Life-cycle cost optimal design of passive dissipative devices

The cost-effective performance of structures under natural hazards such as earthquakes and hurricanes has long been recognized to be an important topic in the design of civil engineering systems. A realistic comprehensive treatment of such a design requires proper integration of (i) methodologies for treating the uncertainties related to natural hazards and to the structural behavior over the entire life-cycle of the building, (ii) tools for evaluating the performance using socioeconomic criteria, as well as (iii) algorithms appropriate for stochastic analysis and optimization. A systematic probabilistic framework is presented here for detailed estimation and optimization of the life-cycle cost of engineering systems. This framework is a general one but the application of interest here is the design of passive dissipative devices for seismic risk mitigation. A comprehensive methodology is initially presented for earthquake loss estimation; this methodology uses the nonlinear time-history response of the structure under a given excitation to estimate the damage in a detailed, component level. A realistic probabilistic model is then presented for describing the ground motion time history for future earthquake excitations. In this setting, the life-cycle cost is uncertain and can be quantified by its expected value over the space of the uncertain parameters for the structural and excitation models. Because of the complexity of these models, calculation of this expected value is performed using stochastic simulation techniques. This approach, though, involves an unavoidable estimation error and significant computational cost, features which make efficient design optimization challenging. A highly efficient framework, consisting of two stages, is discussed for this stochastic optimization. An illustrative example is presented that shows the efficiency of the proposed methodology; it considers the seismic retrofitting of a four-story non-ductile reinforced-concrete building with viscous dampers.     

On the reliability-based design of structures including passive energy dissipation systems

This contribution presents a methodology for stochastic design of structures including vibration protection systems. The approach is then used to investigate the effect of uncertain model parameters on the reliability-based optimal design of structures with a class of passive energy dissipation systems. The uncertainty of structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. The optimal design problem is formulated as a non-linear constrained minimization problem involving multiple design requirements, including reliability constraints related to the structural performance. Failure events defined by a large number of random variables are used to characterize the reliability measures. A sequential optimization approach based on global conservative, convex and separable approximations is implemented for solving the optimization problem. The effects of uncertain model parameters on the performance, robustness and reliability of protected systems is illustrated by two example problems that consider multi-story buildings under stochastic ground excitation.     

Optimum design of tuned mass dampers for different earthquake ground motion parameters and models

Tuned mass dampers are frequently used for passive control of vibrations in civil structures subject to seismic and wind actions. Their efficiency depends on selection of their mechanical properties in relation to main system and excitation characteristics. This paper proposes an optimum design strategy of single tuned mass dampers to control vibrations of principal mode of structures excited by earthquake ground motion. The main purpose of the paper is to investigate the influence of the time modulation of earthquake excitation upon the optimal tuned mass dampers design parameters: frequency and damping ratio. The study is based on numerical analyses carried out with different stochastic models for earthquakes: a simple filtered white noise model and two time modulated filtered white noise models. The numerical analyses are carried out to solve an optimization problem with a performance index defined by the reduction of the standard deviation of either the structure displacement or its inertial acceleration as objective function. To complete the work, the influence of the bandwidth excitation over the values of the optimal tuned mass damper parameters is investigated, as well the optimum mass ratio and the structure frequency. The results of the numeral analyses carried out infer that the earthquake excitation characteristics, including its modulation in time domain, highly affect the optimum tuned mass damper design parameters values.     

Novel decoupled framework for reliability-based design optimization of structures using a robust shifting technique

In a reliability-based design optimization (RBDO), computation of the failure probability (P_f) at all design points through the process may suitably be avoided at the early stages. Thus, to reduce extensive computations of RBDO, one could decouple the optimization and reliability analysis. The present work proposes a new methodology for such a decoupled approach that separates optimization and reliability analysis into two procedures which significantly improve the computational efficiency of the RBDO. This technique is based on the probabilistic sensitivity approach (PSA) on the shifted probability density function. Stochastic variables are separated into two groups of desired and non-desired variables. The three-phase procedure may be summarized as: Phase 1, apply deterministic design optimization based on mean values of random variables; Phase 2, move designs toward a reliable space using PSA and finding a primary reliable optimum point; Phase 3, applying an intelligent self-adaptive procedure based on cubic B-spline interpolation functions until the targeted failure probability is reached. An improved response surface method is used for computation of failure probability. The proposed RBDO approach could significantly reduce the number of analyses required to less than 10% of conventional methods. The computational efficacy of this approach is demonstrated by solving four benchmark truss design problems published in the structural optimization literature.     

