Average Bias Error Research Articles

Decreasing Trend Bumped Probability Distribution: its Properties, Simulations and Application

In this paper, a probability model is proposed which engaged the mathematical combination of Lindley distribution and a trigonometric component known as haversine function〖 δ〗_s. The one parameter model prototype sustains the capacity to forecast multimodal decreasing trend sinusoidal outcomes. By nomenclature, the proposed probability model is called Modified Lindley Trigonometric Distribution (MLTD). Some statistical properties studied include the hazard function, mean residual life function, moments, conditional moments and moment generating function, Bonferroni and Lorenz curve, entropy, asymptotic distribution, order statistics, and parameter estimation; where the hazard function specially features a cyclic or periodic bathtub and inverted bathtub shape in chain format. The numerical behavior of the estimates of the average bias and mean square error were examined under Monte Carlo simulation approach; and an applicative simulation is experimented to underscore the parametric behavior of MLTD in data modeling. A real life flood data is used to illustrate the essence of the development.

Calorific Value Prediction Model Using Structure Composition of Heat-Treated Lignocellulosic Biomass

This study aims to identify an equation for predicting the calorific value for heat-treated biomass using structural analysis. Different models were constructed using 129 samples of cellulose, hemicellulose, and lignin, and calorific values obtained from previous studies. These models were validated using 41 additional datasets, and an optimal model was identified using its results and following performance metrics: the coefficient of determination (R2), mean absolute error (MAE), root-mean-squared error (RMSE), average absolute error (AAE), and average bias error (ABE). Finally, the model was verified using 25 additional data points. For the overall dataset, R2 was ~0.52, and the RMSE range was 1.46–1.77. For woody biomass, the R2 range was 0.78–0.83, and the RMSE range was 0.9626–1.2810. For herbaceous biomass, the R2 range was 0.5251–0.6001, and the RMSE range was 1.1822–1.3957. The validation results showed similar or slightly poorer performances. The optimal model was then tested using the test data. For overall biomass and woody biomass, the performance metrics of the obtained model were superior to those in previous studies, whereas for herbaceous biomass, lower performance metrics were observed. The identified model demonstrated equal or superior performance compared to linear models. Further improvements are required based on a wider range of structural biomass data.

Mathematical models for predicting the higher heating value and ultimate analysis of biomass

The higher heating value (HHV) and elemental composition are important properties of biomass and they are necessary to perform computer simulations of the biomass thermal conversion processes. Both properties require equipment to measure that can be expensive, while the proximate analysis required equipment that is typically found in a laboratory. This work presents a general correlation, based on proximate analysis of biomass, to calculate elemental composition and two new correlations, based on proximate and ultimate analyses of biomass and char used for prediction of the higher heating value. The correlations based on ultimate analysis and proximate analysis show an average absolute error (AAE) of 5.59% and 6.81%, respectively, an average bias error (ABE) of 0.17% and 1.52%, a mean bias error (MBE) of − 0.09 and − 0.06, and root mean square error (RMSE) of 1.52 and 1.98 concerning the value of HHV. To calculate the elemental composition from proximate analysis, the correlations were proposed of C, H and O. The AAE of these correlations were 3.86%, 7.49%, and 5.68%, the ABE were − 1.10%, − 0.22%, − 2.23%, the MBE were 0.58, 0.06, and 1.14 while the RMSE were 2.65, 0.6, 3.45 with respect to measured values of C, H, O, respectively. The AAE values of the correlation proposed in this study using ultimate analysis are lower than those found for the other studied correlations.

Modeling, simulating, and validating a novel three-fluid heat exchanger (TriCoil™) for a residential heating and air-conditioning system integrating water-based thermal energy storage

An experimentally-validated novel three-fluid fin-and-tube heat exchanger (TriCoil™) is proposed for water-based thermal energy storage integration with ducted split systems (DSS) for residential heating and air-conditioning applications. TriCoil™ was modeled and simulated considering three circuitry layouts. The simulations showed that the capacity of the considered coils varied from around 4.5 to 13 kW depending on the operational mode and circuitry layout. With the capacity range of the considered coils, TriCoil™ can be a replacement to an A-shape indoor coil of DSS considering its dimensions with respect to its capacity. Also, fin density and thickness effects on TriCoil™ were investigated to improve its performance. For charging TES mode, the capacity increases by around 95% by increasing the Fin-Tube Ratio by 11%. For modes other than the charging mode, the change in the capacity mostly follows the trend of the air-side effectiveness when changing fin density and fin thickness; the capacity is more responsive to increasing fin density than increasing fin thickness. The TriCoil™ model was validated experimentally for different operational modes, and the average mean absolute error (normalized bias error) among different operational modes compared to the experimental data was 1.3% (0.17%) for the R410A side, 4.2% (-3.03%) for the water side, and 1.4% (-0.03%) for the air side.

The novel Kumaraswamy power Frechet distribution with data analysis related to diverse scientific areas

The study’s major goal is to design a superior creative distribution by using the Kumaraswamy-G family of distributions to power Frechet distribution. The Kumaraswamy power Frechet distribution (KPFD) with four parameters is the full name of the revolutionary model. The distribution’s probability density function may take numerous forms and graphs and can be used to describe complicated data sets efficiently. Several features of the new distribution are obtained, including dependability, hazard rate, quantile, and moments. The estimation of the unknown parameters of KPFD are provided using the KPFD maximum likelihood estimation technique. Furthermore, a study was performed using the Monte Carlo simulation approach to test estimator accuracy regarding average bias (AB) and mean square error (MSE). Last but not least, two genuine data sets are supplied to compare the proposed model to existing models.

Developing a Proximate Component Prediction Model of Biomass Based on Element Analysis

Interest in biomass has increased due to current environmental issues, and biomass analysis is usually performed using element and proximate analyses to ascertain its fuel characteristics. Mainly, element component prediction models have been developed based on proximate analysis, yet few studies have predicted proximate components based on element analysis. Hence, this study developed a proximate component prediction model following the calorific value calculation. Analysis of Pearson’s correlation coefficient showed that volatile matter (VM) and fixed carbon (FC) were positively correlated with hydrogen and oxygen, and with carbon, respectively. Thus, the model correlation was developed using a combination of the “stepwise” and “enter” methods along with linear or nonlinear regressions. The optimal models were developed for VM and ash content (Ash). The VM optimal model values were: R2 = 0.9402, root-mean-square error (RMSE) = 7.0063, average absolute error (AAE) = 14.8170%, and average bias error (ABE) = −11.7862%. For Ash, the values were: R2 = 0.9249, RMSE = 2.9614, AAE = 168.9028%, and ABE = 167.2849%, and for FC, the values were: R2 = 9505, RMSE = 6.3214, AAE = 18.3199%, and ABE = 15.0094%. This study provides a model to predict the proximate component by element analysis. Contrary to existing method, proximate analysis can be predicted based on elemental analysis, and shows that consume samples can be performed at once.

EVALUATION OF MODELS FOR THE PREDICTION OF HIGHER HEATING VALUE OF BIOMASS BASED ON PROXIMATE ANALYSIS

Biomass is a renewable and sustainable source of energy with little greenhouse gas emissions. The higher Heating value (HHV) of biomass is a significant parameter that is used in characterising fuel quality, class and type for energy application systems. Experimental determination of HHV is expensive, takes time and not always available. This brings the need for mathematical models for HHV prediction. In this research, proximate analysis and HHV of ten common biomass samples in Nigeria were determined. The biomass considered included rice husk, rice straw, corn cob, woodchips, groundnut shell, desert date, coconut shell, palm kernel, millet straw and sugarcane bagasse. Eight linear and five non-linear correlations with good performance from the literature were employed for predicting the biomass’ HHV from proximate analysis data. The performance of the models was tested using statistical indicators. Model M1 and M7 were the best among all the tested models with average absolute error (AAE), average bias error (ABE), and root mean square error (RSME) of 3.8389%, 2.5002% and 0.8780 MJ/kg; and 3.8918%, 2.2301% and 0.8701 MJ/kg respectively. Other models also correlated relatively well with the experimental HHV with low error, though, some are good for specific biomass only. This research identifies the best models that have high accuracy and can be used for the prediction of the higher heating value of biomass samples from proximate analysis.

