A hardening load transfer function for rock bolts and its calibration using distributed fiber optic sensing

Confinement of rock bolts by the surrounding rock formation has long been recognized as a positive contributor to the pull-out behavior,yet only a few experimental works and analytical models have been reported,most of which are based on the global rock bolt response evaluated in pull-out tests.This paper presents a laboratory experimental setup aiming to capture the rock formation effect,while using distributed fiber optic sensing to quantify the effect of the confinement and the reinforcement pull-out behavior on a more local level.It is shown that the behavior along the sample itself varies,with certain points exhibiting stress drops with crack formation.Some edge effects related to the kinematic freedom of the grout to dilate are also observed.Regardless,it was found that the mid-level response is quite similar to the average response along the sample.The ability to characterize the variation of the response along the sample is one of the many advantages high-resolution fiber optic sensing allows in such investigations.The paper also offers a plasticity-based hardening load transfer function,representing a"slice"of the anchor.The paper describes in detail the development of the model and the calibration/determination of its parameters.The suggested model captures well the coupled behavior in which the pull-out process leads to an increase in the confining stress due to dilative behavior.

Numerical modelling of resonance mechanisms in jointed rocks using transfer functions

Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions,derived from signals generated through numerical modelling.Resonance is important for a range of engineering situations as it identifies the frequency of waves which will be favourably transmitted.Two different numerical methods are used for this study,adopting the finite difference method and the combined discrete element-finite difference method.The numerical models are validated by replicating results from previous studies.The two methods are found to behave similarly and show the same resonance effects;one operating at low frequency and the other operating at relatively high frequency.These resonance effects are interpreted in terms of simple physical systems and analytical equations are derived to predict the resonant frequencies of complex rock masses.Low frequency resonance is shown to be generated by a system synonymous with masses between springs,described as spring resonance,with an equal number of resonant frequencies as the number of blocks.High frequency resonance is generated through superposition of multiple reflected waves developing standing waves within intact blocks,described as superposition resonance.While resonance through superposition has previously been identified,resonance based on masses between springs has not been previously identified in jointed rocks.The findings of this study have implications for future analysis of multiple jointed rock masses,showing that a wave travelling through such materials can induce other modes of propagation of waves,i.e.spring resonance.

Analysis of the optical quality by determining the modulation transfer function for anterior corneal surface in myopes

AIM: To describe the characteristics of modulation transfer function (MTF) of anterior corneal surface, and obtain the the normal reference range of MTF at different spatial frequencies and optical zones of the anterior corneal surface in myopes. METHODS: Four hundred eyes from 200 patients were examined under SIRIUS corneal topography system. Phoenis analysis software was applied to simulate the MTF curves of anterior corneal surface at vertical and horizontal meridians at the 3, 4, 5, 6, 7mm optical zones of cornea. The MTF values at spatial frequencies of 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60 cycles/degree (c/d) were selected. RESULTS: The MTF curve of anterior corneal surface decreased rapidly from low to intermediate frequency (0-15cpd) at various optical zones of cornea, the value decreased to 0 slowly at higher frequency (>15cpd). With the increase of the optical zones of cornea, MTF curve decreased gradually. 3) In the range of 3 mm- 6 mm optical zones of the cornea, the MTF values measured at horizontal meridian were greater than the corresponding values at horizontal meridian of each spatial frequency, the difference was statistically significant (P<0.05). At 7 mm optical zones of cornea, the MTF values measured at horizontal meridian were less than the corresponding values at vertical meridian at 10-60 spatial frequencies (cpd), and the difference was statistically significant in 25, 30, 35, 40, 45, 50 cpd(P<0.05). CONCLUSION: MTF can be used to describe the imaging quality of optical systems at anterior corneal surface objectively in detail.

Solving the atmospheric scattering optical transfer function using the multi-coupled single scattering method

The atmospheric scattering optical transfer function （OTF） is solved by applying the multi-coupled single scattering （MCSS） method to the three-dimensional radiative transfer equation （RTE） under the periodic ground condition. This approach is a direct hit to the atmospheric scattering OTF using the same original context of modulation transfer function （MTF） measurement, i.e., images of sinusoidal grating at different spatial frequencies. Both the amplitude and phase shift of the OTF at various zenith and azimuth angles can be obtained at an arbitrary spatial frequency.

Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus

Based on the fact that the real inductor and the real capacitor are fractional order in nature and the fractional calculus,the transfer function modeling and analysis of the open-loop Buck converter in a continuous conduction mode（CCM） operation are carried out in this paper.The fractional order small signal model and the corresponding equivalent circuit of the open-loop Buck converter in a CCM operation are presented.The transfer functions from the input voltage to the output voltage,from the input voltage to the inductor current,from the duty cycle to the output voltage,from the duty cycle to the inductor current,and the output impedance of the open-loop Buck converter in CCM operation are derived,and their bode diagrams and step responses are calculated,respectively.It is found that all the derived fractional order transfer functions of the system are influenced by the fractional orders of the inductor and the capacitor.Finally,the realization of the fractional order inductor and the fractional order capacitor is designed,and the corresponding PSIM circuit simulation results of the open-loop Buck converter in CCM operation are given to confirm the correctness of the derivations and the theoretical analysis.

Modulation transfer function characteristic of uniform-doping transmission-mode GaAs/GaAlAs photocathode

The resolution characteristic can be obtained by the modulation transfer function （MTF） of a GaAs/GaA1As photocathode. After establishing the theoretical model of GaAs（100）-oriented atomic configuration and the formula for the ionized impurity scattering of the non-equilibrium carriers, this paper calculates the trajectories of photoelectrons in a photocathode. Thus the distribution of photoelectron spots on the emit-face is obtained, which is namely the point spread function. The MTF is obtained by Fourier transfer of the line spread function obtained from the point spread function. The MTF obtained from these calculations is shown to depend heavily on the electron diffusion length, and enhanced considerably by decreasing the electron diffusion length and increasing the doping concentration. Furthermore, the resolution is enhanced considerably by increasing the active-layer thickness, especially at high spatial frequencies. The best spatial resolution is 860 lp/mm, for the GaAs photocathode of doping concentration 1 ×10^19 cm 3 electron diffusion length 3.6 μm and the active-layer thickness 2 μm, under the 633-nm light irradiated. This research will contribute to the future improvement of the cathode＇s resolution for preparing a high performance GaAs photocathode, and improve the resolution of a low light level image intensifier.

Repetitive PD control strategy with inverse transfer function compensation for CVCF inverter

A novel repetitive control strategy for the output waveform of single-phase CVCF inverters is presented. In this scheme, the inverse transfer function of inverter is used as a compensator to obtain stable and satisfy harmonic rejection. Besides, PD controller is adopted to improve transient performance. Simulation and experimental results, which are gotten from a DSP-based 400Hz, 5.5KW inverter, indicate that the proposed control scheme can achieve not only low THD during steady-state operation but also fast transient response during load step change.

Establishment of a diatom-total phosphorus transfer function for lakes on the Songnen Plain in northeast China

To understand the relationship between planktonic diatoms and environmental variables in the lakes on the Songnen Plain,northeast(NE)China,we investigated water quality and planktonic diatoms from 71 sampling points in 27 lakes,based on which Canonical Correspondence Analysis(CCA)was conducted.The result show that planktonic diatoms displayed certain responses to environment gradients,and the total phosphorus(TP)explained the maximum variation of planktonic diatom species among the 15 environmental variables,suggesting that TP was the most important and significant environmental parameter affecting the distribution of diatom species.In addition,we established a diatom-total phosphorus transfer(DTPT)function,of which component 5 of the weighted averaging partial least squares regression(WAPLS)was chosen to and compared with a series of weighted average regression(WA)models and WA-PLS models.According to the jackknifing statistical test,the component 5 of WA-PLS models provided a lower root-mean-square error prediction(RMSEP=0.202)and a higher correlation coefficient between observation and prediction(R^2_Jack=0.759).After deletion of three outliers,the root-mean-square error prediction of the DTPT function was reduced(RMSEP=0.169)while the correlation coefficient between observation and prediction was increased(R^2_Jack=0.823).Therefore,this DTPT function performed better than other regional TP models in the world.However,it remains demanding for expanding the background dataset to improve the prediction ability of the model.

Mathematical simulations of the galvanic coupling intra-body communication by using the transfer function method

The galvanic coupling intra-body communication （IBC） was mathematically simulated based on the proposed transfer function. Firstly, a galvanic coupling IBC circuit model was developed and the corresponding parameters were discussed. Secondly, the transfer function of the galvanic coupling IBC was derived and proposed. Finally, the signal attenuation characteristics of the galvanic coupling IBC were measured along different signal transmission paths of actual human bodies, while the corresponding mathematical simulations based on the proposed transfer function were carried out. Our investigation showed that the mathematical simulation results coincided with the measured results over the frequency range of 100kHz to 5MHz, which indicated that the proposed transfer function could be useful for theoretical analysis and application of the galvanic coupling IBC.

