Linear and Nonlinear Smooth Orthogonal Decomposition to Reconstruct Local Fatigue Dynamics: A Comparison

2010 ◽  
Author(s):  
David B. Segala ◽  
David Chelidze ◽  
Deanna Gates ◽  
Jonathan Dingwell
Keyword(s):  
Time Series ◽  
Muscle Fatigue ◽  
Power Spectra ◽  
Dimensional Subspace ◽  
Orthogonal Decomposition ◽  
Muscle Injuries ◽  
Data Set ◽  
Individual Muscle ◽  
The Individual ◽  
Smooth Orthogonal Decomposition

Identifying physiological fatigue is important for the development of more robust training protocols, better energy supplements, and/or reduction of muscle injuries. Current fatigue measurement technologies are usually invasive and/or impractical, and may not be realizable in out of laboratory settings. A fatigue identification methodology that only uses motion kinematics measurements has a great potential for field applications. Phase space warping (PSW) features of motion kinematic time series analyzed through smooth orthogonal decomposition (SOD) have tracked individual muscle fatigue. In this paper, the performance of a standard SOD analysis is compared to its nonlinear extension using a new experimental data set. Ten healthy right-handed subjects (27 ± 2.8 years; 1.71 ± 0.10 m height; and 69.91 ± 18.26 kg body mass) perform a sawing motion by pushing a weighted handle back and forth until voluntary exhaustion. Three sets of joint kinematic angles are measured from the elbow, wrist and shoulder as well as surface Electromyography (EMG) from ten different muscle groups. A vector-valued feature time series is generated using PSW metrics estimated from movement kinematics. Dominant SOD coordinates of these features are extracted to track the individual muscle fatigue trends as indicated by mean and median frequencies of the corresponding EMG power spectra. Cross subject variability shows that considerably fewer nonlinear SOD coordinates are needed to track EMG-based fatigue markers, and that nonlinear SOD methodology captures fatigue dynamics in a lower-dimensional subspace than its linear counterpart.

Nonlinear Smooth Orthogonal Decomposition of Kinematic Features of Sawing Reconstructs Muscle Fatigue Evolution as Indicated by Electromyography

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
David B. Segala ◽  
Deanna H. Gates ◽  
Jonathan B. Dingwell ◽  
David Chelidze
Keyword(s):  
Muscle Fatigue ◽  
Fixed Number ◽  
Orthogonal Decomposition ◽  
Muscle Injuries ◽  
Individual Muscle ◽  
Dimensional Reconstruction ◽  
Order Of Magnitude ◽  
Muscle Groups ◽  
The Right ◽  
Smooth Orthogonal Decomposition

Tracking or predicting physiological fatigue is important for developing more robust training protocols and better energy supplements and/or reducing muscle injuries. Current methodologies are usually impractical and/or invasive and may not be realizable outside of laboratory settings. It was recently demonstrated that smooth orthogonal decomposition (SOD) of phase space warping (PSW) features of motion kinematics can identify fatigue in individual muscle groups. We hypothesize that a nonlinear extension of SOD will identify more optimal fatigue coordinates and provide a lower-dimensional reconstruction of local fatigue dynamics than the linear SOD. Both linear and nonlinear SODs were applied to PSW features estimated from measured kinematics to reconstruct muscle fatigue dynamics in subjects performing a sawing motion. Ten healthy young right-handed subjects pushed a weighted handle back and forth until voluntary exhaustion. Three sets of joint kinematic angles were measured from the right upper extremity in addition to surface electromyography (EMG) recordings. The SOD coordinates of kinematic PSW features were compared against independently measured fatigue markers (i.e., mean and median EMG spectrum frequencies of individual muscle groups). This comparison was based on a least-squares linear fit of a fixed number of the dominant SOD coordinates to the appropriate local fatigue markers. Between subject variability showed that at most four to five nonlinear SOD coordinates were needed to reconstruct fatigue in local muscle groups, while on average 15 coordinates were needed for the linear SOD. Thus, the nonlinear coordinates provided a one-order-of-magnitude improvement over the linear ones.

