Performance-based Design Optimization Research Articles

Performance-Based Design Optimization of Structures: State-of-the-Art Review

Performance-Based Design Optimization of Structures: State-of-the-Art Review

Optimization-based design exploration of building massing typologies—EvoMass and a typology-oriented computational design optimization method for early-stage performance-based building massing design

In the past decade, there has been an increasing recognition of the role of computational design optimization in early-stage performance-based architectural design exploration. However, it remains challenging for designers to apply such optimization-based design explorations in practice. To address this issue, this paper introduces a design tool, called EvoMass, and an associated design method that facilitates design exploration for building massing typologies in performance-based design tasks. EvoMass is capable of offering architects design options reflecting performance-related building massing typologies for the design task, without necessitating advanced computational design skills. More importantly, it can provide architects with insights into the underlying performance implications, thereby enhancing early-stage performance-based design exploration. EvoMass and its associated design method overcome the limitation in the conventional typology-first-optimization-second design procedure adopted by most existing tools, and it promotes a typology-oriented design exploration method of using computational optimization in performance-based architectural design. To demonstrate the efficacy of EvoMass, case studies derived from architectural design studio tasks, incorporating daylighting, solar exposure, and subjective design intents, and the result of a user survey are presented, which highlights how EvoMass and the performance-based design optimization and exploration can enable architects to achieve a more performance-aware design.

Sequential simulated annealing for life-cycle optimization of nonlinear stochastic systems via arbitrary polynomial chaos expansion

Quantifying the uncertainties of engineering systems modeled as nonlinear oscillators subject to random excitation is a theoretically complex and computationally demanding task. Consequently, finding an optimal design of such systems considering their life-cycle performance is prohibitive with Monte Carlo simulation methods. In this paper, an efficient performance-based design optimization approach is developed for finding the optimal parameters of engineering systems modeled as nonlinear/hysteretic oscillators subject to stationary and non-stationary excitation. This novel approach utilizes an arbitrary polynomial chaos expansion to estimate the expected cost of failure without performing a computationally expensive integration over the hazard levels. Moreover, we introduce a novel sequential heuristic optimization scheme based on simulated annealing to minimize the total expected cost over the structure life-cycle. Three examples are included in the paper to assess the developed optimization scheme. First, we use the developed framework to optimize a linear single-degree-of-freedom oscillator subject to broadband excitation. Second, a multi-degree-of-freedom oscillator with cubic nonlinearity in damping and stiffness, subject to stationary broadband excitation, is optimized to show the influence of the problem dimensionality in the optimization process. In the last example, a multi-story reinforced concrete shear building modeled as a multi-degree-of-freedom Bouc-Wen oscillator with stiffness and strength degradation and subject to multi-hazards modeled as stationary (wind excitation) and non-stationary (earthquake) stochastic processes, is optimized.

An approach for optimum performance-based seismic design of 3D steel moment frames

An optimal performance-based design (PBD) of a three-dimensional (3D) structure requires repeated evaluation; thus, proposed approaches should attempt to significantly reduce the number of evaluations required during optimization. The current study proposes a multi-step approach for optimal PBD of a 3D steel moment frame in which the structure is examined at each step for one performance level in a specific direction. To advance to the next step, the acceptance criteria for linear static analysis of the steel moment frame from ASCE 41-17 should have been satisfied in the previous step. An objective function has been formulated using the proposed stepped penalty function to achieve a feasible space, the value of which can be determined based on the number of unexamined steps. Finally, the optimal PBDs for 3D three-story and nine-story steel moment frames were evaluated using EVPS and WSA metaheuristic algorithms to evaluate the proposed process. The final optimal designs were assessed using the acceptance criteria of nonlinear static analysis. The number of performance level evaluations in each direction during optimization showed approximately 60 % and 70 % reductions during analysis by the proposed method for the WSA and EVPS algorithms, respectively.

Performance-based design optimization of steel moment frames using capacity controlled search algorithm: a comparison with force-based design approach

The capacity controlled search (CCS) method, which is a recently developed design-driven search algorithm, is implemented for performance-based design optimization (PBDO) of steel moment frames. It is shown that the CCS method is very suitable for PBDO problems since it can locate the optimum solution using a reasonable computational effort unlike metaheuristic search approaches, which often require thousands of structural analyses before converging to a near-optimum solution. Considering the fact that performance-based design (PBD) is a recently emerging design methodology, its comparison with the traditional force-based design (FBD) approach is also carried out extensively in this study. Accordingly, the optimum designs of the investigated steel frames produced according to both design methodologies using the CCS method are compared in terms of structural weight and seismic performance. Unlike most of the previous studies, not only inter-story drifts but also hinge rotation limits are considered as seismic performance criterion during PBDO process of steel moment frames. The numerical applications are presented using three ordinary moment resisting steel frames. It is shown that although the FBD methodology usually leads to heavier designs with respect to the PBD methodology, the optimum designs produced according to the former might fail to satisfy seismic performance requirements.

