Polynomial Curve Fitting Method Research Articles

Penentuan Kurva Kelengkungan Tulang Belakang pada Citra X-ray Skoliosis Menggunakan Metode Fuzzy C-Means

Scoliosis is a disorder that requires X-ray detection. Early detection is needed by patients with scoliosis. Based on information obtained through early detection, it will enable doctors to take the initial steps of treatment quickly. Determination of the spinal curve is the first step that serves to measure how severe the angle of the scoliosis curve. The angular severity of the scoliosis disorder can be calculated using the Cobb angle. Therefore, by estimating the spinal curve, we can also estimate the Cobb's angle. Based on the method from the previous study, the interobserver value can touch 11.8o with an error in the intraobserver measurement of 6o. Thus, during the Cobb Angle calculation process, subjective aspects are common and can still be tolerated today. But this aspect can also be the most frequent problem when using manual measurement methods by doctors. This study proposes an algorithm to measure the curve of the spine with computer-aided of X-ray images quickly with a error level error that is still within tolerance value. The data pre-processing process is carried out using Canny edge detection. The Fuzzy C-Means clustering algorithm (FCM) can detect the center point of the vertebral segment after segmentation of edge detection pre-processing. Formation of the spinal curve is done by the polynomial curve fitting method with the results of accuracy of 2.45o. Based on information on the spinal curve, the severity of the form of the scoliosis curve can be classified into four types, normal, mild, moderate and severe. Of the four levels, this system can be used to detect whether a person has scoliosis or not.

Synthesis of biodiesel via pre-blending of feedstocks: an optimization by the polynomial curve fitting method

Use of abundant indigenous energy crops for biofuel production contributes to enhance the economy and reduce the dependence on fossil fuels. This article aims to shed light on two energy crops available in Pakistan; castor (Ricinus communis L.) and cottonseed (Gossypium hirsutum L.). Although castor has excellent oil content (54%), its high viscosity is not acceptable. Therefore, pre-blending with cottonseed oil was proposed. Physical and chemical properties of crude oils, pure biodiesels and binary blends besides fatty acid composition and degree of unsaturation were analyzed. Biodiesels were checked for quality parameters within limits of American Society for Testing Materials (ASTM) and European Standards. Improvement in kinematic viscosity and density of castor biodiesel were noticed following this concept. Moreover, the developed empirical formula indicated that an optimized blending ratio of 93.86% cottonseed oil and 6.14% castor oil accomplished biodiesel yield of 91.12%, kinematic viscosity of 6 mm2/s and cetane number of 48.79, respectively, which all satisfy ASTM D6751. This technique also indicated that pre-blending can raise the ester content of castor biodiesel. In conclusion, it is recommended to adopt the concept of pre-blending to improve the quality of biodiesel and thus the engine and emission performance in compression ignition engines.

Three-dimensional computer simulation of twill woven fabric by using polynomial mathematical model

This study was carried out to obtain visual simulations of twill woven fabrics on a computer screen using certain fabric characteristic. Based on the Peirce model, the polynomial curve fitting method is utilized to simulate the buckling configuration of twill weave yarns. Polynomial mathematical model was never used in constructing twill weave woven fabric structure in the past studies. In polynomial model, each point on yarn buckling track is calculated through the curvature, the radius of the warp and weft yarn, the geometric density, and the buckling curve height. Moreover, the twill weave structure is displayed through the arrangement of the warp and weft yarns. The polynomial mathematical model method was applied to convert the yarn path to a smooth curve and will be provided for three-dimensional computer simulation of satin weave fabric. Different twill weave is displayed by changing fabric parameters. In the VC++6.0 development environment, according to polynomial mathematical model, the three-dimensional simulation of twill fabric structure was given in details through the OpenGL graphics technology.

Study on Influential Factors of ATSE Transfer Time Based on Orthogonal Polynomial Curve-Fitting

Study on transfer time of Automatic transfer switching equipment (ATSE) has been an important part in the process of switch design and development. Starting from analysis of the electrical operational performance test of ATSE, relationship of all key time parameters during its transfer cycle are researched. Then, the circuit and the test method that can satisfy the requirement of the test are designed, and tests on various types of ATSE are completed. Finally, orthogonal polynomial curve-fitting method is introduced, suitable polynomial for fitting analysis on the test data is explored, key factors influencing the transfer time is discovered, and hidden relationship between each other is found, which provide guidance for designing more stable ATSE and carrying out better electrical performance test.

