Piecewise Cubic Research Articles

Total electricity generation dynamics analysis and renewable energy impacts in South Africa

AbstractThis research explores the dynamics of total electricity generation (TEG) in South Africa through an analysis of data from the International Energy Agency database from 1990 to 2020. A comprehensive examination of various energy sources, including coal, oil, biofuels, nuclear, hydro, solar photovoltaic (PV), solar thermal, and wind, is conducted to ascertain their respective contributions to TEG. Employing the R software environment, the study employs a methodical analytical framework encompassing meticulous data preparation, statistical analysis, and model formulation. The data preparation phase involves intricate processes such as structuring, cleansing, and visualization aimed at eliminating stochastic variables and outliers. Missing data are addressed through the application of the Piecewise Cubic Hermite Interpolating Polynomial method. Subsequent statistical analyses are informed by tests for normality and homogeneity of variance, revealing deviations from normality and disparate variances across energy source groups. Consequently, non‐parametric methodologies such as the Kruskal–Wallis test are adopted. Findings underscore the significant role of nuclear energy in TEG despite facing challenges. Model development entails the construction of multiple linear regression models with varying predictor sizes, with Model m06 emerging as the optimal choice, incorporating key predictors such as coal, nuclear, and solar PV. Rigorous diagnostic assessments confirm the robustness of Model m06 and its suitability for TEG prediction. Comparative analysis against actual data validates its superior performance, characterized by minimal errors and high predictive accuracy. The efficacy of Model m06 in capturing TEG dynamics underscores its utility for informing energy planning initiatives. Recommendations derived from the study advocate for prioritizing renewable energy integration, infrastructure investment, research endeavors, monitoring mechanisms, and public awareness campaigns to advance sustainable energy development goals in South Africa.

Assessment of monthly to daily streamflow disaggregation methods: A case study of the Nile River Basin

Study regionThe Nile River Basin Study focusThe lack of observed streamflow data at a short time scale poses a critical challenge for calibrating and validating hydrologic models. Therefore, many disaggregation methods were developed, resulting in various relative performances without a clear indication of the optimal choice. This study aims to iteratively assess eight monthly to daily streamflow disaggregation methods at 21 major subbasin outlets in the Nile River Basin (NRB) to identify the best-performing ones. These methods include one proportionality method and seven interpolation methods, i.e., linear, 2nd-order spline, 3rd-order spline, Piecewise Cubic Hermite Interpolating Polynomial (Pchip), Modified Akima (MAkima), mean preserved 2nd-order spline, and mean preserved 3rd-order spline. We assessed these methods using three metrics and visual investigations. New hydrologic insights for the regionThe results showed that the interpolation methods performed well, better than the proportionality method. However, their performances decreased at stations with high daily streamflow fluctuations. The interpolation methods’ performances were similar in mimicking the daily values but significantly different in preserving the mass balance. The mean preserving 3rd-order interpolation method (Lai 22) was the best in preserving the mass balance and capturing the low, moderate and high flows and, therefore, selected to generate the daily flow data in the NRB. The results of this study can guide a reliable method for obtaining daily streamflow data, which is important for the hydrologic and water management studies in the NRB.

MCS-ML based line vulnerability for infrastructural resilience assessment with multi-wind speed cyclonic zones

The resilience of critical infrastructure is paramount for power systems prone to cyclonic activities characterized by varying wind speeds. This study conducts a thorough examination of the impact of cyclone lasting for a week on transmission lines for each passing day. Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) is applied to extract hourly wind speed data for the cyclone. Sequential Monte Carlo Simulation (SMCS) is used to model the day-wise hourly transmission line fragility and determination of line vulnerabilities across high, medium, and low wind speed zones. Fragility curves are developed to depict the correlation between wind speeds and line failure probabilities in each zone. The line outage scenarios are generated based on the critical wind speeds and collapse wind speeds for each zone. Line Vulnerability Index (LVI) is proposed to determine the vulnerability and the resilience status of the transmission lines. Machine Learning (ML) based models, FFNN (Feed Forward Neural Network) and RFC (Random Forest Classifier), are proposed for assessment of infrastructure resilience by vulnerability ranking of the lines. Hourly wind speed and hourly line failure probability are the inputs to train the ML models and, LVI and ranking are predicted for the IEEE 30-bus system.

4D hybridisable interpolation methodology aimed at system modelling: application to a fuel cell blower

This paper focuses on providing an empirical model construction methodology based on Piecewise Cubic Hermite Interpolation Polynomials (PCHIP). The proposed methodology is suitable for modelling systems with high non-linearity between system parameters, process variables and/or operation variables. A detailed description of the 4D interpolation methodology is given and a practical application for a fuel cell (FC) blower black-box model obtaining is shown. The results of the algorithm-based model are compared to datasheet specifications to validate the FC blower model. The validation shows a good precision in the operation limits estimation. Additionally, some FC-related applications suitable for the obtained blower model utilization are described.

Interpolation insights: Accurate mass attenuation coefficient and effective atomic number estimation in PbO and BaO doped borosilicate glasses

Interpolation techniques such as Piecewise Cubic Hermite Interpolating Polynomials (PCHIP) and Cubic Splines (CS) were used to estimate the mass attenuation coefficient values (MAC) and the effective atomic number values (Zeff) of borosilicate glasses doped with PbO and BaO. The mathematical models were used to obtain a function between the parameters and the energy of the incoming photons, to provide a better understanding of the glass system. The glasses had a composition of 10Na2O–15PbO-(65-x)B2O3–10SiO2-xBaO, where x = 5, 10, 15, 20, and 25 mol%. The derived values were compared against theoretical data obtained from Phy-X, to determine the accuracy of the mathematical models. The results demonstrate that both the CS and PCHIP methods are useful tools that can accurately be used to determine the MAC and Zeff values of the investigated samples. For instance, at certain energies such as 0.103 MeV, the relative difference between the MAC values obtained through PCHIP and through Phy-X is as low as 0.07, demonstrating the effectiveness of the PCHIP model at these energies. The same is true for the Zeff values, where the same relative difference at 0.384 MeV is as low as 0.0002. Therefore, both the mathematical models demonstrate an effective ability at interpolating the MAC and Zeff values of the investigated glass system.

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

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 environments, which are frequently induced by pedestrian movement. The Generalized Extreme Studentized Deviate algorithm is utilized to discern and eliminate outliers in ranging values and the Piecewise Cubic Hermite Interpolating Polynomial 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.

On Piecewise Cubic Estimates of the Value Function in a Target Control Problem for a Nonlinear System

On Piecewise Cubic Estimates of the Value Function in a Target Control Problem for a Nonlinear System

A Novel Piecewise Cubic Hermite Interpolating Polynomial-Enhanced Convolutional Gated Recurrent Method under Multiple Sensor Feature Fusion for Tool Wear Prediction.

The monitoring of the lifetime of cutting tools often faces problems such as life data loss, drift, and distortion. The prediction of the lifetime in this situation is greatly compromised with respect to the accuracy. The recent rise of deep learning, such as Gated Recurrent Unit Units (GRUs), Hidden Markov Models (HMMs), Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Attention networks, and Transformers, has dramatically improved the data problems in tool lifetime prediction, substantially enhancing the accuracy of tool wear prediction. In this paper, we introduce a novel approach known as PCHIP-Enhanced ConvGRU (PECG), which leverages multiple-feature fusion for tool wear prediction. When compared to traditional models such as CNNs, the CNN Block, and GRUs, our method consistently outperformed them across all key performance metrics, with a primary focus on the accuracy. PECG addresses the challenge of missing tool wear measurement data in relation to sensor data. By employing PCHIP interpolation to fill in the gaps in the wear values, we have developed a model that combines the strengths of both CNNs and GRUs with data augmentation. The experimental results demonstrate that our proposed method achieved an exceptional relative accuracy of 0.8522, while also exhibiting a Pearson's Correlation Coefficient (PCC) exceeding 0.95. This innovative approach not only predicts tool wear with remarkable precision, but also offers enhanced stability.

Accurate Fourier-space statistics for line intensity mapping: Cartesian grid sampling without aliased power

