Nonlinear Curve Fitting Method Research Articles

Measurement error in hydrostatic leveling system due to temperature effect and their reduction method.

Temperature is a crucial factor influencing the accuracy of the hydrostatic leveling system (HLS), necessitating a temperature compensation test for HLS. This paper investigates HLS temperature compensation through theoretical correction and experimental verification. The influence of temperature on the accuracy of hydrostatic level products is determined through temperature tests on 34 hydrostatic level products. The optimal temperature compensation formula is derived using the non-linear curve fitting method. The HLS is enhanced with a temperature compensation algorithm and temperature sensor, resulting in a new, high-precision, and high-stability hydrostatic leveling product with temperature compensation. Experimental findings reveal that the stability of the improved hydrostatic leveling product exceeds 30% compared to products on the market and surpasses 70% compared to the original products.

Ultrafast measurement of photoacoustic parameters with mid-infrared frequency comb transients.

The photoacoustic (PA) effect has been widely used in various applications, including highly sensitive spectroscopy and label-free, non-invasive imaging. In this work, we demonstrate a fast and precise measurement of PA parameters for light-absorbing liquids using mid-infrared asynchronous sampling pump-probe measurements. To simulate the observed PA oscillation signals and extract various PA parameters as a function of pump power, we derived analytical solutions of the PA wave equation driven by a train of ultrashort Gaussian pump pulses. By fitting the analytical solution to the measured PA signals using a nonlinear curve fitting method, we could measure the PA parameters, including damping rate, viscosity, and natural frequency. Furthermore, the dynamic response of thermophysical properties of the chloroform solution is also investigated by measuring the variation of the Grüneisen parameter with pump power. We anticipate that this work will open new possibilities for precise in situ measurements of the thermal properties of light-absorbing liquids.

Statistical Analysis of Sea-Clutter using K-Pareto, K-CGIG, and Pareto-CGIG Combination Models with Noise

In this paper, the combinations of two compound Gaussian distributions plus thermal noise for modeling measured polarimetric clutter data are proposed. The speckle components of the proposed models are formed by the exponential distribution, while the texture components are mainly modeled using three different distributions. For this purpose, the gamma, the inverse gamma, and the inverse Gaussian distributions are considered to describe these modulation components. The study involves the analysis of underlying mixture models at X-band sea clutter data, and the parameters of the combination models are estimated using the non-linear least squares curve fitting method. Compared to existing K, Pareto type II, and KK clutter plus noise distributions, experimental results show that the proposed mixture models are well matched for fitting sea reverberation data across various range resolutions.

A non-singular fractional-order logistic growth model with multi-scaling effects to analyze and forecast population growth in Bangladesh

This paper is primarily concerned with data analysis employing the nonlinear least squares curve fitting method and the mathematical prediction of future population growth in Bangladesh. Available actual and adjusted census data (1974–2022) of the Bangladesh population were applied in the well-known autonomous logistic population growth model and found that all data sets of the logistic (exact), Atangana-Baleanu-Caputo (ABC) fractional-order derivative approach, and logistic multi-scaling approximation fit with good agreement. Again, the existence and uniqueness of the solution for fractional-order and Hyers-Ulam stability have been studied. Generally, the growth rate and maximum environmental support of the population of any country slowly fluctuate with time. Including an approximate closed-form solution in this analysis confers several advantages in assessing population models for single species. Prior studies predominantly employed constant growth rates and carrying capacity, neglecting the investigation of fractional-order methods. Thus, the current study fills a crucial gap in the literature by introducing a more formal approach to analyzing population dynamics. Therefore, we bank on the findings of this article to contribute to accurate population forecasting and planning, national development, and national progress.

