Polynomial Curve Fitting Method Research Articles

A novel approach for harmonic parameters estimation under nonstationary situations

A new class of windows, the even order cosα(x) window (EOCW), is proposed. The main-lobe and side-lobe behaviors of the EOCWs are studied. A EOCW-based weighted dual-point interpolated discrete Fourier transform (WDIpDFT) algorithm for calculating power system harmonic parameters under nonstationary situations is given. The EOCW has a low peak side-lobe level and a high side-lobe decaying rate. Leakage errors and harmonic interferences are thus reduced considerably by weighting samples with the EOCW. The rectification formulae of frequency, amplitude and phase of the fundamental and harmonics were obtained by using the polynomial curve fitting method. The EOCW-based WDIpDFT algorithm is free of solving high order equations, and the overall method can be easily implemented in embedded systems. The effectiveness and correctness of the proposed method were analyzed by means of computer simulations and practical experiments for multi-frequency signals with the variance of the fundamental frequency, the fluctuation of the harmonic voltage as well as with white Gaussian noise.

The Role of CO<sub>2</sub> Emission in Energy Demand and Supply

Problem statement: During the last few years in Malaysia, the amount of Carbon Dioxide (CO2) released into the atmosphere has been rising extensively. The main source of CO2 is power source of automobile and industry that are contributing the main role for these CO2 emissions. But these sectors are also very important for economic growth and developments. The aim of this study is to examine the current status and identify the future trend of energy demand and supply and its impacts on CO2 emissions in Malaysia. Approach: The data for analysis was obtained from the secondary sources. Results: The study discovered that the highest proportion of CO2 emissions comes from energy sector. The future trend of energy demand and supply was estimated by the forecasting polynomial curve fitting method. The increase rate of energy supply and demand can rich up to 170 and 160% respectively during the year 2020 if the current situation last long. The study showed a linear trend of increasing intensity of energy and CO2 emission with respect to Gross Domestic Product (GDP) by the year 2020. Conclusion: A significant share of CO2 emissions can be avoided through improved energy efficiency while providing the same or higher level of energy services. In this regard, greater use of energy efficient, renewable energy and green technologies or options and behavioural changes can substantially reduce CO2 emissions from the energy sector.

Equations of state for amorphous and crystalline nickel by means of molecular dynamics method

There are few theoretical studies on the equation of state (EOS) for amorphous materials while much work has been carried out for crystalline systems. In this study, the EOSs for both crystal- and amorphous-structured nickel are obtained by using an anisotropic molecular dynamics method based on the Voter-Chen formalism of embedded atom method. In order to achieve the EOSs, polynomial curve fitting method has been applied to the data obtained from molecular dynamics simulations carried assuming isothermal and isobaric conditions. Isothermal bulk modulus and their pressure derivatives for both amorphous and crystal structures have also been calculated. The results are compared with the values obtained from well-known Vinet and Davydov EOSs.

Parameter extraction for photovoltaic module based on Lambert W function

In order to solve the problems that engineering model of photovoltaic array has low accuracy (within 5%) and five-parameter model has more parameters which are difficult to obtain, a new method of parameters extraction is presented in this paper. This method is first to use Lambert W function to obtain the analytic expression for photovoltaic module, then to use polynomial curve fitting method to obtain the current-voltage relationship of PV module, and finally to use the subsection integral method to obtain the value of parameters for photovoltaic module. The proposed method shows that the accuracy is within 0.5%. Compared with conductivity method and pattern search method, this method not only has intuitive features but also is easy to use. Furthermore, the obtained photovoltaic module parameters possess smaller errors (within 0.1%).

Research into the Method of Accuracy Optimization in Survey Programming of MATLAB

In the process of survey data processing, solving problem can usually be attributed to linear equations like Ax=b, but under some circumstances, the equations may be ill-conditioned, if conventional method of MATLAB still be used in programming, the solution worked out may not be the true one. To solve this problem, method of introducing symbolic calculation into programming has been proposed in order to make ill-conditioned feature of designed equations better and improve stability and accuracy of parameter, the superiority in GNSS elevation fitting has been proved by triple-order polynomial curve-fitting method.

