Florian Caullery
email: florian.cauller@etu.univ-amu.fr

Alexander Getmanenko
email: getmanenko@ihes.fr

Vito Mandorino
email: vito.mandorino@math.u-psud.fr

Vincent Vong
email: vong@univ-mlv.fr

Semaine D'etude

Yannick Teglia

-TESTING THE RELIABILITY OF A TRUE RANDOM GENERATOR AT RUN TIME

Keywords:

True random number generators. In various algorithmic applications, there arises a need for sequences of numbers with good properties of randomness. Often, as in many programming languages, an algorithm producing pseudo random sequences is sufficient. For more advanced purposes such as information security, an analogue (as opposed to purely digital) hardware unit generating random numbers is attached to the processor. The resulting sequence of numbers possesses randomness due to resumed thermal white noise present in a simple physical system; such a sequence is not predictable algorithmically in principle and therefore is called a true random number sequence.

Applications of true random number generators (TRNG) include generation of cryptographic keys and Counter-measures against Physical Attacks (e.g. Side Channel Attacks, Fault Injection).

An important task is therefore to be able to diagnose whether a given hardware unit generating random numbers functions properly, which means that the random numbers "behave as a sequence independent identically distributed random variables" -an expression whose formal meaning will be addressed later in this report.

Of particular concern for the needs of cryptographic security is a possibility that the TRNG is put under a physical attack to become more predictable, e.g. it is exposed to a laser field, electromagnetic injection, alpha particles, or is malfunctioning due to e.g. power supply or clock glitches. Predictability of a TRNG may lead to vulnerability to cryptographic keys that it generates.

Let us remark that the random number generated by the TRNG are postprocessed digitally to make any malfunctioning of the TRNG as little exploitable as possible. It is the testing at run time of the quality of random numbers before any digital post-processing takes place that will be the subject of this report. 1.2. Mathematical problem. Imagine a small TRNG unit inside a small electronic device (think: cell phone) that needs to quickly diagnose itself before sending an encrypted message. A relatively short sequence of numbers may be generated, there are limitations of memory and processing time, and the cost of a false alarm is potentially the need to replace a part of a cell phone.

Obviously, a sequence that contains too many consecutive 0's or too many consecutive 1's should be rejected, as well as sequences with strong periodic patterns such as 010101010..., as well as sequences where the portion of 1's is significantly different from 50 percent. Other possible tokens of malfunctioning TRNG have been studied, e.g., in [START_REF] Rukhin | A statistical test suite for random and pseudorandom number generators for cryptographic applications[END_REF]. Theoretical developments with respect to this problem include concepts of complexity theory, pseudo-randomness of finite sequences, numerical evaluation of Kolmogorov of short strings, non-linearity of Boolean functions.

The enterprise has quantified the constraints as follows: -one needs to make a yes/no decision with respect to proper functioning of a TRNG based on a string of up to 512 bit (0 or 1) that it has generated.

-2 kb -512 bits of memory available for running computations -programs and relevant constants can be stored in a different, larger memory Further, we have concentrated on detecting periodic regularities in the random sequence, which would correspond to exposure of the TRNG to a periodic perturbation (e.g., by a periodic electromagnetic field).

Rather then trying to write a new chapter in the theory of randomness, we have tested various approaches similar to the existing ones but with a focus on the above mentioned concern and constraints.

2. An algebraic point of view 2.1. Boolean functions based approach. Let F 2 ∼ = (Z/2Z, +, ×) be the finite field with two elements and F n 2 be the vector space of dimension n over F 2 . A function f from F n 2 to F 2 is called a Boolean function. Such functions are entirely determined their truth table and admit a representation as a polynomial in F 2 [x 1 , . . . , x n ] which is called the algebraic normal form of f .

