The “α-Invariant”: An Energy-Based Nonlinear Minimal Damping Model for Robotic Joints With Friction

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Bart Milne ◽  
Chris Hann ◽  
XiaoQi Chen
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Low Frequency ◽  
Friction Model ◽  
Friction Behavior ◽  
Low Frequencies ◽  
Local Linear ◽  
Steady State Responses ◽  
Energy Dissipated ◽  
State Responses

System identification of the sinusoidal steady-state response of the Phantom Omni using a local linear model revealed that friction has a non-negligible effect on the accuracy of a global linear model, particularly at low frequencies. Some of the obvious errors observed with the global linear model at low frequencies were (i) the response amplitude was lower; (ii) local linear model coefficients became physically impossible (e.g., negative) at low frequencies; and (iii) low frequency inputs resulted in a greater nonlinearity in the response compared to higher frequency inputs. While standard friction models such as Coulomb friction could be used to model the nonlinearity, there is a desire to create a friction model that is not only accurate for sinusoidal steady-state responses, but can also be generalized to any input response. One measure that is universally present in dynamical systems is energy, and in this paper the relationship between a generalized measure of energy and damping for modeling the effect of friction is developed. This paper introduces the “α-invariant” as a means of generalizing the friction behavior observed with sinusoidal steady-state responses to other waveforms. For periodic waveforms, the α-invariant is shown to be equivalent to the energy dissipated in each cycle, which demonstrates the physical significance of this quantity. The α-invariant nonlinear model formulation significantly outperforms the linear model for both sinusoidal steady state and step responses, demonstrating that this method accurately represents the physical mechanisms in the Phantom Omni. Overall, the α-invariant provides an efficient way of capturing nonlinear dynamics with a small number of parameters and experiments.

Steady-state BOLD Response to Higher-order Cognition Modulates Low-Frequency Neural Oscillations

2015 ◽  
Vol 27 (12) ◽  
pp. 2406-2415 ◽  
Author(s):  
Yi-Feng Wang ◽  
Gang-Shu Dai ◽  
Feng Liu ◽  
Zhi-Liang Long ◽  
Jin H. Yan ◽  
...  
Keyword(s):  
Steady State ◽  
Evoked Potentials ◽  
Low Frequency ◽  
Higher Order ◽  
Neural Oscillations ◽  
Behavioral Performance ◽  
Frequency Range ◽  
Steady State Responses ◽  
State Responses ◽  
Basic Cognition

Steady-state responses (SSRs) reflect the synchronous neural oscillations evoked by noninvasive and consistently repeated stimuli at the fundamental or harmonic frequencies. The steady-state evoked potentials (SSEPs; the representative form of the SSRs) have been widely used in the cognitive and clinical neurosciences and brain–computer interface research. However, the steady-state evoked potentials have limitations in examining high-frequency neural oscillations and basic cognition. In addition, synchronous neural oscillations in the low frequency range (<1 Hz) and in higher-order cognition have received a little attention. Therefore, we examined the SSRs in the low frequency range using a new index, the steady-state BOLD responses (SSBRs) evoked by semantic stimuli. Our results revealed that the significant SSBRs were induced at the fundamental frequency of stimuli and the first harmonic in task-related regions, suggesting the enhanced variability of neural oscillations entrained by exogenous stimuli. The SSBRs were independent of neurovascular coupling and characterized by sensorimotor bias, an indication of regional-dependent neuroplasticity. Furthermore, the amplitude of SSBRs may predict behavioral performance and show the psychophysiological relevance. Our findings provide valuable insights into the understanding of the SSRs evoked by higher-order cognition and how the SSRs modulate low-frequency neural oscillations.

Predicting Pure-Tone Thresholds with Dichotic Multiple Frequency Auditory Steady State Responses

2005 ◽  
Vol 16 (01) ◽  
pp. 005-017 ◽  
Author(s):  
Dunay Schmulian ◽  
DeWet Swanepoel ◽  
René Hugo
Keyword(s):  
Steady State ◽  
Pure Tone ◽  
Low Frequency ◽  
Tone Burst ◽  
Multiple Frequency ◽  
Recording Time ◽  
Steady State Responses ◽  
Pure Tones ◽  
Auditory Steady State Responses ◽  
State Responses

The accuracy of dichotic multiple frequency auditory steady state in predicting pure-tone thresholds at 0.5, 1, 2, and 4.0 kHz compared to an ABR protocol (click and tone burst at 0.5 kHz) were explored in a group of 25 hearing-impaired subjects across the degree and configuration spectrum. Mean steady state thresholds were within 14, 18, 15, and 14 dB of the pure tones at 0.5, 1, 2, and 4 kHz, compared to the tone-burst ABR at 0.5 kHz pure-tone difference of 24 dB, and a click-evoked pure-tone (2–4 kHz) difference of 9 dB. Recording time for the steady state protocol was 28 minutes (+/-11) compared to 24 minutes (+/- 9) of the ABR protocol. Degree of loss had a significant effect on steady state; configuration of hearing loss had a limited effect. Mf ASSR predicted thresholds with relative accuracy although some configurations showed discrepancies for low-frequency estimates.

