Frequency Coherence Functions Research Articles

Vibration characteristics of mineral composite beams by experimental modal test method

Abstract Some machines, such as heavy presses and rammers, can be exposed to big shock and inertial forces under dynamic severe working conditions. Even if vibration isolation to the foundations of machines operating under dynamic loads is applied, the exposure of these machines to shock and resonance loads may not be adequately prevented. The sensitivity of these machines, the product quality, or life span can also incredibly decrease. Therefore, it is essential to know the vibration behaviors of machine bodies and parts. This study investigates vibration characteristics of polymer matrix composite (PMC) materials by the experimental modal test method. Nine different composite beam samples having sizes of 20 × 25 × 480 mm were produced for modal tests. Composite beams contain different ratios of aggregate and epoxy resin. Each composite beam’s natural frequencies and damping ratios were defined with frequency response and coherence functions taken from the experimental modal tests. The results from the modal analysis revealed that the most influential parameter on the vibration properties was the gravel ratio. As a result of the experimental study, it was concluded that while epoxy-resin, gravel and fine-sand additives increased the stiffness of PMC beam, gravel and fine sand additives also increased the damping rate of PMC beam.

Wave field in a layer with a linear background profile and multiscale random irregularities

The paper addresses the problem of determining the field of a reflected wave in a multiscale inhomogeneous medium, which consists of a background deterministic large-scale irregularity and multiscale random irregularities with scales both larger and smaller than the wavelength. A layer with a linear permittivity profile is taken as the background irregularity. The small-scale irregularities are responsible for wide-angle scattering including backscattering. The first approximation of the perturbation theory is used to account for scattering from these irregularities. As the zero approximation and Green’s function in determining the field backscattered by small-scale irregularities, we utilize the integral representation of the field, obtained in our earlier work by combining the method of double weighted Fourier transform (DWFT) and the Fock proper-time method. Asymptotic methods are used to reduce the sevenfold integral representation of a field to lower-order integrals. Conditions for validity of such representations are obtained. Formulas of the frequency coherence functions of waves reflected and backscattered from the turbulent plasma layer are given. The paper presents the results of the simulation of pulse sounding of a randomly inhomogeneous reflecting plasma layer demonstrating the effect of large-scale irregularities on backscattering by small-scale irregularities.

Development of Acoustic Signal Generators Used for Calibration of Bioacoustic Sensing Devices

Purpose of research: We are developing and researching a BJAS device that senses bioacoustic information of health care related to the longevity of bipedal walking. BJAS-Bone joint acoustic sensor: We are developing a bioacoustic sensor that measures and diagnoses knee joint misalignment, lower limb balance decline, and lower limb muscle strength decline. Background: The number of elderly people who have difficulty walking due to longevity is increasing rapidly. The number of people requiring support and long-term care is increasing, and wasteful spending is increasing. Countermeasures: Building a body with a long walking life, developing an early walking diagnostic device, and its preventive effect will improve walking life. This report: We have developed an acoustic signal generator to test the performance of BJAS. The transfer function of this device was investigated. Transfer function: Gas transfer system and solid transfer system are set, and the input signals are sine sweep and random noise, frequency response function (FRF) and coherence function (Coh.). Result: The transfer function of each system is determined by the magnitude of the input signal, the attenuation of the system, and the eigenvalues of the signal generator. We were able to quantify the frequency characteristic PS of this signal transmission system. Conclusion: Although some corrections were found, this signal generator had sufficient functions for use in calibrating bioacoustic sensing devices.

Coherence properties of high-frequency wave field propagating through inhomogeneous ionosphere with anisotropic random irregularities of electron density: 1. Theoretical background

Rigorous analytic solution is constructed for the first of 2 s-order space position and frequency coherence function (which is alternatively also termed as symmetric) of the high-frequency wave field propagating through the stochastic transionospheric channel with the inhomogeneous layer of the background ionosphere and anisotropic fluctuations of the electron density in the approximation of the appropriate Markov equation. It is obtained employing the anisotropic parabolic model of the effective structure function of the fractional electron density fluctuations with two different scales along and across the Earth's magnetic field. The explicit analytic solution is presented, which is capable of describing the coherence properties of the field for any given inhomogeneous distribution of the electron density in the background ionosphere along a path of propagation. The procedure of calibrating the spatial scales of the anisotropic parabolic model of the electron density fluctuations along and across the Earth's magnetic field lines in order to provide the adequate solution to correspond to the realistic anisotropic inverse power law spectrum of the electron density fluctuations is presented in the companion paper.

