Curve Fitting Processing Research Articles

Structural design of a coaxial-jet vortex powder mixer for multi-material directed energy deposition

Directed energy deposition (DED) offers an unprecedentedly convenient and efficient additive manufacturing approach for novel alloy design. As a critical component of the novel DED system, a powder mixer plays an important role in the stable and uniform mixing of different powders. In this work, the coaxial-jet dome powder mixer (CDPM) was designed based on the convergent-jet cone powder mixer (CCPM). In order to explore a reliable multi-powder mixing mechanism, the gas-solid two-phase flow state in the mixing chamber was simulated by the large eddy simulation and discrete particle model (LES-DPM) method. In addition, the powder delivery stability and mixing uniformity of the mixer were characterized by curve fitting and image processing methods. Finally, CDPM avoids the generation of ineffective vortices that occurred in the mixing chamber. In addition, deposition experiments show that the powder mixer can ensure the uniform distribution of multiple elements in the local forming zone.

Dynamic study of pendulum systems through smartphone-based laboratory experiments

The dynamic study of pendulum systems is considered an indispensable subject for physics and mechanics students in colleges and high schools. In this paper, a detailed methodology is given concerning the use of smartphones in pedagogical practical work for studying the dynamics of pendulum systems. Whereas, three aspects have been discussed through three cases concerning the study of the oscillatory motion, trajectories, and the energy aspect. Besides, some recommendations were provided regarding the process of data acquisition and curve-fitting processing to mitigate measurement errors. Experimental results exhibit a good agreement with theoretical results regarding the period of motion, trajectories, and mechanical energy. This makes the smartphone highlights a real opportunity to be a useful instrument to perform an overall study of the pendulum systems, the thing that was impossible without the intervention of professional equipment.

Quantitative approach to study secondary structure of proteins by FT-IR spectroscopy, using a model wheat gluten system

Amide I and Amide III vibrational modes are frequently used to study protein secondary structure with Fourier transform infrared (FT-IR) spectroscopy. However, for protein mixtures, neither the sole Amide I nor Amide III region provides sufficient information for structural quantitation because of overlapping peaks, especially in the Amide I region. Here, an improved quantitative approach is proposed to estimate secondary structure of protein systems using resolution enhancement and curve-fitting data processing techniques on a gluten model system to investigate structure-function relationships. Twelve different scenarios were prepared to assign bands in the Amide I region. Frequency ranges of 1660–1640 cm−1 and 1665–1660 cm−1 were found to highly contribute to variability in secondary structure contents of samples. Utilization of the Amide III region as a conducive tool to assign bands in the Amide I region led to a better differentiation of some secondary structural motifs and a more accurate quantitation of protein secondary structure. The study presents an understanding of FT-IR data analysis for a quick technique to assess secondary structures of protein mixtures.

An Efficient Lens Structures Segmentation Method on AS-OCT Images.

Lens structures segmentation on anterior segment optical coherence tomography (AS-OCT) images is a fundamental task for cataract grading analysis. In this paper, in order to reduce the computational cost while keeping the segmentation accuracy, we propose an efficient segmentation method for lens structures segmentation. At first, we adopt an efficient semantic segmentation network in the work, and used it to extract the lens area image instead of the conventional object detection method, and then used it once again to segment the lens structures. Finally, we introduce the curve fitting processing (CFP) on the segmentation results. Experiment results show that our method has good performance on accuracy and processing speed, and could be applied to CASIA II device for practical applications.

Experimental investigation of flame propagation in a meso-combustor

The present work aims to study the quenching of propagating flames in meso-combustors for which dimensions are of the order of quenching distances of hydrocarbon fuels. Combustion of gaseous fuels and subsequent flame propagation in a meso-scale combustor duct of square cross-section is studied experimentally. Premixed mixtures of methane, propane, and ethylene with air are considered. Two different variants of flame propagation states are found to occur in the meso-combustor, viz., one undergoing flame propagation till the combustor entry and quenching at the step and the other undergoing wall quenching. Regime transitions across these flame states are mapped comprehensively over a wide range of operating conditions. The radius of curvature of the flame and the dead space between the flame and the wall are determined for those conditions with the aid of curve fitting and image processing techniques using Matlab software. The spatial and temporal variation of both these parameters show a drastic increase during quenching in the wall-quenched case, while it remains nearly constant in the step quenched case. With increasing duct Reynolds number, the flame propagates slower, and the heat conduction to the wall leads to a decrease in the dead space and flattening of the flame, particularly at equivalence ratios corresponding to lower flame speeds. This flame-wall interaction is found to be low for methane, resulting in more heat loss and thereby wall-quenched flames compared to propane and ethylene. None of the ethylene flames were found to suffer wall quenching thereby making it a suitable fuel for meso-/micro-combustors among the three fuels used in the present work.

