Performance-based Design Optimization Research Articles

On the seismic collapse capacity of optimally designed steel braced frames

The main purpose of this study is to respond to an important question in the field of structural engineering: is the seismic collapse capacity of optimally designed concentrically steel braced frames acceptable or not? The present work includes two phases: performance-based design optimization and seismic collapse safety assessment. In the first phase, three nature-inspired metaheuristic algorithms, namely improved fireworks algorithm, center of mass optimization, and enhanced colliding-bodies optimization are employed to carry out the optimization task. In the second phase, seismic collapse capacity of the optimally designed concentrically steel braced frames is evaluated by performing incremental dynamic analysis and generating fragility curves. Two design examples of 5- and 10-story concentrically steel braced frames with two different topologies of braces are presented. The numerical results indicate that the center of mass optimization algorithm outperforms the other algorithms. However, all of the optimal designs found by all algorithms are of acceptable seismic collapse safety.

Integrated Structural–Nonstructural Performance-Based Seismic Design and Retrofit Optimization of Buildings

The assessment of anticipated losses due to damage of both structural and nonstructural components is now recognized to be a key component in the performance-based seismic design or retrofit of buildings. Current performance-based seismic loss estimation procedures are building case-specific, and they do not easily allow for the integrated optimization of structural and nonstructural interventions in a particular building. The main objective of this paper is to develop a general optimization procedure within the performance-based earthquake engineering (PBEE) framework developed by the Pacific Earthquake Engineering Research (PEER) Center and implemented through the FEMA P-58 methodology. Available optimization procedures that can be applied to the PEER-PBEE framework are first reviewed, leading to the selection of the genetic algorithm for this purpose. The implementation of the genetic algorithm within the PEER-PBEE framework, considering integrated structural and nonstructural seismic upgrades, is described. The seismic retrofit case study of a 3-story steel moment-resisting frame archetype building is then conducted for the three different target metrics included in the PEER-PBEE framework: (1) an economic target metric, (2) a downtime target metric, and (3) a casualty-reduction target metric. The results of the case study indicate how this optimization process, based on the genetic algorithm, quickly and reliably converges to different allocations of resources for structural and nonstructural components depending on the target metric selected. Finally, a parametric study on the effects of the owner’s expected internal rate of return and building occupancy time on the optimum retrofit solutions illustrates the utility of the optimization process beyond the single case study.

A new Newton metaheuristic algorithm for discrete performance-based design optimization of steel moment frames

In this paper a new and efficient metaheuristic algorithm is proposed for discrete performance-based seismic design optimization of steel moment frames. The proposed metaheuristic uses the Newton gradient-based method as its updating scheme in a population-based framework and therefore it is termed as Newton Metaheuristic Algorithm (NMA). In order to enable the NMA to effectively explore the discrete design space, a term containing the best solution found is added to the basic updating rule of the algorithm. In addition, a simple and efficient method is proposed in order to establish a balance between local and global search abilities of the proposed algorithm. The efficiency of the NMA is illustrated by presenting two benchmark discrete truss optimization problems. Moreover, three steel moment frames are optimized in the framework of performance-based design by the NMA and the results are compared with those of some recent metaheuristics. The performance of the algorithms is analyzed using statistical parametric and non-parametric tests indicating that NMA outperforms the other algorithms in literature.

Performance based design optimization of an intrinsically compliant 6-dof parallel robot

Parallel robots are preferred over serial robots owing to their enhanced accuracy and rigidity which comes from their higher stiffness. However, there are applications both in industry and in healthcare where higher accuracy is required alongside high compliance (reduced stiffness). Accuracy and compliance being conflicting to each other are difficult to achieve simultaneously. To address this issue, an intrinsically compliant 6-dof parallel robot is proposed in this work. Kinematic and analytical modeling is performed for its conceptual design to obtain the Jacobian matrix and thereby map the joint and Cartesian spaces. Robot’s structure design is analyzed, and the wrench analysis is also carried out to estimate the link forces and stiffness. It is shown that by small changes in the proposed robot design; its compliance can be altered making it suitable for a range of applications. It is also shown mathematically that the robot design can be optimized to maintain higher accuracy together with higher compliance. To carry out design optimization, three important performance criteria, namely; global condition number (for higher accuracies), norm of link forces (to reduce actuator power requirement) and robot compliance (for response to an external wrench) are mathematically formulated. Later, a multi-criteria optimization is performed using an evolutionary algorithm to simultaneously optimize these performance criteria. From the final robot design selected, it is evident that a higher robot compliance with optimal condition number and link forces can be achieved.

