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We investigate the cosmological evolution of the universe for a spatially flat FLRW background space within the context of f(T,B) gravity, which is a recently formulated teleparallel theory that connects both f(T) and f(R) gravity under suitable limits. The analysis focuses on four different f(T,B) cosmological models corresponding to various choices of scale factor, namely, emergent, logamediate, and intermediate. In addition to this, we assume a power law-like function of f(T,B) gravity. The reconstruction of f(T,B) gravity considers the Holographic Ricci Dark Energy (HRDE) as the background fluid. We analyze the equation of state parameters and the squared speed of sound for the reconstructed models. Finally, we conduct a thermodynamical analysis for each reconstructed model. The generalized second law of thermodynamics (GSLT) is valid for the four different f(T,B) cosmological models.

The comment disputes some of the inferences in the paper “Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra”, published in this journal. The key points in the dissent are the following: (1) The number of unknown parameters in the reverse transformation problem using dual quaternions. (2) The reliability of both data and the results. (3) There should be no differences between Euler angles and quaternion methods. Our response is summarized as follows: (1) The problem can be solved using either eight or nine unknown parameters. (2) All the data and results are real. (3) There should be differences between methods because of different calculations.

The scale factor serves as a ruler for converting raw phase measurements into physical displacements and significantly impacts the preprocessing of data from the Laser Ranging Interferometer (LRI) in laser ranging systems. In the current GRACE Follow-On (GRACE-FO) mission for low–low tracking gravity satellites, most of the existing LRI scale factor estimation algorithms heavily rely on cross-calibration between instantaneous/biased ranges from the Ka-Band Ranging Interferometer (KBR) and the LRI. However, due to the nonlinearity of the objective function (which includes terms involving the product of scale and time shifts), the scale factor estimation may absorb errors from timing noise. Moreover, future gravity missions or gravity detection tasks may no longer incorporate KBR ranging instruments. To address these challenges, this paper proposes an energy-based method for scale factor estimation using inter-satellite baseline solutions. Comparative analysis indicates that the proposed method effectively disentangles two parameters in the objective function and can be applied in scenarios where KBR data are unavailable, demonstrating promising prospects for practical application. The experimental results show that when the KBR validation residuals are lower than 0.8 mm, the SYSU LRI1B V01 products exhibit residuals below the payload design accuracy thresholds in the frequency band of 2 mHz to 0.1 Hz. Additionally, the stability of the scale factors obtained from the baseline can reach 10−7. Although this is still below the required precision of better than 10−8 for the laser frequency stability in next-generation gravity satellites, advancements in orbit determination technology and the enhanced stability of GPS receivers offer potential for future precision improvements. Currently, this method appears suitable for roughly extracting the scale factor as a stochastic mean over several months or serving as a backup validation strategy for future missions, but it is not well suited to measure day-to-day variations.

A Friedmann–Lemaitre–Robertson–Walker space–time model with all curvatures k=0, ±1 is explored in f(R,T) gravity, where R is the Ricci scalar, and T is the trace of the energy–momentum tensor. The solutions are obtained via the parametrization of the scale factor that leads to a model transiting from a decelerated universe to an accelerating one. The physical features of the model are discussed and analyzed in detail. The study shows that f(R,T) gravity can be a good alternative to the hypothetical candidates of dark energy to describe the present accelerating expansion of the universe.

This study proposes a universal adaptive control algorithm for an unknown multi-input multi-output (MIMO) system using recursive least squares (RLS) and parameter self-tuning. The issue of adjusting the control and system parameters in response to changes in the platform was discussed. The development of a control algorithm that can consistently achieve reliable and robust control performance in various systems is important. This study aimed to develop a control algorithm that can track the reference value for any unknown MIMO system. For the controller design, an nth-order differential error dynamic model was designed, and an RLS with a scale factor was used to estimate the coefficients of the error dynamics. In the current scenario, the numbers of control inputs and error states in the error dynamics were assumed to be equal. It was designed such that the control input is derived based on the Lyapunov stability concept using the estimated coefficients. The scale factor in the RLS and injection term in the control input based on the sliding-mode approach were computed using a self-tuning methodology. The performance of the proposed universal adaptive control algorithm was evaluated using an actual DC motor and CarMaker (version 8.1.1) software tests under various scenarios.

