PLS Estimation Research Articles

Moving average PLS soft sensor for online product quality estimation in an industrial batch polymerization process

This paper considers the development of multivariate statistical soft sensors for the online estimation of product quality in a real-world industrial batch polymerization process. The batches are characterized by uneven length, non-reproducible sequence of processing steps, and scarce number of measurements for the quality indicators with uneven sampling of (and lag on) these variables. It is shown that, for the purpose of quality estimation, the complex series of operating steps characterizing a batch can be simplified to a sequence of three estimation phases. The switching from one phase to the other one can be triggered by easily detectable events occurring in the batch. For each estimation phase, PLS software sensors are designed, and their performance is evaluated against plant data. The estimation accuracy can be substantially improved if some form of dynamic information is included into the models, either by augmenting the process data matrix with lagged measurements, or by averaging the process measurements values on a moving window of fixed length. In particular, the moving average three-phase PLS estimator shows the best overall performance, providing accurate estimations also during estimation Phase 2, which is characterized by a very large variability between batches.

Measuring and diagnosing innovation excellence – simple contra advanced approaches: a Danish study

PurposeThe purpose of this paper is to examine two approaches to measure and diagnose innovation excellence.Design/methodology/approachThe paper is a conceptual model for innovation excellence and a measurement system is developed. A Danish survey forms the empirical basis for the study, where a simple approach (by using stated importance of different innovation activities) and an advanced approach (by using derived importance based on structural equation modelling and PLS estimation) are demonstrated, discussed and compared.FindingsThe findings in this paper indicate good support for the developed model. When comparing the two approaches for identifying and prioritising improvements, both equalities and differences are found and discussed.Research limitations/implicationsThis study in this paper is limited to one Danish manufacturing company, which is considered to be one of the most innovative and excellent companies in Denmark. However, it is desirable to apply the model in other companies and industries.Practical implicationsThis paper offers a model to understand and measure innovation results and its enablers, and the application of the model will give companies a better chance of attaining innovative excellence.Originality/valueThe paper provides a novel model for innovation excellence, which is based on a solid theoretical foundation, has been proven in practice, and can be an effective framework for identifying and prioritising improvements within innovation.

Buying a sponsor's brand: the role of affective commitment to the sponsored team

Sponsorship is increasingly important in a firm's communication mix. Research to date has focused on the impact of sponsorship on brand awareness and its subsequent consequences for image congruency and consumer attitudes towards sponsors' brands. A lesser studied area is the effect of sponsorship on consumers' purchase intentions and behaviours. We argue that existing models of sponsorship driven purchase behaviour fail to account for affective commitment, which mediates relationship between affiliation with the team and social identification with the team. We propose a modified framework describing the effect of sponsorship on purchase intentions in the context of low and high performing sports teams. The framework is tested using structural equations modelling; employing PLS estimation and data collected via online survey of AFL chat room participants. Results confirm the role of affective commitment in sport sponsorship purchase intentions and indicate that team success has a significant influence on fans' purchase behaviours.

MULTIVARIATE STATISTICAL ESTIMATION OF PRODUCT QUALITY IN THE INDUSTRIAL BATCH PRODUCTION OF A RESIN

A multivariate statistical estimator of the product quality is developed for an industrial batch polymerization process producing a resin. It is shown that, for the purpose of quality estimation, the complex series of operating steps through which a batch is run can be simplified to a sequence of three estimation phases. For each phase, a PLS model for the estimation of the product quality is developed. Switching between one phase to the other one is triggered by easily detectable landmark events occurring in a batch. The performance of the resulting three-phase PLS estimator is very satisfactory.

Partial least squares regression with Curds and Whey

In order to make use of information between correlated responses in calibration, a new PLS method called PLS with Curds and Whey (PLS-C&W) is introduced. It combines PLS regression with a canonical analysis between the PLS estimates and the responses. The estimates are suitably shrunk in the canonical co-ordinate system using generalized cross-validation (GCV). The results obtained from five data sets show that PLS-C&W methods yield calibration models of high prediction ability.

Calculation of PLS prediction intervals using efficient recursive relations for the Jacobian matrix

AbstractSeveral algorithms to calculate the vector of regression coefficients and the Jacobian matrix for partial least squares regression have been published. Whereas many efficient algorithms to calculate the regression coefficients exist, algorithms to calculate the Jacobian matrix are inefficient. Here we introduce a new, efficient algorithm for the Jacobian matrix, thus making the calculation of prediction intervals via a local linearization of the PLS estimator more practicable. Copyright © 2004 John Wiley & Sons, Ltd.

Calibration with absolute shrinkage

AbstractIn this paper, penalized regression using the L1 norm on the estimated parameters is proposed for chemometric calibration. The algorithm is of the lasso type, introduced by Tibshirani in 1996 as a linear regression method with bound on the absolute length of the parameters, but a modification is suggested to cope with the singular design matrix most often seen in chemometric calibration. Furthermore, the proposed algorithm may be generalized to all convex norms like ∑|β j|γ where γ ≥ 1, i.e. a method that continuously varies from ridge regression to the lasso. The lasso is applied both directly as a calibration method and as a method to select important variables/wavelengths. It is demonstrated that the lasso algorithm, in general, leads to parameter estimates of which some are zero while others are quite large (compared to e.g. the traditional PLS or RR estimates). By using several benchmark data sets, it is shown that both the direct lasso method and the regression where the lasso acts as a wavelength selection method most often outperform the PLS and RR methods. Copyright © 2001 John Wiley & Sons, Ltd.

