A Hybrid Particle Swarm—Gradient Algorithm for Global Structural Optimization

Abstract: The particle swarm optimization (PSO) method is an instance of a successful application of the philosophy of bounded rationality and decentralized decision making for solving global optimization problems. A number of advantages with respect to other evolutionary algorithms are attributed to PSO making it a prospective candidate for optimum structural design. The PSO‐based algorithm is robust and well suited to handle nonlinear, nonconvex design spaces with discontinuities, exhibiting fast convergence characteristics. Furthermore, hybrid algorithms can exploit the advantages of the PSO and gradient methods. This article presents in detail the basic concepts and implementation of an enhanced PSO algorithm combined with a gradient‐based quasi‐Newton sequential quadratic programming (SQP) method for handling structural optimization problems. The proposed PSO is shown to explore the design space thoroughly and to detect the neighborhood of the global optimum. Then the mathematical optimizer, starting from the best estimate of the PSO and using gradient information, accelerates convergence toward the global optimum. A nonlinear weight update rule for PSO and a simple, yet effective, constraint handling technique for structural optimization are also proposed. The performance, the functionality, and the effect of different setting parameters are studied. The effectiveness of the approach is illustrated in some benchmark structural optimization problems. The numerical results confirm the ability of the proposed methodology to find better optimal solutions for structural optimization problems than other optimization algorithms.     

Comprehensive nonlinear seismic performance assessment of MR damper controlled systems using virtual real‐time hybrid simulation

Magnetorheological (MR) dampers have gained significant attention in seismic mitigation of structural systems due to their distinguished characteristics such as inherent stability and minimum power requirements. Their performance in control of nonlinear structural response, however, has not been widely investigated. This paper provides comprehensive nonlinear seismic performance assessment of a three‐story benchmark structure equipped with a large‐scale MR damper using virtual real‐time hybrid simulation to efficiently capture the nonlinear behavior of the damper. The framework is first verified by means of available experimental results of an actual RTHS on the same structural system. A set of 12 earthquake ground motions, each one scaled to have 12 different intensities are then utilized to perform nonlinear dynamic analyses. An energy‐based adaptive passive‐on control strategy is proposed, and its performance is compared with passive‐on, passive‐off, and uncontrolled response of the structure in terms of interstory drifts shown by fragility curves, residual drifts, MR damper control force, and the ability to maintain a uniform interstory drift along the height of the structure.     

Optimal seismic design of steel structures by an efficient soft computing based algorithm

The main aim of this study is to propose advanced soft computing techniques for the optimal seismic design of real steel structures subjected to natural ground motion records. For the solution of the optimization problem an efficient combination of the particle swarm optimization (PSO) and adaptive virtual sub-population (AVSP) algorithms is proposed. Also an efficient combination of the adaptive neuro-fuzzy inference system (ANFIS), wavelet transforms (WT) and radial basis function (RBF) neural networks, termed as fuzzy wavelet radial basis function (FWRBF), is proposed to accurately predict the structural responses. The numerical results demonstrate the computational advantages of the proposed methodology.     

Design optimization of tall steel buildings by a modified particle swarm algorithm

Optimal design of tall buildings, as large‐scale structures, is a rather difficult task. To efficiently achieve this task, the computational performance of the employed standard meta‐heuristic algorithms needs to be improved. One of the most popular meta‐heuristics is particle swarm optimization (PSO) algorithm. The main aim of the present study is to propose a modified PSO (MPSO) algorithm for optimization of tall steel buildings. In order to achieve this purpose, PSO is sequentially utilized in a multi‐stage scheme where in each stage an initial swarm is generated on the basis of the information derived from the results of previous stages. Two large‐scale examples are presented to investigate the efficiency of the proposed MPSO. The numerical results demonstrate the computational advantages of the MPSO algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

Hybrid Control of Structures Using Fuzzy Logic

Abstract: This investigation examined the application of control algorithms based on fuzzy logic to a class of hybrid structural control systems. The investigation included both analytical and experimental verification of the fuzzy control algorithm. The objective of the hybrid system under investigation is to obtain an ideal sliding system with perfect base isolation. As the hybrid system approaches the state of ideal isolation, the effects of imperfections, signal noise, uncertainties, modeling errors, and compensation errors start to play a dominant role in the control performance. Fuzzy logic (or fuzzy set theory) provides a simple framework to capture the effects of nonlinearities and uncertainties in a real problem without an explicit model of the plant or controller.
The applicability of this approach was first investigated analytically and then verified using a benchmark experimental model consisting of a 1:4 scale sliding-base isolated system controlled at its base by a servohydraulic actuator with a digital computer to provide the control signal. The fuzzy controller used feedback from either the acceleration of the moving foundation or the force at the interface to produce control forces in a series of shaking-table tests. The results from this study show the feasibility of the implementation of fuzzy logic to highly nonlinear problems.     

