Post on 20-Jan-2023
UNIVERSITÀ DEGLI STUDI DI NAPOLI “FEDERICO II”
DIPARTIMENTO DI INGEGNERIA INDUSTRIALE
CORSO DI LAUREA IN INGEGNERIA AEROSPAZIALE
(Classe delle Lauree in Ingegneria Industriale, Classe N. L-9)
Graduation Thesis
ABOUT VIBRATION BASED SHM TECHNIQUES
FOR METALLIC STRUCTURES
SUPERVISORS: CANDIDATE:
Ing. MASSIMO VISCARDI GIANMARCO SORRENTINO
Ing. DANIELA SIANO Matr. N35/000469
Anno Accademico 2012/2013
Abstract
Structural Health Monitoring is a lively and researched topic that is developing very quickly
in the aeronautical application field for some good reasons. The aging of commercial aircraft
and the need to extend their life requires frequent and intensive inspections and maintenance,
which is a financial drain to operators. The implementation of a good SHM monitoring
systems allows to improve the safety of the aircrafts without increase the rate of the
maintenance in the life cycle cost of the unit. A correct SHM system can indicate the damage
type, location, severity and estimate the remaining life of the structure while the structure is in
use. This paper will begin with an overview on the most used SHM techniques followed by a
focus on the vibration techniques. The second part of this paper will introduce a particular
case whose purpose is to analyze an aluminum panel by a vibration based technique. The
analysis will be supported by the implementation of a special analysis filter (FIR). All the
tests that will be shown in this work have been carried out in the Aerospace Engineering
Department of the University of Naples “Federico II”.
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acknowledgments
La prima persona a cui rivolgo un mio sentito ringraziamento è colui che ha reso possibile questo
lavoro, il mio relatore, l'ing. Massimo Viscardi. Lo ringrazio in particolar modo per essere stato un
esempio di sincera dedizione e di passione al lavoro e di disponibilità verso noi studenti.
Alla mia famiglia. Ai miei genitori che mi hanno sempre supportato e motivato. Li ringrazio
perché, più di chiunque altro, hanno sempre creduto in me. A Carla e Francesco, i miei due
fratelli maggiori il cui esempio mi è stato sempre di insegnamento. A zio Michele e zia Rosaria: è
anche a loro che dedico questo lavoro come ringraziamento per tutto l'aiuto che, da lontano, non
mi hanno mai fatto mancare.
Un ringraziamento a Martina, la mia fidanzata, colei che più di tutte le persone ha dovuto
sopportare le mie ansie e le mie preoccupazioni. La ringrazio per non avermi mai fatto mancare,
al di la dei sentimenti che ci legano, la sua vicinanza e la sua comprensione.
A Simone, ora mio collega: credo che tutte le persone che mi sono state vicine in questi ultimi
anni abbiano avuto la percezione di quanto sia stato importante nel mio percorso universitario.
Non solo collega eccellente ma anche amico insostituibile.
Infine un pensiero particolare va ad una persona che da quasi un anno e mezzo non c'è più, zio
Salvatore. So che sarà felice anche lui lassù.
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Table of contents
• Chapter 1 - SHM - State of art
1.1 Introduction to Structural Health Monitoring
1.2 Data Acquisition, Normalization and Cleansing
1.3 Feature Extraction and Data Compression
1.4 Potential SHM Technologies Considered
• Chapter 2 - Vibration based, our case of study
2.1 Vibration Based
2.2 Type of sensors
2.3 Type of input signals
• Chapter 3 - Data Postprocessing
3.1 Adaptive filter
3.2 RLS algorithm
• Chapter 4 - Application - test phase
4.1 Test unit
4.2 Experimental setup
4.3 Acquisition
4.4 Data processing
• Chapter 5 - Conclusions and further
5.1 Conclusions
5.2 Possible developments for a future analysis
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Chapter 1
1.1 Introduction to Structural Health Monitoring
Increasing reliability and safety of technical systems for vehicles and machines is an effort of
increasing importance for technical development. Safety means protection against damage
due to misuse of instruments, overloading, unexpected events outside of human control,
material defects, improper design and change of material properties due to aging fatigue or
corrosion. This also includes unwanted faulty operation or human failure. In the interest of an
efficient use of materials and energy, a 100% usage of the exploitation of components is
desired. This requires periodical inspections and, if necessary, replacement of the
components. The trend is to accompany or replace the inspections with continuous monitoring
of loading conditions, as well as materials and structural health.
