Modeling of batch processes using explicitly time-dependent artificial neural networks

A neural network architecture incorporating time dependency explicitly, proposed recently, for modeling nonlinear nonstationary dynamic systems is further developed in this paper, and three alternate configurations are proposed to represent the dynamics of batch chemical processes. The first configuration consists of L subnets, each having M inputs representing the past samples of process inputs and output; each subnet has a hidden layer with polynomial activation function; the outputs of the hidden layer are combined and acted upon by an explicitly time-dependent modulation function. The outputs of all the subnets are summed to obtain the output prediction. In the second configuration, additional weights are incorporated to obtain a more generalized model. In the third configuration, the subnets are eliminated by incorporating an additional hidden layer consisting of L nodes. Backpropagation learning algorithm is formulated for each of the proposed neural network configuration to determine the weights, the polynomial coefficients, and the modulation function parameters. The modeling capability of the proposed neural network configuration is evaluated by employing it to represent the dynamics of a batch reactor in which a consecutive reaction takes place. The results show that all the three time-varying neural networks configurations are able to represent the batch reactor dynamics accurately, and it is found that the third configuration is exhibiting comparable or better performance over the other two configurations while requiring much smaller number of parameters. The modeling ability of the third configuration is further validated by applying to modeling a semibatch polymerization reactor challenge problem. This paper illustrates that the proposed approach can be applied to represent dynamics of any batch/semibatch process.