火灾时管片可靠度计算及优化研究

受火灾高温的影响,隧道衬砌结构可靠性降低。笔者通过自由变形理论,解析计算可靠度优化模型中的结构内力,明确了计算中的随机变量;从结构可靠度指标几何意义出发,基于优化思想确定了可靠度计算公式;考虑火灾下衬砌管片的损伤特点,提出了火灾下管片的功能函数,建立了管片高温下可靠度计算优化模型;最后通过案例分析并利用非线性规划求解优化问题,得到火灾下衬砌可靠度的变化规律,并对管片截面厚度进行了优化设计。研究表明,常规设计管片各处可靠度指标差异较大,隧道拱顶可靠度最低,10 min后失效概率大于0.023,通过优化设计可使火灾持续30 min后满足基本安全。     

A proposed structural design method considering fluid viscous damper degradations

The purpose of this study is to perform a seismic assessment of the moment resistant steel structures enhanced with viscous dampers where the dampers are degraded due to possible leak of viscous fluid. This paper proposes a design procedure based on corrected response spectrums as a result of seismic assessments based on nonlinear time series analyses on three‐, five‐, and seven‐story steel frame structures denoted as “generic structures.” The proposed design procedure is a seismic displacement‐based design methodology for buildings with viscous dampers as passive energy dissipation systems. Prior literature on these types of structures often overlook the viscous dampers degradation due to the fluid leak. In this paper, in order to study these effects, a target displacement is specified at first and the lateral forces and required stiffness are obtained. The effectiveness of the proposed procedure is verified with the collapse fragility curves of the generic structures according to the ASCE 7‐10 and displacement‐based design methodology. The results show that the structures designed based on proposed procedure demonstrate acceptable performance with degrading dampers.     

考虑参数随机性的高层建筑风振舒适度的非线性黏滞阻尼器优化布设

以顶层加速度作为概率特征量,建立目标函数,分别采用基于随机等效线性化系统的频域方法和基于概率密度演化理论的非线性系统时域方法,进行了考虑结构参数随机性的高层建筑风振舒适度控制的黏滞阻尼器优化布设研究。结果表明：在总黏滞阻尼器系数相同的条件下,以顶层加速度标准差和失效概率为目标函数的黏滞阻尼器优化布设方案,在确定性激励作用下均能显著降低结构的风振响应,且相对于未优化的阻尼器均匀满布方案更经济、更有效。以加速度标准差为目标函数的传统阻尼器优化布设本质上是确定性分析方法,对结构可靠度的提高作用有限,而以加速度失效概率为目标函数的阻尼器优化布设,以结构响应的概率密度函数为优化对象,能显著地提高结构的可靠度,有利于改善高层建筑结构的风振舒适度性能。     

Semi‐active friction system with amplifying braces for control of MDOF structures

The development and applications of a semi‐active friction damping system with amplifying braces is studied. A system of dampers and braces, defined as the friction damping system with amplifying braces (FDSAB) is considered. Active control theory with velocity and acceleration feedback is used to obtain the control forces in the proposed system. The system can be used efficiently to enhance the damping of a structure and improving its response. The efficiency of the proposed system is demonstrated by the numerical simulation of a seven storey building subjected to earthquakes. The simulation shows that the behaviour of the damped structure with the FDSAB is significantly improved. The required control forces are much less compared with a control system with semi‐active friction dampers connected either to chevron or diagonal braces. Copyright © 2001 John Wiley & Sons, Ltd.     

Simulation-based robust design of mass dampers for response mitigation of tension leg platforms

A robust stochastic design framework is discussed for design of mass dampers. The focus is on applications for the mitigation of the coupled heave and pitch response of Tension Leg Platforms under stochastic sea excitation. The framework presented fully addresses the complex relationship between the coupled dynamics of the platform, the stochastic excitation and the vibration of the dampers. Model parameters that have some level of uncertainty are probabilistically described. In this probabilistic setting, the system reliability is adopted as the design objective. Stochastic simulation is considered for evaluation of the system model response and the overall reliability performance. This way, all nonlinear characteristics of the structural response and environmental excitation are explicitly incorporated into their respective models. An efficient algorithm is discussed for performing the challenging stochastic design optimization. The ideas are illustrated in an application involving a tension leg platform with closely spaced frequencies for the heave and pitch degrees of freedom.     

