Amplitude Coefficients Research Articles

The Temporal and Spatial Evolution of Flow Heterogeneity During Water Flooding for an Artificial Core Plate Model

In the process of reservoir water flooding development, the characteristics of underground seepage field have changed, resulting in increasingly complex oil–water distribution. The original understanding of reservoir physical property parameters based on the initial stage of development is insufficient to guide reservoir development efforts in the extra-high water cut stage. To deeply investigate the spatio-temporal evolution of heterogeneity in the internal seepage field of layered reservoirs during water flooding development, water–oil displacement experimental simulations were conducted based on layered, normally graded models. By combining CT scanning technology and two-phase seepage theory, the variation patterns of heterogeneity in the seepage field of medium-to-high permeability, normally graded reservoirs were analyzed. The results indicate that the effectiveness of water flooding development is doubly constrained by differences in oil–water seepage capacities and the heterogeneity of the seepage field. During the development process, both the reservoir’s flow capacity and the heterogeneity of the seepage field are in a state of continuous change. Influenced by the extra resistance brought about by multiphase flow, the reservoir’s flow capacity drops to 41.6% of the absolute permeability in the extra-high water cut stage. Based on differences in the variation amplitudes of oil–water-phase permeabilities, changes in the heterogeneity of the internal seepage field of the reservoir can be broadly divided into periods of drastic change and relative stability. During the drastic change stage, the fluctuation amplitude of the water-phase permeability variation coefficient is 114.5 times that of the relative stable phase, while the fluctuation amplitude of the oil-phase permeability variation coefficient is 5.2 times that of the stable stage. This study reveals the dynamic changes in reservoir seepage characteristics during the water injection process, providing guidance for water injection development in layered reservoirs.

Towards Optimizing the Downlink Transmit Power in UAV-Integrated IRS Wireless Systems

Air-to-ground interference poses a critical challenge in integrating unmanned aerial vehicles (UAVs) into cellular networks. In downlink scenarios, UAVs can withstand significant interference from co-channel base stations (BSs) due to the guaranteed line-of-sight (LoS) connection with ground users. Our research focuses on power optimization in BSs and applying green energy principles to pave the way for more sustainable and energy-efficient BSs within UAV-integrated wireless systems. To this end, this paper investigates a downlink UAV communication scenario in which the intelligent reflecting surface (IRS) is mounted on the UAV to practically nullify the interference originating from the co-channel BSs. We formulate the IRS beamforming matrix to reduce transmit power by optimizing passive beamforming for IRS elements, incorporating adjustments to phase shifts and amplitude coefficients while considering the positioning of the UAV. The proposed optimization problem is non-convex, and thus a successive convex approximation (SCA) method is adopted to convert all constraints to a quadratic approximation. Simulation results demonstrate that the proposed SCA algorithm provides an efficient transmit power minimization approach with low computational complexity for large IRS since it achieves close-to-optimal performance, and significantly outperforms conventional systems without IRS. In interference scenarios and with different numbers of IRS meta-atoms, the proposed algorithm achieves a power reduction of approximately 8 and 13 dBm, while maintaining the same required signal-to-interference-plus-noise ratio.

Coon unitarity via partial waves

In this paper, we study tree-level four-point scattering amplitudes and present a novel approach to partial-wave unitarity that bypasses a lot of technical difficulties of previous approaches. In passing, we explicitly demonstrate that our approach provides a very suggestive form for the partial-wave coefficients in a natural way which is our main result. We use the Coon amplitude to exemplify this method and show how it makes important properties such as partial-wave unitarity manifest. A secondary by-product of our analysis is simple form for the partial-wave coefficients of the Coon amplitude as a single sum. Published by the American Physical Society 2024

Differentiation of Tumors of the Upper Respiratory Tract Using Optical Metabolic Imaging.

