Rolf Ergon - Academia.edu (original) (raw)

Papers by Rolf Ergon

Chemometrics and Intelligent Laboratory Systems, 2009

The projection based multivariate data methods of principal component regression (PCR) and partia... more The projection based multivariate data methods of principal component regression (PCR) and partial least squares regression (PLSR) are well established in the …eld of process monitoring. Use of score and loading plots for visualization is, however, complicated when many components are required for good predictions, and the information is therefore often compressed into less informative T 2 and contribution plots. The score information may, however, be further compressed by projection onto subspaces spanned by the vectors of prediction coe¢ cients for the response variables. This is especially attractive in the case of two response variables, i.e. when the model reduction results in a single score-loading biplot. Contribution vectors for the process variables, as well as a con…dence ellipse, may also be included in such a plot. As illustrated in an industrial data example, such a score-loading-contribution plot provides means of both failure detection and fault diagnosis.

Modeling, Identification and Control: A Norwegian Research Bulletin, 2002

The noise handling capabilities of principal component regression (PCR) and partial least squares... more The noise handling capabilities of principal component regression (PCR) and partial least squares regression (PLSR) are somewhat disputed issues, especially regarding regressor noise. In an attempt to indicate an answer to the question, this article presents results from Monte Carlo simulations assuming a multivariate mixing problem with spectroscopic data. Comparisons with the best linear unbiased estimator (BLUE) based on Kalman filtering theory are included. The simulations indicate that both PCR and PLSR perform comparatively well even at a considerable regressor noise level. The results are also discussed in relation to estimation of pure spectra for the mixing constituents, i.e. to identification of the data generating system. In this respect solutions to well-posed least squares problems serve as references.

Chemometrics and Intelligent Laboratory Systems, 2006

Avhandling (dr.ing.) - Hogskolen i Telemark / Norges teknisk-naturvitenskapelige universitet

In our master degree program in process automation, traditional modeling and control courses are ... more In our master degree program in process automation, traditional modeling and control courses are supplemented by courses in experimental design and chemometrics. A corresponding inter-disciplinary research program supports this innovation in curricular structure. The background for all this is the recent developments in chemometrics and the strong stand this discipline has in the Scandinavian process engineering and industrial communities. The program curriculum and related research results are presented, together with a summary of student and industrial feedback.

Genetic assimilation results from selection on phenotypic plasticity, but quantitative genetics m... more Genetic assimilation results from selection on phenotypic plasticity, but quantitative genetics models of linear reaction norms considering intercept and slope as traits do not fully incorporate the process of genetic assimilation. We argue that intercept-slope reaction norm models are insufficient representations of genetic effects on linear reaction norms, and that considering reaction norm intercept as a trait is unfortunate because the definition of this trait relates to a specific environmental value (zero) and confounds genetic effects on reaction norm elevation with genetic effects on environmental perception. Instead we suggest a model with three traits representing genetic effects that respectively (i) are independent of the environment, (ii) alter the sensitivity of the phenotype to the environment, and (iii) determine how the organism perceives the environment. The model predicts that, given sufficient additive genetic variation in environmental perception, the environmen...

In the first part of the paper, the optimal estimator for normally nonmeasured primary outputs fr... more In the first part of the paper, the optimal estimator for normally nonmeasured primary outputs from a linear and time invariant dynamic system is developed. The estimator is based on an underlying Kalman filter, utilizing all available information in known inputs and measured secondary outputs. Assuming sufficient experimental data, the optimal estimator can be identified by specifying an output error model in a standard prediction error identification method. It is further shown that static estimators found by the ordinary least squares method or multivariate calibration by means of principal component regression (PCR) or partial least squares regression (PLSR) can be seen as special cases of the optimal dynamic estimator. Finally, it is shown that dynamic system PCR and PLSR solutions can be developed as special cases of the general estimator for dynamic systems.

In many cases, vital output variables in, e.g., industrial processes cannot be measured online. I... more In many cases, vital output variables in, e.g., industrial processes cannot be measured online. It is then of interest to estimate these primary variables from manipulated and measured inputs and the secondary output measurements that are available. In order to identify an optimal estimator from input-output data, a suitable model structure must be chosen. The paper compares use of ARMAX and output error (OE) structures in prediction error identification methods, theoretically and through simulations.

Squared prediction errors (SPE) in bfX{\bf X}bfX are discussed in relation to the conventional PLSR v... more Squared prediction errors (SPE) in bfX{\bf X}bfX are discussed in relation to the conventional PLSR versus bidiagonalization model and algorithm issue concerning residual and prediction consistency, with focus on process monitoring and fault detection. Our analysis leads to the conclusion that conventional PLSR based on the NIPALS algorithm is ambiguous in SPE values caused by process faults. The basic reason for this is that the sample residuals are not found as projections onto the orthogonal complement of the space where the scores and regression solution are located, and where also the statistical itTrm2{\it T}^{\rm 2}itTrm2 limit is defined. The alternative non‐orthogonalized PLSR and bidiagonalization (Bidiag2) algorithms, as well as a simple re‐formulation of the NIPALS algorithm (RE‐PLSR), give unambiguous SPE values, and the last two of these also retain orthogonal score vectors. While prediction results from all of these methods in theory are identical, our conclusion is that methods wh...