Indoor Localization for IoT Using Adaptive Feature Selection: A Cascaded Machine Learning Approach

Evolving Internet-of-Things (IoT) applications often require the use of sensor-based indoor tracking and positioning, for which the performance is significantly improved by identifying the type of the surrounding indoor environment. This identification is of high importance since it leads to higher localization accuracy. This paper presents a novel method based on a cascaded two-stage machine learning approach for highly-accurate and robust localization in indoor environments using adaptive selection and combination of RF features. In the proposed method, machine learning is first used to identify the type of the surrounding indoor environment. Then, in the second stage, machine learning is employed to identify the most appropriate selection and combination of RF features that yield the highest localization accuracy. Analysis is based on k-Nearest Neighbor (k-NN) machine learning algorithm applied on a real dataset generated from practical measurements of the RF signal in realistic indoor environments. Received Signal Strength, Channel Transfer Function, and Frequency Coherence Function are the primary RF features being explored and combined. Numerical investigations demonstrate that prediction based on the concatenation of primary RF features enhanced significantly as the localization accuracy improved by at least 50% to more than 70%.

Classification of Indoor Environments for IoT Applications: A Machine Learning Approach

Evolving Internet-of-Things (IoT) applications often require the use of sensor-based indoor tracking and positioning, for which the performance is significantly improved by classifying the type of the surrounding indoor environment. This classification is of high importance since it leads to efficient power consumption when operating the deployed IoT sensors. This letter presents a machine learning approach for indoor environment classification based on real-time measurements of the radio frequency (RF) signal in a realistic environment. Several machine learning classification methods are explored including decision trees, support vector machine, and $k$ -nearest neighbor using different RF features. Results obtained show that a machine learning approach based on weighted $k$ -nearest neighbor method, which utilizes a combination of channel transfer function and frequency coherence function, outperforms the other methods in classifying the type of indoor environment with an accuracy of 99.3%. The predication time was found to be below 10 $\mu$ s, which verifies that the adopted algorithm is a successful candidates for real-time deployment scenarios.

Two-Frequency Coherence Function for the Field of a Wave Propagating Through a Multiscale Randomly Inhomogeneous Medium

We study the possibilities of integral representation for the two-frequency mutual coherence function of the wave field in a randomly inhomogeneous ionosphere. The integral representation was obtained using the Double Weighted Fourier Transform (DWFT) method. We point out that the conditions of validity of the geometrical-optics approximation for frequency coherence are weaker than the same condition for individual samples. Examples of calculation of the frequency coherence functions for waves in the ionospheric plasma with the irregularities described by the Gaussian spectrum and Shkarofsky’s model are given. Simulation results show that diffraction effects reduce the width of the frequency coherence function. The capabilities of the methods for spatial processing of the wave field and its two-frequency mutual coherence function, which eliminate these effects through the Fresnel and DWFT inversions, are examined.

Theory of corticothalamic brain activity in a spherical geometry: Spectra, coherence, and correlation.

Corticothalamic neural field theory is applied to a spherical geometry to better model neural activity in the human brain and is also compared with planar approximations. The frequency power spectrum, correlation, and coherence functions are computed analytically and numerically. The effects of cortical boundary conditions and resulting modal aspects of spherical corticothalamic dynamics are explored, showing that the results of spherical and finite planar geometries converge to those for the infinite planar geometry in the limit of large brain size. Estimates are made of the point at which modal series can be truncated and it is found that for physiologically plausible parameters only the lowest few spatial eigenmodes are needed for an accurate representation of macroscopic brain activity. A difference between the geometries is that there is a low-frequency 1/f spectrum in the infinite planar geometry, whereas in the spherical geometry it is 1/f^{2}. Another difference is that the alpha peak in the spherical geometry is sharper and stronger than in the planar geometry. Cortical modal effects can lead to a double alpha peak structure in the power spectrum, although the main determinant of the alpha peak is corticothalamic feedback. In the spherical geometry, the cross spectrum between two points is found to only depend on their relative distance apart. At small spatial separations the low-frequency cross spectrum is stronger than for an infinite planar geometry and the alpha peak is sharper and stronger due to the partitioning of the energy into discrete modes. In the spherical geometry, the coherence function between points decays monotonically as their separation increases at a fixed frequency, but persists further at resonant frequencies. The correlation between two points is found to be positive, regardless of the time lag and spatial separation, but decays monotonically as the separation increases at fixed time lag. At fixed distance the correlation has peaks at multiples of the period of the dominant frequency of system activity.

