Nonlinear Least-squares Regression Method Research Articles

On the Short-Term Creep and Recovery Behaviors of Injection Molded and Additive-Manufactured Tough Polylactic Acid Polymer

The creep and recovery behaviors of a tough polylactic acid polymer are investigated experimentally and theoretically. We studied the influence of manufacturing methods and parameters on the viscoelastic responses. Experimental comparisons were carried out on 13 different samples manufactured using fused deposition modeling (FDM) and injection molding methods. The sample variations in the FDM were based on four infill densities (70-100%) and 3 infill directions (0^circ ,45^circ ,90^circ ). Theoretically, the Burgers and Weibull’s models are used to predict the creep and recovery responses of the samples. Our experimental findings suggest that the injection-molded samples perform better in creep for most of the cases. However, at higher stress loadings, the 90 and 100% infill density samples showed excellent creep resistance behaviors at the 90^circ infill direction. On the other hand, the theoretical creep and recovery predictions were based on the nonlinear least-squares regression method. The Burgers model predicted the creep responses with reasonable accuracies. A maximum of 5.83% mean absolute percentage error (MAPE) was found for the 0° infill direction and 80% infill density sample. On the contrary, the model lacks accuracy in recovery strain predictions, showing an average of 173.15% MAPE for all studied samples. Introducing Weibull’s distribution improved the accuracies showing a 3.44% average MAPE for all samples.

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

Nonlinear Estimation of Variables for Heat Release Calculation Using a Gradient Method

Advanced combustion such as the partially premixed combustion (PPC) is characterized by high energy efficiency. However, they are sensitive to the inlet condition and injection of a combustion engine. Therefore, it is essential to use combustion feedback. The accuracy of the feedback variables, derived from the cylinder pressure signal, is crucial for effective combustion feedback control. This paper proposes a nonlinear least-squares regression method to estimate the pressure offsets and variable polytropic exponent in heat release calculation automatically. The combustion feedback variables derived from the auto-tuned heat-release rate were applied to a heavy-duty compression ignition (CI) engine burning with gasoline fuel.

Parameterized lattice strain models for REE partitioning between amphibole and silicate melt

The distribution of rare earth elements (REEs) between amphibole and silicate melt is important for understanding a wide variety of igneous and metamorphic processes in the lithosphere. In this study, we used published experimental REE and Y partitioning data between amphibole and silicate melt, the lattice strain model, and nonlinear least-squares regression method to parameterize key partitioning parameters in the lattice strain model ( D 0 , r 0 , and E ) as a function of pressure, temperature, and both amphibole and melt compositions. Two models, which give nearly identical results, are obtained in this study. In the first model, D 0 depends on temperature and amphibole composition: it positively correlates with Ti content and negative correlates with temperature and Mg, Na, and K contents in the amphibole. In the second model, D 0 depends solely on the melt composition: it positively correlates with Si content and negatively correlates with Ti and Ca contents in the melt. In both the mineral and melt composition models, r 0 negatively correlates with the ferromagnesian content in the M4 site of the amphibole, and E is a constant. The very similar coefficients in the equations for r 0 and best-fit values for E in the two models allow us to connect the two models through amphibole-melt phase equilibria. An application of our model to amphiboles in mantle xenoliths shows that observed major element compositional variations in amphibole alone can give rise to order of magnitude variations in amphibole-melt REE partition coefficients. Together with experimental data simulating fractional crystallization of arc magmas, out models suggest that: (1) REE partition coefficients between amphibole and melt can vary by an order of magnitude during arc magma crystallization due to variation in the temperature and composition of the amphibole and melt, and that (2) amphibole fractional crystallization plays a key role in depleting the middle REEs relative to heavy REEs and light REEs in arc magmas.

