Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct The importance of correlation among flutter derivatives for the reliability based optimum design of suspension bridges Ibuki Kusano ⁎ , Aitor Baldomir, José Ángel Jurado, Santiago Hernández Structural Mechanics Group, School of Civil Engineering, Universidade da Coruña, Campus de Elvina, 15071, Spain ARTICLE INFO Keywords: RBDO Correlation Optimization Reliability analysis Flutter derivatives Random variables Suspension bridge ABSTRACT The design of long-span bridges is constrained by the uncertainty in the evaluation of flutter velocity. Among all the elements that take part in the flutter assessment, the uncertainty level in experimentally obtained flutter derivatives has the most impact. It is therefore important in the evaluation of flutter velocity to assess the uncertainty which is associated with the adopted experimental method for flutter derivatives. By using a method of coupled motion only to identify eight flutter derivations simultaneously, it is also essential to consider cor- relations among the points that define the full set of flutter derivatives since they are not independent from one another. In this research, an experimental campaign was carried out to obtain the statistical information of flutter derivatives and to assemble the correlation matrix. Several cases of reliability analyses were performed to illustrate the importance of considering correlation among random variables as well as the significance of un- certainty level in flutter derivatives on bridge flutter failure. Moreover, a study of Reliability Based Design Optimization (RBDO) was carried out to see the influence of correlations among flutter derivatives on the op- timum designs. The RBDO of a suspension bridge was performed under probabilistic flutter constraint using Reliability Index Approach (RIA) method, and this methodology was applied to the Great Belt East Bridge. 1. Introduction Long-span suspension bridges are highly sensitive to wind loads due to their inherent structural flexibility and low damping. Among all wind related instabilities, flutter phenomenon is one of the most important design considerations because it can lead to the collapse of the struc- ture. For the estimation of critical flutter speed, we need to obtain the aeroelastic parameters called flutter derivatives experimentally from wind tunnel tests. However, these flutter functions contain uncertainty due to the experimental nature of the data as well as the identification method used to extract each function. In fact, some researchers such as Sarkar et al. [1] reported significant variations in the results of wind related variables obtained in different wind tunnels. They concluded that the differences in experimental results depend on the laboratory environment or operational conditions as well as the techniques used to extract the data such as number of degrees of freedom, upstream tur- bulence, sampling rate and time, instrumentation and the system identification method used. Consequently, the consideration of un- certainty in flutter derivatives is essential for the estimation of critical flutter velocity. Reliability analysis of bridge flutter provides information of the probability of structural failure considering uncertainty in parameters that participate in the evaluation of flutter limit state. Several authors carried out reliability analyses of bridge failure due to flutter. Ostenfeld-Rosenthal et al. [2] performed reliability analysis of cable supported bridges by considering uncertainty in extreme wind speeds, conversion from model tests to prototype, turbulence and structural damping. Ge et al. [3] computed probability of failure due to flutter using First Order Reliability Method (FORM), in which an empirical formula was used to evaluate flutter speed in the limit state. Cheng et al. [4] carried out flutter reliability analysis using response surface method. Baldomir et al. [5] performed reliability analyses of bridge flutter considering uncertainty in experimentally obtained points that define flutter derivatives. Canor et al. [6] proposed a generalized for- mulation for stochastic bridge flutter in terms of random eigenvalue analysis. Caracoglia et al. [7] reported experimental errors associated with flutter derivatives and modelling simplifications regarding bridge aerodynamics. Rizzo and Caracoglia [8] studied variability and corre- lation of flutter derivatives in experimental tests and used polynomial chaos expansion to characterize the distribution. However, only a few researchers have worked on the reliability analysis of long-span bridges considering correlated flutter derivatives as random variables. Matsumoto [9] reported correlations among flutter derivatives of a rectangular cylinder while Tubino [10] https://doi.org/10.1016/j.engstruct.2018.06.091 Received 3 November 2017; Received in revised form 23 May 2018; Accepted 25 June 2018 ⁎ Corresponding author. E-mail address: ikusano@udc.es (I. Kusano). Engineering Structures 173 (2018) 416–428 0141-0296/ © 2018 Elsevier Ltd. All rights reserved. T