Single-frequency Model Research Articles

Overbounding Ifree errors based on bayesian Gaussian mixture model for ground-based augmentation system

A dual-frequency measurement is employed in conjunction with an innovative Ifree filtering technique for mitigating the primary sources of Ifree influence on ground-based augmentation systems (GBAS) to safeguard the reliability of GBAS. The protective level achieved through the conventional Gaussian overbounding approach that are considered as much conventional technique. This adherence to tradition results in decreased reliability and a higher likelihood of false alarms. In contrast, the utilization of the Ifree algorithm contributes to reducing errors associated with dual-frequency measurements. This paper proposes the overbounding process according to Bayesian Gaussian mixture model (GMM) for maintaining Ifree-based GBAS range error. The Bayesian GMM is utilized for single-frequency model errors to examine the ambiguity estimations. The Monte Carlo (MC) simulation is established for defining estimated GMM assurance level accuracy which is attained through the general estimation method. Then, the last Bayesian GMM which is utilized for overbounding Ifree error distribution is investigated. According to the property of convolution invariance, the vertical protection in position field is determined without presenting difficult numerical calculations.

Optimal transonic buffet aerodynamic noise PSD predictions with Random Forest: Modeling methods and feature selection

To address challenges such as long computational cycles and high experimental measurement costs in obtaining Power Spectral Density (PSD) of aerodynamic noise, this study aims to enable a rapid assessment of buffet frequency and aerodynamic noise levels. The paper conducts a comparative analysis of the impact of different modeling methods and input features on prediction accuracy, proposing the time domain model, the full frequency domain model, and the single frequency model. The research reveals that the frequency domain model has an advantage over the time domain model in predicting aerodynamic noise, emphasizing the importance of selecting appropriate modeling methods. Additionally, based on whether frequency information is used as input features, the study introduces the full frequency domain model and the single frequency model. Results indicate that the single frequency model can significantly reduce the maximum relative error and Root Mean Square Error of the full frequency domain model by approximately three orders of magnitude, lowering the reconstruction error of the Proper Orthogonal Decomposition method by 2–3 orders of magnitude. Furthermore, this model demonstrates generalization across Mach numbers, angles of attack, and spatial positions, ensuring that the maximum absolute error of discrete peak frequencies is controlled within 1 Hz, and the relative error of discrete narrowband peaks is maintained at around 1 %.

LZER0: A Cost-Effective Multi-Purpose GNSS Platform.

Recent advances in Global Navigation Satellite System (GNSS) technology have made low-cost sensors available to the mass market, opening up new opportunities for real-time ground deformation and structure monitoring. In this paper, we present a new product developed in this framework by the National Institute of Oceanography and Applied Geophysics-OGS in collaboration with a private company (SoluTOP SAS): a cost-effective, multi-purpose GNSS platform called LZER0, suitable not only for surveying measurements, but also for monitoring tasks. The LZER0 platform is a complete system that includes the GNSS equipment (M8T single-frequency model produced by u-blox) and the web portal where the results are displayed. The GNSS data are processed using the RTKLIB software package, and the processed results are made available to the end user. The relative positioning mode was adopted both with real-time and post-processing RTKLIB engines. We present three applications of LZER0-cadastral, monitoring, and automotive-which demonstrate that it is a flexible, multi-purpose platform that is easy to use in terms of both hardware and software, and can be easily deployed to perform various tasks in the research, educational, or professional sectors.