Modelling the dynamics of total precipitation and aboveground net primary production of fescue-feather grass steppe at Askania Nova according to global climate change scenariosModelling the dynamics of total precipitation and aboveground net primary production of fescue-feather grass steppe at Askania Nova according to global climate change scenarios

This article discusses modelling of Aboveground Net Primary Production (ANPP) of steppe (arid grassland ecosystems) plant species in relation to changes in total precipitation over the previous year at the “Stara” study site, Biosphere Reserve “Askania-Nova”, Khersonregion (Ukraine). To investigate linkages between precipitation and Aboveground Net Primary Production, correlation analysis was chosen and a time series regression analysis was based on the data set for the period 1988–2012. The NPP dependence on quantity of precipitation was found to be more significant for the previous autumn-winter-spring period (AWSP) than for the previous 12 month period. A regression model of ANPP’s dependence on AWSP is proposed. This model was further validated by the authors’ samples of ANPP, collected at the “Stara” study site in 2013–2016. The regression model showed a non-linear (quadratic) dependence of net primary production of zonal and intrazonal plant coenoses and total precipitation for the autumn-winter-spring period for arid grasslands with a coefficient of determination equal to 0.54 and significance level less than 0.05. The non-linear equation for these relations, visualized by a parabola curve, was calculated using the Nonlinear Least-Squares Regression Method. The data set, based on calculated predicted values, using the calculated equation, had a similar dynamic to the historical data on ANPP, but the model could not predict critical values. For this reason, additional studies are required for critical precipitation events. Non-linear response, investigated according to regression analysis, reveals optimal zones of plant growth, depending on the total precipitation level before the vegetation peak. For research areas where the dominant species are the turf grasses Stipa ucrainica P. Smirn., S. capillata L., S. lessingiana Trin. & Rupr., Festuca valesiaca Gaudin, Koeleria cristata (L.) Pers.) the optimal precipitation rates were found to be 350–400 mm during AWSP with ANPP at 350 g/m 2 . On the basis of the regression model and current forecasts of changes in precipitation rates we made a forecast of net primary production of plant communities for four climate change scenarios (RCP2.6, RCP4.5, RCP6, and RCP8.5) described in the Fifth Assessment of Intergovernmental Panel on Climate Change (IPCC). For this purpose, bioclimate projections of 10 major climate models (The Community Climate System Model Version 4 (CCSM4), GISS-E2-R, HadGEM2-AO, HadGEM2-ES, IPSL-CM5A-LR, MIROC-ESM-CHEM, MIROC-ESM, MIROC5, MRI-CGCM3, NorESM1-M), used for preparation of the IPCC report, were analyzed and imported to the geographical information system package QGIS. QGIS modelling software was used for geoanalysis and calculation of GIS-layers for Askania-Nova and adjacent arid grasslands. The results of modelling with the 10 climate models were compared and analyzed for each of the four IPCC scenarios, depending on predicted CO 2 levels. The presented modelling results showed a trend to growth in AWSP precipitation and NPP for all scenarios up to 2040–2060. The scenarios RCP2.6, RCP4.5, RCP6 predicted the optimum precipitation zone for current plant diversity for the period of 2040–2060 and scenario RCP8.5 predicted an optimum zone peak after 2080. The study confirmed the importance of monitoring the productivity of herbaceous communities in dry steppe ecosystems ofUkraine.

Nonlinear least squares regression for single image scanning electron microscope signal-to-noise ratio estimation.

A new method based on nonlinear least squares regression (NLLSR) is formulated to estimate signal-to-noise ratio (SNR) of scanning electron microscope (SEM) images. The estimation of SNR value based on NLLSR method is compared with the three existing methods of nearest neighbourhood, first-order interpolation and the combination of both nearest neighbourhood and first-order interpolation. Samples of SEM images with different textures, contrasts and edges were used to test the performance of NLLSR method in estimating the SNR values of the SEM images. It is shown that the NLLSR method is able to produce better estimation accuracy as compared to the other three existing methods. According to the SNR results obtained from the experiment, the NLLSR method is able to produce approximately less than 1% of SNR error difference as compared to the other three existing methods.

Measurement and Modeling for Isobaric Vapor–Liquid Equilibrium of Binary 1,3,5-Trichlorobenzene + 3,5-Dichloroaniline and 3-Chloroaniline + 3,5-Dichloroaniline Systems

The isobaric vapor–liquid equilibrium data for binary systems of 1,3,5-trichlorobenzene (1) + 3,5-dichloroaniline (2) and 3-chloroaniline (1) + 3,5-dichloroaniline (2) were measured experimentally under pressures of 20.00, 60.00 and 101.20 kPa using an inclined ebulliometer. Thermodynamic consistency of the vapor–liquid equilibrium data was tested by means of the Herington semiempirical method, and the isobaric vapor–liquid equilibrium data were correlated with three activity coefficient models, which were Wilson, NRTL and UNIQUAC. The energy interaction parameters were acquired by a nonlinear least-squares regression method for the three thermodynamic models. Results indicate that all the three activity coefficient models can describe the measured isobaric vapor–liquid data acceptably. The isobaric vapor–liquid equilibrium data determined in the present work are important in the design and operation for purification of 3,5-dichloroaniline by distillation.

