PSI - Issue 17

Maria Apostolopoulou et al. / Procedia Structural Integrity 17 (2019) 914–923 Maria Apostolopoulou et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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3.2. Natural hydraulic lime database

After extensive review of the published relevant literature, a database was compiled including all three types of Natural Hydraulic Lime (NHL5, NHL3.5, NHL2). The mortar mix design parameters, selected in order to be used as input parameters in the ANN models, and considered as the most crucial for the development of the compressive strength, were maximum grain size of the sand used as aggregate (MDA), the age of the specimen (CT), the natural hydraulic lime category (5, 3.5, 2) (MEP), the ratio by weight of binder (natural hydraulic lime) to aggregate (BS) and the ratio by weight of water to binder (WB), while the compressive strength was selected as the output parameter (CS). Care was taken to select research mostly published after 2010 when the standard for natural hydraulic limes was updated. At this point of the research, only mortars produced with one type of hydraulic lime as binder were taken into account (in contrast to blended mortars which contain a mix of different NHL types), while none of the mortars included in the database contained any other additives, such as superplasticizer and pozzolans. Mortars which were cured with standard curing were selected, in order to obliterate the influence of variable curing conditions on the compressive strength of the produced mortars, to the extent possible. The database at this point contains a total of 253 datasets, including, as aforementioned, all three categories of natural hydraulic lime. Datasets related to NHL5 mortars amount to 160 in total and were selected from the published research of Figueiredo al 2016b, Zhang et al 2018, Isebaert et al 2016, Kalagri et al 2014, Pozo-Antonio 2015, Amenta et al 2017, Lanas et al 2004, Barr et al 2015, Grist et al 2013, Silva et al 2014 and 2015. Compressive strength for the NHL5 mortars ranged from 0.5 to 15.2 MPa (for all curing times). Datasets related to mortars comprised with NHL3.5 amount to only 26, as most data related to non blended NHL3.5 mortars was either earlier than 2010 or some mix parameters were not included in the relevant publications. The included NHL3.5 datasets were selected from published research of Figueiredo al 2016b, Faria and Silva 2019, Arizzi et al 2015, Garijo et al 2018, Barr et al 2015 and Falchi et al 2015. Compressive strength for the NHL3.5 mortars ranged from 0.5 to 4.2 MPa (for all curing times). Datasets related to mortars comprised with NHL2 amount to 64 in total and were selected from the published research data of Figueiredo et al 2016a, Figueiredo al 2016b, Vysvaril et al 2017, Zhang et al 2018, Pozo-Antonio 2015 and Barr et al 2015. Compressive strength for the NHL2 mortars ranged from 0.36-5.32 MPa. It should be noted that at least to the knowledge of the authors, this is the first time that soft computing techniques have been used to study the development of hydraulic lime mortars’ compressive strength. It is also worth noting that the database (253 datasets) used is among the databases with the most datasets that have been used for the study and simulation of building materials’ mechanical properties using soft computing techniques. For the training of the ANN models the use of a large set of training function such as quasi-Newton, Resilient, One-step secant, Gradient descent with momentum and adaptive learning rate and Levenberg-Marquardt back propagation algorithms has been investigated. From all these algorithms, the best prediction for the non-linear behavior of the mortar compressive strength is achieved, by a significant margin with respect to the rest, by the Levenberg-Marquardt implemented by levmar (Lourakis 2005). This algorithm appears to be the fastest method for training moderate-sized feedforward neural networks (up to several hundred weights) as well as non-linear problems. It also has an efficient implementation in MATLAB® software, because the solution of the matrix equation is a built-in function, so its attributes become even more pronounced in a MATLAB environment. The normalization of data is a pre-processing phase which has been proved to be the most crucial step of any type problem in the field of soft computing techniques such as the ANN techniques. In the present study, during the pre processing stage, the Min-Max (Delen et al. 2006) has been used. In particular, the seven input parameters (Table 1) as well as the single output parameter have been normalized using the Min-Max normalization method. Namely, the input and output parameters have been normalized in the range [0.10, 0.90]. Detailed and in depth works on normalization techniques can be found in the published research of Asteris and Plevris 2017, Cavaleri et al. 2017, Chen et al. 2019 and Asteris and Kolovos 2019. 4. Results and Discussion