Propagation Of Random Errors Research Articles

Multimodel quantification of green and blue water components and its error propagations through parameter transferability approach across input choices

A robust quantitative assessment of water security through efficient water accounting concepts like blue and green water footprints has gained a lot of attention for water resources management at river basin scale. However, such water accounting tools and models have dependencies to the choice of precipitation data used to drive the model, as the input bias propagate into simulated streamflow through interaction with different hydrological processes. This study performs a holistic investigation of sensitivity of water accounting fractions like blue water flow (BWF), green water flow (GWF), green water storage (GWS), and their dependencies on secondary precipitation datasets (SPDs) choices using a lumped conceptual rainfall-runoff model [Hydrological Simulation model (HYSIM)] and a physically based semi-distributed hydrological model [Soil and Water Assessment Tool (SWAT)] in the Damodar River basin, India. These models were driven by seven gridded precipitation datasets, including India Meteorological Department (IMD) data, Indian Monsoon Data Assimilation and Analysis (IMDAA) data, Asian Precipitation-Highly-Resolved Observational Data Integration Towards Evaluation (APHRODITE) data, Watch forcing ERA-Interim data, Climate Hazard Group Infrared Precipitation with Station data (CHIRPS), PRINCETON precipitation data and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Network-Climate Data Records (PERSIANN-CDR) data. The reference IMD based multimodel results revealed that the annual average blue and green water components of the Damoder River were in the range of 558–656 mm/year, 574–728 mm/year and 34–112 mm/year for BWF, GWF, and GWS respectively during 1994–2010 period. The results obtained after applying parameter transferability approach across the input space have revealed exact quantification of choice dependent annual variations in spatial and temporal characteristics of BWF, GWF, and GWS. A further evaluation based on error propagation ratios (γCC, γrRMSE, γB) has revealed a quantification of input choice induced dampening/magnification effects on flow estimations of both the HYSIM and SWAT and these quantifications were free from the compensation effects of recalibration. The findings in this study demonstrate that the change in annual average BWF varies between −46.97% to +41.38% in comparison to benchmark IMD simulations, and the corresponding changes for GWF is between −19.63% and +17.06% and for GWS is between −29.97% to +35.5% with different choices of SPD scenarios. The systematic (γB) and random (γrRMSE) error propagation factors during monsoon season are larger for SWAT model ([0.21–0.78], [0.69–0.89] respectively) than that of HYSIM model ([0.18–0.74], [0.66–0.81], respectively) and it is varying with choice of different SPDs.

Random error analysis of normalized Fourier coefficient in dual-rotating compensator Mueller matrix ellipsometer

Ever since the dual-rotating compensator Mueller matrix ellipsometer (DRC-MME) was developed, improving its measurement accuracy has been an important research topic. Studies indicate that the measurement errors in the Mueller matrix of a DRC-MME, including systematic and random errors, significantly influence the measurement accuracy. Accordingly, this study focuses on random errors. A numerical formula for the random errors of normalized Fourier coefficients was derived and applied to estimate the random errors of the measured Mueller matrix. The formula was validated through simulations and experiments. Furthermore, the use of a random error propagation formula to minimize effect of random error on the final measurement results by setting appropriate configurations, including those of software and hardware, was demonstrated. Finally, for real-time measurements, an improved merit function for nonlinear regression algorithms (such as by Levenberg–Marquardt) is proposed.

Parameters' Confidence Intervals Evaluation for Heterogeneous Strain Field Specimen Designs by Using Digital Image Correlation

This paper aims to compare different heterogeneous test designs from the perspective of the confidence interval quantification of inversely identified parameters, where the influence of a DIC optical system systematic and random error are taken into account. Because the errors in optical measurement can arise from many reasons and sources, our methodology relies on the system's errors determined from initial sets of pictures acquired at the load-free state for hundreds of specimens (over 850 tests over the past three years). In this way, a prior probability distribution of systematic and random error, arisen from the system initial settings and testing procedures are determined. Further, by conducting an inverse identification procedure of linear orthotropic elastic material parameters, the influence of the error distributions is studied for different types of heterogeneous specimens. The presented methodology determines the DIC bias and random error propagation through the inverse identification procedure to individual parameters. For each specimen design, confidence intervals of identified material parameters were determined. The results show the appropriateness of a specimen design for the identification of particular material parameters.

