PSI - Issue 17

Danial J. Armaghani et al. / Procedia Structural Integrity 17 (2019) 924–933 Danial J. Armaghaniet al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Thus, a total of 9 contribution parameters were acknowledged based on earlier experimental studies and which are also supposed to be crucial variables in determining shear capacity of reinforced concrete beams. Based on the above, the database examined here consists of the data and results of 300 experiments on reinforced concrete beams with stirrups. Namely, the database has been is compiled using experimental data that have been published in thirteen (13) pertinent research studies: Clark 1951, Feldman and Siess 1955, Kani 1967, Placas and Regan 1971, Fukuhara and Kokusho 1982, Xie et al. 1994, Yoon et al. 1996, Ghannoum 1998, Angelakos et al. 2001, Tompos and Frosh 2002, Zararis et al. 2009, Ismail 2009, and Londhe 2011. It should be noted that the database compiled has taken into consideration the additional criterion of covering -to the greatest extent- all possible ranges of values of the various parameters involved in the problem under examination. 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 behaviour of the concrete beams shear 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 artificial neural networks 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. In this work, a large number of different ANN models have been developed and implemented. In particular, the following four (4) cases of ANN architectures based on the number of input parametersas well as on the output parameter were examined: Case A. NN models with input parameters the nine input parameters that are presented in Table 1 have been trained and developed, while as output parameter has been used the Shear strength that defined by = (1) where v is the shear concentrated load (shear force), b and d are the width and the effective depth of the beam. Case B. In this case the input parameters are seven (7). The difference from the above case A is that the yield stress of longitudinal reinforcement and the associated reinforcement ratio have been taken into account as one parameter that is defined as the product of these two parameters. The same is also valid for the case of the transverse reinforcement where also the quality and the quantity expressed via only one parameter that is the product of them. Case C. The input parameters for this case are five (5). Specifically this third case is the same with the above second case without two geometrical parameters of the width (b) and the effective depth of beam. This case has been investigated due to the fact that these two geometrical parameters are taken into 3. Results and Discussion