Spectrum Characteristics and Transfer Function of the Hydrograph of the Deep Aqueous System

The fluctuation of most of the hydrograph in the deep aqueous system records the fluid pulsation in lithosphere and variation of the earth's crust. Many observations have verified that groundwater is an ideal information carrier of the crust. In this paper, the series of input (precipitation, air pressure, Earth tide etc.) and output (water level, artesian flow) of the deep aqueous system are studied by using the spectrum analysis and system theory. The application concepts of transfer function and the spectral structure of the hydrograph enrich the knowledge of the deep aqueous system. Two typical spectral structures of the hydrograph of the deep aqueous system are obtained by comparing with many water-bearing systems of the Jizhong depression. One is from well Ma-17 and the other is from the well Xinze-5. Finally, the physical models of forming the spectrum of the hydrograph are constructed on the basis of the spectrum research on the deep aqueous system.

Optical Transfer Function Reconstruction in Incoherent Fourier Ptychography

An optical transfer function （OTF） reconstruction model is first embedded into incoherent Fourier ptychography （IFP）. The leading result is a proposed algorithm that can recover both the super-resolution image and the OTF of an imaging system with unknown aberrations simultaneously. This model overcomes the difficult problem of OTF estimation that the previous IFP faces. The effectiveness of this algorithm is demonstrated by numerical simulations, and the superior reconstruction is presented. We believe that the reported algorithm can extend the original IFP for more complex conditions and may provide a solution by using structured light for characterization of optical systems＇ aberrations.

INTERPOLATION OF HEAD-RELATED TRANSFER FUNCTIONS USING SPHERICAL FOURIER EXPANSION

A new interpolation algorithm for Head-Related Transfer Function （HRTF） is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical harmonics on a spherical surface. Truncated Singular Value Decomposition （SVD） is adopted to calculate the weights of the model. The truncation number is chosen according to Frobenius norm ratio and the partial condition number. Compared with other interpolated methods, our proposed approach not only is continuous but exploits global information of available directions. The HRTF from any desired direction can be and interpolated results demonstrate that our obtained more accurately and robustly. Reconstructed proposed algorithm acquired better performance.

Numerical modeling calculation for the spatial distribution characteristics of horizontal field transfer functions

Applying 3-dimension finite difference method, the distribution characteristics of horizontal field transfer functions for rectangular conductor have been computed, and the law of distribution for Re-part and Im-part has been given. The influences of source field period, the conductivity, the buried depth and the length of the conductor on the transfer functions were studied. The extrema of transfer functions appear at the center, the four corners and around the edges of conductor, and move with the edges. This feature demonstrates that around the edges are best places for transfer functions' observation.

Transfer function of FBS-3A feedback broadband seismometer

FBS-3A feedback broadband seismometer has been widely utilized in observation networks up to now. Therefore, it is very important and practically meaningful for the application of this kind of sensor to fulfill some relative research work about its transfer function and for the analysis to the data recorded and the further development of the seismometer. In this paper, from the viewpoint of achieving its working principle, method of systematic analysis is applied to deduce the transfer functions, including both the transfer function for calibration and that for measurement. Moreover, on the basis of that, the distribution of its zeroes and poles in a complex frequency domain is analyzed, which provides a convincing evidence to simplify this seismometer system from a high-order one to a two-order one. And the emulation of the frequency characteristics of FBS-3A is presented in this paper. On the whole, the aim of this article is to do some theoretical work about the earthquake observation sensor, and also to introduce the method of making systematic analysis in a complex frequency domain to the research and the development of the seismometers.

Testing the transfer functions for the Geonor T-200B and Chinese standard precipitation gauge in the central Qinghai-Tibet Plateau

