Reconstruction and Estimation of Flows Using Resolvent Analysis and Data-Assimilation

A flow reconstruction methodology is presented for incompressible, statistically stationary flows using resolvent analysis and data-assimilation. The only inputs necessary for the procedure are a rough approximation of the mean profile and a single time-resolved measurement. The objective is to estimate both the mean and fluctuating states of experimental flows with limited measurements which do not include pressure. The input data may be incomplete, in the sense that measurements near a body are difficult to obtain with techniques such as particle image velocimetry (PIV), or contaminated by noise. The tools developed in this thesis are capable of filling in missing data and reducing the amount of measurement noise by leveraging the governing equations. The reconstructed flow is capable of estimating fluctuations where time-resolved data are not available and solving the flow on larger domains where the mean profile is not known. The first part of the thesis focuses on how resolvent analysis of the mean flow selects amplification mechanisms. Eigenspectra and pseudospectra of the mean linear Navier-Stokes (LNS) operator are used to characterize amplification mechanisms in flows where linear mechanisms are important. The real parts of the eigenvalues are responsible for resonant amplification and the resolvent operator is low-rank when the eigenvalues are sufficiently separated in the spectrum. Two test cases are studied: low Reynolds number cylinder flow and turbulent channel flow. The latter is studied by considering well-known turbulent structures while the former contains a marginally stable eigenvalue which drowns out the effect of other eigenvalues over a large range of temporal frequencies. There is a geometric manifestation of this dominant mode in the mean profile, suggesting that it leaves a significant footprint on the time-averaged flow that the resolvent can identify. The resolvent does not provide an efficient basis at temporal frequencies where there is no separation of singular values. It can still be leveraged, nevertheless, to identify coherent structures in the flow by approximating the nonlinear forcing from the interaction of highly amplified coherent structures. The second part of the thesis extends the framework of Foures et al. (2014), who data-assimilated the mean cylinder wake at very low Reynolds numbers. The contributions presented here are to assess the minimum domain for successfully reconstructing Reynolds stress gradients, modifying the algorithm to assimilate mean pressure, determining whether weighting input measurements contributes to improved performance, and adapting the method to experimental data at higher Reynolds numbers. The results from data-assimilating the mean cylinder wake at low Reynolds numbers suggest that the measurement domain needs to coincide with the spatial support of the Reynolds stress gradients while point weighting has a minimal impact on the performance. Finally, a smoothing procedure adapted from Foures et al. (2014) is proposed to cope with data-assimilating an experimental mean profile obtained from PIV data. The data-assimilated mean profiles for an idealized airfoil and NACA 0018 airfoil are solved on a large domain making the mean profile suitable for global resolvent analysis. Data-assimilation is also able to fill in missing or unreliable vectors near the airfoil surface. The final piece of the thesis is to synthesize the knowledge and techniques developed in the first two parts to reconstruct the experimental flow around a NACA 0018 airfoil. Preliminary results are presented for the case where α = 0° and Re = 10250. The mean profile is data-assimilated and used as an input to resolvent analysis to educe coherent structures in the flow. The resolvent operator for non- amplified temporal frequencies is forced by an approximated nonlinear forcing. The amplitude and phase of the modes are obtained from the discrete Fourier-transform of a time-resolved probe point measurement. The final reconstruction contains less measurement noise compared to the PIV snapshots and obeys the incompressible Navier-Stokes equations (NSE). The thesis concludes with a discussion of how elements of this methodology can be incorporated into the development of estimators for turbulent flows at high Reynolds numbers.</p

CONTINUOUS MONITORING OF MOVEMENT IN PATIENTS WITH PARKINSON'S DISEASE USING INERTIAL SENSORS

Gait impairment is a hallmark of Parkinson's disease (PD). The assessment of gait and balance in the clinic may not adequately reflect mobility in daily life. It is often reported that patients with PD walk better when they are examined in an outpatient clinic or in a research laboratory than at home. Continuous monitoring of mobility during spontaneous daily activities may provide clinicians and patients with objective measures of the quality of their mobility. We show that continuous monitoring of spontaneous gait with wearable inertial sensors during daily activities is feasible for patients with PD. We tested 13 patients with PD and 8 healthy controls to evaluate the feasibility of using wearable inertial sensors at home for one week. The inertial system successfully detects walking bouts and provides sixteen objective measures that can characterize gait changes in patients with PD

