Third-order Interpolation Research Articles

Dynamic behavior of risers under nonlinear oceanic environmental loading

The riser system acts as the vital link between the subsea blow-out preventer and the drilling platform. Affected by factors like top tension and marine environmental forces, the riser undergoes deformation and wear, carrying the risk of environmental pollution and financial losses upon failure. Hence, this study examines the riser's dynamic response to marine environmental loading. Initially, the motion differential equation for the riser system under the influence of nonlinear oceanic load is deduced using the principle of minimum potential energy and the variational method for extremum seeking. Subsequently, a nonlinear wave-current load model based on the Morrison equation is established, and the resulting equation is discretized into a finite element model using third-order Hermite interpolation function and the Galerkin weighted residual method. Finally, the dynamic response of the riser is scrutinized employing the Newmark numerical integration method. The study also investigates the impact of both oceanic environmental parameters and drilling parameters on the riser’s dynamic behavior. Comparative analysis of the numerical results reveals that the maximum displacement of the riser occurs at the middle section, whereas the maximum deflection angle is observed at the end of the riser. The periodicity of the deflection angle response is influenced by the position of the riser, showing a trend of decreasing and then increasing from the middle section towards the ends. Notably, the top tension and the velocity of the surface tidal current significantly affect the dynamic behavior of the riser. The findings of this study provide a theoretical foundation for the assessment of riser reliability and the determination of operational parameters.

Phase field modeling with large driving forces

There is growing interest in applying phase field methods as quantitative tools in materials discovery and development. However, large driving forces, common in many materials systems, lead to unstable phase field profiles, thus requiring fine spatial and temporal resolution. This demands more computational resources, limits the ability to simulate systems with a suitable size, and deteriorates the capability of quantitative prediction. Here, we develop a strategy to map the driving force to a constant perpendicular to the interface. Together with the third-order interpolation function, we find a stable phase field profile that is independent of the magnitude of the driving force. The power of this approach is illustrated using three models. We demonstrate that by using the driving force extension method, it is possible to employ a grid size orders of magnitude larger than traditional methods. This approach is general and should apply to many other phase field models.

Low-dose dynamic cerebral perfusion CT reconstruction based on voxel-level TAC correction (VTC)

Dynamic cerebral perfusion computed tomography (DCP-CT) is an advanced imaging technique that helps in the clinical diagnosis of cerebrovascular diseases (CVDs). However, radiation dose deposition during repeated CT scans seriously limits its clinical application. Effective DCP-CT imaging method based on low-dose protocol is needed. A regularized least-squares method with high interpretability based on voxel-level time-attenuation curve (TAC) correction (VTC) is proposed in this study for low-dose DCP-CT image reconstruction. The theory of third-order Hermite interpolation (THI) is applied to voxel-level TAC correction during dynamic images reconstruction. The peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) are used to quantitatively evaluate the proposed method in terms of imaging accuracy and noise reduction, while hemodynamic maps, including cerebral blood flow (CBF), cerebral blood volume (CBV) and mean transition time (MTT), are calculated to validate its ability to restore hemodynamic parameters. It is proven that the proposed VTC method for low-dose DCP-CT imaging has better performance than several state-of-the-art dynamic CT imaging methods. It can be expected that the VTC method can play an important role in the promotion of the clinical application of DCP-CT for the diagnosis of CVD.

A Hybrid Full-Discretization Method of Multiple Interpolation Polynomials and Precise Integration for Milling Stability Prediction

As milling chatter can lead to poor machining quality and limit the efficiency of productivity, it is of great significance to learn about milling chatter stability and research the effective and fast prediction of milling stability. In this study, a hybrid full-discretization method of multiple interpolation polynomials and precise integration (HFDM) is proposed for milling stability prediction. Firstly, the third-order Newton interpolation polynomial, third-order Hermite interpolation polynomial and linear interpolation are applied to approximate the state term, delay term and periodic coefficient matrix, respectively. Meanwhile, the matrix exponentials can be calculated based on the precise integration algorithm, which can improve computational accuracy and efficiency. The numerical simulation results indicate that the proposed method can not only effectively generate a stability lobe diagram (SLD) but also obtain better prediction accuracy and computation efficiency. A milling experiment is offered to demonstrate the feasibility of the method.

