Damage-reduction-based structural optimum design for seismic RC frames

The development of structural seismic design is briefly reviewed with an emphasis on different conceptual approaches and their success in practical engineering applications. The concept of damage-reduction-based seismic design is proposed, in which the whole structural system is either physically or functionally designed as two parts, the main-function part and the damage-reduction part. The main-function part satisfies the serviceability requirements of the structural system. The damage-reduction part is composed of several damage-reduction elements, which work under hazard loads to ensure the safety of the main-function part, and further maintain the serviceability of the structural system by specific damage-reduction techniques or even by failure of damage-reduction elements. The formulation of damage-reduction-based optimum design for seismic structures is presented and some related issues are addressed, including a simplified approach to reliability analysis, the evaluation of the structural loss expectation, and the modified enumeration method. Numerical examples of RC frames are examined. The results show that several measures of structural seismic performance, including the life-cycle cost, severe earthquake action, and the story-drift reliability index of the weakest story, can be improved by damage-reduction-based design compared with conventional design.     

Structural reliability under combined random load sequences

An algorithm for the calculation of structural reliability under combined loading is formulated. Loads or any other actions upon structures are modelled as independent random sequences. The relevant limit state criterion is pointwise approximated by a tangent hyperplane. The combination of time-variant actions then reduces to the calculation of the maximum of a sum of random variables which is facilitated through proper, discrete approximation of extreme value and other non-normal distribution functions by normal distributions. The iteration algorithm searches for an approximation point on the limit state criterion where the probability content of the failure domain limited by the tangent hyperplane reaches its maximum. Any type of continuous limit state criterion and any distribution type for the loads can be dealt with. The method is illustrated for a section of a wall without tensile strength loaded by a bending moment and a normal force.     

An inverse-measure-based unilevel architecture for reliability-based design optimization

Reliability-based design optimization (RBDO) is a methodology for finding optimized designs that are characterized with a low probability of failure. Primarily, RBDO consists of optimizing a merit function while satisfying reliability constraints. The reliability constraints are constraints on the probability of failure corresponding to each of the failure modes of the system or a single constraint on the system probability of failure. The probability of failure is usually estimated by performing a reliability analysis. During the last few years, a variety of different formulations have been developed for RBDO. Traditionally, these have been formulated as a double-loop (nested) optimization problem. The upper level optimization loop generally involves optimizing a merit function subject to reliability constraints, and the lower level optimization loop(s) compute(s) the probabilities of failure corresponding to the failure mode(s) that govern(s) the system failure. This formulation is, by nature, computationally intensive. Researchers have provided sequential strategies to address this issue, where the deterministic optimization and reliability analysis are decoupled, and the process is performed iteratively until convergence is achieved. These methods, though attractive in terms of obtaining a workable reliable design at considerably reduced computational costs, often lead to premature convergence and therefore yield spurious optimal designs. In this paper, a novel unilevel formulation for RBDO is developed. In the proposed formulation, the lower level optimization (evaluation of reliability constraints in the double-loop formulation) is replaced by its corresponding first-order Karush–Kuhn–Tucker (KKT) necessary optimality conditions at the upper level optimization. Such a replacement is computationally equivalent to solving the original nested optimization if the lower level optimization problem is solved by numerically satisfying the KKT conditions (which is typically the case). It is shown through the use of test problems that the proposed formulation is numerically robust (stable) and computationally efficient compared to the existing approaches for RBDO.     

Reliability based design with a degradation model of laminated composite structures

Uncertainties in deviations of physical properties lead to a probabilistic failure analysis of the composite materials. The proposed optimization model for laminate composites is based on reliability analysis considering the ultimate failure state. To avoid difficulties associated with the complete analysis of the failure modes, bounds are established for the failure probability of the structural system. These bounds are related with theintact and degraded configurations of the structure. Using thefirst ply failure and thelast ply failure theories and a degradation model for the mechanical properties with load sharing rules we obtain the failure probabilities corresponding to the two above configurations. The failure probability of each configuration is obtained using level 2 reliability analysis and the Lind-Hasofer method.The optimization algorithm is developed based on the problem decomposition into three subproblems having as objectives the maximization of the structural efficiency atintact and degraded configurations of the structure and weight minimization subjected to allowable values for the structural reliability. Additionally, the search for the initial design is performed introducing a weight minimization level. It is expected to explore the remaining load capacity of the structures afterfirst ply failure as a function of the anisotropic properties of the composites. The design variables are the ply angles and the thicknesses of the laminates. The structural analysis for the model developed is performed through the finite element method mainly using the isoparametric degenerated shell finite element. The sensitivities are obtained using the discrete approach through the adjoint variable method. In order to show the performance of the analysis two examples are presented.     

