Robust Bayesian Inference for Gas Identification in Electronic Nose Applications by Using Random Matrix Theory

Abstract

Finding a rapid gas identification algorithm with high accuracy and a closed-form solution that does not require any manual tuning of parameters is the major challenge to overcome in adopting electronic nose technology in daily life applications. Recently, bio-inspired rank-order-based classifiers have been proposed to meet this challenge by transforming multidimensional sensitivity vectors into temporally ordered spike sequences for target gases. The performance of these classifiers, however, is limited when the spike sequences corresponding to all the target gases do not contain sufficient discriminatory information to identify them. Moreover, their identification decision is delayed up to the computation of the sensitivity vectors at steady state, which incurs a long waiting time. In this paper, we adopt a Bayesian parametric method with a normal distribution model as an alternative approach that provides a closed-form solution with only second-order statistics, i.e., mean and covariance. However, for electronic nose applications, a reliable estimation of the covariance matrix is a major challenge with the commonly used maximum likelihood estimate in Bayesian inference because of the limited number of available measurements for each target gas. We exploit random matrix theory principles to reduce randomness in the sample covariance matrix for its reliable estimation. Moreover, transient features are used to accelerate the gas identification. In order to validate the effectiveness of this approach, data of eight gases, namely, C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> , C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> , CH <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O, CL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , CO, CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , NO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , are acquired in the laboratory. We achieve a 7.73% performance improvement as compared with Bayesian inference using the maximum likelihood estimate, and an overall accuracy rate of 99.40% on the experimental data set.