Research into the Method of Accuracy Optimization in Survey Programming of MATLAB

In the process of survey data processing, solving problem can usually be attributed to linear equations like Ax=b, but under some circumstances, the equations may be ill-conditioned, if conventional method of MATLAB still be used in programming, the solution worked out may not be the true one. To solve this problem, method of introducing symbolic calculation into programming has been proposed in order to make ill-conditioned feature of designed equations better and improve stability and accuracy of parameter, the superiority in GNSS elevation fitting has been proved by triple-order polynomial curve-fitting method.

A five-point stencil based algorithm used for phase shifting low-coherence interference microscopy

The phase shifting technique is the most widely used approach for detecting the envelope in low coherence interferometry. However, if the phase shifts calibration contains errors, some parasitic fringe structure will propagate into the calculated envelopes and cause imprecision in the envelope peak detection. To tackle these problems, a five-point stencil algorithm is introduced into the phase shifting interference microscopy. Considering the amount of parasitic fringes, envelope peak detection and computational efficiency, the presented approach leads to satisfactory results in performance. In combination with a simple polynomial curve fitting method the proposed algorithm exhibits good performance on envelope peak detection in surface profiling. Both of the simulated results and the experimental results indicated that the presented approach can be taken as an alternative to the currently existing methods used for phase shifting low-coherence interference microscopy.

Investigation of Raman chemical imaging for detection of lycopene changes in tomatoes during postharvest ripening

Lycopene is a major carotenoid in tomatoes and detecting changes in its content can be used to monitor the ripening of tomatoes. Raman chemical imaging is a new technique that shows promise for mapping constituents of interest in complex food matrices. In this study, a benchtop point-scan Raman chemical imaging system was developed to detect and visualize internal lycopene distribution during postharvest ripening of tomatoes. Tomato samples at different ripeness stages (i.e., green, breaker, turning, pink, light red, and red) were selected and cut open for imaging. Hyperspectral Raman images were acquired from fruit cross-sections in the wavenumber range of 200–2500 cm −1 with a spatial resolution of 1 mm. A polynomial curve-fitting method was used to correct for the underlying fluorescence background in the original spectra. A hyperspectral image classification method was developed based on spectral information divergence to identify lycopene in the tomato cross-sections. Raman chemical images were created to visualize the spatial distribution of the lycopene for different ripeness stages. The system was also configured to test the feasibility of utilizing spatially offset Raman spectroscopy (SORS) technique for subsurface detection of a Teflon slab placed under samples of outer pericarp cut in 5-mm and 10-mm thick slices from green and breaker tomatoes. The results showed that the Raman spectrum of Teflon can be extracted from the SORS measurements of the pericarps placed over the Teflon, demonstrating the potential of the future development of a Raman-based nondestructive approach for subsurface detection of lycopene as an indicator of tomato maturity.

Design of Electrical Driving Circuits for a High-pressure Fuel Injector and Control of Fuel Injection Quantities by using the Polynomial Curve Fitting Method

Various electric driving circuits for the high-pressure (H.P.) GDI injector are required to be designed to be capable of rapid response and precise air-fuel ratio control for GDI engines. In this study, power transistors, IGBTs and power MOSFETs components are adopted respectively to design the electrical driving circuits for the H.P. GDI injector. The designed injector driving circuits are tested to verify its feasibility. The experiments for the GDI injection quantities are conducted under 60-100 bar fuel pressures, 1200~2000μs injecting pulse durations and DC 65V executing supply voltages. Also, the experimental fuel injection quantities of the high-pressure injector fed by the three-stage MOSFETs driving circuits can be modeled by using the polynomial curve fitting method. The polynomial mfuel(tp) equation of degree n fits the data of fuel injection quantities at different engine operating conditions. The fuel injection curve equations can be derived and implemented in developing the ECU to demonstrate its ability to control the fuel injection quantities and injection timing rapidly and precisely.