Structural Health Monitoring (SHM) is the process of reserching and reporting damage and
nonconformities within a structure. SHM is an expansive field encompassing a wide range of
definitions but for use in this paper, structural health monitoring is defined as measuring and
reporting damage in a structure through the use of permanent sensors. This is distinguished
from Non-Destructive Evaluation (NDE) which is the measurement and characterization of
damage performed offline with portable sensors and is used to detect and determine size of
damage in localized areas. It should be noted that structural health monitoring can use the
tools of NDE but those tools are permanent and active so that measurements and observations
can be made during the use phase of the structure. In the field of structural health monitoring
damage can be defined as "changes to the material and/or geometric properties of these
systems". Damage in the structure does not mean failure of the structure but rather
corresponds to a non optimal level of performance. Physical events such as cracking,
corrosion, impacts, and loss of material are examples or damage of concern in SHM .
The advantages of this technique, in addition to safety and reliability, are as follows:
• Maintenance cycles can be extended,
• Condition based maintenance,
• Extended use of components,
• Exploitation of material reserves,
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• Increased retail value.
1.2 Data Acquisition, Normalization and Cleansing
The data acquisition portion of the SHM process involves selecting the excitation methods,
the sensor types, number and locations, and the data acquisition/storage/transmittal hardware.
Again, this process will be application specific. Economic considerations will play a major
role in making these decisions. The intervals at which data should be collected is another
consideration that must be addressed.
Because data can be measured under varying conditions, the ability to normalize the data
becomes very important to the damage identification process. As it applies to SHM, data
normalization is the process of separating changes in sensor reading caused by damage from
those caused by varying operational and environmental conditions. One of the most common
procedures is to normalize the measured responses by the measured inputs. When
environmental or operational variability is an issue, the need can arise to normalize the data in
some temporal fashion to facilitate the comparison of data measured at similar times of an
environmental or operational cycle. Sources of variability in the data acquisition process and
with the system being monitored need to be identified and minimized to the extent possible.
In general, not all sources of variability can be eliminated. Therefore, it is necessary to make
the appropriate measurements such that these sources can be statistically quantified.
Variability can arise from changing environmental and test conditions, changes in the data
reduction process, and unit-to-unit inconsistencies.
Data cleansing is the process of selectively choosing data to pass on to or reject from the
feature selection process. The data cleansing process is usually based on knowledge gained by
individuals directly involved with the data acquisition. As an example, an inspection of the
test setup may reveal that a sensor was loosely mounted and, hence, based on the judgment of
the individuals performing the measurement, this set of data or the data from that particular
sensor may be selectively deleted from the feature selection process. Signal processing
techniques such as filtering and re-sampling can also be thought of as data cleansing
procedures.
Finally, the data acquisition, normalization, and cleansing portion of SHM process should not
be static. Insight gained from the feature selection process and the statistical model
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development process will provide information regarding changes that can improve the data
acquisition process.
1.3 Feature Extraction and Data Compression
The area of the SHM process that receives the most attention in the technical literature is the
identification of data features that allows one to distinguish between the undamaged and
damaged structure. Inherent in this feature selection process is the condensation of the data.
One of the most common feature extraction methods is based on correlating measured system
response quantities, such a vibration amplitude or frequency, with the first-hand observations
of the degrading system. Another method of developing features for damage identification is
to apply engineered flaws, similar to ones expected in actual operating conditions, to systems
and develop an initial understanding of the parameters that are sensitive to the expected
damage. The flawed system can also be used to validate that the diagnostic measurements are
sensitive enough to distinguish between features identified from the undamaged and damaged
system. The use of analytical tools such as experimentally-validated finite element models
can be a great asset in this process. In many cases the analytical tools are used to perform
numerical experiments where the flaws are introduced through computer simulation. Damage
accumulation testing, during which significant structural components of the system under
study are degraded by subjecting them to realistic loading conditions, can also be used to
identify appropriate features. This process may involve induced-damage testing, fatigue
testing, corrosion growth, or temperature cycling to accumulate certain types of damage in an
accelerated fashion. Insight into the appropriate features can be gained from several types of
analytical and experimental studies as described above and is usually the result of information
obtained from some combination of these studies.
