Energy Estimation of Treadmill Walking using On ... - Semantic Scholar

Energy Estimation of Treadmill Walking using On-body Accelerometers and Gyroscopes Harshvardhan Vathsangam, B. Adar Emken, E. Todd Schroeder, Donna Spruijt-Metz and Gaurav S. Sukhatme

Abstract— Walking is the most common activity among people who are physically active. Standard practice physical activity characterization from body-mounted inertial sensors uses accelerometer-generated counts. There are two problems with this - imprecison (due to usage of proprietary counts) and incompleteness (due to incomplete description of motion). We address both these problems by directly predicting energy expenditure during steady-state treadmill walking from a hipmounted inertial sensor comprised of a tri-axial accelerometer and a tri-axial gyroscope. We use Bayesian Linear Regression to predict energy expenditure based on modelling joint probabilities of streaming data. The prediction is significantly better with data from a 6 axis sensor as compared with streaming data from only 2 linear accelerations as is common in current practice. We also show how counts from a commercially available accelerometer can be reproduced from raw streaming acceleration data (up to a linear transformation) with high correlation (.9787 ± .0089 for the X-axis and .9141 ± .0460 for the Y-axis acceleration streams). The paper emphasizes the role of probabilistic techniques in conjunction with joint modeling of tri-axial accelerations and rotational rates to improve energy expenditure prediction for steady-state treadmill walking.

I. INTRODUCTION Regular physical activity (PA) has many health benefits, including reduced obesity, reduced risk for cardiovascular disease, type 2 diabetes, and several forms of cancer [1]. Walking is the most common type of activity among people who are physically active [2]. Hill et al. estimated that that weight gain could be prevented by achieving small changes in behavior, such as 15 minutes per day of walking [3]. Characterizing energy expenditure due to walking could be a vital tool to assess physical activity levels and determine the effectiveness of interventions. The past decade has seen considerable research in the detection and classification of physical activity patterns from body mounted inertial sensors [4]. Traditional techniques use accelerometers to estimate activity-related energy expenditure [5], [6]. Current descriptions of PA by accelerometry have two limitations - imprecision and incompleteness. The first limitation, imprecision, is because commercial accelerometers use proprietary methods to convert linear accelerations into epoch-based counts [7]. The second limitation, incompleteness, arises because accelerometers by definition do not completely describe human body movement. Human body movement consists of both accelerations and rotations. Rotational data cannot This work was supported in part by Qualcomm, Nokia, NSF (CCR0120778) as part of the Center for Embedded Network Sensing (CENS), and the USC Comprehensive NCMHD Research Center of Excellence (P60 MD 002254). Support for H. Vathsangam was provided by the USC Annenberg Doctoral fellowship. H. Vathsangam and G. S. Sukhatme are with the Dept. of Computer Science, Univ. of Southern California, Los Angeles, CA 90089, USA. A. Emken and D. Spruijt-Metz are with the Dept. of Preventive Medicine, Univ. of Southern California, Los Angeles, CA 90089, USA. E.T. Schroeder is with the Division of Biokinesiology and Physical Therapy, Univ. of Southern California, Los Angeles, CA 90089, USA.

be completely extracted from a single triaxial accelerometer. Current count-based accelerometry ignores rotational rates. Augmenting accelerometry with rotational rates with gyroscopes would thus be a valuable tool in completely characterizing movement. Gyroscopes are not influenced by gravity acceleration. For a given body segment movement, a gyroscope provides the same readings irrespective of position as long as the axis of placement is parallel to the measured axis [4]. Accelerometers have been used in combination with linear regression models to quantify energy expenditure for a number of physical activities [8]. Standard linear regression does not mirror the significance of differing amounts of data available to derive model parameters. Additionally, singlevariable linear regression models are limited in the sense that regressional mapping to energy can be made richer by considering multi-dimensional features simultaneously. An alternative approach is probabilistic linear regression where each new prediction has an associated confidence measure that is derived from a training dataset. The aim of this study was to investigate how data from an inertial sensor with both accelerometer and gyroscopic information could be used to predict energy expenditure from steady-state treadmill walking as measured by rate of oxygen consumption (V O2 , mL/min). Steady-state treadmill walking was chosen because of the ease of data collection over a range of walking speeds. Our approach involved modelling joint probabilities of streaming data to train a linear probabilistic model, Bayesian Linear Regression (BLR). BLR [9] represents a Bayesian alternative to conventional least squares linear regression. We showed how one can obtain significantly better estimates of energy expenditure when streaming data from all 6 axes (3 linear accelerations and 3 rotational velocities) are compared with data from only 2 linear accelerations as is common in current practice. We also showed how counts from a commercially available accelerometer, the Actigraph GT1M, can be reproduced from raw streaming acceleration data up to a linear transformation. With these results, we emphasize the role of probabilistic techniques in conjunction with joint modeling of tri-axial accelerations and rotational rates to improve energy expenditure prediction for steady-state treadmill walking. II. P ROBLEM D ESCRIPTION A. Capturing Treadmill Walking Information We captured motion using a modified version of the Sparkfun 6DoF Inertial Measurement Unit (IMU) [10] worn on the right iliac crest. The sensor provided 6 sensor streams conveying triaxial acceleration (Freescale MMA7260Q tri-axial accelerometer) and triaxial rotational rates (2 Invensense IDG300 gyroscopes). The use of sensors in all three axes allowed movement capture in all three planes – sagittal, frontal and transverse. Data were sampled at 100 Hz and transmitted via Bluetooth (RN-41 Bluetooth module) to a

