基于可靠指标的稳定安全系数探讨

桥梁结构当第一类稳定安全系数取4时,能否保证结构在更可能出现的第二类失稳发生时的可靠指标达到目标可靠指标值得研究。对单层单跨刚架桥分别进行了第一类和第二类稳定计算,以第一类稳定计算得到的临界荷载,取第一类稳定安全系数为4,采用一次可靠度方法编制程序得出可靠指标。进而采用第一类稳定可靠指标计算时的荷载效应和第二类临界荷载来计算第二类可靠指标。根据可靠指标探讨结构稳定安全系数取值的合理性。在此基础上,对两类稳定临界荷载进行了参数分析,研究临界荷载的变化对可靠指标的影响。结果表明:稳定分析应区分失稳状态,第一类稳定安全系数取4,但当结构发生第二类失稳时,有些情况下不足以保证可靠指标达到目标可靠指标。     

Error bounds for the reliability index in finite element reliability analysis

This work presents an extension of the goal‐oriented error estimation techniques to the reliability analysis of a linear elastic structure. We use a first‐order reliability method in conjunction with a finite element analysis (FEA) to compute the failure probability of the structure. In such a situation the output of interest that is computed from the FEA is the reliability index β. The accuracy of this output, and thus of the reliability analysis, depends, in particular, on the accuracy of the FEA. In this paper, upper and lower bounds of the reliability index are proposed, as well as simple bounds of the failure probability. An application to linear fracture mechanics is presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Algorithm developments for optimization problems with joint reliability constraints

We propose an algorithm for optimization under uncertainty with joint reliability constraints. Most existing research formulates constraints of random variables/parameters in probabilistic forms such that the probability of individual constraint satisfaction must be higher than a reliability target. However, engineering problems generally define reliability as the probability of satisfying constraints ‘jointly’ rather than individually. Calculating a joint reliability value requires a multiple integration over the feasible domain. This calculation is in most realistic cases impractical by use of exact methods and has become the major challenge in optimization. In this research we propose a filter‐based sequential quadratic programming algorithm with joint reliability constraints approximated by their upper bounds. This upper bound can be obtained analytically by considering the current design location, the reliability of satisfying each constraint, and the angles between every constraint pair. To further improve the efficiency of the algorithm, active‐set strategies are implemented such that intense reliability calculations only required for constraints that are likely to be active. The rest of the constraints are approximated to the level needed to understand whether constraints might become active in the next iteration. The efficiency of the proposed method enables the applications to general complex engineering problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Collaborative optimization with inverse reliability for multidisciplinary systems uncertainty analysis

This article introduces a method which combines the collaborative optimization framework and the inverse reliability strategy to assess the uncertainty encountered in the multidisciplinary design process. This method conducts the sub-system analysis and optimization concurrently and then improves the process of searching for the most probable point (MPP). It reduces the load of the system-level optimizer significantly. This advantage is specifically more prominent for large-scale engineering system design. Meanwhile, because the disciplinary analyses are treated as the equality constraints in the disciplinary optimization, the computation load can be further reduced. Examples are used to illustrate the accuracy and efficiency of the proposed method.     

Multiresponse optimization using multivariate process capability index

Robust design is an efficient method for product and process improvement which combines experimentation with optimization to create a system that is less sensitive to uncontrollable variation. In this article, a simple and integrated modeling methodology for robust design is proposed. This methodology achieves the robustness objective function and input variables constraints simultaneously. The objective function is written in terms of the multivariate process capability vector (MC_pm) of several competing features of the system under study. The proposed methodology is applicable to general functions of the system performance with random variables. The effectiveness of the methodology is verified using two real‐world examples which are compared with those of other robust design methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Second‐order reliability method‐based inverse reliability analysis using Hessian update for accurate and efficient reliability‐based design optimization

