Non-linear dynamic projection to latent structures modelling

Baffi, G.; Martin, E.B.; Morris, A.J.

doi:10.1016/s0169-7439(00)00083-6

Cited by 53 publications

(44 citation statements)

References 15 publications

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“…Calculate the output residual matrix : Baffi et al (1999aBaffi et al ( , 1999bBaffi et al ( , 2000 By combining this error-based input weight updating procedure with the NPLS structure, Baffi et al (1999aBaffi et al ( , 1999b derived the error-based NPLS algorithm, which we summarise in Table 1. When the non-linear inner relation is chosen as the quadratic mapping (6), we refer to this error-based NPLS algorithm as the error-based QPLS algorithm.…”

Section: The Error-based Nplsmentioning

confidence: 99%

“…In this paper, we propose a new updating procedure for the outer input weight l w and inner parameter l b by modifying and extending the error-based method for updating , l w proposed by Baffi et al (1999aBaffi et al ( , 1999bBaffi et al ( , 2000.…”

Section: Modified Nplsmentioning

confidence: 99%

“…This has motivated further research for the input weight updating procedure in the NPLS model. By modifying the input weight updating procedure of Wold et al (1989), Baffi et al (1999aBaffi et al ( , 1999bBaffi et al ( , 2000 have derived an error-based input weight updating approach. The first contribution of this paper is to formulate the weight and parameter updating procedure as a constrained non-linear optimisation problem.…”

Section: Introductionmentioning

confidence: 99%

“…Sequential unconstrained minimisation technique (SUMT) is then utilised to calculate the outer input weights and the parameters of quadratic inner relation. The proposed updating method overcomes the drawbacks of the need for pseudo-inverse and high computational burden that exist in the original error-based input weight updating approach (Baffi et al, 1999a(Baffi et al, , 1999b(Baffi et al, , 2000. The new updating method is combined with the original QPLS in this paper, leading to a modified QPLS (MQPLS) algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…In Section 2, the NPLS is reviewed and the error-based input weight updating procedure due to Baffi et al (1999aBaffi et al ( , 1999bBaffi et al ( , 2000 is introduced. Section 3 proposes a new weight and parameter updating method.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Inferential control with the aid of modified QPLS-based soft sensor for an industrial FCCU fractionator

Tian¹,

Ling²,

Yang³

et al. 2010

IJMIC

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Abstract:A modified quadratic partial least squares (MQPLS) algorithm based on non-linear constrained programming is proposed, in which a sequential unconstrained minimisation technique is employed to calculate the outer input weights and the parameters of inner relationship. Other existing quadratic partial least squares (QPLS) algorithms are also reviewed and compared with the proposed MQPLS in the applications to two datasets, one being an artificial dataset and the other being the real data from an industrial fluidised catalytic cracking unit (FCCU) main fractionator. It is shown that the MQPLS not only can explain better the underlying variability of the data but also achieves improved modelling and predictive performance over the existing QPLS algorithms. An inferential control system is implemented on the distributed control system for an industrial FCCU main fractionator, in which the soft-sensor is built based on the MQPLS algorithm to estimate the diesel oil solidifying point online and the controller is established via a constrained dynamic matrix control algorithm. Experimental results obtained demonstrate that the inferential control system with the aid of the MQPLS soft sensor works much better than the original tray temperature control system and it realises well the bounder control of diesel oil solidifying point.Keywords: non-linear systems; neural networks; non-linear partial least squares; NPLS; soft sensing; inferential control; fractionator; dynamic matrix control; DMC.Reference to this paper should be made as follows: Tian, X., Tu, L., Yang, M. and Chen, S. (2010) 'Inferential control with the aid of modified QPLS-based soft sensor for an industrial FCCU fractionator', Int.

