Elliptical Model Research Articles

Identification of blade vibration parameters based on improved blade tip timing technology and two-factor analysis method

Abstract Long-term complex alternating loads will significantly impact the lifespan of blades. As a non-contact measurement method, Blade tip timing (BTT) is regarded as an efficient technique for blade vibration monitoring as it reflects the condition of blades. Most of the existing parameter identification methods need several sensor and strict probe layout requirements; thus, an inappropriate sensor layout may fail BTT measurements. Using fewer sensors can reduce the impact on the compressor casing strength and the cost of test system.
Considering arrangement, cost, and safety restrictions,in this work, a novel blade vibration parameters identification method via a single BTT sensor is proposed. A method of improved BTT techonlogy is presented which obtain two-channel vibration displacement sequence using a single sensor. The elliptic model between two-channel vibration displacement sequence is established. Based on the model, the relationship between blade vibration parameters and elliptic geometric parameters is derived. Numerical simulation and experimental results show that the method is highly feasible and robust. The advantage of this method is that it utilizes only one sensor and achieves high accuracy identification of blade vibration parameter, which provides a new idea to blade vibration monitoring.

Tracing the Propagation of Shocks in the Equatorial Ring of SN 1987A over Decades with the Hubble Space Telescope

The nearby SN 1987A offers a unique opportunity to investigate the complex shock interaction between the ejecta and circumstellar medium. We track the evolution of the optical hot spots within the equatorial ring (ER) by analyzing 33 Hubble Space Telescope imaging observations between 1994 and 2022. By fitting the ER with an elliptical model, we determine its inclination to be 42.°85 ± 0.°50 with its major axis oriented −6.°24 ± 0.°31 from the west. We identify 26 distinct hot spots across the ER, with additional ones emerging over time, particularly on the western side. The hot spots initially show high velocities ranging from 390 to 1660 km s−1, followed by a deceleration phase around day ∼ 8000. Subsequent velocities vary from 40 to 660 km s−1. The light curves of the hot spots reach maxima between 7000 and 9000 days, suggesting a connection with the deceleration. Many spots are spatially resolved and show elongation perpendicular to the direction of motion, indicative of a short cooling time. To explain these results, we propose that each hot spot comprises dense substructures embedded in less dense gas. The initial velocities are then phase velocities, where the break occurs when the blast wave leaves the ER, while the late velocities reflect the propagation of radiative shocks in the dense substructures. We estimate that the dense substructures have a volumetric filling factor of ∼0.3ne/106cm−3−2% and a total mass of ∼0.24ne/106cm−3−1×10−2M⊙ .

Effect of the shape of microswimmers and slip boundary conditions on the dynamic characteristics of near-wall microswimmers

Although the interaction between microswimmers and walls during near-wall swimming has been extensively studied, the effect of microswimmer shapes and slip boundary conditions on the dynamic characteristics of near-wall microswimmers has received less attention. In this study, elliptical microswimmer models have been developed with various aspect ratios based on circular microswimmers. The lattice Boltzmann method has been used for the numerical simulation of the dynamic behaviour of microswimmers near walls. Under slip boundary conditions, the escape or capture of microswimmers by the walls is influenced by the swimming Reynolds number (Res), wall slip length (ls) and the aspect ratio (Cab) of a microswimmer. Changes in the Cab value of a microswimmer considerably affect its swimming state, especially for puller-type microswimmers. The tendency of pullers to be captured by the wall increases with increasing Cab. Moreover, changes in ls within the slip boundary condition of a puller can induce a transition in its movement state from a wall oscillation state to a stable sliding state and eventually to a wall lock-up state, a process influenced by the Cab value of the puller. Pusher-type microswimmers show a considerably increased tendency to escape from walls with increasing Cab and no wall lock-up state is observed, which is opposite to the case of pullers. Pushers and pullers show an increased tendency to be captured by the wall with increasing initial swimming angle of the microswimmer. The findings of this study enhance our understanding of the swimming patterns of natural microswimmers near walls and are of substantial importance for the design of artificial microswimmers and microfluidic devices.