Water Distribution System Computer‐Aided Design by Agent Swarm Optimization

Optimal design of water distribution systems (WDSs), including the sizing of components, quality control, reliability, renewal, and rehabilitation strategies, etc., is a complex problem in water engineering that requires robust methods of optimization. Classical methods of optimization are not well suited for analyzing highly dimensional, multimodal, nonlinear problems, especially given inaccurate, noisy, discrete, and complex data. Agent Swarm Optimization (ASO) is a novel paradigm that exploits swarm intelligence and borrows some ideas from multiagent‐based systems. It is aimed at supporting decision‐making processes by solving multiobjective optimization problems. ASO offers robustness through a framework where various population‐based algorithms coexist. The ASO framework is described and used to solve the optimal design of WDS. The approach allows engineers to work in parallel with the computational algorithms to force the recruitment of new searching elements, thus contributing to the solution process with expert‐based proposals.     

A comparison of global optimization algorithms with standard benchmark functions and real-world applications using EnergyPlus

There is an increasing interest in the use of computer algorithms to identify combinations of parameters that optimize the energy performance of buildings. For such problems, the objective function can be multi-modal and needs to be approximated numerically using building energy simulation programs. As these programs contain iterative solution algorithms, they introduce discontinuities in the numerical approximation to the objective function. Metaheuristics often work well for such problems, but their convergence to a global optimum cannot be established formally. Moreover, different algorithms tend to be suited to particular classes of optimization problems.

To shed light on this issue, we compared the performance of two metaheuristics, the hybrid CMA-ES/HDE and the hybrid PSO/HJ, in minimising standard benchmark functions and real-world building energy optimization problems of varying complexity. From this, we find that the CMA-ES/HDE performs well on more complex objective functions, but that the PSO/HJ more consistently identifies the global minimum for simpler objective functions. Both identified similar values in the objective functions arising from energy simulations, but with different combinations of model parameters. This may suggest that the objective function is multi-modal. The algorithms also correctly identified some non-intuitive parameter combinations that were caused by a simplified control sequence of the building energy system that does not represent actual practice, further reinforcing their utility.     

Wavelet PSO‐Based LQR Algorithm for Optimal Structural Control Using Active Tuned Mass Dampers

This study presents a new method to find the optimal control forces for active tuned mass damper. The method uses three algorithms: discrete wavelet transform (DWT), particle swarm optimization (PSO), and linear quadratic regulator (LQR). DWT is used to obtain the local energy distribution of the motivation over the frequency bands. PSO is used to determine the gain matrices through the online update of the weighting matrices used in the LQR controller while eliminating the trial and error. The method is tested on a 10‐story structure subject to several historical pulse‐like near‐fault ground motions. The results indicate that the proposed method is more effective at reducing the displacement response of the structure in real time than conventional LQR controllers.     

Particle swarm optimization of tuned mass dampers

Tuned mass dampers (TMD) have been widely used to attenuate undesirable vibrations in engineering. Most optimization problems of TMD are solved by either numerical iteration technique or conventional mathematical methods that require substantial gradient information. The selection of the starting values is very important to ensure convergence. In this paper, we use a novel evolutionary algorithm of particle swarm optimization (PSO) for optimization of the required parameters of a TMD. Optimum parameters of the TMD system attached to a viscously damped single degree-of-freedom main system are obtained by minimizing some response quantities, for examples, the mean square displacement responses and displacement amplitude of the main system under various combinations of different kinds of excitations. The excitations considered include external force and base acceleration modeled as Gaussian white-noise random processes. Harmonic base acceleration with frequency invariant amplitude is also considered. The PSO can be used to find the optimum mass ratio, damper damping and tuning frequency of the TMD system and can be easily programmed for practical engineering applications. Explicit expressions of the optimum TMD parameters are given for engineering designers.     

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.     

