Abstract
A common situation in chemical processes is that the measured data come from a dynamic process, but the available accurate process models only represent steady-state behavior. Furthermore, process data usually contain multiscale features due to different localizations in time and frequency. Existing methods for rectifying dynamic data require an accurate dynamic process model and are best for rectifying single-scale data. This paper presents a multiscale Bayesian approach for rectification of measurements from linear steady-state or dynamic processes with a steady-state model or without a model. This approach exploits the ability of wavelets to approximately decorrelate many autocorrelated stochastic processes and to extract deterministic features in a signal. The decorrelation ability results in wavelet coefficients at each scale that contain almost none of the process dynamics. Consequently, these wavelet coefficients can be rectified without a model or with a steady-state process model. The dynamics are captured in the wavelet domain by the scale-dependent variance of the wavelet coefficients and the last scaled signal. The proposed approach uses a scale-dependent prior for rectifying the wavelet coefficients and rectifies the last scaled signal without a model. In addition to more accurate rectification than existing methods, the multiscale Bayesian approach can eliminate the less relevant scales from the rectification before actually rectifying the data, resulting in significant savings in computation. This paper focuses on the rectification of Gaussian errors, but the approach is general and can be easily extended to other types of error distributions.
| Original language | English |
|---|---|
| Pages (from-to) | 261-274 |
| Number of pages | 14 |
| Journal | Industrial and Engineering Chemistry Research |
| Volume | 40 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2001 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Chemistry(all)
- Chemical Engineering(all)
- Industrial and Manufacturing Engineering
Cite this
Multiscale Bayesian rectification of data from linear steady-state and dynamic systems without accurate models. / Bakshi, Bhavik R.; Nounou, Mohamed; Goel, Prem K.; Shen, Xiaotong.
In: Industrial and Engineering Chemistry Research, Vol. 40, No. 1, 01.01.2001, p. 261-274.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Multiscale Bayesian rectification of data from linear steady-state and dynamic systems without accurate models
AU - Bakshi, Bhavik R.
AU - Nounou, Mohamed
AU - Goel, Prem K.
AU - Shen, Xiaotong
PY - 2001/1/1
Y1 - 2001/1/1
N2 - A common situation in chemical processes is that the measured data come from a dynamic process, but the available accurate process models only represent steady-state behavior. Furthermore, process data usually contain multiscale features due to different localizations in time and frequency. Existing methods for rectifying dynamic data require an accurate dynamic process model and are best for rectifying single-scale data. This paper presents a multiscale Bayesian approach for rectification of measurements from linear steady-state or dynamic processes with a steady-state model or without a model. This approach exploits the ability of wavelets to approximately decorrelate many autocorrelated stochastic processes and to extract deterministic features in a signal. The decorrelation ability results in wavelet coefficients at each scale that contain almost none of the process dynamics. Consequently, these wavelet coefficients can be rectified without a model or with a steady-state process model. The dynamics are captured in the wavelet domain by the scale-dependent variance of the wavelet coefficients and the last scaled signal. The proposed approach uses a scale-dependent prior for rectifying the wavelet coefficients and rectifies the last scaled signal without a model. In addition to more accurate rectification than existing methods, the multiscale Bayesian approach can eliminate the less relevant scales from the rectification before actually rectifying the data, resulting in significant savings in computation. This paper focuses on the rectification of Gaussian errors, but the approach is general and can be easily extended to other types of error distributions.
AB - A common situation in chemical processes is that the measured data come from a dynamic process, but the available accurate process models only represent steady-state behavior. Furthermore, process data usually contain multiscale features due to different localizations in time and frequency. Existing methods for rectifying dynamic data require an accurate dynamic process model and are best for rectifying single-scale data. This paper presents a multiscale Bayesian approach for rectification of measurements from linear steady-state or dynamic processes with a steady-state model or without a model. This approach exploits the ability of wavelets to approximately decorrelate many autocorrelated stochastic processes and to extract deterministic features in a signal. The decorrelation ability results in wavelet coefficients at each scale that contain almost none of the process dynamics. Consequently, these wavelet coefficients can be rectified without a model or with a steady-state process model. The dynamics are captured in the wavelet domain by the scale-dependent variance of the wavelet coefficients and the last scaled signal. The proposed approach uses a scale-dependent prior for rectifying the wavelet coefficients and rectifies the last scaled signal without a model. In addition to more accurate rectification than existing methods, the multiscale Bayesian approach can eliminate the less relevant scales from the rectification before actually rectifying the data, resulting in significant savings in computation. This paper focuses on the rectification of Gaussian errors, but the approach is general and can be easily extended to other types of error distributions.
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U2 - 10.1021/ie990905p
DO - 10.1021/ie990905p
M3 - Article
VL - 40
SP - 261
EP - 274
JO - Industrial and Engineering Chemistry Research
JF - Industrial and Engineering Chemistry Research
SN - 0888-5885
IS - 1
ER -