Propagation of Random Errors by the Discrete Wavelet Transform Algorithm

The paper presents considerations concerning the transfer of random errors from the input to the output of the Discrete Wavelet Transform (DWT) algorithm. The concept of determining an uncertainty of its output data based on the probabilistic error description has been presented. The DWT is discussed as the product of the vector of input quantities and the matrix of algorithm coefficients. Calculations of the uncertainty of a single output result of the algorithm are described with assumption that the input quantities are burdened by random errors of known distributions. Theoretical considerations have been verified by simulation experiments using the Monte Carlo method. Determining the uncertainty at the DWT output is possible due to the specific properties of transferring random errors by linear and additive algorithms.

Uncertainty-based weighted least squares density integration for background-oriented schlieren

We propose an improved density integration methodology for Background Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. The method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge show a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.

The effect of weights observation to estimate the monitoring control point coordinate at sermo dam

The use of weights observation was effected on the estimation of coordinates and its precision. This research aims to identify 3D coordinates and its precision using weights observation from the result of GAMIT processing and the law of error propagation in sequential adjustment method. This research uses GNSS observation data from 10 deformation monitoring control points around Sermo Dam that was measured on doy 250 in 2014 and doy 129 in 2015. Data processing was performed by GAMIT software to get a baseline length and its precision. Baseline length and its precision were used as input in the sequential adjustment method. The values of weight observation were calculated using the result of GAMIT processing and the law of error propagation. The result of this research are 3D coordinates control point and its precision. The coordinate results using weight observation from GAMIT result does not significantly different from the law of random error propagation result, whereas the precision result is different significantly. The differences of precision reached 2 centimetres.

Random error propagation and uncertainty analysis in the dynamic characterization of Tilting Pad Journal Bearings

In this work a new statistical method for the determination of the dynamic coefficients of Tilting Pad Journal Bearings is described. The method is applied to the results obtained testing a 5 pads tilting pad journal bearing with 280 mm diameter. Tests were performed on an advanced experimental apparatus specifically realized for investigations on large size high performance bearings for turbomachinery. The linear coefficient identification procedure is based on the dynamic measurement of forces, accelerations and relative displacements of rotor and bearing, as function of excitation frequency for different operating conditions. The postprocessing of the dynamic data is performed in the frequency domain using the Fast Fourier Transform. Along with a description of the experimental test and identification procedure, this paper presents a least-square minimization technique for determining the dynamic coefficients and a bootstrap statistical technique for estimating their confidence intervals.

Plant carbon assimilation rates in atmospheric CO2 reconstructions.

Fossil plant gas-exchange-based CO2 reconstructions use carbon (C) assimilation rates of extant plant species as substitutes for assimilation rates of fossil plants. However, assumptions in model species adoption can lead to systematic error propagation. We used a dataset of c. 2500 extant species to investigate the role of phylogenetic relatedness and ecology in determining C assimilation, an essential variable in gas-exchange-based CO2 models. We evaluated the effect on random and systematic error propagation in atmospheric CO2 caused by adopting different model species. Phylogenetic relatedness, growth form, and solar exposure are important predictors of C assimilation rate. CO2 reconstructions that apply C assimilation rates from modern species based solely on phylogenetic relatedness to fossil species can result in CO2 estimates that are systematically biased by a factor of >2. C assimilation rates used in CO2 reconstructions should be determined by averaging assimilation rates of modern plant species that are (1) in the same family and (2) have a similar habit and habitat as the fossil plant. In addition, systematic bias potential and random error propagation are greatly reduced when CO2 is reconstructed from multiple fossil plant species with different modern relatives at the same site.

Nutrients in litterfall, forest floor and mineral soils in two adjacent forest ecosystems in Greece

The fluxes of masses and the nutrients Ca, Mg, K, N, P and S were determined in the litterfall of two adjacent forest ecosystems of Hungarian oak (Quercus frainetto L.) and European beech (Fagus sylvatica L.) in a mountainous area of northeastern Greece in 2010–2015. The foliar litterfall for both species reached about 70% of the total litterfall, and was significantly higher from the other two fractions (woody and rest litterfall). The fluxes of masses and nutrients were compared between ecosystems for each fraction separately. Only one significant statistical difference was found, that of K in the woody litterfall. In addition, the stocks of masses and nutrients were calculated in the forest floors and mineral soils of the two ecosystems. Likewise, the stocks of nutrients in the forest floors and mineral soils were compared between ecosystems. In the L horizon of the forest floors, statistical differences, as a result of species effect, were found for the stocks of Ca and N. In the FH horizons, the masses and all the nutrient stocks differed significantly, as the beech plot had much higher quantities of organic matter and nutrients. These higher quantities were probably due to low soil temperatures (microclimate) and high acidity in the beech plot (species effect) that slowed down decomposition. In the mineral soils, the propagation of random error derived from random errors of the individual soil layers was an important factor in the statistical comparisons. Because of the soil acidity in the beech plot, the stocks of exchangeable base cations were significantly higher in the oak plot, whereas the other nutrient stocks did not differ.

