Ensemble wavelet modelling for determination of wheat and gasoline properties by near and middle infrared spectroscopy.

The wavelet transform has been shown to be a useful tool for multivariate calibration. However, the choice of wavelet transform settings (wavelet family, length and number of decomposition levels) for a given application is still an open problem. The present paper proposes an alternative approach, which consists of generating an ensemble model by combining individual models obtained with different wavelet transform settings. The advantages of the proposed method are demonstrated in two analytical problems, namely the determination of moisture and protein in wheat by near infrared spectroscopy and the determination of specific mass and three distillation temperatures (T10, T50, T90) in gasoline by middle infrared spectroscopy. In these problems, the results varied considerably among individual models, which underlines the risk associated to an inadequate choice of wavelet transform settings. In contrast, the ensemble model always provided adequate results in terms of prediction error and noise sensitivity. The proposed method can be seen as an advantageous alternative for multivariate calibration in the wavelet domain, as it frees the analyst from the need to choose a particular configuration for the wavelet transform.