Absolute Bias Error Research Articles

In-situ sensor virtualization and calibration in building systems

• In-situ sensor virtualization method is proposed. • In-situ virtual sensor calibration is proposed for reliable virtual sensing in operation. • Application is conducted for real operational systems. • Findings on virtualization strategies are discussed for better virtual sensing. In this study, in-situ sensor virtualization is proposed to overcome physical sensing limitations, including sensor errors and management costs in long-term building operations. Virtualization is achieved by a backup virtual sensor for a target sensor when the physical sensor is faulty during operation. This requires in-situ virtual sensor modeling and a continuous calibration process for effective virtual sensing in operational building energy systems. The main research question is how the in-situ calibration for a virtualized sensor can be formulated without a physical counterpart/benchmark. The proposed virtualization with in-situ calibration was applied to central heating systems serving university campus buildings with real operational datasets obtained by a building automation system. The case study showed (1) the effectiveness of virtualization when the target physical sensor has absolute bias errors more than approximately 1.0 °C, (2) the virtualized sensor errors (the average root mean square error (RMSE) of 0.88 °C in the four days) in operation, and (3) the high-accuracy virtual sensor with an average RMSE of 0.30 °C in a month (in February) from the in-situ calibration. The in-situ calibration in Case 3 decreased the initial virtualized sensor errors by 44.0 % and 32.9 %, respectively, for bias and random errors, by appropriately defining the correction function, the input feature, and the optimal calibration reference value in the mathematical calibration formulation. Based on the findings, two strategies for virtualization and calibration are proposed with their design tools for suitable problem formulation at the design stage, better accuracy in operation, and automated virtualization in the future.

COMPARATIVE STUDY OF SOME ESTIMATORS OF LINEAR REGRESSION MODELS IN THE PRESENCE OF OUTLIERS

The paper examined the performance of five estimation methods using six different outlier percentages (0%, 5%, 10%, 20%, 30% and 40%) and five different sample sizes (20, 40, 60, 100 and 200) were used to investigate effect of sample size on the performance of each of the estimation methods. The study adopted absolute bias, variances, relative efficiency and root mean square errors as comparison criteria through Monte-Carlo experiment and real life data was used to validate the simulation results. The study found that, under 5%, 10%, 20% and 30% outlying condition Robust-MM is the most preferred estimator across all criteria and sample size except using relative efficiency criterion and when the sample size is 40, 200 and 200 under 5%, 20% and 30% outlying condition and using absolute bias criterion respectively while Robust-LTS is the least preferred estimator except when the sample size is 40, 20 ; 40, 20 ; 20, 200 under 5%, 20% and 30% outliers and using absolute bias, variance and root mean square error respectively. Under 40% outlying condition Robust-MM is the most preferred estimator across all criteria and sample size except using relative efficiency and when the sample size is 20. Furthermore, Robust-MM is the most consistent estimator across the comparison criteria except when using relative efficiency and sample size has little or no effect on the performance of the estimators across all the different outlier levels. R Statistical package was used for the data analysis. This study therefore recommends the used of Robust-MM estimator

On the Investigation of Autocorrelation-Based Vector Doppler Method With Plane Wave Imaging.

Although color flow imaging is one of the representative applications of the Doppler method, it can estimate only the velocity component in the direction of ultrasonic propagation, that is, the axial velocity component. The vector Doppler method with high-frame-rate plane wave imaging overcomes such a limitation by estimating the blood flow velocity vectors using the axial velocities obtained by emitting plane waves in multiple directions. The autocorrelation technique can be used for the estimation of the axial velocity using the phase shift of an ultrasonic echo signal between two transmit-receive events. The technique also requires the frequency of the received echo signal. Although the center frequency of the emitted ultrasonic signal is commonly used in the estimation of axial velocities, the center frequency should be estimated from the received signals. In this study, a method for the estimation of the center frequency designed particularly for the high-frame-rate plane wave imaging was developed. The proposed method estimates the wavenumbers of the received signal in lateral and vertical directions to estimate the wavenumber in the axial direction, from which the center frequency was estimated. The beam steering angle was also estimated from the wavenumbers in the two directions. The effect of the proposed method was validated in simulations. The absolute bias error (ABE) and root-mean squared error in estimated velocity vectors obtained by plane wave imaging with three beam steering angles (-15°, 0°, and 15°) were reduced from 9.27% and 14.80% to 1.15% and 8.75%, respectively, by the proposed method. The applicability of the proposed method to in vivo measurements was also demonstrated using the in vivo recordings of human common carotid arteries. Physiologically consistent blood flow velocity distributions were obtained with respect to three subjects using the proposed method.

