Nonlinear Interpolation Function Research Articles

An Investigation on using Lagrange, Newton and Least Square Methods for Generating Nonlinear Interpolation Function for the Measuring Instruments

This research is considered the milestone for metrologists to choose the appropriate method for determination of the nonlinear interpolation function for the measuring instruments. Three methods of generating the interpolation polynomial equations were investigated; Newton, Lagrange, and Least Square method. The response of the measuring instruments under investigation was calculated and compared with the experimental results. Least Square method was found that it is the most accurate and most realistic approach to determine the interpolation polynomial function for the measuring instruments. It is recommended to use Least Square method rather than other methods to interpolating the polynomial equation. This recommendation is very important for metrologist as well as for measuring instruments applicant. This article is millstone to determine the response of the measuring instrument at non calibrated points in the calibrated range.

Enhancement of Chest X-Ray Images to Improve Screening Accuracy Rate Using Iterated Function System and Multilayer Fractional-Order Machine Learning Classifier

Chest X-ray (CXR) images are usually used to identify the causes of patients’ symptoms, including the classes of lung or heart disorders. In visualization examination, CXR imaging in anterior–posterior (A–P) views is a preliminary screening method used by clinicians or radiologists to diagnose possible lung abnormalities, such as pneumothorax (Pt), emphysema (E), infiltration (In), lung cancer (M), pneumonia (P), pulmonary fibrosis (F), and pleural effusion (Ef). However, the identification of the causes of multiple abnormalities associated with coexisting conditions presents a challenge. In ruling out a suspected lung disease, the signs and symptoms of physical conditions need to be identified to arrive at a definitive diagnosis. In addition, low contrast CXR images and manual inspection restrict automated screening applications. Hence, this study aims to propose an iterated function system (IFS) and a multilayer fractional-order machine learning classifier to rapidly screen the possible classes of lung diseases within regions of interest on CXR images and to improve screening accuracy. For digital image processes, a two-dimensional (2D) fractional-order convolution is used to enhance symptomatic features. The IFS with nonlinear interpolation functions is then used to reconstruct the 2D feature patterns. These reconstructed patterns are self-affine in the same class and thus help distinguish normal subjects from those with lung diseases. The accuracy rate is thus improved. Pooling is performed to reduce the dimensions of the feature patterns and speed up complex computations. A gray relational analysis-based classifier is used to identify the possible classes of the signs and symptoms of lung diseases. For digital CXR images in A-P view, the proposed multilayer machine learning classifier with k-fold cross-validation presents promising results in screening lung diseases and improving screening accuracy rate relative to traditional methods. The proposed classifier is evaluated in terms of recall (99.6%), precision (87.78%), accuracy (88.88%), and F1 score (0.9334).

A Ritz approach for the static analysis of planar pantographic structures modeled with nonlinear Euler–Bernoulli beams

We present a finite element discrete model for pantographic lattices, based on a continuous Euler–Bernoulli beam for modeling the fibers composing the pantographic sheet. This model takes into account large displacements, rotations and deformations; the Euler–Bernoulli beam is described by using nonlinear interpolation functions, a Green–Lagrange strain for elongation and a curvature depending on elongation. On the basis of the introduced discrete model of a pantographic lattice, we perform some numerical simulations. We then compare the obtained results to an experimental BIAS extension test on a pantograph printed with polyamide PA2200. The pantographic structures involved in the numerical as well as in the experimental investigations are not proper fabrics: They are composed by just a few fibers for theoretically allowing the use of the Euler–Bernoulli beam theory in the description of the fibers. We compare the experiments to numerical simulations in which we allow the fibers to elastically slide one with respect to the other in correspondence of the interconnecting pivot. We present as result a very good agreement between the numerical simulation, based on the introduced model, and the experimental measures.

