AN ABSTRACT OF THE DISSERTATION OF Andrew W. Otto for the degree of Doctor of Philosophy in Robotics and Mechanical Engineering presented on August 7, 2019. Title: Orb Web Vibrations: Modeling, Localization, and Measurement Abstract approved: Ross L. Hatton The orb web is a multipurpose structure|serving as a home for its inhabitant spider, as a prey capture device, and as a physical extension of the spider's sensing abilities. Biologists are particularly interested in the spider's ability to locate prey trapped in its web by sensing the vibrations induced from the initial impact and subsequent struggles of an insect. The presented work focuses on the web as a dynamic structure to better understand its role as a sensing tool for the spider by 1) studying vibrations of synthetic, bio-mimetic orb webs in a controlled engineering environment, 2) creating a computational model for orb web vibrations that includes the effects of web geometry, tension, and material composition, 3) proposing a vibration localization framework suitable for synthetic webs, and 4) combining optical flow measurements from high speed video of webs under motion with experimental modal analysis techniques to study vibration in webs of Araneus diadematus. The vibration model is successfully validated against a set of synthetic webs and used to identify cues useful for vibration localization. The performance of these vibration cues is tested on synthetic webs, and several factors influencing the success rate of the proposed vibration localization framework is presented. Novel motion data of orb webs obtained using phase-based optical flow from high speed video is used to characterize the impulse response of webs built by A. diadematus, and the strengths of optical flow for non-contact motion measurement versus standard tools such as the Laser Doppler Vibrometer (LDV) is discussed. c Copyright by Andrew W. Otto August 7, 2019 All Rights Reserved Orb Web Vibrations: Modeling, Localization, and Measurement by Andrew W. Otto A DISSERTATION submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Presented August 7, 2019 Commencement June 2020 Doctor of Philosophy dissertation of Andrew W. Otto presented on August 7,2019 APPROVED: Major Professor, representing Robotics and Mechanical Engineering Director, Robotics Program Dean of the Graduate School I understand that my dissertation will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my dis- sertation to any reader upon request. Andrew W. Otto, Author ACKNOWLEDGEMENTS The author expresses sincere gratitude to Prof. Hatton for his guidance, input, and patience throughout my time at Oregon State. Special thanks is given to Prof. Udell for his close collaboration on the SpiderHarp and his excellent musicianship, without which getting my research in front of others would have proved far more difficult. CONTRIBUTION OF AUTHORS Andrew W. Otto prepared the manuscripts, designed the test fixtures, wrote the computer code, and performed the experiments covered in this dissertation. Ross L. Hatton aided in manuscript preparation and final editing. Damian O. Elias provided feedback on the first manuscript and took part in final editing. TABLE OF CONTENTS Page 1 Introduction 1 2 Modeling Transverse Vibration in Spider Webs Using Frequency-Based Dy- namic Substructuring 4 2.1 Abstract . 5 2.2 Introduction . 6 2.3 Related Work . 7 2.3.1 Web Vibrations . 7 2.3.2 Dynamic Substructuring . 9 2.4 Materials and Methods . 10 2.4.1 Artificial Webs . 10 2.4.2 Vibration Model . 12 2.5 Results and Discussion . 20 2.5.1 Model Validation . 20 2.5.2 Web Architecture Effects . 21 2.5.3 Vibrational Cues for Stimulus Localization . 24 2.6 Conclusion . 28 3 Bioinspired Vibration Localization in Artificial Orb Webs 29 3.1 Abstract . 30 3.2 Introduction . 30 3.3 Materials and Methods . 33 3.3.1 Web Construction . 33 3.3.2 Testing . 34 3.3.3 Vibration Source Location Estimation . 36 3.3.4 Localization Algorithm . 42 3.4 Results . 43 3.4.1 Optimal Parameter Selection . 44 3.4.2 Web Architecture Effects . 46 3.5 Conclusion . 48 4 Video-based Vibration Measurement of Orb Webs 50 4.1 Abstract . 51 4.2 Introduction . 51 4.3 Materials and Methods . 53 4.3.1 Gradient-based Optical Flow . 54 4.3.2 Phase-based Optical Flow . 56 4.3.3 Output-Only Modal Analysis . 62 TABLE OF CONTENTS (Continued) Page 4.3.4 Experimental Setup . 64 4.3.5 Video Processing . 65 4.3.6 Post-Processing . 65 4.3.7 Natural Frequency and Damping Ratio Estimation . 67 4.4 Results . 68 4.4.1 Vibrometer and Optical Flow Comparison . 68 4.4.2 Frequency Domain Decomposition . 73 4.5 Conclusion . 