An Adaptive Orthogonal SSA Decomposition Algorithm for a Time Series

2018 ◽  
Vol 10 (01) ◽  
pp. 1850002 ◽  
Author(s):  
Kenji Kume ◽  
Naoko Nose-Togawa
Keyword(s):  
Time Series ◽  
Correlation Matrix ◽  
Singular Spectrum Analysis ◽  
Dimensional Subspace ◽  
Orthogonal Decomposition ◽  
Gram Matrix ◽  
Diagonal Form ◽  
Window Length ◽  
Original Time ◽  
Basis Vectors

Singular spectrum analysis (SSA) is a nonparametric spectral decomposition of a time series into arbitrary number of interpretable components. It involves a single parameter, window length [Formula: see text], which can be adjusted for the specific purpose of the analysis. After the decomposition of a time series, similar series are grouped to obtain the interpretable components by consulting with the [Formula: see text]-correlation matrix. To accomplish better resolution of the frequency spectrum, a larger window length [Formula: see text] is preferable and, in this case, the proper grouping is crucial for making the SSA decomposition. When the [Formula: see text]-correlation matrix does not have block-diagonal form, however, it is hard to adequately carry out the grouping. To avoid this, we propose a novel algorithm for the adaptive orthogonal decomposition of the time series based on the SSA scheme. The SSA decomposition sequences of the time series are recombined and the linear coefficients are determined so as to maximizing its squared norm. This results in an eigenvalue problem of the Gram matrix and we can obtain the orthonormal basis vectors for the [Formula: see text]-dimensional subspace. By the orthogonal projection of the original time series on these basis vectors, we can obtain adaptive orthogonal decomposition of the time series without the redundancy of the original SSA decomposition.

scholarly journals Predicting Forest Cover in Distinct Ecosystems: The Potential of Multi-Source Sentinel-1 and -2 Data Fusion

2020 ◽  
Vol 12 (2) ◽  
pp. 302 ◽  
Author(s):  
Kai Heckel ◽  
Marcel Urban ◽  
Patrick Schratz ◽  
Miguel Mahecha ◽  
Christiane Schmullius
Keyword(s):  
South Africa ◽  
Time Series ◽  
Forest Cover ◽  
Short Wave ◽  
Optical Data ◽  
Biophysical Parameters ◽  
Data Set ◽  
Area Index ◽  
The Individual ◽  
Sentinel 2

The fusion of microwave and optical data sets is expected to provide great potential for the derivation of forest cover around the globe. As Sentinel-1 and Sentinel-2 are now both operating in twin mode, they can provide an unprecedented data source to build dense spatial and temporal high-resolution time series across a variety of wavelengths. This study investigates (i) the ability of the individual sensors and (ii) their joint potential to delineate forest cover for study sites in two highly varied landscapes located in Germany (temperate dense mixed forests) and South Africa (open savanna woody vegetation and forest plantations). We used multi-temporal Sentinel-1 and single time steps of Sentinel-2 data in combination to derive accurate forest/non-forest (FNF) information via machine-learning classifiers. The forest classification accuracies were 90.9% and 93.2% for South Africa and Thuringia, respectively, estimated while using autocorrelation corrected spatial cross-validation (CV) for the fused data set. Sentinel-1 only classifications provided the lowest overall accuracy of 87.5%, while Sentinel-2 based classifications led to higher accuracies of 91.9%. Sentinel-2 short-wave infrared (SWIR) channels, biophysical parameters (Leaf Area Index (LAI), and Fraction of Absorbed Photosynthetically Active Radiation (FAPAR)) and the lower spectrum of the Sentinel-1 synthetic aperture radar (SAR) time series were found to be most distinctive in the detection of forest cover. In contrast to homogenous forests sites, Sentinel-1 time series information improved forest cover predictions in open savanna-like environments with heterogeneous regional features. The presented approach proved to be robust and it displayed the benefit of fusing optical and SAR data at high spatial resolution.