First‐order reliability method (FORM) has been mostly utilized for solving reliability‐based design optimization (RBDO) problems efficiently. However, second‐order reliability method (SORM) is required in order to estimate a probability of failure accurately in highly nonlinear performance functions. Despite accuracy of SORM, its application to RBDO is quite challenging due to unaffordable numerical burden incurred by a Hessian calculation. For reducing the numerical efforts, a quasi‐Newton approach to approximate the Hessian is introduced in this study instead of calculating the true Hessian. The proposed SORM with the approximated Hessian requires computations only used in FORM, leading to very efficient and accurate reliability analysis. The proposed SORM also utilizes a generalized chi‐squared distribution in order to achieve better accuracy. Furthermore, SORM‐based inverse reliability method is proposed in this study. An accurate reliability index corresponding to a target probability of failure is updated using the proposed SORM. Two approaches in terms of finding an accurate most probable point using the updated reliability index are proposed. The proposed SORM‐based inverse analysis is then extended to RBDO in order to obtain a reliability‐based optimum design satisfying probabilistic constraints more accurately even for a highly nonlinear system. The numerical study results show that the proposed reliability analysis and RBDO achieve efficiency of FORM and accuracy of SORM at the same time. Copyright © 2014 John Wiley & Sons, Ltd.     

Reliability analysis and reliability-based design optimization of roadway horizontal curves using a first-order reliability method

This article presents reliability analysis and reliability-based optimization of roadway minimum radius design based on vehicle dynamics, mainly focusing on exit ramps and interchanges. The performance functions are formulated as failure modes of vehicle rollover and sideslip. To accurately describe the failure modes, analytical models for rollover and sideslip are derived considering nonlinear characteristics of vehicle behaviour using the commercial software TruckSim. The probability of an accident is evaluated using the first-order reliability method and numerical studies are conducted using a single-unit truck model. To propose a practical application for the study, the reliability analysis for the minimum radius recommended by American Association of State Highway and Transportation Officials is conducted. The results show that, even if there are deviations from assumed design conditions of the current design guideline, the proposed design method can guarantee given target margins of safety against rollover and sideslip. Based on the reliability analysis, reliability-based design optimization is carried out and the results indicate new recommendations for minimum radii satisfying given target reliability levels.     

Development of a simple and efficient method for robust optimization

Robust optimization problems are newly formulated and an efficient computational scheme is proposed. Both design variables and design parameters are considered as random variables about their nominal values. To ensure the robustness of objective performance, we introduce a new performance index bounding the performance together with a constraint limiting the performance variation. The constraint variations are regulated by considering the probability of feasibility. Each probability constraint is transformed into a sub‐optimization problem by the advanced first‐order second moment (AFOSM) method for computational efficiency. The proposed robust optimization method has the advantages that the mean value and the variation of the performance function are controlled simultaneously and rationally and the second‐order sensitivity information is not required even in case of gradient‐based optimization process. The suggested method is examined by solving three examples and the results are compared with those for the deterministic case and those available in the literature. Copyright © 2002 John Wiley & Sons, Ltd.     

可靠性优化的一种新的启发式算法

建立了可靠性冗余优化模型,分析了各种优化方法的优缺点。分析了几种常见的启发式算法,根据拉格朗日乘子法和K-T方程,提出了一种新的启发式算法,结果表明该方法比较有效。     

A single-loop optimization method for reliability analysis with second order uncertainty

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush–Kuhn–Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.     

Ant algorithm for single and multiobjective reliability optimization problems

The paper illustrates the application of the ant colony optimization algorithm to solve both continuous function and combinatorial optimization problems in reliability engineering. The ant algorithm is combined with the strength Pareto fitness assignment procedure to handle multiobjective problems. Further, a clustering procedure has been applied to prune the Pareto set and to maintain diversity. Benchmark case examples show the superiority of the ant algorithm to such problems. Copyright © 2002 John Wiley & Sons, Ltd.     