Machine-Learning-Enabled Foil Design Assistant

In this work, supervised Machine Learning (ML) techniques were employed to solve the forward and inverse problems of airfoil and hydrofoil design. The forward problem pertains to the prediction of a foil’s aerodynamic or hydrodynamic performance given its geometric description, whereas the inverse problem calls for the identification of the geometric profile exhibiting a given set of performance indices. This study begins with the consideration of multivariate linear regression as the base approach in addressing the requirements of the two problems, and it then proceeds with the training of a series of Artificial Neural Networks (ANNs) in predicting performance (lift and drag coefficients over a range of angles of attack) and geometric design (foil profiles), which were subsequently compared to the base approach. Two novel components were employed in this study: a high-level parametric model for foil design and geometric moments, which, as we will demonstrate in this work, had a significant beneficial impact on the training and effectiveness of the resulting ANNs. Foil parametric models have been widely used in the pertinent literature for reconstructing, modifying, and representing a wide range of airfoil and hydrofoil profile geometries. The parametric model employed in this work uses a relatively small number of parameters, 17, to describe uniquely and accurately a large dataset of profile shapes. The corresponding design vectors, coupled with the foils’ geometric moments, constitute the training input from the forward ML models. Similarly, performance curves (lift and drag over a range of angles of attack) and their corresponding moments make up the input for the models used in the inverse problem. The effect of various training datasets and training methods in the predictive power of the resulting ANNs was examined in detail. The use of the best-performing ML models is then demonstrated in two relevant design scenarios. The first scenario involved a software application, the Design Foil Assistant, which allows real-time evaluation of foil designs and the identification of designs exhibiting a set of given aerodynamic or hydrodynamic parameters. The second case benchmarked the use of ML-enabled, performance-based design optimization against traditional foil design optimization carried out with classical computational analysis tools. It is demonstrated that a user-friendly real-time design assistant can be easily implemented and deployed with the identified models, whereas significant time savings with adequate accuracy can be achieved when ML tools are employed in design optimization.

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.

A decoupled double-loop method with the adaptive allowable limits for probabilistic performance-based design optimization

In this study, inspired by the idea of the sequential optimization and reliability assessment (SORA) method, a new decoupled double-loop method for probabilistic performance-based design optimization (PPBDO) has been proposed. The highlight of the proposed method is the independence of this method from the type of problem and the limit state function; in such a way that it can be used in non-linear problems with multiple probabilistic constraints with the implicit form of the limit state function. However, it requires less computational effort than conventional double-loop methods. In each cycle of this method, deterministic performance-based design optimization was performed and then the reliability of the optimal design was evaluated. If the results of the reliability assessment are not desirable, the allowable limit of the constraints in the deterministic optimization problem will be changed based on the results of the reliability assessment. This process repeats until the results of the reliability assessment become desirable. The metaheuristic enhanced vibrating particle system algorithm and the Monte Carlo simulation method were used for optimization process and reliability analysis, respectively. To evaluate the efficiency of the proposed method, the optimization problem was defined so as to reduce the structural weight while meeting the acceptance criteria for performance-based design of steel moment frames according to ASCE 41-13. The PPBDO of three- and nine-story steel moment frames were investigated and the results showed that the proposed method was able to reduce the volume of calculations and direct the search path toward a reliable space.

Optimization-aided design: two approaches for reflective exploration of design search space

The role of using performance-based design optimization in early-stage architectural design to prevent poorly designed buildings has been increasingly recognized by researchers and designers. Recently, a large amount of research has been made focusing on technical advancement, which, however, also reflects the limited research on how this technique can be applied to the design process and how it can aid designers when confronting ill-defined design problems. In this regard, this paper centers on the design approaches assisted by using performance-based design optimization. The paper proposes two optimization-aided design approaches that were identified in the previous applications of a design tool, called EvoMass, and showcases these approaches in case-study designs. The case studies demonstrate how the use of performance-based design optimization can facilitate designers’ reflection and exploration. With the demonstration of the design approaches, we discuss the utility of performance-based design optimization in assisting architects in the early design stages.

Seismic collapse safety based optimization of steel Moment-Resisting frames

Structures must have a reasonable seismic safety margin in order to ensure life-safety as well as to prevent structural collapse caused by earthquakes. On the other hand, the cost-efficiency and economy of structures are important and integral parts of structural engineering. The main aim of the current study is to propose an efficient methodology for designing cost-efficient multi-story special steel moment-resisting frames at predefined levels of seismic collapse safety. To achieve this purpose, a seismic collapse safety assessment technique is integrated with performance-based design optimization in the present study. In order to illustrate the advantages of the proposed methodology, three design examples of 3-, 6- and 12-story special steel moment-resisting frames are presented. The numerical results show that by with a 25% increase in the optimal weight of the structures, their seismic collapse capacity increases by more than 50%.