Modeling method of random collision of ellipsoidal particles in mechanical simulation for high energy solid propellant

Abstract It is based on the molecular dynamics algorithm of elliptical optimization to establish a mesostructure model of oval particles of high-energy solid propellant considering gradation and controllable filling rate according to the mesostructure characteristics of high-energy solid propellant. The bilinear cohesion model was applied to describe the interface damage behavior and carry out the high-energy propellant tensile test at three rates. The rationality of the elliptical particle model has been verified between the comparison of the calculated results with the experimental results established to describe the micromechanical behavior of high-energy propellants, which is to reveal the mesoscopic damage law of high-energy solid propellant under different tensile rates in this paper.

Inner–outer interaction of unsteady turbulent flow inside duct with wall corrugations: Augmentation and saturation

This study investigates the inner–outer interaction of the unsteady turbulent flow inside a duct with wall corrugations, where “inner” refers to the trapped flow in a corrugation-induced cavity array and “outer” relates to the mainstream flow transporting through a circular duct. Configurations with different pitch–diameter ratios (P/D) are used to demonstrate the effect of the cavity flow pattern on the mainstream flow variations. An improved delayed detached-eddy simulation with dynamic blending function is performed to acquire high-fidelity turbulent flow data, in which dynamic evolution of multi-scale vortex structures containing hairpin vortices and vortex fragments is clearly resolved. The subsequent statistical analysis reveals a nonlinear variation tendency of the inner–outer interaction intensity, experiencing sudden augmentation first and then a gradual attenuation toward the final saturation. Comparatively, a larger pitch ratio results in a stronger interaction under the effect of bicentric recirculation zones within the cavity array. Moreover, a proper orthogonal decomposition analysis allows for the visualization of energetic flow structures, as consistent velocity variations throughout the duct volume are identified for a larger pitch ratio, while discontinuity at the duct termination is found for a smaller pitch ratio. Finally, an advanced elliptical model based on the spatiotemporal cross correlation analysis is proposed to examine the convection velocity and sweeping velocity of the interactive mainstream flow and cavity flow. The results highlighted the presence of first-augmented and then saturated dynamics and kinematics inside the duct with the cavity array.

A Three-Block Inexact Heterogeneous Alternating Direction Method of Multipliers for Elliptic PDE-Constrained Optimization Problems with a Control Gradient Penalty Term

Optimization problems with PDE constraints are widely used in engineering and technical fields. In some practical applications, it is necessary to smooth the control variables and suppress their large fluctuations, especially at the boundary. Therefore, we propose an elliptic PDE-constrained optimization model with a control gradient penalty term. However, introducing this penalty term increases the complexity and difficulty of the problems. To solve the problems numerically, we adopt the strategy of “First discretize, then optimize”. First, the finite element method is employed to discretize the optimization problems. Then, a heterogeneous strategy is introduced to formulate the augmented Lagrangian function for the subproblems. Subsequently, we propose a three-block inexact heterogeneous alternating direction method of multipliers (three-block ihADMM). Theoretically, we provide a global convergence analysis of the three-block ihADMM algorithm and discuss the iteration complexity results. Numerical results are provided to demonstrate the efficiency of the proposed algorithm.

Geometry-based stochastic channel modeling of a semi-urban environment using simultaneously transmitting and reflecting reconfigurable intelligentsurface

Simultaneously Transmitting and Reflecting (STAR) Reconfigurable Intelligent Surface (RIS) demonstrates the ability to split incoming electromagnetic beams to transmit and reflect signals in a concurrent manner. Thus, compared to conventional RIS, service area coverage is extended on deploying STAR-RIS. This paper presents a geometry-based stochastic channel model (GBSM) of STAR-RIS-assisted outdoor wireless channel. For the considered semi-urban environment, STAR-RIS operates in energy-splitting mode. Channel between a base station (BS) and users (UR/UT) located on the reflect/transmit (R/T) side of STAR-RIS is characterised using a GBSM. An elliptical model incorporates the inevitable presence of scatterers in the considered semi-urban segment. Statistical properties of the wireless channel under test are analysed using space–time cross-correlation function (ST-CCF) and temporal auto-correlation function (ACF). Further, to gain holistic insight about the wireless channel behaviour, normalised Doppler power spectral density (ND-PSD) is estimated for semi-urban segment having three distinct underlying hypothesis as: (i) Wireless channel is governed by Rayleigh fading model, (ii) Wireless Channel is equipped with conventional RIS and (iii) STAR-RIS is an integral part of the considered wireless channel. Simulation results confirm that STAR-RIS performs at par with RIS, however, facilitating an additional degree of coverage. It is observed that temporal ACF and ST-CCF improves with an increase in the number of elements in STAR-RIS.