Fig. 1: An example recording procedure for a single participant. The yellow box indicates sensor mounting. The red box indicates V O2 recording via the mask leading to the metabolic cart.

nearby PC. Additionally, activity patterns in the form of accelerometer counts as generated from a single Actigraph GT1M (10 second epochs) were recorded. The GT1M was mounted firmly on top of the IMU with the X and Y axes of both sensors aligned as close as possible as shown in Figure 1. 1) Participant Statistics: Eight healthy adults (four men, four women) participated in the study. Height and weight of each participant were recorded using a Healthometer balance beam scale. Table I describes participant statistics. Informed written consent was obtained from participants and the study was approved by the Institutional Review Board, University of Southern California. TABLE I: Statistics of participant population Attribute Age (yrs) Height (inches) Weight (lbs) BMI

Mean 34 68 171 25

SD 10 5 48 4

Max 48 75 233 32

Min 22 63 118 20

2) Representing Ground Truth for Energy Expenditure: Rate of oxygen consumption (V O2 , mL/min) was used as the representation of energy expenditure. This was measured using the MedGraphics Cardio II metabolic system with BreezeSuite v6.1B (Medical Graphics Corporation). The metabolic system outputs data at the frequency of every breath. Before each test, the flow meter was calibrated against a 3.0 L syringe and the system was calibrated against O2 and CO2 gases of known concentration. Figure 1 illustrates a typical recording procedure. Each participant was asked to walk at 5 speeds (2.5, 2.8, 3.0, 3.3, and 3.5 mph) on a motorized treadmill for 7 minutes of recording time per speed. Speeds were chosen based on the Compendium of Physical Activities [11]. Following a transition between speeds, V O2 readings were allowed to stabilize for 2 minutes prior to data collection. 3) Data pre-processing: Each sensor stream from the IMU was passed through a lowpass filter with 3dB cutoff at 20 Hz. This frequency was chosen keeping in mind that everyday activities fall in the frequency range of 0.1-10

Hz [12]. The streams from the IMU were partitioned into 10 second intervals or epochs. Within each epoch, feature vectors were extracted from each sensor stream as outlined in Sec. II-A.4. These epochs were manually time-synched with epochs obtained from the GT1M. The V O2 values from the MedGraphics Cardio II metabolic system that fell within each epoch were averaged and matched appropriately. These represented the ground truth on which to train data. Thus data for each user consisted of a sequence of epochs, each containing features from the IMU, counts as generated by the GT1M and the average rate of oxygen consumption (V O2 ) for that epoch. These represent per-user data while walking at five different speeds. 4) Feature Vector Used: The feature vector used was the average integral of the mean-subtracted sensor output for a given time interval (epoch). Consider a signal si (t) (part of a continuous signal s(t)) corresponding to an epoch, εi of length Ti . The feature used to represent this signal within this epoch is given by: Z 1 F Vi = |si (t) − µ (si (t), εi )| dt (1) Ti t∈εi Z 1 µ (si (t), εi ) = si (t)dt (2) Ti t∈εi These are implemented in the digital domain for a time series si [n] and an epoch εi of length Ni as: 1 X |si [k] − µ [si [k] , εi ]| (3) F Vi = Ni k∈εi 1 X µ [si [k] , εi ] = si [k] (4) Ni k∈εi