The operational implementation and diagnostic measurement technologies needed to perform
SHM produce more data than traditional uses of structural dynamics information. A
condensation of the data is advantageous and necessary when comparisons of many feature
sets obtained over the lifetime of the structure are envisioned. Also, because data will be
acquired from a structure over an extended period of time and in an operational environment,
robust data reduction techniques must be developed to retain feature sensitivity to the
structural changes of interest in the presence of environmental and operational variability.
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1.4 Potential SHM Technologies Considered
There is a wide range sensor systems being around and developed or under consideration
where a selection of those is shown in figure below. The sensors and sensor systems are
allocated to a specific physical parameter such as sound, vibration, electromagnetism,
temperature, light or possibly others, being further enhanced and more to come such as at the
nano scale. Some of the ones being considered most are described below.
Figure 1.1: Sensing options for structural health monitoring.
• Vibration based: This approach consists in evaluate the vibration modes of the
structure produced by the use of actuators. If the actuators are piezoelectric devices,
the same units can be used like sensors to register the vibration modes. A variation of
the frequencies or of the amplitudes from the value registered on the non-damaged
configuration reveals the existence of the damage . This approach operate in a low
frequencies range.
• Electrical strain gauges: A very established and reliable technique where strain
gauges are usually bonded onto a structure’s surface. Recently also techniques for
printing those sensors have emerged. The sensors are specifically good for loads
monitoring.
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• Electrical crack wires: A rather simple, reliable and low cost technique that allows
cracks of different size to be recognised. Recently laser printing techniques have been
developed which have been proven to work on various types of carriers.
• Acoustic emission: An NDT technique comprising ‘listening’ to damage (i.e. crack,
delamination) progression having developed during in service operation. The
technique is suitable for global monitoring however needs to operate when the
structure to be monitored is in operation, may only provide signals at the very high but
seldom loads and may suffer from background noise which can complicate the
situation for specific applications. from background noise which can complicate the
situation for specific applications.
• Acousto-ultrasonics: Another well known NDT technique where an actuator (usually
a piezoelectric transducer) sends an acoustic signal into the structure to be monitored
which will then be recorded either by the same transducer (pulse-echo) or a different
sensor (pitch-catch). A reference signal is taken for the undamaged condition and is
compared to all follow-on readings where the difference in signal is considered to be
correlated to damage. So far the transducers are usually attached to or integrated into
the structure on a manual basis.
• Laser vibrometry: The principle of this technique is very similar to acousto-
ultrasonics where the laser now takes over the sensor role by being able to scan a
larger area. An advantage is the wide area scanning. A disadvantage is however the
access to the component to be monitored which the laser requires.
• Comparative vacuum monitoring (CVM): This technique provided by Structural
Monitoring Systems (SMS) in Perth/Australia is based on a two chamber system of
very thin channels introduced into a silicon based sensor. The sensor is placed onto the
location prone to cracking. One of the chambers is evacuated with vacuum to be held.
Once a crack emerges under the evacuated chamber the pressure increases, which
defines the presence of a crack. The method works well for local monitoring where the
location of cracking is well known. However for global monitoring the approach
becomes rather complicated. The technique is currently widely explored and validated
in various trials with aircraft manufacturers and operators.
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• MEMS: This is another multifunctional sensor widely used for monitoring
accelerations and pressures. The sensor is mainly silicon based using micro
machining, etching and coating technologies. It is light weight (possibly less than 1
gram) however requires individual contacting and possibly a circuit board. MEMS
sensors are commercially available however mainly in the low frequency range (up to
10 kHz) only. MEMS sensors operating at higher frequency are feasible and have been
demonstrated. However they have to be tailor made, which requires the appropriate
MEMS design and fabrication facilities to be available making them rather expensive
at this stage.
• Electromagnetic foils: The concept of these foils is similar to the one described before
with regard to the Smart Layer and the acousto-ultrasonics principle. The principle is
the generation of electromagnetic fields in the way this is known from high frequency
eddy current testing. The foils can be purchased commercially from companies such as
either General Electric or Jentek and have been shown in a variety of feasibility
studies that they work well with regard to fatigue and corrosion monitoring in metallic
structures.
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Chapter 2
2.1 Vibration Based
Vibration based is the SHM technique utilized in this paper as case of study for the
experimental tests. This technique has been applied to a reinforced aluminum panel.
