proposed methodology in system reliability analysis of spatial variance frames.     

On fast integration for time variant structural reliability

In evaluating structural reliability under stochastic loadings, the system parameters such as stiffness, damping, strength, excitation frequency content and duration, etc., are usually assumed given. In reality, however, these quantities are seldom perfectly known. Their uncertainties may play a major role as far as the overall structural reliability is concerned. This paper reviews currently available methods to include this parameter uncertainties and a new method is also proposed. The accuracy and analytical and numerical efforts required are compared. Through numerical examples on systems under dynamic excitation, collapse of ductile or brittle redundant systems, the advantages of the proposed method are demonstrated.     

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito–Taylor’s discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations.     

可靠度对随机变量及失效模式相关系数的敏感度分析及其工程应用

客观存在的诸多不确定性因素使得工程不可避免地存在着风险。随着重大工程的不断涌现,人们越来越关心如何提高工程系统的安全度,降低工程结构的风险。遗憾的是如何降低工程系统的风险直至目前还没有固定的科学方法,大多是基于工程师的经验。以可靠度理论为基础,从可靠度对工程结构的某些参数的敏感性及可靠度对失效模式的相关系数入手,探讨如何从加强或削弱结构参数及失效模式间的相关性的角度出发,来进行降低结构风险的研究。给出了两个算例来说明方法在工程中的应用。     

改进响应面法计算钢筋混凝土框架体系可靠度

钢筋混凝土框架结构体系可靠度是评定结构抗震性能的重要指标,也是对既有结构进行加固的评估基础。以框架底层柱端极限弯矩承载力作为参考变量可有效评估框架结构体系可靠度,该方法采用Pushover静力推覆分析,通过研究框架结构底层柱端极限弯矩承载能力对Pushover曲线的影响规律,由Pushover曲线上的基准点推广得到结构失效响应面,从而计算出结构体系可靠度。应用该方法对一榀钢筋混凝土框架进行了体系可靠度计算,计算结果与直接响应面法和蒙特卡洛法分析结果进行对比,结果表明,该方法计算快捷,且能够很好地评估出框架体系抗震可靠度。     

Energy-based collapse assessment of concrete structures subjected to random damage evolutions

The assessment of structural capacity against collapse is conducive to the optimal design of new structures as well as checking the safety of existing structures. However, the evaluation cannot be typically carried out by means of destructive tests on prototype or reduced scale structures. In this regard, the numerical models that adequately represent the prototype structures can be alternatively used. Specifically, both the nonlinearities and randomness as well as their coupling effect of materials need to be represented in a unified manner in structural analysis. The present paper aims at providing an effective approach to incorporate the stochastic nature of damage constitutive relationships in collapse analysis and assessment of concrete structures subjected to earthquake ground motions. Within the framework of stochastic damage mechanics, the spatial variability of concrete is represented by a two-scale stationary random fields. The concept of covariance constraint is introduced to bridge the two-scale random fields such that the scale-of-fluctuation of the random material property is satisfied at both scales. Random damage evolution induced structural collapse analysis is achieved via the nonlinear stochastic finite element method. To address the randomness propagation across scales, the probability density evolution method is employed. By exerting the absorbing boundary condition associated with an energy-based collapse criterion on the generalized probability density evolution equation, the anti-collapse reliability of concrete structures can be evaluated with fair accuracy and efficiency. Numerical investigation regarding an actual high-rise reinforced concrete frame-shear wall structure indicates that the random damage evolution of concrete dramatically affects the structural nonlinear behaviors and even leads to entirely different collapse modes. The proposed method provides a systematic treatment of both uncertainties and nonlinearities in collapse assessment of complex concrete structures.     