A Trunk Support System to Identify Posture Control Mechanisms in Populations Lacking Independent Sitting.

Populations with moderate-to-severe motor control impairments often exhibit degraded trunk control and/or lack the ability to sit unassisted. These populations need more research, yet their underdeveloped trunk control complicates identification of neural mechanisms behind their movements. The purpose of this study was to overcome this barrier by developing the first multi-articulated trunk support system to identify visual, vestibular, and proprioception contributions to posture in populations lacking independent sitting. The system provided external stability at a user-specific level on the trunk, so that body segments above the level of support required active posture control. The system included a tilting surface (controlled via servomotor) as a stimulus to investigate sensory contributions to postural responses. Frequency response and coherence functions between the surface tilt and trunk support were used to characterize system dynamics and indicated that surface tilts were accurately transmitted up to 5 Hz. Feasibility of collecting kinematic data in participants lacking independent sitting was demonstrated in two populations: two typically developing infants, [Formula: see text] months, in a longitudinal study (eight sessions each) and four children with moderate-to-severe cerebral palsy (GMFCS III-V). Adaptability in the system was assessed by testing 16 adults (ages 18-63). Kinematic responses to continuous pseudorandom surface tilts were evaluated across 0.046-2 Hz and qualitative feedback indicated that the trunk support and stimulus were comfortable for all subjects. Concepts underlying the system enable both research for, and rehabilitation in, populations lacking independent sitting.

Frequency coherence function of a space–time radar channel forming images of an anisotropic fractal surface and fractal objects

The theory of the field frequency coherence function is developed and generalized in the Kirchhoff approximation for the case of a space–time radar channel for sensing and formation of radar images of a 2D anisotropic fractal surface and fractal objects. Mathematical modeling of 2D fractal surfaces and extended fractal objects is performed.

The altered vestibular-evoked myogenic and whole-body postural responses in old men during standing

Age-related decrements within the sensorimotor system may lead to alterations and impairments in postural control, but a link to a vestibular mechanism is unclear. The purpose of the present study was to determine whether vestibular control of standing balance is altered with adult aging. Eight old (~77years) and eight young (~26years) men stood without aids on a commercially available force plate with their head turned to the right, arms relaxed at their sides and eyes closed while receiving stochastic vestibular stimuli (0–25Hz, root mean square amplitude=0.85mA). Surface electromyography signals were sampled from the left soleus, medial gastrocnemius and tibialis anterior. Whole-body balance, as measured by the anteroposterior forces and muscle responses, was quantified using frequency (coherence and gain functions) and time (cumulant density function) domain correlations with the vestibular stimuli. Old men exhibited a compressed frequency response of the vestibular reflex with a greater relative gain at lower frequencies for the plantar flexors and anteroposterior forces than young. In the time domain, the peak amplitude of the short latency response was 45–64% lower for the plantar flexors and anteroposterior forces (p≤0.05) in the old than young, but not for the tibialis anterior (p=0.21). The old men had a 190% and 31% larger medium latency response for only the tibialis anterior and anteroposterior forces, respectively, than young (p≤0.01). A strong correlation between the tibialis anterior and the force response was also detected (r=0.80, p<0.01). In conclusion, net vestibular-evoked muscle responses led to smaller short and larger medium latency peak amplitudes in anteroposterior forces for the old. The present results likely resulted from a compressed and lower operational frequency range of the vestibular reflexes and the activation of additional muscles (tibialis anterior) to maintain standing balance.