The basic premise of vibration based damage detection is that the damage will alter the
stiffness, mass or energy dissipation properties of a system, which, in turn, will alter the
measured dynamic response of the system. Modal parameters are utilized to achieve the result
of identify the damage. Modal parameters (notably frequencies, mode shapes, and modal
damping) are functions of the physical properties of the structure (mass, damping, and
stiffness). Therefore, changes in the physical properties will cause changes in the modal
properties. An initial measurement of the undamaged structure as the baseline for future
comparison of measured response is necessary for the identification of the damage.
Critical issues in applying vibration-based SHM methods are :
• Type, location and numbers of sensors,
• Type and location of excitations,
• Types of damage detection algorithms employed,
• The data acquisition/storage/transmission hardware.
2.2 Type of sensors: Piezoceramic devices
In the carried out tests piezoceramic patches Stetner PPK23 have been used as actuators and
sensors, having a square and rectangular shape whose dimension is 30 x 30 mm and a
thickness equal to 0,5 mm.
The piezoceramic patches have been bonded on the structures by means of a bicomponent
epoxy adhesive. The piezoceramic patches are made of piezoelectric material. The
piezoelectricity is the ability of certain crystals to generate a voltage in response to applied
mechanical stress. The word is derived from the Greek “piezein”, which means to squeeze or
press. The piezoelectric effect is reversible; piezoelectric
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crystals, subject to an externally applied voltage, can change shape by a small amount. The
deformation, about 0.1% of the original dimension in PZT, is of the order of nanometers. The
lead zirconium titanate (PZT, also Lead zirconate titanate) is a ceramic perovskite material
that shows a marked piezoelectric effect - that is, it develops a voltage difference across two
of its faces when compressed, and ferroelectric effect. It also features an extremely large
dielectric constant.
Figure 2.1: Piezoceramic device.
In a piezoelectric crystal, the positive and negative electrical charges are separated, but
symmetrically distributed, so that the crystal overall is electrically neutral. Each of these sites
forms an electric dipole and dipoles near each other tend to be aligned in regions called Weiss
domains. The domains are usually randomly oriented, but can be aligned during poling, a
process by which a strong electric field is applied across the material, usually at elevated
temperatures.
When a stress is applied, this symmetry is disturbed, and the charge asymmetry generates a
voltage across the material. For example, a 1 cm cube of quartz with 500 lbf (2 kN) of
correctly applied force upon it, can produce 12.500 V of electricity. Piezoelectric materials
also show the opposite effect, called converse piezoelectricity, where the application of an
electrical field creates mechanical deformation in the crystal. Piezoelectricity is the combined
effect of the electrical behavior of the material:
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Charge Density, D = Permittivity x Electric Field, E
Strain, S = Compliance, s x Stress, T
This may be expressed as:
{S} = [sE]{T} + [d]{E}
{D} = [d]t + [εT]{E}
The bending forces generated by converse piezoelectricity are extremely high, of the order of
tens of millions of pounds (tens of meganewtons), and usually cannot be constrained. The
only reason the force is usually not noticed is because it causes a displacement of the order of
few nanometers.
2.3 Type of input signals
The laboratory tests have been carried out by using various type of sinusoidal signals. The
used signals are:
• Sine
• 4 sine and half
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• 5 sine
The 5 sine signals is formed by a succession of 5 sine signals. Each of those has the same
amplitude and the same frequency. The 4 sine and half, instead, is formed by a succession of
4.5 sine signals, those have the same frequency but they are not characterized from the same
amplitude. In fact the amplitude is distributed according a Gaussian distribution.
In some applications for the vibration based technique is sometimes used also a signal that
takes the name of sweept signal. The sweept signal is shown below, even if it has not been
used here for data acquisition.
• sweept signal
The swept sine is a sinusoidal signal whose amplitude is constant in the selected frequency
range. So it is possible to excite a structure with the same intensity at all frequencies.
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Chapter 3
3.1 Adaptive filter
After the data acquisition stage some particular signal management filters have been used in
post processing phase in order to reconstruct the signal and estimate the variation amount of
the signal. The implementations of these filters was performed on Matlab and in particular
using an algorithm of the RLS type. The used filter is and adaptive filter of FIR type.
