Curve Fitting Tool Research Articles

3D Point Smoothening Using Modified Local Regression for Reverse Engineering Process

This research will introduce an existing statistical curve fitting tool i.e. local regression into reverse engineering process. Instead of using the local regression on statistical data, it will be applied on 3D point clouds obtained from 3D scanners. As most 3D scanners capture the smallest surface details such as textured and non-smooth surfaces, it makes the 3D point cloud to surface conversion process problematic. By modifying this existing statistical tool of local regression with the proposed algorithm, it helps to smooth out rough surfaces obtained from 3D point cloud, minimising the error when generating the virtual surface from smoothened point cloud rather than from raw point cloud. The related method of performing the smoothening process on the 3D point will also be included in this paper. At the end, comparison of the smoothened point cloud and the unsmoothened point cloud will be visualised and discussed.

Theoretical Study of Aerosols Loading and Retention Over Bolgatanga, Ghana

The aerosols loading and retention over West Africa have grave effect on life-forms through the impact on health, farming, rainfall pattern, cloud formation, and regional climate. Bolgatanga can be found on the latitude and longitude of 10.78°N and 0.85°W, respectively. This research is focused on an investigative consideration of the negative effect of atmospheric aerosols over Bolgatanga in Ghana through a conceptual model using analytical and descriptive statistical methods with MATLAB curve-fitting tool. The model was verified using aerosol optical depth data set from satellite imagery—multi-angle imaging specto-reflectometer (MISR)—obtained over a period of 13 years. The highest percentage increase of aerosol retention was 64.27% over the research site. The model was used to estimate the atmospheric constants as 0.67, tuning constants as 0.24, and phase difference as [Formula: see text]. The physical interpretation of the results was analyzed systematically.

Kinetic and equilibrium modelling of adsorption of cadmium on nano crystalline zirconia using response surface methodology

Nano zirconia has been employed for adsorption of cadmium from aqueous solution. Adsorption parameters were optimized using Box-Behnken design. Adsorption parameters Initial concentration, adsorbent dose and temperature were optimized. Optimized conditions were found out at initial concentration=1ppm, adsorbent dose=4g/l and pH=7. The best-fit equations of linear and non-linear forms of kinetics and isotherm models were compared among themselves. Results exhibit that chi-square reduction method in Microcal origin curve fitting tool is better than Error analysis method of solver add in for determination of isotherm parameters. However, linear model explains the system best fit on the basis of R2adj in isotherm analysis. Experimental qe values were slightly closer to theoretical qe values in linear pseudo-second order model as compared to pseudo-first order non linear model. The system follows Langmuir isotherm model and pseudo-second order model. Thermodynamic parameter by partition and Langmuir constant method suggests that the system is spontaneous in nature.

Dynamically Weighted Combination of Fault - based Software Reliability Growth Models

Background/Objective: The Software Reliability Growth Models (SRGMs) are mainly used to plan and execute system testing in the Software Development Life Cycle (SDLC). The objective of this research paper is to propose a dynamically weighted fault based combination model for application during this phase of reliability growth testing of software systems. Methods: A dynamically weighted fault based SRGM, which describes equally well the exponential growth and S-shaped growth of mean value function in a software testing process is proposed. Non-linear regression methodology was deployed for parameter estimation of (SRGMs).The curve fitting tool in MATLABTm is used for this purpose. The coefficient of determination R2 , Sum of Squared Errors (SSE), Root Mean Squared Error (RMSE) is the goodness of fit measures used to assess the quality of fitting of the SRGMs. Findings: It is found that the proposed combination model describes the failure data better than the constituent models used for combining as revealed by the goodness of fit measures. Applications/ Improvements: The new model can be applied to model reliability growth during testing in software projects with varying characteristics. The model additionally provides vital quality metrics, which can be used to manage the current and future software projectsKeywords: Dynamically Weighted Combination Model, Exponential Growth, Goodness of Fit, S-shaped Growth, Software Reliability Growth Model

Kinetic and isotherm parameter determination for the removal of chromium from aqueous solutions by nanoalumina, a nanoadsorbent

Nanoalumina has been employed for the adsorption of chromium from aqueous solutions. The data for best-fit for linear and non-linear forms of kinetic and isotherm models were compared. Non-linear analysis included error analysis using ‘Solver add-in’ of Microsoft Excel, Origin and MATLAB software's curve fitting tool. MATLAB and Origin curve fitting tool (R2>0.96) are better than error analysis method (0.79<R2>0.99) of ‘solver add in’ for determination of isotherm parameters. Adsorption of chromium on nanoalumina is best explained by Langmuir isotherm model. Linear method is better than non-linear methods to determine the kinetic model. The sum of the square of error among linear and non-linear analysis methods for kinetic models is minimum for linear analysis method (0.008) than all other non-linear analysis methods (0.019–0.478). The adsorption of chromium on nanoalumina is governed by pseudo-second-order kinetics.

