scholarly journals Relevance of Frequency-Domain Analyses to Relate Shoe Cushioning, Ground Impact Forces and Running Injury Risk: A Secondary Analysis of a Randomized Trial With 800+ Recreational Runners

2021 ◽  
Vol 3 ◽  
Author(s):  
Laurent Malisoux ◽  
Paul Gette ◽  
Anne Backes ◽  
Nicolas Delattre ◽  
Jan Cabri ◽  
...  

Cushioning systems in running shoes are used assuming that ground impact forces relate to injury risk and that cushioning materials reduce these impact forces. In our recent trial, the more cushioned shoe version was associated with lower injury risk. However, vertical impact peak force was higher in participants with the Soft shoe version. The primary objective of this study was to investigate the effect of shoe cushioning on the time, magnitude and frequency characteristics of peak forces using frequency-domain analysis by comparing the two study groups from our recent trial (Hard and Soft shoe group, respectively). The secondary objective was to investigate if force characteristics are prospectively associated with the risk of running-related injury. This is a secondary analysis of a double-blinded randomized trial on shoe cushioning with a biomechanical running analysis at baseline and a 6-month follow-up on running exposure and injury. Participants (n = 848) were tested on an instrumented treadmill at their preferred running speed in their randomly allocated shoe condition. The vertical ground reaction force signal for each stance phase was decomposed into the frequency domain using the discrete Fourier transform. Both components were recomposed into the time domain using the inverse Fourier transform. An analysis of variance was used to compare force characteristics between the two study groups. Cox regression analysis was used to investigate the association between force characteristics and injury risk. Participants using the Soft shoes displayed lower impact peak force (p < 0.001, d = 0.23), longer time to peak force (p < 0.001, d = 0.25), and lower average loading rate (p < 0.001, d = 0.18) of the high frequency signal compared to those using the Hard shoes. Participants with low average and instantaneous loading rate of the high frequency signal had lower injury risk [Sub hazard rate ratio (SHR) = 0.49 and 0.55; 95% Confidence Interval (CI) = 0.25–0.97 and 0.30–0.99, respectively], and those with early occurrence of impact peak force (high frequency signal) had greater injury risk (SHR = 1.60; 95% CI = 1.05–2.53). Our findings may explain the protective effect of the Soft shoe version previously observed. The present study also demonstrates that frequency-domain analyses may provide clinically relevant impact force characteristics.Clinical Trial Registration:https://clinicaltrials.gov/, identifier: 9NCT03115437.

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dongju Chen ◽  
Shuai Zhou ◽  
Lihua Dong ◽  
Jinwei Fan

This paper presents a new identification method to identify the main errors of the machine tool in time-frequency domain. The low- and high-frequency signals of the workpiece surface are decomposed based on the Daubechies wavelet transform. With power spectral density analysis, the main features of the high-frequency signal corresponding to the imbalance of the spindle system are extracted from the surface topography of the workpiece in the frequency domain. With the cross-correlation analysis method, the relationship between the guideway error of the machine tool and the low-frequency signal of the surface topography is calculated in the time domain.


2016 ◽  
Vol 39 (8) ◽  
pp. 1205-1215 ◽  
Author(s):  
Bahram Mohammadi ◽  
Mohammad Reza Arvan ◽  
Yousof Koohmaskan

Rolling airframe manoeuvring is a type of manoeuvre in which the missile provides continuous roll during flight. Cross-coupling between the angle of attack and sideslip in rolling airframe missiles (RAMs) yields a coning motion around the flight path. As the pitch and yaw cross-coupling effect decreases, the radius of this coning motion decreases and the accuracy of the control system increases. Two-position (on–off) actuators are used in most RAMs. The presence of a two-position actuator in a feedback system makes its characteristics non-linear. A high-frequency signal so-called dither is applied to compensate for the non-linearity effect of the actuator characteristic in the feedback system and to stabilize the coning motion. The amplitude distribution function (ADF) method in dither analysis shows that the smoothed non-linearity characteristic can be computed as the convolution of the original non-linearity and the ADF of the dither signal. According to the four-degrees-of-freedom (4-DOF) equations of RAMs in a non-rolling frame and regarding various dither signals through the ADF approach on a two-position actuator, an analytical condition for dither amplitude in coning motion stability of RAMs is derived. It was shown that the triangular signal with specified amplitude and high enough frequency led to a smoother response of two-position actuators. Finally, by applying beam-riding guidance to a RAM, the performance of dithers for decreasing the distance of the missile from the centre of the beam is validated through simulations. It is illustrated that applying the triangular dither resulted in minimal error.


2010 ◽  
Vol 46 (4) ◽  
pp. 1468-1475 ◽  
Author(s):  
David Díaz Reigosa ◽  
Fernando Briz ◽  
Pablo García ◽  
Juan Manuel Guerrero ◽  
Michael W Degner

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