基于微粒群算法的工程项目质量、费用和工期综合优化

进度、费用和质量称为工程项目的三大控制目标,三者之间相互依存、相互影响。工程项目控制的理想状态是同时实现合理的工期、较低的费用和较高的质量。微粒群算法(PSO)是新近出现的一种仿生算法,具有简单容易实现,而且随机搜索的优点,使得搜索不易陷于局部最优。将该算法引入工程项目优化领域,研究工程项目的质量、费用和工期的综合优化问题。系统介绍微粒群算法原理、流程以及算法的改进发展,研究工程项目质量、费用和工期的优化,并建立质量、费用和工期的多目标综合优化模型,介绍应用微粒群算法编码解决工程项目多目标优化的方法步骤。最后,通过一个应用实例,计算表明微粒群算法可以准确快速地解决工程项目多目标优化问题。     

Advanced energy‐based analyses of trusses employing hybrid metaheuristics

Total potential optimization using metaheuristic algorithm (TPO/MA) is an alternative method in structural analyses, and it is a black‐box application for nonlinear analyses. In the study, an advanced TPO/MA using hybridization of several metaheuristic algorithms is investigated to solve large‐scale structural analyses problems. The new generation algorithms considered in the study are flower pollination algorithm (FPA), teaching learning‐based optimization, and Jaya algorithm (JA). Also, the proposed methods are compared with methodologies using classic and previously used algorithms such as differential evaluation, particle swarm optimization, and harmony search. Numerical investigations were carried out for structures with four to 150 degrees of freedoms (design variables). It has been seen that in several runs, JA gets trapped into local solutions. For that reason, four different hybrid algorithms using fundamentals of JA and phases of other algorithms, namely, JA using Lévy flights, JA using Lévy flights and linear distribution, JA with consequent student phase, and JA with probabilistic student phase (JA1SP), are developed. It is observed that among the variants tried, JA1SP is seen to be more effective on approaching to the global optimum without getting trapped in a local solution.     

Adaptive fuzzy controller for active tuned mass damper of a benchmark tall building subjected to seismic and wind loads

Active tuned mass dampers (ATMDs) are one of the most effective solutions for mitigation of destructive effects of earthquakes and strong winds in tall buildings. In order to achieve optimal performance, these systems are designed and tuned to mitigate effect of either wind or earthquake excitation. However, due to different frequency contents and intensities of wind and earthquake excitations, which will cause contrasting structural modes stimulation, the ATMD designed for one of these disturbances may not work optimally for the other one. This paper addresses a methodological simulation approach for adaptive control design of ATMDs in tall buildings located in regions with high level of seismic activity and recurrent strong winds. For this purpose, a multi‐objective adaptive genetic‐fuzzy controller is proposed for the control of an ATMD of a benchmark 76‐story building subjected to wind load and earthquake disturbances. Simulation results reveal that the optimal ATMD designed for earthquake disturbance does not work adequately for wind load disturbance and vice versa. Furthermore, the proposed adaptive controller has superior performance in suppressing base shear and inter‐story drifts induced by wind load and earthquake excitations. Copyright © 2013 John Wiley & Sons, Ltd.     

Drift design of steel‐frame shear‐wall systems for tall buildings

Drift design methods based on resizing algorithms are presented to control lateral displacements of steel‐frame shear‐wall systems for tall buildings. Three algorithms for resizing of structural members of the steel‐frame shear‐wall systems are derived by formulating the drift design process into an optimization problem that minimizes lateral displacement of the system without changing the weight of a structure. During the drift design process, cost‐effective displacement participation factors obtained by the energy method are used to determine the amount of material to be modified instead of calculating sensitivity coefficients. The overall structural design model with the drift design method for the steel‐frame shear‐wall systems is proposed and applied to the structural design of three examples. As demonstrated in the examples, the lateral displacement and interstorey drift of a frame shear‐wall system can be effectively designed by the drift design method without the time‐consuming trial‐and‐error process. Copyright © 2002 John Wiley & Sons, Ltd.     

Data-driven approach to solve vertical drain under time-dependent loading

Currently, the vertical drain consolidation problem is solved by numerous analytical solutions, such as time-dependent solutions and linear or parabolic radial drainage in the smear zone, and no artificial intelligence (AI) approach has been applied. Thus, in this study, a new hybrid model based on deep neural networks (DNNs), particle swarm optimization (PSO), and genetic algorithms (GAs) is proposed to solve this problem. The DNN can effectively simulate any sophisticated equation, and the PSO and GA can optimize the selected DNN and improve the performance of the prediction model. In the present study, analytical solutions to vertical drains in the literature are incorporated into the DNN–PSO and DNN–GA prediction models with three different radial drainage patterns in the smear zone under time-dependent loading. The verification performed with analytical solutions and measurements from three full-scale embankment tests revealed promising applications of the proposed approach.     

