Sigmoid activation function, defined

NN models are nonlinear mathematical structures built by summing up iteratively nonlinear transformations of linear combinations of certain input variables. NN models can assume many different configurations. In the simplest case, usually called as the feed-forward NN structure, three different layers are employed (Fig. 6.8) the input layer, the hidden layer, and the output layer. The input layer is fed by values of a number of input variables, generally the spectral data measured at certain wavelengths. The output layer provides the desired process response. The backpropagation procedure is normally used to estimate the NN model parameters [77], The nonlinear transformation generally used at each particular node of the NN model is a sigmoidal activation function, defined as... 

In the same year, Peng et al. presented a novel design of a battery pack SOC estimator for electric vehicles (EVs) using a two-layer ANN (one single hidden layer) with four inputs (current, capacity, temperature, and minimum module voltage) and one output (estimated SOC) [3]. The N hidden neurons have a sigmoid activation function defined as... 

An activation function with limits on the amplitude of the output of a neuron. The amplitude range is usually given in a closed interval [0,1] or [-1,1]. Activation function y>(-) defines the output yu of a neuron (see Eq. 3.65) in terms of the activation potential Vk (see Eq. 3.64). Typical activation functions include the unit step change and sigmoid functions. 

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