Least-squares Curve Fitting Method Research Articles

An extended Kalman-Bucy filter for state of charge estimation of 2-RC network modelled Li-ion battery

Li-ion batteries have increased dramatically in the automobile industry over the past few decades. Lithium-ion batteries are viewed more favourably due to their high energy density, specific energy, etc. Optimising the performance of lithium-ion batteries requires accurate modelling and estimation of the state of charge (SOC). This article introduces an efficient second-order resistor-capacitor (2RC) network battery model and an optimised extended Kalman-Bucy filter (EKBF) as the most effective way to model a battery and estimate its state of charge (SOC). The operating parameters of a lithium-ion battery are measured with the least-squares curve fitting method. At a temperature of 20 °C, the proposed method for estimating SOC has a mean absolute error (MAE) of 0.72 % and a root mean square error (RMSR) of 0.71 %. In addition, the operational characteristics of the proposed EKBF were validated by simulating its operation at temperatures ranging from 0 °C to 40 °C. Under all conditions, the proposed method maintained an average error rate of 0.40%. The output of the proposed topology was validated using OPAL-RT (OP5700) hardware-in-the-loop real-time simulator. Consequently, the proposed method is preferable for accurate and dependable SOC estimation in real-time battery management system (BMS) applications.

Dynamical Analysis of Generalized Tumor Model with Caputo Fractional-Order Derivative

In this study, we perform a dynamical analysis of a generalized tumor model using the Caputo fractional-order derivative. Tumor growth models are widely used in biomedical research to understand the dynamics of tumor development and to evaluate potential treatments. The Caputo fractional-order derivative is a mathematical tool that is recently being applied to model biological systems, including tumor growth. We present a detailed mathematical analysis of the generalized tumor model with the Caputo fractional-order derivative and examine its dynamical behavior. Our results show that the Caputo fractional-order derivative provides a more accurate description of the tumor growth dynamics compared to classical integer-order derivatives. We also provide a comprehensive stability analysis of the tumor model and show that the fractional-order derivative allows for a more nuanced understanding of the stability of the system. The least-square curve fitting method fits several biological parameters, including the fractional-order parameter α. In conclusion, our study provides new insights into the dynamics of tumor growth and highlights the potential of the Caputo fractional-order derivative as a valuable tool in biomedical research. The results of this study shell have significant implications for the development of more effective treatments for tumor growth and the design of more accurate mathematical models of tumor development.

A major outbreak of the COVID-19 on the Diamond Princess cruise ship: Estimation of the basic reproduction number.

The COVID-19 pandemic, which broke out in Wuhan, China, in 2019, was declared an international public health emergency by the World Health Organization on January 31, 2020. The outbreak on the Diamond Princess cruise ship had appeared first as a cluster infection outside China during the early pandemic. The incident occurred on February 1, 2020, involved an 80-year-old Hong Kong man who was diagnosed with COVID-19. The cruise ship docked in Yokohama, Japan, for 14 days of onboard quarantine; however, cluster infection outbroke rapidly. We constructed a SIR mathematical model and conducted an epidemiological study of the COVID-19 outbreak on the Diamond Princess cruise ship, covering the period from February 5 (start of quarantine) to February 20 (completion of 14-day quarantine). We estimated the basic reproduction number (R 0 ) using a novel method of nonlinear least-squares curve fitting under Microsoft Excel Solver. The 95% confidence interval (CI) values were estimated by the jackknife procedures. Six hundred thirty-four (17.1%) cases were diagnosed in a total population of 3711 cruise passengers, and 328 (51.7%) cases were asymptomatic. As of April 24, 2020, 712 cases had been diagnosed and 14 (1.96%) deaths had occurred. The R 0 with 95% CI of the COVID-19 outbreak was 3.04 (2.72-3.36). Without an evacuation plan for passengers and crew, we estimated the total number of cumulative cases would reach 3498 (CI, 3464-3541). If the R 0 value was reduced by 25% and 50%, the cumulative cases would be reduced to 3161 (CI, 3087-3254) and 967 (CI, 729-1379), respectively. The abovementioned R 0 value was estimated from the original Wuhan strain. Cruise conditions would accelerate the spread of infectious diseases and were not suitable for onboard quarantine. Early evacuation and isolation of all passengers and crew members would reduce the R 0 value and avoid further infections.