A Wavelet Approach for Identification of Linear Time Invariant System

Wavelet transformation has been applied to various problems of system identification. In this paper, a wavelet based approach for the identification of time-invariant system is proposed. In this approach, mother wavelet is used for excitation to find the impulse response, which can be estimated at half the available number of points of the sampled output sequence. This method has been compared with some other standard techniques such as frequency chirp, coherence function and inverse filtering. In chirp method, wideband excitation such as frequency chirp is used. Frequency response is obtained as the DFT of the output of the system for time-domain input. Inverse method uses SVD function to find pseudoinverse. Coherence function has been used to identify the system using MATLAB function tfestimate. The performances of the methods are demonstrated by means of experimental investigation.

Optimal Settings for Measuring Frequency Response Functions With Weighted Overlapped Segment Averaging

This paper investigates the measurement errors involved in estimating frequency response functions (FRFs) - and related quantities such as the coherence function - from weighted overlapped segment averaging, a technique that has become a standard in modern data analyzers due to its computational advantages. Particular attention is paid to leakage errors, for which this technique has frequently been criticized. Our main result is that a half-sine or diff window with about 2/3 overlap achieves the best compromise to reduce leakage errors in the case of stationary random excitations, and this is independently of the system FRF. This conclusion is to be contrasted with the customary habit of using a Hanning window with 1/2 overlap. The same reasoning confirms that a rectangular window without overlap minimizes measurement errors in the special case of multisine excitations. Moreover, practical formulas are provided to the reader for computing the bias and variance of the frequency response and coherence functions in the general case.

A Fortran 90 library for multitaper spectrum analysis

The spectral analysis of geological and geophysical data has been a fundamental tool in understanding Earth's processes. We present a Fortran 90 library for multitaper spectrum estimation, a state-of-the-art method that has been shown to outperform the standard methods. The library goes beyond power spectrum estimation and extracts for the user more information including confidence intervals, diagnostics for single frequency periodicities, and coherence and transfer functions for multivariate problems. In addition, the sine multitaper method can also be implemented. The library presented here provides the tools needed in multiple fields of the Earth sciences for the analysis of data as evident from various examples.

Dynamic properties of Drosophila olfactory electroantennograms

Time-dependent properties of chemical signals are probably crucially important to many animals, but little is known about the dynamics of chemoreceptors. Behavioral evidence of dynamic sensitivity includes the control of moth flight by pheromone plume structure, and the ability of some blood-sucking insects to detect varying concentrations of carbon dioxide, possibly matched to host breathing rates. Measurement of chemoreceptor dynamics has been limited by the technical challenge of producing controlled, accurate modulation of olfactory and gustatory chemical concentrations over suitably wide ranges of amplitude and frequency. We used a new servo-controlled laminar flow system, combined with photoionization detection of surrogate tracer gas, to characterize electroantennograms (EAG) of Drosophila antennae during stimulation with fruit odorants or aggregation pheromone in air. Frequency response functions and coherence functions measured over a bandwidth of 0-100 Hz were well characterized by first-order low-pass linear filter functions. Filter time constant varied over almost a tenfold range, and was characteristic for each odorant, indicating that several dynamically different chemotransduction mechanisms are present. Pheromone response was delayed relative to fruit odors. Amplitude of response, and consequently signal-to-noise ratio, also varied consistently with different compounds. Accurate dynamic characterization promises to provide important new information about chemotransduction and odorant-stimulated behavior.

Damage localization using transient non-linear elastic wave spectroscopy on composite structures

To reduce the costs related to maintenance of aircraft structures, there is the need to develop new robust, accurate and reliable damage detection methods. A possible answer to this problem is offered by newly developed non-linear acoustic/ultrasonic techniques, which monitor the non-linear elastic wave propagation behaviour introduced by damage, to detect its presence and location. In this paper, a new transient non-linear elastic wave spectroscopy (TNEWS) is presented for the detection and localization of a scattered zone (damage) in a composite plate. The TNEWS analyses the uncorrelations between two structural dynamic responses generated by two different pulse excitation amplitudes by using a time–frequency coherence function. A numerical validation of the proposed method is presented. Damage was introduced and modelled using a multi-scale material constitutive model (Preisach–Mayergoyz space). The developed technique identified in a clear manner the faulted zone, showing its robustness to locate and characterize non-linear sources in composite materials