Alpha Power Extended Inverse Weibull Poisson Distribution: Properties, Inference, and Applications to lifetime data

In this paper, a new four-parameter extended inverse Weibull distribution called Alpha power Extended Inverse Weibull Poisson distribution is introduced using the alpha power Poisson generator. This method adds two shape parameters to a baseline distribution thereby increasing its flexibility and applicability in modeling lifetime data. We study the structural properties of the new distribution such as the mean, variance, quantile function, median, ordinary and incomplete moments, reliability analysis, Lorenz and Bonferroni curves, Renyi entropy, mean waiting time, mean residual life, and order statistics. We use the method of maximum likelihood technique for estimating the model parameters of Alpha power extended inverse Weibull distribution and the corresponding confidence intervals are obtained. The simulation method is carried out to evaluate the performance of the maximum likelihood estimate in terms of their Absolute Bias and Mean Square Error using simulated data. Two lifetime data sets are presented to demonstrate the applicability of the new model and it is found that the new model has superior modeling power when compare to Inverse Weibull distribution, Alpha Power Poisson inverse exponential distribution, Alpha Power Extended Inverse Weibull distribution, and Alpha Power Extended Inverse Exponential distribution.

Estimation of higher heating value (HHV) of bio-oils from thermochemical liquefaction by linear correlation

With increasing interest in renewable energy sources, particularly on biomass, and on the technologies to transform them into liquids fuels comes the need to assess its properties. One of the processes that can convert biomass into liquid fuel, bio-oil, is thermochemical liquefaction. However, the experimental determination of many properties can be time and budget consuming. Thus, the numerical models’ development to compute the higher heating value (HHV), with high accuracy, is needed. This work developed a model based on the linear correlation of a dataset composed of 54 samples. The carbon, hydrogen and oxygen content was correlated with HHV to develop a model. The model was compared with other from literature and finally validated with nine samples. Overall, the model exhibited excellent prediction accuracy. The absolute bias error was relatively low, 0.01%. Besides, the model’s good accuracy could be verified by the low absolute average error, 1.48%. The model’s good precision and performance was also demonstrated by the mean absolute error’s low value.

Simplified multiple linear regression models for the estimation of heating values of refuse derived fuels

With the increasing concerns about fossil fuel’s impact on the environment and its expected depletion, the world strives for new and alternative energy sources. It is believed that biomass and residues are crucial tools to aid in the so required reduction of fossil fuels. One of those sources can be the municipal solid waste (MSW), particularly refused derived fuels (RDFs). With population growth, MSW management is a real problem that must be addressed. However, when carrying preliminary or screening evaluations of residue to assess its calorific value, the resources should be kept as minimum as possible to be the least expensive as possible. The development of empirical and numerical models, with high accuracy, to estimate de calorific value can be useful to decrease the need for experimental data. With a large dataset of RDFs (443 samples), this work developed predictive models based on linear regressions to estimate higher and lower heating value based on ultimate analysis. These models were then validated with a dataset of 15 samples. The models for estimating HHV and LHV have demonstrated excellent prediction accuracy. The absolute bias error was relatively low, 0.02% and 0.03%, for the HHV and LHV models, respectively, demonstrating a minor overestimation of the heating values. Besides that, the absolute average error, both for HHV and LHVmodels, were also low, 1.57% and 1.65%, respectively, indicating good accuracy. The low mean absolute error also confirmed the excellent precision of the developed models.

Validation of OMI seasonal and spatio-temporal variations in aerosol-cloud interactions over Banizoumbou using AERONET data

Aerosols and cloud interaction remains highly important in the climatic process and its validation with space-based Ozone Monitoring Instrument (OMI) and ground-based observation of Aeronet Robotic Network (AERONET) is therefore essential. OMI and AERONET AODs was logrithmically subset and variations observed in both instruments show spatio-temporal quality of being more noticeable, which could lead to changes in the microphysical scale of clouds and instrumental biases. In this study, we have examined the spatio-temporal OMI AODs variations over Banizoumbou and validated results using AERONET AOD, precipitable water and cloud fraction data from Moderate Resolution Imaging Spectroradiometer (MODIS) from the period between 2014 and 2018. Additionally, estimated the absolute mean bias values of both AODs, correlating the results and performing the mean and standard deviation analysis. To validate instrumental error in retrieving AOD values, we calculated the root mean square error (RMSE) and mean absolute error (MAE) with standard error of measurements and perform 7 day kinematic back trajectories at various initial pressures to estimate zonal and meridional jet winds. Additionally, the seasonal loading of aerosols from the Dust Surface Mass Concentration shows aerosols masking cloud. The results show that winter season has period of good AODs agreement and the absolute bias error and its standard deviation for OMI and AERONET AODs is 0.216 ± 0.08. The correlation results obtained with cloud and precipitable water are 0.51, 0.32 and 0.20, −0.18 which show high monsoon AOD dominance the desert. It could be concluded that instrumental performance has spatio-temporal bias.