High-Frequency Damping Analysis and Compensation Method Above Half PWM Sampling Frequency for Train Grid-Connected Converter

There are serious harmonic overvoltage phenomena in the electric railway system caused by the high-frequency resonance or instability issues, which is rooted in the region not only below, but also above half the PWM sampling frequency. To effectively evaluate the high-frequency admittance of train and further suppress the harmful high-frequency instability issue, a multi-frequency averaging model combining sampling sideband components is developed. Compared with the single-frequency model, the multi-frequency model is more accurate in the region near sampling frequency. After simplification, it is found that the time delay of digital control system is the cause of high-frequency negative damping. However, the time delay may make the traditional virtual impedance method fail in the high-frequency domain. Therefore, a virtual-impedance-controller (VIC) with variable damping characteristic is proposed to reshape the train admittance. The proposed VIC has the same structure as PID control. The detailed design method is given to offset the influence of time delay. The multiple high-frequency negative damping regions of train can be eliminated simultaneously by using multiple parallel VICs. The proposed method is applicable when changing the switching frequency. Hardware-in-the-loop test and low-power physical experiments validate the effectiveness of the proposed VIC strategy.

Offshore Surface Evaporation Duct Joint Inversion Algorithm Using Measured Dual-Frequency Sea Clutter

In this paper, high-precision joint inversion of evaporative duct based on dual frequency radar sea clutter data is analyzed to study the abnormal duct environment phenomenon that occurs over offshore surfaces. As the information of duct environment retrieved by radars with different frequencies is inconsistent, a joint optimization model with dynamic penalty factor is proposed, which can improve the degree of conformity between the measured clutter power and the modeled clutter power. Then, a parallel crossover quantum particle swarm optimization algorithm is used to jointly invert the objective function, which adaptively processes the inputs involved in the crossover, and effectively improves the convergence of the inversion. Compared with the single-frequency model commonly used in engineering, the average relative error of the duct height of the dual frequency joint optimization model is reduced by 3.13%, and the average relative error of the duct intensity is reduced by 6.34%, verifying the effectiveness of this method.

Multifrequency Hebbian plasticity in coupled neural oscillators.

We study multifrequency Hebbian plasticity by analyzing phenomenological models of weakly connected neural networks. We start with an analysis of a model for single-frequency networks previously shown to learn and memorize phase differences between component oscillators. We then study a model for gradient frequency neural networks (GrFNNs) which extends the single-frequency model by introducing frequency detuning and nonlinear coupling terms for multifrequency interactions. Our analysis focuses on models of two coupled oscillators and examines the dynamics of steady-state behaviors in multiple parameter regimes available to the models. We find that the model for two distinct frequencies shares essential dynamical properties with the single-frequency model and that Hebbian learning results in stronger connections for simple frequency ratios than for complex ratios. We then compare the analysis of the two-frequency model with numerical simulations of the GrFNN model and show that Hebbian plasticity in the latter is locally dominated by a nonlinear resonance captured by the two-frequency model.

A Multifrequency Model of Electric Locomotive for High-Frequency Instability Assessment

The high-frequency instability (HFI) issue results in serious harmonic overvoltage phenomena in the electrification railway system. This issue is rooted in the range that is not only below, but also above half the switching frequency. The commonly used small-signal averaging model is a single-frequency model in which the corresponding frequency component with perturbation frequency is considered merely. The inherent sampling nature has been neglected by the moving average operator. Therefore, it cannot reveal the effect of sideband components and may not be valid for predicting the high-frequency input admittance of a locomotive. To investigate the HFI issue, the sideband components generated by analog/data (A/D) sampling process and pulse width modulation (PWM) are taken into consideration. Then the multifrequency model of a locomotive is developed for evaluating the influences of sideband components. Meanwhile, the proposed model is validated by means of the frequency scan method, including the identification of PWM transfer functions and crossed-frequency transfer functions. Several HFI cases are summarized for comparing the accuracy between the traditional single-frequency model and the proposed multifrequency model. It denotes that the multifrequency model is more accurate to assess the high-frequency input admittance of a locomotive, especially the regions around the sampling frequency. Hardware-in-loop (HIL) results validate the theoretical analysis.

Numerical Investigation on Static and Rotor-Dynamic Characteristics of Convergent-Tapered and Divergent-Tapered Hole-Pattern Gas Damper Seals.

