Piecewise Cubic Hermite Interpolating Polynomial Research Articles

An improved positioning method based on compensation and optimization of ultra-wideband ranging results

Abstract Achieving precision in positioning under conditions of significant interference remains an unresolved challenge in research. This study introduces a low-cost Ultra-Wideband (UWB) distance compensation model that addresses electromagnetic wave loss in practical indoor settings. This paper employs kurtosis to detect Non-Line-of-Sight (NLOS) environments, which are frequently induced by pedestrian movement. The Generalized Extreme Studentized Deviate (GESD) algorithm is utilized to discern and eliminate outliers in ranging values and the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) algorithm compensates for the eliminated data points. Finally, Kalman filtering is used to improve UWB ranging results, allowing for better error elimination and compensation. Experimental results demonstrate that our proposed algorithm has higher accuracy and the mean square error improvement ratio can reach more than 20% in dynamic positioning tests.

Noise Reduction of Aeromagnetic Data Using Artificial Neural Network

The high-frequency content of high-resolution aeromagnetic data is of particular interest to geophysic ists to identify mineral deposits, shallow faults, and dikes. However, high-resolution aeromagnetic data is contaminated by cultural noise generated from aircraft and man-made features. The culture noise must be removed before starting the interpretation process. Manual techniques are more selective of the noise; however slower and more expensive because they require considerable hands-on interaction. The present study develops a novel method for detecting and removing the culture noise from aeromagnetic data based on an artificial neural network (ANN) in an automatic way and comparing the results with a conventional algorithm using the nonlinear filter. The proposed method is tested using a theoretical example that combine a magnetic anomaly due to a dyke with three sources of cultural noise, besides using a practical example to increase the number of training pattern. The network is trained based on the backpropagation training function, where the algorithm updates the weight and bias states as per the Levenberg–Marquardt optimization. The optimization is reached during the training and validation process after 3,000 iterations. The correlation coefficient ( R) is utilized along with the mean squared error (MSE) as performance indices of the ANN. The ANN demonstrates the capability to detect the spiky data based on the optimal weights, thus allowing for removing and replacing them with clean data using the piecewise cubic Hermite interpolating polynomial (PCHIP) function. The practical utility of the two-method is discussed using high-resolution aeromagnetic data from the Tushka area located in the southwestern desert of Egypt. Comparing the denoising results using the two methods shows that the current approach is more effective in processing and more closely recovering the original magnetic data.

Numerical investigation of upward supercritical water flow with Joule heating effect

By using Joule's Law, resistivity equation, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) functions, and resistivity-temperature correlation established based on the available experimental data, Joule heating heat flux profiles of upward supercritical water heat transfer in the annular tube are modelled and applied as the boundary condition. The calculated wall temperature result is compared to the Razumovskiy et al. experiment dataset. It is discovered that by using the PCHIP-modelled Joule heating profiles, the estimated wall temperature for both the Normal Heat Transfer (NHT) and Deteriorated Heat Transfer (DHT) regimes is comparable to the experiment in terms of trend and magnitude. However, by using the conventional constant heat flux profiles, the upstream and downstream wall temperatures are overestimated and underestimated respectively. This study demonstrated that CFD can adequately replicate experimental heat flux conditions, hence improving CFD estimates of supercritical heat transfer, particularly for the DHT, which has a substantial heat flux variation. With this fine imitation of the Joule heating heat flux, the critical DHT regime can be more accurately predicted.