Quantitative study the effect of 60Co on S3N4/SO2/Si capacitors via capacitance-voltage model

Two kinds Si3N4/SiO2/Si capacitor were fabricated in this work, firstly. Then the two kinds Si3N4/SiO2/Si capacitors were irradiated by 60Co at five radiation doses level (0, 1·103, 2·103, 3·103, 4·103 Gy(Si)). Because voltage dependent capacitance is the key measurement method in determining the electronic property of microelectronic materials, capacitance-voltage of two kinds Si3N4/SiO2/Si capacitors was measured before and after radiation. To quantitative study the effect of 60Co on S3N4/SO2/Si capacitors, an available capacitance-voltage model was applied to generate theoretical curves of experimental results. The fitting results agree very well with the observed curves (capacitance versus voltage). The quantitative relationship between radiation doses and carrier induced by 60Co on unit area was estimated due to this model is integrable. Another objective of this work was to identify the mathematical relationships between radiation doses and function coefficients corresponding to every experimental curve. Based on the calculation results from the non-linear curve fitting method, the radiation dose-dependent the function coefficient was theoretically explained, successfully. It is also appropriate to use function coefficient which mathematical link radiation dose to the parameters of the model in forecasting experimental C–V before one radiation dose is applied.

Cropland and rooftops: the global undertapped potential for solar photovoltaics

The utilization of cropland and rooftops for solar photovoltaics (PVs) installation holds significant potential for enhancing global renewable energy capacity with the advantage of dual land-use. This study focuses on estimating the global area suitable for agrivoltaics (PV over crops) and rooftop PVs by employing open-access data, existing literature and simple numerical methods in a high spatial resolution of 10 km × 10 km. For agrivoltaics, the suitability is assessed with a systematic literature review on crop-dependent feasibility and profitability, especially for 18 major crops of the world. For rooftop PV, a non-linear curve-fitting method is developed, using the urban land cover to calculate the PV-suitable built-up areas. This method is then verified by comparing the results with open-access building footprints. The spatially resolved suitability assessment unveils 4.64 million km2 of global PV-usable cropland corresponding to a geographic potential of about 217 Terawatts (TW) in an optimistic scenario and 0.21 million km2 of rooftop-PV suitable area accounting for about 30.5 TW maximum installable power capacity. The estimated suitable area offers a vast playground for energy system analysts to undertake techno-economic assessments, and for technology modellers and policy makers to promote PV implementation globally with the vision of net-zero emissions in the future.

Indian Regional Navigation Satellite System (IRNSS) Channel Model for Suburban Area

In this work, a robust channel model for the newly developed Indian Regional Navigation Satellite System (IRNSS) has been proposed considering a dynamic scenario due to receiver movement. The channel model takes into account various channel impairments such as random shadow fading with multipath fluctuations as well. Capturing the dynamic range variation, a two-state channel model is proposed here. The versatile Nakagami-lognormal (NL) composite distribution function is used for both the channel states, and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -means clustering algorithm has been used for state separation. An extensive measurement campaign has been conducted at the L5-band of the IRNSS system to obtain real-time fading data, on which the non-linear curve fitting method has been used to extract pertaining channel model parameters. The accuracy of the proposed channel model is measured quantitatively using quantitative metrics such as mean square error (mse) and Kullback–Leibler divergence (KLD). The illustrated results showing the close match between the modeled and empirically obtained data validate the fact that the proposed channel model can be used to capture the combined effect of random shadowing and multipath in the received IRNSS signal.

A Comparative Study of Parameter Identification Methods for Asymmetric Nonlinear Systems with Quadratic and Cubic Stiffness

Understanding the nonlinear dynamic characteristics of engineering structures is challenging, especially for the systems that exhibit asymmetric nonlinear behavior. This paper compared four parameter identification methods for asymmetric nonlinear systems incorporating quadratic and cubic stiffness nonlinearities. Hilbert transform, zero-crossing, direct quadrature, and wavelet transform were used to obtain the backbone, envelope, and restoring force curves from the free vibration time history. A nonlinear curve-fitting method was then applied to estimate the stiffness parameters of the asymmetric systems, and a linear least square fitting approach was utilized to estimate the damping parameters of the asymmetric systems. We used the Helmholtz–Duffing oscillator as a numerical example and a nonlinear vibration absorber with geometric imperfections to verify the feasibility and accuracy of these methods. The advantages and disadvantages of these methods and the deviations in estimated results are discussed.