Research on Al-alloy sheet forming formability during warm/hot sheet hydroforming based on elliptical warm bulging test

An elliptical warm/hot sheet bulging test under different temperatures and pressure rates was carried out to predict Al-alloy sheet forming limit during warm/hot sheet hydroforming. Using relevant formulas of ultimate strain to calculate and dispose experimental data, forming limit curves (FLCS) in tension–tension state of strain (TTSS) area are obtained. Combining with the basic experimental data obtained by uniaxial tensile test under the equivalent condition with bulging test, complete forming limit diagrams (FLDS) of Al-alloy are established. Using a quadratic polynomial curve fitting method, material constants of fitting function are calculated and a prediction model equation for sheet metal forming limit is established, by which the corresponding forming limit curves in TTSS area can be obtained. The bulging test and fitting results indicated that the sheet metal FLCS obtained were very accurate. Also, the model equation can be used to instruct warm/hot sheet bulging test.

Multi-sensor information fusion for remaining useful life prediction of machining tools by adaptive network based fuzzy inference system

Remaining useful life (RUL) prediction of machining tools is a typical multi-sensor information fusion problem. It involves the use of the monitoring information acquired from different types of sensors installed on computer numerical control machine to realize the RUL prediction of the machining tools in cutting process. Owing to the nonlinear and stochastic nature between the extracted features and tool wear level, the promptness and precision of online RUL prediction of machining tools are still difficult to be obtained. In this paper, a multi-sensor information fusion system for online RUL prediction of machining tools is proposed. The system includes sensor signal preprocessing based on ensemble empirical mode decomposition method, statistics feature extraction based on time domain and frequency domain analysis, optimum feature selection based on Pearson correlation coefficient, monotonicity and autocorrelation, feature fusion based on adaptive network based fuzzy inference system and RUL prediction model based on polynomial curve fitting method. We report a practical application of this multi-sensor information system and estimate its prediction performance. The proposed system may be applied to the industrial field. Meanwhile, the comparison between the proposed method and other standard methods is carried out using several statistical indices.

Perspective of safflower (Carthamus tinctorius) as a potential biodiesel feedstock in Turkey: characterization, engine performance and emissions analyses of butanol–biodiesel–diesel blends

ABSTRACTSafflower (Carthamus tinctorius) is widely farmed in Turkey. This study investigates the physicochemical properties of safflower biodiesel and its blends with Euro diesel and butanol. A polynomial curve-fitting method was used to predict kinematic viscosity and density of the ternary blends. Furthermore, characteristics such as DSC, FT-IR, UV-Vis and TGA were adopted to evaluate the influence of butanol addition on biodiesel–diesel blends. Engine performance parameters such as BP, torque and BSFC and emissions such as CO, HC, NOx and EGT were studied. Safflower methyl ester satisfied both EN 14214 and ASTM D 6751 standards regarding viscosity, flash point and density. However, iodine value was quite high. Oxidation stability fails to satisfy either standard. This is due to the high level of unsaturated fatty acids (91.05%). A reduction in BP, torque, HC and CO coupled with an increase in BSFC, NOx emissions and EGT was observed for all blends compared to Euro diesel. Overall, all blends appear to be good alternatives to biodiesel–diesel blends. This work supports that biodiesel can be blended with diesel and butanol as ternary blends (up to 20%) for use as a fuel in compression ignition (CI) engines. Therefore, combustion characteristics of blends shall be further investigated.

Myocardial elastogram using a fast mapping algorithm.

Ultrasound myocardial elastography is a promising technique to estimate regional myocardial function. In this study, we proposed a fast mapping method to map myocardial elastogram. A nude mouse's heart was scanned in supine position by an ultrasound system. The parasternal long-axis view of the heart and the ultrasound radio frequency (RF) signals were acquired for dynamic estimation of myocardial elasticity. The displacement and strain were calculated using analytic minimization (AM) and linear polynomial curve fitting method, respectively. The fast mapping method was proposed to map myocardial elastogram. The results display the contraction of myocardium intuitively. The method in this study is proved to have a potential to estimate viable myocardium in the future.

