Performance-based Optimization Research Articles

Optimization based on performance of lungs in body: Lungs performance-based optimization (LPO)

The development of efficient optimization algorithms is crucial across various scientific disciplines. As the complexity and diversity of optimization problems continue to grow, researchers seek faster and stronger algorithms capable of optimizing a wide range of functions. This paper introduces Lung performance-based optimization (LPO), a novel and efficient algorithm inspired by the regular and intelligent performance of lungs in the human body. LPO draws inspiration from the intricate mechanisms and adaptability of the respiratory system. The lungs exhibit remarkable efficiency in oxygen exchange, demonstrating a high level of optimization in their function. The forced oscillation technique measures air pressure and airflow rate to evaluate the respiratory system as an electrical impedance. The impedance curves have two distinct components, respiratory resistance (ZR) and respiratory reactance (ZX), which can be analyzed clinically and from an engineering perspective to gain insights into the respiratory system's workings. LPO aims to provide an innovative approach to solving complex optimization problems by emulating and harnessing this natural efficiency. To evaluate the effectiveness of LPO, experiments were conducted using the unconstrained optimization functions CEC2005 and CEC2014, as well as engineering design optimization problems. These problems were compared against numerous contemporary algorithms proposed in the literature. The results demonstrate that LPO excels in handling these optimization problems and exhibits the potential to tackle a wide range of modern optimization challenges. The findings highlight the power and effectiveness of LPO as a new optimization algorithm. With its inspiration rooted in the sophisticated performance of the lungs, LPO offers a unique perspective in the optimization landscape. Its ability to handle diverse optimization problems and its potential for application in various domains make LPO a promising algorithm for future research and practical implementation. Note that the source code of the LPO is publicly available at https://www.optim-app.com/projects/lpo.

Shape-Informed Dimensional Reduction in Airfoil/Hydrofoil Modeling

Parametric models have been widely used in pertinent literature for reconstructing, modifying and representing a wide range of airfoil and/or hydrofoil profile geometries. Design spaces corresponding to these models can be exploited for modeling and profile-shape optimization under various performance criteria. Accuracy requirements, along with the need for modeling local features, often lead to high-dimensional design spaces that hinder the process of shape optimization and design through analysis. In this work, we propose a shape-informed dimensional reduction approach that attempts to tackle this deficiency by producing low-dimensional latent design spaces that can be efficiently used in shape representation and optimization. Furthermore, geometric moments are introduced in an attempt to cost-effectively capture analysis-relevant information that is generally expensive to produce. Specifically, geometric integral properties, although intrinsic features of the shape, are quite commonly related to performance indicators employed in performance optimization and therefore provide a cost-effective physics-informed component in the description of the design in the latent space. To this end, we employ the generalized Karhunen-Loève expansion to produce a shape- and physics-informed subspace retaining the highest possible geometric variance and robustness, that is, a lack of invalid designs. At the same time, a series of shape discretizations, encoding the foil’s shape profile, are examined with regard to their effect on the resulting latent space’s quality and efficiency. Our results demonstrate a significant reduction in the dimensionality of the original design space while maintaining a high representational capacity and a large percentage of valid geometries that facilitate fast convergence to optimal solutions in performance-based optimization.

Multi-level performance-based seismic design optimisation of RC frames

Conventional structural optimisation techniques often result in unconventional structural configurations, unrealistic structural elements and ignore actual construction costs. This paper presents an effective performance-based optimisation framework for minimising initial material costs of realistic multi-storey reinforced concrete (RC) frames, while satisfying pre-determined performance targets under multiple seismic hazard levels as well as a set of practical design and construction constraints. A new low computational-cost optimisation method is proposed to directly control specific response parameters at both the element and structural levels (i.e. plastic rotation and inter-storey drift). For the first time, the concept of Uniform Damage Distribution (UDD) is adopted to simplify the complex design optimisation problem of RC buildings with multiple design variables in terms of section sizes and reinforcement ratios. The optimum design solution is achieved by gradually redistributing materials from strong to weak parts of the structure, aiming to fully exploit the material capacity. The efficiency of the proposed optimisation framework is then demonstrated in the optimum designs of 3-, 5-, 10- and 15-storey RC frames under a set of six spectrum-compatible earthquake records. The results indicate that compared to structures designed by current codes, optimum solutions required up to 20 % and 43 % less concrete volume and steel reinforcement weight, respectively. It is also noted that due to more efficient use of materials, optimum structures exhibited considerably lower global damage index (up to 88 %), less maximum inter-storey drift (up to 58 %), and less maximum plastic rotations (up to 78 %). Sensitivity analysis on earthquake record selection shows that using a single earthquake record may not lead to reliable design solutions, in particular for tall buildings, and hence a set of spectrum-compatible records should be used in the optimisation process. This research will lead to more economical and safe design of multi-storey RC structures in seismic regions by developing a practical multi-level optimisation method with low computational costs.