Traditional methods of orthogonal basis function decomposition have been extensively used to detect magnetic anomaly signals. However, the determination of the relative velocity between the detection platform and the magnetic target remains elusive in practical detection. And, the non-ideal uniform motion of the magnetic target further complicates the process and adversely impacts the detector’s performance. To address this challenge, this paper introduces an adaptive scale factor method based on orthogonal basis function decomposition. This new method can be used to adjust the relative velocity between the detection platform and the magnetic target and to refine the characteristic time in the basis functions. In this paper, a mathematical relationship between the scale factor and the relative velocity is established, which is subsequently fitted into a Gauss function curve. The optimal scale factor, denoted as β, is adaptively chosen from the fitting curve when the magnetic target moves at a non-ideal uniform velocity with an unknown motion state. The results of simulations indicate that the scale factor improves the signal-to-noise ratio of the magnetic anomaly signals in a non-ideal state. And, this method can improve the energy value of OBF decomposition by 17.7%. Simultaneously, this method ensures that the moment the magnetic target passes the CPA coincides with the energy peak of the orthogonal basis detection, which improves the accuracy by 54.1% compared with the traditional method. The effectiveness and precision of the proposed method are verified using simulations and practical experiments.

An anastomosing river is a stable multiple-channel system separated by inter-channel wetlands, and there are serious difficulties in observing the hydrodynamics of such river patterns in situ. Therefore, there are few reports on the hydrodynamic data of such rivers, for example, the upper Columbia and Pearl Rivers. In order to obtain the hydrodynamic parameter values at flow cross-sections of anastomosing rivers, without having to observe hydraulic radius, this study proposes a method called the Expression of Channel Morphological Parameters (ECMP) for hydrodynamic estimation. The calculation formula of the ECMP method is based on the shape factor (width–depth ratio), scale factor (mean depth), and gradient factor of the channel cross-sections of anastomosing rivers below a given water level as independent variables. This method can be used to calculate the mean velocity, discharge, specific stream power, and gross stream power of the flow cross-section at different water levels, only requiring the measurements of channel morphological parameters such as the mean depth, width–depth ratio, and gradient at the channel cross-section below the corresponding water level. The applicability of the ECMP method was verified using measured hydrological data. The results showed that the ECMP method is a practical estimation method with higher accuracy that is convenient for calculating the hydrodynamic parameters of anastomosing rivers. It can also be used to reconstruct ancient anastomosing rivers using the channel morphological parameters revealed from the fill sediments in ancient channels.

The coupling efficiency of the fiber ring resonator has an important influence on the scale factor of the resonant fiber gyroscope. In order to improve the scale factor of the gyroscope, the coupling efficiency of the fiber ring resonator and its influential factors on the scale factor of the gyroscope are analyzed and tested. The results show that the coupling efficiency is affected by both the splitting ratio of the coupler and the loss in the cavity. When the coupling efficiency approaches 0.75 at the under-coupling state, the scaling factor of the gyroscope is the highest. This provides a theoretical reference and an experimental basis for the enhancement of the scaling factor of the resonant fiber gyroscope with the fiber ring resonator as the sensitive unit, providing options for multiple applications such as sea, land, sky and space.

The current study examines the realisation of cosmic bounce in two situations involving two distinct scale factor selections, one of which is a scale factor already developed for bouncing and the other of which is a scale factor created by truncating a series expansion of a de Sitter scale factor. Generalized Chaplygin gas (GCG) is assumed to be the background fluid in both situations. When the scale factor is set to the first kind, the pre-bounce scenario’s GCG energy density decreases due to contraction, reaches its lowest point at t=0 during the bounce, and then rises as a result of expansion following the bounce. However, it is noted that the truncation has an impact on the density evolution from pre-bounce in the other scale factor scenario. The influence of bulk viscosity is shown in all circumstances, in addition to the influence of non-viscosity, and the test for stability makes use of the squared speed of sound. At the turn-around places, the null energy criterion is also violated. The final stage of the study includes a cosmographic analysis and a demonstration of the Hubble flow dynamics. In conclusion, we find that inflationary cosmology can also be realized with GCG as the background fluid for two-scale factor options. When the equivalent cosmic parameter is examined for pre-bounce and post-bounce scenarios, a symmetry is frequently seen. The symmetry occurs near the point of bouncing or turning.