Robust and accurate computation of geometric distance for Lipschitz continuous implicit curves

Computing the geometric distance between a point and an implicitly defined curve is widely used in implicit curve fitting and geometric processing. Iterative numerical methods are often used to compute the distance, which may give quite accurate solutions but are usually time-consuming and non-robust. In this paper, a circle double-and-bisect algorithm is proposed to reliably evaluate the accurate geometric distance of a point to an implicit curve. The method's prerequisite is merely the Lipschitz continuity of the implicit function. Moreover, by using gradient norm's upper bound estimation and minor arcs evolution, the efficiency can be improved apparently. Experimental results show that the evaluated distance can describe the fitting result with more fidelity and that some fitting algorithms (for example, the genetic algorithm) re-implemented with the proposed geometric distance converge much faster. Due to these contributions, the proposed method can be applied in diverse applications such as error evaluation, curve fitting and random point cloud generator.

Signal Processing Based Remote Sensing Data Simulation in Radar System

Range cell migration has a serious impact on the precision of image formation, especially for high-resolution and large-scale imaging. To get the full resolution and high quality of the image, the range cell migration correction in the azimuth time domain must be considered. For tackling this problem, this paper presents a novel and efficient range cell migration correction method based on curve fitting and signal processing. By emulating a curve to approximate the range-compressed echo of a strong point, the range location indexes of the strong point along the azimuth direction can be obtained under the least squares criterion. The merits of the proposed method are twofold: (1) the proposed method is robust to the uncertainty of system parameters (strong tolerance) under real flights and (2) the generalization of the proposed method is better and can be easily adapted to different synthetic aperture radar (SAR) modes (e.g., monostatic and bistatic). The experimental results on real remote sensing data from both the monostatic and the bistatic SAR demonstrate the effectiveness. The regressed distance curve is completely coincident with the trajectory of strong points of the echo. Finally, the imaging focus results also validate the efficiency of the proposed method.

Processing the Experimental Data of College Physics Experiment with Origin 8.6

Based on the two examples of Newton Circle experiment and Franck-Hertz experiment, some functions of drawing, curve fitting and data processing were introduced using the software of Origin 8.6. This paper also discussed the data processing in detail, and generalized this approach to other college physics experiments. The method can make dataprocessing easier and diminish the errors of data.

Transition Segments Processing Method Based on Curve Fitting Algorithm

In order to obtain better speed and high accuracy, real-time curve fitting and fitting processing at transition points are often necessary when machining complex contours. Based on the quadratic trigonometric Bézier curve, a new algorithm is presented to realize curve fitting only between transition segments. This method ensures the machining precision and increases the maximum allowable speed at the transition points. Simulation and experiment results show that the transition velocity changes smoothly and steadily as well as the processing efficiency is promoted.

BioDoser: Improved dose-estimation software for biological radiation dosimetry

This paper introduces a software program that was developed with the aims to improve the efficiency and veracity of calibration curve fitting and data processing in radiation biological dosimetry and other biological experiments, and which is termed BioDoser. BioDoser uses least squares and loop testing of monotonicity method and algorithm of non-uniformed confidence interval. In addition, this program enables integration of multiple different biomarkers typically used in biological dosimetry. These include partial body exposure, minimum number of cells to be analyzed, G function correction modules that are helpful in dose estimation when using chromosome aberration frequencies, micronucleus rate, comet assay and other biological methods. The software is freely available at http://bit.ly/kKBSNR.

Theoretical analysis and numerical experiments of variational adjoint approach for refractivity estimation

This paper puts forward possibilities of refractive index profile retrieval using field measurements at an array of radio receivers in terms of variational adjoint approach. The derivation of the adjoint model begins with the parabolic wave equation for a smooth, perfectly conducting surface and horizontal polarization conditions. To deal with the ill‐posed difficulties of the inversion, the regularization ideas are introduced into the establishment of the cost function. Based on steepest descent iterations, the optimal value of refractivity could be retrieved quickly at each point over height. Numerical experiments demonstrate that the method works well for low‐distance signals, while it is not accurate enough for long‐distance propagations. Through curve fitting processing, however, giving a good initial refractivity profile could generally improve the inversions.

