PSI - Issue 48

Mohamed El Amine Ben Seghier et al. / Procedia Structural Integrity 48 (2023) 356–362 Ben Seghier et al / Structural Integrity Procedia 00 (2023) 000 – 000

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1. Introduction It is well understood that main effort during structural reliability analysis is to approximate the reliability index using appropriate framework based on a theoretical probabilistic model (Jafari-Asl et al. 2022; Jafari-Asl, Ohadi, et al. 2021). Therefore, estimating the reliability index or the failure probability is an important task in order to evaluate the influence of various uncertainties such as external loads, material and geometrical properties of structure (Guillal et al. 2020; Keshtegar and Kisi 2018; Ben Seghier, Keshtegar, and Mahmoud 2021).To this end, several analytical or random-simulation methods are deployed to solve structural reliability of diverse engineering problems including pipelines, bridges, dams and others (Jafari-Asl et al. 2020; Jafari-Asl, Ben Seghier, et al. 2021; Seghier, Mustaffa, and Zayed 2022; Taiwo, El Amine Ben Seghier, and Zayed 2023). This latter required the use of limit state function, which can be derived from finite element (FE) models or involve high-dimensional problems. Analytical methods as the first and second-order reliability method (FORM/SORM) using Hasofer-Lind and Rackwitz-Fiessler method (HL-RF) and Conjugate FORM (CFORM) may provide inefficient results based computational burden for problems with high nonlinearity (e.g. As in the case of corroded pipelines with complex performance functions (Bagheri et al. 2020; Keshtegar et al. 2019)). The Monte Carlo Simulation (MCS), on the other hand, required a large number of simulations, which is time consuming for a low failure probability(El Amine Ben Seghier, Keshtegar, and Elahmoune 2018; Seghier et al. 2018). With the rise of artificial intelligence in a variety of fields and disciplines as an effective tool for tackling complex problems, particularly in civil and structural engineering (e.g., modeling corrosion (Seghier, Corriea, et al. 2021; Seghier, Höche, and Zheludkevich 2022) and damage (Ben Seghier et al. 2020) in deteriorated structures), structural reliability theory has benefited from such tools in order to develop new powerful frameworks (Keshtegar et al. 2021; Zhu et al. 2022). As a results, various meta-modelling approaches have been introduced to the structural reliability analyses in order to evaluate the limit state function (LSF) (Keshtegara⁠ and Seghier 2018) . This approach include M5 model tree (M5Tree) (Mohamed el Amine Ben Seghier et al. 2019), polynomial chaos expansions (PCE) (Martinez, Crestaux, and Maı 2009) polynomial response surface method (RSM) (Bucher, Christian G. 1990), Kriging (Kaymaz 2005) and neural network (NN) (Elhewy, Mesbahi, and Pu 2006). Implementation of meta-modeling approaches in the structural analysis gets wide intention from researchers and industry due to the improvements, results accuracy and time saving compared to classical approaches, especially for high-dimensional problems. In this paper, a framework is introduced for the structural reliability analysis by coupling the enhanced first-order reliability method using conjugate search direction (CFORM) with an artificial intelligence technique called support vector regression (SVR). Then the applicability and ability of the developed SVR-CFORM method was investigated on LSF with high nonlinearity, whereas the variables included in this LSF have non-normal distribution. Furthermore, the proposed method's efficiency and robustness were compared to MCS, HL-RF, and CFORM approaches, with the influence of the SVR hype-parameters taken into account. 2. Support Vector Regression The development and implementation of SVR was introduced by Vapnik in 1995 (Vapnik 1995) as a new supervised learning methodology. SVR aims to approximate a function that computes the functional dependency between targets = { 1 , 2 ,…, } defined on R , and inputs = { 1 , 2 ,…, } , whereas ∈ R m and m is the data size. Therefore, this function can be expressed as (Seghier, Kechtegar, et al. 2021): ( ) = ( ) + (1) where ( ) is a high-dimensional feature space, mapped the input space vector X , w is a weight vector and b is a bias. In order to estimate the factors, w and b , the following regularized risk function should be minimized: = 1 ∑ ( ( )− )+ 1 2 ‖ ‖ 2 =1 (2) In equation (2), 1 ∑ ( ( )− ) =1 represents the empirical error, 1 2 ‖ ‖ 2 is the measure of function flatness.