Curve Fitting In Order Research Articles

Investigations on application of curve fitting in power system inertia estimation

ABSTRACT As the share of renewable energy sources in the power system keeps growing, a new issue with frequency stability – diminishing and changing inertia – has emerged. Estimating power system inertia has received a lot of attention lately in order to market design of synthetic inertia as an additional service and implement timely corrective steps for robust frequency control. Curve fitting technique has emerged as one of the promising techniques for estimation of power system inertia, however, many challenging aspects need to be addressed for its practical applications. This study aims to systematically assess the effectiveness of the curve fitting method under a range of operational parameters and conditions, such as the curve fitting order, the length of data to be used for curve fitting after an event begins, and the length of the moving average filter applied to the frequency data to remove oscillatory and noise from the frequency transient. The simulation studies have been performed on DIgSILENT and MATLAB platforms. The results show that very high and very low order curve fitting results are high errors and the 5th order model with mean error in estimated value of inertia less than 1% has outperformed others. The analysis on various window width of moving average filter found that increasing the window width results in more error. For IEEE-9 bus system, a filter up to 850 ms width has a mean percentage error below 1%. The analysis also revealed that the duration of the data used for curve fitting is not significant. For variation of the duration of the data used for the curve fitting from 50 ms to 500 ms, the estimated inertia values are found to be in a close range of 2.4881 s to 2.5262 s, for the single machine system with H = 2.5 s. The analysis presented in this study will be useful for effective application of curve fitting method in inertia estimation.

Non-linear modeling and parameter identification of a bolted joint using substructure synthesis theory

Engineering applications require accurate modeling and parameter identification to anticipate bolted joint behavior under different loading circumstances. Bolted joints are extensively used in civil and mechanical structures. In this research study, cubic stiffness non-linearity is examined and a comprehensive model, which can exhibit the non-linearity of joint behavior, is developed. This is achieved by modeling the bolted joint which is connected at one end of a cantilever beam. Mathematical model is established using concept of sub structure synthesis theory by considering non-linear translational stiffness and non-linear rotational stiffness as a boundary condition. Non-dimensional natural frequencies are estimated by assuming stiffness parameters and joint parameter estimation for translational spring having nonlinear stiffness is calculated using second order curve fitting technique. Furthermore, estimated and exact value of cubic stiffness coefficient are compared. The experimental results shows that the percentage error of estimation for all the modes are less than 8%. The experimentally determined natural frequencies are further contrasted with an analytical results to validate a precision of generated model. Present work contributes in improving the bolted joint analysis by providing a solid non-linear modeling and parameter identification methodology. This methodology enhances design practices and ensures the durability of engineering structures and mechanical systems by improving bolted joint comprehension.

Applicability of the universal thermal climate index for predicting the outbreaks of respiratory tract infections: a mathematical modeling approach

Respiratory tract infections (RTI) are one of the most frequent reasons for medical consultations. As air temperature decreases, but also in connection with other meteorological parameters, evident seasonal fluctuations in the number of consultations for RTI can be observed. The Universal Thermal Climate Index (UTCI) is a complex meteorological index derived from an analysis of human thermal balance that depends on air temperature, air humidity, and wind speed. Our aims were to check if this index, although never used before for that purpose, is an adequate tool for forecasting seasonal increases in RTI prevalence. This study is a retrospective analysis of patients’ consultations with general practitioners in the period of 2012–2015 (453,674 records) recorded in the city of Olsztyn (Poland), which is characterized by a cold climate type (Dfb). The values of air temperature, atmospheric pressure, relative air humidity, wind speed, and UTCI were used for a statistical analysis and a mathematical analysis of curve fitting in order to determine correlations between analyzed meteorological parameters and a number of medical consultations for RTI. Analysis of the number of medical consultations for RTI revealed an evident seasonal pattern in a 4-year observation period, with a strong inverse correlation between the number of patients with RTI and the UTCI. A statistically significant increase in the number of patients with RTI appeared when the UTCI decreased, especially when it reached the classes of strong cold stress and very strong cold stress. In conclusion, the UTCI is a valuable predictive parameter for forecasting seasonal increases in RTI cases. Its decrease may initiate a seasonal increased prevalence. This effect is strongest about the 10th day following a change in the thermal climate conditions and is not continuous. A larger number of consultations for RTI after weekends and holidays (the Monday effect) may blur the results of statistical analyses.