Subacromial Motion Metrics in Painful Shoulder Impingement: A Dynamic Quantitative Ultrasonography Analysis

ObjectivesTo explore the subacromial motion metrics in patients with and without subacromial impingement syndrome (SIS) and to investigate whether the abnormality was associated with rotator cuff pathologies. DesignThis cross-sectional observational study used dynamic quantitative ultrasonography imaging for shoulder joint assessment. SettingOutpatient rehabilitation clinic. ParticipantsIndividuals with SIS on at least 1 shoulder (n=32) and asymptomatic controls (n=32) (N=64). InterventionsNot applicable. Main Outcome MeasuresFrame-by-frame, the humeral greater tuberosity against the lateral edge of the acromion was traced to obtain the minimal vertical acromiohumeral distance (AHD). The rotation angle and radius of the humerus were computed using the least-squares curve fitting method. ResultsApproximately two-thirds of the shoulders with SIS did not have any sonographically identifiable rotator cuff pathologies. There was a consistent trend of nonsignificantly increased humeral rotation angles in painful shoulders. The generalized estimating equation demonstrated that the decreased minimal vertical AHD was associated with painful subacromial impingement (β coefficient: −0.123cm, 95% confidence interval [CI], −0.199 to −0.047). The area under the curve for the minimal vertical AHD to discriminate painful or impinged shoulders ranged from 0.624-0.676. The increased rotation angle (β coefficient: 10.516°; 95% CI, 3.103-17.929) and decreased rotation radius (β coefficient: −2.903cm; 95% CI, −5.693 to −0.111) were shown to be significantly related to the presence of supraspinatus tendinopathy. ConclusionsShoulders with SIS were characterized by a decreased minimal vertical AHD during dynamic examination. Abnormal subacromial metrics can develop in patients with mild (or no) rotator cuff pathologies. More prospective cohort studies are warranted to investigate the changes in subacromial motion metrics in populations at risk for painful or impinged shoulders.

Calibration of the length scale parameter for the stress-driven nonlocal elasticity model from quasi-static and dynamic experiments

The available experimental results in the literature on the quasi-static bending and free flexural vibration of microcantilevers and nanocantilevers are used to calibrate the length scale parameter of the stress-driven nonlocal elasticity model. The Bernoulli–Euler theory is used to define the kinematic field. The closed form solution derived for the bending problem is used to calibrate the length scale parameter by fitting the load–displacement curves to the experimental results. For the vibration problem, the calibration is done using the least-squares curve fitting method for the natural frequencies. The stress-driven nonlocal theory can adequately capture the size-dependent experimental results.

Submergence depth modeling of oil well reservoirs and applications

In oilfield production, it is important to be able to acquire the reservoir status of oil wells in real time, especially for low or ultra-low permeability oil wells. In this paper, based on the reservoir percolation characteristics of the oil layer and combined with the oil well permeability, liquid pressure and oil well pressure formulas, the non-homogeneous linear differential equation for oil well pressure is derived, based on which a submergence depth model of oil well reservoirs is established. The parameter merging is applied to reduce the parameter dimension of the submergence depth model; this approach substantially reduces the parameter dimension and application complexity and effectively improves the model application range. The model not only conforms to the reservoir percolation law of the oil layer but also applies to the balance laws of other substances with potential energy balancing ability. The application methods studied (namely, the extraction of the greatest common divisor, the weighted dichotomy and least-squares curve fitting) successively reduce the calculation error and expand the application scope. The least-squares curve fitting method causes the submergence depth error to reach the minimum of the 2-norm, and the number of iterations can be accurately assessed by the convergence speed of halving the numerical calculation error in every iteration. This method is suitable not only for the zero submergence depth case in the initial state but also for non-zero submergence depth cases. The experimental results show that the proposed submergence depth model for oil well reservoirs accurately reflects the change laws of submergence depth and time. Combined with the proposed application methods, the corresponding submergence depth can be obtained at any time point. The model and application methods provide strong support for formulating scientific oil production plans and implementing reasonable production methods for oil wells.