Multi-objective based demand response strategy optimization considering differential demand on reliability of power system

The reliability of power system will vary with different demand response strategies, and it is significant to make a decision on demand response for satisfying differential reliability demand of power system. First, a peak-valley period partition model with an objective of maximizing silhouette coefficient was established based on the fuzzy clustering and step-wise iteration technology. Second, this paper proposed a multi-objective time of use electricity price optimization model considering the interests of both supply and demand sides, as well as reliability demand, and a multi-objective simulated annealing particle swarm optimization algorithm was developed to obtain solution. Third, the Pareto front curve of the dual-objective function was fitted by using a third-order Hermite interpolation algorithm, and the time of use prices corresponding to the reliability demand was obtained by using the back propagation neural network algorithm. Finally, the proposed model and algorithm were verified by the RBTS system, and the results indicate good rationality and effectiveness of the proposed method.

High Temporal Resolution Total-Body Dynamic PET Imaging Based on Pixel-Level Time-Activity Curve Correction.

Dynamic positron emission tomography (dPET) is currently a widely used medical imaging technique for the clinical diagnosis, staging and therapy guidance of all kinds of human cancers. Higher temporal imaging resolution for the early stage of radiotracer metabolism is desired; however, in this case, the reconstructed images with short frame durations always suffer from a limited image signal-to-noise ratio (SNR) and unsatisfactory image spatial resolution. The appearance of uEXPLORER (United Imaging Healthcare, Inc.) with higher PET imaging sensitivity and resolution may help solving this problem. In this work, based on dynamic PET data acquired by uEXPLORER, we proposed a dPET processing method that denoises images with short frame durations via pixel-level time-activity curve (TAC) correction based on third-order Hermite interpolation (Pitch-In). The proposed method was validated and compared to several state-of-the-art methods to demonstrate its superior performance in terms of high temporal resolution dPET image noise reduction and imaging accuracy. Higher stability and feasibility of the proposed Pitch-In method for future clinical application with high temporal resolution (HTR) dPET imaging can be expected.

Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model

American put options with the regime-switching model is a system of coupled free boundary problems. In this study, we present an accurate finite difference method coupled with the Hermite interpolation for solving this system. To this end, we first employ the logarithmic transformation to map the free boundary for each regime to a fixed interval and then eliminate the first-order derivatives in the transformed model by taking derivatives to obtain a system of partial differential equations which we call the asset-delta-gamma-speed equations. We then discretize the system using the fourth-order compact scheme coupled with the Crank–Nicholson method. At the same time, the influence of other asset options and option sensitivities are estimated based on the third-order Hermite interpolation. As such, the overall scheme consists of four tridiagonal linear systems, which can be easily solved using the Thomas algorithm and the Gauss–Seidel iteration. The obtained scheme is then applied for the model with two, four, and sixteen regimes, respectively. Our results show that the scheme provides an accurate solution that is fast in computation as compared with other existing numerical methods.

Improved Methods for Computing CCT and D uv

ABSTRACT Recently, Ohno proposed a method for computing the correlated color temperature (CCT) of a light source and the shortest distance (with sign) between its chromaticity and that of the Planckian locus (D uv). In Ohno’s method, firstly a lookup table is chosen, and then a hybrid method based on the triangular and parabolic solutions is used to predict the CCT and D uv of a given light source. In this article, we found that spline interpolation is better than the parabolic solution for predicting CCT and D uv. Therefore, we propose two new hybrid methods based on the triangular and either spline interpolation or third-order interpolation using two local function values and two local second-order derivative values. Comprehensive tests using the lookup table with both 1% and 0.25% increments relative to the current selected color temperature demonstrate that the proposed methods outperform Ohno’s method.