Propylene carbonate quantification by its derivative 3,5-diacetyl-1,4-dihydro-2,6-lutidine

Propylene carbonate (PC) is a non-toxic solvent currently used in various pharmaceutical formulations. Consequently, a simple, cost-effective and most accurate analytical method for the quantification of this optical inert solvent is of major interest. Based on a consecutive three-step reaction 3,5-diacetyl-1,4-dihydro-2,6-lutidine was obtained from PC and used for quantification by either UV and fluorescent detection. Data were compared with results from LC-ESI-MS as a reference method. After using Mandel's test for linearity assessment of the calibration curves, linear fitting was used for LC-ESI-MS and spectrofluorimetry, while a polynomial 3rd order curve fitting was used for spectrophotometry. High intra- and inter-day precision as well as high accuracy were confirmed for all three analytical methods (spectrophotometry, spectrofluorimetry and LC-ESI-MS). The comparison of all three methods was assessed using correlation coefficients and Bland–Altman plots, both showing satisfying results with a high degree of agreement. The new method confirmed its applicability for PC quantification in two formulations, namely a PC-enriched cream and polyester microimplants. This new quantification method for PC is a reliable alternative to highly sophisticated chromatographic methods.

Process time and MPPT performance analysis of CF, LUT, and ANN control methods for a PMSG-based wind energy generation system

Due to environmental issues such as global warming and the greenhouse effect, there is a growing interest in renewable sources of energy. Wind energy, which is the most important of these energy sources, can potentially meet a portion of the global energy demand. Numerous studies are being conducted worldwide to determine how the maximum level of power can be obtained from wind energy. In these studies, there is a particular interest in permanent magnet synchronous generators (PMSGs). This is because PMSGs exhibit a good performance within a wide range wind speeds and can be driven directly. In this study, the maximum power point tracking (MPPT) of a PMSG has been carried out by using a prototype built in a laboratory environment. The simulation model has been realized by utilizing MATLAB/Simulink and implemented by using dSPACE. MPPT has been performed by employing such control algorithms as an artificial neural network, a look-up table, and curve fitting in order to carry out comparative performance analyses of these control algorithms. Controllers were analyzed through comparisons between their MPPT and process performance. Based on our analysis results, we were able to identify controllers that were better in terms of power tracking and process performance.

Genetic Algorithm Applying to Calculate the Great Wall Soil Water Electrical Conductivity

In this paper, we report a simple but effective algorithm to estimate the undetermined coefficients in the formula of soil water electrical conductivity value by the soil apparent electrical conductivity method. By doing so, the coefficients can be accurately obtained to further calculate the soil water electrical conductivity. According to the process of calculating the soil solution electrical conductivity based on the apparent conductivity of soil, the error of the calculation equation is effectively calculated by the two order curve fitting method. Meanwhile the genetic algorithm is adopted to reduce the influence of the data error generated by the proposed algorithm, and improve the accuracy of the data as well. The experimental results demonstrate that the solution by the proposed algorithm can be effectively obtained and the error change is in one direction simultaneously. With these advantages, we can use soil water electrical conductivity to calculate the content of soil salt.

Integrated Adaptive Cruise Control for Parallel Hybrid Vehicle Energy Management

The possibility to distribute the traction power in a hybrid electric vehicle powertrain over different prime movers and energy recoverability via recuperative braking as well as buffering the energy on rechargeable batteries, lead to the question of how electrical, mechanical or chemical energy should flow among various hybrid components of the powertrain. It is already known that any information about the future driving condition over either a short or long distance horizon is critically valuable to optimize the hybrid strategy. ACC (Adaptive Cruise Control) is a well-known driving assistant system that allows maintaining a safe longitudinal inter-vehicle speed and distance with other traffic objects. Model Predictive Control (MPC) based ACC system inherently predicts the vehicle velocity and acceleration profile. This information together with sensor data can be used to generate the optimal hybrid control especially while approaching a slower vehicle, which means a recuperation potential for the battery and hybrid energy management system. To achieve this, second order curve fitting is applied to the cost function of Equivalent Consumption Minimization Strategy (ECMS) behaviour. The approximated variant is then used to estimate the look-ahead battery energy and if necessary apply pre-discharge strategies to fully benefit the recuperation energy during deceleration manoeuvres.

Rapid and molecular selective electrochemical sensing of phthalates in aqueous solution.