scholarly journals Search for p-mode Frequencies on Procyon A

2001 ◽  
Vol 203 ◽  
pp. 121-124 ◽  
Author(s):  
M. Martic ◽  
J. C. Lebrun ◽  
J. Schmitt ◽  
J.-L. Bertaux
Keyword(s):  
Time Series ◽  
Frequency Spectrum ◽  
Doppler Shift ◽  
Power Spectra ◽  
Stellar Models ◽  
The Individual ◽  
Excess Power

Following the recent evidence for the presence of an excess of power around 1 mHz in the frequency spectrum of the Doppler shift measurements for Procyon (Martic et al., 1999), we searched for individual frequencies of p-modes from three independent observing runs (5, 10 and 15 nights). All observations (December 1997, November 1998, January 1999) were made with the ELODIE spectrograph on the 1.93 m telescope at Observatoire de Haute Provence. The individual peaks in cleaned power spectra of each time series in the interval of excess power are compared with the predicted p-mode frequencies from stellar models (Chaboyer et al., 1999) for Procyon A.

Smooth Projective Nonlinear Noise Reduction

2013 ◽  
Author(s):  
David Chelidze
Keyword(s):  
Time Series ◽  
Noise Reduction ◽  
Broad Spectrum ◽  
Reduction Method ◽  
Orthogonal Decomposition ◽  
Topological Properties ◽  
Noisy Time Series ◽  
Nonlinear Noise ◽  
Proper Orthogonal ◽  
Smooth Orthogonal Decomposition

Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Locally projective noise reduction is one of the most effective tools. It is based on proper orthogonal decomposition (POD), and works for both map-like and continuously sampled time series. However, POD only looks at geometrical or topological properties of data and does not take into account the temporal characteristics of time series. Here we present a new smooth projective noise reduction method. It uses bundles of locally reconstructed trajectory strands and their smooth orthogonal decomposition (SOD) to identify smooth local subspaces. Restricting trajectories to these subspaces imposes temporal smoothness on the filtered time series. It is shown that SOD-based noise reduction significantly outperforms the POD-based method for continuously sampled noisy time series.

scholarly journals Tracking changes in behavioural dynamics using prediction error

2020 ◽  
Author(s):  
Tom Lorimer ◽  
Rachel Goodridge ◽  
Antonia K. Bock ◽  
Vitul Agarwal ◽  
Erik Saberski ◽  
...  
Keyword(s):  
Time Series ◽  
Escape Response ◽  
Prediction Error ◽  
Dimensional Space ◽  
Behavioural Change ◽  
Automated Analysis ◽  
High Time Resolution ◽  
Data Set ◽  
The Individual ◽  
Behavioural Dynamics

AbstractAutomated analysis of video can now generate extensive time series of pose and motion in freely-moving organisms. This requires new quantitative tools to characterize behavioural dynamics. For the model roundworm Caenorhabditis elegans, body pose can be accurately quantified from video as coordinates in a single low-dimensional space. We focus on this well-established case as an illustrative example and propose a method to reveal subtle variations in behaviour at high time resolution. Our data-driven method, based on empirical dynamic modeling, quantifies behavioural change as prediction error with respect to a time-delay-embedded ‘attractor’ of behavioural dynamics. Because this attractor is constructed from a user-specified reference data set, the approach can be tailored to specific behaviours of interest at the individual or group level. We validate the approach by detecting small changes in the movement dynamics of C. elegans at the initiation and completion of delta turns. We then examine an escape response initiated by an aversive stimulus and find that the method can track return to baseline behaviour in individual worms and reveal variations in the escape response between worms. We suggest that this general approach – defining dynamic behaviours using reference attractors and quantifying dynamic changes using prediction error – may be of broad interest and relevance to behavioural researchers working with video-derived time series.

