Nonlinear Regression Fitting Research Articles

Supervised neural networks learning algorithm for three dimensional hybrid nanofluid flow with radiative heat and mass fluxes

Hybrid nanofluid is an emerging field due to the rapid enhancement of heat transfer and stable nanoparticles in base fluid properties. A three dimensional hybrid nanofluid flow model is constructed over biaxial porous stretching/shrinking sheet with heat transfer, Radiative heat and mass flux (3D-HNF-RHF). Bayesian Regularization technique based on Backpropagated neural networks (BRT-BNNs) is employed to estimate the solution of proposed model. It is the mathematical process which converts nonlinear regression fitting into a well-posed statistical process in the form of ridge regression. This method diminishes length cross validation need and more robust then Backpropagation technique. The proposed flow system 3D-HNF-RHF is transferred to ordinary differential equations (ODEs) possessing physical variations through self-similar transformations. The effect of derived variations such as thermal relaxation parameter, mass flux parameter, Stretching/shrinking parameter, Prandtl number, Skin friction and Nusselt number observed over the velocity and temperature fields. Numerical results of these physical parameters have been presented in tabulated form obtained from a dataset constructed through Homotopy Analysis Method imposed on 3D-HNF-RHF model. Statistical tests through mean square error, histogram curve and regression fitting curves are employed to check the accuracy and convergences of the solution obtained through BRT-BNNs. It is observed that Stretching/shrinking quantity and mass flux parameter slow down the flow rate whereas, increase radiative heat flux upsurges the temperature gradient. The impacts of surface drag force and heat transfer are illustrated through the different graphical illustrations.

Laser Shock Peening Induced Back Stress Mitigation in Rolled Stainless Steel

Abstract Laser shock peening (LSP) is investigated as a potential tool for reducing tensile back stress, shown here applied to rolled and annealed 304L austenitic steel. The back stress of treated and untreated dog-bone samples is extracted from hysteresis tensile testing. Electron back-scatter diffraction (EBSD) and orientation imaging microscopy (OIM) analysis quantify the geometrically necessary dislocation (GND) density distribution of unstrained and strained as well as unpeened and peened conditions. Finite element analysis (FEA) simulation models back stress and residual stress development through tensile testing and LSP treatment using known LSP pressure models and Ziegler's nonlinear kinematic hardening law. Nonlinear regression fitting of tensile testing stress–strain in as-received specimens extracts the kinematic hardening parameters that are used in numerical study. This research shows LSP may be used to overcome manufacturing design challenges presented by yield asymmetry due to back stress in rolled steel.

LF-NMR as a tool for predicting the 3D printability of surimi-starch systems

In this study, surimi from golden pompanos was mixed with starch to form a surimi-starch system. The water properties, rheological properties, and three-dimensional (3D) printability of the surimi-starch were measured. Cluster analysis results showed that the 3D printability was closely related to the type and addition content of starch, and the water and rheological properties. The low-field nuclear magnetic resonance (LF-NMR) parameters were used to predict 3D printability using polynomial regression models. The correlation coefficients (R2) for 3D printing accuracy and stability were 0.88 and 0.93, and the root mean square error (RMSE) values were 0.20% and 4.59%, respectively. In the verification test, the R2 for the two models were 0.85 and 0.89, and the RMSE values were 0.20% and 1.06%, respectively. The nonlinear surface regression fitting exhibited superior predictive performance. Therefore, LF-NMR is a good non-destructive tool for quickly and accurately predicting the 3D printability of the surimi-starch systems.

Research on preparation process of ethanol and C4 olefin based on linear and nonlinear regression fitting algorithm

First of all, aiming at studying the relationship between ethanol conversion, C4 olefin selectivity and temperature for each catalyst using the knowledge of fitting arbitrary data and adopting the basic idea of control variable method, linear regression equation and nonlinear regression equation model are established. Aiming at the solution of linear regression and non-linear regression model, this paper uses the fitting algorithm to calculate the functional relationship between the two variables, and uses Matlab to solve the specific function expression and draw the function relation diagram to further solve the relationship between catalyst combination, temperature and ethanol conversion and C4 olefin selectivity.