Influence of structural parameters on dynamic characteristics and wind-induced buffeting responses of a super-long-span cable-stayed bridge

A 3D finite element (FE) model for the Sutong cable-stayed bridge (SCB) is established based on ANSYS. The dynamic characteristics of the bridge are analyzed using a subspace iteration method. Based on recorded wind data, the measured spectra expression is presented using the nonlinear least-squares regression method. Turbulent winds at the bridge site are simulated based on the spectral representation method and the FFT technique. The influence of some key structural parameters and measures on the dynamic characteristics of the bridge are investigated. These parameters include dead load intensity, as well as vertical, lateral and torsional stiffness of the steel box girder. In addition, the influence of elastic stiffness of the connection device employed between the towers and the girder on the vibration mode of the steel box girder is investigated. The analysis shows that all of the vertical, lateral and torsional buffeting displacement responses reduce gradually as the dead load intensity increases. The dynamic characteristics and the structural buffeting displacement response of the SCB are only slightly affected by the vertical and torsional stiffness of the steel box girder, and the lateral and torsional buffeting displacement responses reduce gradually as the lateral stiffness increases. These results provide a reference for dynamic analysis and design of super-long-span cable-stayed bridges.

Measurement and Correlation of the Vapor Pressure of 3,5-Dichloroaniline

The saturated vapor pressure of pure 3,5-dichloroaniline was measured from (10.25 to 95.81) kPa in the temperature range from (446.60 to 534.94) K using an ebulliometer. The results were fitted by an Antoine equation using a nonlinear least-squares regression method. The calculated saturated vapor pressure agrees well with the experimental values. The ideal gas molar enthalpy and ideal gas entropy of vaporization (ΔgidlHm, ΔgidlSm) of 3,5-dichloroaniline in the temperature range from (446.60 to 534.94) K were calculated by the combination of the Clausius–Clapeyron equation and Antoine equation.

On Chip Kalman Filtering Strategy-Based for VRLA Battery Control Unit

Based on existing understanding of residual capacity, the paper adopts Kalman filtering method on SOC estimation. The battery control unit(BCU) includes voltage, current and temperature sampling module. Due to Lead-Acid battery charging and discharging are a complex electrochemical process, we suggest a non-linear least squares regression method (NLLSRM) on open circuit voltage (OCV) method is proposed to aim at Lead-Acid battery. At the same time, a detailed hardware circuit schemes transfer module and on chip embedded Kalman filter method are employed. Moreover, A Local Interconnect Network (LIN) Bus Communication Technology is applied to communicate to Electronic Control Unit (ECU). Validation experimental results show that the proposed Lead-Acid BCU is high credible and the state of charge (SOC) estimation average relative error is about 3%.

An Analysis of Extinction Coefficients of Particles and Water Moisture in the Stack after Flue Gas Desulfurization at a Coal-Fired Power Plant

ABSTRACT Two important factors that affect in-stack opacity—light extinction by emitted particles and that by water moisture after a flue gas desulfurization (FGD) unit—are investigated. The mass light extinction coefficients for particles and water moisture, k p and k w, respectively, were determined using the Lambert-Beer law of opacity with a nonlinear least-squares regression method. The estimated k p and k w values vary from 0.199 to 0.316 m2/g and 0.000345 to 0.000426 m2/g, respectively, and the overall mean estimated values are 0.229 and 0.000397 m2/g, respectively. Although k w is 3 orders of magnitude smaller than k p, experimental results show that the effect on light extinction by water moisture was comparable to that by particles because of the existence of a considerable mass of water moisture after a FGD unit. The mass light extinction coefficient was also estimated using Mie theory with measured particle size distributions and a complex refractive index of 1.5-ni for fly ash particles. The k p obtained using Mie theory ranges from 0.282 to 0.286 m2/g and is slightly greater than the averaged estimated k p of 0.229 m2/g from measured opacity. The discrepancy may be partly due to a difference in the microstructure of the fly ash from the assumption of solid spheres because the fly ash may have been formed as spheres attached with smaller particles or as hollow spheres that contained solid spheres. Previously reported values of measured k p obtained without considering the effects of water moisture are greater than that obtained in this study, which is reasonable because it reflects the effect of extinction by water moisture in the flue gas. Additionally, the moisture absorbed by particulate matter, corresponding to the effect of water moisture on the particulates, was clarified and found to be negligible. IMPLICATIONS In-stack opacity is used as a surrogate for particle concentration and can be measured using light transmission meters as part of a continuous emission monitoring system. Because emission standards have become increasingly strict, FGD with wet scrubbing is generally used for coal-fired power plants. However, after a FGD unit with wet scrubbing is set up, the concentration of water moisture increases, affecting the measured opacity. This study evaluates the contributions of particles and water moisture to opacity. The results should provide useful information and can be utilized for modifying measurements for monitoring particulate emissions using opacity.