76 5 Conclusion 79 References 81 LIST OF FIGURES Figure Page 2.1 Illustration of the un-tensioned web geometry and parameters used in this study . 11 2.2 (a) Stress-strain data for the parachute cord and shock cord used in the study as well as dragline and viscid spider silk adapted from [22], (b) the test stand and artificial web used in this study . 12 2.3 (a) Tension distribution and (b) strain distribution output from the web pre-processing step for a sample web . 14 2.4 Model (solid, orange) and experimental (dotted, black) frequency re- sponse (taken as the output acceleration magnitude divided by the input acceleration magnitude) for different values of point mass (m) and radial pretension (τ), (a) m = 10 g and τ = 115 N, (b) m = 70 g and τ = 115 N, (c) m = 10 g and τ = 160 N, (d) m = 70 g and τ = 160 N ................................. 22 2.5 Web architecture effects on web frequency response (accelerance A(!)), (a-d) web frequency response at low levels, (e-h) web frequency re- sponse at high levels, (i) web frequency response at nominal level, (j) input (black) and output (colors) locations for web frequency response 23 2.6 Influence of vibration stimulus location (at left, black dot) on leg fre- quency responses (given here as accelerance) and spectral centroid !c (at center) as well as normalized leg energies (at right) for multiple vi- bration stimulus placements within the capture spiral for a single web architecture . 26 3.1 Slack geoemetry and tension distributions of the β = 45◦ web (a{c), and for the β = 0◦ web (d{e) . 35 3.2 Artificial web, test stand, and 3D printed sensor body (located at web center) used in the experiment . 36 3.3 Overview of the orientation estimation process, (a) input pluck loca- tion (black) and accelerometer placements (colors), (b) acceleration time histories from the applied pluck, (c) clipped section of the accel- eration time histories around pluck onset, (d) visualization of the leg RMS values and predicted orientation using the polygon centroid, (e) visualization of the leg correlation values and predicted orientation . 38 LIST OF FIGURES (Continued) Figure Page 3.4 Overview of the range estimation process, (a) input pluck location (black) and accelerometer placements (colors), (b) acceleration time histories near pluck onset, (c) power spectral densities of each ac- celerometer and the mean peak frequency fp, (d) peak frequencies sorted by range from the web center and curve fit to a decaying expo- nential function . 41 3.5 Flowchart of the vibration source localization algorithm . 43 3.6 Response surfaces representing total location error from Eq. (3.3) for each of the web treatments, (a) the 0◦ web at 100 N, (b) the 0◦ web at 120 N, (c) the 45◦ web at 100 N, (d) the 45◦ web at 120 N . 45 3.7 Estimated vs. actual plots of source orientation θ and range R for each of the web treatments at their corresponding optimal time delays, (a{d) estimated vs. actual curves for orientation θ, (e{h) estimated vs. actual curves for range R. Perfect prediction is indicated by a dashed line in all plots . 47 3.8 Boxplots of euclidean distance error for each web treatment and the localization algorithm using optimal values for tθ and tR . 48 4.1 Contours of half maximums (a) and a 1D slice (b) of the Gabor filter bank used in this paper . 59 4.2 The three webs and their respective 40×40 px ROIs used for compar- ison with vibrometer recordings, (a) Web 1, (b) Web 2, and (c) Web 3...................................... 66 4.3 Velocity recordings V (t) from the vibrometer for Web 1 (a{c), Web 2 (d{f), and Web 3 (g{i) . 69 4.4 Average velocities in the x- and y-axis computed using phase-based optical flow for Web 1 (a{c), Web 2 (d{f), and Web 3 (g{i) . 70 4.5 Power spectral densities of vibrometer velocity (a, c, e) and average flow velocity in the y-direction (b, d, f) for the three webs tested in the experiment. Peak frequencies are indicated by fn on each plot. 71 4.6 Vibrometer displacement X(t) computed by numerically integrating the recorded velocity signal for Web 1 (a{c), Web 2 (d{f), and Web 3 (g{i) . 73 4.7 Average displacements in the x- and y-axis computed by numerically integrating the velocities estimated using phase-based optical flow for Web 1 (a{c), Web 2 (d{f), and Web 3 (g{i) . 74 4.8 PSD of displacements . 75 4.9 Web video frame setup and results for Frequency Domain Decomposi- tion (FDD), ROIs used in optical flow estimation (a), FDD spectrum of singular values (b), the mode shape estimated using FDD from the right singular vectors (d) . 78 LIST OF TABLES Table Page 2.1 Web geometry nomenclature .