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Section: The Error-based Nplsmentioning

confidence: 99%

Section: Modified Nplsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Inferential control with the aid of modified QPLS-based soft sensor for an industrial FCCU fractionator

Tian¹,

Ling²,

Yang³

et al. 2010

IJMIC

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Hybrid modeling framework for process analytical technology: Application toBordetella pertussiscultures

Stosch

Oliveria

Peres

et al. 2011

Biotechnology Progress

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In the process analytical technology (PAT) initiative, the application of sensors technology and modeling methods is promoted. The emphasis is on Quality by Design, online monitoring, and closed-loop control with the general aim of building in product quality into manufacturing operations. As a result, online high-throughput process analyzers find increasing application and therewith high amounts of highly correlated data become available online. In this study, an hybrid chemometric/mathematical modeling method is adopted for data analysis, which is shown to be advantageous over the commonly used chemometric techniques in PAT applications. This methodology was applied to the analysis of process data of Bordetella pertussis cultivations, namely online data of near-infrared, (NIR), pH, temperature and dissolved oxygen, and off-line data of biomass, glutamate, and lactate concentrations. The hybrid model structure consisted of macroscopic material balance equations in which the specific reactions rates are modeled by nonlinear partial least square (PLS). This methodology revealed a significant higher statistical confidence in comparison to PLSs, translated in a reduction of mean squared prediction errors (e.g., individual root mean squared prediction errors calibration/validation obtained through the hybrid model for the concentrations of lactate: 0.8699/0.7190 mmol/L; glutamate: 0.6057/0.2917 mmol/L; and biomass: 0.0520/0.0283 OD; and obtained through the PLS model for the concentrations of lactate: 1.3549/1.0087 mmol/L; glutamate: 0.7628/0.3504 mmol/L; and biomass: 0.0949/0.0412 OD). Moreover, the analysis of loadings and scores in the hybrid approach revealed that process features can, as for PLS, be extracted by the hybrid method.

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Orthogonal signal correction: algorithmic aspects and properties

Morris

Martin

2002

Journal of Chemometrics

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The objective of this paper is to present a modified algorithm for the orthogonal signal correction (OSC) filter based on the approaches proposed by Wold, Antti, Lindgren and Öhman (Chemometrics Intell. Lab. Syst. 1998; 44: 175–185) and Fearn (Chemometrics Intell. Lab. Syst. 2000; 50: 47–52). An OSC filter consists of a trio of building blocks: weights, components and loadings, $\font\mathbfit=cmmib10\def\bfit#1{\hbox{\mathbfit #1}} {\bf \{w_{{\bfit j}}, t_{{\bfit j}}, p_{{\bfit j}}\}_{{\bfit j}=1}^{{\bfit A}}}$. The original OSC filter of Wold et al. was based on the framework of the non‐linear iterative partial least squares (NIPALS) algorithm. Adopting this approach enabled the mathematical justification for the selection of the loading vectors p j and components t j, but there was no theoretical foundation for the selection of w j. In contrast, the approach of Fearn described an objective function for the selection of the weight vectors w j, but in this case there is no theoretical justification for either p j or t j. Combining both approaches, within a NIPALS framework, enables a clear theoretical basis for the selection of all three building blocks to be established. A number of orthogonal and optimal properties of the NIPALS‐based OSC algorithm, although previously reported, are also theoretically proven. Finally, it is shown that the modified OSC algorithm is equivalent to Fearn's OSC but is interpretable as a consequence of it being presented from a NIPALS perspective. This enables the possible extension of OSC to dynamic and non‐linear systems. Copyright © 2002 John Wiley & Sons, Ltd.

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Non-linear dynamic projection to latent structures modelling

Cited by 53 publications

References 15 publications

Inferential control with the aid of modified QPLS-based soft sensor for an industrial FCCU fractionator

Inferential control with the aid of modified QPLS-based soft sensor for an industrial FCCU fractionator

Hybrid modeling framework for process analytical technology: Application toBordetella pertussiscultures

Orthogonal signal correction: algorithmic aspects and properties

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