Routing policy of stochastic-flow networks under time threshold and budget constraint

The quickest path problem is to find a path which sends a given amount of data from the source to the sink such that the transmission time is minimized. More specifically, the capacity of each arc in the network is assumed to be deterministic. However, in many real-life networks such as computer systems, telecommunication systems, etc., the capacity of each arc is stochastic due to failure, maintenance, etc. Such a network is named as stochastic-flow network. Hence, the minimum transmission time is not a fixed number. The purpose of this paper is to provide a decision procedure for a stochastic-flow network under the time and budget constraints. We try to evaluate the probability that d units of data can be sent through the network under both time threshold and budget according to the routing policy. Such a probability is named the system reliability, which is a performance index to measure the system quality. An efficient algorithm is proposed to derive the optimal routing policy with highest system reliability. The sensitive analysis can be conducted to improve the most important component which increases the system reliability most significantly.     

Saddlepoint approximation based structural reliability analysis with non-normal random variables

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bo...     

Reliability calculation of time-consuming problems using a small-sample artificial neural network-based response surface method

An important step when designing and assessing the reliability of existing structures and/or structural elements is to calculate the reliability level described by failure probability or reliability index. Since calculating the structural response of complex systems such as bridges is usually a time-consuming task, the utilization of approximation methods with a view to reducing the computational effort to an acceptable level is an appropriate solution. The paper introduces a small-sample artificial neural network-based response surface method. An artificial neural network is used as an approximation (a so-called response surface) of the original limit state function. In order to be as effective as possible with respect to computational effort, a stratified Latin hypercube sampling simulation method is utilized to properly select training set elements. Subsequently, the artificial neural network-based response surface is utilized to calculate failure probability. To increase the accuracy of the determined failure probability, the response surface can be updated close to the failure region. This is performed by finding a new anchor point, which lies close to the design point of the limit state function. The new anchor point is then used to prepare the updated training set. The efficiency of the proposed method is tested for different training set sizes using a nonlinear limit state function taken from the literature, and the reliability assessment of three concrete bridges, one with explicit and two with implicit limit state functions in the form of finite element method models.

     

数据依赖约束下的任务调度资源选择算法

大数据环境下的计算任务往往具有一定数据依赖性关系(如MapReduce),现有的分布式存储系统任务资源选择策略选择离请求者最近的数据块响应服务,忽略了对数据块所在服务器CPU、磁盘I/O与网络等资源负载状态的考虑。在分析研究系统集群结构、文件分块、数据块存储机制的基础上,定义了集群节点矩阵、CPU负载矩阵、磁盘I/O负载矩阵、网络负载矩阵、文件分块矩阵、数据块存储矩阵与数据块存储节点状态矩阵,为任务与数据之间的依赖性构建了基础数据模型,提出了一种数据依赖约束下的最优资源选择算法(ORS2DC)。任务调度节点负责维护基础数据,MapReduce任务与数据块读取任务由于依赖资源不同而采取不同的选择策略。实验结果表明：所提算法能够为任务选择质量更高的资源,提高任务完成质量的同时减轻了NameNode负担,减小了单点故障发生的概率。     

Intervening variables and constraint approximations in safety index and failure probability calculations

The emphasis of this paper is on developing suitable intervening variables and constraint approximations for structural reliability analysis. Traditionally, these procedures are used in structural optimization, whereas this research work adopts these concepts to safety index and failure probability computations. The use of these concepts enables the development of an efficient and stable iteration algorithm for identifying the most probable failure points (MPPs) of the limit state functions. An approximate second-order failure probability is calculated at this MPP with no extra computations of the limit state function and gradients. The efficiency and accuracy of the proposed algorithm are demonstrated by several examples with highly nonlinear, complex, explicit/implicit performance functions.     

Minimization of project time and cost under constrained reliability index in the disjunctive project model

Proposed was a reliability model of the network project as a complex technical system where the probability of failure-free execution of an activity (project component) was used as the quantitative index of its reliability, and the resulting guaranteed lower estimate of the project, as its reliability index. This approach underlies the formulation of the problem of scheduling not only under resource constraints, but also with regard for the project reliability index. Consideration was given to minimization of the project execution time (main criterion) in terms of the constrained cost and estimate of the project reliability index, as well as in terms the cost in the determinate network model of the project (second criterion) where project reliability satisfies the guaranteed lower bound both for the OR-network and the special case of the AND-network. This approach enabled formulation of the scheduling problem not only under the resource, but also reliability constraints.     

