Reduced Noise Effect in Nonlinear Model Estimation Using Multiscale Representation

Mohamed N Nounou,Hazem N Nounou

doi:10.1155/2010/217305

Mohamed N Nounou, Hazem N Nounou

Open Access

https://doi.org/10.1155/2010/217305

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Abstract

Nonlinear process models are widely used in various applications. In the absence of fundamental models, it is usually relied on empirical models, which are estimated from measurements of the process variables. Unfortunately, measured data are usually corrupted with measurement noise that degrades the accuracy of the estimated models. Multiscale wavelet‐based representation of data has been shown to be a powerful data analysis and feature extraction tool. In this paper, these characteristics of multiscale representation are utilized to improve the estimation accuracy of the linear‐in‐the‐parameters nonlinear model by developing a multiscale nonlinear (MSNL) modeling algorithm. The main idea in this MSNL modeling algorithm is to decompose the data at multiple scales, construct multiple nonlinear models at multiple scales, and then select among all scales the model which best describes the process. The main advantage of the developed algorithm is that it integrates modeling and feature extraction to improve the robustness of the estimated model to the presence of measurement noise in the data. This advantage of MSNL modeling is demonstrated using a nonlinear reactor model.

Highlights

Process models are a core element in many process operations, such as process control and optimization [1, 2], and the accuracy of these models has a direct impact on the quality of these operations and on the overall performance of the process
The objective of this work is to improve the prediction accuracy of the well-known class of nonlinear, but linear-in-the-parameters, process models using multiscale representation to account for the presence of measurement noise in the data
We address the problem of empirically estimating linear-in-the-parameters nonlinear models which are less affected by the presence of measurement noise in the data

Summary

Introduction

Process models are a core element in many process operations, such as process control and optimization [1, 2], and the accuracy of these models has a direct impact on the quality of these operations and on the overall performance of the process. The objective of this work is to improve the prediction accuracy of the well-known class of nonlinear, but linear-in-the-parameters, process models using multiscale representation to account for the presence of measurement noise in the data. The presence of measurement noise, even in small amounts, can largely affect the estimated model’s prediction accuracy Such noise needs to be filtered for improved model’s prediction. Modeling of prefiltered measured data does not usually provide satisfactory performance [3]. This is because applying data filtering without taking into account the input-output relationship may result in the removal of certain features from the data which are important for the model. Filtering and modeling need to be integrated for satisfactory model estimation

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