Optimum design of post‐tensioned axially symmetric cylindrical walls using novel hybrid metaheuristic methods

An efficient methodology for various structural design problems is needed to optimize the total cost for structures. Although some methods seem to be efficient for applications, due to using special algorithm parameters, computational cost, and some other reasons, there is still much to be done in order to develop an effective method for general design applications. This paper describes the influence of the selected procedure on the design of cost‐optimized, post‐tensioned axially symmetric cylindrical reinforced concrete walls. In this study, the optimum design of axially symmetric cylindrical walls using several metaheuristic algorithms is investigated. The new generation algorithms used in the study are flower pollination algorithm, teaching–learning‐based optimization, and Jaya algorithm (JA). These algorithms are also compared with one of the previously developed algorithm called harmony search. The numerical examples were done for walls with 4‐ to 10‐m height and for 1, 5, 10, 15, 20, and 25 post‐tensioned load cases, respectively. Several independent runs are conducted, and in some of these runs, JA may trap to a local solution. To overcome this situation, hybrid algorithms such as JA using Lévy flights, JA using Lévy flights with probabilistic student phase (JALS), JA using Lévy Flights with consequent student phase (JALS2), and JA with probabilistic student phase are developed. It is seen that in many respects, the JALS2 and JALS are the most effective within the proposed hybrid approaches.     

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.     

Integrated multi‐type sensor placement and response reconstruction method for high‐rise buildings under unknown seismic loading

Structural health monitoring system has been implemented on high‐rise buildings to provide real‐time measurement of structural responses for evaluating their serviceability, safety, and sustainability. However, because of the complex structural configuration of a high‐rise building and the limited number of sensors installed in the building, the complete evaluation of structural performance of the building in terms of the information directly recorded by a structural health monitoring system is almost impossible. This is particularly true when seismic‐induced ground motion is unknown. This paper thus proposes an integrated method that enables the optimal placement of multi‐type sensors on a high‐rise building on one hand and the reconstruction of structural responses and excitations using the information from the optimally located sensors on the other hand. The structural responses measured from multi‐type sensors are fused to estimate the full state of the building in the modal coordinates using Kalman filters, from which the structural responses at unmeasured locations and the seismic‐induced ground motion can be reconstructed. The optimal multi‐type sensor placement is simultaneously achieved by minimizing the overall estimation errors of structural responses at the locations of interest to a desired target level. A numerical study using a simplified finite element model of a high‐rise building is performed to illustrate the effectiveness and accuracy of the proposed method. The numerical results show that by using 3 types of sensors (inclinometers, Global Positioning System, and accelerometers), the proposed method offers an effective way to design a multi‐type sensor system, and the multi‐type sensors at their optimal locations can produce sufficient information on the response and excitation reconstruction.     

A temporal hybrid dynamic integration algorithm strategy for inelastic time history analysis of high‐rise reinforced concrete structures under strong earthquakes

A complete earthquake time history analysis (THA) requires a stable, accurate, and efficient dynamic integration algorithm. It is not rare to encounter numerical divergence when some implicit algorithms are used to deal with severe materially or geometrically nonlinearities. For explicit algorithms, computational efficiency is always a major concern. A temporal hybrid dynamic algorithm (THDA) strategy, which is specialized in the inelastic THAs of high‐rise reinforced concrete (RC) structures experiencing severe plasticity development, is developed herein. A preliminary evaluation is carried out on three low‐rise structural models, that is, two frame structures and one wall‐frame structure, for each group of collected implicit algorithms and explicit algorithms. From the evaluation, four alternatives are generated for the subsequent detailed assessment. A general framework for the THDA is proposed and implemented on a finite element analytical platform. The four alternatives are assessed based on their performance on a high‐rise frame core‐tube RC structure. The assessment indicates that the proposed THDA strategy can give rise to a more compatible dynamic integration algorithm for the complete THAs of high‐rise building structures when they are experiencing severe damage. The concerns about the computational stability, accuracy, and efficiency of the dynamic algorithms can be well balanced by the THDA.     

Efficiency of active systems in controlling base‐isolated buildings subjected to near‐fault earthquakes

It has been pointed out that base‐isolated structures may be vulnerable during near‐fault earthquakes and special considerations are required in the design of isolated structures in near‐fault areas. This paper investigates the efficiency of active control systems in reducing the responses of base‐isolated structures with various isolation parameters. The design of hybrid control systems using base isolation and active systems are optimized in order to accomplish different design purposes. Also for some cases, equivalent passive control systems are introduced which result in comparable responses with respect to hybrid control systems. Copyright © 2009 John Wiley & Sons, Ltd.