CLASSIC STRAIN ENERGY FUNCTIONS AND CONSTITUTIVE TESTS OF RUBBER-LIKE MATERIALS

ABSTRACT Four classic strain energy density (SED) functions for incompressible rubber-like materials, neo-Hookean, Mooney-Rivlin, Yeoh, and Ogden forms, are briefly reviewed. The strain–stress relations of the above-mentioned SED functions for uniaxial, planar (pure shear), and equibiaxial deformation modes and formulas for transforming tensile data to compressive data of these three special deformation modes are given. Three approximate criteria are proposed for judging the validity of test data obtained from various methods. It is found that Treloar's data are the most reasonable among six groups of published data judged using the proposed criteria. Different combinations of Treloar's data were used to determine the parameters of these SED functions. The effects of three special tests on determining the parameters of various SED functions using the curve-fitting tools provided by ABAQUS were analyzed. Uniaxial tension data were found to be sufficient for determining the neo-Hookean, Yeoh, and first-order Ogden models, whereas both uniaxial and equibiaxial data were necessary for determining the Mooney-Rivlin and Ogden (N = 2, 3) models, and planar data were unnecessary to determine the parameters for all reviewed SED functions.

Design and optimization of a modified Sierpinski fractal antenna for broadband applications

Immense understanding of antenna designers illustrate that a general microstrip antenna demonstrate low efficiency. Various techniques have been adopted to improve the performance characteristics of microstrip antenna. This paper deals with the optimization of Sierpinski fractal antenna structure by utilizing the particle swarm optimization (PSO) and curve fitting method. The required data for optimization and fitting the curve has been obtained by varying different design parameters of the proposed antenna. Electromagnetic solver Ansoft HFSS 13.0 is used for generating the parametric data. The MATLAB curve fitting tool is referred for developing the equations which exhibits the relations between the parameters of proposed antenna design. Particle swarm optimization technique is then applied to find the optimum values of the design parameters for the bandwidth enhancement of proposed antenna. Curve fitting based optimized design represents the remarkable improvement in the bandwidth of conventional microstrip line fed Sierpinski fractal antenna for broadband applications.

Real-Time Enzyme Kinetics by Quantitative NMR Spectroscopy and Determination of the Michaelis–Menten Constant Using the Lambert-W Function

Enzyme kinetics is an essential part of a chemistry curriculum, especially for students interested in biomedical research or in health care fields. Though the concept is routinely performed in undergraduate chemistry/biochemistry classrooms using other spectroscopic methods, we provide an optimized approach that uses a real-time monitoring of the kinetics by quantitative NMR (qNMR) spectroscopy and a direct analysis of the time course data using Lambert-W function. The century old Michaelis–Menten equation, one of the fundamental concepts in biochemistry, relates the time derivative of the substrate to two kinetic parameters (the Michaelis constant KM and the maximum rate Vmax) and to the concentration of the substrate. The exact solution to the Michaelis–Menten equation, in terms of the Lambert-W function, is not available in standard curve-fitting tools. The high-quality of the real-time qNMR data on the enzyme kinetics enables a revisit of the concept of applying the progress curve analysis. This is pa...

Evaluation of Cell Growth and Substrate Consumption Kinetic of Five Different Lactobacilli in a Submerged Batch Whey Culture for Lactic Acid Production

Cell growth and lactose consumption profile of five Lactobacillus Strains: bulgaricus, casei, lactis, delbrueckii and fermentum has been investigated. Experiments of cell growth and substrate utilization were conducted in batch submerged culture of whey with added lactose and some other growth factors. Fitness assessment of experimental data on the cell growth and lactose consumption by Monod kinetic model was performed using the curve-fitting tool in Mat Lab software. Lactobacillus casei subsp. casei PTCC1608 with R2, μmax and Ks as 0.965, 0.435 h-1 and 27.05 g L-1, respectively showed the most fitness with Monod equation. Between the investigated strains, Lactobacillus fermentum PTCC1744 also showed an acceptable consistency with Monod kinetic model (R2= 0.951). Its μmax and Ks values were 0.134 h-1 and 54.46 g L-1, respectively. Lactobacillus delbrueckii subsp. Bulgaricus PTCC1737 (R2= 0.891) and Lactobacillus delbrueckii subsp. lactis PTCC 1743 (R2=0.857) did not have an accepted fitness with Monod kinetic model.