基于统计模型的结构损伤识别

提出了一种基于递推随机有限元方法(RSFEM)的随机结构损伤识别方法。在定义了随机损伤指数概念的基础上,考虑模型误差的不确定性和测量噪声的影响,建立了关于随机损伤指数的控制方程。然后,利用RSFEM得到了结构随机损伤指数的统计特性。数值算例的结果显示,新的方法能在考虑模型误差和测量噪声的情况下对结构损伤进行有效识别,且在结构随机参数有较大涨落情况下,该方法仍能有效识别出结构损伤,识别结果与蒙特卡洛模拟解非常吻合。     

Reliability assessment of structures based upon probabilistic fracture mechanics

The stochastic fatigue crack growth model (termed the Tsurui-Ishikawa model) based upon the Markov approximation method introducing the notion of death point has been proposed, and a great deal of its practical usefulness in the reliability assessment of structures has been demonstrated for those cases where the fatigue crack propagation process plays a crucial role toward their failure. By performing the reliability analysis, based upon the model, in consideration of uncertainties of both initial crack length and their number, the effect of such uncertainties has been clarified on the reliability degradation of a structural component. This result is of much interest from a practical viewpoint because it gives a guideline to determine the safe life (design life or inspection interval) to assure the prescribed level of reliability for random loadings with a variety of correlation times. Further, studies have been made on which parameter is the most significant according to the problem through parameter sensitivity study. With the aid of the proposed model, reliability assurance or reliability-based design can be performed properly against fatigue failure of structures subjected to random loading.     

随机有限元-最大熵法

本文提出一种用于结构可靠性分析的随机有限元-最大熵法。它是利用随机有限元法计算结构响应量的前几阶矩,然后利用最大熵法拟会响应量的概率分布,据此算出结构的失效概率。此法具有精度较高、计算量较小的优点。     

含模糊-区间变量的结构非概率可靠性优化设计

工程结构中存在着诸多不确定性因素,可靠性方法是处理不确定因素的有效途径之一。针对大量工程结构中存在混合不确定信息的问题,提出了一种适用于工程的混合不确定性可靠度计算方法。将模糊变量转化为区间变量,基于体积比的区间可靠性模型,建立了含模糊-区间混合变量的结构非概率可靠性模型。由于该可靠性模型意义明确,对模糊信息的处理也比较合理,可作为混合可靠性计算方法的一种补充。应用此可靠性模型对某飞机机翼结构进行了优化设计,实例计算说明了该文的方法是有效和可行的。     

现有结构抗震维修动态规划决策

本文基于大地震发生的半马尔可夫过程模型,建立了服役结构抗震维修动态规划决策模型。文中考虑了钢筋锈蚀对结构抗力的影响,利用“分枝限界法”计算结构系统可靠度,并进行安全性等级划分,在此离散状态及离散时间的基础上,运用技术经济评价法,建立了动态规划决策模型。最后以一简单框架验证了上述方法的可行性     

不确定爆炸荷载作用下钢梁的可靠度分析

通过对已有爆炸荷载预测公式、计算图表和试验的海量数据的统计分析,建立了作用于建筑结构上爆炸荷载的统计模型;以典型钢梁为研究对象,考虑材料强度和构件尺寸的不确定性,基于单自由度体系理论和蒙特卡洛方法,建立了不确定爆炸荷载作用下钢梁失效概率的计算方法,并开发了实用计算程序;分析了炸药质量以及爆炸荷载和结构材料属性的不确定性等对钢梁失效概率的影响。研究表明:炸药质量和比例距离是影响爆炸荷载作用下钢梁失效概率的重要因素,在建筑结构抗爆分析中,必须考虑爆炸荷载的不确定性。     

Reliability analysis of structures based on a probability‐uncertainty hybrid model

The traditional reliability analysis method based on probabilistic method requires probability distributions of all the uncertain parameters. However, in practical applications, the distributions of some parameters may not be precisely known due to the lack of sufficient sample data. The probabilistic theory cannot directly measure the reliability of structures with epistemic uncertainty, ie, subjective randomness and fuzziness. Hence, a hybrid reliability analysis (HRA) problem will be caused when the aleatory and epistemic uncertainties coexist in a structure. In this paper, by combining the probability theory and the uncertainty theory into a chance theory, a probability‐uncertainty hybrid model is established, and a new quantification method based on the uncertain random variables for the structural reliability is presented in order to simultaneously satisfy the duality of random variables and the subadditivity of uncertain variables; then, a reliability index is explored based on the chance expected value and variance. Besides, the formulas of the chance theory‐based reliability and reliability index are derived to uniformly assess the reliability of structures under the hybrid aleatory and epistemic uncertainties. The numerical experiments illustrate the validity of the proposed method, and the results of the proposed method can provide a more accurate assessment of the structural system under the mixed uncertainties than the ones obtained separately from the probability theory and the uncertainty theory.     