Figure 2a illustrates feature extraction steps and Figure 2b shows how the features evolve for different walking speeds. 5) Interpretation of feature vector: Steady state walking is cyclic [13] and hence can be represented by a sequence of sinusoidal waves. For a given sinusoidal wave:   2πt (5) X(t) = A0 sin T The average integral of the Z mean subtracted signal is: 1 FV = |X(t) − µ (X(t), T )| dt (6) T t∈T   Z 1 A0 sin 2πt dt = (7) T t∈T T 2A0 =⇒ F V = (8) π Equation 8 is the equivalent DC value of the rectified sinusoidal wave from Equation 5. Thus, one interpretation of the feature vector is the rectified DC equivalent of the original periodic signal. 6) Correlation of Feature Vectors with GT1M readings: To ascertain whether the features generated from the IMU X and Y axis acceleration streams corresponded to those generated from the GT1M counts, the Pearson’s correlation coefficients between IMU features and GT1M counts for respective axes were calculated per-participant. These were averaged across all participants. The average correlation across participants was .9787 ± .0089 for the X-axis and .9141 ± .0460 for the Y-axis acceleration streams. Figure 3 illustrates a typical scatter plot of IMU features versus GT1M counts. This result is important because it allows reproduction of GT1M counts upto a linear transformation

(a) An example of the extraction of a feature vector for a single subject. The

(b) A plot of the epoch features as obtained for various

top panel shows raw signals (with mean subtracted out) for five separate epoch snapshots corresponding to five walking speeds with the sensor worn on the right hip plotted side-by-side. Here, only the X-axis acceleration signals are shown though similar signals are seen in the other axes and gyroscope axes as well. The signals show increasingly large variance with increasing speeds. The signals for each speed also are periodic in nature The centre panel shows the rectified signals from the original signals. The bottom panel shows the corresponding average value of the signals as calculated from the rectified signals. This average value is representative of the net DC value for that epoch. There is a clear increasing trend in the features used.

speeds using the techniques outlined in the previous figure for one subject. Features are color coded by V O2 consumption with blue being the minimum and red being the maximum consumption level. The top box shows the acceleration features in 3 axes, the bottom box shows the corresponding gyroscope features. A clear evolution of features and correspondence with V O2 consumption with increasing speed is seen. This indicates that these features could be used to track the increasingly large V O2 consumption values.

Fig. 2: An illustration of the feature extraction procedure to represent energy consumption. Features show the desired properties of being constant for a certain speed and evolving with walking speed.

B. Bayesian Linear Regression Theory Consider a set of K-dimensional data points X = {xi }, i = 1, 2, . . . N each of which are mapped to a corresponding target value: Y = {yi }, i = 1, 2, . . . N . The linear regression problem is to find the optimal parameter set w such that: Y

Fig. 3: Illustration of correlation between IMU generated feature

= WT X + ,  ∼ N (0, β −1 I)

(9)

where β represents the noise variance parameter. For a Gaussian noise model, we can also obtain the conditional posterior distribution of the mapping Y given the input data points X, as: p(Y|X) = N (Y|wT X, β −1 I) (10)

vector and GT1M readings for the X-axis acceleration signal for walking at five different speeds for a single subject. Feature points are color coded by V O2 consumption. Data occurs in 5 distinct patches corresponding to 5 different speeds. The IMU feature vectors showed a strong linear correlation with the GT1M generated counts (.9787 ± .0089 for the X-axis and .9141 ± .0460 for the Y-axis) which means that features could be related to each other by a simple linear transformation.

BLR adopts a Bayesian approach to the treatment of linear regression by fixing a prior over the parameter space w as opposed to a definite value. Specifically, choosing a Gaussian prior over w, p(w) = N (w|0, α−1 I). Using properties of Gaussians and Equation 10 we obtain the posterior distribution of the parameter set as:

for treadmill walking. This is critical when considering that our approach uses streaming acceleration data while the GT1M stores data locally. By using this feature vector, one can potentially apply any GT1M based algorithm using essentially the same “counts” on IMU-streaming acceleration data for steady-state walking.

In a fully Bayesian approach we adopt priors over α and β also. We then iteratively find the best hyperparameters α, β to maximize the evidence function for our dataset and find the ˆ to maximize likelihood until convergence. best parameters w The optimal prediction for a new data point Xnew is then:

p(w|Y) = N (w|mN , SN ) mN = SN βXT Y and S−1 = αI + βXT X N

p(Ynew |Xnew )

=

(11) (12) (13)

N (Ynew |w ˆ T Xnew , β −1 I) (14)

In this experiment, the target quantity Y = {yi }N i=1 is the V O2 reading as output by the metabolic system. Each V O2 prediction has an associated mean and a variance to mirror confidence of prediction. The input data points, X = {xi }N i=1 , are the feature vectors computed using methods described in Sec. II-A.4. BLR was chosen over non-linear regression approaches such as support vector regression (SVR) [14] to map to energy expenditure because nonlinear mapping is predicated by the availability of large quantities of data to derive corresponding nonlinear relationships. Small amounts of data with high noise might result in inferior mappings due to effects of over-fitting. We circumvented the issue of nonlinear mapping by restricting activities measured as being only due to steady-state treadmill walking within a definite range of speeds. III. RESULTS AND DISCUSSION In this section, we examine the effect of introducing additional movement information in the form of Z-axis acceleration and rotational rates on prediction errors using BLR. This was achieved by varying the feature vector input to BLR and comparing prediction errors between models.