Reported research work presents real time non-invasive detection of phthalates in spiked aqueous samples by employing electrochemical impedance spectroscopy (EIS) technique incorporating a novel interdigital capacitive sensor with multiple sensing thin film gold micro-electrodes fabricated on native silicon dioxide layer grown on semiconducting single crystal silicon wafer. The sensing surface was functionalized by a self-assembled monolayer of 3-aminopropyltrietoxysilane (APTES) with embedded molecular imprinted polymer (MIP) to introduce selectivity for the di(2-ethylhexyl) phthalate (DEHP) molecule. Various concentrations (1-100 ppm) of DEHP in deionized MilliQ water were tested using the functionalized sensing surface to capture the analyte. Frequency response analyzer (FRA) algorithm was used to obtain impedance spectra so as to determine sample conductance and capacitance for evaluation of phthalate concentration in the sample solution. Spectrum analysis algorithm interpreted the experimentally obtained impedance spectra by applying complex nonlinear least square (CNLS) curve fitting in order to obtain electrochemical equivalent circuit and corresponding circuit parameters describing the kinetics of the electrochemical cell. Principal component analysis was applied to deduce the effects of surface immobilized molecular imprinted polymer layer on the evaluated circuit parameters and its electrical response. The results obtained by the testing system were validated using commercially available high performance liquid chromatography diode array detector system.

Accelerated pharmacokinetic map determination for dynamic contrast enhanced MRI using frequency-domain based Tofts model.

Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) is widely used in the diagnosis of cancer and is also a promising tool for monitoring tumor response to treatment. The Tofts model has become a standard for the analysis of DCE-MRI. The process of curve fitting employed in the Tofts equation to obtain the pharmacokinetic (PK) parameters is time-consuming for high resolution scans. Current work demonstrates a frequency-domain approach applied to the standard Tofts equation to speed-up the process of curve-fitting in order to obtain the pharmacokinetic parameters. The results obtained show that using the frequency domain approach, the process of curve fitting is computationally more efficient compared to the time-domain approach.

Measuring Method and Error Compensation for Amplitude-Frequency Characteristics of Electromagnetic Voltage Transformer

The amplitude-frequency characteristics of voltage transformer need to be measured accurately when the electrical parameters of inverter module are detected. Using frequency method to measure one electromagnetic voltage transformer entirely, the amplitude-frequency characteristics with waveform distortion and phase delay were tested and analyzed by FFT on some typical frequencies. Amplitude-frequency transfer errors were compensated by nonlinear fitting method mainly on 50Hz, 15kHz , 20kHz segment. One order and two order curve fitting of the least squares function called lsqcurvefit were simulated in the environment of MATLAB, the results proved that the two order curve fitting function has a better compensation effect.

Potential Sources of Errors in Measuring and Evaluating the Specific Loss Power of Magnetic Nanoparticles in an Alternating Magnetic Field

Heat-generating magnetic nanoparticles suspensions are being explored in research and clinical settings as hyperthermia treatment for cancer or as adjuvant in established cancer therapies. In these applications it is essential to use low nanoparticle dosage to prevent any potential side effects including those associated with their accumulation in liver or spleen. Hence, developing particles with superior heating properties continues to remain an active area of research. Specific loss power (SLP), also referred to as specific absorption rate (SAR), represents the power dissipation per unit mass of magnetic nanoparticles in alternating magnetic fields. Accurate measurement of SLP is the key for understanding the parameters that control the heat generation rate, which is required to optimize these systems. However, at presents there are no standards for performing SLP measurements and no accepted calibration materials, making it difficult to compare the performance of various systems reported in literature. Previous work from this group discussed the effect of sample volume and geometry on the SLP data accuracy. In this study, additional analysis and experiments are carried out to investigate the effect of the power dissipation rate, the magnetic properties and the method for temperature slope calculation on the accuracy of the reported power density. Results indicate that when the same heating time is used, the volume at which heat losses become negligible decreases with decreasing sample heating rate. Furthermore, it is shown that for calculating initial temperature slope, a larger error occurs with a longer heating time and higher power level regardless of the curve fitting methods, hence, when power density or heating time increases, a higher order curve fitting (e.g., 2nd polynomial and exponential) is more desirable. In addition, when the magnetization of a nanoparticle suspension is low, the SLP is independent of the sample geometry.