One can see a sequence of length l = 2 n as the truth table of a Boolean function. Hence every sequence define a unique Boolean function and our problem is transformed into deciding if a Boolean function is random. There exists various indicators on a Boolean functions. We have selected two of them to measure their level of "randomness": the non-linearity and the absolute indicator. The decision to consider the non-linearity was motivated by the work of Schmidt and Rodier on the asymptotic distribution of non-linearity of random Boolean function [START_REF] Rodier | Asymptotic nonlinearity of boolean functions[END_REF][START_REF] Schmidt | Nonlinearity measures of random Boolean functions[END_REF]. On the other hand, there is no theoretical background on the distribution of the absolute indicator of random Boolean functions and the decision to consider the absolute indicator entirely relied on numerical experiments.

2.1.1. Non-linearity. Before defining the non-linearity of a Boolean function we need to define the Hamming distance of two functions and the affine functions. Definition 2.1. Let f and g be two Boolean functions from F n 2 to F 2 . The Hamming distance d(f, g) between f and g is defined as:

d(f, g) = x∈F n 2 f (x) + g(x).
This distance is actually the number of time where f (x) and g(x) have a different output. Definition 2.2. A function A : F n 2 → F 2 is said affine if the total degree of the algebraic normal form of A is at most one.

The non-linearity of a Boolean function is defined as follow: Definition 2.3. The non-linearity N L(f ) of a Boolean function is the Hamming distance between f and the set of affine functions:

N L(f ) = min A affine (A, f )
To compute the non-linearity of a function, we use the following formula. Proposition 2.4. We have:

N L(f ) = 2 m-1 - 1 2 sup v∈F n 2 x∈F n 2 (-1) f (x)+v.x .
The computation of the non-linearity can be done in a linear time 0(l) where l = 2 n is the length of the sequence. The details of the algorithm can be found in http://robert.rolland.acrypta.com/telechargements/algebre/Hadamard.pdf

In our study, we focused on sequences of length 2 9 = 512. We computed the non-linearity of 50, 000 random Boolean functions and obtain the following The absolute indicator of a Boolean function f is defined as the maximum absolute value of its auto-correlation function. The autocorrelation function measure the similarities of f with f composed with a shift.

Definition 2.5. Let f : F n 2 → F 2 be a Boolean function. The auto-correlation function AC f of f is defined as AC f (a) = x∈F n 2 (-1) f (x)+f (x+a) . Definition 2.6. Let f : F n 2 → F 2 be a Boolean function. The absolute indicator AI(f ) of f is defined as AI(f ) = max a∈F n 2 -{0} AC f (a).
The computation of absolute indicator is made in O(2 2n ) operation where 2 n is the length of the sequence.

Again, we focused on sequences of length 2 9 = 512. We computed the absolute indicator of 10, 000 random Boolean functions and obtain the following table and graph:

Mean 2.1.3. Summary. The second test we proposed seems a bit better since it discards sequences with longer period but it is also slower. One shall also remark that the non-linearity can be obtain from the computation of the absolute indicator without additional operation. Hence, the combination of the two tests could be a good option if the microchip resources allow it. Otherwise, the non-linearity test seems the best option with this approach.

2.2. Algebraic and computational approach. One of the good notions in order to measure if a sequence is random, is the Kolmogorov complexity. But this quantity is not computable. So, instead of it, we can use other complexity which can be computed, in order to have an approximation of the notion "be random". In our context, we just want to reject two types of binary sequences:

• the periodic ones,

• the linear Boolean functions.

The method is classical: we have to find some functions on words, such that they have an expected behavior on random words, but not for periodic and linear ones. One of the given approach is based on a simple notion, the sub word complexity [START_REF] Berstel | Combinatorics on words-a tutorial. Current trends in theoretical computer science[END_REF]. The another one will be based on the computation of the Lempel-Ziv complexity [START_REF] Lempel | On the complexity of finite sequences[END_REF]. In the sequel, a sequence of bits is seen as a word over the alphabet {0, 1}. Let w be a random word of size 512, and let us consider the finite sequence (CF k (w)) k≤512 . By computer test, we observe the following graph:

. For w a random 300 periodic binary word of size 512, here is the behavior:

. For w a random linear Boolean function of size 512, here is the behavior:

. By heuristic, we directly see that by studying the sequence (CF k (w)), we can determine a form of randomness. As we can observe, only the first terms of the sequence are important, in order to discriminate if a sequence is random. Then, we deduce the following algorithm:

(1) calculate the first terms of the factor complexity (≤ 30) (2) if the behavior is similar to the random one, keep it (3) don't use it otherwise.

