“…Among various ANNs reported in the literature, the feed-forward (back propagation) neural network (FNN) method with a modified Levenberg-Marquardt optimization algorithm (Marquardt, 1963; Levenberg, 1944) is used, which is known to be effective to represent the non-linear relationships between variables in complex systems (Normandin et al, 1993;Mohammadi and Richon, 2010;Rivollet, 2005;Wilamowski et al, 2001;Chouai et al, 2002;Piazza et al, 2006;Scalabrin et al, 2006;Schmitz et al, 2006). To develop this algorithm, reliable literature data are used Hashimoto et al, 2006Hashimoto et al, , 2008Hashimoto et al, , 2010Arjmandi et al, 2007) (see Table 1). The developed algorithm is then employed to predict independent experimental data (not used in developing this tool).…”