Investigation of robotic milling chatter stability prediction under different cutter orientations by an updated full-discretization method

Chatter can easily occur during robotic milling owing to the low rigidity of serial robots. Chatter affects the quality of the workpiece surface and damages the robot equipment, which is a bottleneck that hinders the application of robotic milling. An effective way to ensure milling stability is to rationally select the cutting parameters using high-precision stability lobe diagrams (SLDs). In this study, an updated full-discretization chatter stability prediction method based on the fourth-order Hermite and third-order Newton interpolation polynomial was proposed. A dynamical model of robotic milling was established by considering the regenerative effect, cutter structure modal coupling effect, and the influence of cutter orientations. Based on the established robotic milling dynamic model and the proposed full-discretization method, SLDs related to the axial depth of cut, spindle speed, lead angle, and tilt angle were generated. The dominant influencing factors of the robotic milling chatter stability under different robot postures and cutter orientations were analysed. The robotic milling experiment results show that the dynamic characteristics of the robot are different in each direction. When the milling cutter feeding direction is parallel to the x-axis direction of the global coordinate system, the regenerative effect is dominant. When the feed direction of the milling cutter is parallel to the y-axis of the global coordinate system, the cutter structure modal coupling effect is more obvious. This is possibly because the dynamic characteristics of the tool tip change during the milling process under different robot postures. However, the milling process becomes more stable with an increase in the lead or tilt angle. This is mainly because when the cutting depth is constant, the cutter–workpiece engagement area gradually decreases with an increase in the tool angle.

A numerical framework for hydroelastic analysis of a flexible floating structure under unsteady external excitations: Motion and internal force/moment

An effective numerical framework is constructed in which the discrete-module-beam hydroelasticity method is applied for analyzing the motion and internal force/moment of a flexible floating structure under unsteady external excitations. Procedures for dealing with three kinds of unsteady excitation forces are presented, namely a concentrated force only, a local continuously-distributed force and a combination of waves and unsteady local external loads. The strategy for obtaining hydroelastic responses of any given location of a VLFS is given, especially a hybrid integration-interpolation (HII) method is developed to calculate the VLFS's structural force response. Several loading processes are investigated. The calculated vertical displacements show a rather good agreement with the experimental data or the numerical results from other scholars, which validates the proposed framework. The bending moment distribution curve given by the HII method is compared with that given by the third-order interpolation scheme. The HII method is able to give the real structural force distribution curve at the initial stage of the loading process and shows an abrupt change on the location where a concentrated force is exerted.

Unsupervised arterial spin labeling image superresolution via multiscale generative adversarial network.

Arterial spin labeling (ASL) magnetic resonance imaging (MRI) is an advanced noninvasive imaging technology that can measure cerebral blood flow (CBF) quantitatively without a contrast agent injection or radiation exposure. However, because of the weak labeling, conventional ASL images usually suffer from low signal-to-noise ratio (SNR), poor spatial resolution, and long acquisition time. Therefore, a method that can simultaneously improve the spatial resolution and SNR isneeded. In this work, we proposed an unsupervised superresolution (SR) method to improve ASL image resolution based on a pyramid of generative adversarial networks (GAN). Through layer-by-layer training, the generators can learn features from the coarsest to the finest. The last layer's generator that contains fine details and textures was used to generate the final SR ASL images. In our proposed framework, the corresponding T1-weighted MR image was supplied as a second-channel input of the generators to provide high-resolution prior information. In addition, a low-pass-filter loss term was included to suppress the noise of the original ASL images. To evaluate the performance of the proposed framework, a simulation study and two real-patient experiments based on the in vivo datasets obtained from three healthy subjects on a 3T MR scanner were conducted, regarding the low-resolution (LR) to normal-resolution (NR) and the NR-to-SR tasks. The proposed method was compared to the nearest neighbor interpolation, trilinear interpolation, third-order B-splines interpolation methods, and deep image prior (DIP) with the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) as the quantification metrics. The averaged ASL images acquired with 44 min acquisition time were used as the ground truth for real-patient LR-to-NR study. The ablation studies of low-pass-filter loss term and T1-weighted MR image were performed based on simulation data. For the simulation study, results show that the proposed method achieved significantly higher PSNR ( -value 0.05) and SSIM ( -value 0.05) than the nearest neighbor interpolation, trilinear interpolation, third-order B-splines interpolation, and DIP methods. For the real-patient LR-to-NR experiment, results show that the proposed method can generate high-quality SR ASL images with clearer structure boundaries and low noise levels and has the highest mean PSNR and SSIM. For real-patient NR-to-SR tasks, the structure of the results using the proposed method is sharper and clearer, which are the most similar to the structure of the reference 44 min acquisition image than other methods. The proposed method also shows the ability to remove artifacts in the NR image while superresolution. The ablation study verified that the low-pass-filter loss term and T1-weighted MR image are necessary for the proposedmethod. The proposed unsupervised multiscale GAN framework can simultaneously improve spatial resolution and reduce image noise. Experiment results from simulation data and three healthy subjects show that the proposed method achieves better performance than the nearest neighbor interpolation, the trilinear interpolation, the third-order B-splines interpolation, and DIP methods.

