New optimization algorithm for optimal spatial sampling during non-destructive testing of concrete structures C. Gomez-Cardenas a,b,c , Z.M. Sbartaï a,⇑ , J.P. Balayssac b , V. Garnier c , D. Breysse a a Université de Bordeaux, CNRS, INRA, I2M/GCE, 351 Cours de la libération, 33405 Talence Cedex, France b Université de Toulouse, UPS, INSA, LMDC, 135 avenue de Rangueil, 31077 Toulouse Cedex 4, France c Aix Marseille Université, CNRS, LMA, UPR 7051, IUT, Avenue Gaston Berger, 13 625 Aix en Provence Cedex 1, France article info Article history: Received 26 April 2014 Revised 7 January 2015 Accepted 8 January 2015 Keywords: NDT Optimization Concrete structure Diagnosis Spatial variability abstract Non-destructive Testing (NDT) techniques are essential in order to assess properties or detect anomalies (cracks, pathologies, etc.) in concrete during the diagnosis of structures. However, due to budget limitations, an optimal methodology to estimate the integrity of a structure at minimum cost is required. This paper presents a spatial optimization of NDT measurements (ultrasound) based on their spatial correlation. The optimization is performed in two steps. First, the relationship between the number of measurements organized in a regular grid and the fitness function value are determined using spatial interpolation (kriging method). Then, using an Optimization Spatial Sampling Method developed for this study (OSSM), the fitness function is minimized by changing the positions of a chosen number of NDT measurements. The theoretical development and the results obtained with both simulated and real data are presented and discussed. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Nowadays, most of the structures for human use (buildings, bridges, etc.) are made of concrete. It is of vital importance to ensure that they function correctly during their service life and it has become crucial to find a reliable and efficient method for eval- uating the condition of a structure at different times of its life span. Traditionally, the most commonly used method for the evaluation of a concrete structure has been visual inspection [1]. It is usually carried out by an expert engineer, who defines the most degraded zones of the structure and takes some samples (cores) in order to refine his analysis and eventually propose a reparation procedure. This method, which is subjective and remains informal, can only be used when a number of pathologies in the concrete, like cracking and spalling, are visible. Other pathologies, such as reinforcing steel corrosion are difficult to identify with visual inspection alone. For that reason, non-destructive testing is an interesting complement in the diagnosis of a concrete structure [2–7]. Non-destructive Testing (NDT) started to be used in reinforced concrete structures due to the increasing need to objectively eval- uate their condition. The aim was also to manage the safety of the structure and to eventually set up a maintenance plan [8–10]. NDT also opened up the possibility of preventive maintenance, which is three to twenty times less expensive than repair in terms of energy and financial resources [11]. NDT techniques are sensitive not only to anomalies in the con- crete but also to its physical and mechanical properties. For instance, ultrasound, impact-echo and rebound hammer are used to assess the concrete compressive strength, while electrical resis- tivity and GPR are sensitive to water content. Moreover, concrete inhomogeneity often leads to spatial variability in structures [12–15]. In addition, recent reliability studies have shown that the spatial correlation may govern the reliability of structural components [16]. Some studies have been carried out with the aim of analyzing spatial variability but, to the best of our knowledge none of them has focused on sampling optimization for optimal inspection. Among NDT techniques, some, such as ultrasonic pulse velocity, rebound hammer, and GPR, etc. are fast and inexpensive. The general frame that we promote is that of a two-step approach where a fast technique is first used to obtain a general view of the spatial distribution for a particular property of the concrete (strength, moisture, etc.), and where the critical zones can be ana- lyzed more into details in a second step, with NDT measurements of higher quality and/or cores. This approach takes advantage of the two types of ND investigations (fast and slow) and destructive testing while keeping the cost/benefit ratio within reasonable limits. http://dx.doi.org/10.1016/j.engstruct.2015.01.014 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: zm.sbartai@i2m.u-bordeaux1.fr (Z.M. Sbartaï). Engineering Structures 88 (2015) 92–99 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct