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.     

Time-domain dynamic drift optimisation of tall buildings subject to stochastic wind excitation

Wind-resistant design of tall buildings has been traditionally treated using the equivalent static load approach. In order to account for the uncertainties in random wind excitation, it is necessary to develop a comprehensive and reliable dynamic optimisation technique in the time domain. The optimal lateral stiffness design problem of wind-excited tall buildings consists of (1) identifying the critical dynamic drift response in the time domain and (2) searching for the optimal distribution of element stiffness of the building subject to multiple drift design constraints. The critical time-history drift constraints of a wind-excited building are first treated by the worst-case formulation and then explicitly expressed in terms of element sizing variables using the principle of virtual work. The extreme value distribution and the Gaussian assumption are employed to formulate and simplify the probabilistic drift constraints, which are explicitly considered in the dynamic optimisation problem. The system reliability associated with the interstory drift is estimated approximately by the bound approach to ensure that the most cost-efficient solution also attains an acceptable reliability level. A full-scale 45-story building example under wind tunnel derived time history wind loading is presented to illustrate the effectiveness and practicality of the reliability-based dynamic optimisation technique.     

Total Optimal Synthesis Method for Truss Structures Subject to Static and Frequency Constraints

Abstract: In a previous study, we presented an efficient optimal structural synthesis method for truss structures in which the design variables are coordinates of the panel points, cross-sectional areas, and discrete material kinds subjected to stress and displacement constraints. In this paper, the synthesis method is extended to solve design problems subject to stress, displacement, and fundamental natural-frequency constraints. The design problem is formulated in terms of discrete material kinds and continuous shape and sizing variables and which are approximated by a convex and separable subproblem. The approximate subproblem is expressed in direct and/or reciprocal design variables and shape, material, and sizing sensitivities. Each subproblem is solved by a two-stage minimization process. In the first stage, the continuous shape and sizing variables are optimized by a dual method. Second, the discrete material and continuous sizing variables are improved by a discrete sensitivity analysis. Using the proposed two-stage minimization procedure, both the discrete material kinds and the continuous shape and sizing variables can be systematically improved to obtain an optimal solution. The rigorousness, reliability, and efficiency of the method are illustrated by applying it to the minimum cost design of truss structures subject to stress, displacement, and fundamental natural-frequency constraints.     

空间网格结构的多参数优化设计

空间网格结构优化的设计参数很多,如结构高度、网格数、构件截面尺寸等.这些参数的量级或量纲不同,优化比较困难.运用改进的遗传算法进行空间网格结构的形状和截面优化,考虑了结构变形、压杆稳定、长细比等约束条件.采用拉格朗日乘子法对约束条件和优化函数进行处理.得到用于分析的无约束函数,提高遗传算法的运行效率.使用MATLAB遗传算法工具箱提供的函数编制了包含连续、不连续实数变量和整数变量的混合变量编码的结构优化程序.箅例分析表明,程序可靠.算法收敛较快.     

预应力索-拱结构优化设计

在强度、刚度、尺寸等约束条件下,以结构重量最轻为目标函数建立预应力索-拱结构优化设计的数学模型。对截面尺寸和索力这两种性质不同的设计变量,采用两级优化方法处理,对预应力的优化以结构在荷载（包括自重）和预应力共同作用下结构各构件的应力平方和最小为目标函数建立数学规划模型;对截面尺寸的优化采用浮动应力指数法。算例表明,该方法能有效地克服预应力和截面尺寸这两类变量在数值和性质上的不统一所造成的不易收敛问题,可以较快地收敛到满意结果,适用于预应力钢结构优化设计。     

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.     

Optimal design of steel frames under seismic loading using two meta-heuristic algorithms

In this paper, optimal design of steel frames is performed under seismic loading. The variables of the problem are taken as the cross-sectional areas of the members. These variables are considered as discrete, and are selected from a list of existing cross sections. Here, the charged system search and improved harmony search algorithms are utilized for optimization. For optimal design of steel frames in the first phase a time history analysis with the relative lateral displacement constraints is performed, and in the second phase a simultaneous dynamic–static analysis with the relative displacement and stress constraints is utilized using two meta-heuristic algorithms. Moment frames and their shear frame counterparts are considered, and their performances are compared for optimal design. In the case of moment frames, apart from the columns, the cross sections of the beams are also considered as design variables. The results indicate a good performance of the optimized moment frame and show that considering the effect of both drift and stress constraints, instead of only drift constraints, one obtains a better design. These results also show the suitability of the charged system search algorithm for optimal design of frames under seismic loading, as an extremely nonlinear problem.     