Development of hybrid performance-based optimization algorithm for structures equipped with vibration damper devices

Nowadays, various types of vibration damping systems are being implemented in different buildings to diminish seismic effects on structures. However, engineers are faced with the challenging task of developing an optimum design for structures utilizing a proper type of damping device based on new techniques such as the performance-based design method. Therefore, this research was aimed at developing a multi-objective optimization algorithm by hybridizing the particle swarm optimization (PSO) and gravitational search algorithm (GSA) to obtain an optimum design for structures equipped with vibration damper devices based on the performance-based design method. Then, the developed hybrid algorithm (PSOGSA) would be capable of optimizing the damping system simultaneously with the optimized details of the structural sections, including the steel rebars, by satisfying all the design criteria. For this purpose, a special process for the design of structures equipped with vibration damper devices according to the performance-based design method was developed by considering of a wide range of vibration damping systems. The proposed PSOGSA optimization framework was then implemented to design a 12-storey reinforced concrete structure equipped with different types of dampers to minimize the structural weight while satisfying all the prescribed performance-based design acceptance criteria. The results indicated that the proposed optimization method was able to successfully optimize the details of the structural members as well as the type and properties of the damper, which significantly improved the structural response in terms of the formation of plastic hinges and the structural movements.

A Fast Frequency Sweep approach for performance-based optimization of earthquake-resistant irregular large-scale buildings

Performance-Based Design (PBD) optimization of buildings subjected to seismic excitations has increasingly been applied to regular small-scale structural systems to minimize initial or life-cycle costs. Nonetheless, a comprehensive bibliographic survey reveals that studies dealing with irregular buildings are scarce, although they can present higher seismic vulnerability than regular buildings. Specifically, the PBD optimization of irregular buildings represented by large-scale finite element (FE) models, and considering dozens of discrete design variables, cannot be found to the best of the authors’ knowledge. Hence, this paper presents an original framework for the PBD optimization of irregular buildings subjected to seismic excitations, handling thousands of DOFs and dozens of discrete design variables. To relieve the computational burden, enabling the problem to be solved, a Model Order Reduction (MOR) strategy based on the Well-Conditioned Asymptotic Waveform Evaluation (WCAWE) approach is combined with a hybrid optimization algorithm, which integrates a local optimizer with a restart strategy. The former is employed to speed up the frequency-domain response, while the latter allows for tackling a non-convex and multimodal objective function with many discrete variables. The procedure is adaptatively devised to operate in a robust and fully black-box approach. The application case consists of a stiffness in-plane irregular H-shape building with 16,452 active DOFs and 34 discrete design variables. The proposed scheme largely reduces the computational burden, leading to speed-up factors (SUF) up to 19 times compared to direct frequency-domain solutions.

Performance-based optimization of nonlinear Friction-Folded PTMDs of structures subjected to stochastic excitation

Alternative Tuned Mass Damper (TMD) configurations have been proposed in the literature for performance improvement and maintenance, mainly modifying their restoring force or dissipation mechanisms. In this context, Folded-Pendulum TMDs (FPTMDs) are appealing for tuning low-frequency structures because they are compact and easy to retune while avoiding sliding mechanisms. In turn, Friction Dampers (FDs) are equally attractive due to their minimal maintenance and easy desired capacity adjustment. Nevertheless, despite recent advances in integrating FDs with PTMDs, a comprehensive literature survey reveals that Reliability-Based Design Optimization (RBDO) studies for PTMDs or Folded-PTMDs with FDs cannot be found to the best of the authors’ knowledge. Hence, the present paper aims at performing an original RBDO of single and multiple Friction-Folded-PTMDs in buildings subjected to stochastic excitation. Unlike the existing optimization studies in this field, a complete nonlinear description (dry friction plus large rotations) is employed because the considered applications involve high-intensity excitations, like wind and seismic loading. Finally, scenarios with multiple absorbers are included due to their associated performance and constructional advantages. Optimal design of multiple Folded-PTMDs with FDs has not yet been addressed, as they increase the optimization problem complexity leading to multimodal and convex objective functions. Accordingly, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is used, which allows for finding the optimum solutions with only a few objective function evaluations. The application cases to two distinct buildings subject to wind and seismic loadings show that using Friction-FPTMDs allows for obtaining a control strategy with an appropriate performance while ensuring practical advantages over classical TMDs.