Fractal geometry analysis of chemical structure of natural starch modification as a green biopolymeric product

Public concerns and official pressures around environmental protection as well as exhausting petroleum resources have brought about preferences in studying and applying environmental-friendly polymers instead of synthetic petroleum-based polymers. For this aim, biopolymers can have outstanding advantages in biodegradability by saving time, energy and effort spent on increasingly costs of polymeric wastes. Natural starch (being studied in this work), as one of the most abundant natural resources for polymer materials, is inexpensive and biodegradable. As starch necessarily needs for modifications and processing before being used as ideal green polymer material, it is vital to perform feature extraction and defect detection measures in structure by some method like image analysis. Fractal as a new geometry has circumstantially progressed recently in the fields of image processing, physical space–time, medical image analysis, electrochemical patterns, digital images, sounds etc. Box Count Fractal Dimension as a very important and popular part of fractal geometry can be a useful factor in feature extraction and pattern recognition. This paper presents a new method for defect detection in the structure of natural starch modification images using the fractal dimension (FD) along with mean and standard deviation of image color. This is performed via feature extraction based on artificial intelligence by MatLab R2013a for box counting algorithms. Otsu’s graythresh method by MatLab R2013a is applied to binarize the images. The results of proposed methodology are illustrated as log–log curves where the fractal dimensions are recognized by curve fitting (CF) tool with more than 95% accuracy. The outputs express that starch samples’ FD vary in the range from 1.636 to 1.926 among which the last is identified as non-defective polymer. Non-defective feature is of great importance for quality control measures and chemical reactivity being here highlighted as biodegradability.

Plumbdads and Quarkles: Discussing Modeling Trends with Students Using Fictional Parameters

Helping students develop an understanding of how to interpret experimental data trends is an important part of the introductory physics laboratory. Unfortunately, many of my colleagues have lamented that too many of their students do this poorly. This is a common refrain, and past research has already revealed student difficulties with measurement, uncertainty, and the overall meaning of data.1–3 Like many instructors, I prefer discovery-style labs and in many laboratory investigations students are asked to use curve-fitting tools to discover a relationship.4 But one day in lab, I began to wonder if students were looking at data and curve fitting in a way profoundly different than scientists. Research already indicates significant differences,5,6 but to get a clearer understanding of how students would treat general data, a hypothetical set of data using fictional parameters (plumbdads and quarkles) was given to first day students.

Parameter Identification of Surface Roughness in Ultra-Precision Turning Processing Based on GA-RBF Neural Network

The modeling of surface roughness is the key factor to improve the quality of products and raise the efficiency of process equipment in ultra-precision turning process. In order to analyze the influence of each cutting parameters on surface roughness, the prediction model of surface roughness was constructed, and parameter identification of the prediction model was required. To meet the requirement, the curve fitting tool of MATLAB toolbox and radial basis function neural network optimized by genetic algorithm were respectively used as a case study to validate the feasibility and reliability of the method proposed in this paper. The parameter identification results were given, and the comparison of the parameter identification results shows that the parameter identification based on radial basis function neural network optimized by genetic algorithm has higher prediction accuracy than curve fitting tool of MATLAB toolbox.

Optimization of weld pitch on overlay welding using mathematical method

It is important to overlap the even bead continuously to automate the overlay welding process. To obtain the even surface bead on overlay welded product, optimization of pitch distance between the each pass is one of the methods. Therefore, this study determines the optimal second pass pitch distance with respect to welding parameter such as torch position and welding speed. Variety of welding experiments was carried out with different welding parameters using Central Composite Rotatable Design (CCRD) method. Based on the experimental results, empirical models were developed after analyzing correlation between welding parameters and bead height, width and decentration of overlay welding. Finally, optimized empirical models were developed for predicting bead height and width by analyzing the main effect of each factor which affects bead geometry and their influence on interaction. In addition, a mathematical model was developed which determines the bead profile for visualizing the bead shapes using the Matlab curve fitting tool. These two models were combined for one of the overlay bead shape model. Furthermore, the mathematical model is then used to determine the second pass pitch distance, by allowing the same area above and below the point of interaction between two overlay weld pass.