With over 184,000 new cases and more than 99,000 deaths per year, malignancies of the larynx are a global health problem. Currently, a dedicated screening method enabling a direct onsite diagnosis is missing. This can lead to delayed diagnosis and worse outcomes of the patients. An endoscopic optical method enabling a direct distinction between healthy tissue, dysplastic tissue and cancerous tissue would be an ideal tool for the detection of tumors of the upper aerodigestive tract (UADT). Healthy and tumor cells differ significantly in their metabolic state due to the different metabolic pathways they use (more oxidative phosphorylation in healthy cells, more glycolysis in tumor cells). Optical metabolic imaging (OMI) measuring relative intracellular concentration of NAD(P)H and FAD redox pairs could be a promising approach for early tumor detection and differentiation of suspicious mucosal lesions. In this study, a specially designed endoscopic two-beam two-photon fluorescence lifetime imaging (FLIM) system was used to perform two-photon two-beam FLIM of NAD(P)H and FAD to image the metabolic state in different tissue samples of the UADT. FLIM data sets of 27 tissue samples from 16 patients were recorded directly after surgery ex vivo in a special tissue culture medium at 37°C on a dedicated microscope using multiphoton excitation. Based on the FLIM measurements of NAD(P)H and FAD, six of the most common indices for the characterization of the cells' metabolism were calculated. Three of them, the ratio of the exponential coefficients (amplitudes) of the short and long lifetime components both for NAD(P)H and FAD (NAD(P)H a1/a2 ratio and FAD a1/a2 ratio) and the fluorescence lifetime redox ratio (FLIRR) enabled differentiation between healthy tissue, benign lesions, dysplastic tissue, and cancer tissue with statistical significance. We showed by measurements on freshly collected tissue samples that mucosal lesions of the UADT can be differentiated using our newly designed endoscopic FLIM device. In vivo measurements in healthy volunteers were also possible. By means of this technology, differentiation of cancerous, pre-cancerous, and healthy tissue in the UADT by OMI could be possible. Of six indices used to characterize cell metabolism we calculated, the FLIRR showed the most significant differences between tissue types.

Lift augmentation of a circulation control airfoil in proximity to water waves

Abstract Wave is an important factor affecting the takeoff and landing of seaplanes. In order to study the effect of waves on the moving airfoil in proximity to the water surface, the influence of different wave parameters on the aerodynamic characteristics of the airfoil is investigated through numerical simulation by solving the Reynolds-averaged Navier-Stokes equations. Moreover, the lift-augmentation effect of constant blowing on the circulation control airfoil in proximity to water waves is investigated. The results show that the higher the wave height and the longer the wavelength, the larger the fluctuation amplitude of the lift coefficient of the airfoil. the lift-augmentation efficiency of the circulation control airfoil decreases significantly after the blowing momentum coefficient exceeds a certain value. When the airfoil is close to water waves, the increase of the blowing momentum coefficient not only augments the lift of the circulation control airfoil, but also aggravates the fluctuation of the lift force.

Numerical investigation of the fluid-structure interaction of a three-dimensional flexible pitching plate

This research numerically investigates the effect of flexibility on the hydrodynamic efficiency of a pitching flat plate. A sinusoidal pitching motion of frequency 0.6, 1.5, and 2 Hz is imposed on the flexible plate immersed in a hydrodynamic flow, at a laminar Reynolds number of 2000. The fluid-structure interaction (FSI) problem is solved with the computational fluid dynamics code FINE/Marine using a modal approach. A parametric study is carried out on the pitching frequency and the flexibility of the plate, to characterize the combined effects of FSI and pitching motion on the hydrodynamic loads. This work contributes to the understanding of hydrodynamic performances of structures operating with high-dynamic motions combined with a significant level of flexibility. First, the influence of the pitching frequency for a rigid plate is analyzed. It is shown that the amplitude of the hydrodynamic coefficients increases with the pitching frequency and their phase is shifted, due to the plate's angular acceleration. The production of lift is found to be a combination of the vortex dynamics and the acceleration effects due to pitch oscillation. The acceleration effects become prevalent over the vortex dynamics at higher pitching frequencies. In the flexible case, it is highlighted that the synchronization of the acceleration effects due to the vibration of the plate and the pitching motion has a crucial influence on the hydrodynamic forces. In the studied range of pitching frequencies, the lift is increased by a factor of 5.5 due to the pitching motion and up to a factor of 2 due to the flexibility. A ratio between the pitching frequency and the natural frequency of the plate is introduced to characterize the effect of flexibility.

