Sensitivity vector fields in embedded coordinates

2011 ◽  
Author(s):  
Andrew R. Sloboda ◽  
Bogdan I. Epureanu
Keyword(s):  
Vector Fields ◽  
Sensitivity Vector

High-Sensitivity Mass Sensing Based on Enhanced Nonlinear Dynamics and Attractor Morphing Modes

2006 ◽  
Author(s):  
Shih-Hsun Yin ◽  
Bogdan I. Epureanu
Keyword(s):  
Lead Zirconate Titanate ◽  
Vector Fields ◽  
Experimental System ◽  
High Sensitivity ◽  
Lead Zirconate ◽  
Chaotic Regime ◽  
Nonlinear Feedback ◽  
Regime Changes ◽  
Distribution Of Points ◽  
Sensitivity Vector

This paper demonstrates two novel methods for identifying small parametric variations in an experimental system based on the analysis of sensitivity vector fields (SVFs) and probability density functions (PDFs). The experimental system includes a smart sensing beam excited by a nonlinear feedback excitation through two PZT (lead zirconate titanate) patches symmetrically bonded on both sides at the root of the beam. The nonlinear feedback excitation requires the measurement of the dynamics (e.g. velocity of one point at the tip of the beam) and a nonlinear feedback loop, and is designed such that the beam vibrates in a chaotic regime. Changes in the state space attractor of the dynamics due to small parametric variations can be captured by SVFs which, in turn, are collected by applying point cloud averaging (PCA) to points distributed in the attractors for nominal and changed parameters. Also, the PDFs characterize statistically the distribution of points in the attractors. The differences between the PDFs of the attractors for different changed parameters and the baseline attractor can provide different attractor morphing modes for identifying variations in distinct parameters. The experimental results based on the proposed approaches show that very small amounts of added mass at different locations along the beam can be accurately identified.

Sensitivity vector fields for atomic force microscopes

2009 ◽  
Vol 59 (1-2) ◽  
pp. 113-128 ◽  
Author(s):  
Joosup Lim ◽  
Bogdan I. Epureanu
Keyword(s):  
Vector Fields ◽  
Atomic Force Microscopes ◽  
Atomic Force ◽  
Sensitivity Vector

Structural health monitoring based on sensitivity vector fields and attractor morphing

2006 ◽  
Vol 364 (1846) ◽  
pp. 2515-2538 ◽  
Author(s):  
Shih-Hsun Yin ◽  
Bogdan I Epureanu
Keyword(s):  
Structural Damage ◽  
Vector Fields ◽  
Duffing Oscillator ◽  
Dynamic Responses ◽  
Third Order ◽  
Aeroelastic System ◽  
Aeroelastic Model ◽  
Local Reduction ◽  
Unsteady Supersonic Flow ◽  
Sensitivity Vector

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we analyse the morphology (deformation and movement) of the attractor of the dynamics of the aeroelastic system and the Duffing oscillator. Damages of various locations, extents and levels are shown to be revealed by the attractor-based analysis. For the panel, the type of damage considered is a local reduction in the bending stiffness. For the Duffing oscillator, variations in the linear and nonlinear stiffnesses and damping are considered as damage. Present studies of such problems are based on linear theories. In contrast, the presented approach using nonlinear dynamics has the potential of enhancing accuracy and sensitivity of detection.

Maximizing Sensitivity Vector Fields: A Parametric Study

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Andrew R. Sloboda ◽  
Bogdan I. Epureanu
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Vector Fields ◽  
Nonlinear Feedback ◽  
Baseline System ◽  
Nominal Parameter ◽  
Construction Play ◽  
Sensitivity Vector ◽  
System Attractor ◽  
Made In

Sensitivity vector fields (SVFs) have proven to be an effective method for identifying parametric variations in dynamical systems. These fields are constructed using information about how a dynamical system's attractor deforms under prescribed parametric variations. Once constructed, they can be used to quantify any additional variations from the nominal parameter set as they occur. Since SVFs are based on attractor deformations, the geometry and other qualities of the baseline system attractor impact how well a set of SVFs will perform. This paper examines the role attractor characteristics and the choices made in SVF construction play in determining the sensitivity of SVFs. The use of nonlinear feedback to change a dynamical system with the intent of improving SVF sensitivity is explored. These ideas are presented in the context of constructing SVFs for several dynamical systems.

Parameter Reconstruction Based on Sensitivity Vector Fields

2006 ◽  
Vol 128 (6) ◽  
pp. 732-740 ◽  
Author(s):  
Bogdan I. Epureanu ◽  
Ali Hashmi
Keyword(s):  
State Space ◽  
Vector Fields ◽  
Test Cases ◽  
Novel Approach ◽  
Wide Range ◽  
Parameter Variations ◽  
Dynamic Attractors ◽  
Proper Orthogonal ◽  
Sensitivity Vector ◽  
Parameter Reconstruction

A novel approach to determine very accurately multiple parameter variations by exploiting the geometric shape of dynamic attractors in state space is presented. The approach is based on the analysis of sensitivity vector fields. These sensitivity vector fields describe changes in the state space attractor of the dynamics and system behavior when parameter variations occur. Distributed throughout the attractor in state space, these fields form a collection of snapshots for known parameter changes. Proper orthogonal decomposition of the parameter space is then employed to distinguish multiple simultaneous parametric variations. The parametric changes are reconstructed by analyzing the deformation of attractors which are characterized by means of the sensitivity vector fields. A set of basis functions in the vector space formed by the sensitivity fields is obtained and is used to successfully identify test cases involving multiple simultaneous parametric variations. The method presented is shown to be robust over a wide range of parameter variations and to perform well in the presence of noise. One of the main applications of the proposed technique is detecting multiple simultaneous damage in vibration-based structural health monitoring.

Experimental Enhanced Nonlinear Dynamics and Identification of Attractor Morphing Modes for Damage Detection

2007 ◽  
Vol 129 (6) ◽  
pp. 763-770 ◽  
Author(s):  
Shih-Hsun Yin ◽  
Bogdan I. Epureanu
Keyword(s):  
Lead Zirconate Titanate ◽  
Vector Fields ◽  
Experimental System ◽  
Lead Zirconate ◽  
Chaotic Regime ◽  
Base Line ◽  
Nonlinear Feedback ◽  
Regime Changes ◽  
Distribution Of Points ◽  
Sensitivity Vector

This paper demonstrates two novel methods for identifying small parametric variations in an experimental system based on the analysis of sensitivity vector fields (SVFs) and probability density functions (PDFs). The experimental system includes a smart sensing beam excited by a nonlinear feedback excitation through two lead zirconate titanate patches symmetrically bonded on both sides at the root of the beam. The nonlinear feedback excitation requires the measurement of the dynamics (e.g., velocity of one point at the tip of the beam) and a nonlinear feedback loop, and is designed such that the beam vibrates in a chaotic regime. Changes in the state space attractor of the dynamics due to small parametric variations can be captured by SVFs, which, in turn, are collected by applying point cloud averaging to points distributed in the attractors for nominal and changed parameters. Also, the PDFs characterize statistically the distribution of points in the attractors. The differences between the PDFs of the attractors for different changed parameters and the base line attractor can provide different attractor morphing modes for identifying variations in distinct parameters. Experimental results based on the proposed approaches show that very small amounts of added mass at different locations along the beam can be accurately identified.2

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