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.

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.

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 func-tions 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.

Phase behaviors of transfer functions in Vibrating systems

This paper investigates the applicabilitles of pole-zero model and wave propagation theory in estimating the phase characteristics of vibrating systems. The measured phase spectra are compared with the estlmated reverberant phase limit and wave propagation phase. The relations between transfer function phase and frequency, damping, and separation distance are described. The present results show that the pole-zero model provides a reasonable estimation of the reverberant phase limit in low frequency band below an identified transition frequency.The reverberant phase is linearly dependent on frequency in this band, but from the transition frequency and onwards the phase increases only with the square root of frequency. This behavior is characteristic for free propagating

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.

Experimental study on transfer functions of an active rotor under different flight conditions

Vibrations impose negative impacts on the effectiveness and public acceptance of helicopters.Active rotors with trailing-edge flaps have been proved to be an effective way to actively eliminate helicopter vibrations.For the existing control algorithm based on offline system identification,the transfer functions of an active rotor under different flight conditions are pre-requisites to implement closed-loop vibration control.In this study,a three-bladed active rotor with improved trailing-edge flaps is designed,and wind-tunnel tests are conducted to identify the transfer functions of this active rotor using frequency sweep and phase sweep methods.The experimental results demonstrate that these transfer functions are insensitive to the variation of flight speeds:the amplitude of the transfer function varies slightly,while the phase delay almost remains unchanged.In addition,this finding is validated through closed-loop vibration control tests with the active rotor.The transfer function obtained from the hover test results is also applicable to closed-loop vibration control tests under the forward flight conditions.This will dramatically simplify the implementation and operation of an active rotor.

Heterogeneous transfer functions multi-layer perceptron (MLP) for meteorological time series forecasting

In this paper,we propose to study four meteorological and seasonal time series(TS)coupled with a multi-layer perceptron(MLP)modeling.We chose to combine two transfer functions for the nodes of the hidden layer,and to use a temporal indicator(time index as input)in order to take into account the seasonal aspect of the studied TS.The results of the prediction concern two years of measurements and the learning step,eight independent years.We show that this methodology can improve the accuracy of meteorological data estimation compared to a classical MLP modeling with a homogenous transfer function.

Nullors, and Nullor Circuits;There Applications in Symbolic Circuit Analysis and Design

The objective in this presentation is to introduce some of the unique properties and applications of nullors in active circuit analysis and designs. The emphasis is to discuss the role nullors can play in symbolic representation of transfer functions. To show this we adopt the topological platform for the circuit analysis and use a recently developed Admittance Method (AM) to achieve the Sum of Tree Products (STP), replacing the determinant and cofactors of the Nodal Admittance Matrix (NAM) of the circuit. To construct a transfer function, we start with a given active circuit and convert all its controlled sources and I/O-ports to nullors. Now, with a solid nullor circuit (passive elements and nullors) we first eliminate the passive elements through AM operations. This produces the STPs. Second, the all-nullor circuit is then used to find the signs or the STPs. Finally, the transfer function (in symbolic, if chosen) is obtained from the ratio between the STPs.

A Practical Regular LDPC Coded Scheme for Physical-Layer Information Security

In this paper,we aim to design a practical low complexity low-density parity-check(LDPC)coded scheme to build a secure open channel and protect information from eavesdropping.To this end,we first propose a punctured LDPC coded scheme,where the information bits in a codeword are punctured and only the parity check bits are transmitted to the receiver.We further propose a notion of check node type distribution and derive multi-edge type extrinsic information transfer functions to estimate the security performance,instead of the well-known weak metric bit error rate.We optimize the check node type distribution in terms of the signal-to-noise ratio(SNR)gap and modify the progressive edge growth algorithm to design finite-length codes.Numerical results show that our proposed scheme can achieve a lower computational complexity and a smaller security gap,compared to the existing scrambling and puncturing schemes.

Effective transmittance of Fabry–Perot cavity under non-parallel beam incidence

The Fabry–Perot(FP) resonant cavity is widely used in laser and spectroscopic measurements due to its unique interference transfer function(ITF). In the ideal case of parallel incident light, the ITF of the FP resonant cavity can be expressed by the Airy function. However, in reality, it is difficult to achieve perfect parallelism with collimated beams. In this article, a theoretical model is established for non-parallel light incidence, which assumes that the non-parallel incident light is a cone-shaped beam, and the cone angle is used to quantify the non-parallelism of the beam. The transmittance function of the FP resonant cavity under non-parallel light incidence is derived. The accuracy of the model is experimentally verified. Based on this model, the effects of divergence angle, tilt angle and FP cavity parameters(reflectivity, cavity length)on the ITF are studied. The reasons for the decrease in peak value, broadening and asymmetry of the interference peak under non-parallel light incidence are explained. It is suggested that a fine balance between the interference peak and the collimation effect of the incident light should be considered in the design and application of FP resonant cavities, especially for tilted applications such as angle-scanned spectroscopy. The research results of this article have certain significance for the design and application of FP resonant cavities.