Here is some test for words of length 512: LBF: linear Boolean functions. PW: periodic words. RW: random words.

k CF k of a LBF CF k of
As we can see, for a random word w of size 512, generally CF 25 (w) is greater than 450, but for "special" words, is lesser than 400. So we have a good test in order to reject periodic words, and linear Boolean functions.

The Lempel-Ziv complexity.

Complexity theory is also intimately related to the compression one. Indeed, in this context, a random word is word which compression rate is "bad". Since the Lempel-Ziv complexity is related to a compression algorithm, one can test if this notion gives some results in our problem. Let us recall some definitions, in order to compute the Lempel-Ziv complexity for a word. Definition 2.11. Let w = w 1 w 2 • • • w n be a finite word. We denote by w(i, j) the factor w i • • • w j . The exhaustive history of w is the factorization withe the most factors of w = f 1 • • • f k , such that for i < k, f i is a word satisfying the following properties :

(1)

• if we set f i = a 1 • • • a j (a i is a letter), then f i is not a factor of w ′ = f 1 f 2 • • • f i-1 a 1 a 2 • • • a j-1 , • but a 1 a 2 • • • a j-1 is a factor of v = f 1 f 2 • • • f i-1 a 1 a 2 • • • a j-2 .
The factor f k satisfies the second property.

The factors f i are the components of the exhaustive history, and the Lempel-Ziv complexity of w is the number k, denoted by LZ(w).

The following algorithm determines the exhaustive history of a word w = w 1 • • • w n :

• initialization:

f 1 = w 1 • if we have find f 1 , f 2 ,...,f i , we have w = f 1 • • • f i v.
Then, we search the shortest proper prefix p of v satisfying the conditions (1). If p exists, then f i+1 = p. Otherwise, f i+1 = v, and the algorithm is finished.

Example 2.12. If we set w = 0010100111000, we have:

• initialization: f 1 = w 1 = 0. Then, w = 0 • 010100111000.
• 01 is the shortest proper prefix of 010100111000, satisfying (1). Then, In the following histogram, we represent the Lempel-Ziv complexity of random binary sequences of size 512, and linear Boolean functions of same size:

f 2 =
As we can see, for a random sequence, the value is between 50 and 60. But, for a linear Boolean function, the value is lesser than 20. For one thousand 100-periodic word, we have the following histogram: So, we deduce that a binary word of size 512 may be random if its Lempel-Ziv complexity is between 50 and 60. By the criteria, we can see that linear Boolean function and small periodic word are not random.

Identification of deviance of a random number generator -Spectral approaches

As the device generating random numbers is likely to be subjected to a periodic electromagnetic field due to either an influence of the environment, or by malignant attack, methods based on the Fourier transform (FT) appear to be a natural choice for detecting such perturbation. Such methods are referred to as "spectral methods".

The work that we accomplished and that we are reporting in this section, can be summarized as follows:

Given the goal of detecting periodic perturbations, the size of the data 512 bit, and memory constraints ∼ 2Kb, we have performed a comparative study of various methods inspired by Fourier transform.

There is a whole family of such methods differing by: -a choice of a Fourier transform among various versions, and -a choice of a statistical criterion for quantifying anomalies in the resulting FT coefficients.