Optimisation of Cable Dome Structure Design for Progressive Collapse Resistance

Since the literature lacks an effective analysis method of collapse mechanisms and optimisation design theory for progressive collapse resistance of cable dome structure, a structural performance-based optimisation approach was proposed to improve the progressive collapse resistance for cable dome structures in this study. First, the dynamic response and collapse model of a cable dome structure were analysed after its members were removed using Ansys LS-DYNA and the full dynamic equivalent load-based instantaneous unloading method. Second, the importance coefficients of the members were calculated to determine the contribution of each member to the progressive collapse resistance of the structure. Finally, a stepwise optimisation solution was proposed by integrating a global optimisation model, which uses the mean of the importance coefficients of all members as the optimisation index, with a local optimisation model, which minimises the maximum member importance coefficient. The results indicated that different members exhibited varying levels of importance in the progressive collapse resistance of the structure, with the inner and outer hoop cables demonstrating the highest levels of importance, followed by the inner upper string of the tension hoop. The other members had low levels of importance. Compared with the cable dome structure based on the Geiger topology, the cable dome structure based on the Levy topology was more resistant to progressive collapse; such resistance decreased as the number of cable-truss frames decreased. Additionally, the local optimisation approach based on the genetic algorithm reduced the maximum member importance coefficient (i.e., that of the outer hoop cable) by 60.26%.

Surrogate-based decision-making of community building portfolios under uncertain consequences and risk attitudes

The performance of community building portfolios under extreme events is increasingly been assessed in terms of socioeconomic and environmental consequences. These multiple consequences are expensive to be evaluated, uncertain in nature, and it requires an efficient optimization and decision-making tool for performance enhancements on a community level. In this paper, an efficient multi-objective performance-based optimization and decision-making framework is proposed to assess and enhance the performance of community building portfolios under uncertain consequences. The proposed approach includes (1) performance-based black-box to evaluate the socioeconomic and environmental consequences given community building portfolios by considering all the possible hazard scenarios, (2) surrogate-based multi-objective optimization to efficiently approximate the Pareto-optimal solutions by exploiting Gaussian process models, spectral sampling, non-dominated crowding and sorting, and hyper improvements, among others, and (3) utility theory-based decision-making of a community building portfolios considering multiple performance-objectives over an entire hazard curve and under different risk attitudes. The proposed methodology is illustrated on community building portfolio under seismic hazards of varying intensities and occurrence probabilities. A performance-based black box is utilized along with a proposed optimization technique to assess community-level consequences. Finally, the utility for Pareto-optimal solutions is assessed and discussed for possible performance enhancements and decision-making.

A performance-based optimization framework applied to a classical STM-designed deep beam

The outcomes of experimental and numerical investigations on the design of a classical deep beam with a large opening are presented in this paper. Two structural members were designed using the strut-and-tie method (STM) and the elastic–plastic stress fields method, respectively. In this study, a performance-based optimization framework, called strut-and-tie performance-based optimization, was developed. The method and its application are presented in this paper. The method applies a performance-based optimization process in an STM-designed structural member. The finite element method was used to measure the performance along the optimization process. A large-scale experimental test was conducted on the first specimen. The modified compression-field theory (MCFT) and the digital image correlation technique were used to investigate the failures of the tested specimen. In addition, a numerical simulation strategy that combines damage theory with MCFT was used. The numerical results showed good agreement with the experimental results of the STM-designed specimen. Finally, the same numerical approach was utilized to predict the behavior of the other two members. Comparisons in terms of the use of materials and structural performance demonstrated that the proposed method for the design of deep beams is promising.

