Harmonic Response Components Research Articles

An extended binary subband canonical correlation analysis detection algorithm oriented to the radial contraction-expansion motion steady-state visual evoked paradigm

The radial contraction-expansion motion paradigm is a novel steady-state visual evoked experimental paradigm, and the electroencephalography (EEG) evoked potential is different from the traditional luminance modulation paradigm. The signal energy is concentrated chiefly in the fundamental frequency, while the higher harmonic power is lower. Therefore, the conventional steady-state visual evoked potential recognition algorithms optimizing multiple harmonic response components, such as the extended canonical correlation analysis (eCCA) and task-related component analysis (TRCA) algorithm, have poor recognition performance under the radial contraction-expansion motion paradigm. This paper proposes an extended binary subband canonical correlation analysis (eBSCCA) algorithm for the radial contraction-expansion motion paradigm. For the radial contraction-expansion motion paradigm, binary subband filtering was used to optimize the weighting coefficients of different frequency response signals, thereby improving the recognition performance of EEG signals. The results of offline experiments involving 13 subjects showed that the eBSCCA algorithm exhibits a better performance than the eCCA and TRCA algorithms under the stimulation of the radial contraction-expansion motion paradigm. In the online experiment, the average recognition accuracy of 13 subjects was 88.68% ± 6.33%, and the average information transmission rate (ITR) was 158.77 ± 43.67 bits/min, which proved that the algorithm had good recognition effect signals evoked by the radial contraction-expansion motion paradigm.

Detection and localization of fatigue-induced transverse crack in a rotor shaft using principal component analysis

Rotor shafts subjected to severe operating stresses are prone to develop transverse fatigue cracks at the localized stress raisers. Therefore, the ability to identify and locate the incipient fatigue crack is imperative in order to avoid catastrophic failure. The literature on rotor crack detection discussed the importance of monitoring the steady-state 1X, 2X and 3X harmonic response components of rotors. However, the other rotor faults such as misalignment and unbalance, exhibit similar symptoms. Thus, the main aim is to develop new independent fault-related features which measure the driving principle governing the behaviour of various rotor faults. In this article, the application of principal component analysis–based statistical pattern analysis, as a tool for early detection and localization of fatigue-induced transverse crack in a rotor shaft is investigated. To perform this study, accelerated fatigue experiments are conducted on a customized setup. This developed test rig is novel and unique by itself that facilitates generating a fatigue crack in a shaft, under conditions that mimic a real in-service loading environment of industrial rotors. Unlike conventional methods, noise in the acquired vibration and strain data is denoised via classical principal component analysis method. Time- and frequency-domain statistical features extracted from different vibration and strain sensor signals are used for this study. Damage indices such as Hotelling’s T2-statistic and Q-index are used to detect the presence of the crack. It is observed that irrespective of the sensor location, damage index such as Q-statistic of all the sensors is very effective to detect the presence and time of incipient crack. Partial decomposition contributions method is found to be very effective in identifying the location of the crack. This article provides the most significant vibration-based statistical features, which are sensitive to shaft transverse cracks, for different sensor types and their mounting location. Finally, a new fused health indicator which is highly sensitive to the presence of rotor shaft crack is defined and is found successful when applied to a new experimental data.

Temporal Frequency Abnormalities in Early-Stage Diabetic Retinopathy Assessed by Electroretinography.