Calibration with absolute shrinkage

In this paper, penalized regression using the L1 norm on the estimated parameters is proposed for chemometric calibration. The algorithm is of the lasso type, introduced by Tibshirani in 1996 as a linear regression method with bound on the absolute length of the parameters, but a modification is suggested to cope with the singular design matrix most often seen in chemometric calibration. Furthermore, the proposed algorithm may be generalized to all convex norms like ∑|β j|γ where γ ≥ 1, i.e. a method that continuously varies from ridge regression to the lasso. The lasso is applied both directly as a calibration method and as a method to select important variables/wavelengths. It is demonstrated that the lasso algorithm, in general, leads to parameter estimates of which some are zero while others are quite large (compared to e.g. the traditional PLS or RR estimates). By using several benchmark data sets, it is shown that both the direct lasso method and the regression where the lasso acts as a wavelength selection method most often outperform the PLS and RR methods. Copyright © 2001 John Wiley & Sons, Ltd.

Corrections: Comparisons of Prediction Methods When Only a Few Components are Relevant

Proposition 3 in this article is said to give an asymptotic formula for the prediction error of the (modified) maximum likelihood predictor under the hypothesis of one relevant component for prediction. It is more correct to say that this formula gives the Cramer-Rao lower bound and the asymptotical prediction error for an efficient version of the maximum likelihood predictor. The point is that the likelihood function has several local maxima. By Lehmann (1983), theorem 6.2.3, any consistent sequence of roots of the likelihood equation is efficient, and because the PLS estimator is consistent in this situation, it is better to choose the root of the likelihood equation that is closest to PLS (as measured by the closeness of the regression vectors) than to search for the absolute maximum. Doing this in the simulations systematically leads to improvement of the MML solution, except for the largest irrelevant eigenvalues in Table 1, correspondinig to a rather extreme situation. The values for MML in Table 2 turn out to be about the same as those for PLS. When n is large or the signalto-noise ratio is small, MML performs slightly better than PLS. For instance, in a factorially designed simulation experiment with m = 1 relevant component and two values for n, for p, for the squared multiple correlation coefficient Y? 2, and for each of three parameters characterizing the irrelevant eigenvalues, the mean values of the mean squared prediction errors were:

Predictive binding of beta-carboline inverse agonists and antagonists via the CoMFA/GOLPE approach.

The synthesis and affinities of six new 3-substituted beta-carbolines (6-10, 12) for the benzodiazepine receptor (BzR) are described. These analogs were used both to probe the dimensions of the hydrophobic pocket in the benzodiazepine receptor and to test the predictive ability of a previously reported 3D-QSAR regression model. Of the new analogs synthesized, the gamma-branched derivatives (isobutoxy, 7, IC50 = 93 nM; isopentoxy, 9, IC50 = 104 nM) display significantly higher affinity for the BzR than either the beta-branched (sec-butoxy, 6, IC50 = 471 nM; tert-butyl ketone, 12, IC50 = 358 nM) or delta-branched (isopentoxy, 8, IC50 = 535 nM) analogs. An exception to this rule is the gamma-branched 3-benzyloxy derivative 10 (IC50 > 1000 nM) which appears to have a chain length that is too long to be accommodated by the BzR. The standard error of prediction for these six new beta-carbolines using the original regression model is significantly lower than the standard error estimate of the cross validation runs on the training set, hence the predictions made using this model are much better than expected. In order to obtain more credible predictions, a new procedure called GOLPE (generating optimal linear PLS estimates) was used to eliminate irrelevant electrostatic and steric descriptors from the regression equation. A substantial reduction in the standard error estimate resulted. The predictions from this new regression equation were somewhat less accurate than the ones obtained with the original regression equation; however the standard error of prediction and the standard error estimate are in much closer agreement. Finally, to probe the effect that the quality of the steric and electrostatic potentials has on 3D-QSAR analyses, the semiempirical MNDO parallel PRDDOE geometries and Mulliken charges used in the original analyses were replaced with ab initio 3-21G parallel 6-31G* geometries and electrostatic potential fit charges. A modest decrease in the standard error estimate and increase in cross validated R2 resulted.

Robust inferential control for a packed-bed reactor

In this paper, two different inferential control schemes are applied to an experimental fixed bed methanation reactor. The first scheme, proposed initially by Brosilow, is designed based on Kalman filter estimation. The second less traditional design uses an estimator computed from the partial least squares regression method (PLS). The second approach was found to give superior performance when the nonlinear system under study is operated in a wide range of operating points. Due to the nonlinearity of the system it is essential to address the issue of robustness of the proposed schemes. This is formally done in this work using structured singular value theory. For the robustness analysis it is crucial to develop a realistic but not overly conservative uncertainty description. Since the PLS estimator uses a large number of measurements, a robust design based on the uncertainty associated with each one of the measurements, a robust design based on the uncertainty associated with each one of the measurements would be very conservative. To overcome this problem, a lumped uncertainty description is proposed which is identified directly form experiments.