Determination of heat transfer coefficients by extrapolation and numerical inverse methods in squeeze casting of magnesium alloy AM60

In this work, a different wall-thickness 5-step (with thicknesses as 3, 5, 8, 12, 20 mm) casting mold was designed, and squeeze casting of magnesium alloy AM60 was performed under an applied pressure 30, 60 and 90 MPa in a hydraulic press. The casting–die interfacial heat transfer coefficients (IHTC) in the 5-step casting were determined based on thermal histories throughout the die and inside the casting which were recorded by fine type-K thermocouples. With measured temperatures, heat flux and IHTCs were evaluated using the polynomial curve fitting method and numerical inverse method. For numerical inverse method, a solution algorithm was developed based on the function specification method to solve the inverse heat conduction equations. The IHTCs curves for five steps versus time were displayed. As the applied pressures increased, the IHTC peak value of each step was increased accordingly. It can be observed that the peak IHTC value decreased as the step became thinner. Furthermore, the accuracy of these curves was analyzed by the direct modeling calculation. The results indicated that heat flux and IHTCs determined by the inverse method were more accurately than those from the extrapolated fitting method.

Field Testing and Analyses of a Batter Pile Group Foundation under Lateral Loading

Much of the new I-10 Twin Span Bridge, built over Lake Pontchartrain between New Orleans and Slidell, Louisiana, is supported by driven batter pile group foundations. To assess the methodology used to design and analyze batter pile foundations and to evaluate their performance under lateral loading, a full-scale lateral load test was conducted on an M19 eastbound pier of the new bridge. The M19 pier foundation consisted of 24 precast, prestressed concrete 110-ft-long batter piles; eight piles were instrumented with in-place inclinometers (IPIs), and 12 piles were instrumented with strain gauges. The test was conducted by pulling the M19 eastbound and westbound piers toward each other with high-strength steel tendons. A maximum 1,870-kip lateral load was applied in increments. A high-order polynomial curve-fitting method was applied for each load increment to fit the measured rotation profiles from the IPIs, and the fitted rotation curves were used to deduce the bending moment, shear force, and soil reaction profiles on the basis of specific mathematical derivations. The calculated moments from curve fitting were compared with the moments calculated from strain gauge measurements, and the results showed good agreement. The soils’ p-y curves at different depths were backcalculated from the derived soil reaction profiles. The resulting p-y curves showed no evidence of group effect. The FB-MultiPier program was also used to analyze the behavior of the M19 pier foundation under lateral loading. Comparison of FB-MultiPier results with measured values as well as values calculated from polynomial curve fitting showed that FB-MultiPier overpredicted the lateral deformations of batter pile group foundations.

ECAM Control System Based on Auto-tuning PID Velocity Controller with Disturbance Observer and Velocity Compensator

This paper proposed an ECAM (Electronic cam) control system which has simple and general structure. The proposed cam controller adopted the linear and polynomial curve-fitting method to generates a smooth cam profile curve function. Smooth motion trajectory of master actuator guarantees the good performance of slave motion and has an important effect on the interpolation quality of ECAM. The auto-tuning PID velocity controller was applied to overcome the uncertainties in ECAM, and the gains of the controller are updated continuously to ensure the consistency of system performance under varying working conditions. The robustness of system against the varying load torque disturbances and noises is guaranteed by using the load torque disturbance observer to suppress the disturbance on master actuator. The velocity compensator was applied to compensate the degradation of performance of slave motion caused from the varying driving speed of master motion. The stability and validity of the proposed ECAM control system was verified by simulation results.

Polynomial curve fitting method for refraction-angle extraction in diffraction enhanced imaging

X-ray diffraction enhanced imaging (DEI) is applied to inspect internal structures of weakly absorbing low-Z sample. How to extract phase information from raw images measured in different positions of rocking curve is the key problem of DEI. In this paper, we present an effective extraction method called polynomial curve fitting method, in order to extract accurate information angular in a fast speed. It is compared with the existing methods such as multiple-images statistical method and Gaussian curve fitting method. The experiments results on a plastic cylinder and a black ant at the Beijing Synchrotron Radiation Facility prove that the polynomial curve fitting method can obtain most approximate refraction-angle values and its computation speed is 10 times faster than the Gaussian curve fitting method.