Single-fibre tensile testing of plant fibres: Set-up compliance as a key parameter for reliable assessment of their mechanical behaviour

The use of plant fibres as reinforcements in engineering applications requires reliable determination of their mechanical properties. This work focuses on single-fibre longitudinal tensile testing and the significance of the tensile system compliance for obtaining reliable results. Four types of fibre are tested, namely basalt, aramid, elementary flax fibres and flax fibre bundles. An automated laser scanning method is used to determine their cross-sectional area (CSA) based on circular and elliptical morphological models. The compliance of the tensile system is evaluated by standard and photomechanical analyses, and its influence on the assessment of mechanical properties of the fibres is discussed. Our results show that the evaluation of the compliance is highly dependent on fibre type, but also on the choice of CSA morphological model. The resulting correction on maximum tensile moduli ranges from 6.5 % to 37.6 % for small-diameter fibres, and can reach 55.1 % for large-diameter fibres as flax fibre bundles. Moreover, we evidence that the tensile system compliance is not necessarily constant and evolves with the force range covered during the tensile test. This can have a significant impact on the shape of the stress-strain curves, and hence on the analysis of the overall mechanical behaviour of the fibres.

Interfacial characterization of spinning water film along a concave wall

Abstract Thin liquid film flowing down the inner concave surface of a vertical cylindrical vessel is examined. At the top of the vessel, the water is injected horizontally at high speed circumferentially along the vessel wall and flows downwards due to the action of gravity. This turbulent film flow is modeled using the large eddy simulation (LES) and Reynolds averaged Navier–Stokes (RANS) approaches combined with the volume-of-fluid method. The results of both methods are validated with direct numerical simulation. The Favre-filtered two-phase LES, which is implemented and studied in this paper, can reasonably predict the film thickness similarly to that of the RANS approach using the elliptic blending Reynolds stress model, although it requires fine resolution in the wall region. The effect of volume flow rate on the film structure and thickness is investigated. The film thickness is shown to be nearly constant when the wall is partially wetted and changes as the cubic root of the volume flow rate when the spinning film encloses the entire circumference of the vessel.

Comparison of modeling of the polar cap absorption effect with observations at the AARI ground-based network

An elliptical model of cutoff for solar cosmic rays (SCR) at high latitudes has been calculated for SCR events and geomagnetic storms that occurred in February, March, and September 2014, June 2015, and September 2017 in order to predict the polar cap absorption (PCA) effect. The prediction is compared with observations of the PCA effect at the AARI network of six ionosondes, located in the north of Russia in a wide range of longitudes from 30 to 170 and magnetic latitudes from 56 to 64. We examine the dependence of the cutoff latitude on the magnetic storm strength, as well as the effect of additional ionization of the dayside and nightside ionosphere by SCR protons and electrons. The model demonstrates a satisfactory statistical accuracy up to 0.83 for the PCA prediction. We discuss prospects for further improvement of the elliptical model, such as consideration of the impact of SCRs of higher energies and inclusion of the PC index of energy flux into the polar cap.