3.1. Discrete Fourier Transform and Fast Fourier Transform. Our starting point was the paper [START_REF] Rukhin | A statistical test suite for random and pseudorandom number generators for cryptographic applications[END_REF] where the authors propose to use the discrete Fourier transform (DFT) technique to analyze for periodic patterns. Let us recall the definition: Definition. For a sequence v 0 , ..., v N -1 of complex numbers, define

(2)

F j = N k=0 v k e 2π √ -1kj/N ∈ C.
For the sake of exposition and intuition, it is more convenient to encode the string of random bits v 0 , .., v N -1 as ±1 rather than 0 and 1. Since all v j are real, the resulting sequence F j will have the following symmetry:

(3)

F j = F N -j ,
thus effectively containing only N real numbers. DFT gives a measure of several periodic components in a discrete sequence, see [1, Sec.3.6] and figures therein.

While a straightforward implementation of the formula (2) has time complexity O(N 2 ), the Fast Fourier Transform (FFT) algorithm reduces the complexity to O(N log N ).

To briefly review the idea of the FFT algorithm following [4, Ch.8], let us rewrite the formula (2) in the matrix notation as F = Av and suppose for simplicity that column vectors F and v have length 2 γ . Here, the matrix A has entries

A jk = (ζ j×k ) j,k , ζ = e 2πi/N .
Morally (see [START_REF] Brigham | The Fast Fourier transform and its applications[END_REF] for a precise statement), the matrix A can be represented as a product A (log 2 N ) ...A (1) where matrices A (k) are very sparse (and, of course, independent of the vector v). Multiplication by a constant sparse matrix requires the number of operations equal to the number of its nonzero entries; log 2 N matrix multiplication by matrices each containing O(N ) nonzero entries gives the times complexity of O(N log N ) of the FFT algorithm.

Let us now analize the memory needs of the FFT algorithm. Let us write

F (0) = v F (j) = A (j) F (j-1)
Assuming that the matrices A (j) are pre-calculated and stored in the permanent memory as a part of the algorithm, at each step of the algorithm described in [START_REF] Brigham | The Fast Fourier transform and its applications[END_REF] we need to store vectors F (j) and F (j-1) which makes the total of 2N complex numbers, or 4N real numbers, plus a few loop counters etc. We expect that symmetry reduces this to 2N real numbers.

Let us elaborate a little on the point of symmetry of the complex vectors F (j) originating from the fact that the initial vector v is real. At this point we are not ready to give a precise general statement, but we expect that it may be known to specialists. In a particular example of N = 8, i.e. γ = 3, and using [4, eqs (8.40)-(8.43)], we have in our notation that

F (0),k ∈ R, k = 0, ...7 F (1),k ∈ R, k = 0, ...7 F (2),k ∈ R, k = 0, ...3; F (2),4 = F (2),k+2 , k = 4, 5
and F (3),k has symmetries corresponding to [START_REF] Güner | A study of the shapiro-wilk test for the detection of pulsed sinusoidal radio frequency interference[END_REF]. For a particular N that will be used in an implementation of the algorithm, an ad hoc description of the symmetries will suffice.

In the particular case of N = 512, allocating 4 bytes per real number, the FFT algorithm will require 4 Kilobytes plus a few bytes to store loop counters etc. This is twice as much as is available according to the constraints set by the industrial partner; one solution may be to reduce N to 256 (this approach will be analyzed below in sec.3.6), another -to implement real numbers using 2 bytes only which may be feasible as the real numbers in question are of approximately the same order of magnitude and as the precision-sensitive operation of the division of reals never enters the algorithm.

3.2.

Statistical analysis of the Fourier transformed sequence by the Shapiro-Wilk test. It is well-known, or at least widely accepted, see [START_REF] Rukhin | A statistical test suite for random and pseudorandom number generators for cryptographic applications[END_REF] that if v n ∈ {±1} are independent random variables, then Re F n , Im F n are independent normal random variables with mean 0 and the standard deviation N 2 :

Re F n , Im F n ∼ N 0, N 2 .
Several tests for normality of a sample are available in the literature: Anderson-Darling test, Lilliefors test, Kolmogorov-Smirnov test, Pearson's chi-squared test, and the test that we have chosen based on its good reputation -the Shapiro-Wilk test. With respect to other tests, the Shapiro-Wilk test has the lowest rate of false negatives and it performs well for recommended for sample size up to 3000 -the range that includes our sample size of 512.