Detecting phasic lapses in alertness using pupillometric measures

Small, nonreflexive pupillary changes are robust physiological indicators of cognitive activity. In the present paper, we examined whether measures of pupillary changes could be used to detect phasic lapses in alertness during a vigilance task. A polynomial curve-fitting method for quantifying parameters from single task-evoked pupillary responses (TEPRs) is described. The TEPR parameters associated with long latency responses (indicating low alertness) were compared to the TEPR parameters associated with normal latency responses (indicating an alert state) within a multilevel modeling framework. Three parameters, pupil diameter, linear pupil dilation rate and curvilinear pupil dilation rate, significantly differed between the long latency and normal latency response types. The results provide preliminary evidence that these parameters would be useful neurocognitive markers of operator state in a bio-behavioral alertness monitoring system.

Prediction of volumetric change in the "triple ring" caused by glioma I-125 brachytherapy.

The aim of this study was to reveal the volumetric changes in tumor necrosis, reactive zone, and edema referred to as the "triple ring" appearing after low-dose-rate iodine-125 (I-125) interstitial irradiation of 20 inoperable low-grade gliomas. To enable prediction of these volumetric changes, we provide mathematical expressions that describe the dynamics of the triple ring. Volumes of the three regions on image-fused control CT/MR images were measured for a 24-month period. The delivered dose on the tumor surface was 50-60 Gy. Dose planning and image fusion were performed with Brain-Lab Target 1.19 software; mathematical and statistical computations were carried out with Matlab numeric computation and visualization software. To determine the volumes, control images with the triple rings were fused with the planning images. Relative volumes normalized with respect to the volume of reference dose were calculated and plotted in the time domain. First, the mean values of volumes were determined from the patients' measured data; then, polynomials were fitted to the mean values using the polynomial curve-fitting method. The accuracy of our results was verified by correlating the predicted data with the measured ones. The polynomial prediction approach proposed here reveals the dynamics of the triple ring. These polynomials will assist with (1) designing the best treatment, (2) following the patient's condition, and (3) planning reirradiation if necessary.

Wideband Linear Frequency Modulated Waveform Compensation Using System Predistortion and Phase Coefficients Extraction Method

This letter presents an effective method to compensate for the wideband linear frequency modulated waveform errors using system predistortion coefficients. The coefficients can be readily extracted by measuring and analyzing the changing rates of the period of non-constant beat frequencies generated from a nonlinear system in the time domain. The amplitude distortion components are examined using the polynomial curve-fitting method. In order to experimentally validate the practical feasibility of the waveform generator and the predistortion coefficients extraction module, the waveform's amplitude ripple, range resolution, and peak sidelobe ratios are measured and analyzed. The measured amplitude ripple at 5.3 GHz is improved from 1.835 to 0.333 dB and from 2.793 to 0.75 dB within 50 and 85 MHz bandwidth, respectively. Finally, the range resolution is improved from 4.102 to 3.103 m for 50 MHz bandwidth and the peak sidelobe ratio is improved from 7.78 to 20.55 dB for 85 MHz bandwidth with the applied predistortion.

Methods for Deriving p-y Curves from Instrumented Lateral Load Tests

Abstract With the developments of new deep foundation systems and construction techniques, such as high capacity micro-piles, large diameter piles or drilled shafts, existing p-y criteria that were developed previously for small diameter piles or shafts may no longer be adequate. Deriving p-y curves from lateral load tests on instrumented deep foundations is critical for further refinement or developing pertinent p-y criteria for these new applications. However, there is a lack of a consistent and well verified method for deducing the p-y curves from lateral load tests measurement data. Four existing methods are evaluated using the measured results of eight full-scale field tests on fully instrumented drilled shafts as well as four hypothetical numerical simulation results. It is found that the p-y curves deduced by the piecewise cubic polynomial curve fitting method, when input into the LPILE (or COM624P) computer program, provides the smallest error on the prediction of deflections of a drilled shaft under the applied lateral loads. A procedure for determining an optimum strain gage spacing for instrumentation in a lateral load test to derive representative p-y curves is recommended. Finally, a parametric study has shown that the errors of the deduced p-y curves are mainly due to inaccurate moment profiles from strain gage readings. Accurate estimate of moment-curvature relationship of a reinforced concrete shaft is therefore essential to the accuracy of the deduced p-y curves from strain data.