A Novel Updated Full-Discretization Method for Prediction of Milling Stability

This paper presents an updated full-discretization method for milling stability prediction based on cubic spline interpolation. First, the mathematical model of the time-delay milling system considering regenerative chatter is represented by a dynamic delay differential equation. Then, in a single tooth passing period, the time is divided into a finite time intervals, the state item and the time-delay item are approximated in each time interval by cubic spline interpolation and third-order Newton interpolation, respectively. Afterward, a transition matrix is constructed to represent the transfer relationship of the teeth in a period. Finally, based on Floquet theory, the milling stability lobes can be obtained. Meanwhile, in order to improve computational efficiency, an optimized method is proposed based on the traditional algorithm and the proposed method has high precision without losing high efficiency. Finally, several milling experiments are conducted to verify the accuracy of the proposed method, and the results show that the predicted results agree well with the experimental results.

Fan-ring interpolation method applied to the panorama unwrapping of the deep-hole parts.

Image interpolation is a critical step in panoramic image unwrapping studies. Information calculated in the Cartesian coordinates, although broadly applied, applies to operation between rectangles that will destroy the compressed depth information. The polar coordinates, in contrast, can store depth information by handing between rectangle and circle to obtain more true images. A fan-ring interpolation based on the polar coordinates is proposed for unwrapping panoramic images in this study through replanning the pixel search path in the panorama, and is then supported by redefining third-order interpolation. We validate our method on synthetic and practical images. Compared with competitor models, the unwrapping image obtained from the fan-ring interpolation can provide better quality in subjective and objective evaluation with guaranteed accuracy.

Using the first-order, second-order, and third-order interpolation perturbation theory from quantum mechanics of modern physics to predict the CGM sensor device’s fasting plasma glucose value in the early morning, while analyzing their associated waveform shape similarities over a 14-month period based on GH-Method: math-physical medicine (No. 561)