Considering air density effect on modelling wind farm power curve using site measurements

Manufacturers develop power curves for their wind turbines. Customers use these wind turbine power curves for wind farm planning and estimating nearly total production of planned plant. When wind farm is installed and connected to the grid, these power curves are not useful. In literacy, researchers proposed wind turbine power curve measurement methods to obtain an accurate power curve for turbine on site. But it is not easy to develop power curves for clusters of wind turbines. Developing a single power curve for a wind farm slightly simplifies this problem. Accurate wind farm power curve is a very useful tool for converting wind speed forecasts to power. Also plant owner can use this tool to detect anomalous operations. In this study we developed and tested wind farm power curves by using real site measurements. Two different methods are used to develop power curves. They are polynomial curve fitting and mean bins method. Wind speed and power output relation is investigated. A method is proposed to add effect of air density on power curve. Developed power curve has two inputs. They are hourly mean wind speed and air density values. This approach uses variable air density in calculation of wind farm power output. Results of this study showed that performance of mean bins method is better than polynomial curve fitting. Also proposed air density effect adding method improves performances of obtained power curves.

Determining cutting force coefficients from instantaneous cutting forces in ball end milling

The precise prediction of cutting forces helps in improving the machining performances. This involves the modelling of cutting force components in tangential, radial and axial directions and determination of respective specific cutting force coefficients. In the present work, an improved method of identification of specific cutting force coefficient is proposed for ball end milling cutter using semi-mechanistic force model. The cutter is discretised into a finite number of axial discs along the axis of the cutter. Using the geometry of ball end milling cutter, true uncut chip thickness is modelled based on the trochoidal trajectory of a cutting edge element. Specific cutting force coefficients have been determined through inverse method. Also, a fourth order polynomial curve fitting method has been employed to establish a mathematical relationship between the said coefficients and axial depth of cuts. Several experiments have been carried out at different feed rate and axial depth of cut to determine the specific cutting force coefficients based on the proposed identification method. Validation results show good agreement between predicted and experimental results. Compared to conventional identification model, the specific force coefficient identification process discussed in the present paper is fast, convenient and accurate.

Enhanced optical coherence tomography imaging using a histogram-based denoising algorithm

A histogram-based denoising algorithm was developed to effectively reduce ghost artifact noise and enhance the quality of an optical coherence tomography (OCT) imaging system used to guide surgical instruments. The noise signal is iteratively detected by comparing the histogram of the ensemble average of all A-scans, and the ghost artifacts included in the noisy signal are removed separately from the raw signals using the polynomial curve fitting method. The devised algorithm was simulated with various noisy OCT images, and >87% of the ghost artifact noise was removed despite different locations. Our results show the feasibility of selectively and effectively removing ghost artifact noise.

Analysis of Surface Plasmon Resonance Curves with a Novel Sigmoid-Asymmetric Fitting Algorithm.

The present study introduces a novel curve-fitting algorithm for surface plasmon resonance (SPR) curves using a self-constructed, wedge-shaped beam type angular interrogation SPR spectroscopy technique. Previous fitting approaches such as asymmetric and polynomial equations are still unsatisfactory for analyzing full SPR curves and their use is limited to determining the resonance angle. In the present study, we developed a sigmoid-asymmetric equation that provides excellent curve-fitting for the whole SPR curve over a range of incident angles, including regions of the critical angle and resonance angle. Regardless of the bulk fluid type (i.e., water and air), the present sigmoid-asymmetric fitting exhibited nearly perfect matching with a full SPR curve, whereas the asymmetric and polynomial curve fitting methods did not. Because the present curve-fitting sigmoid-asymmetric equation can determine the critical angle as well as the resonance angle, the undesired effect caused by the bulk fluid refractive index was excluded by subtracting the critical angle from the resonance angle in real time. In conclusion, the proposed sigmoid-asymmetric curve-fitting algorithm for SPR curves is widely applicable to various SPR measurements, while excluding the effect of bulk fluids on the sensing layer.