Considering soil–structure interaction effects on performance-based design optimization of moment-resisting steel frames by an engineered cluster-based genetic algorithm

ABSTRACT An engineered cluster-based genetic algorithm (ECGA) has been used for performance-based design optimization of two dimensional moment-resisting steel frames (MRSF) considering effects of the soil-structure interaction (SSI). Based on the engineering judgments and via using simple specified filters on defined constrained of the problem, an engineered population is generated. To impose this concept for increasing efficiency of the genetic algorithm (GA), first, engineered populations are generated, and then linear analysis of the structure is performed to check some of the constraints, finally in the case of satisfying the first stage constraints, nonlinear static analysis is carried out. The nonlinear spring model has been used to model SSI of the frames in OpenSees software. The constructed model in the OpenSees has been coupled with the GA optimization technique in MATLAB software to minimize weight of the structural elements. Efficiency and accuracy of the proposed method are demonstrated.

School-based optimization for performance-based optimum seismic design of steel frames

The performance-based optimum seismic design of steel frames is one of the most complicated and computationally demanding structural optimization problems. Metaheuristic optimization methods have been successfully used for solving engineering design problems over the last three decades. A very recently developed metaheuristic method called school-based optimization (SBO) will be utilized in the performance-based optimum seismic design of steel frames for the first time in this study. The SBO actually is an improved/enhanced version of teaching–learning-based optimization (TLBO), which mimics the teaching and learning process in a class where learners interact with the teacher and between themselves. Ad hoc strategies are adopted in order to minimize the computational cost of SBO results. The objective of the optimization problem is to minimize the weight of steel frames under interstory drift and strength constraints. Three steel frames previously designed by different metaheuristic methods including particle swarm optimization, improved quantum particle swarm optimization, firefly and modified firefly algorithms, teaching–learning-based optimization, and JAYA algorithm are used as benchmark optimization examples to verify the efficiency and robustness of the present SBO algorithm. Optimization results are compared with those of other state-of-the-art metaheuristic algorithms in terms of minimum structural weight, convergence speed, and several statistical parameters. Remarkably, in all test problems, SBO finds lighter designs with less computational effort than the TLBO and other methods available in metaheuristic optimization literature.

Investigation of Horizontal Micro Kaplan Hydro Turbine Performance Using Multi-Disciplinary Design Optimization

AbstractThis study investigates performance-based design optimization for a Kaplan hydro turbine at a maximum water head of 2.6 m (8.5 ft), a micro-sized horizontal Kaplan turbine with 7.6 cm (3.0 in) diameter that has fixed blades featured to attain the optimum performance for such type and size of hydro turbines. The optimization process includes solving design problems and enhance design development by applying a multi-disciplinary design optimization (MDO) technique. Varying the geometrical parameters of the turbine, i.e., dimensions, number of blades, blade wrap angles, and different rotational speeds (500–3000 rpm), are the relevant proposed disciplines of this study. Two multi-simulation matrices were solved by using the high-performance computing (HPC) cluster of the University of Wisconsin-Milwaukee. The first matrix includes different number of the blades (3, 4, 5, 6, and 7 blades) over six different rotational speeds (500, 1000, 1500, 2000, 2500, and 3000 rpm), while the second matrix includes 121 possible combinations of blade wrap angles starting at 60–60 deg (hub-shroud) angle to 110–110 deg angle with 5 deg increment alternated at both sides, the hub and the shroud.