Elemental reliability index-based system design for skeletal structures

A procedure is presented for the optimization of truss structures undersystem reliability constraints using anelemental reliability approach. The structure is weight-optimally designed by imposing on it a set of elemental reliability constraints. The optimum point is assumed to be on the boundary region and is reached through a recurrence relation based on anoptimality criterion. The approach, different from the one widely adopted from electronic systems in which the failure inducing loads arecomponental and the systems are generally working underlow loading roughness, is based on the fundamentally different phenomenon that failure inducing loads on structural systems aresystemic. The systemic nature of the failure inducing loads on structural systems leads to the so-calledcommon-mode failures and the system reliability is solely determined by the component with the smallest reliability; the weakest link. A less fundamental phenomenon which, nevertheless, emphasizes the approach is that the structural systems as a whole are under a frequentlyhigh loading roughness. Although the conclusion is on the optimistic side, compared to thea priori modelledseries systems for just-stiff configurations, this can be further proven by estimating the structural system reliability of the resulting optimal design by acritical path incremental loading model which highlights theconditional andinterdependent nature of member reliabilities after the weakest is systematically made to fail.     

Application of the homotopy analysis method to determine the analytical limit state functions and reliability index for large deflection of a cantilever beam subjected to static co-planar loading

In this paper, the Homotopy Analysis Method (HAM) is applied to obtain the limit state function, probability of failure and reliability index based on all stochastic and deterministic variables for a cantilever beam subjected to co-planar loading for the first time. First, it is established that a few iterations in the series expansion are sufficient to obtain highly accurate results and a substantial convergence region. After showing the effectiveness of HAM, two limit state functions are introduced as the maximum deflection in the y direction and maximum allowable stress, respectively. Then the first order reliability method (FORM) is employed to obtain reliability index, and omission sensitivity factor analytically. It is shown that HAM is a promising tool to obtain limit state function, probability of failure and reliability index analytically for nonlinear problems. Finally, a sensitivity analysis is done to show that which parameters could be considered deterministic or stochastic variables.     

Computational strategies for reliability-based structural optimization of aeroelastic limit cycle oscillations

Gradient-based optimization, via the adjoint method, is needed to realistically enable the reliability-based design of a nonlinear unsteady aeroelastic system with many random and/or deterministic design variables. The adjoint derivatives of a time-marched system entail a cumbersome reverse-time integration, and so a time-periodic spectral element scheme is used here to efficiently capture the gradients of the limit cycle oscillations. Further reductions in the computational cost of the monolithic-time adjoint vector are obtained with proper orthogonal decomposition, which projects the large system onto a reduced basis. Design reliability is computed with the first order reliability method, which provides an estimate of the failure probability without resorting to sampling-based approaches (infeasible for large systems). Analytical gradients are needed to obtain the most probable point (in the random variable space), as well as the reliability design derivatives. These computational strategies are utilized to locate the optimal thickness distribution of a cantilevered wing operating beyond its flutter point in supersonic flow (via piston theory). Specifically, the wing mass is minimized under both deterministic and non-deterministic limit cycle oscillation amplitude constraints, with both structural and flow uncertainties considered in the latter.     

云计算环境下的可修分布式系统可靠性分析方法

随着云计算技术的进一步发展,越来越多的应用系统托管在云计算平台上,这就对构成云计算平台的众多分布式系统的可靠性提出了更高的要求。传统分析方法难以在系统规模较大时对可修分布式系统做可靠性分析。为了提高服务质量以及降低因违反服务水平协议而导致的经济损失,本文基于马尔可夫模型提出一种适用于可修分布式系统的可靠性分析方法。通过简化系统的状态空间,在系统运行期间对其软硬件状态进行采样,并通过对分布式系统的失效过程和修复过程进行分析,根据给定时间内的失效概率序列、修复概率序列计算分布式系统的节点状态转移矩阵,得出该马尔可夫矩阵对应的稳态向量。根据特定分布式系统的自身特性,对该稳态向量进一步分析,得出系统最终的可靠性衡量指标。最后通过实验验证了该方法的可用性和有效性。     

特殊状态需要特殊修理的诊断可修系统

研究了特殊状态需要特殊修理的诊断可修系统.假设系统有三种运行状态:正常状态、 异常状态和故障状态,有些异常状态和故障状态需要特殊的修理,但哪些异常状态和故障状态 需要特殊修理必须诊断后才能知道.利用概率分析和补充变量方法,求得了系统的重要可靠性 指标.     

