考虑模糊可靠度的抗震结构优化设计

在结构优化的目标函数中，不仅应考虑结构造价，而且应考虑结构服役期的损失期望。为此，我们定义了抗震结构模糊可靠度的概念。利用抗震设计原则和地震危险性分析给出了一个计算模糊可靠度的方法。然后提出了三步优化法；第一步，寻求一系列对应于不同设防烈度的最小造价设计；第二步，同时考虑造价和地震引起的损失期望，寻求最优设防烈度；第三步，寻找相应于此最优烈度的最小造价设计。     

A stochastic optimization model based on adaptive feedback correction process and surrogate model uncertainty for DNAPL-contaminated groundwater remediation design

A stochastic optimization model based on an adaptive feedback correction process and surrogate model uncertainty was proposed and applied for remediation strategy design at a dense non-aqueous phase liquids (DNAPL)-contaminated groundwater site. One hundred initial training samples were obtained using the Latin hypercube sampling method. A surrogate model of a multiphase flow simulation model was constructed based on these samples employing the self-adaptive particle swarm optimization kriging (SAPSOKRG) method. An optimization model was built, using the SAPSOKRG surrogate model as a constraint. Then, an adaptive feedback correction process was designed and applied to iteratively update the training samples, surrogate model, and optimization model. Results showed that the training samples, the surrogate model, and the optimization model were effectively ameliorated. However, the surrogate model is an approximation of the simulation model, and some degree of uncertainty exists even though the surrogate model was ameliorated. Therefore, residuals between the surrogate model and the simulation model were calculated, and an uncertainty analysis was conducted. Based on the uncertainty analysis results, a stochastic optimization model was constructed and solved to obtain optimal remediation strategies at different confidence levels (60, 70, 80, 90, 95%) and under different remediation objectives (average DNAPL removal rate ≥?70,?≥?75,?≥?80,?≥?85,?≥?90%). The optimization results demonstrated that the higher the confidence level and remediation objective, the more expensive was remediation. Therefore, decision makers can weigh remediation costs, confidence levels, and remediation objectives to make an informed choice. This also allows decision makers to determine the reliability of a selected strategy and provides a new tool for DNAPL-contaminated groundwater remediation design.     

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.     

复杂岩性解释模型稳定性和可靠性评价

对解释模型进行评价以及如何选择合适的解释模型是复杂岩性解释中非常重要的问题。本文应用统计学的理论以及非线性优化技术,系统研究了在线性约束条件下对储层参数的置信区域和误差大小进行估计的问题,通过将梯度投影算法与奇异值分解技术相结合的方法给出了计算储层参数置信区域与误差大小的公式,以及对复杂岩性解释模型的稳定性和可靠性进行合理评价的具体方法。最后通过数值计算实例研究了一种能够有效提高解释模型稳定性和可靠性的措施,数值计算结果证明解释模型响应函数的最小非零奇异值大小是影响稳定性和可靠性的一个重要参数,当最小非零奇异值较大时,模型的稳定性往往较好,否则较差,因此通过对解释模型进行适当组合并选取最小非零奇异值较大的综合解释模型,可以大大提高其稳定性和可靠性。     

Cost Optimization of DNAPL Remediation at Dover Air Force Base Site

This study investigates stochastic optimization of dense nonaqueous phase liquid (DNAPL) remediation design at Dover Air Force Base Area 5 using emulsified vegetable oil (EVO) injection. The Stochastic Cost Optimization Toolkit (SCOToolkit) is used for the study, which couples semianalytical DNAPL source depletion and transport models with parameter estimation, error propagation, and stochastic optimization modules that can consider multiple sources and remediation strategies. Model parameters are calibrated to field data conditions on prior estimates of parameters and their uncertainty. Monte Carlo simulations are then performed to identify optimal remediation decisions that minimize the expected net present value (NPV) cleanup cost while maintaining concentrations at compliance wells under the maximum contaminant level (MCL). The results show that annual operating costs could be reduced by approximately 50% by implementing the identified optimal remediation strategy. We also show that recalibration and reoptimization after 50 years using additional monitoring data could lead to a further 60% reduction in annual operating cost increases the reliability of the proposed remediation actions.     