A Fractional Modeling of Tumor\u2013Immune System Interaction Related to Lung Cancer with Real Data

In this study, we investigate a new fractional-order mathematical model which considers population dynamics among tumor cells-macrophage cells-active macrophage cells, and host cells involving the Caputo fractional derivative. Firstly, the stability of the positive steady state of the model is studied. Subsequently, the conditions for existence and uniqueness of the solutions are examined. Then, the least squares curve fitting method (LSCFM) which is one of the prominent methods for parameter estimation is used to fit the parameters of the model. It is aimed to fit the relevant parameters with the help of the tumor tissue samples which were collected from the patient with non-small cell lung cancer who had chemotherapy-naive hospitalized at Kayseri Erciyes University hospital in Turkey. A total of 12 parameters in the model are estimated using the data of lung tumor cells of this patient for 14 days. Moreover, the numerical simulations are given by considering the different fractional orders and different parameters for the model. So, it is achieved how the change in alpha affects the dynamic behavior of the system. In the sequel, to point out the advantages of the fractional-order modeling, the memory trace and hereditary traits are taken into consideration. Finally, the interpretations in terms of biological science are provided in conclusion. We believe that this interdisciplinary study will open new doors for other similar studies and will shed light on the studies to be developed on the use of real data in the mathematical modeling of cancer.

Optimal Control Applied to a Fractional-Order Foot-and-Mouth Disease Model

In this paper, we propose a nonlinear fractional-order model in order to explain and understand the outbreaks of foot-and-mouth disease. The proposed model rely on the Caputo operator. We computed the basic reproduction number and demonstrated that it is an important metric for extinction and persistence of the disease. Utilizing reported foot-and-mouth disease data for Zimbabwe and the nonlinear least-squares curve fitting method we estimated the model parameters. Meanwhile, we performed an optimal control study on the use of animal vaccination and culling of infectious animals as disease control measures against foot-and-mouth disease. Our findings showed combinations of optimal vaccination and culling rates that could lead to the effective management of the disease.

An Empirical Model for the Churning Losses Prediction of Fluid Flow Analysis in Axial Piston Pumps.

The manufacturing development of axial piston pumps usually takes the trend of high speed and miniaturization, and increases power density. Axial piston pumps are usually characterized as high speed to improve the power density; thus, high-speed churning losses caused by the internal rotating components stirring the oil can increase significantly. In order to improve the efficiency, more attention should be given to the churning losses in axial piston pumps, especially in high-speed conditions. Using the method of least-squares curve fitting, this paper establishes a series of formulas based on the churning losses test rig over a wide range of speeds, which enable accurate predictions of churning losses on the cylinder block and pistons. The reduction coefficient of flow resistance of multi-pistons as calculated. The new churning losses formula devoted to the cylinder block and rotating pistons was validated by comparison with experimental evidence in different geometries of axial piston pumps. According to the prediction model of churning losses, some valuable guidance methods are proposed to reduce the energy losses of the axial piston pump, which are the theoretical support for the miniaturization of axial piston pump manufacturing.