The theory of functionals of stochastic backscattered fields

The theory of wave scattering by anisotropic statistically rough surfaces, which is an important part of statistical radiophysics, is considered. A new analytic method is developed and generalized for solving problems of radar imaging. The method involves analytic determination of the functionals of stochastic backscattered fields and can be applied to solve a wide class of physical problems with allowance for the finite width of an antenna’s pattern. The unified approach based on this method is used to analyze the generalized frequency response of a scattering radio channel, a generalized correlator of scattered fields, spatial correlation functions of stochastic backscattered fields, frequency coherence functions of stochastic backscattered fields, the coherence band of a spatial-temporal scattering radar channel, the kernel of the generalized uncertainty function, and the measure of noise immunity characterizing radar probing of the Earth’s surface or extended targets. The introduced frequency coherence functions are applied for thorough and consistent study of techniques for measuring the characteristics of a rough surface, aircraft altitude, and distortions observed when radar signals are scattered by statistically rough, including fractal, surfaces. To exemplify urgent applications, radiophysical synthesis of detailed digital reference radar terrain maps and microwave radar images that was proposed earlier is considered and improved with the use of the theory of fractals.

A new damage detection technique based on wave propagation for rails

This paper presents a novel damage detection technique, tailored at the identification of structural surface damage on rail structures. The damage detection, proposed in this paper, exploits the wave propagation phenomena ( P, S, Rayleigh and guided wave velocities) by identifying discrepancies, due to damage presence, in the dynamic behaviour of the structure. The uncorrelations are generated by waves reflected back to the sensor locations by the flaw surfaces. The peculiarity of the presented approach is the use of a time frequency coherence function for the identification of the arrivals of guided wave reflected back to the sensors by the damage surfaces. The damage detection methodology developed was divided into three steps. In the first step, the presence of the damage on the structure was assessed. In the second step, the arrival time of the reflected wave (or echo) was estimated using the continuous wavelet transform. Then, the detection algorithm was able, through a ray-tracing algorithm, to estimate the location of damage. A numerical investigation of two single damages was carried out. The damage was introduced on the railhead surface to simulate rolling contact fatigue defects. The results showed that the proposed methodology can be used successfully to localise the damage location, however, as expected, the localisation is strongly affected by the frequency range used. The results suggested that the separation and the characterisation of single modes are crucial for the identification of different types of rail defects. Further work is needed to establish the damage severity by relating the magnitude of the changes of the time frequency coherence to reflection and attenuation coefficients of each guided wave used and on the selection of the best range of frequency according to the type of damage to be identified.

Dynamic Properties of Antennal Responses to Pheromone in Two Moth Species

Dynamic properties of pheromone plumes are behaviorally important in some moths for inducing upwind flight, but little is known about the time-dependent properties of odor transduction or the mechanisms that limit receptor dynamic sensitivity. We stimulated male antennae of two moth species, Cadra cautella and Spodoptera exigua, with pheromone plumes in a wind tunnel while recording electroantennograms (EAG) and concentration of a surrogate plume (propylene, which mimics a pheromone plume) using a photoionization detector (PID). Turbulent plumes were produced by mechanical baffles, creating broad frequency range dynamic concentration changes at the antennae. Frequency response functions and coherence functions between PID and EAG signals were used to measure the dynamic responses of the two species to pheromone blends and individual components. A single time constant filter fitted the responses of both species, but S. exigua was about three times faster than C. cautella. Responses to individual pheromone components were significantly different in S. exigua but not in C. cautella. We also fitted the data with a simple block-structured nonlinear cascade. This supported the simple filter model but also suggested that the response saturates at an early stage of chemotransduction.

Quasi‐classic approximation in Markov's parabolic equation for spaced position and frequency coherency

An asymptotic technique to solve Markov's parabolic equation for the second‐order spaced position and frequency coherence function is discussed. Rather than employing separation of variables, the technique is based on the quasi‐classic representation in terms of complex trajectories and is also valid in the case of a nonhomogeneous background medium and does not demand the statistical homogeneity of fluctuations. It has no constraints relevant to the initial conditions in the form of an incident plane wave and produces in automatic fashion different known rigorous solutions, in particular, to the case of quadratic structure function.