Using steepness coefficient to improve artificial neural network performance for environmental modeling

This paper presents results from a research study in which the effects of steepness coefficient (S) for the activation function of a back propagation neural network (BPNN) were investigated, and optimum values of S for each activation function were suggested for environmental modeling purposes. A BPNN algorithm was implemented in Excel Visual Basic for Applications with built-in activation functions of sigmoid, hyperbolic tangent, and sinc. Various steepness coefficients were employed for modeling cyclone Euler numbers for pressure drop estimation with three different activation functions. Best results for sigmoid function were obtained for S = 1.00 with a median value of mean square errors (MSEs) of 4.33*10-4. For hyperbolic tangent function, the optimum value of S was found as 0.2 with a median MSE value of 2.02*10-4. The median value of MSEs obtained with BPNN sinc function was 1.20*10-3 for S = 0.50. Results showed, for environmental modeling problems, that any activation function can be used with satisfactory results provided that an optimized value of the steepness coefficient is used, which is considered problem specific.