Estimation of the variance of sampling of process analytical and environmental emissions measurements

Paakkunainen, Maaret; Рейникайнен, Сату-Пиа; Minkkinen, Pentti

doi:10.1016/j.chemolab.2006.11.001

Cited by 13 publications

(5 citation statements)

References 4 publications

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“…The idea of utilizing variogram for variable selection comes from the fact that a variogram of particular measurement holds the information about the relative error levels of the sampling and analysis of that measurement. Variogram is a fundamental tool within Theory of Sampling (Gy, 2004) and has already been considered in drift estimation (Paakkunainen et al, 2007), temporal uncertainty propagation (Jalbert et al, 2011), fault diagnosis (Kouadri et al, 2012), statistical process control (Minnit, Pitard, 2008), and as a process stability measure (Bisgaard, Kulachi, 2005).…”

Section: Variable Selection Using Variogrammentioning

confidence: 99%

A Variogram-Based Tool for Variable Selection in a Wastewater Treatment Effluent Prediction

Ohenoja

Tomperi

2018

Linköping Electronic Conference Proceedings

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In this study, a variogram method was utilized as a variable selection tool for finding the optimal subsets of variables for developing predictive models for the quality of wastewater treatment effluent. The quality of effluent was here assessed by biological and chemical oxygen demand and suspended solids in biologically treated wastewater. The dataset included, in addition to traditional process measurements, results of a novel optical monitoring device which was used for imaging an activated sludge process in-situ during a period of over one year. The study showed that the variogram based method has potential in fast and computationally easy variable selection. The developed models can be used for proactive monitoring and estimating the quality of effluent in several stages hours before in comparison to laboratory analysis taken from treated wastewater.

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Section: Variable Selection Using Variogrammentioning

confidence: 99%

A Variogram-Based Tool for Variable Selection in a Wastewater Treatment Effluent Prediction

Ohenoja

Tomperi

2018

Linköping Electronic Conference Proceedings

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“…If there is correlation between the uncertainty components, it has to be taken into account by determining their covariance. However, it is often possible to evaluate the combined effect of several components, thus reducing the overall effort involved in the evaluation of the contribution of correlated uncertainty components . Combined uncertainty is calculated using the law of propagation of uncertainty (Equation ).…”

Section: Theorymentioning

confidence: 99%

Evaluation of variation in dynamic processes via online spectrometers

Kohonen

Alatalo

Рейникайнен

2012

Journal of Chemometrics

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Theory of sampling offers powerful tools for process optimization. An adequate sampling interval can be determined for spectral measurements when utilizing a multivariate extension of variography by applying score vectors as independent sources of uncertainty. The traditional way is to apply variographic analyses into single process variables independently. In the multivariate extension, those process variables are replaced with score vectors of principal component analysis. The combined uncertainty found this way depends not only on the variance in the spectra, but also, for example, on the number of utilized score vectors and the preprocessing method. This approach is illustrated with a crystallization process continuously followed with an attenuated total reflectance Fourier transform infrared instrument. The results show that the approach is highly applicable but should only be utilized as an indicative tool. Copyright © 2012 John Wiley & Sons, Ltd.

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“…However, too many samples may be redundant and not independent, since measurement errors are often auto-correlated [36]. For example, uniform sampling during the adaptation phase and the stable phase will lead to redundant and useless samples, because the number of cells in the sample does not change much [37]. A large number of samples will consume experimental resources and only resulting in many similar results.…”

Section: Introductionmentioning

confidence: 99%

A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling

Zhang

2021

Water

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As an important primary producer in aquatic ecosystems, the various parameters within the mathematical models are used to describe the growth of microalgae and need to be estimated by carefully designed experiments. Non-uniform sampling has proved to generate a deliberately optimized sampling temporal schedule that can benefit parameter estimation. However, the current non-uniform sampling method depends on prior knowledge of the nominal values of the model parameters. It also largely ignores the uncertainty associated with the nominal values, thus inducing unacceptable parameter estimates. This study focuses on the uncertainty problem and describes a new sampling design that couples the traditional uniform and non-uniform sampling schedules to benefit from the merits of both methods. Based on D-optimal design, we first derive the non-uniform optimal sampling points by maximizing the determinant of the Fisher information matrix. Then the confidence interval around the non-uniform sampling points is determined by Monte Carlo simulations based on the prior knowledge of parameter distribution. Finally, we wrap the non-uniform sampling points with the uniform sampling points within the confidence interval to obtain the ultimate optimal experimental design. Scenedesmus obliquus, whose growth curve follows a four-parameter model, was used as a case study. Compared with the traditional sampling design, the simulation results show that our proposed coupled sampling schedule can partly eliminate the uncertainty in parameter estimates caused by fixed systematic errors in observations. Our coupled sampling can also retain some advantages belonging to non-uniform sampling, in exploiting information maximization and managing the cost of sampling.

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Estimation of the variance of sampling of process analytical and environmental emissions measurements

Cited by 13 publications

References 4 publications

A Variogram-Based Tool for Variable Selection in a Wastewater Treatment Effluent Prediction

A Variogram-Based Tool for Variable Selection in a Wastewater Treatment Effluent Prediction

Evaluation of variation in dynamic processes via online spectrometers

A Coupled Sampling Design for Parameter Estimation in Microalgae Growth Experiment: Maximizing the Benefits of Uniform and Non-Uniform Sampling

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