Accurately measuring precipitation is integral for understanding water cycle processes and assessing climate change in the Qinghai–Tibet Plateau(QTP).The Geonor T-200B weighing precipitation gauge with a single Alter shield(Geonor)and the Chinese standard precipitation gauge(CSPG)are widely used for measuring precipitation in the QTP.However,their measurements need to be adjusted for wetting loss,evaporation loss and windinduced undercatch.Four existing transfer functions for adjusting the Geonor-recorded and three transfer functions for adjusting the CSPG-recorded precipitation at hourly,daily or event scale has been proposed based on the precipitation intercomparison experiments conducted at a single site in different regions.Two latest transfer functions for the Geonor(which are referred to as K2017a and K2017b)at the half-hour time scale based on the precipitation intercomparison experiments at multiple stations in the northern hemisphere were provided in the World Meteorological Organization Solid Precipitation Intercomparison Experiment.However,the applicability of these transfer functions in the QTP has not been evaluated.Therefore,the current study carried out a precipitation measurement intercomparison experiment between August 2018 and September 2020 at a site in Beiluhe in central QTP.The performance of these transfer functions at this site was also evaluated on the basis of mean bias(MB),root mean squared error(RMSE)and relative total catch(RTC).The results are as follows:First,the unadjusted RTC values of the Geonor for rain,mixed(snow mixed with rain),snow and hail are 92.06%,85.35%,64.11% and 91.82%,respectively,and the unadjusted RTC values of the CSPG for the same precipitation types are 92.59%,81.32%,46.43% and 95.56%,respectively.Second,K2017a has the most accurate adjustment results for the Geonor-recorded snow and mixed precipitation at the half-hour time scale,and the post-adjustment RTC values increased to 98.25% and 98.23%,respectively.M2007e,an event-based transfer function,was found to have the most accurate adjustment results for the Geonorrecorded snow precipitation at the event scale,and the post-adjustment RTC value increased to 96.36%.Third,the existing transfer functions for CSPG underestimate snowfall,while overestimating rainfall.Fourth,hail is a significant precipitation type in central QTP.The catch efficiency of hail precipitation and the temperature when hail precipitation occurs are close to those of rain;moreover,the transfer functions for rain are suitable for hail as well.

Comparison of the retinal modulation transfer function between amblyopes successfully corrected and normal subjects

AIM:To analyze the retinal modulation transfer function between amblyopes whose visual acuity was corrected to 5.0 and normal subjects at the same age. METHODS: RM-800 used to detect contrast sensitivity was adopted to measure MTF of 96 amblyopes (96 eyes) whose visual acuity was corrected to 5.0 and 80 normal controls (80 eyes) at the same age under six interference fringes (IVA=0.06, 0.1, 0.2, 0.4, 0.6, 0.8). RESULTS: The functional values of amblyopes were significantly lower than those of normal subjects in every fringe (P<0.01), especially in medium and high frequency. CONCLUSION: For amblyopes, MTF was still abnormal after stopping the treatments.

A new modulation transfer function for ocean wave spectra retrieval from X-band marine radar imagery

When imaging ocean surface waves by X-band marine radar, the radar backscatter from the sea surface is modulated by the long surface gravity waves. The modulation transfer function （MTF） comprises tilt, hydrodynamic, and shadowing modulations. A conventional linear MTF was derived using HH-polarized radar observations under conditions of deep water. In this study, we propose a new quadratic polynomial MTF based on W-polarized radar measurements taken from heterogeneous nearshore wave fields. This new MTF is obtained using a radar-observed image spectrum and in situ buoy-measured wave frequency spectrum. We validate the MTF by comparing peak and mean wave periods retrieved from X-band marine radar image sequences with those measured by the buoy. It is shown that the retrieval accuracies of peak and mean wave periods of the new MTF are better than the conventional MTF. The results also show that the bias and root mean square errors of the peak and mean wave periods of the new MTF are 0.05 and 0.88 s, and 0.32 and 0.53 s, respectively, while those of the conventional MTF are 0.61 and 0.98 s, and 1.39 and 1.48 s, respectively. Moreover, it is also shown that the retrieval results are insensitive to the coefficients in the proposed MTF.

Fuzzy image restoration using modulation transfer function

The key difficulty of restoring a fuzzy image is to estimate its point spread function( PSF). In the paper,PSF is modelled based on modulation transfer function( MTF). The first step is calculating the image MTF. In the traditional slanted-edge method,a sub-block is always manually extracted from original image and its MTF will be viewed as the result of the whole image. However,handcraft extraction is inefficient and will lead to inaccurate results. Given this,an automatic MTF computation algorithm is proposed,which extracts and screens out all the effective sub-blocks and calculates their average MTF as the final result. Then,a two-dimensional MTF restoration model is constructed by multiplying the horizontal and vertical MTF,and it is combined with conventional image restoration methods to restore fuzzy image. Experimental results indicate the proposed method implementes a fast and accurate MTF computation and the MTF model improves the performance of conventional restoration methods significantly.

Transfer Function Relating Compressive Pressure to Interfacial Stress Sensor for Biomedical Applications

To help comfort for an amputee, it is important to understand the load distribution between the residual limb and the prosthetic socket for a prosthetic socket system. An interfacial stress sensor was presented which was capable of measuring compressive pressure and shear stress simultaneously. A mathematical model was built and an experiment was conducted to obtain the transfer function of interfacial stress sensor to compressive pressure. The results show that the sensor is capable of measuring a range of 30-217 kPa compressive pressure with a relative error of 32.15% in lower range and 6.22% in upper range.