Performance-based optimum seismic design of cable tray system

This study aims to develop a simple yet efficient performance-based design optimization methodology for cable tray systems in building structures. In the paper, the drift ratio between adjacent supports is proposed as a performance index and the acceptable threshold values are specified based on experimental results of shaking table tests for cable tray systems. The seismic performance levels of cable tray systems are presented according to current seismic design codes. A performance-based optimum seismic design procedure for cable tray systems is given and verified by three studied cases. The results show that the proposed performance index (drift ratio between adjacent supports) for cable tray systems is a reasonable criterion for performance-based seismic design and is much more practical and rational than the typical criterion recommended in seismic design codes. The cable tray systems designed according to the proposed procedures can derive the cost-efficient solution and meet the expected seismic performance objectives for cable tray systems as well as control the damage development of the cable tray.

Performance-Based Seismic Design Optimization of Steel MRFs Under System and Component Constraints Using the IWSA Algorithm

Performance-Based Seismic Design Optimization of Steel MRFs Under System and Component Constraints Using the IWSA Algorithm

Exploring the synergy of building massing and façade design through evolutionary optimization

In performance-based architectural design optimization, the design of building massings and façades is commonly separated, which weakens the effectiveness in performance improvement. In response, this study proposes a hybrid massing-façade integrated design generation and optimization workflow to integrate the two elements in an evolutionary design process. Compared with the existing approaches, the proposed workflow emphasizes the diversity of building design generation, with which various combinations of building massing forms and façade patterns can be systematically explored. Two case studies and a corresponding comparison study are presented to demonstrate the efficacy of the proposed workflow. Results show that the optimization can produce designs coupling the potential of building massings and façades in performance improvement. In addition, the optimization can provide information that supports early-stage architectural design exploration. Such information also enables the architect to understand the performance implications associated with the synergy of building massing and façade design.

Design Optimization of Hyperboloid Wooden House Concerning Structural, Cost, and Daylight Performance

The use of parametric and multi-objective optimization (MOO) as a new way of approaching architectural design has been growing in line with current breakthroughs in computational architecture. Wood, on the other hand, is a living and unique building material that provides durability, manufacturing flexibility, and local availability. One of the structure types that provides high structural stability is the hyperboloid. However, the exploration of hyperboloid structures in building design, together with the building daylight objective, is still limitedly reported. This paper presents the application of the parametric approach and multi-objective optimization in optimizing the structure and daylight objectives of a hyperboloid two-story wooden house in Japan, made of 105 mm × 105 mm × 4000 mm Japanese timber. The method involves iterating dynamic parameters such as radius bottom, offset distance, timber members, twisting level, building height, radius-top, and roof slope to optimize the structural objective of minimizing normal force average, displacement, and cost while simultaneously maximizing building volume. Regarding daylight objectives, unit movement and glazing ratio that control the glazing strategies were explored to optimize useful daylight illumination (UDI) in summer and winter. The optimization and exploration yielded 10,098 solutions in structural analysis and 406 solutions in daylight exploration. Based on the data analysis, the proposed methodology has successfully produced the best design solution, discovering the balance between the objective trade-offs. In addition, the most influential parameter that shapes the value of design objectives has been identified. The findings of this research were expected to contribute to and enhance the performance-based design optimization, and support design decision-making process in the early design stage of a wooden house with a hyperboloid structure.

Multi-objective optimization for probabilistic performance-based design of buildings using FEMA P-58 methodology

This research presents an automated performance-based optimal design process by integrating a multi-objective optimization algorithm and a comprehensive probabilistic performance assessment method. This process is used to provide a set of design options that comply with the minimum code requirements and are optimal in terms of both initial cost and mean annual repair cost. The FEMA P-58 methodology is utilized as a modern performance-based methodology to determine the various performance measures such as repair costs, repair time, casualty rates, environmental impacts, and unsafe placarding for the design alternatives. To account for uncertainties in the magnitude and intensity of future earthquakes, the time-based assessment, and to account for inherent uncertainties affecting seismic performance, the Monte Carlo procedure is performed in accordance with FEMA P-58 guideline. The optimization process is carried out using a well-known multi-objective optimization algorithm called NSGA-II for three example office buildings with 3-, 6- and 9-story steel moment frame structures. For each building, a detailed performance model including a set of fragility functions for the structural and non-structural components as well as contents typically present in the building is considered. Three optimal design options are selected from the Pareto front set obtained for each building based on different optimization objectives. They are compared with each other and with the other design alternatives in terms of various performance metrics under different ground motion intensities. The contribution of structural components as well as drift-, acceleration- and velocity-sensitive non-structural components to the repair costs of these optimal designs is investigated. It is shown that drift-sensitive nonstructural components have the largest contribution to the repair costs of optimal structures. The contribution of these components in earthquake events with a 29% probability of exceedance in 50 years (29%/50 yrs) is on average about 71%, which decreases to 55% with increasing seismic intensity to 3%/50 yrs.