In full-field 3D displacement measurement, stereo digital image correlation (Stereo-DIC) has strong capabilities. However, as a result of difficulties with stereo camera calibration and surface merging, 360-deg panoramic displacement measurements remain a challenge. This paper proposes a panoramic displacement field measurement method in order to accurately measure the shape and panoramic displacement field of complex shaped objects with natural textures. The proposed method is based on the robust subset-based DIC algorithm and the well-known Zhang’s calibration method to reconstruct the 3D shape and estimate the full-field displacements of a complex surface from multi-view stereo camera pairs. The method is used in the determination of the scale factor of the 3D reconstructed surface and the stitching of multiple 3D reconstructed surfaces with the aid of the laser point cloud data of the object under test. Based on a discussion of the challenges faced by panoramic DIC, this paper details the proposed solution and describes the specific algorithms implemented. The paper tests the performance of the proposed method using an experimental system with a 360-deg six camera setup. The system was evaluated by measuring the rigid body motion of a cylindrical log sample with known 3D point cloud data. The results confirm that the proposed method is able to accurately measure the panoramic shape and full-field displacement of objects with complex morphologies.

The GRACE follow-on satellites carry the very first interspacecraft Laser Ranging Interferometer (LRI). After more than four years in orbit, the LRI outperforms the sensitivity of the conventional Microwave Instrument (MWI). However, in the current data processing scheme, the LRI product still needs the MWI data to determine the unknown absolute laser frequency, representing the “ruler” for converting the raw phase measurements into a physical displacement in meters. In this paper, we derive formulas for precisely performing that conversion from the phase measurement into a range, accounting for a varying carrier frequency. Furthermore, the dominant errors due to knowledge uncertainty of the carrier frequency as well as uncorrected time biases are derived. In the second part, we address the dependency of the LRI on the MWI in the currently employed cross-calibration scheme and present three different models for the LRI laser frequency, two of which are largely independent of the MWI. Furthermore, we analyze the contribution of thermal variations on the scale factor estimates and the LRI-MWI residuals. A linear model called Thermal Coupling (TC) is derived, which significantly reduces the differences between LRI and MWI to a level where the MWI observations limit the comparison.

When using off-axis digital image correlation (DIC) for non-contact, remote, and multipoint deflection monitoring of engineering structures, accurate calibration of the scale factor (SF), which converts image displacement to physical displacement for each measurement point, is critical to realize high-quality displacement measurement. In this work, based on the distortion-free pinhole imaging model, a generalized SF calibration model is proposed for an off-axis DIC-based video deflectometer. Then, the transversal relationship between the proposed SF calibration method and three commonly used SF calibration methods was discussed. The accuracy of these SF calibration methods was also compared using indoor rigid body translation experiments. It is proved that the proposed method can be degraded to one of the existing calibration methods in most cases, but will provide more accurate results under the following four conditions: (1) the camera’s pitch angle is more than 20°, (2) the focal length is more than 25 mm, (3) the pixel size of the camera sensor is more than 5 um, and (4) the image y-coordinate corresponding to the measurement point after deformation is far from the image center.

Object detection is a fundamental task in computer vision, which is usually based on convolutional neural networks (CNNs). While it is difficult to be deployed in embedded devices due to the huge storage and computing consumptions, binary neural networks (BNNs) can execute object detection with limited resources. However, the extreme quantification in BNN causes diversity of feature representation loss, which eventually influences the object detection performance. In this paper, we propose a method balancing Information Retention and Deviation Control to achieve effective object detection, named IR-DC Net. On the one hand, we introduce the KL-Divergence to compose multiple entropy for maximizing the available information. On the other hand, we design a lightweight convolutional module to generate scale factors dynamically for minimizing the deviation between binary and real convolution. The experiments on PASCAL VOC, COCO2014, KITTI, and VisDrone datasets show that our method improved the accuracy in comparison with previous binary neural networks.