A mixed GA-PSO-based approach for performance-based design optimization of 2D reinforced concrete special moment-resisting frames

A mixed genetic algorithm and particle swarm optimization in conjunction with nonlinear static and dynamic analyses as a smart and simple approach is introduced for performance-based design optimization of two-dimensional (2D) reinforced concrete special moment-resisting frames. The objective function of the problem is considered to be total cost of required steel and concrete in design of the frame. Dimensions and longitudinal reinforcement of the structural elements are considered to be design variables and serviceability, special moment-resisting and performance conditions of the frame are constraints of the problem. First, lower feasible bond of the design variables are obtained via analyzing the frame under service gravity loads. Then, the joint shear constraint has been considered to modify the obtained minimum design variables from the previous step. Based on these constraints, the initial population of the genetic algorithm (GA) is generated and by using the nonlinear static analysis, values of each population are calculated. Then, the particle swarm optimization (PSO) technique is employed to improve keeping percent of the badly fitted populations. This procedure is repeated until the optimum result that satisfies all constraints is obtained. Then, the nonlinear static analysis is replaced with the nonlinear dynamic analysis and optimization problem is solved again between obtained lower and upper bounds, which is considered to be optimum result of optimization solution with nonlinear static analysis. It has been found that by mixing the analyses and considering the hybrid GA-PSO method, the optimum result can be achieved with less computational efforts and lower usage of materials.

An efficient discrete optimization algorithm for performance-based design optimization of steel frames

Performance-based design optimization of steel frames, with element sections selected from standard sections, is a computationally intensive task. In this article, an efficient discrete optimization algorithm is proposed for performance-based design optimization of steel frames. The computational efficiency is improved by searching in a sensible manner, guided by the deformation information of structural elements. To include all standard sections in the design space, the cross-sectional area ( Area) and moment of inertia ( Ix) are selected as the design variables. Based on different relationships between Area and Ix, a twofold strategy is put forward, which includes a quick exploration and an elaborate exploitation. For comparison, a similar algorithm is also proposed, using Area as the only design variable. A fixed relationship between Area and other sectional properties is used. Two numerical examples are presented to minimize the structural weight while satisfying performance constraints. The results indicate that the proposed discrete algorithm can achieve lighter structural designs than the area-only algorithm. Furthermore, the convergence history proves that a high computational efficiency can be realized by using the proposed algorithm.

Performance-based seismic design of steel frames using constraint control method

In this article, the optimum performance-based seismic design of steel frames is performed using the novel constraint control method. This method is based on a simple concept generally used by the engineers in structural design. In this method, the most conservative member sections are initially selected and by gradually reducing the size of the sections through controlling the problem constraints, the solution tends to an optimum design. The capacity curve of the structure is evaluated through static nonlinear analysis and used for the seismic assessment, and the structural weight is optimized by controlling relative displacement constraints at performance levels of operational, immediate occupancy, life safety and collapse prevention. The performance and efficiency of the proposed algorithm in solving for optimum performance-based seismic design are assessed through solving three benchmark problems. The results show that using constraint control method drastically reduces the number of structural analyses required to reach a solution, compared to the more commonly used metaheuristic optimization methods, while producing comparable optimum solutions. For this reason, the constraint control method is found to be particularly suitable as an optimizer for solving solution-extensive problems, such as performance-based optimum design of structures.

Performance-based design optimization of uncertain wind excited systems under system-level loss constraints

The aim of this paper is to define an efficient optimization methodology for the identification of minimum cost wind excited structural systems that satisfy system-level targets on the annual exceedance rate of expected losses. The main challenge to this vision is the need to integrate optimization models for solving design problems involving hundreds of free parameters with performance assessment models that require stochastic simulation over high-dimensional uncertain spaces. To overcome this challenge, a framework is proposed in this work that is based on decoupling the performance assessment model from the optimization problem. This is accomplished through the definition of a high-quality approximate optimization sub-problem that is scalable to high-dimensional design and uncertain spaces. By solving a limited series of these sub-problems, each formulated in the solution of the previous, a sequential optimization strategy is defined for identifying solutions to the original stochastic optimization problem. The efficiency of the method lies in the limited computational effort required to solve each sub-problem. To demonstrate the applicability and the scalability of the proposed framework, two examples are presented that involve the optimal design of the structural system of buildings subject to stochastic wind excitation and system-level constraints on the annual exceedance rate of expected losses.