An impact sensitivity assessment method of spacecraft based on virtual exterior wall

The impact sensitivity assessment of spacecraft is to obtain the probability of spacecraft encountering the OD/M (orbital debris or meteoroid), which is a prerequisite for survivability assessment of on-orbit spacecraft. An impact sensitivity assessment method of spacecraft based on virtual exterior wall was proposed to improve the computational efficiency. This method eliminates determination of the outermost surface elements of the spacecraft before generating the debris rays, which are assumed to originate from a non-concave virtual wall that completely wraps the spacecraft. The DistMesh method was adopted for the generating of the virtual wall to ensure its mesh quality. The influences of the sizes, mesh densities, shapes of the virtual wall on the efficiency and accuracy were considered to obtain the best combination of the size and mesh density of the wall and spacecraft. The results of this method were compared with those of S3DE (Survivability of Spacecraft in Space Debris Environment), BUMPER, MDPANTO, ESABASE2/Debris to verify the feasibility of the method. The PCHIP (Piecewise Cubic Hermite Interpolating Polynomial) was used to fit the size vs. flux relationship of the space debris to acquire the impact probability of OD/M with arbitrary size on the spacecraft.

A CFD-Based Data-Driven Reduced Order Modeling Method for Damaged Ship Motion in Waves

A simple CFD-based data-driven reduced order modeling method was proposed for the study of damaged ship motion in waves. It consists of low-order modeling of the whole concerned parameter range and high-order modeling for selected key scenarios identified with the help of low-order results. The difference between the low and high-order results for the whole parameter range, where the main trend of the physics behind the problem is expected to be captured, is then modeled by some commonly used machine learning or data regression methods based on the data from key scenarios which is chosen as Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) in this study. The final prediction is obtained by adding the results from the low-order model and the difference. The low and high-order modeling were conducted through computational fluid dynamics (CFD) simulations with coarse and refined meshes. Taking the roll Response Amplitude Operator (RAO) of a DTMB-5415 ship model with a damaged cabin as an example, the proposed physics-informed data-driven model was shown to have the same level of accuracy as pure high-order modeling, whilst the computational time can be reduced by 22~55% for the studied cases. This simple reduced order modeling approach is also expected to be applicable to other ship hydrodynamic problems.

Spatial interpolation method comparison for physico-chemical parameters of river water in Klang River using MATLAB

Water quality is one of the most highly debated issues worldwide at the moment. Inadequate water supplies affect human health, hinder food production, and degrade the environment. Using contemporary technology to analyze pollution statistics can help solve pollution issues. One option is to take advantage of advancements in intelligent data processing to conduct hydrological parameter analysis. To perform conclusive water quality studies, a lot of data is necessary. Unfilled data (information gaps) in the long-term hydrological data set may be due to equipment faults, collection schedule delays, or the data collection officer’s absence. The lack of hydrological data skews its interpretation. Therefore, interpolation is used to recreate and fill missing hydrological data. From 2012 to 2017, the Klang River’s biochemical oxygen demand (BOD) in Selangor, Malaysia, was sampled. This study examined three methods of interpolation for their effectiveness using the MATLAB software: piecewise cubic hermite interpolating polynomial (PCHIP), cubic Spline data interpolation (Spline), and modified Akima partitioned cubic hermite interpolation (Makima). The accuracy is assessed using root mean square error (RMSE). All interpolation algorithms offer excellent results with low RMSE. However, PCHIP delivers the best match between interpolated and original data.

Sensitivity analysis of spacecraft in micrometeoroids and orbital debris environment based on panel method