Сравнение моделирования эффекта поглощения в полярной шапке с наблюдениями на сети станций ААНИИ

An elliptical model of cutoff for solar cosmic rays (SCR) at high latitudes has been calculated for SCR events and geomagnetic storms that occurred in February, March, and September 2014, June 2015, and September 2017 in order to predict the polar cap absorption (PCA) effect. The prediction is compared with observations of the PCA effect at the AARI network of six ionosondes, located in the north of Russia in a wide range of longitudes from 30 to 170 and magnetic latitudes from 56 to 64. We examine the dependence of the cutoff latitude on the magnetic storm strength, as well as the effect of additional ionization of the dayside and nightside ionosphere by SCR protons and electrons. The model demonstrates a satisfactory statistical accuracy up to 0.83 for the PCA prediction. We discuss prospects for further improvement of the elliptical model, such as consideration of the impact of SCRs of higher energies and inclusion of the PC index of energy flux into the polar cap.

A perturbative treatment of the Yarkovsky-driven drifts in the 2:1 mean motion resonance

Aims. Our aim is to gain a qualitative understanding as well as to perform a quantitative analysis of the interplay between the Yarkovsky effect and the Jovian 2:1 mean motion resonance under the planar elliptic restricted three-body problem. Methods. We adopted the semi-analytical perturbation method valid for arbitrary eccentricity to obtain the resonance structures inside the Jovian 2:1 resonance. We averaged the Yarkovsky force so it could be applied to the integrable approximations for the 2:1 resonance and the ν5 secular resonance. The rates of Yarkovsky-driven drifts in the action space were derived from the quasi-integrable approximations perturbed by the averaged Yarkovsky force. Pseudo-proper elements of test particles inside the 2:1 resonance were computed using N-body simulations incorporated with the Yarkovsky effect to verify the semi-analytical results. Results. In the planar elliptic restricted model, we identified two main types of systematic drifts in the action space: (Type I) for orbits not trapped in the ν5 resonance, the footprints are parallel to the resonance curve of the stable center of the 2:1 resonance; (Type II) for orbits trapped in the ν5 resonance, the footprints are parallel to the resonance curve of the stable center of the ν5 resonance. Using the semi-analytical perturbation method, a vector field in the action space corresponding to the two types of systematic drifts was derived. The Type I drift with small eccentricities and small libration amplitudes of 2:1 resonance can be modeled by a harmonic oscillator with a slowly varying parameter, for which an analytical treatment using the adiabatic invariant theory was carried out.

Fluctuating wind load encountered by linearly moving vehicles: Investigation on fluctuating wind spectral characteristics

Wind load is one of the controlling loads for moving vehicles. Existing studies on the wind-induced response of vehicles mostly apply traditional wind spectra directly to the vehicles, overlooking their motion status. Fluctuating wind characteristics encountered by linearly moving vehicles were investigated in this paper. The traditional static frame of view was adjusted to a moving one, two principal flow directions were considered and the idea of positional equivalence introduced in Taylor frozen assumption was extended to the moving direction. A fluctuating wind power spectral density (PSD) was proposed. Then a novel test was designed to enable a measuring probe to travel across a wind field. The fluctuating wind characteristics encountered by moving points are quite different from those encountered by a static point. The integral scale decreases as the speed ratio of the measuring point to the wind increases, and an elliptic model was suggested. The proposed PSD aligns well with the test results, indicating that it can be used to accurately characterize the fluctuating wind load encountered by moving vehicles. Both the test results and the numerical analysis showed that as the speed ratio increases, the PSD and energy spectrum as a whole migrate to higher frequencies.

Majority of Ruptures in Large Continental Strike-Slip Earthquakes Are Unilateral: Permissive Evidence for Hybrid Brittle-to-Dynamic Ruptures