ABSTRACT Estimators for n-point clustering statistics in Fourier-space demand that modern surveys of large-scale structure be transformed to Cartesian coordinates to perform Fast Fourier Transforms (FFTs). In this work, we explore this transformation in the context of pixelized line intensity maps (LIM), highlighting potential biasing effects on power-spectrum measurements. Current analyses often avoid a complete resampling of the data by approximating survey geometry as rectangular in Cartesian space, an increasingly inaccurate assumption for modern wide-sky surveys. Our simulations of a $20\, {\times }\, 20\, \text{deg}^2$ 21 cm LIM survey at $0.34\, {\lt }\, z\, {\lt }\, 0.54$ show this assumption biases power-spectrum measurements by ${\gt }\, 20~{{\ \rm per\ cent}}$ across all scales. We therefore present a more robust framework for regridding the voxel intensities on to a 3D FFT field by coordinate transforming large numbers of Monte-Carlo sampling particles. Whilst this unbiases power-spectrum measurements on large scales, smaller scale discrepancies remain, caused by structure smoothing and aliasing from separations unresolved by the grid. To correct these effects, we introduce modelling techniques, higher order particle assignments, and interlaced FFT grids to suppress the aliased power. Using a piecewise cubic spline (PCS) particle assignment and an interlaced FFT field, we achieve sub-per cent accuracy up to 80 per cent of the Nyquist frequency for our 21 cm LIM simulations. We find a more subtle hierarchical improvement in results for higher order assignment schemes, relative to the gains made for galaxy surveys, which we attribute to the extra complexity in LIM from additional discretizing steps. python code accompanying this paper is available at github.com/stevecunnington/gridimp.

Commercial Electric Vehicle Battery Degradation modelling and charging assessing using a real driving cycle

This paper proposes a model to study the degradation of li-ion NMC batteries of commercial electric vehicles. The model takes into account operation variables such as operating C-Rate, Depth of Discharge (DoD), Number of Cycles and Temperature using a 4-D Piecewise Cubic Hermite Interpolating Polynomial (PCHIP). Simulations have been done considering the Worldwide Harmonised Light Vehicles Test Procedure 3 (WLTP3) standard cycle. The model has been implemented in MATLAB. In addition, recommendations on charging procedures are given in order to reduce the degradation of batteries.

Power quality disturbance detection based on IEWT

With the continuous development of distributed generation, power quality problems are more complex. In order to ensure that the power quality of the active distribution network meets the requirements of users, it is of great significance to accurately obtain the power quality disturbance parameters. For the problem that the traditional empirical wavelet transform needs to manually select the number of frequency bands when analyzing unknown power quality disturbances, this paper proposes an improved empirical wavelet transform (IEWT) algorithm. The algorithm uses the Piecewise Cubic Hermite Interpolation (PCHIP) method and the improvement of the transition region to achieve adaptive frequency band division and noise interference reduction, and different amplitude (AM) and pitch (FM) components can be obtained. Then the Normalized Direct Quadrature (NDQ) algorithm and Singular Value Decomposition (SVD) algorithm are used to extract frequency, amplitude and time parameters of the AM-FM components. Simulation and experimental results show that the power quality disturbance parameters extracted by the proposed method are more accurate and less affected by noise.

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.

A comparison of wind turbine blade parametrization schemes for planform design optimization

This work compares nodal, spline and interpolation parametrization schemes for wind turbine blade planform design. The comparison is done on a power coefficient maximization problem, where the aerodynamic properties of the blade are computed using the Blade Element Method. The problem is solved using a gradient-based interior-point method with analytic gradients. We show the variation in planform design for each parametrization scheme when the degrees of freedom of the parametrization varies. We compare how the power coefficient converges with increasing degrees of freedom for each scheme. Our results shows that the B´ezier spline, the Piecewise Cubic Hermite Interpolation Polynomial (PCHIP) and Lagrange interpolation schemes present the best grid convergence out of all studied schemes.

A fourth order orthogonal spline collocation method Interface boundary value problem

Objective: A higher order numerical scheme for two-point boundary interface problem with Dirichlet and Neumann boundary condition on two different sides is propounded. Methods: Orthogonal cubic spline collocation techniques have been used (OSC) for the two-point interface boundary value problem. To approximate the solution a piecewise Hermite cubic basis functions have been used. Findings: Remarkable features of the OSC are accounted for the numerous applications, theoretical clarity, and convenient execution. The stability and efficiency of orthogonal spline collocation methods over B-splines have made the former more preferable than the latter. As against finite element methods, determining the approximate solution and the coefficients of stiffness matrices and mass is relatively fast as the evaluation of integrals is not a requirement. The systematic incorporation of boundary and interface conditions in OSC adds to the list of advantages of preferring this method. Novelty: As against the existing methodologies it becomes clear from our findings that OSC is dominantly computationally superior. A computational treatment has been implemented on the two-point interface boundary value problem with super-convergent results of derivative at the nodal points, being the noteworthy finding of the study. Keywords: Helmholtz problem; Orthogonal spline collocation techniques (OSC); Discontinuous data; Super Convergence; Piecewise cubic Hermite basis functions; Almost block diagonal (ABD) structure

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.

Closed Form Kramers–Kronig Relations With Shape Preserving Piecewise Cubic Interpolation

The derivation of the Kramers-Kronig relations is revisited based on system theory considerations to show their general validity and to emphasize how these relations are connected to the causality of a linear system. Then, the closed form Kramers-Kronig and subtractive Kramers-Kronig relations are introduced based on shape-preserving third-order piecewise cubic interpolation. The advantage of this formulation is that a small number of properly chosen data points are sufficient to produce accurate results over a broad frequency range. The developed formulas are applied to validate the transfer function of a bandpass filter, to determine the phase of the transmission coefficient of a metasurface from the measured amplitude, and to uniquely extract the refractive index of metamaterials.

Real-Time Estimation of R0 for COVID-19 Spread

We propose a real-time approximation of R0 in an SIR-type model that applies to the COVID-19 epidemic outbreak. A very useful direct formula expressing R0 is found. Then, various type of models are considered, namely, finite differences, cubic splines, Piecewise Cubic Hermite interpolation and linear least squares approximation. Preserving the monotonicity of the formula under consideration proves to be of crucial importance. This latter property is preferred over accuracy, since it maintains positive R0. Only the Linear Least Squares technique guarantees this, and is finally proposed here. Tests on real COVID-19 data confirm the usefulness of our approach.

Unit Heads Amidst COVID 19 Pandemic: Work-Life Balance, Talent Management Skills and Institutional Performance

Purpose: The study aims to determine the level of work-life balance, talent management skills, and institutional performance of Northern Iloilo Polytechnic State College (NIPSC) key officials during the COVID 19 pandemic. Methods: This study is descriptive-correlational research using purposive samplings. The 97 key officials from the 7 campuses were selected as respondents of this study. The researcher adopted a questionnaire focused on work balance, talent management skills, and institutional performance. To analyze the data, statistical tools like frequency count, percentage, mean, standard deviation for descriptive, and for inferential were t-test, one-way analysis of variance, and Pearson’s r was utilized. Results: The results revealed that the work-life balance of different units’ heads was ”Highly Balanced”. While the talent management skills were ”Highly Managed”. And, the level of key officials’ institutional performance was ”Outstanding.” Furthermore, the findings also indicate that there are no significant differences in the level of work-life balance, talent management skills, and institutional performance of school officials. The school key officials’ highly balanced lifestyle was able them to cater to the needs of their work and personal life in this catastrophe. Their experiences as key officials improved their management skills and impacted and influenced them to cope with the crisis. Novelty: Higher Education Institutions (HEIs) unit heads should know work-life balance for teachers and management skills to inspire colleagues for institutional performance in this virus crisis. This pandemic teaches key officials to become dynamic and visionary to manage the new educational policies by implementing different modalities and training for teachers. The four mandates such as instruction, research, extension services, and production of the college are prospering despite health protocols restrictions. Keywords: Northern Iloilo Polytechnic State College; key Officials; Pandemic; WorkLife Balance; Management Skills; Institutional Performance 1 Introductionbjective: A higher order numerical scheme for two-point boundary interface problem with Dirichlet and Neumann boundary condition on two different sides is propounded. Methods: Orthogonal cubic spline collocation techniques have been used (OSC) for the two-point interface boundary value problem. To approximate the solution a piecewise Hermite cubic basis functions have been used. Findings: Remarkable features of the OSC are accounted for the numerous applications, theoretical clarity, and convenient execution. The stability and efficiency of orthogonal spline collocation methods over B-splines have made the former more preferable than the latter. As against finite element methods, determining the approximate solution and the coefficients of stiffness matrices and mass is relatively fast as the evaluation of integrals is not a requirement. The systematic incorporation of boundary and interface conditions in OSC adds to the list of advantages of preferring this method. Novelty: As against the existing methodologies it becomes clear from our findings that OSC is dominantly computationally superior. A computational treatment has been implemented on the two-point interface boundary value problem with super-convergent results of derivative at the nodal points, being the noteworthy finding of the study. Keywords: Helmholtz problem; Orthogonal spline collocation techniques (OSC); Discontinuous data; Super Convergence; Piecewise cubic Hermite basis functions; Almost block diagonal (ABD) structure