Experimental and numerical study on high-strength steel flange-welded web-bolted connections under fire conditions

Experimental and numerical study on high-strength steel (HSS) flange-welded web-bolted connections at ambient temperature and under fire conditions are conducted in this study to reveal their fire behaviors. Eurocode 3 Part 1–8, AISC360–16, and GB50017–2017 are compared with the experimental results to verify the applicability of the current specifications on HSS connections. Furthermore, the finite element model validated by experimental results can reasonably simulate the behaviors of HSS flange-welded web-bolted connections under fire conditions and at ambient temperature. At ambient temperature, the provision of Eurocode 3 Part 1–8 on the flexural capacity of the connections seems rather conservative, while those of GB50017–2017 and AISC360–16 are unsafe. Improving the weld quality is significant to avoid weld failure of HSS flange-welded web-bolted connections. In addition, appropriately matching the steel grade and thicknesses of the web, as well as the flange of beam–column components should be considered. The elastic design method and the plastic hinge relocation mechanism should be discussed sufficiently in future optimization design. This study can be employed for performing performance-based optimization analysis and fire-resistance design of HSS flange-welded web-bolted connections.

Surrogate-based fragility analysis and probabilistic optimisation of cable-stayed bridges subject to seismic loads

The lack of computationally efficient, probabilistic performance-based design strategies for cable-stayed bridges hinders their optimal design in seismic regions. Thus, this paper proposes the implementation of parameterised fragility functions (PFFs) for the surrogate-based sensitivity analysis and performance-based optimisation of these structures. In particular, PFFs are exploited to define computationally efficient decision variables and four optimisation strategies that aim to optimise the probability of seismic damage and the direct losses related to the seismic repair cost. To illustrate this overall strategy, a 542 m three-span cable-stayed bridge is considered. The ability to predict dynamic behaviour is improved by using the measured dynamic response of the reference cable-stayed bridge to inform the numerical model’s architecture. Then, key design variables of tower and cable cross-sections are selected for optimisation. The sensitivity analysis shows conflicting demands placed upon design variables by different decision variables (e.g. damage probability and the sum of construction and repair costs, CRC) and the crucial importance of accounting for design variables interaction when making choices on design updating. Therefore, numerical optimisation emerges as the most efficient tool to deal with these issues. With respect to the reference structure, the proposed single-objective optimisation strategies reduced the system-level damage probability by 3.5 times, and yielded an 88% reduction of repair cost, and a 40% decrease of CRC. A Pareto-front of optimal design variables was also calculated to simultaneously optimise system damage probability and CRC.

Multi-level performance-based design optimisation of steel frames with nonlinear viscous dampers

This paper presents a practical multi-level performance-based optimisation method of nonlinear viscous dampers (NVDs) for seismic retrofit of existing substandard steel frames. A Maxwell model is adopted to simulate the behaviour of the combined damper-supporting brace system, with a fractional power-law force–velocity relationship for the NVDs, while a distributed-plasticity fibre-based section approach is used to model the beam-column members thus incorporating the nonlinearity of the parent steel frame in the design process. The optimum height-wise distribution of the damping coefficients of NVDs satisfying given performance requirements is identified via a uniform damage distribution (UDD) design philosophy. The efficiency of the proposed multi-level performance-based design optimisation is illustrated through nonlinear time-history analysis of 3-, 7- and 12-storey steel frames under both artificial and natural spectrum-compatible earthquakes. Sensitivity analysis is performed to investigate the effects of initial height-wise damping distribution, convergence factor and uncertainty in design ground-motion prediction on the optimisation strategy. The efficiency of the final optimum design solution is also investigated by using drift-based, velocity-based, and energy-based UDD approaches to identify the most efficient performance index parameter for optimisation purposes. It is found that regardless of the selected performance parameter, the optimum damping distribution identified by the proposed methodology leads to frames exhibiting lower maximum inter-storey drift, local damage (maximum plastic rotation) and global damage index compared to an equal-cost uniform damping distribution. However, using drift-based UDD approach generally results in a better seismic performance. It is shown that the proposed UDD optimisation method can be efficiently used to satisfy multiple performance objectives at different intensity levels of the earthquake excitation, in line with performance-based design recommendations of current seismic codes. The proposed method is easy to implement for practical design purposes and represents a simple yet efficient tool for optimum seismic retrofit of steel frames with NVDs.