Influence of biodiesel blending on physicochemical properties and importance of mathematical model for predicting the properties of biodiesel blend

The growing demand for green world serves as one of the most significant challenges of modernization. Requirements like largest usage of energy for modern society as well as demand for friendly milieu create a deep concern in field of research. Biofuels are placed at the peak of the research arena for their underlying benefits as mentioned by multiple researches. Out of a number of vegetable oils, only a few are used commercially for biodiesel production. Due to various limitations of edible oil, non-edible oils are becoming a profitable choice. Till today, very little percentage of biodiesel is used successfully in engine. The research is still continuing for improving the biodiesel usage level. Recently, it is found that the blended biodiesel from more than one feedstock provides better performance in engine. This paper reviews the physicochemical properties of different biodiesel blends obtained from various feedstocks with a view to properly understand the fuel quality. Moreover, a short description of each feedstock is given along with graphical presentation of important properties for various blend percentages from B0 to B100. Finally, mathematical model is formed for predicting various properties of biodiesel blend with the help of different research data by using polynomial curve fitting method. The results obtained from a number of literature based on this work shows that the heating value of biodiesel is about 11% lower than diesel except coconut (14.5% lower) whereas kinematic viscosity is in the range of 4–5.4mm2/s. Flash point of all biodiesels are more than 150°C, except neem and coconut. Cold flow properties of calophyllum, palm, jatropha, moringa are inferior to others. This would help to determine important properties of biodiesel blend for any percentage of biodiesel and to select the proper feedstock for better performance.

TecLines: A MATLAB-Based Toolbox for Tectonic Lineament Analysis from Satellite Images and DEMs, Part 2: Line Segments Linking and Merging

Extraction and interpretation of tectonic lineaments is one of the routines for mapping large areas using remote sensing data. However, this is a subjective and time-consuming process. It is difficult to choose an optimal lineament extraction method in order to reduce subjectivity and obtain vectors similar to what an analyst would manually extract. The objective of this study is the implementation, evaluation and comparison of Hough transform, segment merging and polynomial fitting methods towards automated tectonic lineament mapping. For this purpose we developed a new MATLAB-based toolbox (TecLines). The proposed toolbox capabilities were validated using a synthetic Digital Elevation Model (DEM) and tested along in the Andarab fault zone (Afghanistan) where specific fault structures are known. In this study, we used filters in both frequency and spatial domains and the tensor voting framework to produce binary edge maps. We used the Hough transform to extract linear image discontinuities. We used B-spline as a polynomial curve fitting method to eliminate artificial line segments that are out of interest and to link discontinuous segments with similar trends. We performed statistical analyses in order to compare the final image discontinuities maps with existing references map.

An absolute phase to world coordinates method for the defocusing structured light shape measurement system

This paper proposes a flexible calibration method for the defocusing structured light three-dimensional (3D) imaging system. Neither a high accuracy translation stage nor the parameters of the projector is required. Therefore the method is more flexible in many practical applications. World coordinates for calibration are obtained based on the method of coordinates from known plane. The monotonic nonlinear relationships between the absolute phase and each world coordinate have been investigated. Different from other methods, in our method, the 3D shape is directly recovered by the absolute phase to world coordinates method. Experimental results show that, when polynomial curve fitting methods are used, the root-mean-squared (RMS) error for the flat plate reconstruction is less than 0.12mm, and the measurement error of 3D points is less than −0.34%. Furthermore, when comparing the measurement results of our method with the method of coordinates from known plane based on camera calibration, the relative error is less than −0.05%. Therefore, camera calibration is considered as the major error source.

A Novel Parameter Identification Method for Single-Phase Transformers by Using Real-Time Data

Equivalent circuit parameters of transformers are related to the condition of their windings. Information concerning winding deformations, failures, and temperature can be acquired by monitoring these parameters. Methods used for the determination of electrical parameters generally require disconnection of the transformer from the power system. In this paper, a novel method which uses real-time data of the transformer to determine its parameters is presented. Therefore, this method eliminates the need for the disconnection of the transformer from the power system. In the method, winding parameters are obtained by applying the differential equation algorithm to the fundamental frequency components of transformer data. Fundamental frequency components of the currents and voltages are computed by using the discrete cosine transform. Transformer core parameters are also computed via core losses and the polynomial curve-fitting method with the least squares error method. The proposed method has been tested and validated by simulations and experiments.