An adaptive filter is a filter that self-adjusts its transfer function (a mathematical
representation, in terms of spatial or temporal frequency, of the relation between the input and
output of a linear time-invariant system with zero initial conditions and zero-point
equilibrium) according to an optimization algorithm driven by an error signal. Because of the
complexity of the optimization algorithms, most adaptive filters are digital filters. Adaptive
filters are required for some applications because some parameters of the desired processing
operation (for instance, the locations of reflective surfaces in a reverberant space) are not
known in advance. The adaptive filter uses feedback in the form of an error signal to refine its
transfer function to match the changing parameters. Generally speaking, the adaptive process
involves the use of a cost function, which is a criterion for optimum performance of the filter,
to feed an algorithm, which determines how to modify filter transfer function to minimize the
cost on the next iteration. As the power of digital signal processors has increased, adaptive
filters have become much more common and are now routinely used in devices such as
mobile phones and other communication devices, camcorders and digital cameras, and
medical monitoring equipment.
The block diagram, shown in the following figure, serves as a foundation for particular
adaptive filter realizations, such as Least Mean Squares (LMS) and Recursive Least Squares
(RLS). The idea behind the block diagram is that a variable filter extracts an estimate of the
desired signal.
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Figure 3.1 : Block diagram for particular adaptive filter realizations.
To start the discussion of the block diagram we take the following assumptions:
• The input signal is the sum of a desired signal �(�) and interfering noise �(�):
�(�) = �(�) + �(�)
• The variable filter has a Finite Impulse Response (FIR) structure. For such structures the
impulse response is equal to the filter coefficients. The coefficients for a filter of order are
defined as:
�� = [��(0), ��(1), … , ��()]�
• The error signal or cost function is the difference between the desired and the estimated
signal:
�(�) = �(�) − ��(n)
The variable filter estimates the desired signal by convolving the input signal with the impulse
response. In vector notation this is expressed as:
��(�) = �� ∗ �(�)
where:
�(�) = [�(�), �(� − 1), … , �(� − )]�
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is an input signal vector. Moreover, the variable filter updates the filter coefficients at every
time instant:
���� = �� + ∆��
where ∆�� is a correction factor for the filter coefficients. The adaptive algorithm generates
this correction factor based on the input and error signals. LMS and RLS define two different
coefficient update algorithms.
3.2 Recursive Least Squares algorithm
The Recursive Least Squares (RLS) adaptive filter is an algorithm which recursively finds the
filter coefficients that minimize a weighted linear least squares cost function relating to the
input signals. This is in contrast to other algorithms such as the Least Mean Squares (LMS)
that aim to reduce the mean square error. In the derivation of the RLS, the input signals are
considered deterministic, while for the LMS and similar algorithm they are considered
stochastic. Compared to most of its competitors, the RLS exhibits extremely fast
convergence. However, this benefit comes at the cost of high computational complexity.
The idea behind RLS filters is to minimize a cost function � by appropriately selecting the
filter coefficients ��, updating the filter as new data arrives. The error signal �(�) and desired
signal �(�) are defined in the negative feedback diagram of figure 3.1.
The error implicitly depends on the filter coefficients through the estimate ��(�):
�(�) = �(�) − ��(�)
The weighted least squares error function � (the cost function we desire to minimize) being a
function of �(�) is therefore also dependent on the filter coefficients:
�(��) = � ����� (!)�
�"#
where 0 < � ≤ 1 is the "forgetting factor" which gives exponentially less weight to older
error samples.
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The cost function is minimized by taking the partial derivatives for all entries & of the
coefficient vector �� and setting the results to zero:
'(()*)')*(+) = ∑ 2�����(!) '.(�)
')*(+) = ∑ 2�����(!)�(! − &) = 0 ��"#��"# con & = 0,1, … ,
Next, replace �(�) with the definition of the error signal:
∑ ����/�(!) − ∑ ��(0)�(! − 0)12"# 3�(! − &) = 0��"# con & = 0,1, … ,
Rearranging the equation yields:
∑ ��(0)[∑ �����(! − 0)�(! − &)] = ∑ �����(!)�(! − &)��"#��"#12"# con & = 0,1, … ,
This form can be expressed in terms of matrices:
45(�)�� = 675(�)
where 45(�) is the weighted sample correlation matrix for �(�), and 675(�) is the equivalent
estimate for the cross-correlation between �(�) and �(�). Based on this expression we find
the coefficients which minimize the cost function as:
�� = 45��(�)675(�)
This is the main result of the discussion.