To study the influence of taper seal clearance on the static and rotor-dynamic characteristics of hole-pattern damper seals, this paper develops three-dimensional transient computational fluid dynamic methods, which comprise single-frequency and multi-frequency elliptical orbit whirl model, by the transient solution combined with a mesh deformation technique. Through the investigations, it is illustrated that: (1) In the present paper, the leakage rates of convergent-tapered hole-pattern damper seals are less than divergent-tapered hole-pattern damper seals for the same average seal clearance, and the maximum relative variation reaches 16%; (2) Compared with a constant clearance hole-pattern damper seal, the maximum relative variation of the rotor-dynamic coefficients is 1,865% for nine taper degrees in this paper; (3) Convergent-tapered hole-pattern damper seals have smaller reaction forces and effective damping coefficient, larger cross-over frequency, and direct stiffness coefficient, while divergent-tapered damper seals have the opposite effects; (4) Divergent-tapered hole-pattern damper seals alleviate the rotor whirl because of a larger effective damping coefficient when the rotor system has large natural frequency and small eccentricity. Convergent-tapered damper seals provide both sealing and journal bearing capabilities at the same time, and are more advantageous to the stability of the rotor system when rotor eccentricity is the main cause of rotor instability.

Spectral Optical Properties of Polymer Composite Nanomaterials Based on Carbon Nanotubes in a High-Density Polyethylene Matrix

The spectral optical characteristics of polymer composite nanomaterials based on carbon nanotubes (CNTs) in a high-density polyethylene (HDPE) matrix have been measured. The obtained experimental data have been compared with calculated data. The single-frequency model of the Lorentz oscillator is proposed for use as the theoretical model. It has been shown that samples with a carbon nanotube concentration of 10 wt % in a high-density polyethylene matrix provide high optical absorption of 90 ± 1% in the whole measured range from 300 to 800 nm. CNT–HDPE-based polymer composite nanomaterials may find practical applications in different devices of optical radiation attenuation and photoacoustics.

The GIVE Ionospheric Delay Correction Approach to Improve Positional Accuracy of NavIC/IRNSS Single-Frequency Receiver

The Navigation with Indian Constellation (NavIC)/Indian Regional Navigation Satellite System (IRNSS) is an independent navigation system developed for the Indian subcontinent by the Indian Space Research Organisation (ISRO). The positional accuracy of this system is mainly affected by the ionosphere of the low-latitude equatorial Indian subcontinent, as large ionospheric gradients and intense irregularities are present in it. The objective of this study is to improve the positional accuracy of NavIC/IRNSS systems by applying ionospheric correction using the most suitable single-frequency model. The data to be analysed were collected from the NavIC/IRNSS receiver provided by the Space Applications Centre, ISRO. A comparative analysis between the dual-frequency model and single-frequency model (e.g. GIVE model, coefficient-based model) was performed on the data from the NavIC/IRNSS receiver. Different ionospheric models were applied to compute ionospheric delay (ionodelay) on a quiet day (3 < K P < 5). Our result shows that both the single-frequency Grid Ionosphere Vertical Error (GIVE) model and dual frequency model outperform remarkably compared to the traditional coefficient-based model. The GIVE model was also analysed on FAR categorized satellites for different stormy days of different months. It was observed that during stormy days also, the 3D position computed by applying the GIVE model was nearly the same as the dual-frequency model.

Preventing chatter vibrations in heavy-duty turning operations in large horizontal lathes

Productivity and surface finish are typical user manufacturer requirements that are restrained by chatter vibrations sooner or later in every machining operation. Thus, manufacturers are interested in knowing, before building the machine, the dynamic behaviour of each machine structure with respect to another. Stability lobe graphs are the most reliable approach to analyse the dynamic performance. During heavy rough turning operations a model containing (a) several modes, or (b) modes with non-conventional (Cartesian) orientations is necessary. This work proposes two methods which are combined with multimode analysis to predict chatter in big horizontal lathes. First, a traditional single frequency model (SFM) is used. Secondly, the modern collocation method based on the Chebyshev polynomials (CCM) is alternatively studied. The models can be used to identify the machine design features limiting lathe productivity, as well as the threshold values for choosing good cutting parameters. The results have been compared with experimental tests in a horizontal turning centre. Besides the model and approach, this work offers real worthy values for big lathes, difficult to be got from literature.