Less Sacrifice, More Insight: Repeated Low-Volume Sampling of Microbioreactor Cultivations Enables Accelerated Deep Phenotyping of Microbial Strain Libraries.

With modern genetic engineering tools, high number of potentially improved production strains can be created in a short time. This results in a bottleneck in the succeeding step of bioprocess development, which can be handled by accelerating quantitative microbial phenotyping. Miniaturization and automation are key technologies to achieve this goal. In this study, a novel workflow for repeated low-volume sampling of BioLector-based cultivation setups is presented. Six samples of 20 μL each can be taken automatically from shaken 48-well microtiter plates without disturbing cell population growth. The volume is sufficient for quantification of substrate and product concentrations by spectrophotometric-based enzyme assays. From transient concentration data and replicate cultures, valid performance indicators (titers, rates, yields) are determined through process modeling and random error propagation analysis. Practical relevance of the workflow is demonstrated with a set of five genome-reduced Corynebacterium glutamicum strains that are engineered for Sec-mediated heterologous cutinase secretion. Quantitative phenotyping of this strain library led to the identification of a strain with a 1.6-fold increase in cutinase yield. The prophage-free strain carries combinatorial deletions of three gene clusters (Δ3102-3111, Δ3263-3301, and Δ3324-3345) of which the last two likely contain novel target genes to foster rational engineering of heterologous cutinase secretion in C. glutamicum.

Evaluation of Cadastral Work Done Using Total Station Instrument

Total station has become the main tool in most engineering work. Accordingly, evaluation of this work has gained a significant importance. A methodology to evaluate precision of cadastral work done using total station is presented here. The used technique is based on propagation of random errors of quantities measured by total station; i.e., distance and both horizontal and vertical angles. Random error in distance is produced by EDM unit integrated into total station. Whereas, random errors in horizontal and vertical angles are produced by theodolite integrated unit. Moreover, backsight process conducted in field results in addition random error in horizontal angles. This research studies how the above errors affect the resulted rectangular coordinates measured by total station for each observed point. Experiments were done using both simulated and real datasets. Results showed that the calculated errors were close to the expected errors and did not exceed the allowable ones.

Linearity check of an ionisation chamber through 99 mTc half-life measurements

The half-life of 99 mTc was measured at the JRC using the ionisation chamber 'IC1' (type Centronic IG12). The result, T1/2(99 mTc) = 6.00660 (18) h, is in good agreement with literature data. One experiment was performed in IC1's default set-up with the ionisation current being integrated over an air capacitor and read out as a voltage increase over time. This ensured excellent linearity and precision throughout the dynamic range, but the maximum current was limited to 2 nA. In a second test, the current was directly read out with a Keithley 6517 A electrometer. Applying correction factors for the automatic range switching of the electrometer, an acceptable linearity was demonstrated over a range of 12 half-life periods starting at 20 nA. Range switching and autocorrelation of the current readout increase the systematic and random error propagation factors. Piecewise fitting of the decay curve over periods of 6 h yields the same 99 mTc half-life value within 0.04% (0.0025 h) standard deviation over an activity range spanning at least 10 half-life periods (3 orders of magnitude).

Surface Profile Measurement Based on the Concept of Multi-Step Division of Length

Many error separation techniques to separate a surface profile from the parasitic motion of the instrument using multiple sensors and/or multiple scans have been proposed. In recent years, large-scale surface profile measurements have become required. When a measured surface profile is large, the number of sampling points becomes large. As the result, the influence of random error becomes large. Previously, a multi-step technique for the division of length was used to decide the short scale from the large scale. An important requirement of this multi-step technique for the division of length is to keep high accuracy at several key points. We applied this technique to the integration method for surface profile measurement and proposed a combination of the large-scale integration method and the short-scale integration method. The results of the theoretical analysis, simulation, and experiment show that this combination method decreases the influence of random error propagation for surface profile measurement.

