Title: FE model-based feature generation for Structural Health Monitoring
1Where Non-Smooth Systems Appear in Structural
Dynamics
Keith Worden Dynamics Research Group Department
of Mechanical Engineering University of Sheffield
2Nonlinearity
- Nonlinearity is present in many engineering
problems - Demountable structures with clearances and
friction. - Flexible structures large amplitude motions.
- Aeroelasticity limit cycles.
- Automobiles squeaks and rattles, brake squeal,
dampers. - Vibration isolation viscoelastics, hysteresis.
- Sensor/actuator nonlinearity piezoelectrics
- In many cases, the nonlinearity is non-smooth.
3- So, where are the problems in Structural
Dynamics? - System Identification
- Structural Health Monitoring
- Active/passive control of vibrations
- Control
4System Identification
Automotive damper (shock absorber) Designed to be
nonlinear. Physical model prohibitively
complicated. Bilinear.
5System ID
If nonlinearities are linear in the parameters
there are many powerful techniques
available. Even the most basic piecewise-linear
system presents a problem.
6Everything OK if we know d linear in the
parameters. Otherwise need nonlinear
least-squares. Iterative - need good initial
estimates. Can use Genetic Algorithm.
7Genetic Algorithm
- Encode parameters as binary bit-string
Individuals. - Work with population of solutions.
- Combine solutions via genetic operators
- Selection
- Crossover
- Mutation
- Minimise cost function
8Excellent solution Derivative-free. Avoids
local minima. No need to differentiate/integrate
time data. Directly optimises on Model Predicted
Output as opposed to One-step-ahead
predictions.
9Hysteresis
- Systems with memory
- Bouc-Wen model is versatile.
Nonlinear in the parameters. Unmeasured state
z. Can use GA again or Differential Evolution.
10Hydromount
Contains viscoelastic elements. Valves (like
shock absorber) produce non-smooth nonlinearity.
11Freudenberg Model
12Friction
- Very significant for high-speed, high-accuracy
machining. - Need
- Friction models,
- Control strategies.
- Most basic model is Coulomb friction
13- Far too simplistic
- Static/dynamic friction.
- Presliding/sliding regimes.
- Stribeck effect
- Various models in use white/grey/black.
14Stribeck Curve
15LuGre Model
16An Experiment
17(No Transcript)
18Particle Damper
19Structural Health Monitoring
- Rytters hierarchy
- Detection
- Location
- Severity
- Prognosis
- Two main approaches
- Inverse problem
- Pattern Recognition
20Are These Systems Damaged?
Did you use pattern recognition?
21Pattern Recognition D2D
- Data acquisition
- Pre-processing
- Feature extraction
- Classification
- Decision
- Critical step is often Feature Extraction.
22Dog or Cat
23Nonlinearity Again
- Often, the occurrence of damage will change the
structure of interest from a linear system to a
nonlinear system e.g. a breathing crack. - This observation can be exploited in terms of
selection of features, e.g. one can work with
features like Liapunov exponents of time-series
if chaos is observed, system must be nonlinear.
But
24Tests for Nonlinearity
- Homogeneity
- Reciprocity
- Coherence
- FRF distortion
- Hilbert transform
- Correlation functions
25Correlation functions
26Holder Exponent
Acceleration time-histories
Holder exponent (In-Axis)
27SDOF Model of Cracked Beam
Parameter a represents depth of crack
28Bifurcation diagram for a 0.2.
29- Problem is that system bifurcates and shifts in
and out of chaos features like liapunov
exponents, correlation dimension etc. will not
always work and are not monotonically increasing
with damage severity. - Figure shows dependence on frequency, but same
picture appears with crack depth as independent
variable - Are there better features?
30Rocking (Thanks to Lawrie Virgin)
31(No Transcript)
32(No Transcript)
33What needs to be done?
- Development of signal processing tools like
estimator of Holder exponent. - Better friction models (white/grey/black).
- Parameter estimation/optimisation methods (as a
side-issue, convergence results for GAs etc.) - Control methods for non-smooth systems.
- Versatile hysteresis models.
- Understanding of high-dimensional nonlinear
models (e.g. FE).
34- Quantities that increase monotonically with
severity of nonlinearity? - Engineers like random excitation - tools for
stochastic DEs and PDEs with non-smooth
nonlinearities. - Contact/friction models for DEM.
- Sensitivity analysis/uncertainty propagation
methods for systems that bifurcate.
35Acknowledgements
- Lawrie Virgin (Duke University)
- Chuck Farrar, Gyuhae Park (Los Alamos National
Laboratory) - Farid Al Bender (KUL, Leuven)
- Jem Rongong, Chian Wong, Brian Deacon, Jonny
Haywood (University of Sheffield) - Andreas Kyprianou (University of Cyprus)