Free vibration and reliability of composite cantilevers featuring uncertain properties

The problem of free vibration and reliability of cantilever composite beams featuring structural uncertainties is analyzed. The random structural uncertainties involve material properties, thickness and fiber orientation of the individual constituent laminae. Such uncertainties undoubtedly affect the achievable performance as well as their structural reliabilities. In order to investigate the effects of random structural uncertainties on free vibration problem, a stochastic eigenvalue problem of self-adjoint systems is formulated to provide first and second moments of eigenvalues, i.e., their mean and variance. In this context, a stochastic finite element method based on the mean-centered-second-moment method and first-order perturbation technique are employed during the probabilistic discretization of uncertain distributed-parameter structural systems.Sensitivity and reliability analyses for the uncertain beam when subjected to an external oscillatory load are performed. In addition, in order to mitigate the detrimental effects of uncertainties and so, to render the structure more robust to such effects, the structural tailoring technique is implemented and its beneficial effects are revealed.     

基于模型参考自适应算法的非线性结构损伤识别

许多工程结构在遭受飓风、地震之类的动荷载时,存在迟滞非线性现象,因此,对其结构参数进行实时辨识显得尤为必要.针对迟滞非线性结构的力学性质,采用一种基于模型参考自适应算法的参数辨识方法.该方法能够追踪时变的参数,检测损伤,包括损伤的大小和位置,以及损伤发生的时刻.数值仿真的结果表明,该方法对参数变化具有敏感性,非线性结构的仿真结果证实了该方法能够有效检测结构的损伤.     

Development-process-of-nonlinearity-based reliability evaluation of structures

A reliability evaluation approach based on the development process of the structural nonlinearity is presented. The traditional structural system reliability theory for structural safety regarding combination of failure modes is first revisited. It is seen that it stemmed from, and was heavily affected by, the assumption of perfect elasto-plasticity of materials. This will make the number of the failure modes increase in a non-polynomial form against the number of the potential plastic hinges. Moreover, the above methodology does not work appropriately in the case of nonlinearity in general form other than perfect elasto-plasticity, as commonly encountered in engineering practice. Discussions show that total information of the structure is involved in the development process of its nonlinearity, be it a deterministic case or stochastic counterpart. The information needed for reliability evaluation of structures could be extracted, for example, by capturing the probabilistic information of the extreme value of the corresponding response, which could be obtained by using the probability density evolution method. Therefore, the reliability evaluation for structural safety could then be directly evaluated without searching the failure modes. Taking a 10-bar truss as an example, the proposed method is theoretically elaborated and numerically exemplified.     

基于VMD的建筑结构模态参数识别

在建筑结构的健康监测、控制和状态评估中经常遇到的一个关键性问题是如何根据实测响应信号准确估计结构阻尼比及自振频率等模态参数。基于变分模态分解(VMD)提出一种新的结构模态参数识别方法。该方法首先对实测振动信号进行VMD分解,获得单模态信号,然后采用自然环境激励技术(NEXT)得到单模态信号的自由衰减响应,最后利用直接插值法(DI)和曲线拟合获得结构的自振频率和阻尼比。通过三层框架结构的数值模拟验证了该方法的准确性及可靠性。利用该技术对台风“达维”作用下广州中信广场的实测加速度数据进行分析,并将估计的结构模态参数和其他识别方法的分析结果进行对比,进一步验证了该方法的准确性和有效性。     

Enhanced reliability analysis method for multistate systems with epistemic uncertainty based on evidential network

Evidential network is considered to have superiority in conducting reliability analysis for complex engineering systems with epistemic uncertainty. However, existing methods tend to result in combinational explosion when multistate systems are involved in the reliability analysis, which means the reliability analysis cost increases exponentially with the number of components and that of functioning states. Therefore, an enhanced reliability analysis method is proposed in this paper for reliability analysis and performance evaluation of multistate systems with epistemic uncertainty, through which the combination explosion can be significantly alleviated. Firstly, the functioning states of each component are sequenced according to utility functions. Secondly, the basic belief assignment (BBA) of each component is reassigned in terms of commonality function, through which the BBA defined in the power set space is represented by two extreme BBA distributions defined in the frame of discernment. Thirdly, the reliability intervals of the system states are calculated through evidential network, and the system performance level is computed. Two multistate system numerical examples are investigated to demonstrate the effectiveness and efficiency of the proposed method.