PurposeTo define the nature and extent of temporal frequency abnormalities in diabetics who have mild or no nonproliferative diabetic retinopathy (NPDR) by using the flicker electroretinogram (ERG).MethodsLight-adapted flicker ERGs were recorded from 20 diabetics who have no clinically apparent retinopathy, 20 diabetics who have mild NPDR, and 20 nondiabetic, age-equivalent controls. ERGs were elicited by full-field sinusoidal flicker across the temporal frequency range of 6 to 100 Hz and were recorded using conventional techniques. The amplitude and phase of the fundamental and harmonic response components were derived by Fourier analysis and compared among the groups.ResultsAnalysis of variance indicated that compared with the controls, both patient groups had significant amplitude reductions of the fundamental ERG component for temporal frequencies greater than 56 Hz (all P ≤ 0.03). Modeling the amplitude measurements indicated that both patient groups had significant reductions in the high-frequency response cutoff. Response phase, however, did not differ significantly among the groups at any frequency. The amplitude and phase of the high-frequency harmonics (32–96 Hz) of the patients' responses to a low-frequency stimulus (16 Hz) were normal over the temporal frequency range that the fundamental response was abnormal.ConclusionsTaken together, the diabetics' fundamental amplitude attenuation for rapid flicker combined with their normal high-frequency harmonic responses generated by slow flicker suggest that the likely site of the abnormal temporal filtering occurs prior to the nonlinearity that generates the harmonic components of the ERG, implicating a photoreceptor origin.

Changes in the harmonic components of the flicker electroretinogram during light adaptation.

To evaluate the nature and extent of changes in the fundamental and harmonic components of the 31-Hz flicker electroretinogram (ERG) during light adaptation. Full-field ERGs were recorded from five visually normal subjects (ages 21-60 years). Following 30 min of dark adaptation, the subjects were exposed to a uniform adapting field of 50 cd/m(2). The field, which was presented for approximately 15 min, was intermittently modulated sinusoidally at 31.25 Hz. The ERG was recorded during the sinusoidal modulation, and Fourier analysis was used to obtain the amplitude and phase of the fundamental (F), second (2F), and third (3F) harmonic response components. F amplitude increased by almost a factor of two over approximately 6 min (time constant, τ, of 3.0 min). The 2F amplitude increased by a smaller amount, a factor of 1.4, and the time-course was approximately eight times faster than that of F (τ = 0.4 min). The 3F amplitude increased by a factor of 4.6, an increase that was larger than F or 2F, with a time-course that was between that of F and 2F (τ = 1.4 min). F phase was unaffected by light adaptation, whereas the 2F and 3F phases both increased by approximately 45° over similar time-courses (τ = 2.0 min). Light adaptation had different effects on the fundamental, second, and third harmonic components of the 31-Hz flicker ERG, which resulted in a change in waveform shape during light adaptation. The previously reported flicker ERG amplitude growth is driven primarily, but not entirely, by changes in the fundamental.

Crack Detection in a Rotor Dynamic System by Vibration Monitoring—Part II: Extended Analysis and Experimental Results

Abstract An increase in the power-to-weight ratio demand on rotordynamic systems causes increased susceptibility to transverse fatigue cracking of the shaft. The ability to detect cracks at an early stage of progression is imperative for minimizing off-line repair time and cost. The vibration monitoring system initially proposed in Part I is employed herein, using the 2X harmonic response component of the rotor tilt as a signature indicating a transverse shaft crack. In addition, the analytic work presented in Part I is expanded to include a new notch crack model to better approximate experimental results. To effectively capture the 2X response, the crack model must include the local nature of the crack, the depth of the crack, and the stiffness asymmetry inducing the gravity-forced 2X harmonic response. The transfer matrix technique is well suited to incorporate these crack attributes due to its modular nature. Two transfer matrix models are proposed to predict the 2X harmonic response. The first model applies local crack flexibility coefficients determined using the strain energy release rate, while the second incorporates the crack as a rectangular notch to emulate a manufactured crack used in the experiments. Analytic results are compared to experimental measurement of the rotor tilt gleaned from an overhung rotor test rig originally designed to monitor seal face dynamics. The test rig is discussed, and experimental angular response orbits and 2X harmonic amplitudes of the rotor tilt are provided for shafts containing manufactured cracks of depths between 0% and 40%. Feasibility of simultaneous multiple-fault detection of transverse shaft cracks and seal face contact is discussed.

