a comparative study between NARMAX and NARX models developed with ANN and SVM when used to forecast cash demand for ATMs is conducted. A simple methodology for developing SVM-NARMAX models is proposed. The best results were obtained with NARX-ANN models. In addition no significant differences were found between NARX and NARMAX for both ANN and SVM. Hence it seems advisable to choose simpler models, such as NARX and a user-friendly tool like ANN at least for this particular application.
The lack of sensors for some relevant state variables in fermentation processes can be coped by developing appropriate software sensors. In this work, NARX-ANN, NARMAX-ANN, NARX-SVM and NARMAX-SVM models are compared when acting as software sensors of biomass concentration for a solid substrate cultivation (SSC) process. Results show that NARMAX-SVM outperforms the other models with an SMAPE index under 9 for a 20 % amplitude noise. In addition, NARMAX models perform better than NARX models under the same noise conditions because of their better predictive capabilities as they include prediction errors as inputs. In the case of perturbation of initial conditions of the autoregressive variable, NARX models exhibited better convergence capabilities. This work also confirms that a difficult to measure variable, like biomass concentration, can be estimated on-line from easy to measure variables like CO₂ and O₂ using an adequate software sensor based on computational intelligence techniques.
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