Imputação De Dados Faltantes Em Séries Temporais De Concentrações De Material Particulado Inalável

Pinto, Wanderson de Paula; Reisen, Valdério Anselmo; Lima, Gemael Barbosa; Monte, Edson Zambon

doi:10.37423/211004793

Cited by 1 publication

(6 citation statements)

References 27 publications

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“…In light of this factor and considering that the ratios describe the averages that are normally employed for the interpretation of experimental data, ratios were used instead of moments for modeling purposes, as shown in eq 5. The probability distributions of the remaining measured variables, such as concentration C and the zeroth-order moment μ 0 , were assumed to be Gaussian because of the restricted number of replicates normally available in most experimental investigations and the large number of replicates needed (normally larger than 30) to fully characterize the probability distribution of the measurements.…”

Section: Probability Distributionmentioning

confidence: 99%

“…The sample linear correlation coefficient can also be used to infer the expected joint variation of the data obtained in different experiments as ρ x̅ , y̅ = S x̅ , y̅ 2 S x̅ S y̅ which considers two random variables, x and y , and the sample covariance is calculated as S x̅ , y̅ 2 = 1 N R − 1 ∑ j = 1 N R false( x j − x̅ false) ( y j − y̅ ) …”

Section: Measurement Correlationmentioning

confidence: 99%

“…As discussed in Section , the measured variables are subject to random errors. The knowledge of the probability distribution associated with these errors is crucial for the correct determination of the confidence intervals of the obtained results and the inference of the most probable parametric values of the model. ,, Therefore, the probability distributions related to the moments of the population balance model are described in detail in the following paragraphs. It is important to emphasize that the statistical characteristics of moments measured experimentally have been largely disregarded in previous publications in this field.…”

Section: Probability Distributionmentioning

confidence: 99%

“…The sample mean and variance can be used to evaluate the confidence intervals of the true values of the distributions, assuming normality, as discussed in Section . Using the Student’s t distribution, the “true” mean is expected to lie in the following range y̅ − t a , N normalR − 1 N R S y̅ < μ y < y̅ + t a , N normalR − 1 N R S y̅ For a confidence interval a = 95% with N R – 1 = 2 degrees of freedom, it can be calculated that t 0.95,2 = 4.30 and, consequently, y̅ − 3.04 S y̅ < μ y < y̅ + 3.04 S y̅ According to the chi-squared distribution (χ 2 ), the “true” variance is in the following range N R − 1 χ false( 1 − a false) / 2 , N normalR − 1 2 S y̅ 2 < σ y 2 < N R − 1 χ false( 1 + a false) / 2 , N normalR − 1 2 S y̅ 2 In the analyzed case, using the same previously defined confidence level and degree of freedom, χ 0.025,2 2 = 0.0506 and χ 0.975,2 2 = 7.377, achieving<...…”

Section: Measurement Correlationmentioning

confidence: 99%

“…As the measured variables vary through time, the respective autocovariance spectra can also be calculated using C y k = 1 N − k − 1 ∑ i = 1 N − k false( y i − y̅ 0 false) ( y i + k − y̅ k ) where y̅ 0 and y̅ k are the sample means of the first and the last N – k values sampled along the time series, respectively. Table shows the autocorrelation data for the concentration, zeroth-order moment, and the ratios between the moments.…”

Section: Measurement Correlationmentioning

confidence: 99%

See 4 more Smart Citations

Statistical Analyses of a Population Balance Model of a Batch Crystallization Process

Lima,

Barreto Correa,

de Moraes

et al. 2023

Crystal Growth & Design

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Crystallization is a widely employed separation technique that has received significant attention due to its industrial relevance, notably in the pharmaceutical industry. While numerous studies have described the underlying kinetic crystallization phenomena using population balance models, simplifying assumptions are usually considered, such as disregarding variable correlations without accounting for the statistical and numerical consequences. Therefore, this lack of detailed statistical analyses can compromise the reliability of at least some of these results. In this regard, the present work performs the statistical characterization of a potassium sulfate crystallization process with the help of population balance models. In order to do that, the model parameters were determined using reparameterization procedures and experimental data collected from multiple batches to mitigate the undesired effects of high correlation in measured variables, which characterize these experimental systems and respective model parameters. It is shown that the proposed approach can successfully represent the solute concentration, the zeroth-order moment, and the ratios between higher-order and zeroth-order moments, considering the available experimental data set. Particularly, the particle swarm optimization (PSO) method was applied for the characterization of the confidence regions of the parameter values. The obtained results indicate that the model-based quantitative analysis of crystallization models can significantly benefit from more statistical interpretation of parameter estimates and variable correlation effects.

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Section: Probability Distributionmentioning

confidence: 99%