Estimation of cable safety factors of suspension bridges using artificial neural network‐based inverse reliability method

The design of the main cables of suspension bridges is based on the verification of the rules defined by standard specifications, where cable safety factors are introduced to ensure safety. However, the current bridge design standards have been developed to ensure structural safety by defining a target reliability index. In other words, the structural reliability level is specified as a target to be satisfied by the designer. Thus, calibration of cable safety factors is needed to guarantee the specified reliability of main cables. This study proposes an efficient and accurate algorithm to solve the calibration problem of cable safety factors of suspension bridges. Uncertainties of the structure and load parameters are incorporated in the calculation model. The proposed algorithm integrates the concepts of the inverse reliability method, non‐linear finite element method, and artificial neural networks method. The accuracy and efficiency of this method with reference to an example long‐span suspension bridge are studied and numerical results have validated its superiority over the conventional deterministic method or inverse reliability method with Gimsing's simplified approach. Finally, some important parameters in the proposed method are also discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

过盈联结的可靠性分析与优化

在机械制造,特别是重型机械制造中,过盈联结具有十分显著的经济效益,但传统的计算方法不仅复杂,而且无法对过盈联结的工作可靠性给出定量的评价,因此影响了过盈配合的工作质量,妨碍了过盈配合的广泛应用,从可靠性理论和优化技术出发,对过盈联结的可靠性进行分析,并对过盈联结可靠度的优化进行研究,建立了计算模型,编制了相应的通用计算机程序,该方法和程序,不仅可以对过盈联接的可靠度进行分析,而且可以对过盈量进行优化,有效地提高配合系统的可靠度。     

Reliability‐based design optimization with equality constraints

Equality constraints have been well studied and widely used in deterministic optimization, but they have rarely been addressed in reliability‐based design optimization (RBDO). The inclusion of an equality constraint in RBDO results in dependency among random variables. Theoretically, one random variable can be substituted in terms of remaining random variables given an equality constraint; and the equality constraint can then be eliminated. However, in practice, eliminating an equality constraint may be difficult or impossible because of complexities such as coupling, recursion, high dimensionality, non‐linearity, implicit formats, and high computational costs. The objective of this work is to develop a methodology to model equality constraints and a numerical procedure to solve a RBDO problem with equality constraints. Equality constraints are classified into demand‐based type and physics‐based type. A sequential optimization and reliability analysis strategy is used to solve RBDO with physics‐based equality constraints. The first‐order reliability method is employed for reliability analysis. The proposed method is illustrated by a mathematical example and a two‐member frame design problem. Copyright © 2007 John Wiley & Sons, Ltd.     

渐开线行星轮系参数优选及可靠性优化设计

将渐开线行星齿轮传动参数优选的结果用于可靠性优化设计中,包括按两轮滑动率相等原则分配外啮合变位系数和X1∑;按提高内啮合副轮齿接触强度并保证具有较高重合度来确定内啮合角αH;按等强度原则寻求最佳m/a值,最后对该传动进行可靠性优化设计。     

Structural design of high-performance capacitive accelerometers using parametric optimization with uncertainties

Electrostatic or capacitive accelerometers are among the highest volume microelectromechanical systems (MEMS) products nowadays. The design of such devices is a complex task, since they depend on many performance requirements, which are often conflicting. Therefore, optimization techniques are often used in the design stage of these MEMS devices. Because of problems with reliability, the technology of MEMS is not yet well established. Thus, in this work, size optimization is combined with the reliability-based design optimization (RBDO) method to improve the performance of accelerometers. To account for uncertainties in the dimensions and material properties of these devices, the first order reliability method is applied to calculate the probabilities involved in the RBDO formulation. Practical examples of bulk-type capacitive accelerometer designs are presented and discussed to evaluate the potential of the implemented RBDO solver.     