大地电磁阻尼粒子群优化反演法研究

粒子群优化算法（PSO）是模仿鸟群寻找食物的社会行为的一种全局最优化算法,在多维空间函数寻优、动态目标寻优等方面有着收敛速度快、解质量高且需要设置的参数较少等优点.本文在研究常规粒子群优化算法的基础上,对常规的粒子群算法进行了改进,提出了一种新的惯性权重ω参数振荡递减策略,加快了PSO算法的收敛速度,构造的新算法称为阻尼粒子群优化算法.在MATLAB 6.5 编程环境中对阻尼PSO算法进行了数值实验,并对大地电磁测深的理论模型和实测数据进行了反演试算,结果表明,阻尼PSO算法不依赖于初始模型、能够搜索到全局极值,不易陷入局部极值,是一种快速有效的地球物理反演方法.     

Optimal seismic-resistant design of a planar steel frame

This paper illustrates the design of a four-storey, three-bay, moment-resisting, planar steel frame. Non-linear step-by-step integration is used as the analysis technique within the design process itself rather than as a check at the end of the design process. The method of design directly quantifies the accepted seismic-resistant design philosophy that a properly designed structure: (1) resists moderate ground motion without structural damage, and (2) resists severe ground motion without collapse. Actual ground motion accelerograms are selected and scaled to levels representing moderate and severe ground motions. Constraints quantifying structural damage and limited non-structural damage are constructed for the case of moderate ground motion, along with constraints quantifying collapse and limited structural damage for the case of severe ground motion. In addition serviceability constraints are imposed on structural behaviour under gravity loads only. Objective functions include the minimization of structural volume as well as the minimization of response quantities such as storey drifts and inelastically dissipated energy. A sophisticated optimization algorithm is utilized to solve the resulting mathematical programming problem. Comparative results concerning the computational phase as well as performance of both preliminary and final designs are presented. The practicality and reliability of the design method are assessed.     

Performance‐based design using structural optimization

A new methodology for seismic design is proposed based on structural optimization with performance‐based constraints. Performance‐based criteria are introduced for the seismic design of new buildings. These criteria are derived from the National Guidelines for Seismic Rehabilitation of Buildings (Reference [19], Federal Emergency Management Agency (FEMA), ‘NHERP Guidelines for seismic rehabilitation of buildings’, Report Nos 273 and 274, Washington, DC, 1997) for retrofitting existing structures. The proposed design methodology takes into account the non‐linear behaviour of the structure. The goal is to incorporate in the design the actual performance levels of the structure, i.e. how much reserve capacity the structure has in an earthquake of a given magnitude. The optimal design of the structure minimizes the structural cost subjected to performance constraints on plastic rotations of beams and columns, as well as behavioural constraints for reinforced concrete frames. Uncertainties in the structural period and in the earthquake excitation are taken into account using convex models. The optimization routine incorporates a non‐linear analysis program and the procedure is automated. The proposed methodology leads to a structural design for which the levels of reliability (performance levels) are assumed to be quantifiable. Furthermore, the entire behaviour of the structure well into the non‐linear range is investigated in the design process. Copyright © 2000 John Wiley & Sons, Ltd.     

A method for reliability-based optimization with multiple non-normal stochastic parameters: a simplified airshed management study

We develop methodologies to enable applications of reliability-based design optimization (RBDO) to environmental policy setting problems. RBDO considers uncertainty as random variables and parameters in an optimization framework with probabilistic constraints. Three challenges in environmental decision-making problems not addressed by current RBDO methods are efficient methods in handling: (1) non-normally distributed random parameters, (2) discrete random parameters, and (3) joint reliability constraints (e.g., meeting constraints simultaneously with a single reliability). We propose a modified sequential quadratic programming algorithm to address these challenges. An active set strategy is combined with a reliability contour formulation to solve problems with multiple non-normal random parameters. The reliability contour formulation can also handle discrete random parameters by converting them to equivalent continuous ones. Joint reliability constraints are estimated by their theoretical upper bounds using reliability indexes and angles of normal vectors between active constraints. To demonstrate the methods, we consider a simplified airshed example where CO and NOx standards are violated and are brought into compliance by reducing the speed limits of two nearby highways. This analytical example is based on the CALINE4 model. Results show the potential of this approach to handle complex large-scale environmental regulation problems.     

