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.     

Reliability-based optimization in structural engineering

In this paper reliability-based optimization problems in structural engineering are formulated on the basis of the classical decision theory. Several formulations are presented: Reliability-based optimal design of structural systems with component or systems reliability constraints, reliability-based optimal inspection planning and reliability-based experiment planning. It is explained how these optimization problems can be solved by application of similar techniques. The reliability estimation is limited to first order reliability methods (FORM) for both component and systems reliability evaluation. The solution strategies applying first order non-linear optimization algorithms are described in detail with special attention to sensitivity analysis and stability of the optimization process. Furthermore, several practical aspects are treated as: Development of the reliability-based optimization model, inclusion of the finite element method as the response evaluation tool and how the size of the problem can be made practicable. Finally, the important task of model evaluation and sensitivity analysis of the optimal solution is treated including a strategy for model-making with both pre and post-analysis.     

Structural dynamic optimal design based on dynamic reliability

In this work, dimension and shape optimization of structures under stochastic process excitation is addressed in the context of element or system dynamic reliability constraints, where the structural gross mass is taken to be the objective function. Firstly, based on the dynamic response analysis of truss structures under stochastic process loads, the dynamic reliability constraints are developed and simplified, and the normalization of design variables is discussed to avoid some variables being drowned by others during optimization due to their different dimensions and orders of magnitude. The optimal models of dimension and shape with element or system dynamic reliability constraints are then presented. Two numerical examples are finally used to illustrate the results of different optimal designs, which demonstrate that the efficiency to solve the structural optimization with dynamic reliability constraints can be significantly improved if the design variables and their initial values are selected properly.     

Reliability analysis of linear dynamical systems using approximate representations of performance functions

A method to carry out reliability analysis of linear systems with random structural parameters and random excitation is presented. Probability that design conditions are satisfied within a given time period is used as a measure of system reliability. An efficient importance sampling technique is used to estimate the failure probabilities. This technique is combined with high quality approximations of the performance functions in terms of uncertain structural parameters. The number of dynamic analyses required during the estimation process is minimized since the simulations are carried out by evaluating explicit expressions. The explicit quantities correspond to approximate representations of the performance functions in terms of the uncertain structural parameters. A numerical example corresponding to problem 2, sub-case 2 of the benchmark study is presented to illustrate the accuracy and computational efficiency of the proposed computational procedure.     

Lifetime reliability-based optimization of reinforced concrete cross-sections under corrosion

This paper presents a lifetime reliability-based approach to the optimization of reinforced concrete (RC) cross-sections in an aggressive environment. The lifetime structural performance is evaluated by using a general methodology for time-variant analysis of RC structures subjected to diffusive attacks from aggressive agents with corrosion of the reinforcement. The lifetime probabilistic optimization is formulated at the cross-sectional level and is aimed to minimize the material cost under a time-dependent constraint on the structural reliability. The optimization problem is solved by combining a discrete gradient-based optimization method with a Monte Carlo simulation. The obtained results demonstrate that in a lifetime-oriented design the amount and location of the steel reinforcement and the value of the concrete cover play a crucial role for the optimal achievement of the desired lifetime structural performance.     

Multi-criterion stochastic optimal selection of a double glazing system

In this paper, the authors present the multi-criterion stochastic optimal selection of a double glazing system for a given office building. Four elements are required for a multi-criterion stochastic optimal design: an accurate and fast simulation model, an optimization solver, correct handling of the multi-criterion decision problem, and consideration of the stochastic performance quantification. Since stochastic optimal design is a double-exponential problem, the Gaussian Process (GP) emulator, as a surrogate to EnergyPlus, was used to achieve computational efficiency. The GP emulator was derived based on the training set generated from EnergyPlus simulation runs. A genetic algorithm and Pareto optimality were then applied to deal with the multi-criterion optimization. Stochastic performance quantification was performed using a stochastic objective function and Latin Hypercube Samplings (LHS). Using the aforementioned four elements, the authors realized the multi-criterion stochastic optimal design of a double glazing system. The differences in the mean values of energy consumption and PMV between EnergyPlus and both GP emulators are 0.27 (kWh/m²) and 0.16 (kWh/m²), respectively, and 0.01 and 0.00, respectively. In addition, 13 non-dominated Pareto optimal solutions were successfully obtained. The approach presented in this paper improves computation efficiency for a multi-criterion stochastic optimal design problem and contributes to higher-fidelity simulation-based decision making.     