Electrical Skin Impedance at Acupuncture Points

Objective: To test whether electrical skin impedance at each of three acupuncture points (APs) is significantly lower than at nearby sites on the meridian (MP) and off the meridian (NP). Design: Two instruments—Prognos (MedPrevent GmbH, Waldershof, Germany), a constant-current (DC) device, and PT Probe (designed for this study), a 100-Hz sinusoidal-current (AC) device—were used to record electrical impedance at three APs (right Gallbladder 14, right Pericardium 8, and left Triple Energizer 1), and two control sites for each AP. Each AP, MP, and NP was measured four times in random order with each device. Setting: The study was conducted over a period of 4 days at the Oregon College of Oriental Medicine (OCOM). Subjects: Twenty (20) healthy adults (14 women and 6 men), all recruited from the OCOM student body and faculty, participated in the study. Results: The Prognos measurements had an intraclass correlation (ICC) 0.84 and coefficient of variation (CV) 0.43. The PT Probe had ICC 0.81 and CV 0.31. Impedance values at APs were not significantly less than at MPs or NPs. Impedance values at MPs were also not significantly less than NPs, although their individual p values were 0.05 in 4 of 6 cases. There was a significant trend of increasing impedance with repeated measurements with both the Prognos (p 0.003) and the PT Probe (p 0.003). Conclusions: Within the reliability limits of our study methods, none of the three APs tested has lower skin impedance than at either of the nearby control points. These results are not consistent with previous studies that detected lower skin impedance at APs than nearby sites. Further study is necessary to determine whether MPs have lower skin impedance than nearby NPs. Our study suggests caution is warranted when developing, using, and interpreting results from electrodermal screening devices. Further studies are needed to clarify the clinically important and controversial hypothesis that APs are sites of lower impedance

Inertial and Time-of-Arrival Ranging Sensor Fusion

Wearable devices with embedded kinematic sensors including triaxial accelerometers, gyroscopes, and magnetometers are becoming widely used in applications for tracking human movement in domains that include sports, motion gaming, medicine, and wellness. The kinematic sensors can be used to estimate orientation, but can only estimate changes in position over short periods of time. We developed a prototype sensor that includes ultra wideband ranging sensors and kinematic sensors to determine the feasibility of fusing the two sensor technologies to estimate both orientation and position. We used a state space model and applied the unscented Kalman filter to fuse the sensor information. Our results demonstrate that it is possible to estimate orientation and position with less error than is possible with either sensor technology alone. In our experiment we obtained a position root mean square error of 5.2 cm and orientation error of 4.8° over a 15 min recording

Cerebellar-inspired algorithm for adaptive control of nonlinear dielectric elastomerbased artificial muscle

© 2016 The Author(s) Published by the Royal Society. All rights reserved. Electroactive polymer actuators are important for soft robotics, but can be difficult to control because of compliance, creep and nonlinearities. Because biological control mechanisms have evolved to deal with such problems, we investigated whether a control scheme based on the cerebellum would be useful for controlling a nonlinear dielectric elastomer actuator, a class of artificial muscle. The cerebellum was represented by the adaptive filter model, and acted in parallel with a brainstem, an approximate inverse plant model. The recurrent connections between the two allowed for direct use of sensory error to adjust motor commands. Accurate tracking of a displacement command in the actuator's nonlinear range was achieved by either semi-linear basis functions in the cerebellar model or semi-linear functions in the brainstem corresponding to recruitment in biological muscle. In addition, allowing transfer of training between cerebellum and brainstem as has been observed in the vestibulo-ocular reflex prevented the steady increase in cerebellar output otherwise required to deal with creep. The extensibility and relative simplicity of the cerebellar-based adaptive-inverse control scheme suggests that it is a plausible candidate for controlling this type of actuator. Moreover, its performance highlights important features of biological control, particularly nonlinear basis functions, recruitment and transfer of training

Visual-tactile sensory map calibration of a biomimetic whiskered robot

© 2016 IEEE. We present an adaptive filter model of cerebellar function applied to the calibration of a tactile sensory map to improve the accuracy of directed movements of a robotic manipulator. This is demonstrated using a platform called Bellabot that incorporates an array of biomimetic tactile whiskers, actuated using electro-active polymer artificial muscles, a camera to provide visual error feedback, and a standard industrial robotic manipulator. The algorithm learns to accommodate imperfections in the sensory map that may be as a result of poor manufacturing tolerances or damage to the sensory array. Such an ability is an important pre-requisite for robust tactile robotic systems operating in the real-world for extended periods of time. In this work the sensory maps have been purposely distorted in order to evaluate the performance of the algorithm