Development of a Raman chemical imaging detection method for authenticating skim milk powder

This research developed a Raman chemical imaging method for detecting multiple adulterants in skim milk powder. Ammonium sulfate, dicyandiamide, melamine, and urea were mixed into the milk powder as chemical adulterants in the concentration range of 0.1–5.0 %. A Raman imaging system with a 785-nm laser was used to acquire hyperspectral images in the wavenumber range of 102–2,538 cm−1 for a 25 × 25 mm2 area of each mixture. A polynomial curve-fitting method was used to correct for the fluorescence background in the Raman images. An image classification method was developed based on single-band fluorescence-free images at unique Raman peaks of the adulterants. Raman chemical images were created to visualize identification and distribution of the multiple adulterant particles in the milk powder. A linear relationship was found between adulterant pixel number and adulterant concentration, demonstrating the potential of this Raman chemical imaging method for quantitative analysis of adulterants in the milk powder.

Modal Testing and Parameters' Identification of Spray Boom

In order to research dynamic characteristics of the spray boom, this paper described a modal testing about a self-designed spray boom, the testing introduced the way that multi points and multi directions exciting, one point and one direction response to obtain the FRFs, after importing the dates to the computer, accorded to the stability diagram which calculated based on STAR7 from the obtained FRFs, four physical poles of the spray boom in the band between 0.25Hz and 30Hz were determined, then, two kinds of curve fitting method (POLYNOMIAL, GLOBAL) were used to identify the modal parameters. The result showed: the modal parameters identified through POLYNOMIAL curve fitting method is more accurate. For the first frequency of spray boom is 8.97Hz, in the band of ground exciting frequency. This may lead to spray booms deformation easily. So, to optimize the spray boom by increase the first frequency is necessary.

Multi-objective optimization of aircraft design for emission and cost reductions

Pollutant gases emitted from the civil jet are doing more and more harm to the environment with the rapid development of the global commercial aviation transport. Low environmental impact has become a new requirement for aircraft design. In this paper, estimation method for emission in aircraft conceptual design stage is improved based on the International Civil Aviation Organization (ICAO) aircraft engine emissions databank and the polynomial curve fitting methods. The greenhouse gas emission (CO2 equivalent) per seat per kilometer is proposed to measure the emissions. An approximate sensitive analysis and a multi-objective optimization of aircraft design for tradeoff between greenhouse effect and direct operating cost (DOC) are performed with five geometry variables of wing configuration and two flight operational parameters. The results indicate that reducing the cruise altitude and Mach number may result in a decrease of the greenhouse effect but an increase of DOC. And the two flight operational parameters have more effects on the emissions than the wing configuration. The Pareto-optimal front shows that a decrease of 29.8% in DOC is attained at the expense of an increase of 10.8% in greenhouse gases.

A comparative evaluation of physical and chemical properties of biodiesel synthesized from edible and non-edible oils and study on the effect of biodiesel blending

Traditionally, biodiesel has been produced from edible oils due to their low free fatty acids. However, their use has elevated some issues such as food versus fuel and many other problems that have negatively affected their economic viability. Therefore, exploration of non-edible oils may significantly reduce the cost of biodiesel especially in poor countries which can barely afford the high cost of edible oils. This paper aims to produce biodiesel from several edible and non-edible oils that are readily available in the South East Asian market. These oils include; Jatropha curcas, Calophyllum inophyllum, Sterculia foetida, Moringa oleifera, Croton megalocarpus, Patchouli, Elaeis guineensis (palm), Cocos nucifera (coconut), Brassica napus (canola) and Glycine Max (soybean) oils. This was followed by an investigation of physico-chemical properties of the produced biodiesel. This paper also discusses the concept of biodiesel blending to improve some of the properties of these feedstocks. For instance, blending of SFME and CoME improves the viscosity of SFME from 6.3717 mm2/s to 5.3349 mm2/s (3:1), 4.4912 mm2/s (1:1) and 3.879 mm2/s (1:3). The properties of other biodiesel blends were estimated using the polynomial curve fitting method.