To reduce the risk of mission failure caused by the MM/OD impact of the spacecraft, it is necessary to optimize the design of the spacecraft. Spacecraft survivability assessment is the key technology in the optimal design of spacecraft. Spacecraft survivability assessment includes spacecraft impact sensitivity analysis and spacecraft component vulnerability analysis under MM/OD environment. The impact sensitivity refers to the probability of a spacecraft encountering an MM/OD impact while in orbit. Vulnerability refers to the probability that each component of a spacecraft may fail or malfunction when impacted by space debris. Yet this paper mainly analyzes the impact sensitivity and proposes a spacecraft sensitivity assessment method under the MM/OD environment based on a panel method. Under this panel method, a spacecraft geometric model is discretized into small panels, and whether they are impacted by MM/OD or not is determined through the analysis of the shielding or shadowing relationships between panels. The number of impacts on each panel is obtained through calculation, and accordingly the probability of each spacecraft component encountering MM/OD impact can be acquired, thus generating the impact sensibility. This paper extracts data from the NASA's ORDEM2000, the ESA's MASTER8 as well as the SDEEM2015 (Space Debris Environmental Engineering Model developed by HIT), and uses the PCHIP (Piecewise Cubic Hermite Interpolating Polynomial) method to interpolate and fit the size-flux relationship of space debris. Compared with linear interpolation and cubic spline interpolation, the fitting results through the method are relatively more accurate. The feasibility of this method is also demonstrated through two actual examples shown in this paper, whose results are close to those from ESABASE, although there are some minor errors mainly due to different debris data input. Through the cross-check by three risk assessment software - BUMPER, MDPANTO and MODAOST - under standard operating conditions, the feasibility of this method is again verified.

Electromagnetic Wave Propagation From Low-Earth Orbit Satellite to Ground Station Considering Interpolated Atmospheric Environments

We propose a novel method to calculate the electromagnetic (EM) wave propagation from low-earth orbit satellite (LEO) to a ground station based on the physical optics (PO), ray tracing technique, and geometric optics (GO) considering interpolated atmospheric environments. Our method includes the reflector antenna analysis using PO, the interpolation of the meteorological data using PCHIP and Kriging interpolation, transmission analysis using ray tracing and geometrical optics. Tropospheric and stratospheric environments are modeled using meteorological data-air pressure and temperature, relative humidity, and rain rate-measured at 9 different radiosonde observatories in and around South Korea. Furthermore, we utilize Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) and Kriging-exponential methods for vertical and horizontal interpolations of the raw meteorological data, respectively. Hence, the interpolated atmospheric environments are amenable to the best use of ray tracing technique and GO. Subsequently, effective refractive indices of the stratified media can be extracted via millimeter-propagation-model93. The simplified Appleton-Hartree equation characterizes the ionospheric environment. Considering a sun-synchronous orbit satellite passing through South Korea, we calculate atmospheric attenuation, boresight error, received power, and compensation angle of satellite antenna for various conditions.

An Improved Empirical Wavelet Transform for Noisy and Non-Stationary Signal Processing

Empirical wavelet transform (EWT) has become an effective tool for signal processing. However, its sensitivity to noise may bring side effects on the analysis of some noisy and non-stationary signals, especially for the signal which contains the close frequency components. In this paper, an improved empirical wavelet transform is proposed. This method combines the advantages of piecewise cubic Hermite interpolating polynomial (PCHIP) and the EWT, and is named PCHIP-EWT. The main idea of the proposed method is to select useful sub-bands from the spectrum envelope. The proposed method selects the maximum points of the spectrum to reconstruct the spectrum envelope on the basis of PCHIP. Then, a new concept and a threshold named the Local Power (LP) and λ are defined. Based on the new concept LP and the λ, the useful sub-bands can be obtained. Finally, the experimental results demonstrate that the PCHIP-EWT is effective in analyzing noise and non-stationary signals, especially those that contain the closely-spaced frequencies.

RRT-A*-BT approach for optimal collision-free path planning for mobile robots

This paper deals with the problem of optimal collision-free path planning for mobile robots evolving inside indoor cluttered environments. Addressing this challenge, a hybrid approach is proposed combining Rapidly-exploring Random Trees (RRT), A-Star (A*) and Back-Tracking (BT) algorithms (RRT-A*-BT). Thus, a vision system is used for a nearly-exact modeling of the environment through image processing. Moreover, each iteration of the basic RRT approach is guided by A* algorithm while trying to take the shortest path linking the robot current position to target . In case of a blockage, BT algorithm is used to get out the robot from this situation. Finally, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) is used to smooth the generated optimal path. RRT-A*-BT approach is validated through different scenarios; obtained results are compared with previous works on same environments with same conditions. The results prove that RRT-A*-BT is better and faster than other algorithms of the literature, such as Genetic Algorithms and Conventional RRT, in terms of (i) computation time,(ii) path length and (iii) transfer time..

