Evaluation of Calibration Equations by Using Regression Analysis: An Example of Chemical Analysis

A calibration curve is used to express the relationship between the response of the measuring technique and the standard concentration of the target analyst. The calibration equation verifies the response of a chemical instrument to the known properties of materials and is established using regression analysis. An adequate calibration equation ensures the performance of these instruments. Most studies use linear and polynomial equations. This study uses data sets from previous studies. Four types of calibration equations are proposed: linear, higher-order polynomial, exponential rise to maximum and power equations. A constant variance test was performed to assess the suitability of calibration equations for this dataset. Suspected outliers in the data sets are verified. The standard error of the estimate errors, s, was used as criteria to determine the fitting performance. The Prediction Sum of Squares (PRESS) statistic is used to compare the prediction ability. Residual plots are used as quantitative criteria. Suspected outliers in the data sets are checked. The results of this study show that linear and higher order polynomial equations do not allow accurate calibration equations for many data sets. Nonlinear equations are suited to most of the data sets. Different forms of calibration equations are proposed. The logarithmic transformation of the response is used to stabilize non-constant variance in the response data. When outliers are removed, this calibration equation’s fit and prediction ability is significantly increased. The adequate calibration equations with the data sets obtained with the same equipment and laboratory indicated that the adequate calibration equations differed. No universe calibration equation could be found for these data sets. The method for this study can be used for other chemical instruments to establish an adequate calibration equation and ensure the best performance.

In situ calibration of two FDR gauges under saline soil conditions in the hyperarid of Chile

A calibration method was developed for two FDR sensors (GS3 and POGO) in saline soil conditions with predominantly fine textures and electrical conductivities that fluctuate between 4.4 and 16.5 dS.m-1. The methodology included the use of infiltration trenches and the recording of the variation of the water content (Ɵ) over time. The results showed that there is an overestimation of Ɵ as a function of the salt content. The standard error obtained with the manufacturer's calibration was 0.09 and 0.19 cm3.cm-3 for GS3 and POGO, respectively. After calibration, the standard error decreased to 0.04 and 0.05 cm3.cm-3, respectively. The R2 of the calibration equations for GS3 and POGO were 0.94 and 0.86 respectively, not being necessary a differentiated calibration by salinity ranges. The GS3 sensor performed better than the POGO in the salinity conditions encountered.

Biomarker-Calibrated Macronutrient Intake and Chronic Disease Risk among Postmenopausal Women

ABSTRACT Background Knowledge about macronutrient intake and chronic disease risk has been limited by the absence of objective macronutrient measures. Recently, we proposed novel biomarkers for protein, protein density, carbohydrate, and carbohydrate density, using established biomarkers and serum and urine metabolomics profiles in a human feeding study. Objectives We aimed to use these biomarkers to develop calibration equations for macronutrient variables using dietary self-reports and personal characteristics and to study the association between biomarker-calibrated intake estimates and cardiovascular disease, cancer, and diabetes risk in Women's Health Initiative (WHI) cohorts. Methods Prospective disease association analyses are based on WHI cohorts of postmenopausal US women aged 50–79 y when enrolled at 40 US clinical centers (n = 81,954). We used biomarker intake values in a WHI nutritional biomarker study (n = 436) to develop calibration equations for each macronutrient variable, leading to calibrated macronutrient intake estimates throughout WHI cohorts. We then examined the association of these intakes with chronic disease incidence over a 20-y (median) follow-up period using HR regression methods. Results In analyses that included doubly labeled water–calibrated total energy, HRs for cardiovascular diseases and cancers were mostly unrelated to calibrated protein density. However, many were inversely related to carbohydrate density, with HRs (95% CIs) for a 20% increment in carbohydrate density of 0.81 (0.69, 0.95) and 0.83 (0.74, 0.93), respectively, for primary outcomes of coronary heart disease and breast cancer, as well as 0.74 (0.60, 0.91) and 0.87 (0.81, 0.93) for secondary outcomes of heart failure and total invasive cancer. Corresponding HRs (95% CIs) for type 2 diabetes incidence in relation to protein density and carbohydrate density were 1.17 (1.09, 1.75) and 0.73 (0.66, 0.80), respectively. Conclusions At specific energy intake, a diet high in carbohydrate density is associated with substantially reduced risk of major chronic diseases in a population of US postmenopausal women. This trial was registered at clinicaltrials.gov as NCT00000611.