Tracking Physiological Fatigue in Prolonged Load Carriage Walking Using Phase Space Warping and Smooth Orthogonal Decomposition

2008 ◽  
Author(s):  
David B. Segala ◽  
David Chelidze ◽  
Albert Adams ◽  
Jeffrey M. Schiffman ◽  
Leif Hasselquist
Keyword(s):  
Time Series ◽  
Oxygen Consumption ◽  
Phase Space ◽  
Surface Electromyography ◽  
Orthogonal Decomposition ◽  
Load Carriage ◽  
Leg Muscles ◽  
Smooth Orthogonal Decomposition ◽  
Phase Space Warping ◽  
Gait Variable

The ability to track and predict the onset of physiologic fatigue using easily measurable variables is of great importance to both civilian and military activities. In this paper, biomechanical gait variables are used to reconstruct fatigue evolution in subjects walking with a 40 kg load on a level treadmill for two hours. Fatigue is reconstructed in two steps: (1) phase space warping based feature vectors are estimated from gait variable time series; and (2) smooth orthogonal decomposition is used to extract fatigue related trends from these features. These results are verified using independently obtained measures of fatigue from breath-by-breath oxygen consumption (V˙O2) and surface electromyography (EMG) from a set of leg muscles. V˙O2 based measures for some subjects show no discernable trends. However, for a subject showing monotonically increasing oxygen consumption, the reconstructed dominant fatigue variable closely track V˙O2 measure reflecting global systemic fatigue. For the muscles showing variation in EMG-based fatigue measures, the reconstructed fatigue variables also closely track these local muscle trends. The results show that kinematic angles, which are easier quantities to measure in the field, can be used to track and predict the onset of fatigue.

Slow-Time Changes in Human EMG Muscle Fatigue States Are Fully Represented in Movement Kinematics

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Miao Song ◽  
David B. Segala ◽  
Jonathan B. Dingwell ◽  
David Chelidze
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Muscle Fatigue ◽  
Time Series Data ◽  
Series Data ◽  
Dimensional Manifold ◽  
Movement Kinematics ◽  
Individual Muscle ◽  
Time Changes ◽  
Low Dimensional

The ability to identify physiologic fatigue and related changes in kinematics can provide an important tool for diagnosing fatigue-related injuries. This study examined an exhaustive cycling task to demonstrate how changes in movement kinematics and variability reflect underlying changes in local muscle states. Motion kinematics data were used to construct fatigue features. Their multivariate analysis, based on smooth orthogonal decomposition, was used to reconstruct physiological fatigue. Two different features composed of (1) standard statistical metrics (SSM), which were a collection of standard long-time measures, and (2) phase space warping (PSW)–based metrics, which characterized short-time variations in the phase space trajectories, were considered. Movement kinematics and surface electromyography (EMG) signals were measured from the lower extremities of seven highly trained cyclists as they cycled to voluntary exhaustion on a stationary bicycle. Mean and median frequencies from the EMG time series were computed to measure the local fatigue dynamics of individual muscles independent of the SSM- and PSW-based features, which were extracted solely from the kinematics data. A nonlinear analysis of kinematic features was shown to be essential for capturing full multidimensional fatigue dynamics. A four-dimensional fatigue manifold identified using a nonlinear PSW-based analysis of kinematics data was shown to adequately predict all EMG-based individual muscle fatigue trends. While SSM-based analyses showed similar dominant global fatigue trends, they failed to capture individual muscle activities in a low-dimensional manifold. Therefore, the nonlinear PSW-based analysis of strictly kinematic time series data directly predicted all of the local muscle fatigue trends in a low-dimensional systemic fatigue trajectory. These results provide the first direct quantitative link between changes in muscle fatigue dynamics and resulting changes in movement kinematics.

scholarly journals The SPARC water vapour assessment II: Profile-to-profile comparisons of stratospheric and lower mesospheric water vapour data sets obtained from satellites

2018 ◽  
Author(s):  
Stefan Lossow ◽  
Farahnaz Khosrawi ◽  
Michael Kiefer ◽  
Kaley A. Walker ◽  
Jean-Loup Bertaux ◽  
...  
Keyword(s):  
Time Series ◽  
Water Vapour ◽  
Data Sets ◽  
General Behaviour ◽  
Data Set ◽  
Observational Database ◽  
Comparison Results ◽  
Wide Range ◽  
The Individual ◽  
Mean Time