A comparison of piecewise cubic Hermite interpolating polynomials, cubic splines and piecewise linear functions for the approximation of projectile aerodynamics

Abstract Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions. An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics. The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions: they are continuous, differentiable at least once, and have a relatively low degree. The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools, and then compares Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), cubic splines, and piecewise linear functions, and their variant, as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile. A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics, and its evaluation against a set of criteria. Finally, the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.

Fitting Rainfall Data by Using Cubic Spline Interpolation

This study discusses the application of two cubic spline i.e. natural and not-a-knot end boundary conditions to visualize and predict the rainfall data. The interpolation and the analysis of the rainfall data will be done on a monthly basis by using the MATLAB software. The rainfall data is obtained from Malaysia Meteorology Department for Ipoh and Petaling Jaya in year 2014 and 2015. The interpolating curves are then being compared and if there is any negative value on the interpolating curve on some sub-interval, that part will be replaced by using the Piecewise Cubic Hermite Interpolating Polynomial (PCHIP). We discuss the missing data imputation by using both splines.

3D light fields based foreground segmentation in static scenes

To address the problem of extracting foreground objects from complex scenes,a 3D light field based method for foreground segmentation of static scenes was presented. Firstly,the method relies on densely sampled 3D light field formed by stacking a sequence of images captured at different viewpoints. These viewpoints were equally spaced along a linear path so that object trace was smooth in epipolar plan image( EPI).Secondly,line segment detection( LSD) method was performed to extract edges and compute the corresponding depth in EPI,based on which a depth map of the scene was obtained through a fast local depth interpolation algorithm. Piecewise cubic Hermite interpolating polynomial( PCHIP) algorithm proved to have desirable results in this phase. Finally,the recovered dense depth information was exploited to facilitate foreground segmentation. A threshold approach was used to separate different objects in scenes. Preliminary experimental results show that our method is able to estimate the correct relative spatial relation of multiple objects and our proposed foreground segmentation method reduces over-segmentation effects existed in traditional methods based on region clustering and mathematical morphology.

Fin design for conjugate heat transfer optimization in double pipe

Optimal design of longitudinal fins augmented to the outer surface of the inner pipe in a double pipe, is investigated for maximizing conjugate heat transfer coefficient. Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) has been used for fin-surface representation at each step of the optimization process with control points as the design variables. Genetic algorithm has been employed as the optimizer together with the Discontinuous Galarkin Finite Element Method (DG-FEM) as the solver of the governing equations. The results show that the optimal fin design is greatly influenced by the characteristic length, the number of fins, the conductivity of the material of heated surface and the number of control points. Optimal designs based on the equivalent diameter give upto 289% improvement in the heat transfer coefficient and those based on the hydraulic diameter render such improvement upto 70%. Optimal fin shape has also out-performed the conventional fin shapes present in the literature and shown upto 203%, 263% and 227% increase in the heat transfer coefficient relative to the equivalent diameter for trapezoidal, triangular and parabolic fins respectively. For the case of hydraulic diameter, these figures are respectively 482%, 70% and 117%. The optimal designs based on the equivalent diameter corresponding to Ω = 500 have proven to be the best in view of cost, frictional loss and heat transfer coefficient. These give upto 39% higher heat transfer coefficient than the corresponding increase in frictional loss due to augmentation of the fins to the double pipe. The validity and accuracy of the present results has been shown by comparison with the available literature results.

A Load Scheduling Algorithm for the Smart Home Using Customer Preferences and Real Time Residential Prices

A load scheduling method in the Smart Home using a combination of customer preferences and the price of electricity is presented. To translate the customer preference of loads into a time-varying priority curve, the Analytical Hierarchy Process (AHP) and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) methods are used. The resulting curves of customer priority are combined with the available time-varying pricing information for determining the schedule for each load. An example with four loads is presented to demonstrate the effectiveness of the algorithm.

