Polynomial Mapping Function Research Articles

Modeling Temperature-Dependent Thermoelectric Performance of Magnesium-Based Compounds for Energy Conversion Efficiency Enhancement Using Intelligent Computational Methods

Eco-friendly magnesium-based thermoelectric materials have recently attracted significant attention in green refrigeration technology and wasted heat recovery applications due to their cost effectiveness, non-toxicity, and earth abundance. The energy conversion efficiency of these thermoelectric materials is controlled by a dimensionless thermoelectric figure of merit (TFM), which depends on thermal and electrical conductivity. The independent tuning of the electrical and thermal properties of these materials for TFM enhancement is challenging. The improvement in the TFM of magnesium thermoelectric materials through scattering and structural engineering is experimentally challenging, especially if multiple elements are to be incorporated at different concentrations and at different doping sites. This work models the TFM of magnesium-based thermoelectric materials with the aid of single-hidden-layer extreme learning machine (ELM) and hybrid genetic-algorithm-based support vector regression (GSVR) algorithms using operating absolute temperature, elemental ionic radii, and elemental concentration as descriptors. The developed TFM-G-GSVR model (with a Gaussian mapping function) outperforms the TFM-S-ELM model (with a sine activation function) using magnesium-based thermoelectric testing samples with improvements of 17.06%, 72%, and 73.03% based on correlation coefficient (CC), root mean square error (RMSE), and mean absolute error (MAE) assessment metrics, respectively. The developed TFM-P-GSVR (with a polynomial mapping function) also outperforms TFM-S-ELM during the testing stage, with improvements of 14.59%, 55.31%, and 62.86% using CC, RMSE, and MAE assessment metrics, respectively. Also, the developed TFM-G-ELM model (with a sigmoid activation function) shows superiority over the TFM-S-ELM model with improvements of 14.69%, 79.52%, and 83.82% for CC, RMSE, and MAE assessment yardsticks, respectively. The dependence of some selected magnesium-based thermoelectric materials on temperature and dopant concentration on TFM was investigated using the developed model, and the predicted patterns align excellently with the reported values. This unique performance demonstrated that the developed intelligent models can strengthen room-temperature magnesium-based thermoelectric materials for industrial and technological applications in addressing the global energy crisis.

Uncertainty Assessment of Wave Elevation Field Measurement Using a Depth Camera

The present study suggests a methodology for acquiring wave elevation fields using a depth camera sensor, with assessment results for the test uncertainty. The depth camera module of an Azure Kinect is calibrated using marker arrays on the optic table, to obtain a polynomial mapping function between the pixel-wise and physical position. For installation of the depth camera in a wave channel, the system is aligned using the built-in inertial measurement unit of Azure Kinect to be perpendicular to the calm water surface. The systematic and random standard uncertainties were evaluated from the analysis of calibration and repeated tests, respectively. The wave height measurement results for the depth camera were compared to those for the capacitance-type and ultrasonic wave height gauges. The test uncertainty of the depth camera increased in large wave stiffness conditions, where the time-of-flight sensor has a disadvantage in measurement.

Semi-supervised manifold learning based on polynomial mapping for localization in wireless sensor networks

Localization of sensor nodes is becoming an interesting research area in wireless sensor networks(WSNs). In recent years, some localization algorithms are presented based on manifold learning which can achieve good performance. In this paper, based on the need of practical application and the development of manifold learning theory in WSNs, the localization problem is considered for fast determining the locations of unknown nodes in large scale WSNs. For this purpose, a new semi-supervised manifold learning algorithm is proposed based on polynomial mapping which is the combination of Gaussian kernel embedding and polynomial kernel embedding algorithms. This method is to compute a polynomial mapping function between the high dimensional location data space and the low dimensional physical space, which can obtain an explicit nonlinear feature mapping and has a high discriminative ability. At last, comparing with some related localization approaches, the performance of the proposed algorithm is evaluated and analyzed under different signal noise, anchor nodes, and communication range, respectively. In terms of the root-mean-square error and computational complexity, the experiment results demonstrate that the proposed algorithm has faster speed for large scale sensor nodes and higher accuracy with a small amount of known nodes.

Volumetric calibration of a plenoptic camera.

