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Limits of Modal Insensitivity for Laser Vibrometry, Spectral Reduction Requires Super-Symmetry

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Limits of Modal Insensitivity for Laser Vibrometry, Spectral Reduction Requires Super-Symmetry Limits of Modal Insensitivity for Laser Vibrometry, Spectral Reduction Requires Super-symmetry Michael C. Kobold1 AUGUST 2014 Distribution unlimited and unclassified 1 Personal: [email protected], Work: Michael.C.Kobold @ Navy.mil, Code X-12, Science, Technology, Analysis and Simulation Department, NSWC Panama City Division, Naval Surface Warfare Center PCD, 110 Vernon Ave, BL 110, 3B24W, Panama City, FL, USA 32407-7001, O 850.230.7212, (after-hours M 321.591.3679) Modal Insensitivity ABSTRACT Laboratory measurements showed that identification (ID) and monitoring of objects using remote sensing of their vibration signatures are limited in a couple of rare cases. This work provides two necessary conditions to infer that the remote identification of common targets to within prescribed bounds is practical; failure to ID the spectrum is shown to be rare. Modal modulation of laser return produces data clusters for adequate spectral ID using slowly swept sine (SSS) and small deflection multi-modal (MM) analyses. Results using these completely different calculations lead to practical removal of a remote sensing concern, spectral “reduction” (SR) of return used for object ID. The optical return adequately provides structural mode ID for non-imaging detection and classification of vehicles. Calculations using a large spot size to completely paint the vibrating object provide insight for SR found in laboratory measurements which use spot size as a variable. Non-imaging analytical calculations comparing SSS and MM approximations match to second order. Numerical SSS and MM calculations show vibrating rectangular plates have spatially integrated (non-imaging) return that varies substantially among low-frequency vibration modes. The clustering of data from these two methods is a necessary condition for ID. The theories for SSS and MM describe the signal processing physics for a modal recognition capability and how pure one-dimensional modal targets and super-symmetric square plates can frustrate classification. i Modal Insensitivity Contents FOREWORD ................................................................................................................................. iv PREFACE ....................................................................................................................................... iv 1.0 Introduction ............................................................................................................................... 1 1.1 Prior Laboratory Measurements ........................................................................................... 3 1.2 Prior Laser Vibrometry Measurements and Vehicle ID ....................................................... 6 1.3 Prior Simulation .................................................................................................................... 7 1.4 Adequate Modal Classification .......................................................................................... 11 1.5 Introduction to Modal Representation by Separation of Spectral Phase ............................ 11 2.0 Plane Wave Solutions .............................................................................................................. 15 2.1 Geometry of the Optics Used to Classify Vibration Modes ................................................ 16 2.2 Geometry of the Return, Sum of N Chladni Zones, Area Held Constant ........................... 18 2.3 Bias in Slowly Swept Sine Response (SSS) ........................................................................ 19 2.4 Assumptions of the Plane Wave Solutions .......................................................................... 19 2.5 Structural Considerations of Integration Over Chladni Zones ............................................ 23 2.6 Optical Phase, Time-independent Relations ........................................................................ 24 3.0 Slowly Swept Sine (SSS) Spectral Elimination ...................................................................... 26 Non-Imaging Detected Signal, Numerical Integration .............................................................. 28 a. Analytical SSS approximation ........................................................................................ 29 4.0 Multi-Modal (Small W) Spectral Reduction ........................................................................... 31 4.1 Details of the MM Un-approximated Plot ........................................................................... 37 4.2 Comparison of SSS and MM Theory with Detectibilities: SR versus SU .......................... 