Statistically optimized adsorption of Pb(II) ion on Corn Husk activated carbon – An application of Response Surface Method

In this study, the Response Surface Method statistically optimized Pb(II) adsorption on activated carbon prepared using corn husk. The full central composite design was the statistical method selected for optimization using adsorption capacity as a response factor. The quadratic model best explained the process. Adsorption parameters optimized were solution pH, contact time, temperature, and adsorbent dose. The respective optimum values were 4.5, 64 min, 50°C, and 0.4 g L-1. Adsorption isotherm and kinetics studies evaluated the data obtained at different temperatures using different isotherm and kinetics models. The non-linear curve fitting method determined the model with the best fit. Freundlich’s model best accommodated the isotherm data, whereas the pseudo-second-order kinetic model best modeled the kinetics data. Weber-Morris intraparticle diffusion model revealed the existence of multiple rate-controlling processes. The activation energy for the adsorption of Pb(II) ions was 30.17 kJ mol-1. The thermodynamics studies showed that the process was an entropy-driven endothermic process. Gibb’s free energy (ΔG) values were negative at the studied temperatures, and the spontaneity increased with the increase in temperature. The enthalpy (ΔH) and entropy change (ΔS) was 43.78 kJ mol-1 and 154.2 J mol K-1. The study concluded that the statistical method simplified the optimization of the adsorption process and produced an efficient adsorbent from corn husk.

Enzyme hydrolyzed bael fruit liquefaction and its kinetic study

The study aims to explore the mechanism and optimize the process of enzyme hydrolyzed bael fruit (Aegle marmelos) liquefaction using two different enzymes: pectinase and macerozyme r-10 (enzyme mixture). A full factorial design was applied for the factors with 0.05–1.5% (w/w) enzyme concentration (EC), 30–60 °C temperature, and incubation time of 30–240 min for pectinase and 60–360 min for macerozyme. Quadratic polynomial models were developed, showing R2 ≥ 0.94. Multi-objective numeric optimization was followed to maximize the increase in yield, total reducing sugar (TRS), clarity, and minimizing EC, temperature and time. Enzyme-treated juice extracts were acceptable on the sensory scale with overall acceptability >5. Maximum pomace reduction of 58.8% and 78.9% along with rise in mono and disaccharides were observed after treating with pectinase (t = 240 min) and macerozyme (t = 360 min), respectively at identical 0.775% EC and 45 °C temperature. With the pectinase enzyme, an optimum Δyield of 32.4% was obtained at 0.82% EC, 43 °C temperature in 169.4 min. Subsequently, with the macerozyme, an optimum Δyield of 39.6% was attained at 0.96% EC, 45.6 °C temperature in 245.9 min. Substrate degradation in bael fruit by enzymatic hydrolysis with pectinase (EC = 0.01–1.50%, time = 2.5–240 min) and macerozyme (EC: 0.01–1.50%, time: 5–360 min) was studied at their respective optimum temperatures. The modified Michaelis-Menten showed a good fit (R2 > 0.98) with the non-linear curve fitting method. Macerozyme treatment showed slower enzyme activity with higher substrate degradation but lower nutrient content compared to the pectinase treatment.

Fluorogenic recognition of Zn2+, Cd2+ by a new Pyrazoline-based Multi-Analyte chemosensor and its application in live cell imaging

A novel multi-response pyrazoline-based fluorescent probe 1 was designed and synthesized with a very simple molecular structure, which exhibited high sensitivity for detecting Zn2+ and Cd2+ in ethanol aqueous solution state based on the dissuasion of intramolecular charge transfer (ICT) and chelation-enhanced fluorescence (CHEF) effect. The binding modes of the complexes were determined to have 1:1 complexation stoichiometry and the binding constants were calculated to be 1.284 × 104 M−1 for Zn2+ and 4.313 × 103 M−1 for Cd2+ using the nonlinear curve-fitting method. Zn2+ and Cd2+ sensor have high anti-interference ability. Under optimal conditions, the detection limits were determined to be 0.9274 μM for Zn2+ and 0.8158 μM for Cd2+. Notably, the probe was found to have good biological compatibility and was employed to detect Zn2+/ Cd2+ in living Hela cells.