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Chapter 4
4.1 Test unit
In this chapter both the instruments and the test-article are reported. Tests have been executed
is the Laboratory of the Department of Aeronautical Engineering of the University of Naples
“Federico II”.
The structural component that has been tested consists in an aluminum panel reinforced by 4
stringers with L-shape. This means that in the panel there are three bays. Each stringer is
attached to the panel with the aid of rivets. In each bay was housed a piezoceramic
sensor/actuator glued with two-component glue. Each sensor has been identified by a number
as shown in the figure below.
Figure 4.1:
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The target that of these tests is to analyze the variation of the vibration behavior of the panel
from a configuration with the panel without damage to a configuration with damages on the
panel.
Three types of damage have been made:
1)First cut of 3 mm in correspondence of a hole in the central bay.
2)Second cut of 3 mm in correspondence of the same hole, bringing the total cut to 6 mm.
3)Removal of a rivet from one of the stringers of the panel
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Both the cuts were made with a triangular blade.
4.2 Experimental Set-up
The acquisition of the processed data has been permitted by the use of a signal generator, by
an amplifier and by an oscilloscope that can analyze the spectrums display signals. The
oscilloscope that has been used can store and save data on USB devices.
Figure 4.2: Oscilloscope: Agilent Technologies DSO7014A.
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Figure 4.3: Generator of signals: Helewet Packard 33120A.
Figure 4.4: Amplifier: Megaris.
4.3 Acquisition
The data acquisitions have been made for the following signals types :
• sine,
• 4 sine and half,
• 5 sine,
Obviously, the test started from the non damaged configuration.
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For the first three signals acquisitions were completed for the following frequencies: 4khz ,
7KHz , 9kHz , 11kHz , 13KHz . For each frequency were made acquisitions for amplitudes
equal to: 20v , 30v , 40v .
For each amplitude , frequency and type of the signal was done a sampling of five tests in
such as to obtain a variability of statistic relevance.
The first acquisition phase, when the panel was not damaged, was performed using
alternately the three piezoceramics as actuators . From these acquisitions, particularly those
carried out by using as the piezoceramic actuators 3 and 1 , it was noted the effect of the
reflections of the edges . These reflections have caused a disturbance in the signal read by the
sensors . The disturb can be seen in the fig below.
Figure 4.5: Signal read by piezoceramic sensor number 3 - Input signal: sine 4khz 20v.
For this reason the acquisitions to damaged panel were made using only the central
piezoelectric (number 2 ) such as restricting the task of the lateral piezoelectric to the
acquisition of the signal.
4.4 Data processing
The next step has been the data processing . The signals have been acquired has seen in the
previous pages.
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Fig 4.7: Time History - sine signal - Actuator piezoceramic Number 1
Fig 4.8: Time History - 4.5 sine signal - Actuator piezoceramic Number 1
Fig 4.9: Time History - 5 sine signal - Actuator piezoceramic Number 1
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The data were imported into MATLAB. An algorithm that allows to visualize in a simple way
the various spectrums of the signals has been created. This algorithm allows to overlay the
spectrums .
Subsequently , for each sampling ( consisting of 5 elements ) , was calculated mean and
variance . The variance was taken as an index of acceptability of the measure. It has been
established a maximum threshold of acceptability equal to:
threshold: 10�8
If the variance assumes values below this threshold then the measure proves to be acceptable .
All measures were under this threshold and the average variance was found in order of
10�9. This means that any errors and / or deviations from the real value are the result of an
absolutely normal variability of the experiment .
The next step was to process the data acquired by the piezoceramic number 1 and from the
piezoceramic number 3 . The step of processing the data has permitted to compute for each
signal 1002 coefficients of the FIR filter. The utilized algorithm is the following (shown for
sine input signal):
%% FIR FIILTER ANALYSIS clc; clear all; %% STEP 1: Load data loaddatifull.mat; %% STEP 2: Finestramento del segnale somma_input=zeros(1000,1); somma_out1=zeros(1000,1); somma_out2=zeros(1000,1); media_input=zeros(1000,15); media_out1=zeros(1000,15); media_out2=zeros(1000,15); varianza_input=zeros(1000,15); varianza_out1=zeros(1000,15); varianza_out2=zeros(1000,15); i=1; forindex=0:5:70 media_input(:,i)=mean([seno2{index+1,1}.data(:,2),seno2{index+2,1}.data(:,2), ... seno2{index+3,1}.data(:,2),seno2{index+4,1}.data(:,2),seno2{index+5,1}.data(:,2)],2); media_out1(:,i)=mean([seno2{index+1,1}.data(:,3),seno2{index+2,1}.data(:,3), ... seno2{index+3,1}.data(:,3),seno2{index+4,1}.data(:,3),seno2{index+5,1}.data(:,3)],2); media_out2(:,i)=mean([seno2{index+1,1}.data(:,4),seno2{index+2,1}.data(:,4), ...