Simulation and forecasting of atmospheric CO2 using RAMS

Concentration of carbon dioxide as the main greenhouse gas has been increasing, which has serious impacts on climate change, ecosystem, and human health. This study uses the Regional Atmospheric Modeling System (RAMS V6.2) with the Simple Biosphere (SiB-2) sub-model to simulate and forecast the concentration of carbon dioxide over the Daintree Rainforest in Australia. To evaluate the performance of the model, results are compared with the satellite product (MultiInstrumentFusedXCO2). This work evaluates the impact of various grid sizes, different combinations of diffusion parameters, and boundary conditions on CO2 simulations. Results reveal that RAMS can remarkably improve the statistical measures of the simulations particularly compared with the previous modeling analysis. The maximum mean bias error and RMSE in this study for all simulations are smaller than 1.85 and 2.07 ppm, respectively. The most proper simulation type (type III) leads to the average bias error and RMSE of 0.34 and 0.94 ppm, respectively. Furthermore, results show that the fuzzy algorithm is a proper method to provide initial CO2 in forecasting. This study shows that RAMS can be efficiently used in CO2 simulation and forecasting, which is valuable for CO2 monitoring, climate, environment, and management applications.

Effect of specimen thickness on mode I stress intensity factor for additive manufactured compact tension specimen

In this paper Mode I stress intensity of compact tension specimen was studied for different specimen thicknesses built by additive manufacturing system. Three sets of compact tension specimen of five different thicknesses of 4, 8, 12, 16 and 20 mm were prepared and tested for mode I stress intensity factor according to ASTM D 5045–14. Finite element analysis (FEA) was also performed by modelling compact tension specimen in ABAQUS software to obtain J - integral from which stress intensity factor was calculated. The values of mode I stress intensity factors obtained were 18.61, 51.45, 60.82, 66.93 and 63.31 MPa.mm1/2 for specimen with thickness of 4, 8, 12, 16 and 20 mm, respectively, with maximum value for 16 mm specimen. Also, mode I stress intensity factors obtained by finite element analysis using ABAQUS software are close to the experimental results with average bias error equal to 4.08 %.

Improved ANN-Based Approach Using Relative Impact for the Prediction of Thermal Coal Elemental Composition Using Proximate Analysis.

The basic properties of coal influence various procedures of power generation, such as the design of power generation plants, estimation of the current condition of boilers, and total efficiency of power plants. The elemental composition is a needed factor in evaluating the process of chemical conversion and predicting the flow of flue gas and the quality of air in coal combustion. In the past, several relationships have been established using ultimate and proximate analyses. This study aims to predict the elemental compositions of 104 thermal coals used for coal-fired power plants in South Korea using an artificial neural network (ANN) that uses proximate analysis values as input parameters. The ANN-based model was optimized with six activation functions and four hidden layers after evaluating various performance indices, including R2, mean square error (MSE), and epoch, then additional calculations were derived to compare performances from previous research using the mean absolute error (MAE), average absolute error, and average bias error. It was found that the best topology was established using the Levenberg–Marquardt activation function and 10 hidden layers, resulting in the highest R2 value and smallest MSE of all topologies tested. As a result, the relative impact on calculation accuracy was derived from ANN hidden layers to analyze prediction accuracies of carbon, hydrogen, and oxygen compositions. Accuracy was improved over previous results by 4.71–0.91% via coal rank division topology optimization. Based on the MAE, the current results are even close in performance to those of adaptive neuro-fuzzy inference systems. They also outperformed previous research models by 5.40 and 7.39% in terms of MAE accuracy. Applicability of the ANN was also analyzed with limitations of the chemical composition of ANNs and present reinforcement measures in the future studies through qualitative analysis comparisons based on Fourier transform infrared spectroscopy. Consequently, the relative effect was derived from the ANN hidden layer weight for specific calculation of the relationship between elemental composition and proximate analysis properties. As a result, it was possible to qualitatively analyze how the proximate analysis value affects the composition of elements and calculate the ratio accordingly. The findings of this study provide an improved and efficient approach to predicting the elemental composition of thermal coal, based on data from South Korean power plants. Also, further research can follow schematics from this study with the applicability and accessibility of the ANN.