Optimal probabilistic design of seismic dampers for the protection of isolated bridges against near-fault seismic excitations

A probabilistic, simulation-based framework is presented in this paper for risk assessment and optimal design of supplemental dampers for multi-span bridge systems supported on abutments and intermediate piers through isolation bearings. The adopted bridge model explicitly addresses nonlinear characteristics of the isolators and the dampers, the dynamic behavior of the abutments, and the effect of pounding between the neighboring spans against each other as well as against the abutments. Nonlinear dynamic analysis is used to evaluate the bridge performance, and a realistic stochastic ground motion model is presented for describing the time history of future near-fault ground motions and relating their characteristics to the seismic hazard for the structural site. A probabilistic foundation is used to address the various sources of structural and excitation uncertainties and ultimately characterize the seismic risk for the bridge. This risk is given by the expected value of the system response over the adopted probability models. Stochastic simulation is used for evaluating the multi-dimensional integral representing this expected value and for performing the associated optimization when searching for the most favorable damper characteristics. An efficient probabilistic sensitivity analysis is also established for identifying the importance of each of the uncertain model parameters in affecting the overall risk. An illustrative example is presented that considers the design of nonlinear viscous dampers for the protection of a two-span bridge.     

Safety analysis of structures with probability and evidence theory

In safety analysis of structures, classical probabilistic analysis has been a popular approach in engineering. However, it is not always to obtain sufficient information to model all uncertain parameters of structures system by probability theory, especially at early stage of design. Under this circumstance, probability theory (used to model random uncertainty) combined with evidence theory (used to model epistemic uncertainty) may be utilized in safety analysis of structures. This paper proposed a novel method for safety analysis of structures based on probability and evidence theory. Firstly, Bayes conversion method is used as the way for precision of evidence body, and the mean and variance of epistemic uncertain variables is defined. Then epistemic uncertainty variables is transformed to normal random variables by reflection transformation method, and the checking point method (J-C method) is used to solve most probability point and reliability. A numerical example and two engineering examples are given to demonstrate the performance of the proposed method. The results show both precision and computational efficiency of the method is high. Moreover, the proposed method provides basis for reliability-based optimization with the hybrid uncertainties.     

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.     

Structural Model Updating and Health Monitoring with Incomplete Modal Data Using Gibbs Sampler

Abstract:   A new Bayesian model updating approach is presented for linear structural models. It is based on the Gibbs sampler, a stochastic simulation method that decomposes the uncertain model parameters into three groups, so that the direct sampling from any one group is possible when conditional on the other groups and the incomplete modal data. This means that even if the number of uncertain parameters is large, the effective dimension for the Gibbs sampler is always three and so high-dimensional parameter spaces that are fatal to most sampling techniques are handled by the method, making it more practical for health monitoring of real structures. The approach also inherits the advantages of Bayesian techniques: it not only updates the optimal estimate of the structural parameters but also updates the associated uncertainties. The approach is illustrated by applying it to two examples of structural health monitoring problems, in which the goal is to detect and quantify any damage using incomplete modal data obtained from small-amplitude vibrations measured before and after a severe loading event, such as an earthquake or explosion.     

Stochastic dependency in life-cycle cost analysis of multi-component structures

It is crucial to assure that civil engineering structures can operate properly and safely, as damages during the service life may lead to catastrophic loss of property, fatalities and long-term consequences. The approaches for structural management through a life-cycle cost analysis need to address explicitly the dependencies between elements. The evaluation of the life-cycle maintenance cost of structures in this article considers stochastic, degradation and economic dependencies. A new approach to include stochastic and degradation dependencies, structural redundancy and load redistribution in structural management is developed herein. The proposed model uses the fault tree analysis and the conditional probabilities to take into account stochastic dependencies between the structural elements. The degradation consequences are evaluated and a method is proposed to account for load redistribution. Also, a practical formulation to approximate the reliability of systems formed by interrelated components is proposed, by the mean of a redundancy factor that can be computed by structural analysis. The proposed approach provides effective optimal maintenance decisions for civil engineering structures by considering the interaction between elements.     