Let us briefly review the Shapiro-Wilk test following [START_REF] Güner | A study of the shapiro-wilk test for the detection of pulsed sinusoidal radio frequency interference[END_REF]. The basic idea is to compare the sorted sample with an expected sorted sample from the normal distribution. Starting with a sorted sample of real numbers y = (y 1 , ..., y N ), y 1 ≤ ... ≤ y N , the test is based on the quantity

W = ( N i=1 a i y i ) 2 N i=1 (y i -m)
, where m = mean y, and the coefficients a i are independent of the sample, well-studied real constants (see [START_REF] Royston | Approximating the shapiro-wilk w-test for non-normality[END_REF]) that can be stored as a part of the algorithm. The quantiles of the test quantity for a given sample size are also well-known.

The R language provides a function shapiro.test. The calculation of W involves sorting of N numbers, which takes time of O(N log 2 N ), while for N = 512 the memory of 1 Kb will clearly be enough.The sum of N real numbers takes time of order O(N ) and a negligible and constant amount of memory.

Selection of test examples and confidence level.

To evaluate and compare performance of different methods of detecting periodic regularities in a sequence of random numbers, we have generated perturbed random sequences according to the formula [START_REF] Brigham | The Fast Fourier transform and its applications[END_REF] v n = sign(N (0, 1) + b * sin(kn))

where N (0, 1) are pseudo random numbers, normally distributed around the origin with unit variance, generated by the programming language R, and b = 0, 0.01, 0.02, ... 2.00 strength of the perturbation k = 0, 0.1, ..., 3.2 frequency of the perturbation Note this choice includes perturbations with non-integer period.

We will reject a sequence as non-random if the P -value of a given statistical test is < 0.001.

3.4.

Implementing the FFT + Shapiro-Wilk test. We implemented our algorithm in the R language. Both Fast Fourier transform and the Shapiro-Wilk test are available as standard functions of the language. Here is the code for the algorithm.

# a s s i g n i n g t h e l e n g t h o f our s e q u e n c e s l e n = 512 # i n i t i a l i z e t h e v e c t o r o f i n t e r e s t which c o u n t s t h e number o f s t r i n g s .

One of the runs of the algorithm gave the data in fig. 1. We can see that for values of the strength parameter b in (4) which are below approximately 0.2 the test does not detect any deterioration in the quality of the random bits, while almost all strings generated with b ≥ 0.7 are rejected as nonrandom at significance level 0.001.

3.5.

Variant #1: Hadamard-Walsh Transform. Having proposed and tested one possibility for the detection of periodic perturbations, we continued with exploration of various variants of this approach.

The first variant is to run the Shapiro-Wilk test on the data coming not from the Discrete Fourier Transform, but rather from the Hadamard-Walsh transform (HWT) of the sequence of bits v.

In case of strings of bits of length N = 512, the Hadamard-Walsh transform can be thought of an analogue of the DFT with the group Z 2 Z 9 replacing Z 512 Z Indeed, the DFT described above is equivalent to calculating

F χ = k v n χ(n)
for every character χ of the discrete group Z/512Z χ : Z/512Z → C.

Hadamard transform repackages the 512 numbers v n as parametrized by {0, 1} 9 . The HWT is thus calculated by the formula ( 5)

H χ = n v n χ(n)
for every character χ of the group (Z/2Z) 9 :

χ : (Z/2Z) 9 → {±1} ⊂ C.
There is an analogue of the FFT algorithm for the HWT with the complexity of O(N log N ). However, the advantage of the HWT is that it computes with integers only which saves time and relieves the memory shortage difficulty that we encountered in the analysis of the usual DFT algorithm, page 10. One may expect however that a method based on the HWT will heavily stress periods of length 2 k .