28
seno2{index+3,1}.data(:,4),seno2{index+4,1}.data(:,4),seno2{index+5,1}.data(:,4)],2); varianza_input(:,i)=var([seno2{index+1,1}.data(:,2),seno2{index+2,1}.data(:,2), ... seno2{index+3,1}.data(:,2),seno2{index+4,1}.data(:,2),seno2{index+5,1}.data(:,2)],0,2); varianza_out1(:,i)=var([seno2{index+1,1}.data(:,3),seno2{index+2,1}.data(:,3), ... seno2{index+3,1}.data(:,3),seno2{index+4,1}.data(:,3),seno2{index+5,1}.data(:,3)],0,2); varianza_out2(:,i)=var([seno2{index+1,1}.data(:,4),seno2{index+2,1}.data(:,4), ... seno2{index+3,1}.data(:,4),seno2{index+4,1}.data(:,4),seno2{index+5,1}.data(:,4)],0,2); i=i+1; end %figure(1) %plot(seno2{1,1}.data(:,1),[seno2{1,1}.data(:,3) seno2{2,1}.data(:,3) seno2{3,1}.data(:,3) seno2{4,1}.data(:,3) seno2{5,1}.data(:,3) media_out1(:,1)]) %legend('p1', 'p2', 'p3', 'p4', 'p5', 'media') %grid on %figure(2) %plot(seno2{1,1}.data(:,1),varianza_out1(:,1)) %legend('varianza') %grid on %% STEP 3: FIR FILTER numero_coefficienti=1002; numero_prove = length(media_input(1,:)); coefficienti=zeros(numero_coefficienti,numero_prove); for j=1:15 l = numero_coefficienti; lambda = 1; invcov = 10*eye(numero_coefficienti); ha = adaptfilt.rls(l,lambda,invcov); [y,e] = filter(ha,media_input(:,j),media_out1(:,j)); coefficienti(:,i)=ha.coefficients; end %% Plot section 3 %plot(seno2{1,1}.data(:,1),[media_out1(:,1), y]) %grid on %legend('segnale reale','segnale ricostruito')
In this way the signal has been reconstructed. The adaptive filter utilized uses a RLS
algorithm. In the next page will be shown the trend of the coefficients calculated.
29
Fig 4.10: Example of the trend of coefficients - piezoceramic number 1 - Input signal
sine, in sequence are represented: no damage, 3 mm cut, 6 mm cut, removal of a rivet.
-0,04
-0,02
0
0,02
0,04
0 200 400 600 800 1000 1200
13kHz 40V
13kHz 40V
-0,04
-0,02
0
0,02
0,04
0 200 400 600 800 1000 1200
13kHz 40V
13kHz 40V
-0,05
0
0,05
0 200 400 600 800 1000 1200
13kHz 40V
13kHz 40V
-0,04
-0,02
0
0,02
0,04
0,06
0 200 400 600 800 1000 1200
13kHz 40V
13kHz 40V
30
The reconstruction phase of the signal allowed , ultimately , to extrapolate some
characteristic indexes . The indexes have been calculated both for signals and
coefficients. Thanks to these indices has been possible to analyze, in a right way,
changes in the signal from the condition of the not damaged panel to the condition of
panel damaged. For each test the index was obtained as the sum in absolute value of the
difference of signal or of the coefficient (calculated with the FIR filter) starting from the
condition of the panel intact reference unless the respective values of the condition of
damage analyzed. This procedure was done both for the signal and for the coefficients.
This was done for the times ranging from 0 to 600 milliseconds.
Fig 4.11: Signal sine - is shown the index 0-600 absolute for the coefficients for the
frequency of 13KHz in function of the voltage for various conditions of damage.
Fig 4.12: Signal sine - is shown the index 0-600 absolute for the signal for the
frequency of 13KHz in function of the voltage for various conditions of damage.
