Comparison of methods for estimation of the covariance matrix of measurement errors

Feital, Thiago; Prata, Diego Martinez; Pinto, José Carlos

doi:10.1002/cjce.22063

Cited by 11 publications

(3 citation statements)

References 16 publications

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“…In addition, it could suggest that estimating the error relative to the different samples could be of interest if the result has to be used in further calculations to modify the algorithm [42] or determine uncertainty of models [17,43]. The results set the scene for further works that could include the investigation and evaluation of other methods for the estimation of covariance matrices of the measurement errors [44] and the comparison with covariance matrices constructed [45] by incorporating known sources of errors. Another interesting aspect could deal with the propagation of error when applying signal filters (as studied for the Kalman Filter [46]) or spectra preprocessing [47].…”

Section: Study Of the Influences Of Time Of Background And Sessionmentioning

confidence: 99%

On the Importance of Investigating Data Structure in Miniaturized NIR Spectroscopy Measurements of Food: The Case Study of Sugar

Gorla

Taborelli

Alamprese

et al. 2023

Foods

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Alongside the increasing proofs of efficacy of miniaturized NIR instruments in food-related scenarios, it is progressively growing the number of end-users, even incentivized by the low-cost of the sensors. While attention is paid to the analytical protocol–from sampling to data collection, up to the data processing, the importance of error investigation in raw data is generally underestimated. Understanding the sources and the structure of uncertainty related to the raw data improves the quality of measurements and suggests the correct planning of the experiments, as well as helps in chemometric model development. The goal of chemometric modeling is to separate information from noise; therefore, a description of the nature of measurement error structure is necessary. Among the different approaches, we present the study of the Error Covariance Matrices (ECMs) and their decomposition in a bilinear structure as a powerful method to study the main sources of variability when using miniaturized NIR sensors in the actual way of use. Granulated and lump sugar samples were chosen as the case study and analyzed with two miniaturized spectrometers working in the NIR regions around 1350–2550 nm and 900–1750 nm, respectively, in dispersive reflectance mode. Results show that having some insights on multivariate measurement errors associated with spectra could be interesting in paving the way for several applications.

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Section: Study Of the Influences Of Time Of Background And Sessionmentioning

confidence: 99%

On the Importance of Investigating Data Structure in Miniaturized NIR Spectroscopy Measurements of Food: The Case Study of Sugar

Gorla

Taborelli

Alamprese

et al. 2023

Foods

View full text Add to dashboard Cite

show abstract

“…The first stages of the implemented procedure involved pre-treatment and characterization of the data. As a matter of fact, proper understanding of some characteristics of the data are fundamental for adequate implementation of the data reconciliation stage [24]. The initial characterization of the data was performed offline and using historical data available in the data acquisition system of the industrial site.…”

Section: Methodsmentioning

confidence: 99%

Modeling of Spiral Wound Membranes for Gas Separations—Part II: Data Reconciliation for Online Monitoring

et al. 2020

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The present work presents a methodology based on data reconciliation to monitormembrane separation processes reliably, online and in real time for the first time. The proposed methodology was implemented in accordance with the following steps: data acquisition; data pre-treatment; data characterization; data reconciliation; gross error detection; and critical evaluation of measured data with a soft sensor. The acquisition of data constituted the sloweststage of the monitoring process, as expected in real-time applications. The pre-treatment stage was fundamental to assure the robustness of the code and the initial characterization of collected datawas carried out offline. The characterization of the data showed that steady-state modeling of the process would be appropriate, also allowing the implementation of faster numerical procedures for the data reconciliation step. The data reconciliation step performed well, quickly and consistently. Thus, data reconciliation allowed the estimation of unmeasured variables, playing the role of a soft sensor and allowing the future installation of a digital twin. Additionally, monitoring of measurement bias constituted a tool for measurement diagnosis. As shown in the manuscript, the proposedmethodology can be successfully implemented online and in real time for monitoring of membrane separation processes, as shown through a real dashboard web application developed for monitoring of an actual industrial site.

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“…This requires the uncertainties of measurements to be evaluated somehow, which is not always easy. Regarding on-line operational measured data, which may contain gross errors, the standard deviation of measurement data may not be suitable for uncertainty evaluation and some techniques have been proposed for on-line characterization of process data for real-time applications [157,158]. An alternative to evaluate the standard deviations of measurement errors based on measuring instrument nominal accuracy is [159]:…”

Section: A Short Note On the Performance Metricmentioning

confidence: 99%

Numerical Aspects of Data Reconciliation in Industrial Applications

et al. 2017

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Abstract:Data reconciliation is a model-based technique that reduces measurement errors by making use of redundancies in process data. It is largely applied in modern process industries, being commercially available in software tools. Based on industrial applications reported in the literature, we have identified and tested different configuration settings providing a numerical assessment on the performance of several important aspects involved in the solution of nonlinear steady-state data reconciliation that are generally overlooked. The discussed items are comprised of problem formulation, regarding the presence of estimated parameters in the objective function; solution approach when applying nonlinear programming solvers; methods for estimating objective function gradients; initial guess; and optimization algorithm. The study is based on simulations of a rigorous and validated model of a real offshore oil production system. The assessment includes evaluations of solution robustness, constraint violation at convergence, and computational cost. In addition, we propose the use of a global test to detect inconsistencies in the formulation and in the solution of the problem. Results show that different settings have a great impact on the performance of reconciliation procedures, often leading to local solutions. The question of how to satisfactorily solve the data reconciliation problem is discussed so as to obtain improved estimates.

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Comparison of methods for estimation of the covariance matrix of measurement errors

Cited by 11 publications

References 16 publications

On the Importance of Investigating Data Structure in Miniaturized NIR Spectroscopy Measurements of Food: The Case Study of Sugar

On the Importance of Investigating Data Structure in Miniaturized NIR Spectroscopy Measurements of Food: The Case Study of Sugar

Modeling of Spiral Wound Membranes for Gas Separations—Part II: Data Reconciliation for Online Monitoring

Numerical Aspects of Data Reconciliation in Industrial Applications

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