The volumetric calibration of a plenoptic camera is explored to correct for inaccuracies due to real-world lens distortions and thin-lens assumptions in current processing methods. Two methods of volumetric calibration based on a polynomial mapping function that does not require knowledge of specific lens parameters are presented and compared to a calibration based on thin-lens assumptions. The first method, volumetric dewarping, is executed by creation of a volumetric representation of a scene using the thin-lens assumptions, which is then corrected in post-processing using a polynomial mapping function. The second method, direct light-field calibration, uses the polynomial mapping in creation of the initial volumetric representation to relate locations in object space directly to image sensor locations. The accuracy and feasibility of these methods is examined experimentally by capturing images of a known dot card at a variety of depths. Results suggest that use of a 3D polynomial mapping function provides a significant increase in reconstruction accuracy and that the achievable accuracy is similar using either polynomial-mapping-based method. Additionally, direct light-field calibration provides significant computational benefits by eliminating some intermediate processing steps found in other methods. Finally, the flexibility of this method is shown for a nonplanar calibration.

An InSAR Fine Registration Algorithm Using Uniform Tie Points Based on Voronoi Diagram

Interferometric synthetic aperture radar (InSAR) image coregistration is a nontrivial task for its skew and distorted image pair, especially in severe decorrelated areas. In this letter, a new InSAR coregistration method, which considers both the coherence of the reference points and their topographical distribution, is proposed to perform accurate coregistration. First, a conventional cross-correlation registration method is performed, and a number of high coherent points are extracted as the reference points. Then, some well-distributed reference points are selected by utilizing the Voronoi diagram-based distribution optimization algorithm. Their subpixel correspondences are selected by finding the maximum values of the cross-correlation functions. Some singular correspondences are rejected by the random sample consensus method. Based on these accurate correspondences, the parameters of polynomial mapping function are estimated via the weighted least squares method. It improves the accuracy of geometrical mapping functions and overcomes the limitation of the conventional registration method when the reference points locate in low coherent area. C-band airborne repeat-pass acquired SAR data with 0.5-m resolution are used to validate the proposed algorithm by comparing with the conventional registration algorithm in accuracy. Experimental results prove the effectiveness of the proposed algorithm.

Piecewise Polynomial Mapping Method and Corresponding WENO Scheme with Improved Resolution

AbstractAbstract. The method of mapping function was first proposed by Henrick et al. [J. Comput. Phys. 207:542-547 (2005)] to adjust nonlinear weights in [0,1] for the fifth order WENO scheme, and through which the requirement of convergence order is satisfied and the performance of the scheme is improved. Different from Henrick’s method, a concept of piecewise polynomial function is proposed in this study and corresponding WENO schemes are obtained. The advantage of the new method is that the function can have a gentle profile at the location of the linear weight (or the mapped nonlinear weight can be close to its linear counterpart), and therefore is favorable for the resolution enhancement. Besides, the function also has the flexibility of quick convergence to identity mapping near two endpoints of [0,1], which is favorable for improved numerical stability. The fourth-, fifth- and sixth-order polynomial functions are constructed correspondingly with different emphasis on aforementioned flatness and convergence. Among them, the fifth-order version has the flattest profile. To check the performance of the methods, the 1-D Shu-Osher problem, the 2-D Riemann problem and the double Mach reflection are tested with the comparison of WENO-M, WENO-Z and WENO-NS. The proposed new methods show the best resolution for describing shear-layer instability of the Riemann problem, and they also indicate high resolution in computations of double Mach reflection, where only these proposed schemes successfully resolved the vortex-pairing phenomenon. Other investigations have shown that the single polynomial mapping function has no advantage over the proposed piecewise one, and it is of no evident benefit to use the proposed method for the symmetric fifth-order WENO. Overall, the fifth-order piecewise polynomial and corresponding WENO scheme are suggested for resolution improvement.

