Time–Frequency Analysis of a Variable Stiffness Model for Fault Development

Cohen, Leon; Galleani, Lorenzo; Hedges, Robert A.; Hughes, David H.; Loughlin, Patrick J.; Suter, Bruce W.

doi:10.1006/dspr.2002.0458

Cited by 7 publications

(3 citation statements)

References 4 publications

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“…If the instantaneous “resonant” angular frequencies are not constant, then the normalized squared “natural” angular frequency and the universal damping ratio associated to each of the vibrational modes are time-varying and can be estimated as follows [40] , [70] : where If the system is second-order, by knowing the matrix we can reconstruct (27) from (44), and by having defined we can compute (2) from (27), obtaining an estimation of the stiffness and damping in the time domain, namely: Furthermore, by knowing , and can be readily estimated from (18).…”

Section: Methodsmentioning

confidence: 99%

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

et al. 2012

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This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.

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Section: Methodsmentioning

confidence: 99%

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

et al. 2012

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“…In general, the normalized resonant frequency η 2 ( t ) and normalized damping factor Γ( t ) are time-varying and can be estimated as follows [29]:

normalΓ false(t false) = - σ \frac{{\dot{ω}}_{i}}{2 ω_{i}}; η^{2} false(t false) = ω_{i}^{2} + σ^{2} + \frac{σ {\dot{ω}}_{i}}{ω_{i}} - \dot{σ}

where

σ false(t false) = \frac{d}{d t} ln A false(t false) = \frac{\dot{A} false(t false)}{A false(t false)}

…”

Section: Methodsmentioning

confidence: 99%

Multijoint arm stiffness during movements following stroke: Implications for robot therapy

Piovesan

Casadio

Mussa-Ivaldi

et al. 2011

2011 IEEE International Conference on Rehabilitation Robotics

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Impaired arm movements in stroke appear as a set of stereotypical kinematic patterns, characterized by abnormal joint coupling, which have a direct consequence on arm mechanics and can be quantified by the net arm stiffness at the hand. The current available measures of arm stiffness during functional tasks have limited clinical use, since they require several repetitions of the same test movement in many directions. Such procedure is difficult to obtain in stroke survivors who have lower fatigue threshold and increased variability compared to unimpaired individuals. The present study proposes a novel, fast quantitative measure of arm stiffness during movements by means of a Time-Frequency technique and the use of a reassigned spectrogram, applied on a trial-by-trial basis with a single perturbation. We tested the technique feasibility during robot mediated therapy, where a robot helped stroke survivors to regain arm mobility by providing assistive forces during a hitting task to 13 targets covering the entire reachable workspace. The endpoint stiffness of the paretic arm was estimated at the end of each hitting movements by suddenly switching of the assistive forces and observing the ensuing recoil movements. In addition, we considered how assistive forces influence stiffness. This method will provide therapists with improved tools to target the treatment to the individual’s specific impairment and to verify the effects of the proposed exercises.

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“…Time-frequency analysis is a signal analysis method that transforms time-domain signals into time-frequency images. It describes the spectral components of the signal at different times, so it contains more information [35]. In this paper, the Hilbert transform is used to convert the denoised one-dimensional time-domain signal into a three-dimensional time-frequency image, and the spectrum of typical AE signals in the four stages is selected, as shown in Figure 12.…”

Section: Time-frequency Feature Extraction Of the Ae Signalmentioning

confidence: 99%

Noise Reduction Based on Improved Variational Mode Decomposition for Acoustic Emission Signal of Coal Failure

et al. 2023

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Acoustic emission (AE) signal processing and interpretation are essential in mining engineering to acquire source information about AE events. However, AE signals obtained from coal mine monitoring systems often contain nonlinear noise, limiting the effectiveness of conventional analysis methods. To address this issue, a novel denoising approach using enhanced variational mode decomposition (VMD) and fuzzy entropy is proposed in this study. The denoised AE signal’s spectral multifractal features are analyzed. The optimization algorithm based on VMD with a weighted frequency index is introduced to avoid mode mixing and outperform other decomposition methods. The characteristic parameter Δα of the AE spectral multifractal parameter serves as an early warning indicator of coal instability. These findings contribute to the accurate extraction of time–frequency features and provide insights for on-site AE signal processing.

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Time–Frequency Analysis of a Variable Stiffness Model for Fault Development

Cited by 7 publications

References 4 publications

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

Multijoint arm stiffness during movements following stroke: Implications for robot therapy

Noise Reduction Based on Improved Variational Mode Decomposition for Acoustic Emission Signal of Coal Failure

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