Optimization of planar PIV-based pressure estimates in laminar and turbulent wakes

The performance of four pressure estimation techniques using Eulerian material acceleration estimates from planar, two-component Particle Image Velocimetry (PIV) data were evaluated in a bluff body wake. To allow for the ground truth comparison of the pressure estimates, direct numerical simulations of flow over a circular cylinder were used to obtain synthetic velocity fields. Direct numerical simulations were performed for $$Re_\mathrm{D} = 100$$ , 300, and 1575, spanning laminar, transitional, and turbulent wake regimes, respectively. A parametric study encompassing a range of temporal and spatial resolutions was performed for each $$Re_\mathrm{D}$$ . The effect of random noise typical of experimental velocity measurements was also evaluated. The results identified optimal temporal and spatial resolutions that minimize the propagation of random and truncation errors to the pressure field estimates. A model derived from linear error propagation through the material acceleration central difference estimators was developed to predict these optima, and showed good agreement with the results from common pressure estimation techniques. The results of the model are also shown to provide acceptable first-order approximations for sampling parameters that reduce error propagation when Lagrangian estimations of material acceleration are employed. For pressure integration based on planar PIV, the effect of flow three-dimensionality was also quantified, and shown to be most pronounced at higher Reynolds numbers downstream of the vortex formation region, where dominant vortices undergo substantial three-dimensional deformations. The results of the present study provide a priori recommendations for the use of pressure estimation techniques from experimental PIV measurements in vortex dominated laminar and turbulent wake flows.

Archival photogrammetric analysis of river–floodplain systems using Structure from Motion (SfM) methods

AbstractIn this study we evaluate the extent to which accurate topographic data can be obtained by applying Structure from Motion (SfM) photogrammetric methods to archival imagery. While SfM has proven valuable in photogrammetric applications using specially acquired imagery (e.g. from unmanned aerial vehicles), it also has the potential to improve the precision of topographic data and the ease with which can be produced from historical imagery. We evaluate the application of SfM to a relatively extreme case, one of low relative relief: a braided river–floodplain system. We compared the bundle adjustments of SfM and classical photogrammetric methods, applied to eight dates. The SfM approach resulted in data quality similar to the classical approach, although the lens parameter values (e.g. focal length) recovered in the SfM process were not necessarily the same as their calibrated equivalents. Analysis showed that image texture and image overlap/configuration were critical drivers in the tie‐point generation which impacted bundle adjustment quality. Working with archival imagery also illustrated the general need for the thorough understanding and careful application of (commercial) SfM software packages. As with classical methods, the propagation of (random) error in the estimation of lens and exterior orientation parameters using SfM methods may lead to inherent systematic error in the derived point clouds. We have shown that linear errors may be accounted for by point cloud registration based on a reference dataset, which is vital for the further application in quantitative morphological analyses when using archival imagery. Copyright © 2016 John Wiley & Sons, Ltd.

Regional Reproducibility of BOLD Calibration Parameter M, OEF and Resting-State CMRO2 Measurements with QUO2 MRI.

The current generation of calibrated MRI methods goes beyond simple localization of task-related responses to allow the mapping of resting-state cerebral metabolic rate of oxygen (CMRO2) in micromolar units and estimation of oxygen extraction fraction (OEF). Prior to the adoption of such techniques in neuroscience research applications, knowledge about the precision and accuracy of absolute estimates of CMRO2 and OEF is crucial and remains unexplored to this day. In this study, we addressed the question of methodological precision by assessing the regional inter-subject variance and intra-subject reproducibility of the BOLD calibration parameter M, OEF, O2 delivery and absolute CMRO2 estimates derived from a state-of-the-art calibrated BOLD technique, the QUantitative O2 (QUO2) approach. We acquired simultaneous measurements of CBF and R2* at rest and during periods of hypercapnia (HC) and hyperoxia (HO) on two separate scan sessions within 24 hours using a clinical 3 T MRI scanner. Maps of M, OEF, oxygen delivery and CMRO2, were estimated from the measured end-tidal O2, CBF0, CBFHC/HO and R2*HC/HO. Variability was assessed by computing the between-subject coefficients of variation (bwCV) and within-subject CV (wsCV) in seven ROIs. All tests GM-averaged values of CBF0, M, OEF, O2 delivery and CMRO2 were: 49.5 ± 6.4 mL/100 g/min, 4.69 ± 0.91%, 0.37 ± 0.06, 377 ± 51 μmol/100 g/min and 143 ± 34 μmol/100 g/min respectively. The variability of parameter estimates was found to be the lowest when averaged throughout all GM, with general trends toward higher CVs when averaged over smaller regions. Among the MRI measurements, the most reproducible across scans was R2*0 (wsCVGM = 0.33%) along with CBF0 (wsCVGM = 3.88%) and R2*HC (wsCVGM = 6.7%). CBFHC and R2*HO were found to have a higher intra-subject variability (wsCVGM = 22.4% and wsCVGM = 16% respectively), which is likely due to propagation of random measurement errors, especially for CBFHC due to the low contrast-to-noise ratio intrinsic to ASL. Reproducibility of the QUO2 derived estimates were computed, yielding a GM intra-subject reproducibility of 3.87% for O2 delivery, 16.8% for the M value, 13.6% for OEF and 15.2% for CMRO2. Although these results focus on the precision of the QUO2 method, rather than the accuracy, the information will be useful for calculation of statistical power in future validation studies and ultimately for research applications of the method. The higher test-retest variability for the more extensively modeled parameters (M, OEF, and CMRO2) highlights the need for further improvement of acquisition methods to reduce noise levels.