FUZZY MODELING AND COMPENSATION OF SCALE FACTOR FOR MEMS GYROSCOPE

The scale factor error of MEMS gyroscope is severe and therefore vital to analyze and compensate the error to improve the performance of gyroscope. Based on the operational principle of Dual Gimbaled MEMS gyroscope, it is analyzed that the physical origin of offset, nonlinear and asymmetry errors of scale factor. The error model of scale factor is proposed. The fuzzy logic, a method to compensate scale factor, is presented. The experimental results show that the dynamic raw error of gyroscope is 4053.2º/h (1σ), and error compensated by the fuzzy logic is improved to 79.0º/h (1σ). Compared with the conventional methods of 1th order curve fitting and segmented methods, the precision of gyroscope compensated by fuzzy logic is improved 15.4 and 7.5 times respectively. It verifies the accuracy of the fuzzy model and compensation, and improves of gyroscope in dynamic maneuvering.http://dx.doi.org/10.5755/j01.mech.17.4.571

MULTIVARIATE REGRESSION APPLIED TO THE PERFORMANCE OTIMIZATION OF A COUNTERCURRENT ULTRACENTRIFUGE - A PRELIMINARY STUDY

In this work, the least-squares methodology with covariance matrix is applied to determine a data curve fitting in order to obtain a performance function for the separative power U of an ultracentrifuge as a function of variables that are experimentally controlled. The experimental data refer to 173 experiments on the ultracentrifugation process for uranium isotope separation. The experimental uncertainties related to the independent variables measurements are considered in the calculation of the experimental separative power values, determining an experimental data input covariance matrix. The process control variables, which significantly influence the U values, are chosen in order to give information on the ultracentrifuge behaviour when submitted to several levels of feed flow F and cut . After the model goodness-of-fit validation, a residual analysis is carried out to verify the assumed basis concerning its randomness and independence and mainly the existence of residual heteroscedasticity with any regression model variable. The response curves are made relating the separative power with the control variables F and , to compare the fitted model with the experimental data and finally to calculate their optimized values.

Concentration estimation via curve fitting: quantification of negative inotropic agents by using a simple mathematical method in guinea pig atria

We created a simple method based on curve fitting in order to assess the concentration of pharmacological agonists or antagonists in the microenvironment of the receptors. We tested our method in electrically driven guinea pig left atria by estimating the concentration of N 6-cyclopentyladenosine (CPA; A 1 adenosine receptor agonist), acetyl- β-methylcholine (muscarinic receptor agonist) and verapamil (L-type Ca 2+ channel inhibitor) added previously to the atria in known amounts. Our results validated the fitness of the model under specified conditions. In addition, our data suggest a relatively slow elimination of CPA in isolated, practically bloodless guinea pig atrial myocardium.

Explicit Aquifer Diffusivity Estimation Using Linearly Varying Stream Stage

For a stream fully penetrating an unconfined aquifer, different approaches are available to estimate aquifer diffusivity. However, these approaches involve an interpolation of tabulated values or type-curve matching. Certain solutions also require curve fitting in order to compute hydraulic gradient at the stream-aquifer interface. Thus, in these approaches it is possible to incur errors. An alternative is to develop explicit equations of aquifer diffusivity that may not require any sort of curve fitting to extract hydraulic gradient or interpolation of tabular values. For a linearly varying stream stage, it has been possible to develop such an alternative approach. The present study develops an explicit relationship for the estimation of aquifer diffusivity using the available series or tabular solutions in the literature. An error analysis indicates that the proposed equation is capable of estimating the point-aquifer diffusivity within a maximum error of 3%.

LOCATING STRUCTURAL DAMAGE BY DETECTING BOUNDARY EFFECTS

This paper presents a method of pinpointing structural damage locations using operational deflection shapes (ODSs) measured by a scanning laser vibrometer. The method assumes the form C1cosβx +C2sin βx+C3coshβx +C4sinh βx for an ODS to match with its experimental data using a sliding-window least-squares method to determine the four coefficients Ci. It is shown thatC1 represents the central solution of displacement, C3the boundary-layer solution of displacement caused by boundary constraints, C2β the central solution of slope, andC4β the boundary-layer solution of slope. Moreover,C1 *C3is proportional to the difference of kinetic and elastic energy densities,C3 −C1is proportional to the curvature, andC4 −C2is proportional to the spatial derivative of the curvature. Because cracks on a structure introduce new boundaries to the structure and these coefficients change significantly at boundaries, crack locations are clearly revealed by the peaks on the C1*C3curve, sign change of C4, peaks on the fitting error curve, and sudden changes of C3−C1andC4 −C2. Moreover, numerical and experimental results show that each of these coefficients requires a different length of data points for curve fitting in order to smooth the curve. Based on this different data length requirement and the peaks and sign change of these coefficients we derive a boundary effect detection (BED) method for finding damage locations. A non-linear sliding-window least-squares fitting technique is also derived for estimating the extent of structural damage. Numerical and experimental studies on beams with different damages have been performed to prove the accuracy and reliability of the BED method.