Multiphonon effects on the optical emission spectra of the nitrogen-vacancy center in diamond at different temperatures

We theoretically investigate the multiphonon effects on the optical emission spectra of the negatively charged nitrogen-vacancy (NV−) center in diamond and find that the fluorescence emission spectra described by the single frequency model agree quite well with the experimental data. From a comparison between our theory and the experimental results, we also find a reduction of the anti-Stokes shift of the emission spectra at high temperature. This is contradictory to the linear hole-phonon interaction model. We resolve this contradiction by adding the quadratic hole-phonon interaction to our model. Our theoretical analyses show that this may reduce the lattice relaxation energy. As a consequence, fewer phonons are emitted in the optical transition, therefore explaining the reduction of the anti-Stokes shift at high temperature.

Accuracy assessment of single and double difference models for the single epoch GPS compass

The single epoch GPS compass is an important field of study, since it is a valuable technique for the orientation estimation of vehicles and it can guarantee a total independence from carrier phase slips in practical applications. To achieve highly accurate angular estimates, the unknown integer ambiguities of the carrier phase observables need to be resolved. Past researches focus on the ambiguity resolution for single epoch; however, accuracy is another significant problem for many challenging applications. In this contribution, the accuracy is evaluated for the non-common clock scheme of the receivers and the common clock scheme of the receivers, respectively. We focus on three scenarios for either scheme: single difference model vs. double difference model, single frequency model vs. multiple frequency model and optimal linear combinations vs. traditional triple-frequency least squares. We deduce the short baseline precision for a number of different available models and analyze the difference in accuracy for those models. Compared with the single or double difference model of the non-common clock scheme, the single difference model of the common clock scheme can greatly reduce the vertical component error of baseline vector, which results in higher elevation accuracy. The least squares estimator can also reduce the error of fixed baseline vector with the aid of the multi-frequency observation, thereby improving the attitude accuracy. In essence, the “accuracy improvement” is attributed to the difference in accuracy for different models, not a real improvement for any specific model. If all noise levels of GPS triple frequency carrier phase are assumed the same in unit of cycles, it can be proved that the optimal linear combination approach is equivalent to the traditional triple-frequency least squares, no matter which scheme is utilized. Both simulations and actual experiments have been performed to verify the correctness of theoretical analysis.

Simulation of light-limited algae growth in homogeneous turbulence

A study is performed of the effect of turbulent mixing on algae growth rate under light-limiting conditions. In order to isolate the effect of light fluctuations and to eliminate possible effects of mass transfer and other side effects of mixing, a numerical model of algae growth is employed. The study examines three aspects of turbulent mixing using models of increasing complexity. First, mixing increases the depth of the “mixed layer”—the layer of approximately uniform algae concentration—spreading the algae produced near the surface over a thicker fluid region. We demonstrate that mixed layer depth has no effect on the net algae production rate. Second, mixing causes motion of algae cells across the optical gradient. A single-frequency harmonic model is used to demonstrate the influence of periodic motion on algae production rate for different frequencies and concentration values. The model results explain previous apparently contradictory experimental observations. Significant enhancement of algae production rate with mixing is observed for small values of the ratio of illuminated layer depth to total fluid depth; however, growth rate enhancement saturates beyond a certain mixing frequency. Third, turbulent mixing involves a broad range of fluid time and length scales. A direct numerical simulation of homogeneous turbulence coupled to the algae growth model is used to show that the main conclusions of the single-frequency model can be carried over to a more realistic turbulent flow by appropriate choice of the mixing time scale.