Study of mid-latitude retrieval XCO2 greenhouse gas: Validation of satellite-based shortwave infrared spectroscopy with ground-based TCCON observations

Carbon dioxide (CO2) is a major greenhouse gas. This study investigated the performance of three common algorithms, namely NIES, ACOS, and Remo Tec (SRFP). These algorithms were compared using GOSAT observation satellite data with reference data obtained from TCCON during the period 2009–2021. According to statistical evaluation, the SRFP and NIES algorithms achieved the lowest and highest correlation values of the 13 year (2009_2021) average of all sites, respectively. The average bias error values of NIES and ACOS was estimated to be less than that of SRFP approximately 0.5 ppm, while the bias within SRFP was of about 2 ppm. Comparing the RMSE and CRMS error values showed that the highest and lowest error values were related to the SRFP and NIES algorithms respectively, which were 0.37–1.67 and ppm 1.46–7.9. The researchers also compared them with monthly time changes based on ground measurements, and observed a time series of CO2 concentration changes that well matched the trend of gas concentration values at ground stations obtained by NIES algorithm. The results showed that in most cases NIES was an effective algorithm to retrieve carbon dioxide gas concentrations, allowing the researchers to identify the main sources of greenhouse gas emissions in different areas. The clustering result in the study area showed that the continental CO2 columnar concentration has a specific seasonal cycle, with the maximum and minimum values appearing in winter-early spring and spring-late summer, respectively. In conclusion, cluster analysis can classify the surface CO2 column concentration values and determine the spatial distribution pattern of CO2.

Carbon Black Sensor and Neural Network Model for Sensing Angle in Soft Pneumatic Actuators

Accurate control of soft robots is critical for positioning, locomotion, and manipulation applications. These soft systems, however, are currently limited by the lack of soft multi-axis sensor designs as well as a lack of models for interpreting complex soft sensor signals. In this work, we demonstrate a unique scheme for embedding soft carbon black strain sensors into a soft multi-axis pneumatic bellows actuator. In order to utilize the soft strain sensors for estimating orientation, the strain signals from each of the 12 sensors are compared against signals from a reference inertial measurement unit. Then, a time-based recurrent neural network is used to map the hysteretic soft sensor data to determine the yaw, pitch, and roll motions of the actuator. Results show that high accuracy estimates are achieved with average bias errors between 0 to 1.5 degrees and error standard deviations between 3 to 6 degrees. This novel application of soft multi-axis embedded sensors and neural network models demonstrates how fully soft actuators and sensors can be used to accurately determine robot orientation.

Correlations for the prediction of higher heating values of liquid fuels from their densities, viscosities, and flash points values

In this study, correlations of the higher heating values (HHV) of three groups of liquid fuels, vegetable oils, alkanes, and alcohols were developed through experimentation and prediction with the aid of the statistical software package MINITAB 16 (PA, USA). The HHVs (in kJ/kg), of the samples were obtained as a function of the density, viscosity, and flash points physical tests. Reliability of models were evaluated through statistical validation and cross-validation standard error of estimate (S), coefficient of determination (R2), predicted residual error of the sum of square statistics (PRESS statistics), error estimations (average bias error, ABE, and AAE, average absolute error), and the residual versus fitted values plot. For the vegetable oils, the best correlation was HHV = -29.5 + 77.8ρ -0.0124μ + 0.00549β (R2 = 79.6%, p-value = 0.147, AAE = 0.515, ABE = 0.005). For alkanes it was: HHV = 66.0322 – 38.3421ρ + 2.9392μ (R2 = 100%, p-value = 0.002, AAE = 0.033, ABE = 7.27 × 10-5). For alcohols; HHV = -100 + 171ρ (R2 = 86.4%, p-value = 0.070, AAE = 4.193, ABE = 0.316). These correlations could be instrumental to achieving maximum productivity with minimal utilization of energy in industry and could be extended to other liquid fuels after minor modification.