Advantages and Caveats When Recording Steady-State Responses to Multiple Simultaneous Stimuli

2002 ◽  
Vol 13 (05) ◽  
pp. 246-259 ◽  
Author(s):  
M. Sasha John ◽  
David W. Purcell ◽  
Andrew Dimitrijevic ◽  
Terence W. Picton
Keyword(s):  
Steady State ◽  
Evoked Potential ◽  
Low Frequency ◽  
Single Stimulus ◽  
Multiple Response ◽  
Signal To Noise ◽  
Multiple Stimulus ◽  
Steady State Responses ◽  
Time Required ◽  
State Responses

This article considers the efficiency of evoked potential audiometry using steady-state responses evoked by multiple simultaneous stimuli with carrier frequencies at 500, 1000, 2000, and 4000 Hz. The general principles of signal-to-noise enhancement through averaging provide a basis for determining the time required to estimate thresholds. The advantage of the multiple-stimulus technique over a single-stimulus approach is less than the ratio of the number of stimuli presented. When testing two ears simultaneously, the advantage is typically that the multiple-stimulus technique is two to three times faster. One factor that increases the time of the multiple-response recording is the relatively small size of responses at 500 and 4000 Hz. Increasing the intensities of the 500- and 4000-Hz stimuli by 10 or 20 dB can enhance their responses without significantly changing the other responses. Using multiple simultaneous stimuli causes small changes in the responses compared with when the responses are evoked by single stimuli. The clearest of these interactions is the attenuation of the responses to low-frequency stimuli in the presence of higher-frequency stimuli. Although these interactions are interesting physiologically, their small size means that they do not lessen the advantages of the multiple-stimulus approach.

Reduced-Order Modeling of Bladed Disks With Friction Ring Dampers

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Seunghun Baek ◽  
Bogdan Epureanu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Friction Model ◽  
Contact Friction ◽  
Bladed Disks ◽  
Transient Dynamic Analysis ◽  
Reduced Order ◽  
Bladed Disk ◽  
Steady State Responses ◽  
State Responses

An efficient methodology to predict the nonlinear response of bladed disks with a dry friction ring damper is proposed. Designing frictional interfaces for bladed-disk systems is an important approach to dissipate vibration energy. One emerging technology uses ring dampers, which are ringlike substructures constrained to move inside a groove at the root of the blades. Such rings are in contact with the bladed disk due to centrifugal forces, and they create nonlinear dissipation by relative motion between the ring and the disk. The analysis of the dynamic response of nonlinear structures is commonly done by numerical integration of the equations of motion, which is computationally inefficient, especially for steady-state responses. To address this issue, reduced-order models (ROMs) are developed to capture the nonlinear behavior due to contact friction. The approach is based on expressing the nonlinear forces as equivalent nonlinear damping and stiffness parameters. The method requires only sector-level calculations and allows precalculation of the response-dependent equivalent terms. These factors contribute to the increase of the computational speed of the iterative solution methods. A model of a bladed disk and damper is used to demonstrate the method. Macro- and micro-slip are used in the friction model to account for realistic behavior of dry friction damping. For validation, responses due to steady-state traveling wave excitations are examined. Results computed by ROMs are compared with results from transient dynamic analysis (TDA) in ansys with the full-order model. It is found that the steady-state responses predicted from the ROMs and the results from ansys are in good agreement, and that the ROMs reduce computation time significantly.

Estimating the Audiogram Using Multiple Auditory Steady-State Responses

2002 ◽  
Vol 13 (04) ◽  
pp. 205-224 ◽  
Author(s):  
Andrew Dimitrijevic ◽  
Sasha M. John ◽  
Patricia Van Roon ◽  
David W. Purcell ◽  
Julija Adamonis ◽  
...  
Keyword(s):  
Steady State ◽  
Correlation Coefficients ◽  
Behavioral Threshold ◽  
Behavioral Thresholds ◽  
Sensorineural Hearing Impairment ◽  
Steady State Responses ◽  
Auditory Steady State Responses ◽  
Tonal Stimuli ◽  
Conductive Hearing ◽  
State Responses

Multiple auditory steady-state responses were evoked by eight tonal stimuli (four per ear), with each stimulus simultaneously modulated in both amplitude and frequency. The modulation frequencies varied from 80 to 95 Hz and the carrier frequencies were 500, 1000, 2000, and 4000 Hz. For air conduction, the differences between physiologic thresholds for these mixed-modulation (MM) stimuli and behavioral thresholds for pure tones in 31 adult subjects with a sensorineural hearing impairment and 14 adult subjects with normal hearing were 14 ± 11, 5 ± 9, 5 ± 9, and 9 ± 10 dB (correlation coefficients .85, .94, .95, and .95) for the 500-, 1000-, 2000-, and 4000-Hz carrier frequencies, respectively. Similar results were obtained in subjects with simulated conductive hearing losses. Responses to stimuli presented through a forehead bone conductor showed physiologic-behavioral threshold differences of 22 ± 8, 14 ± 5, 5 ± 8, and 5 ± 10 dB for the 500-, 1000-, 2000-, and 4000-Hz carrier frequencies, respectively. These responses were attenuated by white noise presented concurrently through the bone conductor.

Weighted averaging of steady-state responses

2001 ◽  
Vol 112 (3) ◽  
pp. 555-562 ◽  
Author(s):  
M.Sasha John ◽  
Andrew Dimitrijevic ◽  
Terence W Picton
Keyword(s):  
Steady State ◽  
Weighted Averaging ◽  
Steady State Responses ◽  
State Responses
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