Curve Fitting Approximation Research Articles

Synthesis and dosimetric characterization of lithium tetraborate (Li2B4O7:Cu,Ag) thermoluminescent dosimeter with improved reproducibility and reusability

A nano-sized, tissue equivalent, polycrystalline Li2B4O7:Cu, Ag phosphor was synthesized for dosimetric applications. Repeated annealing, irradiation and readouts may alter the color and affect the sensitivity of the phosphor. One of the aims of the present work was to dope Li2B4O7 with an appropriate amount of Ag and Cu atoms in order to diminish such effects and consequently improve reproducibility and reusability of the dosimeter. For this purpose, Li2B4O7 was primarily doped with Ag ions, and the Cu atoms were introduced with minimal concetration. A sample co-doped with 0.35 wt% Ag and 0.015 wt% Cu exhibited optimum TL response. To facilitate handling of the material, the powdered sample was also reproduced in pellet form. Linear integrated TL response was observed from 1 mGy to 20 Gy. No change in material's sensitivity and color was observed after repeated annealing, irradiation and readout episodes. Response of the material was found to be reproducible with a COV between 1.7 and 2.3%. Thermal quenching effects with increasing heating rate were seen for the current material. Less than 5% fading was observed during a two month study. The obtained glow curve was very simple having a main dosimetric peak at about 200 ± 10 °C with two small shoulder peaks. Kinetic analysis of the glow curve was performed by an experimental method (Tm-Tstop) and by curve fitting approximation. Kinetic parameters (b, s and E) were found within the prescribed limits. The promising dosimetric characteristics and the optimal glow curve favours this new material for use as a field dosimeter.

Optimal Long-Term Distribution System Planning: Network Reconfiguration and DG Integration

In this paper, a long-term Distribution System Planning Model (DSPM) considering network reconfiguration and Distributed Generation (DG) integration, is presented. The DSPM objective functions are power loss reduction and voltage stability enhancement. The proposed model handles long-term load increase and seeks to define when and where the reinforcements, such as network reconfiguration (NR) and DG integration, are required to meet the load increase. A Binary Particle Swarm Optimization algorithm (BPSO) is used for network reconfiguration while optimal DG allocation and sizing are performed using the Voltage Stability Margin Index (VSMI) and curve fitting approximation. The planning horizon of each solution is determined through load forecasting using a Nonlinear Autoregressive neuronal network with exogenous variables (NARX) technique. The performance of the proposed model is evaluated considering several case studies on the IEEE 33-bus test system. Results demonstrate the effectiveness of the proposed approach.

Design of Fractional-Order Lead Compensator for a Car Suspension System Based on Curve-Fitting Approximation

An alternative procedure for the implementation of fractional-order compensators is presented in this work. The employment of a curve-fitting-based approximation technique for the approximation of the compensator transfer function offers improved accuracy compared to the Oustaloup and Padé methods. As a design example, a lead compensator intended for usage in car suspension systems is realized. The open-loop and closed-loop behavior of the system is evaluated by post-layout simulation results obtained using the Cadence IC design suite and the Metal Oxide Semiconductor (MOS) transistor models provided by the Austria Mikro Systeme 0.35 m Complementary Metal Oxide Semiconductor (CMOS) process. The derived results verify the efficient performance of the introduced implementation.

Parametrization of CPW for Photonics Application with the Use of Closed Form Formulas

In this paper parametrized analysis of CPW (Coplanar Waveguide) applied in photonics is presented. The analysis is based on analytical formulas, which were delivered and modified from conformal mapping technique, and also after review of available literature from analytical models for the conventional CPW. Adjustment of the already reported CPW formulas was performed to properly model thin films CPW structures in PIC (Photonic Integrated Circuit). Thus, a closed expressions were proposed to simulate basic parameters, like: per unit length (p.u.l.) R (resistance), L (inductance), C (capacitance), G (conductance) and propagation quantity like characteristic impedance Zo versus frequency. The CPW line dedicated for the PIC application, is based on InP (Indium Phosphide) substrate and with air or BCB (Benzocyclobutene) surroundings of the metallization on the top. The modified formulas are curve-fitting approximations, with new fitting coefficients. Essential modifications are for p.u.l. C and p.u.l. L. Usefulness and effectiveness of the modified method was verified through results comparison with simulations in full-wave Electronic Design Automation software, with the circuit simulator QUCS and with real measurements, conducted with the use of PNA (Performance Network Analyzer). The paper novelty are new coefficients for analytical formulas, implementation of modified formulas in the octave code and model parametrization for geometrical parameters.