The moving-base gravimeter is one of the key instruments used for Earth gravity survey. The accuracy of the survey data is closely related to the calibration precision of several key parameters, such as the damping delay time, the drift coefficient, the gravity scale factor, and the measurement accuracy. This paper will introduce the development of the CHZ-II gravimeter system in which a cylindrical sampling mass suspended vertically by a zero-length spring acts as a sensitive probe to measure specific force. Meanwhile, a GNSS (Global Navigation Satellite System) positioning system is employed to monitor the carrier motion and to remove the inertia acceleration. In order to achieve high-precision calibrations for the key parameters, a new calibration method performed along forward and reverse overlapping lines is proposed, which is used to calibrate the above parameters and to estimate the measurement accuracy of the instrument used for a normal gravity survey. The calibration principle and the shipboard calibration data processing method are introduced. The calibration was performed for three moving-base gravimeters and the corresponding results are determined, indicating that the method can significantly improve the accuracy of the parameters. For the CHZ-II gravimeter, the measurement accuracy of the survey is 0.471 mGal (1 mGal = 10−5 m/s2), which improved by 19.5% after applying the calibrated parameters. This method is also practical for use with aviation, marine and even vehicle-carried moving-base gravimeters.

Although deep learning has received extensive attention and achieved excellent performance in various scenarios, it suffers from adversarial examples to some extent. In particular, physical attack poses a greater threat than digital attack. However, existing research has paid less attention to the physical attack of object detection in UAV remote sensing images (RSIs). In this work, we carefully analyze the universal adversarial patch attack for multi-scale objects in the field of remote sensing. There are two challenges faced by an adversarial attack in RSIs. On one hand, the number of objects in remote sensing images is more than that of natural images. Therefore, it is difficult for an adversarial patch to show an adversarial effect on all objects when attacking a detector of RSIs. On the other hand, the wide height range of the photography platform causes the size of objects to vary a great deal, which presents challenges for the generation of universal adversarial perturbation for multi-scale objects. To this end, we propose an adversarial attack method of object detection for remote sensing data. One of the key ideas of the proposed method is the novel optimization of the adversarial patch. We aim to attack as many objects as possible by formulating a joint optimization problem. Furthermore, we raise the scale factor to generate a universal adversarial patch that adapts to multi-scale objects, which ensures that the adversarial patch is valid for multi-scale objects in the real world. Extensive experiments demonstrate the superiority of our method against state-of-the-art methods on YOLO-v3 and YOLO-v5. In addition, we also validate the effectiveness of our method in real-world applications.

The research is devoted to steel structure diagnostics by the acoustic emission (AE) method. The existing regulatory documents for AE diagnostics of metals and alloys do not take into account some critical factors, among which one is the scale factor should be highlighted. As a result, this can lead to an unreliable assessment of the danger degree of defects in structures when using standard AE diagnostic criteria. This paper presents a quantitative assessment of the scale factor impact on the AE data during the static tension test of steel specimens to failure. Experimental studies were carried out on flat specimens of various thicknesses with a side notch made of high-quality alloyed steel 30 KhGSA. It was established that AE data changed (rise in the AE signals amplitudes and AE activity) within the increase of specimen thickness. Growth in the recorded AE signals cumulative energy was registered with a greater specimen thickness. Partial correlation dependences of the mean count frequency and cumulative energy of AE signals on the specimen thickness were obtained. It was shown that such an effect occurred due to both a general increase in the deformed metal volume and greater strain intensity during the tension of thick specimens. The obtained dependences may contribute to the development of AE diagnostics of metallic materials which is invariant to the scale factor impact.

Ground-based time-variable gravimetry with high accuracy is an important approach in monitoring geodynamic processes. The uncertainty of instruments including scale factor (SF) and drift rate are the primary factors affect the quality of observation data. Differing from the conventional gravity adjustment procedure, this study adopted the modified Bayesian gravity adjustment (MBGA) method, which accounts for the nonlinear drift rate, and where the SF is considered as one of the hyperparameters estimated using Akaike’s Bayesian information criterion. Based on the terrestrial time-variable gravity datasets (2018–2020) from the southeastern Tibetan Plateau, errors caused by nonlinear drift rate and SF were processed quantitatively through analysis of the gravity difference (GD) residuals and the mutual difference of the GD. Additionally, cross validation from absolute gravity (AG) values was also applied. Results suggest that: (1) the drift rate of relavive instruments show nonlinear characteristics, and owing to their different spring features, the drift rate of CG-5 is much larger than that of LCR-G gravimeters; (2) the average bias between the original and optimized SF of the CG-5 gravimeters is approximately 169 ppm, while that of the LCR-G is no more than 63 ppm; (3) comparison of the differences in gravity values (GV) suggests that the uncertainty caused by the nonlinear drift rate is smaller than that attributable to SF. Overall, the novel approach adopted in this study was found effective in removing errors, and shown to be adaptive and robust for large-scale hybrid surface gravity campaign which providing high accuracy gravity data for the geoscience research.

