Constrained neural networks

Artificial Neural Networks (NNs) are very functional tools employed in regression, forecasting, classification, pattern recognition, data-based process modeling, and nonlinear process control. However, the data-based process modeling via NNs may be problematic since the field of chemical engineering has many strict rules in the form of implicit or explicit inequality and/or equality constraints that need to be satisfied, such as the mass and energy balances, bounds on mole fractions, conversion limits, and safety limits. The purpose of the thesis is to develop novel methods to implement equality and/or inequality constraints on/between the outputs of a feedforward NN during its training phase so that constraint violations of the model constructed by the NN are within the tolerable limits both in the training and testing phases. For this purpose, two alternative methods are developed. In the first method, the functions of MATLAB?s NN Toolbox are utilized however an unconstrained or a constrained generic optimizer from MATLAB?s Optimization Toolbox is employed for the training of the NN. In the second method, the algorithm is the same as in the first method however the NN building and NN topology functions of NN Toolbox are not used, instead these are coded explicitly. Direct or indirect (penalty function) constraint handling approaches are used for the implementation of inequality and/or equality constraints. The two methods of Constrained Neural Networks (CNNs), tested on six examples, accomplished the purpose of the thesis; they successfully learn the equality and/or inequality constraints imposed on/between the outputs of the NN together with the relations between the input and output data. The performances of the CNNs are more pronounced especially in realistic cases where the data, corrupted by measurement errors, do not satisfy the constraints. The CNNs act as model-/constraint-based filters and can learn and forecast process behavior even under noise-corrupted data via satisfying the imposed inequality and/or equality constraints.