Efficient leak detection in single and branched polymeric pipeline systems by transient wave analysis

The widespread use of plastic pipes in different fluid conveyance systems has greatly driven the recent development and application of transient-based methods (TBMs) for leak detection in viscoelastic/polymeric pipelines. Current TBMs for viscoelastic pipe leak detection are usually achieved by a two-step procedure, namely viscoelastic parameters identification and leak detection, which requires the pre-knowledge of intact system states (i.e., non-leak) for comparative analysis. This paper presents an efficient single-step frequency domain inverse transient analysis (FDITA) method for simultaneous identifications of viscoelastic parameters and leaks in plastic pipes, so as to enhance the applicability and accuracy of TBMs. Both the single and branched polymeric pipe systems are applied for the method development and application. To this end, analytical solutions of single and branched systems from the transfer matrix method are firstly derived to represent the transient frequency responses of viscoelastic pipelines with leaks. A global optimized nonlinear curve fitting method is then employed to identify both viscoelastic parameters and potential leaks by knowing/measuring other system and flow conditions. Extensive experimental validations and numerical applications of both single and branched pipe systems demonstrate the very good efficiency and accuracy of the developed method for leak detection in different viscoelastic pipe systems. Furthermore, the mechanism of transient wave-leak-viscoelasticity is analysed based on these application results and theoretical evidence. Finally, a sensitivity analysis is performed to quantify and discuss the advantages and potential limitations of the developed method in the paper.

A new heat transfer correlation for supercritical water flowing in a vertical tube - an hitherto approach

This paper provides an hitherto new approach of a heat transfer correlation based on heat flux to mass flux ratio for predicting wall temperature of supercritical water flowing in a bare vertical tube. Totally 10,174 numbers of experimental data were collected, Out of which 4236 data are heat flux/mass flux ≤0.4 and 5938 data are heat flux/mass flux>0.4. These data were obtained from various experimental resources and Lookup table and it covers q/G ranges from 0.085 to 1.295, mass flux ranges from 201 to 3500 kgm−2 s−1, heat flux ranges from 129 to 1600 kWm−2, pressure ranges from 225 to 320 bar, diameter of the tube 4.4 to 38 mm and bulk fluid enthalpy ranges of 250 to 3200 kJkg−1 of vertical tube working at various supercritical working conditions based on normal, enhancement and deteriorated heat transfer regions. By using these data, a new heat transfer correlation is derived for finding the wall temperature by Levenberg-Marquardt (LM) algorithm of multi dimensionless analysis method with Nonlinear curve fitting method. A general form of forced convection heat transfer correlation was obtained by Buckingham Π theorem. The Wall temperatures predicted by various 7 existing correlations along with this new correlation are found by Visual basic program and compared with experimental data for evaluating the deviations. The rank was provided based on error band from ±0.5% to ±50% etc., and error analysis were conducted for proving the best fitting correlation.

Optimal Control Applied to a Fractional-Order Foot-and-Mouth Disease Model

In this paper, we propose a nonlinear fractional-order model in order to explain and understand the outbreaks of foot-and-mouth disease. The proposed model rely on the Caputo operator. We computed the basic reproduction number and demonstrated that it is an important metric for extinction and persistence of the disease. Utilizing reported foot-and-mouth disease data for Zimbabwe and the nonlinear least-squares curve fitting method we estimated the model parameters. Meanwhile, we performed an optimal control study on the use of animal vaccination and culling of infectious animals as disease control measures against foot-and-mouth disease. Our findings showed combinations of optimal vaccination and culling rates that could lead to the effective management of the disease.