Evidence for and Analysis of Multiple Hidden Coronal Strands in Cross-sectional Emission Profiles: Further Results from NASA’s High-resolution Solar Coronal Imager

Abstract Previous work utilizing NASA’s High-resolution Coronal Imager (Hi-C 2.1) 172 Å observations revealed that, even at the increased spatial scales available in the dataset, there may be evidence for coronal structures that are still not fully resolved. In this follow-up study, cross-section slices of coronal strands are taken across the Hi-C 2.1 field of view. Following previous loop-width studies, the background emission is removed to isolate the coronal strands. The resulting intensity variations are reproduced by simultaneously fitting multiple Gaussian profiles using a nonlinear least-squares curve-fitting method. In total, 183 Gaussian profiles are examined for possible structures that are hinted at in the data. The full width at half maximum is determined for each Gaussian, which are then collated and analyzed. The most frequent structural widths are ≈450–575 km with 47% of the strand widths beneath NASA’s Solar Dynamics Observatory Atmospheric Imaging Assembly (AIA) resolving scale (600–1000 km). Only 17% reside beneath an AIA pixel width (435 km) with just 6% of the strands at the Hi-C 2.1 resolving scale (≈220–340 km). These results suggest that non-Gaussian shaped cross-sectional emission profiles observed by Hi-C 2.1 are the result of multiple strands along the integrated line of sight that can be resolved, rather than being the result of even finer sub-resolution elements.

Buried objects detection in heterogeneous environment using UWB systems combined with curve fitting method

A new method is proposed to improve the accuracy of locating buried objects in heterogeneous environments using shifted time pulses with radio impulse ultra wide band (IR-UWB), time-hopping pulse position modulation (TH-BPSK UWB), binary phase shift keying (TH-BPSK UWB) systems combined with the least square curve fitting method (LSCFM). The analytical expression is validated by simulation and the locating errors used to assess the performance of systems. The numerical results indicate that the proposed method has higher accuracy than the conventional ones.

A Novel Trilateration Algorithm for RSSI-Based Indoor Localization

This paper proposed a novel trilateration algorithm for indoor localization based on received signal strength indication (RSSI). Firstly, all the raw measurement data are preprocessed by a Gaussian filter to reducing the influence of measurement noise. Secondly, the transmit power and the path loss exponent are estimated by a novel least-squares curve fitting (LSCF) method in the RSSI-based localization. Thirdly, a novel trilateration algorithm is proposed based on the extreme value theory, which constructs a nonlinear error function depending on distances and anchor nodes position. To minimize the function, a Taylor series approximation can be used for reduce the computational complexity. And, an iteration condition is designed to further improve the positioning accuracy. Afterward, Bayesian filtering is used to smoothing the localization error, and decrease the influence of the process noise. Both the simulation and experimental results demonstrate the effectiveness of the proposed methodology.

Received Signal Strength Indicator-Based Indoor Localization Using Distributed Set-Membership Filtering.

Most of the existing localization schemes necessitate a priori statistical characteristic of measurement noise, which may be unrealistic in practical applications. This article addresses the problem of indoor localization by implementing distributed set-membership filtering based on a received signal strength indicator (RSSI) under unknown-but-bounded process and measurement noises. First, the transmit power and the path-loss exponent are estimated by a novel least-squares curve fitting (LSCF) method in RSSI-based localization. Since the localization process of trilateration is susceptible to inaccuracy caused by the noise-affected distance measurements, a convex optimization method is then developed to obtain the state ellipsoid estimation under the unknown-but-bounded noises. Third, a recursive algorithm is established to compute the global ellipsoid that guarantees to locate the true target at every time step. Finally, experimental validation is presented to demonstrate the accuracy and effectiveness of the proposed set-membership filtering method for indoor localization.

Study of the Dielectric Properties of Condenser Material Used in SF6 Insulated RIP Bushing

All In the frequency range of 10−1∼106Hz and the temperature range of -100∼200°C, the experimental dielectric spectrum of the condenser material used in UHVDC RIP bushing has been measured by Novocontrol broadband dielectric spectroscopy. The measured data has been fitted applied to nonlinear numerical calculation of the Havriliak-Negami (HN) equation, by which the characteristic parameters of HN mathematical model have been got. The studies show that the genetic algorithm combining with the least-square curve fitting method can ensure the uniqueness and accuracy of the fitting parameters. In the frequency range of 10−1∼106Hz and the temperature range of -40∼60°C, β relaxation process mainly takes place in the condenser material. In temperature range of 70∼150°C, α and β relaxation processes can be observed. In the temperature range of 160∼200°C, the α relaxation and DC conduction processes are obvious. The DC conductivity and relaxation time have significant temperature dependence which can be fitted well with Arrhenius equation.