Performance-based seismic design of moment resisting steel frames: Adaptive optimisation framework and optimum design load pattern

In this study, a performance-based optimisation framework is proposed for optimal cross-sectional distribution of steel moment resisting frames (MRFs) subject to earthquake excitations. For the first time, the concept of uniform distribution of damage (UDD) is adopted for the complex optimisation of moment resisting steel frames under dynamic earthquake excitations. To enhance the computational efficiency of the optimisation process, a novel adaptive algorithm is proposed, where the power functions change based on the demand to capacity ratio of the structural elements. The framework is then used for optimisation of 3, 5, 7, 10 and 15-storey steel MRFs under a set of representative earthquake records. Maximum plastic rotations and strength-based demand to capacity ratios are considered as the main performance parameters for deformation-controlled and force-controlled members, respectively. The results indicate that the proposed method is very efficient at improving the seismic performance of the designed structures in only a few steps by satisfying all the prescribed performance targets. It is shown that, for the same performance level, the optimum design frames require up to 38% less structural-weight compared to their code-based design counterparts. The average storey shear force distributions of the optimum frames under the design spectrum-compatible earthquakes are then used to obtain more efficient lateral load patterns for seismic design of steel MRFs. It is shown that by adopting the proposed load pattern in the conventional seismic design process, the frames exhibit significantly (up to 70%) less global damage compared to the similar frames designed based on code suggested load pattern.

Performance-based optimization of LQR for active mass damper using symbiotic organisms search

The linear-quadratic regulator (LQR) has been applied to structural vibration control for decades; however, selection of the weighting matrices of an LQR mostly depends on trial and error. In this study, a novel metaheuristic optimization method named as symbiotic organisms search (SOS) algorithm is applied to tuning LQR weighting matrices for active mass damper (AMD) control systems. A 10-story shear building with an active mass damper installed at the top is adopted as a benchmark for numerical simulation in order to realize the optimization performance considering three objective functions for mitigation of structural acceleration. Two common optimization methods including genetic algorithm (GA), and particle swarm optimization (PSO) are also applied to this benchmark for comparison purposes. Numerical simulation results indicate that SOS is superior to GA and PSO on searching the minimized solution of the three objective functions. Meanwhile, minimizing the square root of the sum of the squares of peak modal acceleration achieves the best control performance of structural acceleration among the three objective functions. In addition, force saturation is proposed and applied in the optimization process such that the control force level is close to the force capacity of AMD under specified earthquake intensity. Furthermore, the control performance of the optimized LQR is compared with that of the LQR designed by applying three common weighting selection methods when the 10-story building is subjected to various earthquake excitations. Simulation results demonstrate that the optimized LQR significantly outperforms the three LQRs on structural acceleration responses as expected and reduces story drift slightly better than the three LQRs. Finally, the performance-based optimized LQR is experimentally validated by conducting shake table testing in the laboratory. The experimental results and structural control performance are discussed and summarized thoroughly.

Mainshock–aftershock low-cycle fatigue damage evaluation of performance-based optimally designed steel moment frames

Considering the widespread damages of connections in steel moment frame (SMF) structures due to destructive earthquakes, seismic assessment of these structures for cumulative low-cycle fatigue (LCF) is of utmost importance and must be carefully taken into account in the design process of SMFs. To calculate the LCF damage index for SMFs, the Palmgren-Miner’s rule is applied on the history of relative drift of the stories based on non-linear response history analysis and existing experimental fatigue curves. On the other hand, repeated earthquakes strongly affect the inelastic response of structures and can increase building vulnerability. Therefore, the primary objective of this study is to numerically assess the mainshock-aftershock LCF damage index for performance-based optimally designed SMFs. Two illustrative design examples of 6- and 12-story SMFs are presented and designed for optimal initial and total costs in the context of performance-based design. The LCF damage index is evaluated for these structures by conducting nonlinear response-history analysis for a suite of real strong multiple earthquakes. The results showed that the optimally designed SMFs are highly vulnerable against LCF damage due to mainshock-aftershock seismic sequences. Subsequently, a simple procedure is proposed to increase the safety of optimally designed SMFs against the LCF damage. To this end, performance-based optimization process is performed for 6- and 12-story SMFs by considering higher seismic confidence levels and the results demonstrate the effectiveness of this strategy in controlling the LCF damage of SMFs caused by seismic sequences.