Field calibration of DFM capacitance probes for continuous soil moisture monitoring

This study was undertaken to derive textural and lumped site-specific calibration equations for Dirk Friedhelm Mercker (DFM) capacitance probes and evaluate the accuracy levels of the developed calibration equations for continuous soil moisture monitoring in three selected soil types. At each site, 9 probes (3 per plot) were installed in 2 m2 plots, for continuous soil moisture measurements at 5 different depths (viz. 10, 20, 30, 40 and 60 cm) under dry, moist and wet field conditions. Textural site-specific calibration equations were derived by grouping the same soil textural classes of each site regardless of soil depth, while lumped site-specific calibration equations were derived by grouping all datasets from each site, regardless of soil depth and textural classes. Sensor readings were plotted against gravimetrically measured volumetric soil moisture (θv) for different textural classes as a reference. The coefficient of determination (r2) was used to select the best fit of the regression function. The developed calibration equations were evaluated using an independent dataset. The results indicated that all developed textural and lumped site-specific calibration equations were linear functions, withr2 values ranging from 0.96 to 0.99. Relationships between the measured and estimated θv from calibration equations were reasonable at all sites, with r2 values greater than 0.91 and root mean square error (RMSE) values ranging from 0.010 to 0.020 m3∙m-3. The results also indicated that textural site-specific calibration equations (RMSE < 0.018 m3∙m-3) should be given preference over lumped site-specific calibrations (RMSE < 0.020 m3∙m-3) to attain more accurate θv measurements. The findings of this study suggest that once DFM capacitance probes are calibrated per site, they can be reliably used for accurate in-situ soil moisture measurements. The developed calibration equations can be applied with caution in other sites with similar soil types to attained reliable in-situ soil moisture measurements.

Acceleration predicts energy expenditure in a fat, flightless, diving bird

Energy drives behaviour and life history decisions, yet it can be hard to measure at fine scales in free-moving animals. Accelerometry has proven a powerful tool to estimate energy expenditure, but requires calibration in the wild. This can be difficult in some environments, or for particular behaviours, and validations have produced equivocal results in some species, particularly air-breathing divers. It is, therefore, important to calibrate accelerometry across different behaviours to understand the most parsimonious way to estimate energy expenditure in free-living conditions. Here, we combine data from miniaturised acceleration loggers on 58 free-living Adélie penguins with doubly labelled water (DLW) measurements of their energy expenditure over several days. Across different behaviours, both in water and on land, dynamic body acceleration was a good predictor of independently measured DLW-derived energy expenditure (R2 = 0.72). The most parsimonious model suggested different calibration coefficients are required to predict behaviours on land versus foraging behaviour in water (R2 = 0.75). Our results show that accelerometry can be used to reliably estimate energy expenditure in penguins, and we provide calibration equations for estimating metabolic rate across several behaviours in the wild.

Features of сalibration еequations for IR scanners in determining the amino acid composition of soy proteins

Из 20 аминокислот, входящих в состав растительных белков, 17 лучше всего определяются с помощью высокоэффективной жидкостной хроматографии. Но эта технология затратна по времени, в том числе из-за подготовки проб, что делает ее малопригодной при проведении массовых анализов, например при оценке селекционного материала. В этом случае наиболее приемлемы технологии, основанные на сканировании в ближнем инфракрасном диапазоне излучения. Несмотря на то что ИК-сканеры способны по одному калибровочному уравнению выявлять большое количество компонентов, необходима постоянная коррекция при определении состава аминокислот и приведении его в процентное соотношение. В статье рассматриваются варианты создания калибровочных уравнений для расчета аминокислотного состава белков сои с помощью компьютерных программ (Nir 42, ISI), обеспечивающих работу ИК-сканеров типа NIR-4250 или FOSS NIRSystem 5000. Установлено, что при создании калибровочных уравнений содержание каждой аминокислоты наиболее корректно выражать в абсолютных единицах (г на 100 г белка), а не относительных (%). 17 of the 20 amino acids, included in the composition of plant proteins, are most effectively determined using liquid chromatography. The technology of high-performance liquid chromatography is to a certain extent costly in time, among other things because of sample preparation that makes it unsuitable for mass analysis, for example, when evaluating a breeding material. In this case, the technology based on scanning in the near infrared radiation band are the most acceptable. Despite the fact that IR scanners are able to determine a sufficiently large number of components on the basis of one calibration equation, a constant correction is required when determining the composition of amino acids and reducing it to a percentage ratio. The options for creating calibration equations for determining the amino acid composition of soybean proteins for computer programs (Nir 42, ISI), which provide the operation of IR scanners, such as NIR-4250 or FOSS NIRSystem 5000 are considered in the article. It was found that when creating calibration equations, it is most correct to set for each amino acid its mass content (g per 100 g of protein), and not the relative portion (in %).