Modelling of multifrequency IRMPD for laser isotope separation

The process of infrared multiple photon dissociation (IRMPD) of molecules is of great fundamental importance and has practical significance, such as isotope separation etc. Unfortunately, a clear insight into the process has been hindered by the bewildering array of important variables affecting MPD. The dissociation probability γ (φ) i.e. the yield has been found to be a sensitive function of laser fluence φ along with numerous other parameters like laser frequency, gas pressure etc. We have shown that in single frequency IRMPD, an accurate quantitative characterization of the dissociation probability can be adequately expressed by a ‘power law’ model with two fitting parameters namely critical fluence, φc and multiphoton order,m. This model was exploited in analysing our MPD results on various systems. However, the small isotope shift encountered in heavy elements and the sticking phenomenon observed in small light molecules restrict respectively the separation factor and the dissociation yield. These problems can effectively be tackled by irradiation with multifrequency laser beams which can be chosen appropriately on the basis of spectroscopic features. Based on our success in single frequency model, multifrequency IRMPD is modelled by a functional form containing the product of power law terms for individual fluences on irradiation frequencies. This model is successfully benchmarked with our experimental results on multifrequency LIS of tritium. Such knowledge can be utilized for appropriate separation process design, evaluation and optimization.

Temperature dependencies of excited states lifetimes and relaxation rates of 3–5 phonon (4–6 μm) transitions in the YAG, LuAG and YLF crystals doped with trivalent holmium, thulium, and erbium

Abstract The temperature dependencies of the nanosecond multiphonon relaxation (MR) rates of the 3 F 3 state of Tm3+ in the YLF crystal and of the 5 F 5 state of Ho3+ ion in the YAG and LuAG crystals and of the microsecond MR rates of the 4 F 9/2 ( 2 H 9/2 ) state of Er3+ ions in YLF were measured in the wide temperature range using direct laser excitation and selective fluorescence kinetics decay registration. For YLF the observed relations are explained by 4-phonon process in the frame of a single-frequency model with hω eff =450±30 cm −1 for the 3 F 3 state of Tm3+ and by 5-phonon process with hω eff =445 cm −1 for the 4 F 9/2 ( 2 H 9/2 ) state of Er3+. For YAG and LuAG crystals these dependencies are explained by the 3-phonon process with hω eff =630 cm −1 . The decrease of the relaxation rate with the temperature in the range from 13 to 80 K was observed for the 4 F 9/2 ( 2 H 9/2 ) state of Er3+ in the YLF crystal. It is explained by the redistribution of excited electronic states population of erbium ions over the higher lying Stark levels with different MR probabilities. A good fit of experimental temperature dependence (including the dropping part of the experimental curve) was obtained for single-frequency model ( hω eff =450 cm −1 ) with W 01 =8.0×10 4 s −1 and W 02 =4.7×10 4 s −1 accounting Boltzmann distribution of population over two excited Stark levels of the excited state of erbium ions. Employment of this model improves the fit between the experiment and the theory for the 5 F 5 state of Ho3+ ion in YAG as well. Strong influence of the parameters of the non-linear theory of MR, i.e. the reduced matrix elements U(k) of electronic transitions and the phonon factor of crystal matrix η on the spontaneous MR rates was observed experimentally. The smaller these parameters the slower the spontaneous MR W0. This fact can be used for searching new active crystal laser media for the mid-IR generation.

Theoretical investigations of the temperature dependence of zero-field splitting for in crystals

In this paper, we carry out a detailed theoretical investigation of the temperature dependence of zero-field splitting (characterized by of crystals by taking into account both the static contributions due to the thermal expansion of crystal and the vibrational contributions due to the electron - phonon interaction. The static contributions are calculated from the spin - orbit coupling mechanism, the relativistic mechanism, the covalency and overlap mechanism and the spin - spin interaction mechanism. Similar to the studies on the specific heat of crystals, the vibrational contribution of phonons of acoustic branches is given using the long-wavelength approximation and that of phonons of optical branches is calculated using a single-frequency model. The calculated results show that the contribution coming from the coupling with optical phonons is comparable with that due to the thermal expansion and that, to reach good fits between the theoretical and experimental , all the contributions from the thermal expansion and the electron - phonon (including the optical and acoustic phonons) interaction should be taken into account.