A multi-objective structural optimization method for serviceability design of tall buildings

Structural optimization design aims to identify optimal design variables corresponding to a minimum objective function with constraints on performance requirements. To this end, many optimization frameworks have been proposed to determine optimal structural systems that are subjected to seismic and wind hazards in isolation. However, some modern tall buildings are sensitive to seismic and wind excitation owing to their complex structural systems and geographic regions. Therefore, a proper structural optimization method for such buildings is required to ensure that the expected performance is achieved in a multi-hazard scenario. This study proposes a multi-objective serviceability design optimization methodology for buildings in multi-hazard seismic and wind environments by combining optimality criteria and the nondominated sorting genetic algorithm II (NSGA-II). Seismic and wind effects can be instantaneously updated due to changes in the structural dynamic properties during the optimal design process. A neural-network-based surrogate model with self-updating is proposed to predict the structural natural frequency so that the overall computation time of the optimization process can be reduced. The proposed method was used to optimize a 50-story frame-tube building and was compared against the general genetic algorithm and general NSGA-II to verify the feasibility and effectiveness.     

Probability density evolution analysis of stochastic nonlinear structure under non-stationary ground motions

In the present paper, a framework of dimension-reduction modeling method is developed for a dual stochastic dynamic structural system of spectrum-compatible non-stationary stochastic ground motion processes and stochastic structures. With the aid of the proposed method, the random variables used to describe the stochastic characteristics of the non-stationary ground motion processes and the structural parameters are respectively represented by the one-elementary-random-variable functions, contributing to an entire stochastic dynamic structural system readily described by merely two elementary random variables. Owing to the fact that the number of the elementary random variables needed is extremely small, the set of the representative points associated with the elementary random variables can thus be selected by the widely-used number theoretical method, and then the probability density evolution method can be conveniently combined to conduct the dynamic response analysis and dynamic reliability evaluation of nonlinear stochastic structures. In the numerical examples, the probability density evolution analysis of an eight-storey reinforced concrete frame structure with random parameters subjected to spectrum-compatible non-stationary stochastic ground motion processes is investigated as a case study. Numerical results fully demonstrated the effectiveness and robustness of the proposed method.     

Structural optimization of jacket supporting structures for offshore wind turbines using colliding bodies optimization algorithm

Considering the size and dimension of offshore wind turbine structures, structural optimization of such structures, notwithstanding being outstandingly fruitful, is a tedious task. Nonetheless, in this paper, a metaheuristic algorithm named as colliding bodies optimization is employed when investigating the optimal design of jacket supporting structures for offshore wind turbines. The OC4 reference jacket is considered as the case study, validating the outcomes of this research. To do so, MATLAB is utilized in modeling the structure. The structural optimization is then performed when both ultimate limit state and frequency constraints are being considered. During the optimization process, the weight of the structure is approximately halved, and its first and second frequencies are kept within the considered soft–stiff range (0.21–0.32 Hz).     

Multi-objective reliability-based optimization of prestressed concrete beams

A general approach to the multiobjective reliability-based optimum (MORBO) designs of prestressed concrete beams (PCB) is presented in this paper. The proposed approach incorporates all behavior and side constraints specified by the American Concrete Institute (ACI) code for prestressed concrete. Loading, material properties, prestressing force and the models used to predict structural performance at various stages—initial, final and ultimate—are all treated as random variables. A general MORBO methodology is solved by integrating PCB design and reliability analysis computer programs with an automated design optimization package. Only bi- and tri- multiobjective (MO) formulations, subjected to eleven reliability constraints and four geometrical constraints, are considered. The competing objectives in the multiobjective optimization of PCB are selected from, minimization of the overall cost of the PCB, maximization of the system reliability index, maximization of the flexural strength reliability index, and maximization of the tensile stress reliability index at service stage. The design variables consist of six geometrical dimensions that shape the PCB cross section and one that represents the amount of prestressing steel. Numerical examples illustrate the application of the proposed approach to the MORBO of PCB are presented. The -constraint (trade-off) approach is used for the solution of the MORBO.     

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.     

Optimized topology extraction of steel-framed DiaGrid structure for tall buildings

This study presents an optimal angle and a topology extraction of diagonal members in a DiaGrid structural system for tall buildings. The angle and topology of diagonal members are achieved by using a computer-oriented SIMP topology optimization. The objective function for the design optimization is to both maximize Eigenfrequency for resisting dynamic responses and minimize mean compliance for static responses. Relative densities subjected to SIMP penalty law are used for both optimization design variables and material properties, and then finite element analysis is carried out by using the relative element density. Frequency and mean compliance sensitivities with respect to relative density are straightforwardly derived by discrete sensitivity formulations. Based on the design sensitivity analysis, an initial topology with a given fixed support is shifted toward a final topology charged by almost voids (0) and solids (1) during every optimization procedure. An optimal DiaGrid topology with the highest stiffness is finally determined to resist both static and dynamic behaviors. Numerical examples with varied fixed support models are studied to find out optimal angles and topologies of diagonal members for a DiaGrid system design.     

Genetic Algorithms in Topologic Design of Grillage Structures

The paper describes the use of genetic algorithms in determining the optimal layout and sizing of two-dimensional (2D) and three-dimensional (3D) grillage structures for stress, displacement, and element buckling constraints. The design space for this problem is highly nonconvex and not readily amenable to traditional methods of nonlinear programming. The approach develops an optimal topology from a set of predefined structural universe so as to satisfy kinematic stability requirements and other constraints on structural response. A two-level genetic algorithm–based search is used, wherein the kinematic stability constraints are imposed at one level, followed by the treatment of stress and displacement constraints at a second level of optimization. Since genetic algorithms search for an optimal design from a discrete set of alternatives in the design space, their adaptation in the topologic design problem is natural and is governed only by issues related to computational efficiency. Strategies designed to alleviate the computational requirements of a genetic algorithm–based search are discussed in the paper.     