A Software Improvement Technique for Platinum Resistance Thermometers

Temperature measurement is essential in industries. The advantages of resistance temperature detectors (RTDs) are high sensitivity, repeatability, and long-term stability. The measurement performance of this thermometer is of concern. The connection between RTDs and a novel microprocessor system provides a new method to improve the performance of RTDs. In this study, the adequate piecewise sections and the order of polynomial calibration equations were evaluated. Systematic errors were found when the relationship between temperature and resistance for PT-1000 data was expressed using the inverse Callendar-Van Dusen equation. The accuracy of these calibration equations can be improved significantly with two piecewise equations in different temperature ranges. Two datasets of the resistance of PT-1000 sensors in the range from 0 °C to 50 °C were measured. The first dataset was used to establish adequate calibration equations with regression analysis. In the second dataset, the prediction temperatures were calculated by these previously established calibration equations. The difference between prediction temperatures and the standard temperature was used as a criterion to evaluate the prediction performance. The accuracy and precision of PT-1000 sensors could be improved significantly with adequate calibration equations. The accuracy and precision were 0.027 °C and 0.126 °C, respectively. The technique developed in this study could be used for other RTD sensors and/or different temperature ranges.

Development of a Simplified Radiometric Calibration Framework for Water-Based and Rapid Deployment Unmanned Aerial System (UAS) Operations

The current study sets out to develop an empirical line method (ELM) radiometric calibration framework for the reduction of atmospheric contributions in unmanned aerial systems (UAS) imagery and for the production of scaled remote sensing reflectance imagery. Using a MicaSense RedEdge camera flown on a custom-built octocopter, the research reported herein finds that atmospheric contributions have an important impact on UAS imagery. Data collected over the Lower Pearl River Estuary in Mississippi during five week-long missions covering a wide range of environmental conditions were used to develop and test an ELM radiometric calibration framework designed for the reduction of atmospheric contributions from UAS imagery in studies with limited site accessibility or data acquisition time constraints. The ELM radiometric calibration framework was developed specifically for water-based operations and the efficacy of using generalized study area calibration equations averaged across variable illumination and atmospheric conditions was assessed. The framework was effective in reducing atmospheric and other external contributions in UAS imagery. Unique to the proposed radiometric calibration framework is the radiance-to-reflectance conversion conducted externally from the calibration equations which allows for the normalization of illumination independent from the time of UAS image acquisition and from the time of calibration equation development. While image-by-image calibrations are still preferred for high accuracy applications, this paper provides an ELM radiometric calibration framework that can be used as a time-effective calibration technique to reduce errors in UAS imagery in situations with limited site accessibility or data acquisition constraints.

Estimation of NDVI with visible images (RGB) obtained with drones

The NDVI (Normalized Difference Vegetation Index) is a vegetation index widely used to evaluate the health conditions of vegetation, whether preserved or derived from anthropic actions, such as agriculture. NDVI's estimation with drones is still quite precarious as it requires different studies to assess their accuracy. The aim of this study is to evaluate the NDVI estimate obtained with images of the visible attention to radiometric calibrations. Radiometric calibration equations that were widely disseminated for the use of Landsat 5 satellite were used. These equations were used to calibrate drone images. The results showed that the calibrations raised the level of accuracy of NDVI estimates with drone images. It is concluded that it is of paramount importance the radiometric calibration of the images obtained with drones so that they allow more accurate estimates, such as NDVI. The use of drone products to estimate NDVI is quite promising. But it is necessary to study more robust radiometric calibration procedures, increasing the quality of data products from drones and making it more comparable between sites, sensors, and schedules.Estimativa do NDVI com imagens do visível (RGB) obtidas com drones R E S U M OO NDVI (Normalized Difference Vegetation Index) é um índice de vegetação muito utilizado para avaliação das condições de saúde da vegetação, seja ela preservada ou advinda das ações antrópicas, como por exemplo, agricultura. A estimativa do NDVI com drones ainda é bastante precária uma vez que necessita de diferentes estudos para avaliar a precisão deles. O objetivo deste estudo é avaliar a estimativa do NDVI obtidas com imagens do visível atentando para as calibrações radiométricas. Foram utilizadas equações de calibração radiométricas bastantes difundidas para uso do satélite Landsat 5. Essas equações foram utilizadas para calibração de imagens de drones. Os resultados mostraram que as calibrações elevaram o nível de acurácia das estimativas do NDVI com imagens de drones. Conclui-se que é de suma importância a calibração radiométrica das imagens obtidas com drones para que elas possibilitem estimativas mais precisas, como por exemplo o NDVI. O uso de produtos de drones para estimativa de NDVI é bastante promissor. Mas, se faz necessário o estudo de mais procedimentos robustos de calibração radiométrica, aumentando a qualidade dos produtos de dados advindos de drones e tornando mais comparáveis entre sites, sensores e horários.Palavras-chave: Calibração radiométrica, condições ambientais, monitoramento.