Analysis of novel fractional COVID-19 model with real-life data application

The current work is of interest to introduce a detailed analysis of the novel fractional COVID-19 model. Non-local fractional operators are one of the most efficient tools in order to understand the dynamics of the disease spread. For this purpose, we intend as an attempt at investigating the fractional COVID-19 model through Caputo operator with order χ∈(0,1). Employing the fixed point theorem, it is shown that the solutions of the proposed fractional model are determined to satisfy the existence and uniqueness conditions under the Caputo derivative. On the other hand, its iterative solutions are indicated by making use of the Laplace transform of the Caputo fractional operator. Also, we establish the stability criteria for the fractional COVID-19 model via the fixed point theorem. The invariant region in which all solutions of the fractional model under investigation are positive is determined as the non-negative hyperoctant R+7. Moreover, we perform the parameter estimation of the COVID-19 model by utilizing the non-linear least squares curve fitting method. The sensitivity analysis of the basic reproduction number R0c is carried out to determine the effects of the proposed fractional model’s parameters on the spread of the disease. Numerical simulations show that all results are in good agreement with real data and all theoretical calculations about the disease.

Quantitative study of the effect of gamma radiation on lateral PNP bipolar transistor

Bias-emission voltage and dose-dependent current gain is a key parameter in detecting the physical properties of the bipolar transistor. The first objective of this work is to measure the influences of gamma radiation on current gain in lateral PNP bipolar transistors. Substantial differences of the current gain as a function of voltage between bias and emission are observed. Then, based on the calculated results from the non-linear curve fitting method, the voltage between bias and emission-dependent current gain is theoretically explained successfully via the asymmetric peak function. The simulations agree very well with the observed curves (current gain versus voltage). The minimum correlation coefficient between the experimental and calculated data is 0.998. The average relative errors between the measured and modeled values do not exceed 9.14% in all considered cases. Finally, the mathematical relationships between the parameters, which serve to link the current gain and voltage together with dose, are obtained. Consequently, the current gain can be predicted by both voltage between bias and emission and dose using only one function. To the best knowledge of the author, the effects of gamma irradiation on the lateral PNP transistors are quantitatively discussed for the first time in current gain.

Evidence for and Analysis of Multiple Hidden Coronal Strands in Cross-sectional Emission Profiles: Further Results from NASA’s High-resolution Solar Coronal Imager

Abstract Previous work utilizing NASA’s High-resolution Coronal Imager (Hi-C 2.1) 172 Å observations revealed that, even at the increased spatial scales available in the dataset, there may be evidence for coronal structures that are still not fully resolved. In this follow-up study, cross-section slices of coronal strands are taken across the Hi-C 2.1 field of view. Following previous loop-width studies, the background emission is removed to isolate the coronal strands. The resulting intensity variations are reproduced by simultaneously fitting multiple Gaussian profiles using a nonlinear least-squares curve-fitting method. In total, 183 Gaussian profiles are examined for possible structures that are hinted at in the data. The full width at half maximum is determined for each Gaussian, which are then collated and analyzed. The most frequent structural widths are ≈450–575 km with 47% of the strand widths beneath NASA’s Solar Dynamics Observatory Atmospheric Imaging Assembly (AIA) resolving scale (600–1000 km). Only 17% reside beneath an AIA pixel width (435 km) with just 6% of the strands at the Hi-C 2.1 resolving scale (≈220–340 km). These results suggest that non-Gaussian shaped cross-sectional emission profiles observed by Hi-C 2.1 are the result of multiple strands along the integrated line of sight that can be resolved, rather than being the result of even finer sub-resolution elements.