Convergence of Levenberg-Marquardt Estimates of Nonlinear Parameters in EIS Analysis of Coated Aluminum Panels

Equivalent circuit models are frequently employed to analyze electrochemical impedance spectroscopy (EIS) data. However, aside from some simple cases in which the equivalent circuit element parameters can be estimated directly from a plot of the data, the parameters for each of the equivalent circuit elements must often be estimated through the implementation of a nonlinear least-squares regression method. One frequently-used approach is the powerful Levenberg-Marquardt algorithm. This algorithm functions as a damped least-squares method that performs an interpolation between the steepest-descent and the Gauss-Newton methods for estimating nonlinear parameters. However, there are several challenges to using a Levenberg-Marquardt algorithm to model EIS data. The nonlinear nature of the impedance equations along with the difference in the magnitude of the parameter values can result in the algorithm failing to converge to a local minimum in the parameter space. This convergence challenge can be seen in determining equivalent circuit values for undamaged coating systems that have a high pore resistance, a small capacitance, as well as contributions from the underlying metal substrate. A Levenberg-Marquardt algorithm, along with a heuristic approach to use the raw data to improve the initial parameter estimates, is implemented that provides an improved approach for nonlinear regression fits of equivalent circuit models. A comparison of three equivalent circuit models fits, with residuals, for a two-layer coating system on an aluminum substrate is shown in the attached figure.Figure caption: Plot of EIS data (+ symbols) from a cured coating system prior to any environmental exposures compared with 3 equivalent circuit model fits (solid lines). The model fits were obtained using an NRL-developed Levenberg-Marquardt nonlinear regression fitting routine.The Department of Defense Strategic Environmental Research and Development Program (SERDP) sponsored this project under work unit 5399. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Office of Naval Research, the U.S. Navy, the Department of Defense, or the U.S. government. Figure 1

All-position welding control system based on machine vision and nonlinear regression

Aiming at the problems of poor welding quality and low degree of automatic welding on the engineering site, a welding process parameter control method based on machine vision and nonlinear regression technology is proposed. Firstly, a vision unit and a peripheral sensor unit are designed to obtain the information of each influencing factor of the welding process parameters. Secondly, a clustering algorithm is used to improve the extraction accuracy of feature point coordinates of weld images. Thirdly, a nonlinear regression fitting method is proposed to determine the mathematical relationship between welding quality at different welding positions and corresponding process parameters. Experimental results show that the control system is easy to operate, and the flexible control of welding process parameters in the whole process is realized. The weld cumulative height and width deviations are less than 0.5 and 0.3 mm, respectively. The welding surface is stable and meets welding requirements. Therefore, this method is of great practical significance in engineering field welding.

Calcium aluminate cements under high‐temperature compression tests

AbstractThis investigation is about the damage generated with high‐temperature compression tests in pure calcium aluminate cement pastes (CACP) with quartz. Two types of formulations of CACP were manufactured and later exposed to a compression of .3 MPa at 800°C for 16 h. Samples had a water to cement ratio (W/C) of .40. The formulations were characterized using laser granulometry, X‐ray fluorescence, X‐ray diffraction, thermogravimetric analysis, and scanning electron microscopy. The theta projection model parameters for creep were estimated using nonlinear regression fit methods. The activation energy, minimum time of creep, minimum creep rate, and other parameters were calculated. The creep micro‐mechanisms were established as well. The activation energy was obtained exclusively by creep for the formulations CACP 71–0 wt% and CACP 71–20 wt% of 2.98 kJ/mol and 7.04 kJ/mol, respectively.

Laboratory Adsorption Studies on Ni(II) and Zn(II) Solutions by Sugarcane-Bagasse Ash