Frequency content analysis of the probable earthquake in Kopet Dagh region—Northeast of Iran

This paper aims to describe a probabilistic frequency analysis procedure to develop seismic hazard maps of Kopet Dagh region in north and northeast of Iran which with mostly shallow earthquakes is a high active seismic area. The existence of Khangiran super gas reservoir increases the importance of this region. By application of the probabilistic methodology of Cornell, an extensive numerical analysis based on several deterministic and probabilistic indices, the frequency content of ground motions recorded during seismic events were carried out by EZFRISK computer code, Matlab programming environment, and generated graphical user interface C# computer code. In this paper, definition of a seismotectonic model of the whole region based on geologic, tectonics, and seismic information the potential seismic sources introduced and their seismic characteristics were determined. Among the different applied attenuation relationships, the proposed one by Ambraseys et al. (J Earthq Eng Struct Dyn 25(4):371–400, 1996) was considered and the results are expressed in a series of contour maps of expected PGA for 63 % probability. The elimination of fore and aftershocks and also put some abilities such as capability for result exporting in several format which can be defined by user for other mathematical generic curve fitting tools were carried out by a generated code in Matlab programming environment. Obtained hazard maps indicated that maximum accelerations will be occurred in northwest-central trend which has a well matching with Quchan-Robat and Esfarayen-Robat Gharabil faults. The relevant frequency analysis showed that form 0.1 to 10 Hz, PGA directly increased by frequency and then up to 20 Hz with a sharpen shape, decreased by frequency increasing. The trend continues by gradual reduction up to 100 Hz. Maximum acceleration will be occurred in the basement in frequency content of 10 Hz.

Self-intersections of rational Bézier curves

Rational Bézier curves provide a curve fitting tool and are widely used in Computer Aided Geometric Design, Computer Aided Design and Geometric Modeling. The injectivity (one-to-one property) of rational Bézier curve as a mapping function is equivalent to the curve without self-intersections. We present a geometric condition on the control polygon which is equivalent to the injectivity of rational Bézier curve with this control polygon for all possible choices of weights. The proof is based on the degree elevation and toric degeneration of rational Bézier curve.

Non-Structured Kinetic Model of Aspergillus niger Growth and Substrate Uptake in a Batch Submerged Culture

Aims: To investigate cell growth profile of Aspergillus niger in a batch submerged culture medium and then evaluation of cell kinetic behavior using some different non-structured kinetic models. Methodology: Experiments of cell growth and substrate utilization were conducted in batch submerged cultures with identified medium composition. Fitness assessment of experimental data on the cell growth and glucose consumption by models was performed using the curve-fitting tool in Mat Lab software. This report is the first in the kinetic investigation of Aspergillus niger PTCC 5010 with the studied models. This work was performed in Department of Chemical Engineering, Islamic Azad University, Qaemshahr Branch between April 2013 to September 2013. Results: Based on the obtained results; Moser kinetic model with R2 equal to 0.913 and Gompertz kinetic model with R2 equal to 0.949 were the best fitted models to describe the growth behavior of Aspergillus niger PTCC 5010 in the applied culture condition. Maximum specific cell growth rate with Moser and Gompertz kinetic models were 0.024 and 0.003h-1, respectively. Other kinetic constants for all studied models were also Original Research Article British Biotechnology Journal, 4(9): 970-979, 2014 971 determined at the applied culture conditions. The consistency of the experimental data with Monod, Verhulst and Contois kinetic models wasn't in an acceptable range. Conclusion: In scale up biochemical projects by Aspergillus niger PTCC 5010 for some industrial products, Moser and Gompertz kinetic models are able to demonstrate cell growth behavior and its substrate uptake profile. In continuous processes, dilution rate could be determined based on obtained maximum specific cell growth rate equal to 0.024 h-1.

Non-Structured Kinetic Model for the Cell Growth of Saccharomyces cerevisiae in a Batch Culture

Saccharomyces cerevisiae is known as the most widely used eukaryotic microorganism for biological studies. In present study, cell growth profile of Saccharomyces cerevisiae in a batch submerged culture was evaluated with three different non-structured kinetic models. Fitness assessment of experimental data on cell growth by models was performed using the curve-fitting tool in Excel and Mat-lab software. Obtained results showed Verhulst kinetic model with R equal to 0.97 was the most 2

The application of non-linear curve fitting routines to the analysis of mid-infrared images obtained from single polymeric microparticles