The author utilizes the first-order, second-order, and third-order interpolation perturbation equations from quantum mechanics of modern physics to his medical research work, which he has previously written a few medical articles on this topic. This equation is the simplest application using one selected “perturbation factor” to generate perturbed results with high prediction accuracy and waveform shape similarity. During November 2021, he has applied the statistics regression analysis model to analyze the relationship among many biomarkers where he wrote ~20 medical articles. In this study, he predicts his fasting plasma glucose (FPG) value from his body temperature (BT) and body weight (BW) in the early morning. As a comparison, he chose two separate perturbation values of 0.4 for BT perturbation factor and 0.6 for BW perturbation factor to calculate and predict his FPG value. He then compares the predicted FPG dataset against his measured sensor FPG dataset. This comparison study also contains the following two final measurement yardsticks to confirm the usefulness of the perturbed method. The first yardstick is to verify the prediction accuracies of the perturbed FPG dataset against his measured FPG dataset. The second yardstick is to examine the waveform shape similarity via the calculated correlation coefficient between the predicted or perturbed, FPG curve and the measured FPG curve. In summary, the purpose of this study is to investigate the prediction accuracy and the waveform shape similarities between a perturbed or predicted FPG waveform and his measured FPG waveform over a 14-month period, which is a total of 420 days from 10/1/2020 to 11/24/2021. He utilizes the first-order, second-order, and third-order of interpolation perturbation equations with two different perturbation factor values of 0.4 for BT and 0.6 for BW. The author has selected these two slightly different slopes, i.e., perturbation values, to study the sensitivity results. The two conclusions drawn from this research work are listed as follows: First, the 3 perturbation equations for the BT and BW cases offered an identical match for waveform shape similarity with a 100% correlation coefficient. Second, the 3 perturbation equations also provided extremely high prediction accuracies as outlined: Prediction Accuracy for BT Case (Perturbation Value 0.4) First-order: Accuracy = 96% Second-order: Accuracy = 95% Third-order: Accuracy = 94%Prediction Accuracy for BW case (Perturbation Value 0.6) First-order: Accuracy = 98% Second-order: Accuracy = 96% Third-order: Accuracy = 95% All 6 prediction accuracies are higher than 94%. It seems that the higher the slope (perturbation value), the higher prediction accuracy will be achieved.

UAV Path Planning of Combining Ant Colony and Beetle Antennae Algorithm Using Intelligent Wireless Communication

In order to settle the problem of UAV path planning under mountain, an algorithm which based on the combination of ant colony algorithm and beetle antennae algorithm is proposed. Three dimensional environment model is established and objective function is constructed. It used ant colony algorithm to initialize the search path and the particle coordinates of all the next steps are updated by the beetle antennae algorithm. The improved algorithm adopted a new step update rule to speed up the convergence of the algorithm and used third-order B-spline interpolation method to smooth the path. Simulation results show that improved fusion algorithm has faster convergence speed and high stability by comparing with other algorithms under the same conditions, which verifies its effectiveness.

High-order semi-discretization methods for stability analysis in milling based on precise integration

The third-order and fourth-order semi-discretization methods (3rd SDM and 4th SDM) are presented to predict milling stability based on precise integration. Firstly, the milling system is mathematically represented by a delay differential equation (DDE) and re-expressed in the state space. After dividing the tooth passing period into free and forced vibration time intervals, the forced vibration time interval is equally discretized into many small-time intervals. Then, the DDE is integrated on any small-time interval and solved in the framework of the semi-discretization algorithm. Subsequently, the 3rd SDM and 4th SDM are derived for predicting the stability limits in milling. In the 3rd SDM and 4th SDM, the third-order and fourth-order interpolation polynomials are used to approximate the delayed term, respectively. The periodic-coefficient matrix is approximated by linear interpolation polynomial. The convergence rates of the one degree of freedom (one-DOF) milling system and the milling system with multiple modes are conducted. The results indicate the convergence rates of the 3rd SDM and 4th SDM are higher than those of the benchmark methods. Besides, no matter for large or low radial immersion conditions, the stability lobe diagrams (SLDs) obtained by the proposed 3rd SDM and 4thSDM are closer to the reference than those obtained by the benchmark methods. The computational efficiency of the 3rd SDM and 4th SDM is also evaluated. Compared with the benchmark methods, the presented 3rd SDM and 4th SDM are superior in computational efficiency. Generally, the main advantage of the proposed methods is the improvement of computational efficiency. The proposed 3rd SDM and 4th SDM can use a smaller discrete number for achieving the desired accuracy to reduce the size of the state transition matrix and improve the computational efficiency.