Abstract Finite-element models of neotectonics require transform faults to rupture seismically even where preseismic shear stresses are low, presumably by dynamic-weakening mechanisms. A long-standing objection is that, if a rupture initiated at an asperity with high static friction stresses, which then transitioned to low dynamic-weakening stresses, local stress drop would be near total and on the order of 80 MPa, which is 4×–40× greater than observed. But the 5 Mw ≥ 7.8 transform earthquakes since 2000 initially ruptured on the branch faults of small net slip (Stein and Bird, 2024). If the slip initiates on a branch fault with different slip physics and no dynamic weakening, this solves the stress-drop problem. We propose that most large shallow earthquakes are hybrid ruptures, which begin on branch faults of small slip with high shear stresses, and then continue propagating on a connected dynamically weakened fault of large slip, even where shear stresses are low. One prediction of this model is that most large shallow ruptures should be unilateral. We test this prediction against the 100 largest (m ≥ 6.49) shallow continental strike-slip earthquakes 1977–2022, using information from the Global Centroid Moment Tensor and International Seismological Centre catalogs. The differences in time and location between the epicenter and the epicentroid define a horizontal “migration” velocity vector for the evolving centroid of each rupture. Early aftershock locations are summarized by a five-parameter elliptical model. Using the geometric relations between these (and mapped traces of active faults) and guided by a symmetrical decision table, we classified 55 ruptures as apparently unilateral, 30 as bilateral, and 15 as ambiguous. Our finding that a majority (55%–70%) of these ruptures are unilateral permits the interpretation that a majority of ruptures are hybrids, both in terms of geometry (branch fault to transform) and in terms of the physics of their fault slip.

A general semi-parametric elliptical distribution model for semi-supervised learning

ABSTRACT This research proposes a novel semi-parametric elliptical distribution model for application in semi-supervised learning tasks. We use labelled and unlabelled data to develop a pseudo maximum likelihood method for estimation and classification. The proposed estimator outperforms the estimator based solely on labelled data and achieves the semi-parametric efficiency bound with a suitable size of unlabelled data. We efficiently maximise the objective function by utilising low-dimensional groupwise pseudo-likelihood functions in a block coordinate descent manner while ensuring numerical stability and convergence through appropriate bandwidth selectors and initial parameter estimates. Additionally, the study comprehensively investigates the impact of labelled and unlabelled data on the pseudo maximum likelihood estimator and classifier. Simulation studies and empirical data applications illustrate the superiority of our methodology.

A new approach for 3D structure characterization of rock mass using an improved elliptical discrete fracture network model

Fracture structures in rock masses profoundly affect the stability of deep rock engineering, whereas conventional methods utilizing local surface fracture data on rock mass and disk models are limited in characterizing complex three-dimensional (3D) fractures. This raises two critical inquiries: How to enhance the comprehensiveness of fracture parameter collected on-site? And how to improve the accuracy of 3D fracture reconstruction? Hence, we proposed an approach for characterizing 3D fractures of rock mass by optimizing on-site acquisition techniques and discrete fracture network model. By integrating unmanned aerial vehicle (UAV) and borehole TV imaging techniques, we extracted comprehensive fracture parameters (e.g., trace length, orientation, and spacing) from the surface to the interior of the engineered rock mass. Leveraging the capability of the non-similar elliptical discrete fracture network model to more accurately represent fracture shapes, we introduced a dual-parameter correction method that integrates rotation angle and volume density adjustments into Monte Carlo simulation, resulting in an improved comprehensive parameter elliptical discrete fracture network (CPE-DFN) model. This model exhibited a substantial improvement in accuracy compared to previous disk models, achieving enhancements ranging from 11.2% to 24.9%. Finally, we validated the applicability and precision of this new method for 3D fracture characterization using comprehensive fracture data collected from a deep tunnel in western Sichuan, China, with an error of less than 8%. This work holds potential applications in investigating preferential flow paths as well as evaluating rock mass integrity and fractured zones in rock masses.

Predictive modeling of buckling in composite tubes: Integrating artificial neural networks for damage detection

Tubular structural composites are widely used in applications where high stiffness and low weight are required. This work proposes the study and evaluation of the influence of damage on the structural responses of thin-walled structures made of composite materials, as well as the development of a buckling prediction model using artificial intelligence. The methodology is approached on a few main fronts, namely: i) numerical modeling of the direct problem of the structure in finite elements, ii) modeling and parameterization of delamination in the elliptical shell model; iii) obtaining a database through finite element updating and iv) formulation and construction of the regression and prediction model using artificial neural networks. The numerical results showed that, as expected, the presence of delamination has a significant impact on the occurrence of buckling. The study also showed that it is possible to predict buckling values, with extremely satisfactory results - an error of around 1%, provided that more complex regression methods are used, such as regression by artificial neural networks, since the relationship between damage and buckling values is not trivial.