Simulation of groundwater level in a coastal aquifer

The groundwater levels can have a significant impact on structures and infrastructures of coastal areas. The simulation of the hydraulic behavior of coastal aquifers is very important due to its specific boundary conditions. In this study, the groundwater level in the Bandar-e-Gaz coastal aquifer in the Gorgan Gulf region located in northern Iran is simulated using the MODFLOW mathematical model. The modeling of the coastal aquifer behavior carried out in two calibrations (steady and unsteady states). The validation periods (unsteady state), the mean absolute error (MAE) and mean bias error (MBE) were used to evaluate the results. The values of MAE and MBE criteria for the steady state were 0.31 (m) and –0.08 (m), while the average of these criteria in the unsteady state in calibration period were 0.46 and –0.39, and in the validation period were 0.42 (m) and –0.31 (m), respectively. The mentioned results confirm the precision of the model for the entire simulation period, they also indicate that the simulation has a limited underestimation behavior. Moreover, it shows that the precision of the results has a negligible variability, which means the simulation also has considerable reliability. The highest and lowest amount of error in the winter and summer seasons are in accordance with the lowest and highest seawater levels, and it shows the significant sea effect on the hydraulic behavior of the coastal aquifer.

Higher heating value prediction of torrefaction char produced from non-woody biomass

The higher heating value of five types of nonwoody biomass and their torrefaction char was predicted and compared with the experimental data obtained in this paper. The correlation proposed in this paper and the ones suggested by previous researches were used for prediction. For prediction using proximate analysis data, the mass fraction of fixed carbon and volatile matter had a strong effect on the higher heating value prediction of torrefaction char of non-woody biomass. The high ash fraction found in torrefied char resulted in a decrease in prediction accuracy. However, the prediction could be improved by taking into account the effect of ash fraction. The correlation developed in this paper gave a better prediction than the ones suggested by previous researches, and had an absolute average error (AAE) of 2.74% and an absolute bias error (ABE) of 0.52%. For prediction using elemental analysis data, the mass fraction of carbon, hydrogen, and oxygen had a strong effect on the higher heating value, while no relationship between the higher heating value and mass fractions of nitrogen and sulfur was discovered. The best correlation gave an AAE of 2.28% and an ABE of 1.36%.

Estimation of Monthly Average Sunshine Duration over China Based on Cloud Fraction from MODIS Satellite Data

The sunshine duration (SSD) model described herein combines meteorological observation data from an extensive network of weather stations, MODIS satellite cloud cover data, and a high-resolution digital elevation model to produce high-resolution SSD maps of China. The model yielded low difference between the measured and estimated values at 672 standard weather stations. The mean absolute bias error (MABE) of the monthly mean daily SSD for 2001-2003 was 0.15-0.26 h and the relative bias error (RABE) was 2.34-4.64%. To further validate the model, the observation data from the intensive weather stations (with high spatial resolution) in Jiangsu and Qinghai not used in the calculations, were used for comparison with the estimated values. The annual mean MABE values in Jiangsu and Qinghai during 2001-2003 were less than 0.5 h, and the annual mean RABE values below 5%. Thus, one can conclude that the SSD model is reliable and stable. The spatial distribution of the SSD was also examined, which indicated that the macroscopic distribution of SSD in China determined using MODIS satellite data was more objective and more detailed than the distribution by interpolation of weather station observations of SSD.

On the Performance of Generalized Regression Estimator for Small Domains

This article describes different types of indirect methods of estimation for small domains such as synthetic ratio estimation, synthetic regression estimation, composite estimation combining direct ratio with synthetic ratio estimation, generalized regression estimation and direct ratio estimation. We also compared the performances of the corresponding estimators in terms of absolute relative bias (ARB) and simulated relative standard errors (SRSE), which are computed by means of a simulation study of the crop acreage for the Inspector Land Revenue Circles (ILRCs) of state Rajasthan, India, considered as small domains. Further we consider the calibration approach to estimation for small domains and compare the performance of these estimators.

