Reliability-Based Design Optimization of Structures Considering Uncertainties of Earthquakes Based on Efficient Gaussian Process Regression Metamodeling

Abstract

The complexity of earthquakes and the nonlinearity of structures tend to increase the calculation cost of reliability-based design optimization (RBDO). To reduce computational burden and to effectively consider the uncertainties of ground motions and structural parameters, an efficient RBDO method for structures under stochastic earthquakes based on adaptive Gaussian process regression (GPR) metamodeling is proposed in this study. In this method, the uncertainties of ground motions are described by the record-to-record variation and the randomness of intensity measure (IM). A GPR model is constructed to obtain the approximations of the engineering demand parameter (EDP), and an active learning (AL) strategy is presented to adaptively update the design of experiments (DoE) of this metamodel. Based on the reliability of design variables calculated by Monte Carlo simulation (MCS), an optimal solution can be obtained by an efficient global optimization (EGO) algorithm. To validate the effectiveness and efficiency of the developed method, it is applied to the optimization problems of a steel frame and a reinforced concrete frame and compared with the existing methods. The results show that this method can provide accurate reliability information for seismic design and can deal with the problems of minimizing costs under the probabilistic constraint and problems of improving the seismic reliability under limited costs.

Mathematical Description of the Aerodynamic Characteristics of Stationary Flows in a Vertical Conical Diffuser When Air Is Supplied through Various Tube Configurations

“…The mathematical description of the function TI = f (w) for the first section (H1 = 10 mm) when air is supplied through round (5), square (6), and triangular (7) tubes has th following form (approximation reliability not less than 0.89): The patterns of speed reduction in the upward flow direction are described with sufficient accuracy by the exponential dependence w = a•e -b•H . At the same time, the shape of the tube cross section does not actually affect the intensity of the drop in the air flow velocity along the set-up's height.…”

“…All this testifies to the importance of studying the aerodynamics of process units with conical diffusers from the point of view of gas-dynamic improvement and finding ways to control flow characteristics. Moreover, it is necessary to obtain reliable experimental data on the features of gas flow dynamics and their mathematical formulation in order to improve engineering methods for calculating conical diffusers and to refine mathematical models [5,6].…”

Seismic Fragility Analysis of Mega-Frame with Vibration Control Substructure Based on Dual Surrogate Model and Active Learning

“…The AL sampling strategy should be able to improve this accuracy. U function [32,37] is a widely used learning function in AL sampling. For the approximation of logarithmic EDP, the U function is described as:…”

“…In AL-RA, if the U function value of a point is greater than 2, the probability of a wrong prediction of the safety state for this point is less than 2.3%. It is usually taken as the stopping condition of the AL-RA methods that the U function values of all candidate points are greater than 2 [37]. With reference to this condition, the proportion of candidate points with an MU value less than 2 is used in the proposed method as the indicator for the decision to stop sampling, which is expressed as:…”

Active Learning-Based Kriging Model with Noise Responses and Its Application to Reliability Analysis of Structures

“…Effective strategies are needed for quantifying and optimizing uncertainties in the design of structures and other engineering systems. Reliability-based design optimization (RBDO) [5,6] and reliablity-based topology optimization (RBTO) [7,8] have emerged as comprehensive approaches to achieving optimal designs with a low failure probability, ensuring that the likelihood of violating specified constraints remains below a predefined target level. The integration of diverse reliability analysis methods has been a subject of study in this context, and readers interested in a comprehensive overview can refer to [9] for a state-of-the-art review on RBD/TO and its applications.…”