The Influence of Different Retinal Subcircuits on the Nonlinearity of Ganglion Cell Behavior

Y-type retinal ganglion cells show a pronounced, nonlinear, frequency-doubling behavior in response to modulated sinewave gratings. This is not observed in X-type cells. The source of this spatial nonlinear summation is still under debate. We have designed a realistic biophysical model of the cat retina to test the influence of different retinal cell classes and subcircuits on the linearity of ganglion cell responses. The intraretinal connectivity consists of the fundamental feedforward pathway via bipolar cells, lateral horizontal cell connectivity, and two amacrine circuits. The wiring diagram of X- and Y-cells is identical apart from two aspects: (1) Y-cells have a wider receptive field and (2) they receive input from a nested amacrine circuit consisting of narrow- and wide-field amacrine cells. The model was tested with contrast-reversed gratings. First and second harmonic response components were determined to estimate the degree of nonlinearity. By means of circuit dissection, we found that a high degree of the Y-cell nonlinear behavior arises from the spatial integration of temporal photoreceptor nonlinearities. Furthermore, we found a weaker and less uniform influence of the nested amacrine circuit. Different sources of nonlinearities interact in a multiplicative manner, and the influence of the amacrine circuit is approximately 25% weaker than that of the photoreceptor. The model predicts that significant nonlinearities occur already at the level of horizontal cell responses. Pharmacological inactivation of the amacrine circuit is expected to exert a milder effect in reducing ganglion cell nonlinearity.

Nonlinear dynamic behaviour of guy cables in turbulent winds

Large amplitude cable vibrations are difficult to predict using linear theory due to the presence of sag in the suspended profile. A numerical study was therefore undertaken to investigate the dynamic behaviour of inclined cables excited by imposed displacements. To model the nonlinear nature of cable response, a time domain finite element approach was adopted using nonlinear catenary cable elements. Two types of horizontal displacement patterns were enforced at the upper end of the guy. In the first phase of the study, harmonic displacement histories with a wide range of forcing frequencies were considered. In the second phase, random enforced displacements were used to simulate the motion of a guyed mast in gusty winds. The influence of aerodynamic drag and damping forces was investigated by performing analyses under still air, steady wind, and turbulent wind conditions. It was found that nonlinear coupling of related harmonic response components was significant at certain critical frequencies, particular when the excitation was harmonic and acted in the plane of the guy. Positive aerodynamic damping was shown to effectively suppress resonant and nonlinear coupling response.Key words: cables, structural dynamics, wind loading, finite element method, nonlinear analysis, guyed towers.

Nonlinear dynamic behaviour of guy cables in turbulent winds

Large amplitude cable vibrations are difficult to predict using linear theory due to the presence of sag in the suspended profile. A numerical study was therefore undertaken to investigate the dynamic behaviour of inclined cables excited by imposed displacements. To model the nonlinear nature of cable response, a time domain finite element approach was adopted using nonlinear catenary cable elements. Two types of horizontal displacement patterns were enforced at the upper end of the guy. In the first phase of the study, harmonic displacement histories with a wide range of forcing frequencies were considered. In the second phase, random enforced displacements were used to simulate the motion of a guyed mast in gusty winds. The influence of aerodynamic drag and damping forces was investigated by performing analyses under still air, steady wind, and turbulent wind conditions. It was found that nonlinear coupling of related harmonic response components was significant at certain critical frequencies, particular when the excitation was harmonic and acted in the plane of the guy. Positive aerodynamic damping was shown to effectively suppress resonant and nonlinear coupling response.Key words: cables, structural dynamics, wind loading, finite element method, nonlinear analysis, guyed towers.

The response of cat visual cortex to flicker stimuli of variable frequency.

