On robust nonlinear modeling of a complex process with large number of inputs using m-QRcp factorization and C-p statistic

The problem of modeling complex processes with a large number of inputs is addressed. A new method is proposed for the optimization of the models in m inimum C-p statistic sense using QR with a modified scheme of column pivoti ng (m-QRcp) factorization. Two different classes of multilayer nonlinear mo deling problems are explored: 1) in the first class of models, each layer c omprises multiple linearly parameterized submodels or cells; the individual cells are optimally modeled using QR factorization, and m-QRcp factorizati on ensures optimal selection of variables across the layers. 2) The nonhomo geneous feedforward neural network is chosen as the second class of models, where the network architecture and structure are optimized in terms of bes t set of hidden links land nodes) using m-QRcp factorization. In both the c ases, the optimization is shown to be direct and conclusive. The proposed i s a generic approach to the optimal modeling of complex multilayered archit ectures, which leads to computationally fast and numerically robust par sim onious designs, free from collinearity problems, The method is largely free from heuristics and is amenable to automated modeling.