Estimation of the Higher Heating Value of Lignocellulosic Materials

In the world of renewable energies, biomass will play a fundamental role in the coming years, this is how the interest in taking advantage of biomass from lignocellulosic materials is increasing. The objective of the present investigation was to develop a mathematical model for the prediction of the higher heating value (HHV) of lignocellulosic materials. Based on the proximate analysis of the raw materials, 598 data were collected from which possible correlations were established that allowed the development and validation of five statistical models; the best model proposed in the present study considers fixed carbon and ash content as variables, this model presents an average absolute error of 7.03% and an average bias error of 0.91%, in addition to presenting an R2 of 0.801. Being the equation that provides the smallest error in relation to the higher heating value observed. DOI: http://dx.doi.org/10.17807/orbital.v13i1.1547

Comparison of the RADM2 and RACM chemical mechanisms in O3 simulations: effect of the photolysis rate constant

Since the photolysis rate plays an important role in any photoreaction leading to compound sink and radical formation/destruction and eventually O3 formation, its impact on the simulated O3 concentration was evaluated in the present study. Both RADM2 and RACM were adopted with and without updated photolysis rate constants. The newly developed photolysis rates were determined based on two major absorption cross-section and quantum yield data sources. CMAQ in conjunction with meteorological MM5 and emission data retrieved from Taiwan and East Asia were employed to provide spatial and temporal O3 predictions over a one-week period in a three-level nested domain [from 81 km × 81 km in Domain 1 (East Asia) to 9 km × 9 km in Domain 3 (Taiwan)]. Four cases were analyzed, namely, RADM2, with the original photolysis rates applied in Case 1 as a reference case, RADM2, with the updated photolysis rates applied in Case 2, and RACM, with and without the updated photolysis rates applied in Cases 3 and 4, respectively. A comparison of the simulation and observed results indicates that both the application of updated photolysis rate constants and RACM instead of RADM2 enhanced all three error analysis indicators (unpaired peak prediction accuracy, mean normalized bias error and mean absolute normalized gross error). Specifically, RADM2 with the updated photolysis rates resulted in an increase of 12 ppb (10%) in the daily maximum O3 concentration in southwestern Taiwan, while RACM without the updated photolysis rates resulted in an increase of 20 ppb (17%) in the daily maximum O3 concentration in the same area. When RACM with the updated photolysis rate constants was applied in the air quality model, the difference in the daily maximum O3 concentration reached up to 30 ppb (25%). The implication of Case 4 (RACM with the updated photolysis rates) for the formation and degradation of α-pinene and d-limonene was examined.

Bayesian Estimation of Entropy for Burr Type XII Distribution under Progressive Type-II Censored Data

With the rapid development of statistics, information entropy is proposed as an important indicator used to quantify information uncertainty. In this paper, maximum likelihood and Bayesian methods are used to obtain the estimators of the entropy for a two-parameter Burr type XII distribution under progressive type-II censored data. In the part of maximum likelihood estimation, the asymptotic confidence intervals of entropy are calculated. In Bayesian estimation, we consider non-informative and informative priors respectively, and asymmetric and symmetric loss functions are both adopted. Meanwhile, the posterior risk is also calculated to evaluate the performances of the entropy estimators against different loss functions. In a numerical simulation, the Lindley approximation and the Markov chain Monte Carlo method were used to obtain the Bayesian estimates. In turn, the highest posterior density credible intervals of the entropy were derived. Finally, average absolute bias and mean square error were used to evaluate the estimators under different methods, and a real dataset was selected to illustrate the feasibility of the above estimation model.

Evaluation of heterogeneity and heterogeneity interval estimators in random-effects meta-analysis of the standardized mean difference in education and psychology.