Fig. 4: Illustration of comparison of IMU feature vector with Actigraph counts averaged across all participants when trained using BLR. Each bar shows average RMS error ± 1 standard deviation. RMS error using the IMU feature vector is smaller than that from using Actigraph counts. This is reasoned to be because the sensor is more closely attached to the body than the GT1M leading to better motion capture. The IMU also has a higher sampling rate and account for zero bias.

A. Testing Procedure From each participant’s data, a fraction was randomly sampled and partitioned into training data, the remaining fraction constituting test data. Different BLR models were trained with the same training data but with different feature vectors. After each training phase, the algorithm was tested on the remaining data points to predict V O2 values. RMS error was calculated as a measure of accuracy. This was repeated over 100 trials for different randomly sampled data and results averaged. This was repeated for training data percentages from 10% to 90% and constituted a per-subject measure of performance. The results were then averaged over all subjects. To understand the relative magnitude of the errors, it must be noted that the V O2 values are in the range of 400-1000 mL/min. B. Comparison of IMU features with GT1M counts Figure 4 illustrates the difference in Average RMS prediction error of energy expenditure when comparing IMU defined features from the IMU accelerometer X,Y axes

Fig. 5: Illustration of effect of introducing Z-axis acceleration to train data using BLR. Each bar shows average RMS error ± 1 standard deviation. Additional movement information by way of Z-axis readings provides redundancy to improve prediction errors.

alone with X,Y counts generated by the GT1M. The error when using IMU features alone was found to be less than that from using GT1M counts. Since the GT1M was by design mounted on the outside of the IMU unit as shown in Figure 1, it would capture features based on slightly different movement signals from the IMU. Care was taken minimize this by mounting both the sensors as firmly, securely and close to each other as possible. The variation due to this was minimal as evidenced by the strong linear correlation between readings per epoch. Aside the from this, the IMU had a higher sampling frequency (100 Hz) than the GT1M (30 Hz). The feature vectors calculated as per Equation 3 represent a quantity averaged over a time interval. For a higher sampling frequency, due to a larger number of samples available for the same time interval the average value would have a higher precision. This suggested that even though the Nyquist criterion states that a minimum sampling frequency of 20 Hz is enough to capture movement information, higher sampling would be beneficial in obtaining even more finegrained features. This is the subject of further investigation. Also, the IMU would output a constant value during rest whereas the GT1M would output a zero count. This bias term could be interpreted as a certain amount of energy that is expended regardless of the activity performed. Addition of a bias term would not affect the correlation coeffcient but would affect prediction results by altering the weights. A bias term also guards against over-fitting. C. Effect of Adding Z-axis information Figure 5 describes the effect of adding Z-axis acceleration information to the feature vector. Error is reduced with the addition of Z-axis information (p0.05 using ANOVA when averaged across all users). This variance indicates how RMS prediction error changes from subject to subject. Individual walking styles and physiological characteristics of each participant (as described by age, BMI and height) while showing an adequate proof of concept per-subject, contributed to the variance across participants. The algorithm shows a small per-user variance as shown in Figure 7. This means that using current techniques, a unified model cannot be applied across all users. However the relative errors arising from different feature vectors bear the same relationship to each other in all users, even though the magnitude of differences vary from user to user. This constant relative relationship among errors encourages using additional movement information to complement accelerometer X,Y data to provide a more accurate description of motion.

IV. C ONCLUSION This paper described how joint modelling of real-time accelerometer and gyroscopic information using Bayesian Linear Regression (BLR) could be used to predict energy expenditure from steady-state treadmill walking as measured by rate of oxygen consumption (V O2 , mL/min). We defined a candidate feature vector to represent energy expenditure and showed how this feature vector could reproduce counts generated by a commercial accelerometer, the Actigraph GT1M up to a linear transformation (Correlation coefficient = .9787 ± .0089 for the X-axis and .9141 ± .0460 for the Y-axis acceleration streams). We then showed how energy prediction accuracy as measured by RMS prediction error significantly improves (p