### Abstract

Many operations, such as monitoring and control, require the availability of some key process variables. When these variables are difficult to measure, it is usually relied on inferential models that can be used to estimate these variables from other easier-to-measure variables. Latent variable regression (LVR) techniques, such as principal component regression (PCR), partial least square (PLS), and regularized canonical correlation analysis (RCCA), are commonly used as inferential models. In this paper, these linear LVR modeling techniques are first reviewed, and then a new algorithm that extends these LVR modeling techniques to nonlinear processes is presented. The developed nonlinear LVR (NLLVR) modeling algorithm utilizes nonlinear functions in the form of polynomials to capture the nonlinear relationships between the latent variables are the model output. The structures of these polynomials as well as the number of latent variables used are optimized using cross validation. The performances of the developed NLLVR modeling techniques are illustrated and compared with those the conventional linear LVR techniques (PCR, PLS, and RCCA). This comparison is performed using two examples, one using synthetic data and the other using simulated distillation column data. The results of both examples show that a significant improvement in model predictions can be achieved using the NLLVR modeling methods.

Original language | English |
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Title of host publication | Proceedings of the 2013 IEEE Symposium on Computational Intelligence in Control and Automation, CICA 2013 - 2013 IEEE Symposium Series on Computational Intelligence, SSCI 2013 |

Pages | 81-88 |

Number of pages | 8 |

DOIs | |

Publication status | Published - 2013 |

Event | 2013 3rd IEEE Symposium on Computational Intelligence in Control and Automation, CICA 2013 - 2013 IEEE Symposium Series on Computational Intelligence, SSCI 2013 - Singapore, Singapore Duration: 16 Apr 2013 → 19 Apr 2013 |

### Other

Other | 2013 3rd IEEE Symposium on Computational Intelligence in Control and Automation, CICA 2013 - 2013 IEEE Symposium Series on Computational Intelligence, SSCI 2013 |
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Country | Singapore |

City | Singapore |

Period | 16/4/13 → 19/4/13 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications

### Cite this

*Proceedings of the 2013 IEEE Symposium on Computational Intelligence in Control and Automation, CICA 2013 - 2013 IEEE Symposium Series on Computational Intelligence, SSCI 2013*(pp. 81-88). [6611667] https://doi.org/10.1109/CICA.2013.6611667

**Nonlinear latent variable regression.** / Madakyaru, Muddu; Nounou, Mohamed; Nounou, Hazem.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 2013 IEEE Symposium on Computational Intelligence in Control and Automation, CICA 2013 - 2013 IEEE Symposium Series on Computational Intelligence, SSCI 2013.*, 6611667, pp. 81-88, 2013 3rd IEEE Symposium on Computational Intelligence in Control and Automation, CICA 2013 - 2013 IEEE Symposium Series on Computational Intelligence, SSCI 2013, Singapore, Singapore, 16/4/13. https://doi.org/10.1109/CICA.2013.6611667

}

TY - GEN

T1 - Nonlinear latent variable regression

AU - Madakyaru, Muddu

AU - Nounou, Mohamed

AU - Nounou, Hazem

PY - 2013

Y1 - 2013

N2 - Many operations, such as monitoring and control, require the availability of some key process variables. When these variables are difficult to measure, it is usually relied on inferential models that can be used to estimate these variables from other easier-to-measure variables. Latent variable regression (LVR) techniques, such as principal component regression (PCR), partial least square (PLS), and regularized canonical correlation analysis (RCCA), are commonly used as inferential models. In this paper, these linear LVR modeling techniques are first reviewed, and then a new algorithm that extends these LVR modeling techniques to nonlinear processes is presented. The developed nonlinear LVR (NLLVR) modeling algorithm utilizes nonlinear functions in the form of polynomials to capture the nonlinear relationships between the latent variables are the model output. The structures of these polynomials as well as the number of latent variables used are optimized using cross validation. The performances of the developed NLLVR modeling techniques are illustrated and compared with those the conventional linear LVR techniques (PCR, PLS, and RCCA). This comparison is performed using two examples, one using synthetic data and the other using simulated distillation column data. The results of both examples show that a significant improvement in model predictions can be achieved using the NLLVR modeling methods.

AB - Many operations, such as monitoring and control, require the availability of some key process variables. When these variables are difficult to measure, it is usually relied on inferential models that can be used to estimate these variables from other easier-to-measure variables. Latent variable regression (LVR) techniques, such as principal component regression (PCR), partial least square (PLS), and regularized canonical correlation analysis (RCCA), are commonly used as inferential models. In this paper, these linear LVR modeling techniques are first reviewed, and then a new algorithm that extends these LVR modeling techniques to nonlinear processes is presented. The developed nonlinear LVR (NLLVR) modeling algorithm utilizes nonlinear functions in the form of polynomials to capture the nonlinear relationships between the latent variables are the model output. The structures of these polynomials as well as the number of latent variables used are optimized using cross validation. The performances of the developed NLLVR modeling techniques are illustrated and compared with those the conventional linear LVR techniques (PCR, PLS, and RCCA). This comparison is performed using two examples, one using synthetic data and the other using simulated distillation column data. The results of both examples show that a significant improvement in model predictions can be achieved using the NLLVR modeling methods.

UR - http://www.scopus.com/inward/record.url?scp=84886080835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886080835&partnerID=8YFLogxK

U2 - 10.1109/CICA.2013.6611667

DO - 10.1109/CICA.2013.6611667

M3 - Conference contribution

AN - SCOPUS:84886080835

SN - 9781467358934

SP - 81

EP - 88

BT - Proceedings of the 2013 IEEE Symposium on Computational Intelligence in Control and Automation, CICA 2013 - 2013 IEEE Symposium Series on Computational Intelligence, SSCI 2013

ER -