Effects of demand parameters in the performance-based multi-objective optimum design of steel moment frame buildings

This paper investigates the effects of various demand parameters involved in the optimal performance-based design of steel moment frame buildings. These parameters include the peak values of story drift ratio, floor velocity, floor acceleration, and residual drift ratio. The performance-based design is performed to minimize two conflicting objectives, including the initial construction cost and the expected annual repair cost of the building under the design constraints. FEMA P-58 is utilized as a comprehensive and popular methodology for seismic risk assessment and building loss estimation in this paper. It evaluates the building performance in a probabilistic manner in terms of several metrics such as repair cost, repair time, carbon emissions, embodied energy, injuries, and fatalities. The Monte Carlo analysis is used to consider various uncertainties affecting seismic performance. A set of three steel moment-resisting frame (MRF) buildings representative of low-to mid-rise frames are selected as a case study in this research. The results of this study indicate that the story drift ratio has a major role in the performance-based optimal design of steel MRFs. Accordingly, despite increasing the two parameters of floor acceleration and floor velocity due to increasing the initial cost of structural moment frames, the annual repair cost of the building decreases when the story drift ratio decreases.

Asymptotic Bayesian Optimization: A Markov sampling-based framework for design optimization

This paper presents a Markov sampling-based framework, called Asymptotic Bayesian Optimization, for solving a class of constrained design optimization problems. The optimization problem is converted into a unified two-phase sample generation problem which is solved by an effective Markov chain Monte Carlo simulation scheme. First, an exploration phase generates designs distributed over the feasible design space. Based on this information, an exploitation phase obtains a set of designs lying in the vicinity of the optimal solution set. The proposed formulation can handle continuous, discrete, or mixed discrete-continuous design variables. Appropriate adaptive proposal distributions for the continuous and discrete design variables are suggested. The set of optimal solutions provides valuable sensitivity information of the different quantities involved in the problem with respect to the design variables. Representative examples including an analytical problem involving nonlinear benchmark functions, a classical engineering design problem, and a performance-based design optimization problem of a structural system under stochastic excitation are presented to show the effectiveness and potentiality of the proposed optimization scheme. Validation calculations show that the scheme is a flexible, efficient and competitive choice for solving a wide range of classical and complex engineering design problems.

Seismic collapse safety analysis of performance-based optimally designed reinforced concrete frames considering life-cycle cost

The present paper aims to assess the seismic collapse capacity of reinforced concrete (RC) frames optimized in the context of performance-based design. The proposed methodology in this work consists of two main phases namely, performance-based design optimization and seismic collapse safety assessment. In the first phase, an efficient metaheuristic algorithm is employed to carry out single-objective optimization of RC frames in the framework of performance-based design with two different objective functions including initial construction cost and total cost. In the second phase, the seismic collapse capacity of optimally designed RC frames is evaluated by conducting seismic fragility analysis. Three illustrative examples of 3-, 6-, and 12-story RC frames are presented to demonstrate the capability of the proposed methodology for designing of cost-efficient structures with considerable seismic collapse safety.

Performance-based design optimization of embankments resting on soft soil improved with T-shaped and conventional DCM columns

Performance-based design optimization of embankments resting on soft soil improved with T-shaped and conventional DCM columns

Wind data extrapolation and stochastic field statistics estimation via compressive sampling and low rank matrix recovery methods

A methodology based on compressive sampling is developed for incomplete wind time-histories reconstruction and extrapolation in a single spatial dimension, as well as for related stochastic field statistics estimation. This relies on l1-norm minimization in conjunction with an adaptive basis re-weighting scheme. Indicatively, the proposed methodology can be employed for monitoring of wind turbine systems, where the objective relates to either reconstructing incomplete time-histories measured at specific points along the height of a turbine tower, or to extrapolating to other locations in the vertical dimension where sensors and measurement records are not available. Further, the methodology can be used potentially for environmental hazard modeling within the context of performance-based design optimization of structural systems. Unfortunately, a straightforward implementation of the aforementioned approach to account for two spatial dimensions is hindered by significant, even prohibitive in some cases, computational cost. In this regard, to address computational challenges associated with higher-dimensional domains, a methodology based on low rank matrices and nuclear norm minimization is developed next for wind field extrapolation in two spatial dimensions. The efficacy of the proposed methodologies is demonstrated by considering various numerical examples. These refer to reconstruction of wind time-histories with missing data compatible with a joint wavenumber-frequency power spectral density, as well as to extrapolation to various locations in the spatial domain.