Steady state creep behavior of short fiber composites by mapping, logarithmic functions (MF) and dimensionless parameter (DP) techniques

A new mathematical insight based on logarithmic, polynomial mapping functions (MF), and dimensionless parameter (DP) models is presented for determination of some unknowns in the steady state creep stage of short fiber composites subjected to axial loading. These unknowns are displacement rate in outer surface of the unit cell, shear and equivalent stresses at interface and outer surface of the unit cell, and average axial stress in fiber. Dimensionless parameter technique is presented for determination of displacement rate and equivalent stress in outer surface of the unit cell. However, the polynomial mapping function is presented for determination of average axial stress in fiber. Most important novelty of the present research work is determination of the mentioned unknowns in steady state creep by DP and MF techniques without using the shear-lag theory unlike the previous researches. Good agreements are found among the new approaches and previous analytical results based on the shear-lag theory and also numerical solutions (FEM) for predicting the steady state creep behavior in short fiber composites.

AUTOMATED SAR REFERENCE IMAGE PREPARATION FOR NAVIGATION

The preparation of good navigational synthetic aperture radar (SAR) reference image is critical to the SAR scene matching aided navigation system, especially for complex terrain. However, few papers discuss the problem, and almost none of the methods proposed by them are fully automatic. Based on the practical requirements, a fully automated method of SAR reference image preparation is introduced. Firstly, a number of distinctive control points (CP) in the simulated SAR image is detected based on a method of image segmentation and clustering. Then, the corresponding tie-points in the real SAR image are searched based on local similarity by means of template matching. To improve the accuracy of CP, a method for segmentation threshold calculation, outlier screening and sub-pixel location computation is presented. Finally, the real SAR image is warped to the simulated one, and then projected to the frame of digital elevation model (DEM) by the polynomial mapping function. Experimental results on real data sets demonstrate the accuracy and e-ciency of the proposed method.

Correction of distortion due to thermal drift in scanning probe microscopy

A common source of distortion in scanning probe microscope (SPM) images is "thermal drift," the slow thermal expansion of different materials in the sample and microscope due to small changes in temperature over the course of a scan. We describe here a method for correcting this distortion by immediately following each image scan with a rescan of a small, narrow portion of the same area with the slow and fast scan axes reversed. The original, full image is corrected using a low-order polynomial mapping function, with coefficients determined by a pixel-wise comparison between the original full and rescanned partial images. We demonstrate here that this method can correctly remove distortion from a wide range of images with a precision of better than one pixel, and is also robust to common imaging artifacts. We also address some of the programming considerations that have gone into implementing this computationally intensive technique, which can now be performed using standard desktop hardware in times that range between a few seconds and a few minutes.

On the sensitivity of IMRT dose optimization to the mathematical form of a biological imaging-based prescription function

Voxel-based prescriptions of deliberately non-uniform dose distributions based on molecular imaging, so-called dose painting or theragnostic radiation therapy, require specification of a transformation that maps the image data intensities to prescribed doses. However, the functional form of this transformation is currently unknown. An investigation into the sensitivity of optimized dose distributions resulting from several possible prescription functions was conducted. Transformations between the radiotracer activity concentrations from Cu-ATSM PET images, as a surrogate of tumour hypoxia, and dose prescriptions were implemented to yield weighted distributions of prescribed dose boosts in high uptake regions. Dose escalation was constrained to reflect clinically realistic whole tumour doses and constant normal tissue doses. Optimized heterogeneous dose distributions were found by minimizing a voxel-by-voxel quadratic objective function in which all tumour voxels were given equal weight. Prescriptions based on a polynomial mapping function were found to be least constraining on their optimized plans, while prescriptions based on a sigmoid mapping function were the most demanding to deliver. A prescription formalism that fixed integral dose was less sensitive to errors in the choice of the mapping function than one that boosted integral dose. Integral doses to normal tissue and critical structures were insensitive to the shape of the prescription function. Planned target dose conformity improved with smaller beamlet dimensions until the inherent spatial resolution of the functional image was matched. Clinical implementation of dose painting depends on advances in absolute quantification of functional images and improvements in delivery techniques over smaller spatial scales.