The latest gravity survey of the gravity base network in Qinghai Province, China, was conducted with six Scintrex CG gravimeters and this gravity survey was tied to existed gravity reference stations. In this gravity network with long segments and very rugged topography, the calibration of scale factors is a time-consuming progress and its accuracy may be affected by many uncertainties, and the change in drift rates of the relative gravimeters are complex over time in this long-term survey. The reasonable calculation of scale factors and drift rates plays an important role in improving the gravity estimation accuracy. In this paper, based on the least squares, robust least squares, and Bayesian methods, various parameter calculation methods were employed to process this gravity network. The performance and practicality of each method were analyzed in terms of internal and external accuracy. The results indicated that the scale factors calibrated in the baseline field had poor applicability due to insufficient gravity difference, in this case, the scale factors estimated by the adjustment models were more accurate, which weakened the correlation between gravity differences and mutual differences. The drift rates estimated by the Bayesian method were relatively smooth over time, while drift rates estimated using symmetric observations were more practical for the gravimeter with highly variable drift. The weight constraints of observations can be optimized by the robust least squares method, the gravity values obtained by it were more consistent with absolute gravity values than those obtained by the least squares method, and the robust least squares method was recommended to process gravity data in plateau areas.

The on-site measurement of transient voltages is of great significance in analyzing the fault cause of power systems and optimizing the insulation coordination of power equipment. Conventional voltage transformers normally have a narrow bandwidth and are unable to accurately measure various transient voltages in power systems. In this paper, a wideband parallel resistive–capacitive voltage divider is developed, which can be used for online monitoring of transient voltages in a 220 kV power grid. The structures of the high-voltage and low-voltage arms were designed. The internal electric field distribution of the high-voltage arm was analyzed. The influence factors and improvement techniques of the upper frequency limit were studied. The parameters of the elements of the divider were determined. The voltage withstand performances and scale factors under lightning impulses and AC and DC voltages, the temperature stabilities of scale factors and the step response and bandwidth of the developed voltage divider were tested. The results show that the deviations of the scale factors under various voltage waveforms and different temperatures ranging from −20 to 40 °C are within 3%. The withstand voltage meets the relevant requirements specified in IEC60071-1-2011. The step response 10~90% rise time is approximately 29 ns, and the 3 dB bandwidth covers the range of DC to 10 MHz.

In this paper, we study the corrections to the Friedmann equations due to fast fluctuations in the universe scale factor. Such fast quantum fluctuations were recently proposed as a potential solution to the cosmological constant problem. They also induce strong changes to the current sign and magnitude of the average cosmological force, thus making them one of the potential probable causes of the modification of Newtonian dynamics in galaxy-scale systems. It appears that quantum fluctuations in the scale factor also modify the Friedmann equations, leading to a considerable modification of cosmological evolution. In particular, they give rise to the late-time accelerated expansion of the universe, and they may also considerably modify the effective universe potential.

The fire growth rate index (FIGRA), which is the ratio of the maximum value of the heat release rate (Qmax) and the time (tmax) to reach the maximum heat release rate, is a general method to evaluate a material in the fire-retardant performance in fire technology. The object of this study aims to predict FIGRA of the polyethylene foam pipe insulation in accordance with the scale factor (Sf), the volume fraction of the pipe insulation (VF) and the ignition heat source (Qig). The compartments made of fireboard have been mock-up with 1/3, 1/4, and 1/5 reduced scales of the compartment as specified in ISO 20632. The heat release rate data of the pipe insulation with the variation of Sf, VF, and Qig are measured from 33 experiments to correlate with FIGRA. Based on a critical analysis of the heat transfer phenomenon from previous research literature, the predictions of Qmax and tmax are presented. It is noticeable that the fire-retardant grade of the polyethylene foam pipe insulation could have Grade B, C, and D in accordance with the test conditions within ±15% deviation of the predicted FIGRA. In case of establishing the database of various types of insulation, the prediction models could apply to evaluate the fire-retardant performance.