An experimental comparison of the methods based on FFT and HWT, in both cases followed by the Shapiro-Wilk test with significance level 0.001, is presented on figure 2.

Figure 2. Comparison between the FFT + Shapiro-Wilk test (red curve) and HWT + Shapiro-Wilk test (blue curve), same axes as on fig. 1

Here is the R code for this method. The Hadamard-Walsh transform is available in the package boolfun. For a sequence of v n=0,...,N -1 with N = 2 γ , the non-linearity can be equivalently defined as

N (v) = max χ:(Z/2Z) γ →C |H χ |
where the maximum is taken over all characters of the group (Z/2Z) γ and H χ is the Hadamard-Walsh transform as in [START_REF] Lempel | On the complexity of finite sequences[END_REF].

Unusually low values of non-linearity is a sign of low quality of generated random numbers.

To our knowledge, the distribution of N (v) is not yet fully understood theoretically, so we have calculated the histogram of its distribution in case N = 512 by using the R pseudo-random numbers, fig. 4 We found experimentally the 0.001-quantile to be 203, thus in our test we are going to reject a string as non-random if its non-linearity is ≤ 203.

The advantage of non-linearity is that it can be calculated within the time O(N ) working entirely with integers; however the first order statistics is a much cruder test of normality than the more expensive Shapiro-Wilk test. The performance of Non-linearity test compared to other tests presented earlier is given on figure 5, followed by the related R code which uses the nl function from the boolfun package. .

A quick look at the data (not shown here) suggests that the non-linearity test has some particular "blind spots" by not detecting strong perturbations (large b) for some special values of the frequency parameter j of the equation (4).

3.8. Concluding remarks. Above, we have listed different spectral methods of testing for periodic regularities in a sequence of bits. We can see a clear progression from more sensitive and costly (in terms of time and memory) to less sensitive but lighter, and it is up to the engineers to find where to strike the balance.

We note that the DFT method taken directly from [1, sec.3.6] performs significantly less well than our other methods

The combination of the DFT and the maximum absolute value statistics

(v n ) 512 n=1 DF T → (F k ) 511 k=0 → max k |F k |
remains to be tested. We also reiterate our opinion that a FFT transform bases on 2-byte real arithmetic should also be tested.

3 . 2 .

 32 Statistical analysis of the Fourier transformed sequence by the Shapiro-Wilk test 3.3. Selection of test examples and confidence level 3.4. Implementing the FFT + Shapiro-Wilk test 3.5. Variant #1: Hadamard-Walsh Transform 3.6. Variant #2: halving the string length 3.7. Variant #3: Hadamard-Walsh Transform + non-linearity test 1. Introduction -Industrial context 1.1.

  100.0625 Median 100 Standard deviation 24.1242 Numerical experiments on absolute indicator Absolute indicator distribution From this experiments, we could deduce the following test: (1) Consider a sequence of length 512 as the truth table of f : F 9 2 → F 2 (2) calculate the absolute indicator of f (3) if it is between 85 and 115 keep it (4) don't use it otherwise This test enabled us to discard sequences with a period up to 280.

2. 2 . 1 .

 21 Sub word complexity and pseudo-randomness. Let w = w 1 w 2 • • • w n be a word over {0, 1}. Let us define the sub word complexity of a word. Definition 2.7. Let f and w be two finite words. The word f is a factor of w if there exists two words u and v such that w = uf v. Example 2.8. If w = 1011011, then f = 1101 is a factor of w, since w = 10 • f • 1. Definition 2.9. Let w be a finite word. The subword complexity of w is the number of the different factors of w. We denote by CF (w) the sub word complexity of w, by CF k (w), the number of factors of size k of w, and by F actor k (w) the set of factors of size k of w. Example 2.10. If w = 01001101, then: F actor 4 (w) = {0100, 1001, 0011, 0110, 1101}, and CF 4 (w) = 5.