Large volumes of sugarcane-bagasse ash are produced as residues from the sucro-alcohol industry and have some practical applications. The use of this ash as an adsorbent for the removal of Ni(II) and Zn(II) is studied in the present paper. Effects of pH, adsorbent concentration and equilibrium time have been studied in order to establish the best conditions for the removal of metal ions. The kinetic parameters, i.e. the constant rate, equilibrium sorption capacity and related coefficients of each kinetic model (pseudo-first order, pseudo-second order and Elovich), have been evaluated by means of nonlinear regression fit: the pseudo-second order best describes the kinetics of the process. The experimental data obtained from the equilibrium study were analysed using nonlinear Freundlich, Langmuir, Temkin and Toth models: the Langmuir and Toth isotherms best represent the sorption of the metal ions. The highest experimental sorption capacities obtained as regards the removal of Ni(II) and Zn(II) from the sugarcane-bagasse ash were 0.0298 and 0.0416 mmol g−1, respectively. The adsorption mechanism through the formation of covalent bonds and hydrogen bonds demonstrates the affinity between the adsorbent and the adsorbates. The studies were conducted separately, using independent solutions of each metal.

Cloning data with unchanged estimates of estimable non-linear functions of parameters

Non-linear regression models occur in the fields of biology, banking, economics, and sociology, population and biological growth. The absolute growth, growth of humans, and most importantly, an economic variable is appropriately described by non-linear regression models. In this article, we present cloned datasets for bivariate and multivariate non-linear regression models with the same non-linear regression fit. The application of such cloned datasets is used for the confidentiality of sensitive data for publication purposes. In this article, we present cloned data sets which will yield the same fitted non-linear regression models.

Determining Stability Constants of Complexes Between Ester Betulin Derivatives and β-Cyclodextrin by Affinity Capillary Electrophoresis

Inclusion complexes of ester betulin derivatives (pentacyclic lupane triterpenoids) with β-cyclodextrin (β-CD) were studied by affinity capillary electrophoresis. Stability constants were calculated from dependencies of viscosity-corrected effective electrophoretic mobilities on β-CD concentration (0-10 mM) in background electrolytes using nonlinear regression fitting. Logarithms of stability constants at 25 °C for 1:1 and 1:2 β-CD complexes of betulin 3,28-diphthalate, betulin 3,28-disuccinate and betulin 3,28-disulfate (95 % confidence interval) are 4.25 (4.16-4.32) and 7.27 (6.73-7.50), 4.38 (4.26-4.48) and 7.58 (6.90-7.84), 4.04 (4.00-4.08) and 5.91 (4.60-6.20), respectively

Physical Modeling of a Sliding Clamp Mechanism for the Spreading of ParB at Short Genomic Distance from Bacterial Centromere Sites.

SummaryBacterial ParB partitioning proteins involved in chromosomes and low-copy-number plasmid segregation are cytosine triphosphate (CTP)-dependent molecular switches. CTP-binding converts ParB dimers to DNA clamps, allowing unidimensional diffusion along the DNA. This sliding property has been proposed to explain the ParB spreading over large distances from parS centromere sites where ParB is specifically loaded. We modeled such a “clamping and sliding” mechanism as a typical reaction-diffusion system, compared it to the F plasmid ParB DNA binding pattern, and found that it can account neither for the long range of ParB binding to DNA nor for the rapid assembly kinetics observed in vivo after parS duplication. Also, it predicts a strong effect on the F plasmid ParB binding pattern from the presence of a roadblock that is not observed in ChIP-sequencing (ChIP-seq). We conclude that although “clamping and sliding” can occur at short distances from parS, another mechanism must apply for ParB recruitment at larger genomic distances.

Formulae for calculating body surface area in modern U.S. Army Soldiers.

Body surface area (BSA) is an important measurement for many thermophysiological, pharmaceutical, toxicological, environmental, and military applications. Unfortunately, BSA is difficult to quantify, and existing prediction methods are not optimized for contemporary populations. The present study analyzed data body measurements from 5603 male and female participants of a US Army Anthropometric Survey to determine optimal methods for estimating BSA in modern US Army Soldiers. This data included 94 individual body measurements as well as three dimensional (3D) whole body scans for each participant. We used this data to assess and compared 15 existing equations to the measured data. We also derived best fitting nonlinear regression models for estimating BSA from different combinations of sex, height, and weight and iteratively included the remaining 91 measurements to determine which combinations resulted in the highest goodness-of-fit. We found that inclusion of armspan measurements as a third body dimension maximized the model goodness-of-fit. Some of the existing formulae provide reasonable estimates of 3D-scanner derived BSA; while our new formulae derived from this study allows for more accurate estimates of BSA using one or more common input variables.