Dynamic computation of 2D segment-to-segment frictional contact for a flexible multibody system subject to large deformations

A new formulation is presented to simulate the segment-to-segment frictional contact dynamics of planar multibody systems that are subjected to large deformations and large motions. The contact bodies are meshed via planar elements of the absolute nodal coordinate formulation, which offers a C1-continuous surface representation for contact regions. To maintain the optimal convergence, the mortar method is used to discretize the contact constraints, which are established in an integral form on the nonconforming contact surface. By using Coulomb's friction law, the switch between stick and slip status can be realized. The penalty approach and return mapping algorithm are adopted to enforce contact constraints. The rescale and reconstruction strategy proposed in the previous study of authors is improved to recover the gap functions and the tangential friction force. In the mortar space, the magnitudes of the normal contact force and tangential friction force are discretized via the third-order Hermite interpolation, while their directions are along the normal vector and tangential vector of the contact surface, respectively. Several numerical examples are presented to demonstrate the effectiveness of the formulation.

Временные корреляционные методы оценки задержки комплексных сигналов, некратной периоду дискретизации, на основе полиномиальной интерполяции.

This paper deals with the problem of subsample time delay estimation of complex signal based on polynomial interpolation. Time delay estimation is performed by cross-correlation time approach. Three polynomial interpolation techniques applied to the discrete complex cross-correlation function in the neighborhood of its maximum are proposed. These methods show high processing speed and allow obtaining accurate real-valued time delay estimation when digital complex signals are processed. The comparative analysis between these methods is performed. A rigorous analytical solution for the correction of time delay estimation for one of the proposed methods is obtained for the case of the third-order polynomial interpolation. This solution is applied for an equidistant grid of discrete cross-correlation function samples. One can improve the accuracy of time delay estimates by using aforementioned correction. A numerical simulation is performed to quantify the accuracy of the time delay estimates when using the proposed methods for the case where a stationary random process described by the first-order autoregressive mode is chosen as a model of original signal. The main results were presented and discussed at XIV All-Russian conference “Radar and telecommunication”.

Application of Higher-Order Interpolation Perturbation Theory on Postprandial Plasma Glucose Waveform of a Single Lunch Based on GH-Method: Math-Physical Medicine (No. 426)

In this particular research note, the author arbitrarily selects the postprandial plasma glucose (PPG) data and waveforms from his lunch on 3/31/21 as the reference base. He then applies the higher-order, including first-order, second-order, and third-order interpolation perturbation theory to generate three approximated PPG waveforms to compare them against the measured nonlinear PPG waveform. The two major purposes of this study is to check the waveform shape similarity via correlation coefficients and the prediction accuracy via comparison of the averaged PPG values using the “higher order” interpolation perturbation theory. One obvious conclusion can be drawn from this article is that the higher-order perturbation equation provides a better approximate solution. However, in reality, there are very few patients who understand the perturbation theory of quantum mechanics, let alone to be able to conduct the complex mathematical calculations in order to achieve their desired glucose projection.

Displacement-based formulation of Koiter's method: Application to multi-modal post-buckling finite element analysis of plates

Koiter's asymptotic method enables the calculation and deep understanding of the initial post-buckling behaviour of thin-walled structures. For the single-mode asymptotic analysis, Budiansky (1974) presented a clear and general formulation for Koiter's method, based on the expansion of the total potential energy function. The formulation from Budiansky is herein revisited and expanded for the multi-modal asymptotic analysis, of primordial importance in structures with clustered bifurcation modes. Given the admittedly difficult implementation of Koiter's method, especially for multi-modal analysis and during the evaluation of the third– and fourth–order tensors involved in Koiter's analysis; the presented study proposes a formulation and notation with close correspondence with the implemented algorithms. The implementation is based on state-of-the-art collaborative tools: Python, NumPy and Cython. The kinematic relations are specialized using von Kármán shell kinematics, and the displacement field variables are approximated using an enhanced Bogner-Fox-Schmit (BFS) finite element, modified to reach third-order interpolation also for the in-plane displacements, using only 4 nodes per element and 10 degrees-of-freedom per node, aiming an accurate representation of the second-order fields. The formulation and implementation are verified by comparing results for isotropic and composite plates against established literature. Finally, results for multi-modal displacement fields with up to 5 modes and corresponding post-buckling factors are reported for future reference.