Evaluation of heat flux intensity factor for a V-notched structure by the isogeometric boundary element method

The conventional boundary element method using piecewise polynomial interpolation cannot accurately simulate the singular heat flux field around the vertex of the V-notch. Herein, the singularity eigen-analysis combined with the isogeometric boundary element method is proposed to calculate the singular heat flux field. The V-notched structure is divided into two parts, in which one is the heat flux singularity sector near the vertex and the other is the remained structure without heat flux singularity. In the singularity sector, the asymptotic expansion of the heat flux is introduced to transform the heat conduction governing equation into ordinary differential eigen equation, from which the singularity orders and eigen angular functions can be determined, except for the amplitude coefficients in the asymptotic expansion. The boundary integral equations for the heat conduction analysis established on the remained structure are discretized by the non-uniform rational B-spline (NURBS) elements. The amplitude coefficients, which are corresponding to the heat flux intensity factors, can be yielded by coupling the isogeometric boundary integral equations with the singularity asymptotic expansion analysis. A coordinate system transformation method is then proposed to transform the heat conduction governing equations of orthotropic and anisotropic material into the one of the isotropic material, and the heat flux intensity factors are approved to be invariable before and after coordinate transformation. Since the NURBS elements are used, fewer elements are required to evaluate the heat flux intensity factors compared with the conventional boundary element method.

Impact of salinity and body size on sperm motility in three California smelt species

Three smelt species in California, USA—the endangered delta smelt Hypomesus transpacificus and longfin smelt Spirinchus thaleichthys and the introduced wakasagi H. nipponensis—experience ecological pressures, including habitat alterations, temperature changes, and fluctuating salinity levels that can affect their survival and reproductive success. The present study investigates how salinity during the spawning process influences sperm motility by analyzing 13 sperm motility traits across three salinity levels (0.4, 5, and 10 ppt). Using Principal Component Analysis, we found that the first two principal components accounted for over 65 % of the total variance. Consequently, two predominant traits from each principal component were selected to evaluate sperm motility. Specifically, the amplitude of lateral head displacement (ALH), linearity coefficient (LIN), curvilinear velocity (VCL), progressive motility (PM), and wobble coefficient (WOB) predominantly contributed to these components for both longfin smelt and wakasagi. Results showed that the salinity significantly impacts these traits, except for ALH in delta smelt and longfin smelt, and WOB and LIN in wakasagi. In addition, we found the salinity and temperature difference between the activating water and extender interact differently across species. In delta smelt, interactions between the activating water and extender temperatures significantly affected most traits, whereas in wakasagi, only the interaction between activating water salinity and extender temperature showed significant effects. No significant influence from these interactions was observed in longfin smelt. Additionally, the impact of body size (e.g., fork length) on sperm motility varies across species, with a significant influence observed in longfin smelt, while no effect was detected in delta smelt and wakasagi. Future research should focus on exploring the physiological mechanisms behind the observed effects of salinity, temperature, and body size on sperm motility, as well as examining these interactions in other species to develop broader conservation strategies under changing environmental conditions.

Identification of muscle-activation-dependent human-exoskeleton coupling parameters

This paper proposed a muscle-activation-dependent human-exoskeleton model for predicting human-exoskeleton coupling parameters to improve the studies of coupling dynamics. With a newly designed platform and the help of 20 volunteers (10 males and 10 females, age: 24.45 ± 2.31 years old, height: 167.70 ± 8.35 cm, weight: 66.50 ± 18.74 kg), coupling parameters were identified with surface electromyographic (EMG) signals monitored to represent muscle activation. Then convolutional neural network (CNN) was used to predict coupling parameters with six EMG features as inputs:mean absolute value (MAV), mean absolute value slope (MAVSLP), waveform length (WL), Willison Amplitude (WAMP), variance (VAR), and auto regressive (AR) coefficients. Finally, sensitivity analysis of the CNN’s performance identified AR, MAV, and VAR as the key determinants of the coupling parameters. Further analysis unveiled strong correlation between coupling stiffness and both MAV and VAR. The novelty and contribution are the design of coupling experimental platform and the establishment of muscle-activation-dependent human-exoskeleton coupling model which provides a possibility to obtain coupling parameter identification form complex human-exoskeleton interaction scenarios.