Performance-based bi-objective design optimization of wind-excited building systems

This paper proposes a framework for the bi-objective optimization of uncertain and dynamic wind-excited systems whose susceptibility to system-level damage is modeled through probabilistic fragility-based loss measures. In particular, the proposed framework is based on first reformulating the bi-objective stochastic optimization problem into a suite of single-objective optimization problems through the ε-constraint approach. Secondly, a new optimization sub-problem is introduced for efficiently solving the single-objective problems, whose formulation is based on combining the auxiliary variable vector approach with a new kriging-enhanced approximation scheme. Because the sub-problem can be fully calibrated and subsequently solved from the results of a single performance assessment carried out in a fixed point of the design space, efficiency and scalability to high-dimensional problems is achieved. Through solving a sequence of sub-problems, solutions to the ε-constraint problems are obtained leading to the identification of the Pareto-optimal solutions of the original bi-objective optimization problem. To illustrate the applicability, efficiency and scalability of the proposed framework, an example of application to a large-scale structure is presented, where structural material volume and a system-level loss measure defined in terms of expectation and standard deviation of the total repair cost are simultaneously minimized.

Performance-based Optimal Design of Cantilever Retaining Walls

Modern buildings should provide some degree of safety against severe earthquakes. However, it is not economically feasible to construct buildings that withstand extreme loads without avoiding damage. In performance-based design, structural engineers and owners work together to achieve the best possible balance between construction cost and seismic performance. In this study, by employing a metaheuristic optimization, we have tried to extend the concept of performance-based design to retaining wall structures. According to the AASHTO LRFD Bridge Design Specifications, permanent displacement of retaining structures are tolerable, as long as the movement does not lead to unacceptable damage to the structure or facilities located in or near the moving earth. The decision on performance expectations needs to be made by owners with structural engineers providing a realistic assessment of the cost of designing to avoid the movement. To make this assessment possible, we developed a multi-objective optimization framework for simultaneous minimization of the construction cost and the permanent displacement of cantilever retaining walls. The effectiveness of the proposed framework was evaluated in the design of a typical cantilever retaining wall of 8 meters in height, once with both a toe and heel slab and once with either of them. The results indicated that obtaining the Pareto front of optimal solutions for these objectives, provides useful information that helps owners to select a solution that is the most economical in a trade-off between the construction cost and performance expectation.

An improved multi-objective optimization approach for performance-based design of structures using nonlinear time-history analyses

Performance-based design (PBD) of buildings can be properly addressed in a multi-objective optimization framework. However, computational costs of such an approach will be very expensive especially if nonlinear time-history analysis (NTHA) is used as the evaluation tool. In this paper, significant reductions in computational costs of solving structural multi-objective optimization problems is achieved by proposing a new metaheuristic surrogate model called Surrogate FC-MOPSO. In this method, which is an extension of FC-MOPSO algorithm, NTHA and pushover analysis (PA) are simultaneously employed for evaluating system responses. PAs are adopted as an approximation tool in the surrogate model while the responses corresponding to feasible solutions are always evaluated from NTHAs. The final Pareto optimal solutions, which yield tradeoffs between initial and life-cycle costs (LCCs), are already evaluated based on NTHAs. It is shown that application of the proposed method results in substantial reductions of runtime of the considered problems. It is also demonstrated that adopting PAs as the only evaluation tool in optimal performance-based design of structures can result in unreliable solutions.

Performance-based design optimization for minimal surface based form

ABSTRACTCurrently, many studies are being done using optimization tools. However, optimization studies done with complex geometry are limited. Even so, the move toward complex geometric forms is a feature in the world of contemporary architecture. Hence, in this study, the minimal surface form, away from the Euclidean geometry, is considered as the roof cover of the building and optimization of the form is considered to be done according to the daylighting, radiation and covered area parameters. In this context, using a genetic algorithm based multi-objective optimization tool, a model is developed whose objectives are reducing radiation, increasing daylight in the space and increasing the floor surface area of the form. The results, which are obtained at the end of the optimization simulation, are evaluated. The complex forms, which are the result of optimization, are also modelled in the form of related Euclidean geometries and analyzed. The energy efficiency of the two forms is compared, and the complex forms are found to be more energy efficient than those with Euclidean geometry. When a complex form admits more daylight, a similar form made with a Euclidean geometry admits less daylight. Likewise, while the complex form is exposed to a lower radiation, a form of Euclidean geometry of similar form experiences a greater radiation.