  01, and w = 0 • 01 • 0100111000. • By the same arguments, we have f 3 = 0100, f 4 = 11, and f 5 = 1000. • Finally, w = 0 • 01 • 0100 • 11 • 1000, and LZ(w) = 5.

  a c c e p t e d a s random # f o r a g i v e n p e r t u r b a t i o n s t r e n g t h b . We u s e 201 p o s s i b l e v a l u e s f o r b . count = m a t r i x ( 0 , nrow = 2 0 1 , n c o l = 1 ) # l o o p i n g on d i f f e r e n t v a l u e s o f t h e p e r t u r b a t i o n s t r e n g t h b and o f t h e f r e q u e n c y j . # For each c o u p l e o f v a l u e s ( b , j ) we r e p e a t t h e t e s t 15 t i m e s f o r ( b i n 0 : 2 0 0 ) { f o r ( j i n 0 : 3 2 ) { f o r ( h i n 1 : 1 5 ) { s e q u e n c e = s i g n ( rnorm ( l e n ) +(b/ 1 0 0 ) * c o s ( ( j / 1 0 ) * c ( 0 : ( l e n -1) ) ) ) #g e n e r a t e a pseudo-random s e q u e n c e a c c o r d i n g t o f o r m u l a (4) c o e f f s = f f t ( s e q u e n c e ) #u s e t h e Fast F o u r i e r Transform t o g e t t h e F o u r i e r c o e f f i c i e n t s o f t h e s e q u e n c e SW_Data = c ( Re ( c o e f f s [ 1 : ( f l o o r ( l e n / 2 ) +1) ] ) , Im ( c o e f f s [ 2 : f l o o r ( l e n / 2 ) ]) ) #g e t r i d o f t h e s y m m e t r i e s (3) #t o g e t t h e v e c t o r which i s t o be f e d t o t h e S h a p i r o -Wilk t e s tSW_Pval = s h a p i r o . t e s t (SW_Data ) $p . v a l u e #g e t t h e p-v a l u e g i v e n by t h e S h a p i r o -Wilk t e s t . We a r e g o i n g t o a c c e p t t h e s e q u e n c e a s random #i f i t s p-v a l u e i s >= 0 . 0 0 1 count [ b+1] = count [ b+1] + (SW_Pval >= 0 . 0 0 1 ) #count t h e number o f a c c e p t e d s t r i n g s under p e r t u r b a t i o n s t r e n g t h b }}} p e r c e n t = count * ( 1 0 0 / 33 * 1 5 ) #c o n v e r t c o u n t i n g t o p e r c e n t a g e s f o r p l o t p u r p o s e s p l o t ( p e r c e n t )

Figure 1 .

 1 Figure 1. Performance of the Discrete Fourier Transform followed by the Shapiro-Wilk test. Here the horizontal axis corresponds to the strength of the periodic perturbation b as in (4).

  l e n = 512 count = m a t r i x ( 0 , nrow = 2 0 1 , n c o l = 1 ) f o r ( b i n 0 : 2 0 0 ) { f o r ( j i n 0 : 3 2 ) { f o r ( h i n 1 : 1 5 ) { s e q u e n c e = ( s i g n ( rnorm ( l e n ) +(b/ 1 0 0 ) * c o s ( ( j / 1 0 ) * c ( 0 : ( l e n -1) ) ) ) >= 0 ) #we go back t o s e q u e n c e s o f 0 ' s and 1 ' s s i n c e t h i s i s t h e p r o p e r s e t t i n g f o r HWT SW_Data = walshTransform ( s e q u e n c e ) SW_Pval = s h a p i r o . t e s t (SW_Data ) $p . v a l u e count [ b+1] = count [ b+1] + (SW_Pval >= 0 . 0 0 1 ) }}} p e r c e n t = count * ( 1 0 0 / 33 * 1 5 ) p l o t ( p e r c e n t )

.

3. 6 .

 6 Variant #2: halving the string length. As the FFT algorithm proposed earlier struggles with memory constraints, see page 10, we have also considered and evaluated the possibility to start with only 256-bit strings of 0's and 1's. Halving the input data size naturally leads to somewhat lower performance, fig 3.