Least Squares Interpolation Methods for LTE SystemChannel Estimation over Extended ITU Channels

Abstract — Performance of pilot-aided channel estimation techniques such as the Least Squares (LS) method depends on not only on the signal-to-noise ratio (SNR), channel conditions and pilot ratio, but also on the choice of interpolation method for deriving channel estimates at non-pilot subcarriers. This paper investigates the bit-error-rate (BER) performance of linear, spline and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation methods in LS channel estimation over the three extended ITU channel profiles defined for Long Term Evolution (LTE) testing. Simulation results show that applying the linear interpolation method produces the best BER performance over the fading channel with the smallest multipath delay spread. It is also shown that the choice of best interpolation method actually depends on the SNR in some of the fading channel profiles. Index Terms—ITU, LS, LTE, PCHIP, spline. I. INTRODUCTION Orthogonal frequency division multiplexing (OFDM) technology has been adopted in many of the next generation communication systems such as Long Term Evolution (LTE) and Worldwide Interoperability for Microwave Access (WiMAX) [1]. OFDM is preferred not only because it offers high data rate transmission but also because of its flexibility and robustness against multipath fading [1]. Multipath channel fading exists when multiple delayed copies of a transmitted signal are received at the receiver, thereby resulting in the distortion of the transmitted signal. These distortions are collectively termed „channel fading‟, causing reception errors and hence increased bit-error-rate (BER). Channel fading can be broadly classified as time-selective and/or frequency selective, depending on the relationship between the fading channel and the transmitted signal parameters [2]. To combat multipath fading and improve BER, some form of channel estimation method is required in order to estimate the channel distortion effect for each of the active subcarriers within an OFDM symbol [3].

Seabed loging data curve fitting using cubic splines

Deep water and deep target environment for Seabed Loging (SBL) has been a challenge, and the better delineation method is needed. This paper describes the curve fitting methods namely smoothing spline and piecewise cubic Hermite interpolating polynomial (PCHIP) to give better delineation. In this work we simulated five geophysical layers namely air (500m), sea water (2000m), over burden (1000m), hydrocarbon (100m) and under burden (1000m) respectively. Target depth was increased gradually by 500m from 1000m to 3000m at constant frequency of 0.125Hz and 1250A current. Due to the weak electromagnetic signal from deep target of SBL we had chosen curve fitting methods to describe hydrocarbon reservoir. The results show that smoothing spline is quantified as compare to the PCHIP due to the existence of various noises in the SBL data. Several numerical results will be presented.

Optimal fin shape in finned double pipe with fully developed laminar flow

Optimal shape of longitudinal fins augmented to the outer surface of the inner pipe enclosed within a concentric outer pipe, is investigated for maximizing the Nusselt number in a steady laminar and fully-developed flow. The wall-fin assembly is made up of highly conductive material and is subjected to the uniform heat flux boundary condition. Taking triangular cross-section as the initial profile, the fin shape is represented by Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) at each step of the optimization process with control points as the design variables. Genetic algorithm and trust region method have been used as the optimizers with FEM as the solver of the governing equations. The results show that the optimal profile is strongly dependent on the number of fins, the ratio of radii, the number of control points and the characteristic length. It gives improvement in the Nusselt number upto 138%, 312% and 263% over the conventional fins of trapezoidal, triangular and parabolic shapes for the case of equivalent diameter and for the case of hydraulic diameter it gives such improvements upto 212%, 59% and 90% respectively. For large number of fins the optimal fin shape based on the equivalent diameter is usually triangular on smaller inner pipes and wavy on larger inner pipes. More and more articulates appear as the larger number of higher fins is employed on bigger inner pipes. For the case of hydraulic diameter, it may either be regarded as parabolic or wavy. Comparison of the present results with the available literature results proves their validity and accuracy.