具自复位功能的同心斜撑构架耐震行为研究

一般而言,同心斜撑构架(CBF)通过对角配置斜撑来消散地震力。然而在地震过后结构物留下过大的残留变形,使得结构物难以修复。故该文对具自复位功能同心斜撑构架受震后可减少残留变形的可行性进行探讨。在类似的文件中,由于在梁柱接合处将两者分开,受地震时令梁端可在柱面上进行摇摆,而并没有引发任何损坏。提出通过梁翼板底部所安装的摩擦阻尼器或在斜撑上安装摩擦阻尼器或摩擦铰阻尼器,为验证此设计想法,该文设计一个实际尺寸的构架,此构架为单层单垮的同心斜撑构架,并在横向进行循环反复载重试验。而研究参数包含能量消散的形式不同或是位置不同与摩擦材料的不同,如磷青铜和黄铜。而试验的结果显示,具自复位功能同心斜撑构架可实现少量的残留变形与适当的耐震性能。由所有的试验可看出,使用磷青铜摩擦阻尼器的斜撑比其他形式斜撑消散较多能量。     

预应力锚索抗滑桩结构稳健优化设计

稳健优化设计是稳健设计与最优化技术、计算机技术的结合,当前已成为工程稳健设计研究的一个热点。按照这种方法进行预应力锚索抗滑桩设计,既能在设计阶段保证工程质量的稳健性,又能利用优化设计中众多数学模型和成熟的求解方法,更好地解决多变量、多目标、带约束问题的求解。针对正交设计的不足,用均匀设计代替正交设计,应用专业软件模拟计算不同工况下预应力锚索抗滑桩结构顶部水平位移,通过多元回归分析,用回归模型y(xi)代替函数模型y(xi)作为目标函数,设计参数作为优化变量,规范及合同要求作为约束条件,提出一种预应力锚索抗滑桩结构稳健优化设计方法。以昆洛路K1+440～K1+780边坡为例,阐述用MATLAB语言进行预应力锚索抗滑桩稳健优化设计的方法。     

Probabilistic stability analysis of geosynthetic-reinforced slopes under pseudo-static and modified pseudo-dynamic conditions

An efficient and accurate reliability-based design of the geosynthetic-reinforced slopes (GRS) using the pseudo-static and modified pseudo-dynamic framework is proposed in the present study. Deterministic formulation used in the present study is made robust with the help of nonlinear constrained optimization. The collocation based stochastic response surface method (CSRSM) is used to probabilistically analyze the GRS. The critical modes of failure pertaining to the internal and external stability of the GRS are considered in the formation of the performance functions. The horizontal seismic acceleration coefficient (k_h), internal friction angle of soil (φ), soil unit weight (γ), shear wave velocity (V_s), and friction angle at the interface between soil and reinforcement (φ_b) are chosen as the random variables, owing to their high influence on the stability of the GRS. The influence of correlation on the stability of the reinforced slope is illustrated considering the internal and external stability. System reliability analysis considering the internal and external modes of failure is also performed. An illustrative example is presented showing the steps to design a GRS using the proposed formulation. The results confirm the necessity of performing the system reliability analysis to estimate an accurate value of probability of failure of GRS.     

Reliability-based design optimization with discrete design variables and non-smooth performance functions: AB-PSO algorithm

The purpose of reliability-based design optimization (RBDO) is to find a balanced design that is not only economical but also reliable in the presence of uncertainty. Practical applications of RBDO involve discrete design variables, which are selected from commercially available lists, and non-smooth (non-differentiable) performance functions. In these cases, the problem becomes an NP-complete combinatorial optimization problem, which is intractable for discrete optimization methods. Moreover, the non-smooth performance functions would hinder the use of gradient-based optimizers as gradient information is of questionable accuracy. A framework is presented in this paper whereby subset simulation is integrated with a new particle swarm optimization (PSO) algorithm to solve the discrete and non-smooth RBDO problem. Subset simulation overcomes the inefficiency of direct Monte Carlo simulation (MCS) in estimating small failure probabilities, while being robust against the presence of non-smooth performance functions. The proposed PSO algorithm extends standard PSO to include two new features: auto-tuning and boundary-approaching. The former feature allows the proposed algorithm to automatically fine tune its control parameters without tedious trial-and-error procedures. The latter feature substantially increases the computational efficiency by encouraging movement toward the boundary of the safe region. The proposed auto-tuning boundary-approaching PSO algorithm (AB-PSO) is used to find the optimal design of a ten-bar truss, whose component sizes are selected from commercial standards, while reliability constraints are imposed by the current design code. In multiple trials, the AB-PSO algorithm is able to deliver competitive solutions with consistency. The superiority of the AB-PSO algorithm over standard PSO and GA (genetic algorithm) is statistically supported by non-parametric Mann-Whitney U tests with the p-value less than 0.01.     