Adsorption of Sudan-IV contained in oily wastewater on lipophilic activated carbons: kinetic and isotherm modelling.

Up to nine kinetic and fourteen isotherm adsorption models are employed to model the adsorption of Sudan IV, a lipophilic model pollutant present in a biphasic mixture of cyclohexane-water system to simulate oily wastewater. Six different modified activated carbons were used as adsorbents. The highest amount adsorbed of Sudan IV was found in the material prepared by successive treatments of the parent commercial activated carbon Norit ROX 0.8 with nitric acid and urea, followed by thermal treatment at 800°C under continuous flow of nitrogen. Kinetic and isotherm adsorption models can be employed to simulate the process, since the effect of the presence of water in the adsorption of Sudan IV from the cyclohexane phase was found to be negligible, owing to the high lipophilic character of both adsorbent and adsorbate. All kinetic and isotherm coefficients, coupling with statistical parameters (r2, adjusted r2 and sum of squared errors), are determined by non-linear regression fitting and compared to literature data. The model of Avrami is found to be the most appropriate model to represent the adsorption of the pollutant in any of the six modified carbons tested, the highest value of the kinetic constant being 0.055min-1. The isotherm adsorption is well-modelled by using the general isotherm equation of Tóth and the multilayer Jovanović expression for the adsorption of Sudan-IV on that material, resulting in a high monolayer uptake capacity (qm = 193.6mgg-1).

Oxygen isotope effects during microbial sulfate reduction: applications to sediment cell abundances

The majority of anaerobic biogeochemical cycling occurs within marine sediments. To understand these processes, quantifying the distribution of active cells and gross metabolic activity is essential. We present an isotope model rooted in thermodynamics to draw quantitative links between cell-specific sulfate reduction rates and active sedimentary cell abundances. This model is calibrated using data from a series of continuous culture experiments with two strains of sulfate reducing bacteria (freshwater bacterium Desulfovibrio vulgaris strain Hildenborough, and marine bacterium Desulfovibrio alaskensis strain G-20) grown on lactate across a range of metabolic rates and ambient sulfate concentrations. We use a combination of experimental sulfate oxygen isotope data and nonlinear regression fitting tools to solve for unknown kinetic, step-specific oxygen isotope effects. This approach enables identification of key isotopic reactions within the metabolic pathway, and defines a new, calibrated framework for understanding oxygen isotope variability in sulfate. This approach is then combined with porewater sulfate/sulfide concentration data and diagenetic modeling to reproduce measured 18O/16O in porewater sulfate. From here, we infer cell-specific sulfate reduction rates and predict abundance of active cells of sulfate reducing bacteria, the result of which is consistent with direct biological measurements.

Numerical Simulation of Donghu Lake Hydrodynamics and Water Quality Based on Remote Sensing and MIKE 21

Numerical simulation is an important method used in studying the evolution mechanisms of lake water quality. At the same time, lake water quality inversion technology using the characteristics of spatial optical continuity data from remote sensing satellites is constantly improving. It is, however, a research hotspot to combine the spatial and temporal advantages of both methods, in order to develop accurate simulation and prediction technology for lake water quality. This paper takes Donghu Lake in Wuhan as its research area. The spatial data from remote sensing and water quality monitoring information was used to construct a multi-source nonlinear regression fitting model (genetic algorithm (GA)-back propagation (BP) model) to invert the water quality of the lake. Based on the meteorological and hydrological data, as well as basic water quality data, a hydrodynamic model was established by using the MIKE21 model to simulate the evolution rules of water quality in Donghu Lake. Combining the advantages of the two, the best inversion results were used to provide a data supplement for optimization of the water quality simulation process, improving the accuracy and quality of the simulation. The statistical results were compared with water quality simulation results based on the data measured. The results show that the water quality simulation of chlorophyll a and nitrate nitrogen mean square errors fell to 17% and 24%, from 19% and 31% respectively, after optimization using remote sensing spatial information. The model precision was thus improved, and this is consistent with the actual pollution situation of Donghu Lake.