Reconstruction of Velocity Distribution in Partially-Filled Pipe Based on Non-Uniform Under-Sampling

In the process of research on the flow velocity distribution in a partially filled pipe, the under-sampling of measurement data often occurs. For the first time, this problem is solved by the improved non-uniform B-spline curve fitting approximation (NBSC) method. The main innovation of this method is to reconstruct the flow velocity distribution fitting curve with a small amount of non-uniform feature points containing flow velocity information. First, the curvature of a whole discrete sampled data is analyzed, then the weighted threshold is set, and the sampled points that satisfy the threshold are extracted as the initial velocity distribution feature points. Next the node vectors were constructed according to the initial feature points, and the initial interpolation fitting curves are generated. Secondly, by using the relative deviation between the initial approximation curve and each sampled point, new feature points were added where the curve allowable deviation exceeded the specified tolerance, and then a new interpolation fitting curve was obtained. The above procedure was repeated until the fitting curve reached expected accuracy, thus the appropriate feature points were determined. Experimental results showed that, in the case of the same approximation deviation, the proposed NBSC method can solve the problem of under-sampling of measurement data better.

Integration of distributed generation in electrical grid: Optimal placement and sizing under different load conditions

This paper proposes a novel approach for the placement and sizing of distributed generation (DG) ensuring voltage stability and reducing total power losses in electrical grid. The main concern of the proposed method is to guarantee voltage stability along with load fluctuations, while selecting optimal DG sites and power capacities. First, vulnerable buses are determined using Voltage Stability Margin Index (VSMI). Optimum size of DG unit is computed using Matlab curve-fitting approximation. For each load level, optimal DG size and its corresponding site are recomputed. General expressions for DG power capacity are established. For different load scenarios, the determined DG locations and size are always valid. The proposed method is implemented on the 33-bus and the 69-bus distribution systems using PSAT MATLAB toolbox and results are compared to other techniques published in the literature. The obtained results prove the effectiveness, the robustness and the good performances of the proposed method.

Frequency Response Based Curve Fitting Approximation of Fractional–Order PID Controllers

Abstract Fractional-order PID (FOPID) controllers have been used extensively in many control applications to achieve robust control performance. To implement these controllers, curve fitting approximation techniques are widely employed to obtain integer-order approximation of FOPID. The most popular and widely used approximation techniques include the Oustaloup, Matsuda and Cheraff approaches. However, these methods are unable to achieve the best approximation due to the limitation in the desired frequency range. Thus, this paper proposes a simple curve fitting based integer-order approximation method for a fractional-order integrator/differentiator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Simulation results in the frequency domain show that the proposed approach produces better parameter approximation for the desired frequency range compared with the Oustaloup, refined Oustaloup and Matsuda techniques. Furthermore, time domain and stability analyses also validate the frequency domain results.

Investigation on a new compact wideband rhombic dielectric resonator antenna

In this article, a new rhombic dielectric resonator antenna (DRA) is proposed. Dominant mode and a few of the higher order modes that are excited in this DRA are identified through eigen mode analysis performed through computer simulation technology (CST) simulation. Empirical formulae for calculating the resonant frequency of these identified modes are developed through curve-fitting approximation. Feeding techniques and possible ways of exciting some of these modes generated in such DRA are also detailed. Investigations are further carried out to identify appropriate feed positions to achieve broadband operation of such DRA geometry. The radiation patterns at different frequencies and variation of gain within the antenna bandwidth are measured for a fabricated prototype and compared with the simulation results.

Modeling and Analysis of an Air-Breathing Flexible Hypersonic Vehicle

By using light-weighted material in hypersonic vehicle, the vehicle body can be easily deformed. The mutual couplings in aerodynamics, flexible structure, and propulsion system will bring great challenges for vehicle modeling. In this work, engineering estimated method is used to calculate the aerodynamic forces, moments, and flexible modes to get the physics-based model of an air-breathing flexible hypersonic vehicle. The model, which contains flexible effects and viscous effects, can capture the physical characteristics of high-speed flight. To overcome the analytical intractability of the model, a simplified control-oriented model of the hypersonic vehicle is presented with curve fitting approximations. The control-oriented model can not only reduce the complexity of the model, but also retain aero-flexible structure-propulsion interactions of the physics-based model and can be applied for nonlinear control.

