Simultaneous estimation of odor classes and concentrations using an electronic nose with function approximation model ensembles

Abstract

This paper sets up a practical electronic nose for simultaneously estimating many kinds of odor classes and concentrations. Mathematically, such simultaneous estimation problems can be regarded as multi-input/multi-output (MIMO) function approximation problems. After decomposing an MIMO approximation task into multiple many-to-one tasks, we can use multiple many-to-one approximation model ensembles to implement them one after another. A single approximation model may be a multivariate logarithmic regression, a quadratic multivariate logarithmic regression, a multilayer perceptron, or a support vector machine. An ensemble is made up of the above four models, represents a special kind of odor, and realizes the relationship between sensor array responses and the represented odor concentrations. Naturally, all members in the ensemble are trained only by the samples from the represented odor. The real outputs of ensembles are the average predicted concentrations and the relative standard deviations (R.S.D.s). The ensemble with the smallest R.S.D. finally gives the label and concentration of an odor sample, which can be looked upon as the use of the average and the minimum combination rules. The predicted results for four kinds of fragrant materials, ethanol, ethyl acetate, ethyl caproate, and ethyl lactate, 21 concentrations in total, show that the proposed approximation model ensembles and combination strategies with the electronic nose are effective for simultaneously estimating many kinds of odor classes and concentrations.