310 エンジンマウント系の流体関連振動の解析

This paper is to introduce the method of acquiring an accurate constitutive model of elastic rubber material from test data. Uniaxial tension and compression tests of vibration isolation rubber for hydraulic damped engine mount are done. The experimental data are carefully processed with curve fitting in order to obtain stable parameters of constitutive law. Various constitutive forms for different scales of strain are analyzed. Due to the nonlinear property of rubber, different forms of constitutive law should be adopted for different range of strain. The constitutive forms obtained will be applied to the simulation and design of hydraulic damped engine mount. This modeling technique can also be useful for modeling of other kind of rubber materials.

Versal Deformation and Local Bifurcation Analysis of Time-Periodic Nonlinear Systems

In this study a local semi-analytical method of quantitativebifurcation analysis for time-periodic nonlinear systems is presented.In the neighborhood of a local bifurcation point the system equationsare simplified via Lyapunov–Floquet transformation whichtransforms the linear part of the equation into a dynamically equivalenttime-invariant form. Then the time-periodic center manifoldreduction is used to separate the `critical' states and reduce thedimension of the system to a possible minimum. The center manifoldequations can be simplified further via time-dependent normal formtheory. For most codimension one cases these nonlinear normal forms arecompletely time-invariant. Versal deformation of thesetime-invariant normal forms can be found and the bifurcation phenomenoncan be studied in the neighborhood of the critical point. However, ingeneral, it is not a trivial task to find a quantitatively correctversal deformation for time-periodic systems. In order to do so, onemust find a relationship between the bifurcation parameter of theoriginal time-periodic system and the versal deformation parameter ofthe time-invariant normal form. Essentially one needs to find theeigenvalues of the fundamental solution matrix of the time-periodicproblem in terms of the system parameters, which, in general, cannot bedone due to computational difficulties. In this work two ideas areproposed to achieve this goal. The eigenvalues of the fundamentalsolution matrix can be related to the versal deformation parameter bysensitivity analysis and an approximation of any desired order can beobtained. This idea requires a symbolic computational procedure whichcan be very time consuming in some cases. An alternative method issuggested for faster results in which a second or higher order curvefitting technique is used to find the relationship. Once thisrelationship is established, closed form post-bifurcation steady-statesolutions can be obtained for flip, symmetry breaking, transcritical andsecondary Hopf bifurcations. Unlike averaging and perturbation methods,the proposed technique is applicable at any bifurcation point in theparameter space. As physical examples, a simple and a double pendulumsubjected to periodic parametric excitation are considered. A simple twodegrees of freedom model is also studied and the results are comparedwith those obtained from the traditional averaging method. All resultsare verified by numerical integration. It is observed that the proposedtechnique yields results which are very close to the numericalsolutions, unlike the averaging method.

Analysis and experimental investigation of dielectrophoretic force in a planar electrode structure

In this paper, we have analyzed the dielectrophoretic (DEP) force in a planar electrode structure and compared the force with the values from the experiments. The analysis is made by an FEM package program. The motion of yeast cells in the electrode array is analyzed with curve fitting in order to calculate the force from the experiments. The DEP force from the analysis is one order higher than that from the experiments when the cells move afloat by from the bottom.

MANPOWER REQUIREMENTS IN PEDIATRIC INTENSIVE CARE

This study 1) measured manpower requirements for patient care in the pediatric ICU and 2) correlated manpower needs with measures of severity of illness (Physiologic Stability Index: PSI) and quantity of care (Therapeutic Intervention Scoring System: TISS) to assess their usefulness in predicting staffing needs. Methods: 9 randomly selected observation shifts (8 hours) were studied. Manpower needs were measured by an intermittent time sampling technique. PSI and TISS scores were determined for the observation shift, previous shift and previous 24 hours. Results: 91 patients were observed. Total personnel hr/pt = 8.1 ± .5 (range .7-16.4), MD hr/pt = 1.2 ± .2 (range 0-10.1) and respiratory therapy (RT) hr/pt = 0.3 ± .1 (range 0-2.4). Correlations of manpower times with PSI and TISS scores were significant (p <.01). For the observation shift these were: Observation shift manpower times were also significantly correlated with previous shifts and previous 24 hour PSI and TISS scores. Higher order curve fitting did not improve the correlations. Conclusions: Manpower requirements for pediatric ICU's are extensive. PSI and TISS scores which are routinely collected in many ICU's can assess trends in staffing needs but not individual patient manpower needs.