Propagation of Error from Registration Parameters to Transformed Data.

Methods to register two sets of data have existed for quite some time. However, these sets of data are rarely error-free. Consequently, any registration based on this data will be affected by the error. Moreover, if the corresponding registration matrix is then used to transform data from one coordinate system to another, any error from the registration will also get propagated to the transformed data. In this paper, we will characterize this propagation of random error, or noise, through a mathematical perspective and will illustrate its use with data obtained from physical experiments and with quasi-simulated sets of data. In addition, we will discuss the limitations of this propagation of error when systematic bias is present in the data.

Error analysis of cine phase contrast MRI velocity measurements used for strain calculation

Cine Phase Contrast (CPC) MRI offers unique insight into localized skeletal muscle behavior by providing the ability to quantify muscle strain distribution during cyclic motion. Muscle strain is obtained by temporally integrating and spatially differentiating CPC-encoded velocity. The aim of this study was to quantify CPC measurement accuracy and precision and to describe error propagation into displacement and strain. Using an MRI-compatible jig to move a B-gel phantom within a 1.5T MRI bore, CPC-encoded velocities were collected. The three orthogonal encoding gradients (through plane, frequency, and phase) were evaluated independently in post-processing. Two systematic error types were corrected: eddy current-induced bias and calibration-type error. Measurement accuracy and precision were quantified before and after removal of systematic error. Through plane- and frequency-encoded data accuracy were within 0.4mm/s after removal of systematic error – a 70% improvement over the raw data. Corrected phase-encoded data accuracy was within 1.3mm/s. Measured random error was between 1 to 1.4mm/s, which followed the theoretical prediction. Propagation of random measurement error into displacement and strain was found to depend on the number of tracked time segments, time segment duration, mesh size, and dimensional order. To verify this, theoretical predictions were compared to experimentally calculated displacement and strain error. For the parameters tested, experimental and theoretical results aligned well. Random strain error approximately halved with a two-fold mesh size increase, as predicted. Displacement and strain accuracy were within 2.6mm and 3.3%, respectively. These results can be used to predict the accuracy and precision of displacement and strain in user-specific applications.

A new approach to the determination of the uncertainty in neutron diffraction experiments with isotopic substitution method

Neutron diffraction experiment with isotopically substituted substances is a powerful approach claiming to yield unambiguous information about the local atomic structure in disordered materials. This information is expressed in the partial structure factors, and extracting them from a series of measurements requires solution of a set of linear equations that is affected by experimental errors. In this article, we suggest a method for the determination of the optimal set of H/D compositions with or without taking into account the experimental error. For the case of water, our investigations show that the selection of the isotope concentrations and the distribution of measurement time among the various samples have a critical role if one wants to utilize the limited neutron beam time efficiently.It is well known that measurements of pure H2O introduce fairly large errors in the partial structure factors due to its very strong incoherent scattering. In water and methanol as examples, we investigated the propagation of random errors to the partial structure factors using partial pair-correlation functions from molecular dynamics simulation. It is shown in the example of water that it is not worthwhile to measure pure H2O.

Generalized Two-Point Method for Straightness Profile Measurement - Error Propagation and Experimental Results

In the straightness profile measurement of a mechanical workpiece, hardware datums have been the traditional standard. However, when the straightness profile is measured using a scanning displacement sensor set on an X-stage as the hardware datums, output of a displacement sensor includes the signal of straightness profile and the sensor’s parasitic motion, i.e. straightness error motion. Then, error separation techniques of the straightness profile from parasitic motions have been developed. For example, two-point method uses two displacement sensors and separates the sensor’s straightness error motion from the straightness profile. However, the conventional two-point method cannot measure a large-scale workpiece because the large sampling number causes random error amplification. In this article, the influence of the random error of generalized two-point method is shown. As the result of the theoretical analysis and numerical analysis, random error propagation decrease when sampling number increase. Further, experimental results obtained by generalized two-point method with large sampling number are analyzed using Wavelet transform and influence of error of the generalized two-point method is discussed in the space-spatial frequency domain.