Numerical investigation on transonic flutter characteristics of an airfoil with split drag rudder

In this paper, a series of flutter simulations are carried out to investigate the effects of split drag rudder (SDR) on the transonic flutter characteristic of rigid NACA 64A010. A structural dynamic model addressing two-degree-of-freedom pitch-plunge aeroelastic oscillations was coupled with the unsteady Reynolds-averaged Navier-Stokes equations to perform flutter simulation. Meanwhile, the influence mechanism of SDR on flutter boundary is explained through aerodynamic work and the correlated shock wave location. The results show that the SDR delays the shock wave shifting downstream, and the Mach number corresponding to reaching freeze region increases as the split angle increases. Therefore, the peak value of aerodynamic moment coefficient amplitude and the sharp ascent process of phase occurs at higher Mach number, which leads to the delay in the occurrence of the transonic dip. Besides, before the transonic dip of airfoil without SDR occurs, the aerodynamic moment phase of airfoil with the SDR decreases slowly due to the decrease in the speed of shock wave moving downstream. This results in an increased flutter speed when employing the SDR before the transonic dip of airfoil without SDR occurs. Meanwhile, the effects of asymmetric split angles on the transonic flutter characteristics are also investigated. Before the transonic dip of airfoil without SDR occurs, the flutter characteristic is dominated by the smaller split angle.

Quantitative Evaluation of Deformation in High-Speed Magnetic Flux Leakage Signals for Weld Defects in Oil and Gas Pipelines

Complex multiphase flow in oil and gas pipelines raises safety risks. Magnetic flux leakage (MFL) detection effectively identifies pipeline defects. However, the high-speed movement of MFL inspection tools induces motion-induced eddy currents (MIECs), complicating defect recognition and quantification. Most prior research has primarily focused on rectangular defects, leaving a gap in understanding the impact of MIECs on weld defects. This paper proposes the amplitude and shape deformation coefficients to analyze the influence of velocity on various weld defects, including internal reinforcement, lack of penetration, crack, external corrosion, internal corrosion, porosity, and lack of fusion. Utilizing these coefficients, this study examines the influence of the defect size and magnetizer configuration on these velocity-induced effects. The results show that the shape deformation coefficients range from 2.75 to 3.57 for Bx and from −0.13 to −0.3 for By, indicating a significant change in the MFL signal shape at 10 m/s compared to 0 m/s. The amplitude deformation coefficients for lack of penetration, internal corrosion, and porosity range from −0.01 to 0.1 for Bx, and from 0.86 to 0.98 for By, suggesting a decrease in peak-to-peak values. In contrast, other defects exhibit an increase in peak-to-peak values, indicating that the velocity effect may enhance the MFL signal. Also, the defect size and magnetizer configuration can affect the velocity effect on signals. These findings provide essential guidance for quantifying defect sizes and a solid foundation for designing more effective magnetization devices.

Analytic amplitudes for a pair of Higgs bosons in association with three partons

The pair production of Higgs bosons at the LHC can give information about the triple Higgs boson coupling. We perform an analytic one-loop calculation of the amplitudes for a pair of Higgs bosons in association with three partons, retaining the exact dependence on the quark mass circulating in the loop. These amplitudes constitute the real radiation corrections in the calculation of Higgs boson pair production at next-to-leading order in the strong coupling. The results of an analytic generalised-unitarity computation are simplified via analytic reconstruction in spinor variables. Compact ansätze for kinematic pole residues are iteratively fitted via p-adic evaluations near said poles and subtracted until no pole remains. A new ansatz construction is introduced to minimally parametrise coefficients of amplitudes with multiple massive external legs. The simplified expressions are faster to evaluate than automatic codes and can lead to more stable results near singular regions.

Research on the electromagnetic ultrasonic detection method of initiation crack based on multi-acoustic coefficients fusion

Abstract The traditional single acoustic coefficient cannot judge the different degrees of fatigue damage such as initiation crack and crack extension. Based on the law between the structural evolution of dislocation pile-up initiating crack and acoustic coefficients, a multi-acoustic coefficients fusion feature-fatigue damage stage detection method is proposed. By extracting the nonlinear features as well as linear features of the multi-point detection signals for a single fatigue-damaged aluminum plate, achieves the fatigue damage state. Experiments verified multi-acoustic coefficients with different features corresponding to different fatigue stages such as initiation crack and crack extension.The peak points of the acoustic nonlinear coefficients are used for the judgment of the initiation crack stage, and the peak-to-peak amplitude of the acoustic linear coefficients are used for the judgment of the crack extension stage. Comparing and analyzing the results of electromagnetic ultrasonic detection and microscopic observation of different fatigue damage stages, the proposed method provides early warning of the initiation crack and crack extension by studying the characteristics of acoustic coefficients of different fatigue damage stages. This study provides theoretical and experimental basis for the application of electromagnetic ultrasonic assessment of fatigue damage in metallic materials.