Distributed optic fiber sensing for a full-scale PC girder strengthened with prestressed PBO sheets

Fiber Reinforcement Polymer (FRP) has been widely accepted as an innovative material for renovation and strengthening of existing infrastructures. Among the FRP materials, poly-p-phenylene benzobisoxazole (PBO) fiber sheets attracted great attention in recent years because of the high strength, high Young modulus and high energy absorption capability. In this study, a PBO Prestressing Upgrading Technique (P-PUT) including an air bag system and end anchoring system for the strengthening of a full-scale prestressed concrete girder is proposed at first. Then, for the purpose of evaluating the strengthening efficiency of the PBO sheets, performance of the strengthened PC girder, especially the compressive and tensional strain distribution of concrete and PBO sheet under different load levels and bonding performance of PBO sheets on concrete surface, optic fiber sensing system with a strain/loss analyzer based on the Brillouin Optical Time Domain Deflectometry (BOTDR) technique is employed. Two types of bonding methods for optic fiber installation called the Point Fixed (PF) method and Overall Bonding (OB) method are proposed and investigated. Finally, a kind of polynomial curve fitting method is presented to process the field data contaminated with noise.

Data analysis for surface plasmon resonance sensors using dynamic baseline algorithm

Needs of accurate and robust responses from surface plasmon resonance (SPR) sensor systems put high requirements to the data analysis methods used. The output of an SPR sensor comprises data of reflected light intensity as function of either wavelength or angle of incidence (SPR curve). As reported in the literature, commonly used methods for analysing the SPR curve are polynomial curve fitting methods and the centroid method. These methods have their drawbacks in either being sensitive to correlated noise or drift from the light source, or generating high noise on the SPR response. We propose a modified analysis algorithm, where a baseline for selection of data from the SPR curve is adjusted dynamically according to a pre-defined ratio between the areas of the SPR curve below and above the baseline. It is shown in a mathematical model, numerical simulations as well as in experiments that the proposed dynamic baseline algorithm is insensitive to optical power correlated noise/drift. The algorithm is mathematically simple and it can be readily combined with commonly used data analysis methods.

On the Development of a Multifunction Millimeter-Wave Sensor for Displacement Sensing and Low-Velocity Measurement

A new multifunction millimeter-wave sensor operating at 35.6 GHz has been developed and demonstrated for measurement of displacement and low velocity. The sensor was realized using microwave integrated circuits and monolithic microwave integrated circuits. Measured displacement results show unprecedented resolution of only 10 /spl mu/m, which is approximately equivalent to /spl lambda//sub 0//840 in terms of free-space wavelength /spl lambda//sub 0/, and maximum error of only 27 /spl mu/m. A polynomial curve-fitting method was also developed for correcting the error. Results indicate that multiple reflections dominate the displacement measurement error. The sensor was able to measure speed as low as 27.7 mm/s, corresponding to 6.6 Hz in Doppler frequency, with an estimated velocity resolution of 2.7 mm/s. A digital quadrature mixer (DQM) was configured as a phase-detecting processor, employing a quadrature sampling signal-processing technique, to overcome the nonlinear phase response problem of a conventional analog quadrature mixer. The DQM also enables low Doppler frequency to be measured with high resolution. The Doppler frequency was determined by applying linear regression on the phase sampled within only fractions of the period of the Doppler frequency. Short-term stability of the microwave signal source was also considered to predict its effect on measurement accuracy.