An effective optimization-based parameterized interval analysis approach for static structural response with multiple un
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ORIGINAL ARTICLE
An effective optimization‑based parameterized interval analysis approach for static structural response with multiple uncertain parameters D. Dinh‑Cong1,3 · Ngo Van Hoa2,4 · T. Nguyen‑Thoi2,3 Received: 13 August 2018 / Accepted: 13 June 2019 © Springer-Verlag London Ltd., part of Springer Nature 2019
Abstract The framework of parameterized interval analysis (PIA) and optimization and anti-optimization problems (OAP) was recently proposed for considerably reducing or eliminating the overestimation of the interval solution arising in the classical interval analysis. However, reducing the computational effort of this framework still remains a challenging task, especially for large-scale structures with a large number of uncertain parameters. In this regard, an effective approach formulated in the framework is proposed for evaluating the static structural response with multiple uncertain-but-bounded parameters. First, the PIA is used to describe uncertain input properties incorporated into the interval stiffness matrix and the interval load vector of finite element model. Subsequently, the parametric inverse of the stiffness matrix is handled using a Neumann series expansion. To efficiently solve the objective function of OAP, a robust optimization solver known as lightning attachment procedure optimization algorithm is applied in the field of IFEM for the first time. Finally, the numerical investigations on three kinds of structures concerning truss, frame and plate structures with multiple uncertain parameters are presented to demonstrate the accuracy and effectiveness of the proposed approach. Keywords Parameterized interval analysis · Interval finite element method (IFEM) · Uncertain parameters · Optimization and anti-optimization · Lightning attachment procedure optimization (LAPO)
1 Introduction
* T. Nguyen‑Thoi [email protected] D. Dinh‑Cong [email protected] Ngo Van Hoa [email protected] 1
Division of Construction Computation, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam
2
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam
3
Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
In real-world engineering structures, the physical parameters of a structural system are always affected by uncertainties due to geometry or material properties, external loads, model inaccuracies and so on. The ability to incorporate the uncertainties into the modeling and analysis process of the structural system is of paramount importance for the purpose of realistic reliability assessment of engineering components and systems. Therefore, this topic has received increasing interest of many researchers over the last decades, especially in the fields of material modeling and structural design [1–6]. Traditionally, probabilist
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