0
0,5
1
1,5
2
2,5
20 30 40
f = 13 kHz PZ1 - (I-D3)
PZ1 - (I-D6)
PZ1 - (I-Dr)
PZ3 - (I-D3)
PZ3 - (I-D6)
PZ3 - (I-Dr)
0
10
20
30
20 30 40
f = 13 kHz PZ1 - (I-D3)
PZ1 - (I-D6)
PZ1 - (I-Dr)
PZ3 - (I-D3)
PZ3 - (I-D6)
31
Fig 4.13: Signal 4.5 sine - is shown the index 0-600 absolute for the coefficients for the
frequency of 13KHz in function of the voltage for various conditions of damage.
Fig 4.14: Signal 4.5 sine - is shown the index 0-600 absolute for the coefficients for the
frequency of 11KHz in function of the voltage for various conditions of damage.
Fig 4.15: Signal 4.5 sine - is shown the index 0-600 absolute for the signal for the
frequency of 13KHz in function of the voltage for various conditions of damage.
0
2
4
6
8
20 30 40
f = 13 kHz PZ1 - (I-D3)
PZ1 - (I-D6)
PZ1 - (I-Dr)
PZ3 - (I-D3)
PZ3 - (I-D6)
2
3
4
5
6
20 30 40
f = 11 kHz PZ1 - (I-D3)
PZ1 - (I-D6)
PZ1 - (I-Dr)
PZ3 - (I-D3)
PZ3 - (I-D6)
0
2
4
6
8
20 30 40
f = 13 kHz PZ1 - (I-D3)
PZ1 - (I-D6)
PZ1 - (I-Dr)
PZ3 - (I-D3)
PZ3 - (I-D6)
32
Fig 4.16: Signal 5 sine - is shown the index 0-600 absolute for the coefficients for the
frequency of 13KHz in function of the voltage for various conditions of damage.
Fig 4.17: Signal 5 sine - is shown the index 0-600 absolute for the signal for the
frequency of 13KHz in function of the voltage for various conditions of damage.
0
1
2
3
20 30 40
f = 13 kHz PZ1 - (I-D3)
PZ1 - (I-D6)
PZ1 - (I-Dr)
PZ3 - (I-D3)
PZ3 - (I-D6)
0
20
40
60
20 30 40
f = 13 kHz PZ1 - (I-D3)
PZ1 - (I-D6)
PZ1 - (I-Dr)
PZ3 - (I-D3)
PZ3 - (I-D6)
33
Chapter 5
5.1 Conclusions
From the analysis of the data it was possible to achieve the following results:
1) The tests are very repeatable. repeating the tests for the same values of frequency,
amplitude, and for a same condition of the panel the results are very similar. this allows to
obtain a very low variance. . this means that the probability of pulling out false alarms is very
low.
2) The results show that for low frequencies (4 - 7 - 9 kHz) there isn't a well defined trend of
coefficients in the case of damage of three and six millimeters. The damage is only well
visualized from high frequency (11 - 13 kHz).
In the case of the removal of the rivet, damage is already well identified in the low
frequencies range. The trend of the coefficients is, in fact, well defined in this case.
It is also possible to note that the index's trend calculated on the coefficient is more stable
than that calculated on the signal. For which the use of filters fir is justified precisely by this
result.
3) It is not definitely possible to identify the location of the damage and its entity within the
panel because of two fundamental problems. The first is the presence of many reflected waves
that do not allow a clear reading of the signal. The second reason is instead given by the fact
that have been used a low number of sensors. A more dense grid of sensor would have been
necessary to better describe the damage in terms of position, type and entity.
4) The interval that contains the coefficients is equal to [1.5 , 2.5] with few coefficients that
exceed the value of 2,5. The analyzed functions show, for a same frequency and by increasing
voltage, a monotonically increasing trend. Thus increasing the voltage also increases the
coefficient. Moreover, for a fixed frequency and a fixed voltage, the value of the index
decreases when the damage increases.
34
5.2 Possible developments for the future
The experiments conducted have led to the conclusions discussed in the previous page. From
these results it is possible to define the possible corrective changes for future tests.
In order to have more information which may characterize the damage would be appropriate
to repeat the tests using a more dense grid of sensors. In this way it's possible to have more
information on the location, type and extent of damage.
Finally, a further corrective action may be to use higher frequencies. To move the analysis
toward more high frequencies makes it possible to identify smaller damage.
36
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