Study dy of Iner erti tia a Weight ight Pa Parameter er for Boundar ndary y Ele lement ment Inver erse se Analysis lysis to Det etect ect RC C Corr rrosio osion Syarizal Fonna, Syifaul Huzni Program StudiTeknik Mesin, Universitas Syiah Kuala, Jl. Tgk. Syech Abdul Rauf No. 7, Darussalam, Banda Aceh 23111 Gunawarman JurusanTeknik Mesin, Universitas Andalas, Kampus Limau Manis, Padang 25163
Corrosion of rebar
The failures of RC structures due to corrosion A Bridge collapse (source: Material Overpass highway, Quebec, Canada, 2006 Performance, July 2000) (www.ctv.ca) Jakarta, 25 September 2011 The collapse of the Algo Centre Mall’s roof, Canada, 2013 (http://megapolitan.kompas.com) (www.northernontariobusiness.com)
Direct Corrosion Monitoring Potential Mapping Concrete Resistivity Kampung. Jawa, Banda Aceh
Limitation of Direct Analysis Potential Mapping Method Less Accurate Important ! Laborious Time Consuming Effective NDE Method
PROPOSED METHOD: INVERSE ANALYSIS BOUNDARY ELEMENT PARTICLE SWARM METHOD OPTIMIZATION BOUNDARY ELEMENT INVERSE ANALYSIS (BEIA) S. Fonna et. al. 2013
Previous study Best Constant W S. Fonna et. al. 2013 Parsopoulos and Vrahatis (2010) suggested to use inconstant W for better result The purpose of this study: To investigate the effect of inconstant W (with W up = 0.5 and W low ≤ 0.5) on the performance of BEIA in detecting rebar corrosion in concrete
Modeling of Corrosion Problems 2 2 Laplace ’ s Equation = + = In 2 0 2 2 x y Boundary conditions: Polarization curve: 1 2 = 0 i = i 0 Ridha et al. 2005 BEM: Solving the Laplace’s Eq. Obtain: and i in the whole
WHY PSO ??? S. Fonna et. al. 2013 • Simple algorithm • Comparable accuracy
Particle Swarm Optimization ❑ Introduced by kennedy and eberhart in 1995 ❑ Population-based search algorithm ❑ Inspired by flocking behavior of birds Calculate W using Eq. c Peudocode of PSO
Boundary Element Inverse Analysis The flowchart of inverse analysis using PSO Minimize cost function:
Numerical Simulation Setup, Results and Discussion Constant κ = 0,007 Ω -1 m -1 ; ε 0 ≤ 10 -4 ; a 1 = a 2 = 0.5; BEM simulation result with parameters and N = 15 corrosion location at x=50 cm and size 2 cm Generated from the polarization curves
The values of W up and W low for the simulation Simulation no. 1 CL obtain on iteration 14 th with Error=0.26% 70 1 0.9 Actual CL=50 cm 60 Corrosion Location, z (cm) 0.8 50 0.7 Particle 1 0.6 Particle 2 40 W 0.5 Particle 3 30 0.4 Particle 4 0.3 Particle 5 20 0.2 W 10 0.1 0 0 0 5 10 15 20 Iteration The particle movement and the value of W during iteration for W up = 0.5 and W low = 0.5
Simulation No. 2 CL obtain on iteration 11 th with Error=0.46% 70 1 0.9 Actual CL=50 cm 60 0.8 Corrosion Location, z (cm) 50 0.7 Particle 1 0.6 Particle 2 40 W 0.5 Particle 3 30 0.4 Particle 4 0.3 20 Particle 5 0.2 W 10 0.1 0 0 0 5 10 15 20 Iteration The movement of particles and value of W during iteration for W up = 0.5 and W low = 0.2
Simulation No. 3 CL obtain on iteration 14 th with Error=0.33% 70 1 0.9 Actual CL=50 cm 60 Corrosion Location, z (cm) 0.8 50 0.7 Particle 1 0.6 Particle 2 40 W 0.5 Particle 3 30 0.4 Particle 4 0.3 20 Particle 5 0.2 W 10 0.1 0 0 0 5 10 15 20 Iteration The movement of particles and value of W during iteration for W up = 0.5 and W low = 0.01
Resume of all simulation 5 4 Ave Error Error (%) 3 2 Min Error 1 Less Max Error than 5% 0 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 Gradient of W during iteration (Wup = 0.5 and Wlow ≤ 0.5) The error in detecting actual corrosion for W up = 0.5 and W low ≤ 0.5
Conclusions ▪ The effect of inconstant W on BEIA when detecting rebar corrosion in concrete was explored ▪ the inconstant W with W up = 0.5 and W low ≤ 0.5 did not influence the performance of the BEIA in detecting rebar corrosion ▪ The error with respect to the actual location of corrosion (inconstant W with W up = 0.5 and W low ≤ 0.5 ) was less than 5% Further study: important to conduct further research to study the effect of W up > 0.5 for inconstant W
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