A simulation method for time-dependent structural reliability

A one-dimensional simulation procedure is developed for use in estimating structural reliability in multi-dimensional load and resistance space with the loads represented as stochastic process. The technique employed is based on the idea of using ‘strips’ of points parallel to each other and sampled on the limit state hyperplanes. The ‘local’ outcrossing rate and the zero time failure probability P_f(0) associated with the narrow strips are derived using the conditional reliability index. When the domain boundary consists of a set of limit states, second order bounds are used to obtain a lower bound approximation of the outcrossing rate and P_f(0) associated with the union of a set of λ strips. It is shown by examples that for high reliability problems, λ may be much less than the number of limit states without significant loss of accuracy and with considerable saving in computation time. It was also found that the rate of convergence of the simulations is quite fast even without using importance sampling.     

Computation of the failure probability of deteriorating structural systems

Structural system deterioration is one of the least attended topics in time-dependent structural reliability analysis. There are basically two types of problems in structural deterioration analysis; one is the need for models to simulate the behaviour of deteriorating structural material. This will be done through case by case study in this paper. The other problem is that when both the applied loads and resistance vary with time, the current methods to generate limit state functions for the structural system need validating. To avoid this problem, an alternative formulation for time-dependent reliability is proposed, where the reliability analysis of a deteriorating structural system is based on the reliability of its structural members, which constitute a failure sequence for the structure. The advantage of the proposed approach is that it has effectively obviated the use of global limit state functions and that it is applicable to structures subject to various types of loads and with different structural material properties. An application example is given to illustrate the computation procedure.     

基于资源状态可靠度的网格工作流调度算法

针对执行时间限制严格类型的DAG类型网格工作流提出一种新的基于资源状态可靠度的网格工作流调度算法。该算法根据用户提交的工作流执行时间要求,利用Chapman-Kolmogorov向后方程来计算出DAG图中关键路径上各资源在任务到达时刻均处于“闲状态”的概率大小,然后选择一组资源组合的状态可靠度大于用户要求的信任度置信水平α且总费用较低的一组资源。最后通过实验验证了该算法的有效性。     

A sequential approximate programming strategy for reliability-based structural optimization

Although reliability-based structural optimization (RBSO) is recognized as a rational structural design philosophy that is more advantageous to deterministic optimization, most common RBSO is based on straightforward two-level approach connecting algorithms of reliability calculation and that of design optimization. This is achieved usually with an outer loop for optimization of design variables and an inner loop for reliability analysis. A number of algorithms have been proposed to reduce the computational cost of such optimizations, such as performance measure approach, semi-infinite programming, and mono-level approach. Herein the sequential approximate programming approach, which is well known in structural optimization, is extended as an efficient methodology to solve RBSO problems. In this approach, the optimum design is obtained by solving a sequence of sub-programming problems that usually consist of an approximate objective function subjected to a set of approximate constraint functions. In each sub-programming, rather than direct Taylor expansion of reliability constraints, a new formulation is introduced for approximate reliability constraints at the current design point and its linearization. The approximate reliability index and its sensitivity are obtained from a recurrence formula based on the optimality conditions for the most probable failure point (MPP). It is shown that the approximate MPP, a key component of RBSO problems, is concurrently improved during each sub-programming solution step. Through analytical models and comparative studies over complex examples, it is illustrated that our approach is efficient and that a linearized reliability index is a good approximation of the accurate reliability index. These unique features and the concurrent convergence of design optimization and reliability calculation are demonstrated with several numerical examples.     

Reliability-based optimum design of a symmetric laminated plate subject to buckling

This study is concerned with the buckling reliability maximization of a symmetric laminated composite plate with respect to the mean ply orientation angle. The reliability is evaluated by modelling the buckling failure as a series system consisting of potential eigenmodes. The mode reliability is obtained by the first-order reliability theory (FORM), where material constants and orientation angles of individual layers, as well as the applied loads are treated as random variables. In order to keep track of the intended buckling mode during the reliability analysis, the mode tracking method is utilized. Then, the failure probability of the series system is approximated by Ditlevsen's upper bound. The reliability maximization problem is formulated as a nested problem with two levels of optimization. Through numerical calculations, the reliability-based design is demonstrated to be important for the structural safety in comparison with the deterministic buckling load maximization design.