Digital elevation model (DEM) generation using multi-aspect synthetic aperture radar (SAR) imagery applying radargrammetry has become a hotspot. The traditional radargrammetric method is to solve the rigorous radar projection equations to obtain the three dimensional coordinates of targets. In this paper, we propose a new DEM generation method based on the offset between multi-aspect images formed on ground plane. The ground object will be projected to different positions from different viewing aspect angles if the height of object is not equal to the height of imaging plane. The linear relationship between the offset of imaging positions and height of the object is derived and scale factor is obtained finally. Height information can be retrieved from offset of imaging positions directly through the DEM extraction model presented in this paper. Thus the solution to nonlinear equations point by point can be avoided. Real C band airborne circular SAR images is used to verify the proposed approach. When extracted DEM applied in multi-aspect imaging process, superimposition of multi-aspect images will no longer be defocusing and can achieve finer observation of the scanned scene.

Obstructive sleep apnea (OSA) is an independent cardiovascular risk factor to which autonomic nervous dysfunction has been reported to be an important contributor. Ninety subjects recruited from the sleep center of a single medical center were divided into four groups: normal snoring subjects without OSA (apnea hypopnea index, AHI < 5, n = 11), mild OSA (5 ≤ AHI < 15, n = 10), moderate OSA (15 ≤ AHI < 30, n = 24), and severe OSA (AHI ≥ 30, n = 45). Demographic (i.e., age, gender), anthropometric (i.e., body mass index, neck circumference), and polysomnographic (PSG) data were recorded and compared among the different groups. For each subject, R-R intervals (RRI) from 10 segments of 10-minute electrocardiogram recordings during non-rapid eye movement sleep at stage N2 were acquired and analyzed for heart rate variability (HRV) and sample entropy using multiscale entropy index (MEI) that was divided into small scale (MEISS, scale 1–5) and large scale (MEILS, scale 6–10). Our results not only demonstrated that MEISS could successfully distinguish normal snoring subjects and those with mild OSA from those with moderate and severe disease, but also revealed good correlation between MEISS and AHI with Spearman correlation analysis (r = −0.684, p < 0.001). Therefore, using the two parameters of EEG and ECG, MEISS may serve as a simple preliminary screening tool for assessing the severity of OSA before proceeding to PSG analysis.

Using 1000 successive points of a pulse wave velocity (PWV) series, we previously distinguished healthy from diabetic subjects with multi-scale entropy (MSE) using a scale factor of 10. One major limitation is the long time for data acquisition (i.e., 20 min). This study aimed at validating the sensitivity of a novel method, short time MSE (sMSE) that utilized a substantially smaller sample size (i.e., 600 consecutive points), in differentiating the complexity of PWV signals both in simulation and in human subjects that were divided into four groups: healthy young (Group 1; n = 24) and middle-aged (Group 2; n = 30) subjects without known cardiovascular disease and middle-aged individuals with well-controlled (Group 3; n = 18) and poorly-controlled (Group 4; n = 22) diabetes mellitus type 2. The results demonstrated that although conventional MSE could differentiate the subjects using 1000 consecutive PWV series points, sensitivity was lost using only 600 points. Simulation study revealed consistent results. By contrast, the novel sMSE method produced significant differences in entropy in both simulation and testing subjects. In conclusion, this study demonstrated that using a novel sMSE approach for PWV analysis, the time for data acquisition can be substantially reduced to that required for 600 cardiac cycles (~10 min) with remarkable preservation of sensitivity in differentiating among healthy, aged, and diabetic populations.

The best Weibull distribution methods for the assessment of wind energy potential at different altitudes in desired locations are statistically diagnosed in this study. Seven different methods, namely graphical method (GM), method of moments (MOM), standard deviation method (STDM), maximum likelihood method (MLM), power density method (PDM), modified maximum likelihood method (MMLM) and equivalent energy method (EEM) were used to estimate the Weibull parameters and six statistical tools, namely relative percentage of error, root mean square error (RMSE), mean percentage of error, mean absolute percentage of error, chi-square error and analysis of variance were used to precisely rank the methods. The statistical fittings of the measured and calculated wind speed data are assessed for justifying the performance of the methods. The capacity factor and total energy generated by a small model wind turbine is calculated by numerical integration using Trapezoidal sums and Simpson’s rules. The results show that MOM and MLM are the most efficient methods for determining the value of k and c to fit Weibull distribution curves.