Analysis of diffraction gratings displayed in spatial light modulators at the Nyquist limit: Application to the triplicator grating

In this work we analyze diffraction gratings displayed on a pixelated spatial light modulator (SLM) at its spatial resolution limit (Nyquist limit) i.e., with largest diffraction angle, where the binary phase profile is the only alternative. Their implementation is influenced by the effect of a sinc envelope and the multiple replicas of the diffraction pattern that arise from the SLM pixelation, where the fill factor plays an essential role. We use the Fourier transform theory to analyze the binary phase grating in a pixelated device in terms of the pixel size, fill factor and phase difference between the two levels in the grating. This convolutional approach probes very useful to gain physical insight of the different contributions to the diffraction orders, and analytical expressions for the complex amplitude coefficients and intensities are obtained. Experimental verification is provided by encoding binary phase triplicator gratings with different periods on a high-resolution liquid-crystal on silicon SLM. The effect of the device pixelation and pixel crosstalk on the diffraction efficiency and on the conditions to obtain a Nyquist triplicator phase grating are studied. These results can be interesting for applications requiring programmable and large beam steering angles.

Cognitive correlates of circadian rhythm and sleep-wake behaviour in chronic obstructive pulmonary disease patients

ABSTRACT Chronic obstructive pulmonary disease (COPD) patients often experience reduced physical activity, sleep disturbances, and cognitive impairment. However, reports on measurement of rest-activity rhythm and sleep-wake behavior and their impact on cognitive functions in COPD patients are limited. This study aimed to objectively measure circadian rhythms (rest-activity and ambient illuminance) and sleep behaviors in clinically stable COPD patients and their relationship with cognitive functions. The study involved 65 male COPD patients and 50 age-matched controls, monitored over 3–7 days using actigraphy. Cognitive status was assessed using the Montreal Cognitive Assessment (MoCA) followed by short interbal time estimation via time production and reproduction with reaction time measurement using TimeProd software. Findings indicated significant disruptions in circadian rhythms in COPD patients, characterized by lower mesor, amplitude, and autocorrelation coefficients compared to controls. Patients also reported poorer sleep quality and higher sleep fragmentation, with 85.7% displaying cognitive impairment. Notably, longer time estimations, increased variability in task performance, and slower reaction times suggested cognitive deterioration. Positive correlations emerged between rhythm parameters (amplitude and circadian quotient) and cognitive performance metrics. This highlights the relevance of circadian and sleep disturbances in COPD, suggesting that addressing these rhythms could help mitigate cognitive decline, potentially through chronotherapeutic strategies.

A simultaneous ultrasonic measurement method for lubrication film thickness and coating wear depth with thermal effect

Lubrication film thickness and coating wear depth are two important parameters indicating tribological condition in tribological elements. In this paper, a new ultrasonic model was proposed to measure the lubricant film thickness and the coating wear depth simultaneously. A ratio coefficient, which was constructed by dividing the echo signal reflected from the oil film layer to that reflected from the pad-coating interface, was established, and the amplitude and phase of this ratio coefficient were used to measure the film thickness and wear depth, respectively. A pre-calibration test was conducted to help eliminate the effect of the temperature and a dynamic calibration test rig was built to construct series known oil film thickness and wear depth under various temperature. The calibration tests demonstrated that the proposed ultrasonic method could measure the lubricant film thickness and coating wear depth simultaneously under varying temperature. This paper can provide an effective means to observe the evolution characteristics between lubrication and wear.

Evaluation of the effectiveness of incomplete phase pulse width modulation algorithms in the converter-electric motor system