Abstract. Within the framework of the second SPARC (Stratosphere-troposphere Processes And their Role in Climate) water vapour assessment (WAVAS-II), profile-to-profile comparisons of stratospheric and lower mesospheric water vapour were performed considering 33 data sets derived from satellite observations of 15 different instruments. These comparisons aimed to provide a picture of the typical biases and drifts in the observational database and to identify data set specific problems. The observational database typically exhibits the largest biases below 70 hPa, both in absolute and relative terms. The smallest biases are often found between 50 hPa and 5 hPa. Typically, they range from 0.25 ppmv to 0.5 ppmv (5 % to 10 %) in this altitude region, based on the 50 % percentile over the different comparison results. Higher up, the biases are overall increasing with altitude but this general behaviour is accompanied by considerable variations. Characteristic values vary between 0.3 ppmv and 1 ppmv (4 % to 20 %). Obvious data set specific bias issues are found for a number of data sets. In our work we performed a drift analysis for data sets overlapping for a period of at least 36 months. This assessment shows a wide range of drifts among the different data sets that are statistically significant at the 2σ uncertainty level. In general, the smallest drifts are found in the altitude range between about 30 hPa to 10 hPa. Histograms considering results from all altitudes indicate the largest occurrence for drifts between 0.05 ppmv decade−1 and 0.3 ppmv decade−1. Comparisons of our drift estimates to those derived from comparisons of zonal mean time series only exhibit statistically significant differences in slightly more than 3 % of the comparisons. Hence, drift estimates from profile-to-profile and zonal mean time series comparisons are largely interchangeable. Like for the biases, a number of data sets exhibit prominent drift issues. In our analyses we found that the large number of MIPAS data sets included in the assessment affects our general results as well as the bias summaries we provide for the individual data sets. This is because these data sets exhibit a relative similarity with respect to the remaining data sets, despite that they are based on different measurement modes and different processors implementing different retrieval choices. Because of that, we have by default considered an aggregation of the comparison results obtained from MIPAS data sets. Results without this aggregation are provided on multiple occasions to characterise the effects due to the numerous MIPAS data sets. Among other effects, they cause a reduction of the typical biases in the observational database.

scholarly journals Tracking changes in behavioural dynamics using prediction error

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0251053
Author(s):  
Tom Lorimer ◽  
Rachel Goodridge ◽  
Antonia K. Bock ◽  
Vitul Agarwal ◽  
Erik Saberski ◽  
...  
Keyword(s):  
Time Series ◽  
Escape Response ◽  
Prediction Error ◽  
Dimensional Space ◽  
Behavioural Change ◽  
Automated Analysis ◽  
High Time Resolution ◽  
Data Set ◽  
The Individual ◽  
Behavioural Dynamics

Automated analysis of video can now generate extensive time series of pose and motion in freely-moving organisms. This requires new quantitative tools to characterise behavioural dynamics. For the model roundworm Caenorhabditis elegans, body pose can be accurately quantified from video as coordinates in a single low-dimensional space. We focus on this well-established case as an illustrative example and propose a method to reveal subtle variations in behaviour at high time resolution. Our data-driven method, based on empirical dynamic modeling, quantifies behavioural change as prediction error with respect to a time-delay-embedded ‘attractor’ of behavioural dynamics. Because this attractor is constructed from a user-specified reference data set, the approach can be tailored to specific behaviours of interest at the individual or group level. We validate the approach by detecting small changes in the movement dynamics of C. elegans at the initiation and completion of delta turns. We then examine an escape response initiated by an aversive stimulus and find that the method can track return to baseline behaviour in individual worms and reveal variations in the escape response between worms. We suggest that this general approach—defining dynamic behaviours using reference attractors and quantifying dynamic changes using prediction error—may be of broad interest and relevance to behavioural researchers working with video-derived time series.

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