Optimal FIR Filter Design based on Curve Fitting Approximation for Uncertain 2–1 Sigma–Delta Modulator

Uncertain components in the integrators of 2–1 Sigma–Delta modulators cannot eliminate the first stage quantization noise completely, and the signal-to-noise ratio in analogue-to-digital converters is not reduced perfectly either. In order to solve the matching problem, older filter designs based on convex optimization are mathematically complicated, computationally intensive and not so efficient in application. In this paper, we propose a design method based on curve fitting approximation for uncertain linearized model of the modulator which is simple in principle and practical in application. Simulation results show that the optimal filter has better performance on multiple validations when compared to other modulator filters.

Bit error rate improvement for chaos shift keying chaotic communication systems

The bit error rate (BER) performance of chaos shift keying is improved for an additive white Gaussian noise channel by applying a trimming operation to the Chebyshev polynomial function of order 2 and the piecewise linear map to make the input source more Gaussian distributed. Analytical expressions for the improved BER are also derived based on the curve-fitting approximation. Numerical results show that the proposed method can achieve performance gains of up to 3.5 dB in signal-to-noise ratio over the conventional method without trimming.

Numerical Simulation of Air-He Shock Tube Flow with Equilibrium Air Model

In this study, a compressible multi-component Navier-Stokes flow solver with real gas effect is developed for studying the high-speed flow in an air-He shock tube. For compressible multi-component flow simulation, a reduced five-equation model in conjunction with HLLC approximate Riemann solver is employed. For the real gas effect, a curve-fitting approximation for equilibrium air constructed from Grabau-type transition functions is adopted. In addition, Baldwin-Lomax turbulence model is used for turbulent flow simulation. In this work, several typical test cases will be demonstrated first. Subsequently, air-He shock tube simulations with the real gas effect will be performed by using parallel computation. Based on the present results, the real gas effect shows significant influence on the temperature behind the reflected shock. In addition, the driver gas contamination and the development of shock bifurcation are presented by flow visualization.

Rapid Calculation of Oxygen in Streams: Approximate Delta Method

The “approximate delta method” is a simple procedure for simultaneous calculation of the stream reaeration coefficient, primary production rate, and respiration rate from a single-station stream diurnal profile of dissolved oxygen (DO). It approximates the exact graphs of results for the “delta method” reported in 1991 by Chapra and Di Toro by means of simple logistic curve-fitting approximations. The necessity of reading graphs or of obtaining numerical solutions is thereby avoided, so making it suitable for inclusion in a decision support system, particularly for streams reaeration coefficients less than 10 day−1 and for moderate photoperiods (10–14 h) . Worked examples are given for streams in the USA and in New Zealand. Results are used to show that the constellation of parameters for the three fundamental processes is much more important than their individual values in calculating diurnal DO profiles. Independent measurement of the reaeration coefficient enhances the utility of the method, by enablin...

Accurate Three-Term Approximation of the Angular Distribution of the Radiation Intensity

A very accurate approximation for the exponential integral £2 ( K ) was achieved by approximating the thermal radiation intensity by the first six terms of Legendre polynomial. The six constants in the three- 3 term expression for £2 ( K) = 2: Q; e- b; K through algebraic manipu- i = I lations were found. Unlike curve fitting approximations for £2 ( K ), the present three-term approximation gives accurate values for all optical thicknesses. For the sake of testing the new developed approximation, radiative equilibrium for planar participating gray media is considered. The radiative heat flux and the temperature distribution are compared with P-l and P-3 method results. Using the developed approximation for attacking radiative heat transfer in nongray medium is illustrated.

A continuous-dilution calibration technique for flame atomic-absorption spectrophotometry

Calibration in atomic-absorption spectrometry is achieved by means of a concentrationgradient chamber using a single concentrated standard solution. Calibration is rapid and extends over the entire working concentration range of the analyte, irrespective of the shape of the conventionally obtained calibration curve. No curve-fitting approximations are involved. With well-designed apparatus, deviations are less than 1%.