About vibration based SHM techniques for metallic structures

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), ...

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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


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


Fig 4.14: Signal 4.5 sine - is shown the index 0-600 absolute for the coefficients for the


Fig 4.15: Signal 4.5 sine - is shown the index 0-600 absolute for the signal for the


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


Fig 4.17: Signal 5 sine - is shown the index 0-600 absolute for the signal for the


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

Bibliography

1. N. Meyendorf , B. Frankenstein, L. Schubert - "Structural Health Monitoring for

Aircraft, Ground Transportation Vehicles, Wind Turbines and Pipes – Prognosis" -

18th World Conference on Nondestructive Testing, 16-20 April 2012, Durban, South

Africa.

2. N. Brigman - " Structural Health Monitoring in Commercial Aviation"- Master Of

Science In Aeronautics And Astronautics at the Massachusetts Institute Of

technologies - June 2012.

3. I. Bovio - "Innovative Method for Damage Identification and Structural Health

Monitoring Based on Vibration Measurement" - Master Of Science of transport -

University of Study of Naples "Federico II".

4. K.L. Nishitha, R. Ravi Kumar - "Health Monitoring System" - International Journal

of Innovative Research in Science, Engineering and Technology , Vol. 2, Issue 5, May

2013.

5. C. Boller, N. Meyendorf - "State-of-the-Art in Structural Health Monitoring for

Aeronautics" - Proc. of Internat. Symposium on NDT in Aerospace, Fürth/Bavaria,

Germany, December 3-5, 2008.

6. M.H. Hayes - "Statistical Digital Signal Processing and Modeling" (1996) Wiley -

ISBN 0-471-59431-8.

7. S. Haykin - "Adaptive Filter Theory" - Prentice Hall 2002 - ISBN 0-13-048434-2.

8. B. Widrow, D. S. Stearns - "Adaptive Signal Processing " Englewood Cliffs NJ

1985 Prentice Hall. ISBN 0-13-004029-0.

9. J. C. Chamberlain - "Durability Testing of an Aircraft Structural Health Monitoring

System" - Master Of Science In Aeronautics And Astronautics at the Massachusetts

Institute Of technologies - September 2006.

About vibration based SHM techniques for metallic structures

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