An analytical method to estimate the accuracy representation index of circular and elliptical disc models for rectangular fractures with application to seepage analysis

Constructing a suitable discrete fracture network (DFN) to represent rock fractures proves vital for tackling engineering projects involving rock masses. Among the commonly used models for constructing DFN, the circular disc model (CDM) and elliptical disc model (EDM) stand out. The selection between these models has been facilitated by the introduction of the Accuracy Representation Index (ARI), which quantitatively assesses their suitability. The existing methods for calculating ARI based on Monte Carlo simulations are time-consuming. In order to quickly estimate the ARI for CDM and EDM concerning any length-width ratio (kr) of rectangular fracture, the paper derives analytical formulas based on the geometric relationships between circles and ellipses with rectangles. These formulas show that: (a) for the CDM, ARI is only related to kr, and its value decreases as kr increases; (b) for the EDM, ARI is dependent on the relationship between kr and the long-short axis length ratio (ke) of the ellipse, and it has been theoretically proven that ARI reaches its maximum value of 0.91 when kr is equal to ke. Moreover, we apply ARI to the study of rock mass seepage characteristics, and the results show that ARI could reflect the error rate of permeability of the CDM and EDM for rock masses with rectangular fractures.

Force model of ultrasonic empowered minimum quantity lubrication grinding CFRP

As a weight-reducing material in aerospace applications, carbon fiber reinforced polymer (CFRP) requires precision grinding to ensure the accuracy and assembly of mating positioning surfaces. However, achieving low-damage machining of CFRPs remains challenging. Flood cooling reduces the mechanical properties, while dry grinding deteriorates the surface integrity, making minimum quantity lubrication (MQL) a viable alternative. However, nanolubricants struggle to penetrate the grinding area due to gas barrier obstruction. Consequently, a new CFRP grinding approach using multiangle 2D ultrasonic vibration-empowered nanolubricant MQL was proposed. An analytical force model is crucial for optimizing machining strategies and adjusting parameters. The aim is to reveal grinding mechanics and develop a force model under different ultrasonic and lubrication-cooling conditions. First, a uniform random fiber distribution model and a grinding wheel model were established, and the mechanical properties of the interface were predicted. Then, the intermittent grinding behavior and dynamic stiffnesses of the multiangle 2D ultrasonic vibration-assisted grinding (UVAG) system were investigated based on the geometric kinematics of the grains' trajectory. Furthermore, based on the deformation deflection curve, bending fracture force models for 45°, 90°, and 135° fibers were established with different contact and boundary conditions. The material removal mechanisms of shear and tension-compression buckling in 0° CFRP grinding were revealed, and an elliptical contact normal force model was established. The interlayer shear in 45° CFRPs was analyzed. The longitudinal compressive matrix cracking and fiber shear fracture in the 90° CFRPs were elucidated. Fiber microbuckling and fiber bundle removal of 135° CFRPs were investigated. Finally, grinding force models with different fiber orientation angles (FOAs) were interconnected and experimentally assessed. Experimental assessments demonstrated that the grinding force model has acceptable estimation error and effectively captures the mechanics of CFRPs with different FOAs.

Satellite impact on astronomical observations based on the elliptical orbit model

Space-based and ground-based telescopes have extensively documented the impact of satellites on astronomical observations. With the proliferation of satellite mega-constellation programmes, their influence on astronomical observations has become undeniable. Quantifying the impact of satellites on telescopes is crucial. To this end, we enhanced the circular orbit model for satellites and introduced a methodology based on two-line element orbit data. This involves constructing a satellite probability distribution model to evaluate the impact of satellites on telescopes. Using our method, we assessed the satellite impact on global grounded observatories. Our results indicate that the regions most severely affected by satellite interference at present are those near the equator, with latitudes of around ±50 and ±80 degrees experiencing the most significant impact from low-Earth-orbit satellites. Furthermore, we validated the reliability of our method using imaging data obtained from the focal surface acquisition camera of the LAMOST telescope.