Multiscale Bayesian rectification of data from linear steady-state and dynamic systems without accurate models

A common situation in chemical processes is that the measured data come fro m-a dynamic process, but the available accurate process models only represe nt steady-state behavior. Furthermore, process data usually contain multisc ale features due to different localizations in time and frequency. Existing methods for rectifying dynamic data require an accurate dynamic process mo del and are best for rectifying single-scale data,,This paper presents a mu ltiscale Bayesian approach for rectification of measurements from linear st eady-state or dynamic processes with a steady-state model or without a mode l. This approach exploits the ability of wavelets to approximately decorrel ate many autocorrelated stochastic processes and to, extract deterministic features in a signal. The decorrelation ability results in wavelet coeffici ents at each scale that contain almost none of the process dynamics. Conseq uently, these wavelet coefficients can be rectified without a model or with a steady-state process model. The dynamics are captured in the wavelet dom ain by the scale-dependent variance of the wavelet coefficients and the las t scaled signal. The proposed approach uses a scale-dependent prior for rec tifying the wavelet coefficients and rectifies the last scaled signal witho ut a model. In addition to more accurate rectification than existing method s, the multiscale Bayesian approach can eliminate the less relevant scales from the rectification before actually rectifying the data, resulting in si gnificant savings in computation. This paper focuses on the rectification o f Gaussian errors, but the approach is general and can be easily extended t o other types of error distributions.