A Simple Method for Soil Moisture Determination From LST–VI Feature Space Using Nonlinear Interpolation Based on Thermal Infrared Remotely Sensed Data

Soil moisture is an important parameter that is widely used for drought monitoring and characterizing environment. Based on the universal triangular space constructed by the normalized land surface temperature (LST) and normalized difference vegetation index (NDVI), this study proposes a simple method to estimate surface soil moisture (SSM) using a nonlinear interpolation function with theoretical limiting edges derived from the energy balance principle. As an interpolation function, the quadratic polynomial equation is used to reveal the relationships among soil moisture, LST, and fractional vegetation cover (FVC), which are determined and validated by the simulation data from the Noah land surface model (Noah LSM). The developed function is much simpler than Carlson's function because the number of coefficients is reduced by half. The proposed method is applied to the North China Plain. The estimation results are also validated by the in situ measurements of soil water content at 10 and 20 cm depths at the Yucheng meteorological station; the corresponding biases are as high as 0.02 and 0.12 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> /m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> , respectively, and the root-mean-square errors (RMSEs) are approximately 0.04 and 0.10 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> /m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> , respectively. The results indicate that this method has high-estimation accuracy and overcomes the weakness induced by the effects of atmospheric conditions on different days. This study provides insight into the comparable soil moisture estimation from remotely sensed data on a regional scale.

Numerical study and design of skewed X-type branch plate-to-circular hollow section connections

Structural systems, including space-frames, cable stayed roof systems and bridges, with elements that intersect at non-orthogonal angles necessitating rotated and complex connection geometries, have become commonplace. Non-orthogonal plate-to-circular hollow section (CHS) connections with branch members rotated about their own axis (skewed) have been absent in international literature and design guidelines. A numerical finite element parametric study is presented on the behaviour of skewed X-type plate-to-CHS connections loaded under branch plate tension. A total of 91 connections with wide-ranging values of geometric properties were modelled and analysed using commercially available finite element software. The numerical finite element analysis indicated a smooth sigmoidal (S-shaped) transition between longitudinal and transverse orthogonal extremes. A non-linear interpolation function was developed, for application between longitudinal and transverse design recommendations, that adequately predicts skewed connection behaviour over a wide range of geometric connection configurations. A partial design strength function for skewed X-type plate-to-CHS, which builds on existing design recommendations for non-skewed plate connections, is hence proposed with lower bound reduction (resistance) factors.

Nonlinear interpolation fractal classifier for multiple cardiac arrhythmias recognition

This paper proposes a method for cardiac arrhythmias recognition using the nonlinear interpolation fractal classifier. A typical electrocardiogram (ECG) consists of P-wave, QRS-complexes, and T-wave. Iterated function system (IFS) uses the nonlinear interpolation in the map and uses similarity maps to construct various data sequences including the fractal patterns of supraventricular ectopic beat, bundle branch ectopic beat, and ventricular ectopic beat. Grey relational analysis (GRA) is proposed to recognize normal heartbeat and cardiac arrhythmias. The nonlinear interpolation terms produce family functions with fractal dimension (FD), the so-called nonlinear interpolation function (NIF), and make fractal patterns more distinguishing between normal and ill subjects. The proposed QRS classifier is tested using the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database. Compared with other methods, the proposed hybrid methods demonstrate greater efficiency and higher accuracy in recognizing ECG signals.

Reconstruction of 3D medical images: A nonlinear interpolation technique for reconstruction of 3D medical images

Three-dimensional medical images reconstructed from a series of two-dimensional images produced by computerized tomography, magnetic resonance imaging, etc., present a valuable tool for modern medicine. Usually, the interresolution between two cross sections is less than the intraresolution within each cross section. Therefore, interpolations are required to create a 3D visualization. Many techniques, including voxel-based and patch tiling methods, apply linear interpolations between two cross sections. Although those techniques using linear interpolations are economical in computation, they need much cross-sectional data and are unable to enlarge because of aliasing. Hence, the techniques that apply two-dimensional nonlinear interpolation functions among cross sections were proposed. In this paper, we introduce the curvature sampling of the contour of a medical object in a CT (computerized tomography) image. Those sampled contour points are the candidates for the control points of Hermite surfaces between each pair of cross sections. Then, a nearest-neighbor mapping of control points between every two cross sections is used for surface formation. The time complexity of our mapping algorithm is O( m + n), where m and n are the numbers of control points of two cross sections. It is much faster than Kehtarnavaz and De Figueiredo's merge method, whose time complexity is O( n 3 m 2).