Kinetics of Catalytic Pyrolysis of Heavy Gas Oil Derived from Canadian Synthetic Crude Oil

The catalytic pyrolysis of heavy gas oil derived from Canadian synthetic crude oil on zeolite catalyst was conducted in a confined fluidized bed reactor. The optimal reaction temperature, weight hourly space velocity, steam-to-oil weight ratio, and catalyst-to-oil weight ratio were 660 °C, 9.5 h–1, 0.6, and 20, respectively. The yield of total light olefins was 36.4 wt % under these optimal conditions. The overall reactants and products were classified into seven species, and a seven-lump kinetic model with 15 rate constants and a catalyst deactivation constant was proposed. Kinetic constants at 620, 640, 660, and 680 °C were estimated by a nonlinear least-squares regression method. Preexponential factors and apparent activation energies were then calculated according to the Arrhenius equation. The feed lump had larger rate constants and smaller apparent activation energies than did the intermediate product lumps. The seven-lump kinetic model showed high calculation precision and the predicted yields agre...

Kinetic Study of Catalytic Pyrolysis of C4 Hydrocarbons on a Modified ZSM-5 Zeolite Catalyst

The reaction mechanism for catalytic pyrolysis of C4 hydrocarbons on a modified ZSM-5 catalyst was analyzed. With the overall reactants and products classified into six species, a 6-lump kinetic model was established to describe the reactions with appropriate assumption. Rate constants of the kinetic model at 480, 500, 530, and 560 °C were estimated by a nonlinear least-squares regression method. Pre-exponential factors and apparent activation energies were then calculated according to the Arrhenius equation. The 6-lump kinetic model showed good prediction performance, with predicted yields close to the experimental ones. The variation in ethene and propene yields with reaction temperature and the weight hourly space velocity of C4 hydrocarbons were predicted using the lump model as basis.

Solubility of 4,4′-Bis[[4-morpholino-6-(p-sulfonatoanilino)-1,3,5-triazin-2-yl]amino]stilbene-2,2′-disulphonate in Sodium Chloride + Water from (273.15 to 313.95) K

The solubilities of 4,4′-bis[[4-morpholino-6-(p-sulfonatoanilino)-1,3,5-triazin-2-yl]amino]stilbene-2,2′-disulphonate (FBA 210) in sodium chloride + water were measured by a synthetic method in the temperature range from (273.15 to 313.95) K. The solubility data are correlated with the modified Apelblat equation, and the parameters are estimated by the nonlinear least-squares regression method. Computation shows that the equation can predict the observed solubility behavior with an average deviation of about 2.1 %. The parameters A, B, and C are expressed as a function of the mass fraction (w) of sodium chloride in sodium chloride + water. The solubilities of FBA 210 in sodium chloride + water can be calculated by interpolation with acceptable precision for an industrial application.

Electron paramagnetic resonance study of free-radical kinetics in ultraviolet-light cured dimethacrylate copolymers.

A spin-trapping technique and direct kinetic measurements of electron paramagnetic resonance spectra were used to investigate the kinetics of radical production in the cross-linking photo-initiator system based on camphoroquinone and dimethyl-aminoethylmethacrylate in the presence of the corresponding monomer dimethacrylate copolymer mixture, as well as in the pure photo-initiator system. Consequently, in both cases, the kinetics of radical production and decay was measured. From the measured data the formal kinetic parameters of particular radical processes were calculated by the non-linear least-squares regression method.