Uncertain linear systems in dynamics: Retrospective and recent developments by stochastic approaches

This paper provides an overview along with a critical appraisal of available methods for uncertainty propagation of linear systems subjected to dynamic loading. All uncertain structural properties are treated as random quantities by employing a stochastic approach. The loading can be either of deterministic or stochastic nature, described by white noise, filtered white noise, and more generally, by a Gaussian stochastic process.The assessment of the variability of the uncertain response in terms of the mean and variance is described by reviewing the random eigenvalue problem and procedures to evaluate the first two moments of the stochastic (uncertain) response. Computational procedures which are efficiently applicable for general FE-models are the focus of this work.Most recent developments for the reliability assessment–besides a retrospective review–are summarized, with particular emphasis on numerical Monte Carlo Simulation approaches. This review comprises methods to assess the first excursion probability directly by efficient numerical methods. General “black box” procedures and approaches applicable only for linear systems are critically discussed. Specific procedures applicable to linear systems subjected to general Gaussian excitation are subsequently addressed. Methods applicable for deterministic structural systems are introduced first. Finally, a procedure to exploit the solutions for deterministic linear systems for stochastic uncertain systems in an efficient manner is described.     

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.     

Optimization of structures under stochastic loads

The objective of this study is to develop a method for design under multiple stochastic loads based on optimization. The objective function, such as cost, is minimized under the constraint that the probabilities of various limit states being reached are within allowable limits. The loads are treated as random processes and their combined effects evaluated by the load coincidence method. The limit states considered are either yielding or first plastic hinge at the member level or plastic collapse at the system level. A penalty function approach and a Sequential Unconstrained Minimization method are used. Sensitivity studies with respect to the load parameters are carried out. The dependence of the resultant optimal design on the constraints used, e.g. at the member or system level, is investigated. The proposed approach to the problem is shown to be a viable method and the design using bi-level (member and system) reliability constraints is shown to yield more risk-consistent results.     

An Engineering Approach to Multicriteria Optimization of Bridge Structures

Abstract: This paper presents an approach to multicriteria optimization of engineering structures and structural systems based on the use of the constraint approach for generating efficient solutions and compromise programming for selecting the "best" or satisficing solution. The criteria of minimax and minimum Euclidian distance provide the designer with a rationale for the choice of the best solution. For system optimization problems, the definition of a dominant criterion and compromise programming lead to a practical approach to the design of large-scale structural systems. The approach is illustrated by two examples of optimizing prestressed concrete highway bridges, including selection of the optimal system.     

Probabilistic Evaluation of Structural Fire Resistance

The work described herein seeks to investigate a probabilistic framework to evaluate the fire resistance of structures given uncertainty in the fire load and structural resistance parameters. The methodology involves (i) the identification and characterization of uncertain parameters in the system, (ii) a stochastic analysis of the thermo-mechanical response of the structure, and (iii) the evaluation of structural reliability based on a suitable limit state function. The methodology is demonstrated through the analysis of a protected steel beam using Monte Carlo simulation with embedded finite element simulations. Model dimensionality is reduced using a response sensitivity analysis, and limit state functions are defined based on limiting deflection criteria used in fire resistance tests. Results demonstrate that the 1-h rated beam resists a natural fire exposure with a failure probability of less than ten percent, although additional discussion is warranted regarding what might be considered an acceptable level of risk in structural fire design. The study also demonstrates that probabilistic analysis of structural fire resistance provides an enhanced understanding of the factors affecting the resistance of structures to fire and offers a means for rationally improving structural designs to meet target performance objectives.     

基于鱼群算法的耦合地震作用下钢结构-控制系统协同优化设计

鉴于目前土木工程的结构抗震优化设计方法尚未考虑到结构设计与控制设计之间的耦合相关性,极有可能丧失系统最优解,故运用协同优化策略对钢结构与控制系统进行一体化设计。首先建立耦合地震作用下含磁流变阻尼器(MRD)的运动方程,采用瞬时最优控制策略对其进行地震响应控制;进一步建立钢结构和MRD的优化模型,采用鱼群算法处理结构和MRD的多目标优化问题。优化结果表明:经协同优化设计后的受控结构性能优于串行设计的;耦合地震作用的优化结果稍大于只考虑水平地震作用的。