Process modeling by Bayesian latent variable regression

Mohamed Nounou, Bhavik R. Bakshi, Prem K. Goel, Xiaotong Shen

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

Large quantities of measured data are being routinely collected in various industries and used for extracting linear models for tasks such as process control, fault diagnosis, and process monitoring. Existing linear modeling methods, however, do not fully utilize all the information contained in the measurements. A new approach for linear process modeling makes maximum use of available process data and process knowledge. Bayesian latent-variable regression (BLVR) permits extraction and incorporation of knowledge about the statistical behavior of measurements in developing linear process models. Furthermore, BLVR can handle noise in inputs and outputs, collinear variables, and incorporate prior knowledge about regression parameters and measured variables. The model is usually more accurate than those of existing methods, including OLS, PCR, and PLS. BLVR considers a univariate output and assumes the underlying variables and noise to be Gaussian, but it can be used for multivariate outputs and other distributions. An empirical Bayes approach is developed to extract the prior information from historical data or maximum-likelihood solution of available data. Examples of steady-state, dynamic and inferential modeling demonstrate the superior accuracy of BLVR over existing methods even when the assumptions of Gaussian distributions are violated. The relationship between BLVR and existing methods and opportunities for future work based on this framework are also discussed.

Original languageEnglish
Pages (from-to)1775-1793
Number of pages19
JournalAICHE Journal
Volume48
Issue number8
DOIs
Publication statusPublished - 1 Aug 2002
Externally publishedYes

Fingerprint

Noise
Linear Models
Process monitoring
Gaussian distribution
Maximum likelihood
Failure analysis
Process control
Normal Distribution
Industry
Polymerase Chain Reaction

ASJC Scopus subject areas

  • Biotechnology
  • Environmental Engineering
  • Chemical Engineering(all)

Cite this

Process modeling by Bayesian latent variable regression. / Nounou, Mohamed; Bakshi, Bhavik R.; Goel, Prem K.; Shen, Xiaotong.

In: AICHE Journal, Vol. 48, No. 8, 01.08.2002, p. 1775-1793.

Research output: Contribution to journalArticle

Nounou, M, Bakshi, BR, Goel, PK & Shen, X 2002, 'Process modeling by Bayesian latent variable regression', AICHE Journal, vol. 48, no. 8, pp. 1775-1793. https://doi.org/10.1002/aic.690480818
Nounou, Mohamed ; Bakshi, Bhavik R. ; Goel, Prem K. ; Shen, Xiaotong. / Process modeling by Bayesian latent variable regression. In: AICHE Journal. 2002 ; Vol. 48, No. 8. pp. 1775-1793.
@article{337bee6dbd7144428e987ca283e19f9f,
title = "Process modeling by Bayesian latent variable regression",
abstract = "Large quantities of measured data are being routinely collected in various industries and used for extracting linear models for tasks such as process control, fault diagnosis, and process monitoring. Existing linear modeling methods, however, do not fully utilize all the information contained in the measurements. A new approach for linear process modeling makes maximum use of available process data and process knowledge. Bayesian latent-variable regression (BLVR) permits extraction and incorporation of knowledge about the statistical behavior of measurements in developing linear process models. Furthermore, BLVR can handle noise in inputs and outputs, collinear variables, and incorporate prior knowledge about regression parameters and measured variables. The model is usually more accurate than those of existing methods, including OLS, PCR, and PLS. BLVR considers a univariate output and assumes the underlying variables and noise to be Gaussian, but it can be used for multivariate outputs and other distributions. An empirical Bayes approach is developed to extract the prior information from historical data or maximum-likelihood solution of available data. Examples of steady-state, dynamic and inferential modeling demonstrate the superior accuracy of BLVR over existing methods even when the assumptions of Gaussian distributions are violated. The relationship between BLVR and existing methods and opportunities for future work based on this framework are also discussed.",
author = "Mohamed Nounou and Bakshi, {Bhavik R.} and Goel, {Prem K.} and Xiaotong Shen",
year = "2002",
month = "8",
day = "1",
doi = "10.1002/aic.690480818",
language = "English",
volume = "48",
pages = "1775--1793",
journal = "AICHE Journal",
issn = "0001-1541",
publisher = "American Institute of Chemical Engineers",
number = "8",

}

TY - JOUR

T1 - Process modeling by Bayesian latent variable regression

AU - Nounou, Mohamed

AU - Bakshi, Bhavik R.

AU - Goel, Prem K.

AU - Shen, Xiaotong

PY - 2002/8/1

Y1 - 2002/8/1

N2 - Large quantities of measured data are being routinely collected in various industries and used for extracting linear models for tasks such as process control, fault diagnosis, and process monitoring. Existing linear modeling methods, however, do not fully utilize all the information contained in the measurements. A new approach for linear process modeling makes maximum use of available process data and process knowledge. Bayesian latent-variable regression (BLVR) permits extraction and incorporation of knowledge about the statistical behavior of measurements in developing linear process models. Furthermore, BLVR can handle noise in inputs and outputs, collinear variables, and incorporate prior knowledge about regression parameters and measured variables. The model is usually more accurate than those of existing methods, including OLS, PCR, and PLS. BLVR considers a univariate output and assumes the underlying variables and noise to be Gaussian, but it can be used for multivariate outputs and other distributions. An empirical Bayes approach is developed to extract the prior information from historical data or maximum-likelihood solution of available data. Examples of steady-state, dynamic and inferential modeling demonstrate the superior accuracy of BLVR over existing methods even when the assumptions of Gaussian distributions are violated. The relationship between BLVR and existing methods and opportunities for future work based on this framework are also discussed.

AB - Large quantities of measured data are being routinely collected in various industries and used for extracting linear models for tasks such as process control, fault diagnosis, and process monitoring. Existing linear modeling methods, however, do not fully utilize all the information contained in the measurements. A new approach for linear process modeling makes maximum use of available process data and process knowledge. Bayesian latent-variable regression (BLVR) permits extraction and incorporation of knowledge about the statistical behavior of measurements in developing linear process models. Furthermore, BLVR can handle noise in inputs and outputs, collinear variables, and incorporate prior knowledge about regression parameters and measured variables. The model is usually more accurate than those of existing methods, including OLS, PCR, and PLS. BLVR considers a univariate output and assumes the underlying variables and noise to be Gaussian, but it can be used for multivariate outputs and other distributions. An empirical Bayes approach is developed to extract the prior information from historical data or maximum-likelihood solution of available data. Examples of steady-state, dynamic and inferential modeling demonstrate the superior accuracy of BLVR over existing methods even when the assumptions of Gaussian distributions are violated. The relationship between BLVR and existing methods and opportunities for future work based on this framework are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0036706987&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036706987&partnerID=8YFLogxK

U2 - 10.1002/aic.690480818

DO - 10.1002/aic.690480818

M3 - Article

AN - SCOPUS:0036706987

VL - 48

SP - 1775

EP - 1793

JO - AICHE Journal

JF - AICHE Journal

SN - 0001-1541

IS - 8

ER -