We examined the possibility that neurons or groups of neurons along the retino-cortical transmission chain have properties of tuned oscillators: To this end, we studied the resonance properties of the retino-thalamo-cortical system of anaesthetized cats by entraining responses with flicker stimuli of variable frequency (2-50 Hz). Responses were assessed from multi-unit activity (MUA) and local field potentials (LFPs) with up to four spatially segregated electrodes placed in areas 17 and 18. MUA and LFP responses were closely related, units discharging with high preference during LFP negativity. About 300 ms after flicker onset, responses stabilized and exhibited a highly regular oscillatory patterning that was surprisingly similar at different recording sites due to precise stimulus locking. Fourier transforms of these steady state oscillations showed maximal power at the inducing frequency and consistently revealed additional peaks at harmonic frequencies. The frequency-dependent amplitude changes of the fundamental and harmonic response components suggest that the retino-cortical system is entrainable into steady state oscillations over a broad frequency range and exhibits preferences for distinct frequencies in the theta- or slow alpha-range, and in the beta- and gamma-band. Concomitant activation of the mesencephalic reticular formation increased the ability of cortical cells to follow high frequency stimulation, and enhanced dramatically the amplitude of first- and second-order harmonics in the gamma-frequency range between 30 and 50 Hz. Cross-correlations computed between responses recorded simultaneously from different sites revealed pronounced synchronicity due to precise stimulus locking. These results suggest that the retino-cortical system contains broadly tuned, strongly damped oscillators which altogether exhibit at least three ranges of preferred frequencies, the relative expression of the preferences depending on the central state. These properties agree with the characteristics of oscillatory responses evoked by non-temporally modulated stimuli, and they indicate that neuronal responses along the retino-cortical transmission chain can become synchronized with precision in the millisecond range not only by intrinsic interactions, but also by temporally structured stimuli.

The first and second harmonics of the macular flicker electroretinogram: differential effects of retinal diseases.

We evaluated the effects of retinal diseases on the macular electroretinogram first and second harmonic components, which are dominated by outer and inner retinal activity, respectively. Macular electroretinograms in response to a uniform field (9 degrees x 9 degrees) flickering sinusoidally at either 32 or 8 Hz (peak frequencies of the first and second harmonics, respectively) were recorded in 14 patients with maculopathies involving photoreceptors (e.g., age-related macular degeneration), in 16 patients with postreceptoral macular diseases (e.g., branch occlusion of central retinal artery), and in 38 normal controls. Amplitude and phase of the first and second harmonic response components were evaluated by Fourier analysis. When compared to controls, patients with photoreceptor diseases had reduction in both first and second harmonic mean amplitudes and second harmonic phase delay; patients with postreceptoral diseases had normal first harmonic components but reduced and delayed second harmonic components. A discriminant analysis, by using first and second harmonic values, correctly classified 13 of 14 patients with photoreceptor diseases and 14 of 16 patients with postreceptoral disorders. These results indicate that combined evaluation of the macular electroretinogram first and second harmonic components is a useful test for identifying the site(s) of retinal dysfunction in patients with macular diseases.

Binocular interactions in the cat's dorsal lateral geniculate nucleus. I. Spatial-frequency analysis of responses of X, Y, and W cells to nondominant-eye stimulation

1. X, Y, and W cells in the A and C layers of the cat's dorsal lateral geniculate nucleus (LGN) were tested for responses to stimulation of the nondominant eye. The main purpose was to determine the incidence of nondominant-eye excitation and inhibition among different classes of cells and to examine the spatial-frequency tuning of responses to the nondominant eye. 2. Of 198 cells that were tested with drifting sine-wave gratings presented to the nondominant eye, 109 (55%) showed statistically significant responses. Four types of responses were observed: an increase in the mean discharge rate (F0 excitation), a decrease in the mean discharge rate (F0 inhibition), an increased modulation at the fundamental frequency of the grating (F1 excitation), and a decreased modulation at the fundamental frequency of the grating (F1 inhibition). Overall, 29% of the cells responded with inhibition, 24% responded with excitation, and 2% showed both excitation and inhibition, depending upon the spatial frequency and/or the harmonic response component. The relative incidence of excitation and inhibition was similar for X, Y, and W cells, for cells with on-center and off-center receptive fields, for cells with different receptive-field eccentricities, and for cells in each LGN layer. In addition, within layers A and A1, responses were similar for cells at different distances from the laminar borders. 3. Spatial-frequency response functions indicated that cells could have band-pass or low-pass spatial-frequency tuning through the nondominant eye. Band-pass cells tended to be narrowly tuned (less than or equal to 1 octave), and low-pass cells responded to a broader range of spatial frequencies. These properties were similar for X, Y, and W cells. Spatial resolution tended to be low (less than or equal to 0.8 c/deg for most cells), although a few cells responded to the highest spatial frequency tested (5.4 c/deg). Likewise, optimal spatial frequency was low (less than or equal to 0.2 c/deg) for most cells. These properties were similar for X and Y cells, and there was a weak tendency for X and Y cells to have higher optimal spatial frequencies and spatial resolutions than W cells. 4. In terms of absolute change in activity, responses to drifting gratings were weak. However, cells that were inhibited generally showed 20-60% decreases in activity to the optimal spatial frequency, and cells that were excited generally showed 40-100% increases. Response amplitudes were similar for X, Y, and W cells.(ABSTRACT TRUNCATED AT 400 WORDS)