Performance-based optimal distribution of viscous dampers in ‎structure using hysteretic energy compatible endurance time excitations

Performance-based optimization of energy dissipation devices in structures necessitates massive and repetitive dynamic analyses. In the endurance time method known as a rather fast dynamic analysis procedure, structures are subjected to intensifying dynamic excitations and their response at multiple intensity levels is estimated by a minimal number of analyses. So, this method significantly reduces computational endeavors. In this paper, the endurance time method is employed to determine the optimal placement of viscous dampers in a weak structure to achieve the desired performance at various hazard levels, simultaneously. The viscous damper is one of the energy dissipation systems which can dissipate a large amount of seismic input energy to the structure. To this end, hysteretic energy compatible endurance time excitation functions are used and the validity of the results is investigated by comparing them with the results obtained from a suite of ground motions. To optimize the placement of the dampers, the genetic algorithm is used. The damping coefficients of the dampers are considered as design variables in the optimization procedure and determined in such a way that the sum of them has a minimum value. The behavior of the weak structure before and after rehabilitation is also investigated using endurance time and nonlinear time history analysis procedures in different hazard levels.

Chaotic optimization algorithm for performance-based optimization design of composite moment frames

In this paper, performance-based optimization design of steel concrete composite moment resistance frames is presented using a chaotic optimization algorithm based on Chebyshev chaotic map. The strategy is applied to two examples of an 8-story frame and a 20-story frame. The structure is designed to respond to different levels of seismic hazard levels for the minimization of total weight. To achieve this goal, three main steps are conducted. In the first step, the five best designs for each of the frames were obtained by solving the optimization problem. Nonlinear pushover analysis was conducted to arrive at each performance level. In the next step, the fragility curves are plotted for five selected designs for each frame, and finally, damage margin ratios were calculated for each damage level and the best design for each frame was selected based on the damage margin ratio values. Results illustrate a desirable performance of the algorithms in both obtaining lower weight and selecting the best design based on the seismic behavior of the structure.

A performance-based optimization approach for diffusive surface topology design

Different numerical techniques have been used in the last decades for the acoustic characterization and performance optimization of sound diffusive surfaces. However, these methods require very long calculation times and do not provide a rapid feedback. As a result, these methods can hardly be applied by designers at early stages of the design process, when successive design iterations are necessary from an aesthetic point of view. A suitable alternative could be the use of parametric modeling in combination with performance investigations during the design process of sound diffusive surfaces. To this aim, this study presents a design process for diffusive surfaces topology optimization based on the combination of parametric models and geometrical acoustic simulations. It aims to provide architects and designers with rapid visual feedback on acoustic performances at a preliminary stage of the design process. The method has been tested on different case studies, which have been modelled based on geometric guidelines for diffusive surface optimization. The sensitivity of the method showed that it could be a very useful tool for comparisons among surface design alternatives. Finally, the advantages and limitations of the integrated optimization in comparison with conventional optimizations are discussed.

Updating strategy of a domain decomposition preconditioner for parallel solution of dynamic fracture problems

Iterative methods used for analysis of multiphysics problems that result in localized solution features may be highly demanding from a computational standpoint and often require special treatment to be more efficient. Dynamic fracture of metals is one such example in which a nonlinear thermo-mechanical system leads to strain localization, resulting in shear bands and/or cracks, in which iterative solvers may have difficult time converging.In the current paper, we develop a novel updating domain decomposition preconditioner for parallel solution of dynamic fracture problems, in which shearbands are modeled using a temperature-dependent viscoplastic material model and fracture is modeled by the phase-field method. The domain decomposition method is based on the Additive Schwarz Method (ASM).The key idea is to decompose the computational domain into two subdomains, a localized subdomain that includes all localized features of the solution and a healthy subdomain for the remaining part of the domain. In this way, one can apply different solvers in each subdomain, i.e. focus more effort in the localized subdomain. In this work, an LU solver is applied in both subdomains, however, while the localized subdomain is solved exactly at every nonlinear iteration, the healthy subdomain LU operator is reused and only selectively updated. Hence, significant CPU time savings associated with the setup of the preconditioner can be achieved.To this end, we propose a strategy for updating the preconditioner in the healthy subdomain. The strategy is based on an idealized performance-based optimization procedure that takes into account machine on-the-fly execution time. Three dynamic fracture problems corresponding to different failure modes are investigated. Excellent performance of the proposed updating preconditioner is reported in serial and parallel computers.

Discussion of “Performance-Based Wind-Resistant Optimization Design for Tall Building Structures” by Ting Deng, Jiyang Fu, Qingxing Zheng, Jiurong Wu, and Yonglin Pi

Discussion of “Performance-Based Wind-Resistant Optimization Design for Tall Building Structures” by Ting Deng, Jiyang Fu, Qingxing Zheng, Jiurong Wu, and Yonglin Pi