For the first time, we report a series of time resolved images of a single PLGA microparticle undergoing hydrolysis at 70 °C that have been obtained using attenuated total reflectance-Fourier transform infrared spectroscopic (ATR-FTIR) imaging. A novel partially supervised non-linear curve fitting (NLCF) tool was developed to identify and fit peaks to the infrared spectrum obtained from each pixel within the 64 × 64 array. The output from the NLCF was evaluated by comparison with a traditional peak height (PH) data analysis approach and multivariate curve resolution alternating least squares (MCR-ALS) analysis for the same images, in order to understand the limitations and advantages of the NLCF methodology. The NLCF method was shown to facilitate consistent spatial resolution enhancement as defined using the step-edge approach on dry microparticle images when compared to images derived from both PH measurements and MCR-ALS. The NLCF method was shown to improve both the S/N and sharpness of images obtained during an evolving experiment, providing a better insight into the magnitude of hydration layers and particle dimension changes during hydrolysis. The NLCF approach facilitated the calculation of hydrolysis rate constants for both the glycolic (kG) and lactic (kL) acid segments of the PLGA copolymer. This represents a real advantage over MCR-ALS which could not distinguish between the two segments due to colinearity within the data. The NLCF approach made it possible to calculate the hydrolysis rate constants from a single pixel, unlike the peak height data analysis approach which suffered from poor S/N at each pixel. These findings show the potential value of applying NLCF to the study of real-time chemical processes at the micron scale, assisting in the understanding of the mechanisms of chemical processes that occur within microparticles and enhancing the value of the mid-IR ATR analysis.

A software program to investigate the nucleation kinetics of solution grown crystals using MATLAB platform

A software program has been developed on the MATLAB platform, which is useful for studying the nucleation kinetics of crystals grown from solutions. Nucleation parameters such as interfacial energy (σ), metastable zone width (ΔTmax), volume free energy (ΔGv), critical energy barrier for nucleation (ΔG∗), radius of the critical nucleus (r∗) and nucleation rate (J) of the crystals are determined from classical nucleation theory. The Metastable Zone Width (MZW) of the crystals is explored by using the relation based on solubility and enthalpy of nucleation. A new polynomial equation has been generated by this software program, and the results are checked with the experimental data of crystal growth/formation. Nucleation temperature as a function of supersaturation ratio was successfully evaluated using MZW. The equation relating to the nucleation kinetics and MZW can easily be solved with the help of a newly designed software program in the MATLAB platform. In addition, a program has been developed that highlights changes in nucleation parameters when the supersaturation ratio is changed. A plot of temperature vs energy barrier, nucleation rate and interfacial energy is also drawn. Program summaryProgram title: NucleationCatalogue identifier: AERG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERG_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 6305No. of bytes in distributed program, including test data, etc.: 616560Distribution format: tar.gzProgramming language: MATLAB (MathWorks Inc.) version R2013a. Statistics Toolbox and Curve Fitting Toolbox requiredComputer: Any computer running MATLAB (MathWorks Inc.)Operating system: Tested on Windows XP, but generally it would work on any computer running MATLAB (MathWorks Inc.)RAM: 32 MBClassification: 8Nature of problem:In crystal growth, the knowledge of nucleation thermodynamical parameters like interfacial energy, metastable zone width (supercooling temperature), volume free energy, critical energy barrier for nucleation, radius of critical nucleus and nucleation rates is essential for the growth of good quality bulk single crystals. In these parameters, metastable zone width determination is very useful for growth. Also some curve fitting tool is needed to obtain more information about nucleation kinetics.Solution method:In this program, an attempt has been made to calculate nucleation parameters theoretically to understand the role of these nucleation thermodynamical parameters for crystallization. A linear fit is done to calculate enthalpy of solution and polynomial fitting is used to derive the saturation concentration equation. Metastable zone width was calculated by the enthalpy–supersaturation relation. Supersaturation control is a decisive parameter for optimizing growth conditions during crystallization processes. The effects of metastable zone width and nucleation rate of crystals caused by changes in different supersaturation ratios were analyzed.Running time:Interactive and instantaneous.

Magnetic Lens Pole Piece Axial Field Distribution Model

Axial field distribution model of pole piece has a certain theory value in the design of magnetic lenses. In this paper, on the base of analyzing pole piece axial field distribution model which other authors had deduced, using the nonlinear least square method and the curve fitting tool of MATLAB software, the Gaussian model for axial field distribution is obtained. By comparing these models, the Gaussian model has higher precision and also has a certain practical reference value.