INHIBITORY ACTIVITY OF THE ACTIVE COMPOUND OF ETHYL ACETATE FRACTION OF TAMOENJU (Hibiscus surattensis L.) LEAVES AGAINST α-GLUCOSIDASE AND DIPEPTIDYL PEPTIDASE-4 ENZYMES

The ethyl acetate fraction (EAF) of tamoenju (Hibiscus surattensis L.) leaves, used as a traditional antidiabetic agent in Central Sulawesi, has high inhibitory activity against α-glucosidase and dipeptidyl peptidase-4 (DPP-4). The aim of this study was to isolate the active compound of EAF that was carried out by step gradient polarity extraction, then separated and purified by chromatography. The structure was identified and characterized using NMR spectroscopy and LC-MS. α-glucosidase inhibitory activity was evaluated using the in vitro standard α-glucosidase inhibition test, while DPP-4 activity was evaluated by ex vivo DPP-4 inhibitor test using rat blood serum as the enzyme source. IC50 values were determined by nonlinear regression curve and fit using GraphPad Prism 8 and were expressed as mean ± SEM. In this research, we obtained the isolated compound was identified as kaempferol, which was isolated for the first time from this plant. The isolate exhibited potent α-glucosidase and DPP-4 inhibition with IC50 values of 27.78 ± 0.86 and 7.37 ± 0.06 μg/mL, respectively. Acarbose and sitagliptin as positive control had IC50 values of 17.80 ± 0.27 and 25.56 ± 0.43 μg/mL, respectively. The isolate level by LC-MS was estimated to be 182.23 mg/g isolate. Therefore, tamoenju leaves have great potential as functional foods and in the development of antidiabetic drugs. Keywords: α-Glucosidase, Antidiabetic, Dipeptidyl peptidase-4, Kaempferol, Tamoenju, Hibiscus surattensis L

ASSESSMENT OF EFFECTIVE BLOOD CONCENTRATION READINGS FROM CLINICAL DATA ON PATIENTS WITH HEART FAILURE DISEASES AFTER DIGOXIN INTAKE: A PROJECTION BASED ON THE INVERSE PROBLEM ALGORITHM

In this study, a projection of effective blood concentration (EBC) readings of digoxin is made using the inverse problem algorithm based on clinical data for patients with heart failure diseases. Seven factors, including body surface area (BSA), blood urine nitrogen (BUN), creatinine, sodium (Na), potassium (K), magnesium (Mg) ion readings, and mean arterial pressure (MAP) were compiled with nonlinear regression fit to develop a projection function having 29 terms obtained from an inverse problem algorithm via the default function run in STATISTICA. Accordingly, data collected from the clinical 168 heart failure patients were normalized to be included in same domain range ([Formula: see text]1 to +1), and then calculated by the specific algorithm to optimize the numerical solution to evaluate EBC readings of digoxin. The evaluated first-order regression fit owned an optimal loss function ([Formula: see text]) coupled with correlation coefficient [Formula: see text] = 0.892 and variance of 89.20%. Furthermore, 45 patients having similar clinical syndromes were also adopted to verify the projection and implied with high agreement. The BUN factor dominated the projection and defined as the most significant coefficient in the analysis, and K ion, MAP, BSA, and Mg ion factors exhibited minor contributions to the projection. The repeated trials to lower number of factors from seven to a smaller number (namely 6, 5, 4, 3, 2, and 1) for simplifying method but resulting with unaccepted outcomes, with high loss function values and low linearity. However, the algorithm held its accuracy to handle the verified data that were out of the original bounds. The proposed algorithm demonstrated a useful analysis to handle the drug administration in pharmaceutical field.

A spectral weighting function for abiotic photodegradation based on photochemical emission of CO2 from leaf litter in sunlight