On the equivalent ZIP parameter extraction of desktop computer cases and LCD monitors connected in parallel

Constant-impedance, constant-current and constant-power ZIP models of electrical loads are commonly used in smart grid and residential load applications. Some of residential loads are of nonlinear nature such as LCD monitors and computers. In this study, first, equivalent ZIP model formulas of parallel-connected electrical loads are derived. Then, the ZIP models of an LCD monitor, a computer case and the computer case and the monitor connected in parallel have been obtained using experimental data and least-squares curve fitting method. Finally, the equivalent ZIP model formulas are tested with the experimental data. It has been found that for the rectifier nonlinear loads with different ZIP parameters, the formulas do not give acceptable errors. Therefore, for rectifier nonlinear loads, the measurement-based approach for load modeling must be performed.

The effect of different inorganic anions on mineralization of acrylic acid in wet air oxidation.

Wet Air Oxidation (WAO) process is being developed as a very promising technique for efficient removal of high-concentration organic pollutants. However, because of the technical constraints, many chemical wastewater contain inorganic anions (e.g., Cl-, SO42-, PO43- and NO3-). These inorganic salts can cause equipment corrosion and also affect WAO reactivity. But very limited studies of the effect of inorganic anions on WAO in chemical wastewater have been performed. Here we for the first time intensively investigate the effect of different inorganic anions on kinetics and pathways of WAO reaction, acrylic acid was selected as substrate. We used a nonlinear least-squares curve fitting method using Matlab 2014® to obtain the kinetic model. Importantly, it was demonstrated that this proposed kinetic model represented the experimental data well, and acetic acid was the only residual short-chain carboxylic acid. Moreover, the higher concentration anions the higher selectivity of WAO of CO2 by acrylic acid. And the selectivity order of WAO to acetic acid is PO43->NO3->Cl->SO42- at low concentration (100mmolL-1). Finally, the theory calculation disclosed the feasibility of the reactions between these anions and acrylic acid, calculation results revealed that atoms 1#, 7# and 8# have the strongest chargeability and are more vulnerable to oxidant attack because of their high charge density. And the Total Organic Carbon (TOC) removal was positively correlated with the electronegativity of the central atom of oxidizing acid.

Reference-free determination of tissue absorption coefficient by modulation transfer function characterization in spatial frequency domain

BackgroundSpatial frequency domain (SFD) measurement allows rapid and non-contact wide-field imaging of the tissue optical properties, thus has become a potential tool for assessing physiological parameters and therapeutic responses during photodynamic therapy of skin diseases. The conventional SFD measurement requires a reference measurement within the same experimental scenario as that for a test one to calibrate mismatch between the real measurements and the model predictions. Due to the individual physical and geometrical differences among different tissues, organs and patients, an ideal reference measurement might be unavailable in clinical trials. To address this problem, we present a reference-free SFD determination of absorption coefficient that is based on the modulation transfer function (MTF) characterization.MethodsInstead of the absolute amplitude that is used in the conventional SFD approaches, we herein employ the MTF to characterize the propagation of the modulated lights in tissues. With such a dimensionless relative quantity, the measurements can be naturally corresponded to the model predictions without calibrating the illumination intensity. By constructing a three-dimensional database that portrays the MTF as a function of the optical properties (both the absorption coefficient μa and the reduced scattering coefficient mu^{prime}_{s}) and the spatial frequency, a look-up table approach or a least-square curve-fitting method is readily applied to recover the absorption coefficient from a single frequency or multiple frequencies, respectively.ResultsSimulation studies have verified the feasibility of the proposed reference-free method and evaluated its accuracy in the absorption recovery. Experimental validations have been performed on homogeneous tissue-mimicking phantoms with μa ranging from 0.01 to 0.07 mm−1 and mu^{prime}_{s} = 1.0 or 2.0 mm−1. The results have shown maximum errors of 4.86 and 7% for mu^{prime}_{s} = 1.0 mm−1 and mu^{prime}_{s} = 2.0 mm−1, respectively. We have also presented quantitative ex vivo imaging of human lung cancer in a subcutaneous xenograft mouse model for further validation, and observed high absorption contrast in the tumor region.ConclusionsThe proposed method can be applied to the rapid and accurate determination of the absorption coefficient, and better yet, in a reference-free way. We believe this reference-free strategy will facilitate the clinical translation of the SFD measurement to achieve enhanced intraoperative hemodynamic monitoring and personalized treatment planning in photodynamic therapy.