Seismic design and assessment of structures with viscous dampers at limit state levels: Focus on probability of damage in devices

During large earthquakes, the seismic demand of viscous dampers may exceed their capacity. In this regard, current design codes must consider extreme conditions and preserve the damper at limit state levels. Here, by adjusting the damping coefficient, a procedure is introduced to mitigate device damages during severe earthquakes. To assess the procedure, 15 special moment resisting frames with a different number of stories (two, four, and eight) were designed by three methods: The recommended novel procedure, the seismic provisions of ASCE7, and the procedure proposed by Miyamoto et al. 1 for structures, installed with supplemental damping devices. A series of incremental dynamic analyses were then performed by modeling the limit state behavior of viscous dampers. Results indicated that the novel method reduces the damage probability of dampers as well as the maximum demands on the structure at different seismic hazard levels.     

Continuous pulse and hybrid control of structures

In recent years, passive as well as active control methods have been implemented for structural motion reduction of tall buildings in earthquakes. An active control method for the inelastic response of tall buildings is presented. The proposed method of continuous pulse control uses closed-loop feedback control as a combination of two algorithms. The first is a linear control algorithm-instantaneous optimal control-and the second is a pulse control algorithm-the pulse control algorithm-which applies a corrective pulse when a prespecified structural velocity threshold is exceeded. The control forces required by active control systems to reduce the seismic response of tall buildings can be quite large. On the other hand, passive control systems such as the viscoelastic dampers do not require external energy for their operation. The possibility of combining viscoelastic dampers and the active bracing system for reducing the required control forces is examined. The combination of passive and active devices improves safety, serviceability and the comfort of the building's occupants.     

Reliability-based capacity design for reinforced concrete bridge structures

In the seismic design of reinforced concrete (RC) bridge structures, there should be no brittle failures, such as shear failures, in the components, and a plastic hinge should be formed at the bottom of the bridge pier. These are important concepts in capacity design to guarantee the safety of bridges subjected to severe earthquakes. These concepts can maximise post-event operability and minimise the cost of repairing bridges after a severe earthquake. In this article, a reliability-based methodology to carry out capacity design with partial factors is proposed and applied to the seismic design of RC bridge structures. This ensures that (i) all of the components undergo the desired ductile failure mode, (ii) the damage due to an earthquake is induced only at the bottom of the bridge pier and (iii) the probability of failure is at most equal to a specified value.     

Optimal placement of metallic dampers for seismic upgrading of multistory buildings based on a cost‐effectiveness criterion using genetic algorithm

In this paper, an optimal placement methodology for metallic dampers is proposed to upgrade the seismic performance of multistory buildings. Most previous studies on optimal damper placement (ODP) problems have been focused on minimizing the seismic responses, whereas the present study aims to utilize the minimum total cost of dampers to achieve a prescribed level of seismic response. To this end, the optimization objective is constructed based on a cost‐effectiveness criterion, and the optimization constraint is defined based on a desired level of seismic response. An improved integer‐coded genetic algorithm is presented for solving the ODP problem. A 16‐story shear building is illustrated to verify the proposed optimal placement methodology. It is shown that the proposed methodology can be used to achieve the predetermined performance level while minimizing the retrofitting cost. Moreover, different algorithms, objective functions, and levels of accuracy on the optimization are also compared. Finally, a two‐step optimization approach is proposed for achieving better placement schemes with less computational efforts.     

Shape design of arch dams under load uncertainties with robust optimization

Due to an increased need in hydro-electricity, water storage, and flood protection, it is assumed that a series of new dams will be build throughout the world. The focus of this paper is on the non-probabilistic-based design of new arch-type dams by applying means of robust design optimization (RDO). This type of optimization takes into account uncertainties in the loads and in the material properties of the structure. As classical procedures of probabilistic-based optimization under uncertainties, such as RDO and reliability-based design optimization (RBDO), are in general computationally expensive and rely on estimates of the system’s response variance, we will not follow a full-probabilistic approach but work with predefined confidence levels. This leads to a bi-level optimization program where the volume of the dam is optimized under the worst combination of the uncertain parameters. As a result, robust and reliable designs are obtained and the result is independent from any assumptions on stochastic properties of the random variables in the model. The optimization of an arch-type dam is realized here by a robust optimization method under load uncertainty, where hydraulic and thermal loads are considered. The load uncertainty is modeled as an ellipsoidal expression. Comparing with any traditional deterministic optimization method, which only concerns the minimum objective value and offers a solution candidate close to limit-states, the RDO method provides a robust solution against uncertainty. To reduce the computational cost, a ranking strategy and an approximation model are further involved to do a preliminary screening. By this means, the robust design can generate an improved arch dam structure that ensures both safety and serviceability during its lifetime.