A combined approach of self-referencing and Principle Component Thermography for transient, steady, and selective heating scenarios

Proposed manuscript describes the implementation of a two step processing procedure, composed of the self-referencing and the Principle Component Thermography (PCT). The combined approach enables the processing of thermograms from transient (flash), steady (halogen) and selective (induction) thermal perturbations. Firstly, the research discusses the three basic processing schemes typically applied for thermography; namely mathematical transformation based processing, curve-fitting processing, and direct contrast based calculations. Proposed algorithm utilizes the self-referencing scheme to create a sub-sequence that contains the maximum contrast information and also compute the anomalies’ depth values. While, the Principle Component Thermography operates on the sub-sequence frames by re-arranging its data content (pixel values) spatially and temporally then it highlights the data variance. The PCT is mainly used as a mathematical mean to enhance the defects’ contrast thus enabling its shape and size retrieval. The results show that the proposed combined scheme is effective in processing multiple size defects in sandwich steel structure in real-time (<30 Hz) and with full spatial coverage, without the need for a priori defect-free area.

Bayesian adaptive nonparametric M-regression

Nonparametric regression has been popularly used in curve fitting, signal denosing, and image processing. In such applications, the underlying functions (or signals) may vary irregularly, and it is very common that data are contaminated with outliers. Adaptive and robust techniques are needed to extract clean and accurate information. In this paper, we develop adaptive nonparametric M-regression with a Bayesian approach. This general approach fits M-regression using piecewise polynomial functions with an unknown number of knots at unknown locations, all treated as parameters to be inferred through Reversible Jump Markov Chain Monte Carlo (RJMCMC) of Green (1995, [9]). The Bayesian solution presented in this paper with computational details can be considered as an approximation to the general optimal solution for M-regression with free knots as described in Stone (2005, [22]). Numerical results show that the Bayesian approach performs well in various cases, especially with discontinuous underlying functions. AMS 2000 subject classifications: Primary 60K35, 60K35; secondary 60K35.

An analytical comparison of three spatio-temporal regularization methods for dynamic linear inverse problems in a common statistical framework

Dynamic inverse problems, which occur in medical imaging and other fields, are inverse problems in which the quantities to be reconstructed vary in time, although they are related to the measurements through spatial operators only. Traditional methods solve these problems by frame-by-frame reconstruction, then extract temporal behaviour of the objects or regions of interest through curve fitting and other image-based processing. These approaches solve the inverse problem while exploiting only the spatial relationship between the object and the measurement data at each time instant, without using any temporal dynamics of the underlying process, and thus are not optimal unless the solution is temporally uncorrelated. If the spatial operators are linear, and if one, by contrast, solves the whole spatio-temporal process jointly, it falls into the category of general linear least-squares problems. Such approaches are generally difficult, both due to the challenge of modelling the temporal dynamics appropriately as well as to the high dimensionality of the associated large linear system. Several recent reports have approached this problem in different ways, making different prior assumptions on the spatial and temporal behaviour. In this paper we discuss three such approaches, which have been introduced from different points of view, in a common statistical regularization framework, and illuminate their relationships. The three methods are a state-space model, the separability condition and a multiple constraints model. The key result is that there is a clear relationship among the three methods; specifically, the inverse of the spatio-temporal autocovariance matrix has a block tri-diagonal form, a Kronecker product form or a Kronecker sum form, respectively. Some simple simulation examples are presented to illustrate the theoretical analysis.

A kernel-based Adaline for function approximation

In this work the kernel Adaline algorithm is presented. The new algorithm is a generalisation of Widrow's and Hoff's linear Adaline, and allows to approximate non-linear functional relationships. Similar to the linear adaline, the proposed neural network algorithm minimises the least-mean-squared (LMS) cost function. It can be guaranteed that the kernel Adaline's cost function is always convex, therefore the method does not suffer from local optima as known in conventional neural networks. The algorithm uses potential function operators due to Aizerman and colleagues to map the training points in a first stage into a very high dimensional non-linear “feature” space. In the second stage the LMS solution in this space is determined by the algorithm. Weight decay regularisation allows to avoid overfitting effects, and can be performed efficiently. The kernel Adaline algorithm works in a sequential fashion, is conceptually simple, and numerically robust. The method shows a high performace in tasks like one dimensional curve fitting, system identification, and speech processing.

Fast algorithm for generating Bernstein-Bezier polynomials

In this paper a new algorithm for generating values of Bernstein-Bezier polynomials is proposed and investigated. Opposite to the known algorithms, its computational complexity does not depend on the degree of a calculated polynomial. However, it allows to calculate only approximate values of the polynomial. These features allow to recommend the proposed algorithm for solving curve fitting and image processing problems in which processing a large number of data is necessary. The proposed method is based on a probabilistic interpretation of Bernstein-Bezier (BB-) polynomials and its properties are investigated in the statistical language. As a byproduct, a local nature of BB-polynomial approximation is displayed.