Decomposition of unpolarized emissivity

Many satellite remote sensors perform unpolarized measurements. A systematic procedure to decompose measured unpolarized emissivity is proposed using the definition of total reflectivity and the relationship between vertically and horizontally polarized reflectivity. Two polarizations are retrieved for various view angles with mixed emissivity simulated using the refractive index of water for ultraviolet, visible, infrared and microwave wavelengths. The results indicate that the absolute bias errors are small and consistent within Brewster angles, irrespective of the wavelengths. However, the relative bias is less than 4% and 5% for vertical and horizontal polarization, respectively, for any instrument working at infrared and microwave wavelengths. The relative bias for horizontal polarization is 20–30% for ultraviolet and visible wavelengths due to small absolute reflectivity values. Consequently, the method proposed in this study is applicable to specular surfaces for various view angles without the dielectric properties of a medium being required.

Quantifying the uncertainties of transpiration calculations with the Penman–Monteith equation under different climate and optimum water supply conditions

The uncertainties of transpiration calculations with the Penman–Monteith equation were quantified under different climate conditions of Brazil, Germany and Israel using maize as a common crop type. All experiments were carried out under non-limiting growing conditions. Canopy resistance was determined by scaling to canopy level specific relations between in situ measurements of incident radiation and stomatal conductance using a light penetration model. The model was tested against heat-pulse measured sap flow in plant stems. The root mean square error (RMSE) of daily calculated transpiration minus measured sap flow was 0.4 mm/day. It was dominated by its variance component (variance = 0.2 {mm/day} 2; bias = 0.0 mm/day). Calculated transpiration closely matched the measured trends at the three locations. No significant differences were found between seasons and locations. Uncertainties of canopy conductance parameterizations led to errors of up to 2.1 mm/day. The model responded most sensitively to a 30% change of net radiation (absolute bias error = 1.6 mm/day), followed by corresponding alterations of canopy resistances (0.8 mm/day), vapour pressure deficits (0.5 mm/day) and aerodynamic resistances (0.34 mm/day). Measured and calculated 30-min or hourly averaged transpiration rates are highly correlated ( r 2 = 0.95; n = 10634), and the slope of the regression line is close to unity. The overall RMSE of calculated transpiration minus measured sap flow was 0.08 mm/h and was dominated by its variance component (0.005 {mm/h} 2). Measured sap flow consistently lagged behind calculated transpiration, because plant hydraulic capacitance delays the change of leaf water potential that drives water uptake. Calculated transpiration significantly overestimated sap flow during morning hours (mean = 0.068 mm/h, n = 321) and underestimated it during afternoon hours (mean = −0.065 mm/h; n = 316). The Penman–Monteith approach as implemented in the present study is sufficiently sensitive to detect small differences between transpiration and water uptake and provides a robust tool to manage plant water supply under unstressed conditions.

PARAMETERIZATION OF INCOMING LONGWAVE RADIATION IN HIGH-MOUNTAIN ENVIRONMENTS

Some ecological applications and energy budget calculations of the earth's surface require accurate estimates of incoming longwave radiation. As cloud cover observations are not conducted frequently in high-mountain environments, a new model for the parameterization of daily mean incoming longwave radiation is proposed based on global radiation instead of cloud cover. Besides global radiation, the new model requires data for air temperature, relative humidity, and an estimate of daily mean cloudless global radiation. The model was calibrated with data from high-mountain and lowland stations and the results are compared with existing models. The new model yielded consistent results under all cloud-cover conditions, for different sites, and for all seasons. For the conditions tested, the absolute mean bias error was generally less than 10 Wm-2 and the root mean square error was always between 11 Wm-2 and 16 Wm-2. Of the other models tested, some did not perform well under cloudless conditions and others yielded large errors under overcast conditions or were not applicable to high mountain sites. The new model is a viable alternative to the existing longwave parameterization models, especially for high-mountain environments, and it can be applied without the resource-consuming observation of cloud cover. [Key words: longwave radiation, global radiation, cloud cover, high mountains, model.]

Evaluation of stem taper functions for estimating log volume assortments

Using three recently fitted taper functions, this note evaluates the accuracy and precision of log volume assortment estimates for five major Saskatchewan timber species. All three functions showed similarly good performance for the five species examined. The results indicated that the magnitude of both absolute bias and standard error of estimate depended on the average volume of the particular log assortments; larger average volumes had greater bias and standard errors of estimate. The coefficients of variation were inversely related to average log assortment volume, with the smallest assortment volumes having the largest coefficients. This results from the high variation relative to those small averages. This also means that estimates of log volume assortments would always be less accurate than those of the entire merchantable stem. Key words: forest mensuaration, Saskatchewan, log volume estimation, stem taper functions