结构动力测试技术及其应用

介绍了结构动力测试方法的一般程序,以昆明市某写字楼车库为例,建立三维有限元模型,采用加速度传感器测量车库的动力输出和结构的动力响应,并探讨了结构测试中应注意的几个问题,以达到正确评价结构可靠度的目的。     

Topology Design of Truss Structures in a Multicriteria Environment

As an analogy of the general design process, this article presents a novel design approach that could generate structural design alternatives having different topologies and then select the optimal structures from them together with simultaneously determining the optimal design variables related to geometry and member size subjected to a multiple objective design environment. For this purpose, a specialized genetic algorithm, called StrGA_ DeAl +MOGA, that can handle the design alternatives and multicriteria problems very effectively is developed for the optimal structural design. To validate the developed method, plain-truss design problems are considered as illustrative examples. To begin with, the promising topologies are generated under the name of "design alternatives" with consideration of the given multiobjective environment. Based on the selected topology of truss structures, the sizing or geometric optimization process starts to determine the optimal design parameters. Three-bar and ten-bar truss problems are treated in the article to test the concept and methodology.     

Structural reliability analysis using a standard deterministic finite element code

A method for performing a reliability analysis of structural systems within a standard finite element code is presented. This numerical procedure can be implemented in any finite element (f.e.) code having an internal optimization routine. The design points of structural problems are determined by calculating the minimum distance from the origin to the failure surface in a set of normalized variables, by using the minimization routine of the f.e. code. In order to test the procedure, simple structural systems are solved and the results are compared with those obtained by using different approaches. Some examples of application of the procedure for the reliability analysis of real structures are presented.     

Performance-based seismic fragility analysis of retaining walls based on the probability density evolution method

Seismic fragility analysis is an efficient way to study the seismic behaviour and performance of structures under the excitation of earthquakes of varying intensity, and an essential part of the seismic risk assessment of structures. A recently developed dynamic reliability methodology, the probability density evolution method (PDEM), is proposed for the dynamic reliability and seismic fragility analysis of a retaining wall. The PDEM can obtain an instantaneous probability density function of the seismic responses and easily acquire the seismic reliability of the structural system. An important advantage of the PDEM is its high efficiency relative to that of the Monte Carlo simulation method, which is often used in the reliability and fragility analysis of structures. The present study uses a typical gravity retaining wall to illustrate stochastic seismic responses and fragility curves that can be obtained by the PDEM. The combined uncertainties of the seismic force and soil properties are explicitly and systematically modelled by stochastic ground motions and random variables respectively. The performance of the retaining wall is analysed for different acceptable levels of backfill settlement. Additionally, seismic fragility curves are constructed without assuming the distribution of the seismic response.     

Reliability and performance-based design

Structural failures in recent earthquakes and hurricanes have exposed the weakness of current design procedures and shown the need for new concepts and methodologies for building performance evaluation and design. A central issue is proper consideration and treatment of the large uncertainty in the loadings and the complex building behavior in the nonlinear range in the evaluation and design process. A reliability-based framework for design is proposed for this purpose. Performance check of the structures is emphasized at two levels corresponding to incipient damage and incipient collapse. Minimum lifecycle cost criteria are proposed to arrive at optimal target reliability for performance-based design under multiple natural hazards. The issue of the structural redundancy under stochastic loads is also addressed. Effects of structural configuration, ductility capacity, 3-D motions, and uncertainty in demand versus capacity are investigated. A uniform-risk redundancy factor is proposed to ensure uniform reliability for structural systems of different degree of redundancy. The inconsistency of the reliability/redundancy factor in current codes is pointed out.     

Structural optimization for performance-based design in earthquake engineering: Applications of neural networks

This work addresses an approach to performance-based design in the context of earthquake engineering. The objective is the optimization of the total structural cost, under constraints related to minimum target reliabilities specified for the different limit states or performance requirements. The problem involves (1) the use of a nonlinear, time-stepping dynamic analysis to investigate the responses of relevance to the performances’ evaluation and (2) the integration of the responses into measures of damage accumulated during the earthquake. The random responses are deterministically obtained for different combinations of the design parameters and the intervening random variables, of which some are associated with the structure and some with the earthquake characteristics. The approach uses a neural network representation of the responses and, for each one, the variability associated with different earthquake records is accommodated by developing two networks: one for the mean response over the records, and another for the corresponding standard deviation. The neural network representation facilitates the estimation of reliability by Monte Carlo simulation, and the reliability achieved in each performance level, for a specific combination of the design parameters, is itself represented with a neural network. This is then used within an optimization algorithm for minimum total cost under reliability constraints. An application example uses a reinforced concrete, multi-storey plane structure with seismic demands corresponding to the city of Mendoza, Argentina.