Intensity−duration−frequency (IDF) curves are empirical mathematical formulations that have been used for years in engineering for planning, design, and operation of hydraulic projects. The expression proposed by Sherman (1931) has been validated and used largely by many researchers. In all cases, the four parameters of this formulation are obtained through a numerical procedure. Although these parameters are obtained from historical rainfall observations, the optimization of these parameters implies an infinite combination between them and all those solutions would be valid. Of the four parameters, only one of them (C) has units, and for this reason, a physical sense of parameter C is searched for. Having certainty that some of them can be measured in situ would represent a great advance for modern hydrology. With data from 523 storms monitored every minute, a parametric adjustment was made to the Sherman equation and the typical duration of storms at each site was also obtained. To demonstrate how rainfall intensities vary with the change in C value, rainfall intensities calculations for of 5, 10, 15, and 20 min rainfall duration are used to validate the proposed methodology. The results show that typical storm duration is correlated with the additive parameter of Sherman’s formula.

In this paper, a novel temperature compensation method for a dual-mass MEMS gyroscope is proposed based on drive mode vibration characteristic compensation using a temperature variable resistor. Firstly, the drive and sense modes of the gyroscope re analyzed and investigated, and it is found that the scale factor is proportional to the drive mode amplitude controlling reference voltage. Then, the scale factor temperature compensation method is proposed, and a temperature variable resistor is utilized to compensate the drive amplitude working point and make it change with temperature. In addition, the temperature compensation circuit is designed and simulated. After that, the temperature bias drift is compensated in a modular output. The experimental results show that scale factor and bias variation during the temperature range from −40 °C to 60 °C decrease from 3.680% to 1.577% and 3.880% to 1.913%, respectively. In addition, the bias value improves from 103.395 °/s to 22.478 °/s (optimized 78.26%). The bias stability and angular rate walking parameter are also optimized to 45.97% and 16.08%, respectively, which verify the method proposed in this paper.

Rotating Accelerometer Gravity Gradiometers (RAGGs) play a significant role in applications such as resource exploration and gravity aided navigation. Scale factor calibration is an essential procedure for RAGG instruments before being used. In this paper, we propose a calibration system for a gravity gradiometer to obtain the scale factor effectively, even when there are mass disturbance surroundings. In this system, four metal spring-based accelerometers with a good consistency are orthogonally assembled onto a rotary table to measure the spatial variation of the gravity gradient. By changing the approaching pattern of the reference gravity gradient excitation object, the calibration results are generated. Experimental results show that the proposed method can efficiently and repetitively detect a gravity gradient excitation mass weighing 260 kg within a range of 1.6 m and the scale factor of RAGG can be obtained as (5.4 ± 0.2) E/μV, which is consistent with the theoretical simulation. Error analyses reveal that the performance of the proposed calibration scheme is mainly limited by positioning error of the excitation and can be improved by applying higher accuracy position rails. Furthermore, the RAGG is expected to perform more efficiently and reliably in field tests in the future.

Flexible structures are the main components in many precision measuring and research systems. They provide miniaturization, repeatability, minimal damping, low measuring forces, and very high resolution. This article focuses on the modeling, development, and comparison of three typical flexible micro- nano-structures: flexible helicoids, atomic force microscopy (AFM) cantilevers, and concave notch hinges. Our theory yields results which allow us to increase the accuracy and functionality of these structures in new fields of application such as the modeling of helicoidal DNA molecules’ mechanics, the definition of instantaneous center of rotation in concave flexure notch hinges, and the estimation of the increase of spring constants and resolution at higher mode vibration in AFM cantilevers with an additional concentrated and end extended mass. We developed the original kinetostatic, reverse conformal mapping of approximating contours, and non-linear thermomechanical fluctuation methods for calculation, comparison, and research of the micromechanical structures. These methods simplify complicated solutions in micro elasticity but provide them with necessary accuracy. All our calculation results in this article and in all corresponding referenced author’s publications are in a good agreement with experimental and finite element modeling data within 10% or less.

Spin rate of a high-speed spinning-rotor gyroscope will make a significant impact on angular rate sensor performances such as the scale factor, resolution, measurement range, and bias stability. This paper presents the spin rate effects on performance indicators of a microelectromechanical systems (MEMS) gyroscope where a free-spinning rotor is electrostatically suspended in an evacuated vacuum cavity and functions as a dual-axis angular rate sensor. Theoretical models of the scale factor and measurement range of such a spinning-rotor gyroscope are derived. The experimental results indicate that the measured scale factors at different settings of the spin rate match well with the theoretical predication. In order to separate the disturbance component of the rotation control loop on the gyroscope output, a testing strategy is proposed by operating the gyroscope at different spin rates. Experimental results on a prototype gyroscope show that the squared drive voltage generated by the rotation control loop is approximately proportional to the noise of the gyroscope output. It was further investigated that an improved performance of such spinning-rotor gyroscopes can be achieved by operating the gyroscope rotor at an optimal spin rate.