Photodegradation can be a significant driver of leaf litter decomposition although the spectral effectiveness of sunlight in driving this process is not well characterized. We developed spectral weighting functions (WFs) for the photochemical emission of CO2 from three leaf litter types using 10 cutoff filters that provided contrasting polychromatic sunlight under clear skies in Tempe, AZ, USA. An iterative nonlinear least-squares regression fitting procedure was used to estimate how effective sunlight at a given wavelength was in eliciting CO2 emission. Although absolute CO2 emission rates varied appreciably among litter types, their WFs were very similar. Using the average WF of all litter types, the effectiveness of sunlight declined from 300 nm by one and two orders of magnitude at 399 and 498 nm, respectively. The slope of the WF was most similar to WFs for CO emission from terrestrial leaf litter and photobleaching of dissolved organic matter in lakes, and was much more gradual than WFs addressing UV damage to biotic processes. Peak effectiveness of clear-sky noon sunlight with our WF occurred at 330 nm, with UV-B (280–320 nm), UV-A (320–400 nm) and visible (400–550 nm) wavebands responsible for 9, 61 and 30% of CO2 emission, respectively. Results from past field studies suggest that solar UV is typically less effective in driving litter mass loss than our WF predicts; we discuss possible reasons for this discrepancy. The gradual slope of our WF implies that differences in UV-B irradiance associated with stratospheric ozone thickness or latitude are unlikely to significantly influence photochemical litter emission.

Predicting Growing Stock Volume of Eucalyptus Plantations Using 3-D Point Clouds Derived from UAV Imagery and ALS Data

Estimating forest inventory variables is important in monitoring forest resources and mitigating climate change. In this respect, forest managers require flexible, non-destructive methods for estimating volume and biomass. High-resolution and low-cost remote sensing data are increasingly available to measure three-dimensional (3D) canopy structure and to model forest structural attributes. The main objective of this study was to evaluate and compare the individual tree volume estimates derived from high-density point clouds obtained from airborne laser scanning (ALS) and digital aerial photogrammetry (DAP) in Eucalyptus spp. plantations. Object-based image analysis (OBIA) techniques were applied for individual tree crown (ITC) delineation. The ITC algorithm applied correctly detected and delineated 199 trees from ALS-derived data, while 192 trees were correctly identified using DAP-based point clouds acquired from Unmanned Aerial Vehicles (UAV), representing accuracy levels of respectively 62% and 60%. Addressing volume modelling, non-linear regression fit based on individual tree height and individual crown area derived from the ITC provided the following results: Model Efficiency (Mef) = 0.43 and 0.46, Root Mean Square Error (RMSE) = 0.030 m3 and 0.026 m3, rRMSE = 20.31% and 19.97%, and an approximately unbiased results (0.025 m3 and 0.0004 m3) using DAP and ALS-based estimations, respectively. No significant difference was found between the observed value (field data) and volume estimation from ALS and DAP (p-value from t-test statistic = 0.99 and 0.98, respectively). The proposed approaches could also be used to estimate basal area or biomass stocks in Eucalyptus spp. plantations.

Catalyst-free aza-Michael addition for C–N coupling in active pharmaceutical ingredient synthesis: Modelling of thermodynamic, reaction kinetics and mass transfer considerations

The present research study describes a combined experimental-modelling approach to examine the three-phased catalyst-free reversible aza-Michael addition of NH3 to the vinyl sulfone pharmaceutical intermediate in water. A series of batch experiments using gaseous NH3 were performed to thoroughly evaluate the impact of reaction temperature, NH3 pressure, starting material loading, and starting material quality on reactant solubility, convective mass transfer, and reaction kinetics in the system. A rigorous in-house mechanistic mathematical model was developed. All unknown parameters were determined through nonlinear regression fitting of experimental and simulated quantitative results. Aza-Michael addition kinetics and starting material equilibrium solubility were found to be highly temperature-dependent and had the biggest applicative effect on the maximum aza-Michael reaction rate, which was also confirmed by sensitivity analysis technique. Boundary diffusion of reactants was shown not to be the limiting controlling factor under the chosen operating conditions. Ammonia pressure was found to be important through its impact on the saturated concentration of NH3. Varying starting material load had impact solely on the time required to reach system equilibrium due to solute concentration limitations. Reverse NH3 elimination reaction kinetics was shown to be independent on changing all input operating conditions. The specific methodology grants a novel engineering approach for treating complex interrelated multi-phased heterogeneous compositions in active pharmaceutical ingredient reaction systems, which may be applied early in industrial process development, when a small continuous amount of raw data sets is available, the quantity of impurities varies, and simulations can aid intensification. It may be easily transferred to other similar environments for assistance in process development, optimization, and scale-up.