The structure of the terminal arborizations of physiologically identified retinal ganglion cell Y axons in the kitten.

Retinal ganglion cell (r.g.c.) axons (n = 17) in the optic tract of 4-5 week-old kittens and adult cats (n = 4, this study, n = 27 from other reports) were studied both physiologically and morphologically. Axons were initially classified during extracellular recording with a battery of physiological tests that included Fourier analysis of the response to a sinusoidally counterphased sine-wave grating. Y axons had a significant second harmonic response component (greater than twice the fundamental) present independent of the spatial phase position of the grating. These axons were then recorded from intracellularly and subsequently filled ionophoretically with horseradish peroxidase (HRP). The HRP filled the axons' terminal arborizations in the dorsal lateral geniculate nucleus (l.g.n.). The innervation pattern and and structure of the terminal arborizations of the kitten r.g.c. Y axons were compared to those of the adult. The kitten Y axons innervated the l.g.n. in a pattern similar to that of the adult (individual branches from a single axon always innervated lamina A or A1 and may also have innervated lamina C, the medial interlaminar nucleus (m.i.n.) and/or sent branches that coursed medial to the l.g.n.). Fourteen of seventeen of these Y axons in the kitten innervated either of the A-laminae heavily (greater than 200 terminal boutons per axon). The remaining three r.g.c. Y axons in the kitten had only small arborizations within lamina A (less than fifty terminal boutons per axon) but heavily innervated lamina C. The structure of the terminal boutons on the kitten r.g.c. Y axons was highly variable when compared to axons of adult cats. Some of the boutons were spherical or crenulated as in the adult. Many others had filopodia and growth cone-like terminals with fine extensions. This variable maturation of terminal boutons was seen both between axons and on individual axons. The number of boutons on the kitten r.g.c. Y axons in the A-laminae was significantly less than that of adult Y axons. The mean numbers of boutons per axon were 476 and 1553 in the kittens and adult cats, respectively (P less than 0.001, Mann-Whitney U test). The width of the terminal arborization of individual Y axons in the A-laminae of the kittens was considerably smaller than in adult cats (mean widths of the terminal arborizations are 192 and 293 micron in the kittens and adult cats, respectively).(ABSTRACT TRUNCATED AT 400 WORDS)

Different patterns of harmonics in frequency-following responses.

Preliminary studies (Krogh et al., 1977) indicated pronounced intersubject differences with respect to harmonic distortion in the frequency-following responses (FFRs) elicited by high intensity, low frequency stimuli and recorded by means of surface electrodes from man. In the present investigation it was confirmed that the responses from 10 test subjects could be divided into three significantly different patterns on the basis of the relative amplitudes of the fundamental (first harmonic) and the second harmonic response component as measured by spectral analyses. In three of the subjects the ratio of the fundamental to the second harmonic was greater than 10 dB (which were termed a type I response). In five, the ratio was between 0 and 10 dB (type II response) and in two the second harmonic was equal to or greater than the fundamental (type III response). The possible causes of harmonic distortion if FFRs are discussed, but not definite explanation of the interindividual differences can be given. A psychoacoustical evaluation of the second harmonic distortion using a tone-on-tone octave masking technique (TOM) showed no correlation between TOM results and FFR type in 10 subjects.