Meta-analyses are conducted to synthesize the quantitative results of related studies. The random-effects meta-analysis model is based on the assumption that a distribution of true effects exists in the population. This distribution is often assumed to be normal with a mean and variance. The population variance, also called heterogeneity, can be estimated numerous ways. Research exists comparing subsets of heterogeneity estimators over limited conditions. Additionally, heterogeneity is a parameter estimated with uncertainty. Various methods exist for heterogeneity interval estimation, and similar to heterogeneity estimators, these evaluations are limited. The current simulation study examined the performance of Bayesian (with 5 prior specifications) and non-Bayesian estimators over conditions found after a review of meta-analyses of the standardized mean difference in education and psychology research. Three simulation conditions were varied: (a) number of effect sizes per meta-analysis, (b) true heterogeneity, and (c) sample size per effect size within each meta-analysis. Estimators were evaluated over average bias and means square error. Methods of interval estimation were then evaluated with the estimators found to operate optimally. Interval estimators were evaluated based on coverage probability, interval width, and coverage of the estimated value. Overall, the Paule and Mandel estimator, in conjunction with the Jackson method of interval estimation, is recommended if no knowledge exists with regards to the expected value of heterogeneity when synthesizing the standardized mean difference effect size. If heterogeneity is expected to be small (e.g., < .075), then REML with the profile likelihood interval estimator is recommended. Sensitivity analysis evaluating differences in substantive conclusions with a suite of heterogeneity estimators, such as Paule and Mandel, REML, and Hedges and Olkin, is recommended. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Basic study on estimation method of wall shear stress in common carotid artery using blood flow imaging

In this paper, we propose a method for adaptive selection of the kernel size used in estimation of the wall shear stress (WSS) based on flow velocity profiles obtained by the blood flow imaging method based on enhancement of RF echo signals from blood cells using a singular value decomposition based clutter filter. Two simulation phantom experiments with the Field II program were performed to validate the proposed method. In the simulation experiments, the average bias error (BE) between the WSSs estimated by the conventional method and theoretical one was 16.5%. The proposed method could reduce the average BE to 12.3%. Also, the proposed method was applied to RF echo signals from a common carotid artery (CCA) of a healthy male subject. The WSSs in the CCA were estimated during one cardiac cycle and in a range similar to that in previous reports.

Estimation and Tracking of Blood Pressure Using Routinely Acquired Photoplethysmographic Signals and Deep Neural Networks.

Retrospective cohort study with split sampling for model training and testing. A single urban academic hospital. Three-hundred twenty-nine adult patients admitted to a critical care unit. None. One hundred thirty-six thousand four-hundred fifty-nine photoplethysmography waveforms of length 30 seconds were used for training (60%), validation (20%), and testing (20%) of the blood pressure estimation network. Each sample had an associated systolic, mean, and diastolic blood pressures extracted from concurrently recorded invasive arterial line waveforms. Blood pressure estimation using photoplethysmography waveforms is achieved using advanced machine learning methods (convolutional neural networks and a Siamese architectural configuration) calibrated for each patient on a single, first available photoplethysmography sample and associated blood pressure reading. The average estimation bias error was 0.52, 0.1, and -0.76 mm Hg for diastolic, mean, and systolic blood pressure, respectively, with associated mean absolute errors of 4.11, 5.51, and 7.98 mm Hg. If used to identify clinically important changes in blood pressure from the initial baseline, with a threshold of a 10 mm Hg increase or decrease in blood pressure, our algorithm shows an accuracy of 85%, 78%, and 74% for diastolic, mean, and systolic blood pressure, respectively. We also report the network's performance in detecting systolic and diastolic hypo- or hypertension with accuracies ranging from 86% to 97%. Using advanced machine learning tools, we show that blood pressure estimation can be achieved using a common noninvasively recorded signal, the photoplethysmography. Such tools can allow for better monitoring of patients that do not have invasively recorded blood pressure, both in the critical care setting and on inpatient wards.

Experimental Evaluation of Reducing Cable-Strain Energy of Tension-Truss Surface with Compression Members

Cable network used to form the parabolic surface of an antenna can be designed to reduce its weight. However, the strain energy in the cable increases with an increase in the number of cables. This is because the aperture diameter and surface accuracy increase. Accordingly, to maintain a precise surface, the support structure must be enhanced by increasing its rigidity. Therefore, a surface-design method is introduced wherein several compression members, instead of tensile cables, are inserted into the support structure to reduce the total strain energy. Nevertheless, it is difficult to achieve the required surface accuracy when the manufacturing error (i.e., cable-length error) is considered during cable fabrication. In this study, an experimental evaluation is conducted to determine the admissible cable-length error with respect to constructing a precise surface. Results suggest that controlling the average bias error of the cable length is vital in obtaining a precise surface. Additionally, the strain energies of the rod-and-cable web and cable web are compared; results demonstrate that the strain energy in the former can be reduced when the cable-length error is considered during the manufacturing process.