Damage‐controlled performance‐based design optimization of steel moment frames

SummaryIn the present paper, performance‐based design of steel moment‐resisting frames (SMRFs) is implemented to minimize total cost of the structures. The total cost is summation of the initial construction cost and the seismic damage cost in operational lifetime of the structures subjected to seismic loading. In order to evaluate the seismic damage cost, Park–Ang damage index (DI), as one of the most realistic measures of structural seismic damage, is utilized. To calculate the DI, nonlinear time‐history response of the structure needs to be evaluated during the optimization process. As the computational burden of the process is very high, neural network techniques are utilized to predict the required nonlinear time‐history structural responses. As the design constraints, besides the drift checks at immediate occupancy and collapse prevention performance levels, the global DI is also checked at collapse prevention level to control the amount of seismic damage. In order to achieve the optimization task, a sequential enhanced colliding bodies optimization II is proposed. Numerical studies are conducted to demonstrate the efficiency of the proposed methodology involving 2 illustrative examples of a 6‐story SMRF and a 12‐story SMRF.

Performance-based optimal design of tuned impact damper for seismically excited nonlinear building

This paper proposes a performance-based optimal design method for a tuned impact damper system, which is composed of a solid mass in a container and is located at the top of a 20-story complex nonlinear benchmark building of the third generation. This benchmark building is a steel frame, accounting for nonlinear response via material non-linearity (bi-linear hysteresis) concentrated at the ends of moment-resisting beam-column joints, and is designed for the SAC PhaseIIISteel Project. In order to illustrate the real-world implementable optimal design approach for designing an optimal tuned impact damper system attached to practical complex structures, a reduced-order data-driven physical model is developed by using the response data specifically from finite element model and the optimization-based parameter identification algorithm. The reduced-order model has been iteratively constructed to be consistent favorably with the finite element model on the aspects of both modal frequencies and mode shapes. Based on the reduced-order model, the optimal parameters of the tuned impact damper system are subsequently designed by adopting proposed performance indices and the differential evolution algorithm conveniently. The optimal vibration control effects are evaluated by using the original finite element model structure with the optimal tuned impact damper. Such optimal performance is also compared with that of the original finite element model with a conventionally designed tuned impact damper system. The results show that the optimal designed tuned impact damper system not only can significantly mitigate the peak and root mean square values of dynamic displacements, but also can reduce effectively the number of plastic hinges of the nonlinear benchmark structure compared with that with the conventional design. Furthermore, the performance-based optimal design can lead to a better robust performance of the tuned impact damper system in the cases of the main structure subjected to unknown earthquake excitations.

Multi-objective seismic design optimization of steel frames by a chaotic meta-heuristic algorithm

In this study, multi-objective optimization is applied to implement performance-based design of steel moment-resisting frame (SMRF) structures. In order to efficiently achieve this purpose, a chaotic multi-objective firefly algorithm (CMOFA) is proposed to find the Pareto optimal front for the multi-objective performance-based optimum design (MO-PBOD) problem of SMRFs. The structural weight and the maximum inter-story drift at performance levels are taken as the conflicting objective functions of the MO-PBOD problem which should be optimized simultaneously subject to serviceability and ultimate limit-state constraints. In order to illustrate the efficiency of the proposed CMOFA meta-heuristic, two benchmark truss examples and three MO-PBOD examples of SMRFs are presented. The numerical results demonstrate the better computational performance of the proposed CMOFA meta-heuristic in comparison with some existing multi-objective algorithms.

Analytical investigation on the behavior of smart recentering T-stub components with superelastic shape memory alloy (SMA) bolts and performance-based optimal design

Analytical investigation on the behavior of smart recentering T-stub components with superelastic shape memory alloy (SMA) bolts and performance-based optimal design

Performance indicator of tunnel linings under geotechnical uncertainty

AbstractIn the process of dimensioning a tunnel lining support an optimized structural system is pursued that can accommodate the inherent uncertainties associated with the geotechnical, hydro‐geological, and environmental conditions. Particularly for geotechnics, uncertainty has become a major issue of scientific discussion according to a number of recent publications. At the same time, advanced performance criteria often require probabilistic assessments in order to quantify a structure's safety and reliability or to inform life‐cycle engineering decisions. This contribution demonstrates a novel design approach for the design assessment of concrete tunnel linings. The Index for the Capacity Utilization of Linings in Tunnels (CULT‐I) introduced herein, facilitates the quantification of reliability of a tunnel lining support, while it aids toward a rationalized, performance‐based design optimization with considerations on geotechnical uncertainty. A typical case of a shallow urban tunnel excavated in soft ground using the TBM method is presented, demonstrating the practical application and feasibility of the proposed approach.