1. Structural Damage Identification
LOW FREQUENCY TECHNIQUES
Patrick Guillaume

2. Damage Detection Philosophy
Rytter (1993*,**) introduced a damage state classification
system which has been widely accepted by the community
dealing with damage detection and SHM. Following these
lines, the damage state is described by answering the following
questions (Sohn et al. (2003)):
(1) Is there damage in the system? (existence)
(2) Where is the damage in the structure? (location)
(3) What kind of damage is present? (type)
(4) How severe is the damage? (extent)
(5) How much useful life remains? (prognosis)

3. The Monitoring Process (1/2)
1. Operational Evaluation
Operational evaluation answers questions related to the
damage detection system implementation, such as economic
issues, possible failure modes, operational and environmental
conditions and data acquisition related limitations.
2. Data Acquisition, Fusion and Cleansing
Data acquisition is concerned with the quantities to be measured,
the type and quantity of sensors to be used, the locations
where these sensors are to be placed, sensor resolution,
bandwidth, and hardware.
Data fusion, as a discipline of SHM, is the ability to integrate
data acquired from the various sensors in the measurement
chain.
Data cleansing is the process of selecting significant data
from the multitude of information, i.e., the determination of
which data is necessary (or useful) in the feature selection
process.

4. The Monitoring Process (2/2)
3. Feature Extraction and Information Condensation
Feature extraction is the process of identifying damage sensitive properties,
which allow one to distinguish between the damaged and undamaged
structural states.
Information condensation becomes increasingly advantageous
and necessary as the quantity of data increases, particularly
if comparisons are to be made between sets of data
obtained over the life cycle of a system.
4. Statistical Model Development for Feature Discrimination
An important issue in the development of statistical models
is to establish the model features sensitivity to damage
and to predict false damage identification.

5. Damage in Composite Materials
The use of fibre reinforced plastics (FRP) as an alternative
to conventional materials, such as metallic alloys, is undergoing
increasing growth, especially in the aeronautical, naval
and automotive industries, because of their excellent mechanical
properties, low density and easy of shaping.
Composite materials possess specific strengths and Young’s
moduli many times greater than those of the most widely used
metallic materials, such as steel, aluminum and titanium.
However, the extreme sensitivity of composite materials to
impact loads constitutes a hindrance to their utilization. In
aeronautical structures, for example, the components may have
to undergo (i) low energy impacts caused by dropped tools or
mishandling during assembly and maintenance, (ii) medium
energy impacts caused in-service by foreign objects such as
stones or birds and (iii) high energy impacts caused by military
projectiles (Matthews (1999), Silva (2001) and Carvalho
(2003)).

6. Some Damage Detection Techniques
Static Stiffness Variations
Linear stiffness in function of the number of fatigue cycles
Static stiffness variations during crack growth in a slat track A320

7. Some Damage Detection Techniques
Natural Frequencies and FRFs
The development of modal analysis techniques for damage
detection and SHM arose from the observation that changes
in the structural properties have consequences on the natural
frequencies. Nevertheless, the relatively low sensitivity of
natural frequency to damage requires high levels of damage
and measurements made with high accuracy in order to
achieve reliable results. Moreover, the capacity to locate
damage is somewhat limited, as natural frequencies are global
parameters and modes can only be associated with local
responses at high frequencies.

8. Some Damage Detection Techniques
Natural Frequencies and FRFs
Messina et al. (1992) proposed the damage location assurance
criterion (DLAC) in location j, which is a correlation
similar to the modal assurance criterion (MAC) of Allemang
and Brown (1982), and is given by:
the experimental frequency shift vector
the analytical frequency shift vector
A zero value indicates no correlation and a unity value indicates
perfect correlation between the vectors involved in the DLAC
relationship. Damage location and dimension is identified
by maximizing this objective function.

9. Some Damage Detection Techniques
Natural Frequencies and FRFs
Zang et al. (2003a) presented criteria's to correlate
measured frequency responses from multiple sensors and proposed
using them as indicators for structural damage detection.
One criterion is the global shape correlation (GSC)
function, which is sensitive to mode shape differences but
not to relative scales, being defined as:
is a column of FRF baseline data
is a column of the current measured FRF data

10. Some Damage Detection Techniques
Mode Shape Changes (MAC)
The MAC value (Modal Assurance Criteria),
which is probably the most common way of establishing a
correlation between experimental and analytical models, is
defined by Allemang and Brown (1982) as:
West (1984*) uses the MAC to determine the level of correlation
between modes from the test of an undamaged Space Shuttle Orbiter
body flap and the modes from the test of the flap after loading.

11. Some Damage Detection Techniques
Mode Shape Changes (COMAC)
Although the MAC can provide a good indication of the disparity
between two sets of data, it does not show explicitly where in the
structure is the source of discrepancy. The co-ordinate MAC
(COMAC) has been developed from the original MAC. It is
the reverse of the MAC in that it measures the correlation at
each degree-of-freedom (DOF) averaged over the set of correlated
mode pairs. The COMAC identifies the co-ordinates
at which two sets of mode shapes do not agree, and is
defined as (Lieven and Ewins (1988)):

12. Some Damage Detection Techniques
Mode Shape Curvature
As an alternative to the use of mode shapes as damage features, mode shape
curvature (i.e., second order derivative) can be used to obtain spatial information
about vibration changes. It has been reported in literature that absolute changes in
mode shape curvature can be a good indicator of structural damage (Pandey et al.,
1991).

13. Some Damage Detection Techniques
Changes in Modal Flexibility
Another class of damage identification methods makes use of the dynamically
measured flexibility matrix to estimate changes in the static behaviour of the structure.
Typically, damage is assessed by comparing the measured flexibility matrix, computed
on a basis of the reference modal data, to the measured flexibility matrix
computed on a basis of the damaged condition.

14. Some Damage Detection Techniques
Changes in Strain Energy
Instead of using mode shape curvature directly, derived quantities, such as strain
energy, can be chosen as damage features. The Changes in Strain Energy (CSE)
method localizes structural damage as a decrease in modal strain energy between
2 structural DOFs (Stubbs et al., 1992). For a linear elastic beam structure, the
strain energy can be computed on a basis of the mode shape curvature. In that
case, the damage index for element i centered around DOF i, can be written as

15. Some Damage Detection Techniques
Sensitivity-based Approach
The last method is based on the interpretation of changes in natural frequency
by means of the sensitivity of the natural frequencies of a reference condition to
local mass changes in an experimental DOF or local stiffness changes between two
adjacent DOFs. The method requires both the natural frequencies and normalized
mode shape estimates of the structure in its reference condition as well as the
corresponding natural frequency estimates of the damaged condition.

16. Some Damage Detection Techniques
Sensitivity-based Approach
Combined approach

17. Some Damage Detection Techniques
Sensitivity-based Approach
Iterative Weighted Pseudo Inverse

18. Experimental Validation

19. Experimental Validation

20. Experimental Validation
MAC

21. Experimental Validation
COMAC

22. Experimental Validation
Mode Shape Curvature

23. Experimental Validation
Strain Energy

24. Experimental Validation
Modal Flexibility

25. Experimental Validation
Sensitivity-based Approach

26. Experimental Validation
Sensitivity-based Approach (combined approach)

27. Experimental Validation
Sensitivity-based Approach (combined approach)
Iterative Weighted Pseudo Inverse

28. Experimental Validation

29. Experimental Validation

30. Experimental Validation

31. Experimental Validation

32. Experimental Validation