Modeling induction-based steam distillation system by using nonlinear auto-regressive with exogenous input (NLARX) structure

Abstract

This paper presents the performance of NonLinear Auto Regressive with Exogenous input (NLARX) model structure that is applied in modeling of induction based steam distillation system. The input is PseudoRandom Binary Sequence (PRBS) and the output is temperature. The input-output data was split into two equal set for model estimation and model validation. All the data are transferred to MATLAB R2013a software for analysis. Wavelet Network, Sigmoid Network, Tree partition Network and Feedforward Neural Network are the nonlinearity estimators used to build the NLARX model structure and their performances have been compared. The validation of estimated model will be based on best fit (R²), final prediction error (FPE), loss function, auto-correlation function (ACF) and cross correlation function (CCF). The result showed that NLARX with Feedforward neural network is the most suitable estimator among others due to it yields the highest percent of best fit (R²), lowest final prediction and loss function, and all the coefficients are within the confidence limit for CCF test.

Nonlinear System Identification for Aqueous PVA Degradation in a Continuous UV/H2O2 Tubular Photoreactor

“…5 Therefore, the objectives of this study are to construct a dynamic model, in which parameters are estimated from online measurements and to investigate the performance of ARX and NARX models in representing the UV/H 2 O 2 photoreactor system for PVA degradation in wastewater streams. Similar to the study conducted by Ismail et al, 17 the tree partition networkbased NARX model outperformed all other dynamic models in estimating the studied process due to its highest fitness to the training data set and validation data set and lowest MSE while satisfying the characteristics of an open-loop stable, white (random and uncorrelated residues), and independent process model. However, sigmoid network-based NARX is considered when studying a more complex chemical process since it is the most suited to represent the output response of a chemical process due to the nature of signals from these processes.…”

“…It consists of a scaling factor similar to that of a neural network and a wavelet function in which the activation function is presented with three layers, including an input layer, hidden layers, and an output layer. 15,17 The wavelet network comes with a quick convergence time. 18,19 However, it is limited to a small input dimension with weak noise and a complete data set.…”

“…21,22 Even though the sigmoid network is robust in mapping, it requires a substantial number of parameter values to model a nonlinear system, making it less efficient. 17,23 Finally, the tree partition network, also known as the binary tree partition, is a set of piecewise linear functions that can be viewed as an approximation to a nonlinear amplifier. 22,24 A binary tree partition is a nonlinear two-dimensional data structure organized so that the algorithm branches relate the process inputs to outputs based on the number of nodes.…”

“…First, the wavelet network scheme is characterized as a combination of wavelet decomposition, also known as frequency transform, and neural network signal processing. It consists of a scaling factor similar to that of a neural network and a wavelet function in which the activation function is presented with three layers, including an input layer, hidden layers, and an output layer. , The wavelet network comes with a quick convergence time. , However, it is limited to a small input dimension with weak noise and a complete data set . Second, the sigmoid network is the most common form of activation function used in nonlinear system identification, especially in the artificial neural network.…”

“…Second, the sigmoid network is the most common form of activation function used in nonlinear system identification, especially in the artificial neural network. The sigmoid activation function is the most suited to represent the output response of a chemical process. , Even though the sigmoid network is robust in mapping, it requires a substantial number of parameter values to model a nonlinear system, making it less efficient. , Finally, the tree partition network, also known as the binary tree partition, is a set of piecewise linear functions that can be viewed as an approximation to a nonlinear amplifier. , A binary tree partition is a nonlinear two-dimensional data structure organized so that the algorithm branches relate the process inputs to outputs based on the number of nodes . Growing research in the treatment of industrial wastewater containing soluble polymers is an important reason to study reliable control techniques for AOPs.…”