IMPROVING NONLINEAR PROCESS MODELING USING MULTIPLE NEURAL NETWORK COMBINATION THROUGH BAYESIAN MODEL AVERAGING (BMA)

Improving model generalization of aggregated multiple neural networks for nonlinear dynamic process modeling using Bayesian Model Averaging (BMA) is proposed in this paper. Using BMA method, the posterior probability of a particular network being the true model is used as the combination weight for aggregating the network despite of using fixed combination weight as the model. The posterior probabilities are calculated using the sum square error (SSE) from the training data on each of the sample time, and tested to the testing data. The selections for the final weight are based on the least SSE calculated when each of the posterior probability is applied to the testing data. The likelihood method is employed for calculating the network error for each input data. Then, it is used to calculate the combination weight for the networks. Two non-linear dynamic system-modeling case studies are selected for this proposed method, which are water tank level prediction and pH neutralization process. Application result demonstrates that the combination using BMA technique can significantly improve model generalization compared to other linear combination approaches.