Design of passive systems for control of inelastic structures

A design strategy for control of buildings experiencing inelastic deformations during seismic response is formulated. The strategy is using weakened, and/or softened, elements in a structural system while adding passive energy dissipation devices (e.g. viscous fluid devices, etc.) in order to control simultaneously accelerations and deformations response during seismic events. A design methodology is developed to determine the locations and the magnitude of weakening and/or softening of structural elements and the added damping while insuring structural stability. A two‐stage design procedure is suggested: (i) first using a nonlinear active control algorithm, to determine the new structural parameters while insuring stability, then (ii) determine the properties of equivalent structural parameters of passive system, which can be implemented by removing or weakening some structural elements, or connections, and by addition of energy dissipation systems. Passive dampers and weakened elements are designed using an optimization algorithm to obtain a response as close as possible to an actively controlled system. A case study of a five‐story building subjected to El Centro ground motion, as well as to an ensemble of simulated ground motions, is presented to illustrate the procedure. The results show that following the design strategy, a control of both peak inter‐story drifts and total accelerations can be obtained. Copyright © 2008 John Wiley & Sons, Ltd.     

Minimum‐cost optimization of nonlinear fluid viscous dampers and their supporting members for seismic retrofitting

This paper presents an effective approach for achieving minimum‐cost designs for seismic retrofitting using nonlinear fluid viscous dampers. The damping coefficients of the dampers and the stiffness coefficients of the supporting braces are designed by an optimization algorithm. A realistic retrofitting cost function is minimized subject to constraints on inter‐story drifts at the peripheries of frame structures. The cost function accounts for costs related to both the topology and the sizes of the dampers. The behavior of each damper‐brace element is defined by the Maxwell model, where the force–velocity relation of the nonlinear dampers is formulated with a fractional power law. The optimization problem is first posed and solved as a mixed integer problem. For the reduction of the computational effort required in the optimization, the problem is then reformulated with continuous variables only and solved with a gradient‐based algorithm. Material interpolation techniques, which have been successfully applied in topology optimization and in multi‐material optimization, play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for 3‐D irregular frames are presented and discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Reliability-based optimal design of nonlinear viscous dampers for the seismic protection of structural systems

Viscous dampers are widely employed for enhancing the seismic performance of structural systems, and their design is often carried out using simplified approaches to account for the uncertainty in the seismic input. This paper introduces a novel and rigorous approach that allows to explicitly consider the variability of the intensity and characteristics of the seismic input in designing the optimal viscous constant and velocity exponent of the dampers based on performance-based criteria. The optimal solution permits controlling the probability of structural failure, while minimizing the damper cost, related to the sum of the damper forces. The solution to the optimization problem is efficiently sought via the constrained optimization by linear approximation (COBYLA) method, while Subset simulation together with auxiliary response method are employed for the performance assessment at each iteration of the optimization process. A 3-storey steel moment-resisting building frame is considered to illustrate the application of the proposed design methodology and to evaluate and compare the performances that can be achieved with different damper nonlinearity levels. Comparisons are also made with the results obtained by applying simplifying approaches, often employed in design practice, as those aiming to minimize the sum of the viscous damping constant and/or considering a single hazard level for the performance assessment.     

基于正交枚举法的给水管网抗震加固优化研究

从系统全局出发,以管道单元动态抗震可靠度和震后给水管网各节点的动态自由水压为参数,以优化加固后的管网系统震后水压总降幅最小或系统加固总投入最小为优化目标,对加固方案进行优选,从而给出管网系统的抗震加固优化策略。根据管网系统的功能要求、震害特点,将优化变量转化为较少的离散变量,并利用正交枚举法进行简化计算,从而避免了大规模非线性规划求解的困难,为给水管网的抗震加固优化提供了实用有效的方法。     

Dynamic analysis of track nonlinear energy sinks subjected to simple and stochastice excitations