38 5.0 Discussion ............................................................................................................................... 42 6.0 Conclusions ............................................................................................................................ 43 6.1 Primary Conclusions ........................................................................................................... 43 6.2 Secondary Conclusions ....................................................................................................... 45 Appendix A: System Coherence for Detectability .......................................................................... 1 Appendix B: Adequacy of a Non-Unity Diagonal .......................................................................... 1 ii Modal Insensitivity List of Figures Figure 1. Reducing the spot size re-acquires the 1 kHz mode2,8 (compare to Figure 2). 4 Figure 2. A large spot size removes the 1 kHz line2,8(compare to Figure 1) 4 Figure 3. Between return from target and spill clutter is a time delay — filter clutter with time gating. 6 Figure 4. For two different times: at left are the FEA deformations, at right the received radiant flux 8 Figure 5. Diagonal of the structural-optical CSC: Large spike outliers are few and narrow. Mean CSC ≈ 1. 9 Figure 6. Condition for equivalent phase in two dimensions (wavy surface) illuminated from above 12 Figure 7. An UMP model (at left) helps analyze the mode distribution of a physical system (at right) 14 Figure 8. Modes shapes for (A) 1-D bar vibration M=0, N=1 and (B) 2-D plate vibration M=2, N=1 17 Figure 9. Non-imaging SSS return from large spot size probe on bars □ versus plates ● 29 Figure 10. Multi-mode small deflection stack-up and non-imaging remote irradiance by max mode N. 36 Figure 11. Spectral reduction and elimination as a function of spot size variation 40 Figure 12. Structural vibration bandwidth N affects spectral uniformity, variation of Chladni zone size 41 List of Tables Table 1. Remote signatures using laser vibrometry support adequate classification conclusions ............................... 2 Table 2. Forms of spectral detection deficiencies .......................................................................................................... 5 Table 3. Modulation term, a function of bandwidth N using different calculations (SSS vs. MM) .............................. 44 iii Modal Insensitivity FOREWORD This extension of the author’s Air Force Institute of Technology 2006 thesis provides mitigation of a concern in the laser vibrometry field. This stand-alone product is not a deliverable of existing projects but is a foundation for many. Variations of this type of sensing include interferometry sensing for buried object detection. This type of remote sensing is used and proposed by X-12 primarily for vehicle identification including a ground-based type of Identify Friend or Foe (IFF) to provide added safety to our troops during complex operations. Michael C. Kobold, PE, author. PREFACE The author would like to thank the US Naval Surface Warfare Center Panama City Division (NSWC PCD) scientists. For substantial review assistance: Dr. Paul Schippnick (retired) and especially Dr. Jeff Rish III. For beneficial discussions: NSWC PCD managers of ONR projects Dr. Harold (Dick) Suiter and John Holloway, University of Dayton Professor Partha Banerjee and Director Joseph Haus, Air Force Research Laboratory (AFRL), and Air Force Institute of Technology (AFIT) professors Stephen Cain (my thesis advisor), William Baker, Richard Cobb, and Robert Canfield. The author’s thesis was encouraged by Dr. Matt Dierking (AFRL/SNJM), Dr. Robert Williams (AFRL/SNAT), and GD-AIS, whose support is greatly appreciated. Photos of the experimental apparatus, Figure 1 and Figure 2, were graciously authorized by Royal Australian Air Force (RAAF) Flight Lieutenant Ngoya Pepela whose AFIT thesis provides a pertinent experimental physical example of the insensitivity subject, spectral elimination. iv Modal Insensitivity 1.0 Introduction Laser vibrometry is a mature field. Definition of vibration modes is a purpose and region of engineering unto itself. Applications of methods to identify modes of vibration of distant objects continue to expand into different domains from microscopic to astronomical, from geological to geospatial, and from biomedical diagnosis to ‘health monitoring’ of potentially dangerous mechanical equipment. While ordinary acousto-optic modulation is in-surface aligned,1 the use of lasers to probe vibration states (laser vibrometry) involves out-of-plane to near-normal reflection from the surface. Probe distances vary from standoff range (mm or cm) to remote sensing range (2 km < R ~ 10 km). Astronomical radio vibrometry could assume an entire target (body of fluid) is illuminated. However, this article restricts analysis to the range
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