The well‐known nonlinear iterative partial least squares (NIPALS) algorithm is commonly used for ... more The well‐known nonlinear iterative partial least squares (NIPALS) algorithm is commonly used for computation of components in partial least squares regression (PLSR) with orthogonalized score vectors. Based on generalized inverse formalism, Pell et al.[1] have recently claimed that the NIPALS results are inconsistent with respect to model spaces for residual‐based outlier detection and prediction purposes. This theoretically important result is supported by the present paper, where it is also shown that a simple re‐interpretation of the results from the NIPALS algorithm solves the problem. This is valid for cases with both one and several response variables (PLS1 and PLS2). It is also shown, however, that the price to pay for this solution is that the latent variables in the model will no longer be completely independent of the residual noise. Since the original PLSR model with non‐orthogonal score vectors does not have the same inconsistency, a method for orthogonalization of this ...

Principal component regression (PCR) based on principal component analysis (PCA) and partial leas... more Principal component regression (PCR) based on principal component analysis (PCA) and partial least squares regression (PLSR) are well known projection methods for analysis of multivariate data. They result in scores and loadings that may be visualized in a score-loading plot (biplot) and used for process monitoring. The difficulty with this is that often more than two principal or PLS components have to be used, resulting in a need to monitor more than one such plot. However, it has recently been shown that for a scalar response variable all PLSR/PCR models can be compressed into equivalent PLSR models with two components only. After a summary of the underlying theory, the present paper shows how such two-component PLS (2PLS) models can be utilized in informative score-loading biplots for process understanding and monitoring. The possible utilization of known projection model monitoring statistics and variable contribution plots is also discussed, and a new method for visualization ...

Modeling, Identification and Control: A Norwegian Research Bulletin

Living organisms adapt to changes in environment by phenotypic plasticity and evolution by natura... more Living organisms adapt to changes in environment by phenotypic plasticity and evolution by natural selection (or they migrate). At detailed genetic levels these phenomena are complicated, and quantitative genetics attempts to capture essential processes at a higher abstraction level. Phenotypic plasticity is then commonly modeled by reaction norms, which describe how individual traits in a population are expressed in response to changes in environmental variables. The mean reaction norms are evolvable, and here I present a general quantitative genetics state-space model for evolutionary reaction norm dynamics. Reaction norms make use of a reference environment, which is traditionally set to zero. This is problematic when the reference environment is the environment a population is adapted to, for the reason that this environment is a population property, which in itself may be evolvable. With reference to Ergon (2018), I describe models that take such evolvability into account. The resulting models are fundamentally different from most engineering system models, where given reference values are constant, and therefore without consequences can be set to zero. For simplicity I assume only temporal variations in environment, although there obviously are a lot of spatial variations in nature, and I assume that no mutations are involved. Fundamentals from quantitative evolutionary theory are given in appendices.

Ecology and Evolution

Reaction norms are extensively used in evolutionary modeling of population systems where the indi... more Reaction norms are extensively used in evolutionary modeling of population systems where the individuals have the ability of phenotypic plasticity, that is, where organisms can change their phenotypes in response to changes in the environment (Chevin &

In industrial plants and other types of dynamic systems, it is a common situation that measuremen... more In industrial plants and other types of dynamic systems, it is a common situation that measurements of primary system outputs are not available on-line. The primary outputs may for example be quality properties, that can be determined only through costly laboratory analyses, ie they ...

Journal of Chemometrics, 2010

Journal of Chemometrics, 2014

ABSTRACT Orthogonal projections to latent structures (OPLS) and target projection (TP) are two al... more ABSTRACT Orthogonal projections to latent structures (OPLS) and target projection (TP) are two alternative methods for separation of predicting and non-predicting parts of the predictor matrix in partial least squares regression (PLSR), which can also be applied on principal component regression (PCR). An additional new method called PLSO is developed in the paper. In all three methods, the predicting score vector is a scaled version of the fitted response vector. Otherwise, the resulting score and loading vectors are different, although OPLS and TP are identical within similarity transformations. All these relations are here found by simple projections of the fitted predictor matrix from PLSR or PCR, and the similarities and differences are illustrated in discriminant analysis examples. Copyright © 2014 John Wiley & Sons, Ltd.

Mathematical and Statistical Methods in Food Science and Technology, 2013

Oikos, 2011

Delayed density-dependent demographic processes are thought to be the basis for multi-annual cycl... more Delayed density-dependent demographic processes are thought to be the basis for multi-annual cyclic fluctuations in small rodent populations, but evidence for delayed density dependence of a particular demographic trait is rare. Here, using capture-recapture data from 22 sites collected over nine years, we demonstrate a strong effect of population density with a one-year lag on the timing of the onset of spring reproduction in a cyclically fluctuating population of field voles (Microtus agrestis, L.) in northern England. The mean date for the onset of spring reproduction was delayed by about 24 days for every additional 100 voles/ha in the previous spring. This delayed density dependence is sufficient to generate the type of cyclic population dynamics described in the study system.