Track nonlinear energy sinks (track NESs) have been shown to be an effective and applicable strategy to mitigate structural response in recent years. However, previous studies on track NESs has mainly focused on demonstrating the benefits of track NESs through numerical simulations and experiments, with relatively little attention paid to the analytical understanding of the unique dynamics of track NESs. This study analyzes the responses of a track NES when subjected to impulsive and harmonic excitations by the harmonic balance method. Special attention is given to the cause and effect of the peaking behavior that is a prominent characteristic of the track NES's restoring force–displacement relationship. Analytical results reveal that the special energy–frequency characteristics of track NESs can be, at times, utilized to enhance the energy robustness that is absent in the conventional cubic NESs. Based on the analytical response expression, an equivalent linearization method (ELM) for the track NESs is developed for stochastic analysis. This ELM is numerically validated on the systems with strong nonlinearities. Stochastic optimization built on the ELM is performed to obtain design parameters of the track NES that can lead to minimum response variances of the primary structure. In particular, the proposed optimization procedure can be applied to seismic optimum design in which the seismic excitations are modeled as filtered white-noise ground motions. The analytical techniques provided in this study lay the groundwork for the practical implementation of track NESs as a robust and effective control strategy for engineering structures.     

Probabilistic performance‐based optimum design of seismic isolation for a California high‐speed rail prototype bridge

Previous comparison studies on seismic isolation have demonstrated its beneficial and detrimental effects on the structural performance of high‐speed rail bridges during earthquakes. Striking a balance between these 2 competing effects requires proper tuning of the controlling design parameters in the design of the seismic isolation system. This results in a challenging problem for practical design in performance‐based engineering, particularly when the uncertainty in seismic loading needs to be explicitly accounted for. This problem can be tackled using a novel probabilistic performance‐based optimum seismic design (PPBOSD) framework, which has been previously proposed as an extension of the performance‐based earthquake engineering methodology. For this purpose, a parametric probabilistic demand hazard analysis is performed over a grid in the seismic isolator parameter space, using high‐throughput cloud‐computing resources, for a California high‐speed rail (CHSR) prototype bridge. The derived probabilistic structural demand hazard results conditional on a seismic hazard level and unconditional, i.e., accounting for all seismic hazard levels, are used to define 2 families of risk features, respectively. Various risk features are explored as functions of the key isolator parameters and are used to construct probabilistic objective and constraint functions in defining well‐posed optimization problems. These optimization problems are solved using a grid‐based, brute‐force approach as an application of the PPBOSD framework, seeking optimum seismic isolator parameters for the CHSR prototype bridge. This research shows the promising use of seismic isolation for CHSR bridges, as well as the potential of the versatile PPBOSD framework in solving probabilistic performance‐based real‐world design problems.     

DUAL-LEVEL SEISMIC DESIGN: A RELIABILITY-BASED METHODOLOGY

The seismic design provisions of most building codes in the United States specify ground motion parameters for various regions of the country and provide simple formulae to determine a distribution of lateral forces for which the structure should be designed. Although the code provisions are very simple to use, they oversimplify a complex problem and are based on many implicit assumptions which many designers may not appreciate. Furthermore, the reliability of the final design is not easily determined. This paper describes a reliability-based seismic design procedure for building structures. It is a performance-based design procedure which requires the designer to verify that a particular structural design satisfies displacement-based performance criteria. An equivalent system methodology and uniform hazard spectra are used to evaluate structural performance. The performance criteria are expressed in probabilistic terms, and deterministic design-checking equations are derived from these criteria. The design-checking equations incorporate design factors (analogous to load and resistance factors) which account for the uncertainty in the seismic hazard, the uncertainty in predicting site soil effects, and the approximate nature of the simplified models of the structure. The alternative procedure should enable designers to achieve code-specified target performance objectives for moderate and severe levels of earthquake excitation.     

Towards realistic minimum-cost optimization of viscous fluid dampers for seismic retrofitting

This paper presents an effective approach for achieving minimum cost designs for seismic retrofitting using viscous fluid dampers. A new and realistic retrofitting cost function is formulated and minimized subject to constraints on inter-story drifts at the peripheries of frame structures. The components of the new cost function are related to both the topology and to the sizes of the dampers. This constitutes an important step forward towards a realistic definition of the optimal retrofitting problem. The optimization problem is first posed and solved as a mixed-integer problem. To improve the efficiency of the solution scheme, the problem is then re-formulated and solved by nonlinear programming using only continuous variables. Material interpolation techniques, that have been successfully applied in topology optimization and in multi-material optimization, play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for 3-D irregular frames are presented and compared with those achieved using genetic algorithms.     