Sol–gel tantalum pentoxide thin films with tunable refractive index for optical sensing applications

Present study aims at development of thin films of sol–gel Ta2O5 with tunable refractive index that could be used as an active medium for volatile organic compound (VOCs) optical detection. In order to tune the refractive index, mesoporosity is introduced through soft templating approach where series of co-polymers (Pluronics) are utilized as structure-directing agents. Thin films are prepared by spin-coating method using tantalum sol synthesized from TaCl5 as a precursor and ethanol as a solvent. The temperature annealing at 320 °C finalizes the tantalum oxide lattice formation and decomposes the template being used. The morphology and elemental composition of the films are studied by transmission electron microscopy (TEM) and energy dispersive X-ray spectroscopy in STEM, respectively, and the amorphous status of the films is confirmed by selected area electron diffraction. Non-linear curve fitting method and non-destructive UV–Vis reflectance measurements are used for determination of optical parameters of the films. The free volume fraction in the films is estimated through modeling of refractive index by Bruggeman effective medium approximation. The films are exposed to acetone vapors as a commonly studied VOC. The reaction of the film due to vapors’ exposure is recorded as a change in the reflection spectra of the film and the adsorbed acetone quantity is estimated. The influence of template composition on optical and sensing properties of Ta2O5 films is revealed and discussed.

The difference of surface electromyography data processing method based on simulated manal-lifting-task

Objective: To study the differences of different signal processing method of surface electromyography (sEMG) in judging muscle fatigue. Methods: From July to October 2019, based on the model of simulated manual lifting operation, the original sEMG signals from 13 volunteers of brachial radial muscle, brachial two-headed muscle, triangle muscle, left vertical spine muscle, right vertical spine muscle and lateral femoral muscle were collected in the operation activities. Three different electromyography signal processing methods (all signal from motion beginning to the end, peak signal and ehe specified motion signal) were used to analyze the original data in time domain (RMS) and frequency domain (MDF) , the data difference between different electromyography signal processing methods was analyzed by using Wilcoxon rank and sum test and nonlinear curve fitting method. Results: The age of the subjects of the simulated lifting operation was (24.31±2.02) years old, height (173.78±4.84) cm, weight (66.28±5.58) kg, body mass index (BMI) 21.94±1.58. The thickness of triceps skinfold was (14.08±4.86) mm, and the thickness of the skin fold under the scapula was (15.54±3.59) mm. After processing the original signal data by using different sEMG signal interception methods, the normality test, Levene's test, and the Wilcoxon test showed that, except for the MDF index of the brachial two-headed muscle, the differences in the RMS and MDF signals of the other muscles were statistically significant (P<0.016) . The all signal processing method dealed with data distribution dispersion better than other methods, and the rate of change of RMS signal slope was higher than other methods. Non-linear regression results showed that all signal processing method had low volatility in processing data, and the regression equation had a high degree of fit. Conclusion: Different electromyography signal processing methods have differences. The all signal processing method which intercepts from starting point to the end point of action cycle has the least data volatility, and electromyography time domain and frequency domain index with the highest sensitivity of time, which is suitable for the application of surface electromyography to judge muscle fatigue in dynamic and complex operations.

Prediction of the “Tipping Point” to Widespread Uptake of Battery Electric Vehicles in China via Nonlinear Curve-Fitting Method

&lt;p&gt;The “Tipping Point” is a term that is widely used today to describe that a time or threshold once being surpassed would result in exponential growth in technology adoption or product sales in a specific industry. China’s BEV industry has grown tremendously in the past 10 years and recently, and China has been leading both BEV sales and manufacturing in the world. Thus, this paper aims to investigate the “Tipping Point” timeframe for Battery Electric Vehicles (BEVs) penetration in China. The major work is conducted in 3 steps. 1. This paper firstly defined the exactitude of “Tipping Point” as a 16% market penetration rate from Roger’s technology adoption model. 2. Then this paper used a simple exponential curve formula using the Levenberg–Marquardt Algorithm (LMA) calculation method to conduct nonlinear curve fitting modeling for various nations and testify the validity of our formula used. 3. Finally, after getting a positive result from these sample countries, this paper continues using this method to predict the 16% “Tipping Point” from several current predictions reports. It concludes with a calculated assumption that this 16% BEV market penetration rate would most likely occur by the end of 2024.&lt;/p&gt;