Correcting image distortion in the X-ray digital tomosynthesis system for PCB solder joint inspection

X-ray digital tomosynthesis (DT), which makes a cross-sectional image of 3D objects, has been researched and implemented in industrial applications nowadays, such as printed circuit board (PCB) inspection and inspection of electronic parts and other industrial parts/products. In this method, a cross-section image is obtained from a synthesis of more than two images projected from different views. However, distortion in X-ray images in practical imaging situation breaks the correspondences between those images and prevents us from acquiring accurate cross-section images. In this research, we propose a series of image correction method, which is composed of a neural network-based feature extraction for the distorted image and building a polynomial mapping function. The distorted raw image is sequentially corrected in terms of shape and intensity by using a reference pattern. To avoid corruption in feature extraction for the distorted image, an edge-filtered image is utilized rather than using a binarized one. Kohonen neural network is then employed to automatically group the edge points and localize the features, the pattern centers, without any pre-knowledge about the characteristics of the distortion. The proposed correction method is implemented to an actual DT system by carrying out a series of experiments on PCB. The results reveal the validity of the proposed image correction method and also verify the usefulness of the developed system for application of solder joint inspection.

A two–dimensional Eshelby problem for two bonded piezoelectric half–planes

The present paper concerns a two–dimensional Eshelby problem for an inclusion of arbitrary shape embedded within one of two bonded dissimilar piezoelectric halfplanes. The elastic and piezoelectric constants of the inclusion and its surrounding half–plane are assumed to be the same. A simple explicit solution is derived in terms of some auxiliary functions which can be determined using several related conformal mappings of the inclusion shape. The obtained solution is exact provided that the expansions of all conformal mappings include only a finite number of terms. On the other hand, if an exact conformal mapping includes infinite terms, a truncated polynomial mapping function should be used and then the method gives an approximate solution. The existing solutions obtained in an earlier work for a homogeneous piezoelectric plane or half–plane can be derived from the present solution as special cases. In particular, the closed–form solutions are given for the Eshelby problem of an arbitrarily shaped inclusion in a piezoelectric half–plane with various mixed surface conditions, such as rigid insulating surface or traction–free conducting surface. These solutions are used to study the effects of various surface electrical conditions on an electro–elastic field in a piezoelectric half–plane.

Elastic fields in two jointed half-planes with an inclusion of arbitrary shape

In this paper, a general method is presented for the analytic solution of Eshelby's problem concerned with an inclusion of arbitrary shape within one of two jointed dissimilar elastic half-planes. The method, based on the use of an auxiliary function and analytic continuation, is sufficiently general to accommodate an inclusion of arbitrary shape. The auxiliary function is constructed using a simple approach, from the conformal mapping which maps the exterior of the inclusion onto the exterior of the unit circle. The boundary value problem is studied in the physical plane rather than in the image plane. The solution obtained is exact provided that the expansion of the mapping function reduces to only a finite number of terms. When the number of terms in the expansion is infinite, a truncated polynomial mapping function can be used to obtain an approximate solution. Explicit expressions for the general solution of the governing equations are derived in terms of the auxiliary function. It is shown that existing solutions for an inclusion of arbitrary shape in a homogeneous plane or half-plane can be obtained, as special cases, from the present solution. In particular, the solution in this paper reduces to a very simple form in the case of a thermal inclusion. Several examples are used to illustrate the construction of the auxiliary function.

Analytic Solution for Eshelby's Problem of an Inclusion of Arbitrary Shape in a Plane or Half-Plane

Despite extensive study of the Eshelby's problem for inclusions of simple shape, little effort has been made to inclusions of arbitrary shape. In this paper, with aid of the techniques of analytical continuation and conformal mapping, a novel method is presented to obtain analytic solution for the Eshelby's problem of an inclusion of arbitrary shape in a plane or a half-plane. The boundary of the inclusion is characterized by a conformal mapping which maps the exterior of the inclusion onto the exterior of the unit circle. However, the boundary value problem is studied in the physical plane rather than in the image plane. The conformal mapping is used to construct an auxiliary function with which the technique of analytic continuation can be applied to the inclusion of arbitrary shape. The solution obtained by the present method is exact, provided that the expansion of the mapping function includes only a finite number of terms. On the other hand, if the exact mapping function includes infinite terms, a truncated polynomial mapping function should be used and then the method gives an approximate solution. In particular, this method leads to simple elementary expressions for the internal stresses within the inclusion in an entire plane. Several examples of practical interest are discussed to illustrate the method and its efficiency. Compared to other existing approaches for the two-dimensional Eshelby's problem, the present method is remarked by its elementary characters and applicability to inclusions of arbitrary shape in a plane or a half-plane.