Unsteady Aerodynamic Force Sensing from Strain Data

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain. Velocities and accelerations of the structure are computed using the autoregressive moving average model, online parameter estimator, low-pass filter, and a least-squares curve fitting method, together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm. A cantilevered rectangular wing is used to validate the simple approach. Unsteady aerodynamic forces as well as wing deflections, velocities, accelerations, and strains are computed using the CFL3D computational fluid dynamics code and the MSC/NASTRAN finite element analysis code; and these CFL3D/NASTRAN-based results are assumed as measured quantities. Computed deflections, velocities, accelerations, and unsteady aerodynamic forces are compared with the CFL3D/NASTRAN-based results. Computed aerodynamic forces based on lifting-surface theory at subsonic speeds are in good agreement with the target aerodynamic forces generated using CFL3D code with the Euler equation. This research demonstrates the feasibility of obtaining induced drag and lift forces through the use of distributed sensor technology with measured strain data.

Optical constants of e-beam evaporated titanium dioxide thin films in the 25.5- to 612-eV energy region

The optical constants of titanium dioxide (TiO2) have been experimentally determined at energies in the extreme ultraviolet and soft x-ray spectral regions, from 25.5 to 612 eV. Measuring angle-dependent reflectance of amorphous TiO2 thin films with synchrotron radiation at the BEAR beamline of Synchrotron ELETTRA. The experimental reflectivity profiles were fitted to the Fresnel equations using a genetic algorithm applied to a least-square curve fitting method, obtaining values for δ and β. We compared our measurements with tabulated data. All samples were grown on Si (100) substrates by the electron-beam evaporation technique, with a substrate temperature of 150°C and deposition rates of 0.3 to 0.5 Å/s. Complete films characterization have been carried out with structural (XRD, ellipsometry, and profilometry), compositional (x-ray photoelectron spectroscopy), and morphological (atomic force microscopy) analyses.

The variation trends of SFRP2 methylation of tissue, feces, and blood detection in colorectal cancer development.

The susceptibility of secreted frizzled-related protein 2 (SFRP2) methylation in colorectal cancer (CRC) has been studied previously. The aim of this study was to determine the risk sizes and variation trends of SFRP2 methylation in CRC development in Chinese populations. Subgroup meta-analysis and the least-squares curve-fitting method were carried out to analyze the risk of SFRP2 methylation in tissue, feces, and blood detection from 2221 samples, including a total of 1103 cases of CRC, 459 cases of adenoma, 257 cases of polyps, and 402 controls. The data showed that odds ratios (95% confidence intervals) between CRC and controls for tissue, feces, and blood detection were 334.01 (104.42-1068.39), 63.76 (20.62-197.63), and 133.75 (18.32-976.32), respectively. There were also significant differences between tissue and feces or blood as well as between feces and blood methylation frequency. These results showed that the risk size in tissue was much greater than that in feces and that in blood. The results pointed out that three curves in tissue, feces, and blood detection described the variation trends of methylation incidence from the control to polyp, to adenoma and to CRC, and that the variation trend of the risk size of SFRP2 methylation was synchronized with the histological evolution process of CRC. The variation trend of the risk size of SFRP2 methylation incidence is consistent with the histological evolution process of CRC. The susceptibility to SFRP2 methylation is an important biomarker in the study of early diagnosis of CRC and high-risk patients.