Convergence control of the iterative procedure for performance-measure-based probabilistic structural design optimization

The advanced mean value (AMV) iterative scheme is commonly used to evaluate probabilistic constraints in the performance measure approach (PMA) for probabilistic structural design optimization (PSDO). However, the iterative procedure of PSDO may fail to converge. In this article, the chaotic dynamics theory is suggested to investigate and attack the non-convergence difficulties of PMA-based PSDO. Essentially, the AMV iterative formula forms a discrete dynamical system with control parameters. If the AMV iterative sequences present the numerical instabilities of periodic oscillation, bifurcation, and even chaos in some control parameter interval, then the outer optimization loop in PSDO cannot converge and acquire the correct optimal design. Furthermore, the stability transformation method (STM) of chaos feedback control is applied to perform the convergence control of AMV, in order to capture the desired fixed points in the whole control parameter interval. Meanwhile, PSDO is solved by the approaches of PMA two-level and PMA with the sequential approximate programming (SAP)—PMA with SAP. Numerical results of several examples illustrate that STM can smoothly overcome the convergence failure of PSDO resulting from the periodic oscillation, bifurcation, and chaotic solutions of AMV iterative procedure for evaluating the probabilistic constraints. Moreover, the probabilistic optimization with uniform random variables, which is widely recognized as a highly nonlinear and fairly difficult problem, can be attacked through introducing the strategy of chaos control. In addition, the approach of PMA with SAP combining with STM is quite effective and efficient.     

Practical solutions for multi-objective optimization: An application to system reliability design problems

For multiple-objective optimization problems, a common solution methodology is to determine a Pareto optimal set. Unfortunately, these sets are often large and can become difficult to comprehend and consider. Two methods are presented as practical approaches to reduce the size of the Pareto optimal set for multiple-objective system reliability design problems. The first method is a pseudo-ranking scheme that helps the decision maker select solutions that reflect his/her objective function priorities. In the second approach, we used data mining clustering techniques to group the data by using the k-means algorithm to find clusters of similar solutions. This provides the decision maker with just k general solutions to choose from. With this second method, from the clustered Pareto optimal set, we attempted to find solutions which are likely to be more relevant to the decision maker. These are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. To demonstrate how these methods work, the well-known redundancy allocation problem was solved as a multiple objective problem by using the NSGA genetic algorithm to initially find the Pareto optimal solutions, and then, the two proposed methods are applied to prune the Pareto set.     

基于模糊设计准则的机械可靠性优化设计研究

按照应力-强度分布干涉和模糊理论,对机械模糊可靠性优化设计方法进行系统的研究,提出了剩余可靠度的概念,建立了数学模型,给出了设计实例。研究表明：仅仅以实现要求的可靠度为目标的一般模糊可靠性设计由于不能考虑其他条件对设计变量取值的约束作用,往往导致设计结果不具可行性而失去实际意义。可靠性优化设计将模糊可靠性条件与其他所有限制条件一起作为设计约束,在设计空间围成一个可行设计域,然后按照设计目标要求用一定方法寻求可行域内的最优设计点,从而保证了设计结果既具可靠性,又具可行性和最优性。     

Port-of-entry safety via the reliability optimization of container inspection strategy through an evolutionary approach

Up to now, of all the containers received in USA ports, roughly between 2% and 5% are scrutinized to determine if they could cause some type of danger or contain suspicious goods. Recently, concerns have been raised regarding the type of attack that could happen via container cargo leading to devastating economic, psychological and sociological effects. Overall, this paper is concerned with developing an inspection strategy that minimizes the total cost of inspection while maintaining a user-specified detection rate for “suspicious” containers. In this respect, a general model for describing an inspection strategy is proposed. The strategy is regarded as an (n+1)-echelon decision tree where at each of these echelons, a decision has to be taken, regarding which sensor to be used, if at all. Second, based on the general decision-tree model, this paper presents a minimum cost container inspection strategy that conforms to a pre-specified user detection rate under the assumption that different sensors with different reliability and cost characteristics can be used. To generate an optimal inspection strategy, an evolutionary optimization approach known as probabilistic solution discovery algorithm has been used.