A study of the temperature dependence of g factor for MgO:V 2+ crystal

The temperature dependence of EPR g factor for MgO:V 2+ crystal has been studied theoretically by considering both the static contribution due to the thermal expansion of crystal and the vibrational contributions due to the electron-phonon interaction of the acoustic and optical branches. The static contribution is calculated from the high-order perturbation formula of g factor and the thermal expansion coefficients α( T) at various temperatures. The vibrational contribution of acoustic phonons is obtained by using a Debye model for the lattice vibrations and that ohe optical phonons is calculated by use of a single frequency model. The calculated results show that for the g factor at various temperatures, the static contribution is dominant, but for the temperature dependence of g factor, i.e., ( dg dT ) p or Δg( T)= g( T)− g(0), the vibrational contributions from the acoustic and optical phonons are comparable with the static contribution due to thermal expansion. It appears that a reasonable theoretical explanation for the temperature dependence of g factor should take all of these contributions into account.

Theoretical studies of the temperature dependence of zero-field splitting of Cr3+ centers in ruby.

Detailed theoretical studies of the temperature dependence of the zero-field splitting [characterized by \ensuremath{\Delta}D(T)=D(T)-D(0) or dD/dT] of ruby have been made by taking into account both the static contribution due to the thermal expansion of the lattice and the vibrational contribution due to the electron-phonon interaction. The static part is calculated by using the local thermal expansion coefficients ${\mathrm{\ensuremath{\alpha}}}_{\mathit{i}}$ in the vicinity of the ${\mathrm{Cr}}^{3+}$ ions, which are obtained from the local compressibilities ${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$ and the well-known relation ${\mathrm{\ensuremath{\alpha}}}_{\mathit{i}}$=${\mathit{C}}_{\mathit{v}}$\ensuremath{\gamma}${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$/V. The vibrational part includes the contributions from the acoustic and optical phonons. As in specific-heat studies of crystals, the vibrational contribution of phonons of the acoustic branches is calculated using the long-wavelength approximation, and that of phonons of the optical branches is calculated using a single-frequency model. The calculated results show that, to explain satisfactorily the temperature dependence of the zero-field splitting (ZFS), all of the contributions from the thermal expansion and the electron-phonon interaction should be considered. The static contribution is due mainly to the variations of bond angles as the temperature changes, which results in the static part of the temperature dependence of ZFS being opposite in sign to the observed temperature dependence. Thus the contribution due to the thermal expansion cannot be regarded as the main one. Among the various contributions, the contribution of acoustic phonons is the greatest in magnitude, and it has the same sign as the observed value. The contribution of optical phonons is the smallest and yet cannot be ignored. \textcopyright{}1996 The American Physical Society.

Investigations of the temperature dependence of the electron paramagnetic resonance g-factor for the MgO: crystal

Detailed theoretical studies of the temperature dependence of EPR g-factor for the MgO: crystal have been made by considering both the static contribution due to the thermal expansion of crystal and the vibrational contributions due to the electron - phonon (including the acoustic and optical phonons) interaction. The static contribution is calculated from the macroscopic thermodynamic method and the microscopic crystal-field method. The results from both methods are close to each other, suggesting that the two methods are applicable to studies of temperature dependence of the g-factor. The vibrational contribution due to acoustic phonons is obtained by using a Debye model for the lattice vibrations, and that due to optical phonons is calculated by use of a single-frequency model. The calculated results show that, for the g(T)-factors at various temperatures, the static contribution is dominant; however, for the temperature dependence of the g-factor, i.e. , the vibrational contributions are large and should be taken into account.