AAK Theorem and a Design of Multidimensional BIBO Stable Filters

Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank.

Analysis of Quenching Resistor Effect to Improve Stability of TIA Circuit for APD-A Secondary Publication

In this paper,since the Avalanche Photo Diode(APD)for Light-to-Voltage LTV conversion uses a high voltage in the operating range unlike other Photo Diodes(PD),the quenching resistor must be connected in series to prevent overcurrent when using the Transimpedance Amplifier(TIA).In such a case,quenching resistance may affect the transfer function of the TIA circuit,resulting in serious stability.Therefore,in this paper,by analyzing the effect of APD quenching resistance on the voltage and current loop transfer function of TIA,we proposed a loop analysis and a method for determining the quenching resistance value to improve stability.A TIA circuit with quenching resistance was designed by the proposed method and its operational stability was verified through simulation and chip fabrication.

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.

Analysis of the Heat Transfer Efficiency of an Automobile Engine under Different Grille Opening and Closing Conditions

Computational Fluid Dynamics is used to assess the thermal(heat transfer)performances of an automobile engine considering different grille opening and closing degrees.For this purpose the entire vehicle is modelled and three fundamental aspects are examined,namely,the open area of the air intake grille,the position of the upper and lower grilles and their shape.The results show that the opening area and position of the grille have some influence also on the aerodynamic characteristics of the automobile.With an increase in the opening angle of the grille,the CD(Drag Coefficient)value of the whole vehicle becomes higher.When the air intake grille of the car is fully open or closed,the CD value is 0.35434 or 0.31777,respectively,that is,the flow resistance in the engine compartment accounts for 10.32%of the CD value for the whole automobile.

Grey GM(1,1) Model with Function-Transfer Method for Wear Trend Prediction and its Application

Trend forecasting is an important aspect in fault diagnosis and work state supervision. The principle, where Grey theory is applied in fault forecasting, is that the forecast system is considered as a Grey system; the existing known information is used to infer the unknown information’s character, state and development trend in a fault pattern, and to make possible forecasting and decisions for future development. It involves the whitenization of a Grey process. But the traditional equal time interval Grey GM (1,1) model requires equal interval data and needs to bring about accumulating addition generation and reversion calculations. Its calculation is very complex. However, the non equal interval Grey GM (1,1) model decreases the condition of the primitive data when establishing a model, but its requirement is still higher and the data were pre processed. The abrasion primitive data of plant could not always satisfy these modeling requirements. Therefore, it establishes a division method suited for general data modeling and estimating parameters of GM (1,1), the standard error coefficient that was applied to judge accuracy height of the model was put forward; further, the function transform to forecast plant abrasion trend and assess GM (1,1) parameter was established. These two models need not pre process the primitive data. It is not only suited for equal interval data modeling, but also for non equal interval data modeling. Its calculation is simple and convenient to use. The oil spectrum analysis acted as an example. The two GM (1,1) models put forward in this paper and the new information model and its comprehensive usage were investigated. The example shows that the two models are simple and practical, and worth expanding and applying in plant fault diagnosis.

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 5 MHz, which indicated that the proposed transfer function could be useful for theoretical analysis and application of the galvanic coupling IBC.

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.

Multiple Scattering Between Adjacent Sound Sources in Head-Related Transfer Function Measurement System

To accelerate head-related transfer functions(HRTFs)measurement,two or more independent sound sources are usually employed in the measurement system.However,the multiple scattering between adjacent sound sources may influence the accuracy of measurement.On the other hand,the directivity of sound source could induce measurement error.Therefore,a model consisting of two spherical sound sources with approximate omni-directivity and a rigid-spherical head is proposed to evaluate the errors in HRTF measurement caused by multiple scattering between sources.An example of analysis using multipole re-expansion indicates that the error of ipsilateral HRTFs are within the bound of±1.0 dB below a frequency of 20 kHz,provided that the sound source radius does not exceed 0.025 m,the source distance relative to head center is not less than 0.5 m,and the angular interval between two adjacent sources is not less than 20 degrees.Similar conclusions under different conditions can also be analyzed and discussed by using this calculation method.Furthermore,the results are verified by measurements of HRTFs for a rigid sphere and a KEMAR artificial head.

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.

Geomagnetic vertical transfer function revealed from multi-interval geomagnetic data

The geomagnetic vertical transfer functions(VTFs)are useful to constrain the conductivity structure in the deep Earth.In this study,we propose an approach of estimating the geomagnetic VTFs in the wide:period range from the multi-interval geomagnetic data.Applying the above method to the different interval(such as one-second,one-minute,one-hour)data from some geomagnetic observatories in China,we obtain the corresponding VTFs in the wide period range from 64 s to 9,830,400 s.In order to evaluate the possible ocean effect on different observatories,we make close investigations of the real geomagnetic induction vectors at QZH,SYG and XIC observatories.The results indicate that the ocean effect is clear at the coastal observatory like QZH.However,the ocean effect tends to decrease for the inland observatories(such as SYG and XIC)with the increasing distance from the coast.