Aim. This study evaluates the effectiveness of incomplete-phase algorithms for pulse width modulation of three-phase voltages in frequency control of electric drives, using integral current dispersion in the load as the criterion. Materials and methods. This study examines pulse width modulation processes in frequency-controlled electric drives, focusing on the converter-electric motor system. Methods from electric circuit theory are used, with proposed algorithms illustrated through drawings, and these drawing can be implemented in the matrix laboratory software. Results. The process of pulse width modulation in the converter-electric motor system is considered. It is demonstrated that to minimize the number of switching keys in the frequency converter, incomplete-phase pulse width modulation algorithms are beneficial. Expressions for local dispersion of the interphase current in single-phase and two-phase modulation are analyzed. An expression for local current dispersion in a three-phase bridge circuit load is derived, and the concept of integral current dispersion in a three-phase load is derived. Indicators for evaluating the effectiveness of algorithms for incomplete-phase pulse width modulation are proposed. Graphs the efficiency coefficient, characterizing incomplete-phase pulse width modulation with a minimum number of switching of key elements in the function of the amplitude coefficient and in the function of the relative frequency of modulation are constructed. Conclusion. The results aid in developing algorithms for controlling frequency converters in asynchronous electric drive systems.

Investigation on the unsteady aerodynamic performance of the Drela AG 08 and Boeing B29 airfoils subjected to heaving motion

This article aims to investigate the unsteady flow characteristics of Drela AG08 and Boeing B29 airfoils when subjected to heaving motion. The influence of heave amplitude, heave frequency in terms of instantaneous force coefficients of the airfoil is investigated at Re = 5 × 104. Furthermore, the flow field investigations were carried out to analyze the Leading Edge Vortex (LEV) formation and its convection airfoil’s suction side. From the findings, a variation in the oscillation amplitude of force coefficients was observed and a non-sinusoidal behavior was also noticed. Additionally, a remarkable change in the instantaneous force coefficients (both qualitatively and quantitatively) is also observed with respect to the slight change in aforementioned parameters. A transition in the wake pattern from drag inducing to thrust producing is observed under certain conditions. It is observed that the flow separates at the leading edge by forming LEV on both airfoil’s suction side and pressure side. It is also noticed that whenever the flow departs the trailing edge, these vortices convect downstream of the airfoil and form alternating pattern of coherent vortices. With the increase in number of cycles, these vortices interfere with the previously shed vortices and affects the airfoil’s aerodynamic characteristics. From the investigations, it is observed that, by controlling the system parameters, the adverse effects of the LEV can be minimized.

Research on a new pressure pulsator

Pulsators are widely used to study the dynamic characteristics of liquid flow components. However, it is difficult to adapt the existing actuators to the excitation requirements under high pressures, low temperatures, and toxic media. This study describes the design of a novel pressure pulsation device and presents the results of simulations and experimental tests. The flow field is simulated under a series of working conditions, and the effects of the rotation speed, flow rate, inlet pressure, and gap between the rotor and stator on the peak-to-peak amplitude, spectral amplitude, and flow resistance coefficient of the actuator outlet are analyzed. A prediction model for the corresponding parameters is developed using multiple linear regression. In high-pressure (20 MPa) hydraulic pipeline tests, the excitation device can generate pulsating flow with peak-to-peak amplitudes of more than 7 MPa in the time domain and 2 MPa in the frequency domain. The upstream and downstream regions of the internal flow field are periodically joined and detached by the blade rotation, which results in periodic variations in flow velocity and pressure. The relative error between the model predictions and the three-dimensional simulation and experimental values is less than 7%, satisfying industrial requirements. This work facilitates a solution to the problem of dynamic excitation when analyzing the response characteristics of fluid equipment in high-pressure pipelines and provides a method for forecasting actuator output effects.

How attentive is a student in class? A concentration evaluation method based on head Euler angle

How attentive is a student in class? It is an interesting and challenging question in the field of education research. In this paper, a concentration evaluation method based on head Euler angle is proposed. First, a fine large-small-interval video sampling strategy is advocated and concepts of dynamic threshold and action amplitude coefficient are defined, which are fused together to get the head up rate. Second, head front-facing rate is computed through analyzing the yaw angle, which is obtained from a proposed spatial physical model of camera and student seat position. Third, for any given time period, class concentration of a student is derived by fusing and normalizing the head up rate and head front-facing rate based on Euclidean-distance. Finally, accuracy experiments are conducted, where the proposed method achieves an average accuracy of 89.8% compared with the average score from the questionnaire given by 22 reviewers. Also, robust experiments on several head pose estimation models are facilitated, which achieves an average accuracy of 98.43% on recorded video dataset, indicates insensitivity to the head pose estimation model used for data collection and verifies that the proposed method is independent on any specific head pose estimation model. The experimental results show that the proposed method is accurate, effective and robust for the concentration evaluation in class.