RGB-D cameras offer both color and depth images of the surrounding environment, making them an attractive option for robotic and vision applications. This work introduces the BRISK_D algorithm, which efficiently combines Features from Accelerated Segment Test (FAST) and Binary Robust Invariant Scalable Keypoints (BRISK) methods. In the BRISK_D algorithm, the keypoints are detected by the FAST algorithm and the location of the keypoint is refined in the scale and the space. The scale factor of the keypoint is directly computed with the depth information of the image. In the experiment, we have made a detailed comparative analysis of the three algorithms SURF, BRISK and BRISK_D from the aspects of scaling, rotation, perspective and blur. The BRISK_D algorithm combines depth information and has good algorithm performance.

Spiral-coil-type horizontal ground heat exchangers (GHEs) have been increasingly used in ground source heat pump (GSHP) systems due to their higher heat transfer performance. Many attempts have been made to investigate the heat transfer mechanism and establish design methods for the spiral-coil-type ground heat exchangers. Nevertheless, a universal design method for horizontal GHEs has not been reported due to its complexity. In contrast to the spiral-coil-type horizontal GHEs, straight-line-type horizontal GHEs have been widely adopted since they are easy to design for use in industry. In this study, a scale factor model, which could be used to design the coil-type exchanger based on the design length of a straight-line-type heat exchanger, was presented. The ratio of the mean thermal transfer energy between the straight-line-type and spiral-coil-type heat exchangers was numerically investigated by considering weather condition, configuration of GHE, and thermal properties of the ground. Using the numerical results for a total of 108 cases, artificial neural network and linear regression methods were employed for the model development. The proposed model of the scale factor may provide an alternative way to design the spiral-coil-type horizontal GHEs.

Audio dual compression detection is an important part of audio forensics. It is of great significance to judge whether the audio has been falsified and forged. This study found that the advanced audio coding (AAC) audio scale factor gradually decreases with the number of compressions increases. Based on this, we propose an AAC double compression audio detection algorithm based on the statistical characteristics of the scale factor difference before and after audio re-compression. The experimental results show that the algorithm can accurately classify dual compressed AAC audio. The average accuracy of AAC audio classification between low-bit-rate transcoding to high-bit-rate is 99.91%, and the accuracy rate between the same bit rate is 97.98%. In addition, experiments with different durations, different noises, and different encoders also proved the better performance of this algorithm.

This paper proposes an effective method to calibrate the microelectromechanical systems (MEMS) vibratory gyroscope based on the virtual Coriolis force. This method utilizes a series of voltage signals to simulate the Coriolis force input, and the gyroscope output is monitored to obtain the scale factor characteristics of the gyroscopes. The scale factor and bias parameters of the gyroscope can be calibrated conveniently and efficiently in the sense-mode open loop. The calibration error of the scale factor based on the turntable and the virtual Coriolis force method is only 1.515%, which proves the correction of the method proposed in this paper. Meanwhile, the non-linearity and bias value of the turntable and the virtual Coriolis force method are 742 ppm and 42.04 mV and 3389 ppm and 0.66 mV, respectively.

A miniature vacuum-packaged silicon microgyroscope (SMG) with symmetrical and decoupled structure was designed to prevent unintended coupling between drive and sense modes. To ensure high resonant stability and strong disturbance resisting capacity, a self-oscillating closed-loop circuit including an automatic gain control (AGC) loop based on electrostatic force feedback is adopted in drive mode, while, dual-channel decomposition and reconstruction closed loops are applied in sense mode. Moreover, the temperature effect on its zero bias was characterized experimentally and a practical compensation method is given. The testing results demonstrate that the useful signal and quadrature signal will not interact with each other because their phases are decoupled. Under a scale factor condition of 9.6 mV/o/s, in full measurement range of ± 300 deg/s, the zero bias stability reaches 15o/h with worse-case nonlinearity of 400 ppm, and the temperature variation trend of the SMG bias is thus largely eliminated, so that the maximum bias value is reduced to one tenth of the original after compensation from -40 oC to 80 oC.