Optimal maintenance strategies for structures in seismic zones

In this paper an approach is developed for establishing optimal maintenance (repair) strategies of structures in seismic zones. The approach is based on expected future costs and the main decision variable is a damage threshold for repair given an acceptable reliability level. It is considered that structural damage accumulates over a number of earthquakes until a threshold is reached or exceeded, after which the structure is repaired so that there is no remaining damage. A Markov model is implemented for such a process of damage accumulation during future earthquakes. An algorithm is proposed for computing non‐linear structural response to earthquakes using a damage function model. This algorithm is used to evaluate transition probabilities between damage states based on simulations of future earthquakes of given intensities. Expressions are derived for evaluating expected life‐cycle damage costs and structural reliability as a function of time and of the damage threshold for repair. As an application, a single‐degree‐of‐freedom structural system is studied. In addition, the paper addresses the case of instrumented structures where information from earthquake response records is available. Such information is incorporated into the formulation for maintenance strategies by means of a Bayesian approach for updating the probability distribution of structural damage and of non‐linear behaviour parameters so that predictions about costs and reliability are improved. Copyright © 2002 John Wiley & Sons, Ltd.     

Reliability‐based control algorithms for nonlinear hysteretic systems based on enhanced stochastic averaging of energy envelope

Current reliability‐based control techniques have been successfully applied to linear systems; however, incorporation of stochastic nonlinear behavior of systems in such control designs remains a challenge. This paper presents two reliability‐based control algorithms that minimize failure probabilities of nonlinear hysteretic systems subjected to stochastic excitations. The proposed methods include constrained reliability‐based control (CRC) and unconstrained reliability‐based control (URC) algorithms. Accurate probabilistic estimates of nonlinear system responses to stochastic excitations are derived analytically using enhanced stochastic averaging of energy envelope proposed previously by the authors. Convolving these demand estimates with capacity models yields the reliability of nonlinear systems in the control design process. The CRC design employs the first‐level and second‐level optimizations sequentially where the first‐level optimization solves the Hamilton–Jacobi–Bellman equation and the second‐level optimization searches for optimal objective function parameters to minimize the probability of failure. In the URC design, a single optimization minimizes the probability of failure by directly searching for the optimal control gain. Application of the proposed control algorithms to a building on nonlinear foundation has shown noticeable improvements in system performance under various stochastic excitations. The URC design appears to be the most optimal method as it reduced the probability of slight damage to 8.7%, compared with 11.6% and 19.2% for the case of CRC and a stochastic linear quadratic regulator, respectively. Under the Kobe ground motion, the normalized peak drift displacement with respect to stochastic linear quadratic regulator is reduced to 0.78 and 0.81 for the URC and CRC cases, respectively, at comparable control force levels. Copyright © 2017 John Wiley & Sons, Ltd.     

Optimum seismic design of reinforced concrete frames according to Eurocode 8 and fib Model Code 2010

Traditional seismic design, like the one adopted in Eurocode 8 (EC8), is force‐based and examining a single level of seismic action. In order to provide improved control of structural damage for different levels of seismic action, the new fib Model Code 2010 (MC2010) includes a fully fledged displacement‐based and performance‐based seismic design methodology. However, the level of complexity and computational effort of the MC2010 methodology is significantly increased. Hence, the use of automated optimization techniques for obtaining cost‐effective design solutions becomes appealing if not necessary. This study employs genetic algorithms to derive and compare optimum seismic design solutions of reinforced concrete frames according to EC8 and MC2010. This is important because MC2010 is meant to serve as a basis for future seismic design codes. It is found that MC2010 drives to more cost‐effective solutions than EC8 for regions of low seismicity and better or similar costs for regions of moderate seismicity. For high‐seismicity regions, MC2010 may yield similar or increased structural costs. This depends strongly on the provisions adopted for selecting the set of ground motions. In all cases, MC2010 provides enhanced control of structural damage. Copyright © 2016 John Wiley & Sons, Ltd.