Figure 3 .

 3 Figure 3. FFT + Shapiro-Wilk test for 512-bit and 256-bit strings, respectively, as well as HWT + Shapiro-Wilk test for 512bit and 256-bit strings.

3. 7 .

 7 Variant #3: Hadamard-Walsh Transform + non-linearity test. The Non-linearity test discussed in the framework of algebraic methods, sec. PUT A CROSS-REFERENCE HERE!, fits in the picture of the spectral methods as follows.

Figure 4 .

 4 Figure 4. The experimental histogram for the distribution N (v) provided the entries v are i.i.d. binomial random variables with equal probability of ±1.

Figure 5 . 3 4

 53 Figure 5. Comparative performance of the non-linearity test

calculate the non-linearity of f (3) if it is between 215 and 225 keep it (4) don't use it otherwise This test enabled us to discard sequences with a period up to 260. 2.1.2. Absolute indicator.

		table
	and graph:
	Mean	219.1854
	Median	220
	Variance	15.1837
	Standard deviation	3.8966
	Numerical experiments on non-linearity
	Non-linearity distribution
	From this experiments, we could deduce the following test:
	(1) Consider a sequence of length 512 as the truth table of f : F 9 2 → F 2
	(2)

  70 PW CF k of 150 PW CF k of 400 PW CF k of RW

	3	6	8	8	8	8
	5	10	32	32	32	32
	7	14	58	91	124	124
	15 30	70	150	400	493
	25 66	70	150	400	488
	30 86	70	150	400	483


Eli Voet
email: eli.voet@ugent.be

Tahira Ahmed

Eric Lindner

Geert Luyckx

Anders Brødsjø

Joris Degrieck

SMALLER DIAMETER OPTICAL FIBRE SENSOR FOR AUTOMATED EMBEDDING IN COMPOSITE LAMINATES

Keywords: fibre Bragg gratings, automated fibre placement, embedded sensors, fibre reinforced composites, strain monitoring

In the framework of the FP7-project SMARTFIBER (http://www.smartfiber-fp7.eu/) an optical fibre prototype has been developed with a cladding diameter of approximately 60 µm. Draw Tower fibre Bragg gratings (DTG®s) are inscribed in this fibre which show identical strain optic and thermo optic characteristics compared to the standard commercial available 125 µm version, moreover they show superb ultimate failure strain of more than 7%. This characteristic plays an important role when automatic fibre embedding processes are envisaged. In this paper, the developed 60 µm fibre prototypes are successfully been applied during automated fibre placement on prepreg material. The results of the calibration tests and of the strain evolution of the DTG® during automated fibre placement will be presented in this paper

INTRODUCTION

SMARTFIBER is a EU FP7 funded research project aiming at implementing a smart miniaturized system for "health monitoring" of composite materials, which integrates optical fibre sensor technology, nano-photonic chip technology and low power wireless technology. The work presented in this paper focusses on the work package specific dealing with automatically embed small diameter fibre Bragg grating (FBG) sensors in composite materials. When an optical fibre is embedded in composite materials and is not properly designed, it can negatively affect its mechanical properties because of local stress concentrations and hence distortion of the material occurs.

To avoid these detrimental effects, the boundaries of the FBG technology is pushed by developing an FBG sensor with a reduced diameter, which will allow to minimize the impact of the embedded fibre on the mechanical properties of the composite material. This advanced sensor is being manufactured using an innovative full automatic production process from FBGS-Technologies GmbH (Jena), which allows writing Fibre Bragg Gratings during the drawing of the fibre (Draw Tower Gratings -DTG®s [START_REF]Trademark of FBGS-technologies GmbH[END_REF]).

A key issue when dealing with FBGs for in-situ health monitoring of composite materials, is the embedding strategy. Current (manual/semi-automated) methods for FBG embedding are labor intensive, and do not ensure a good placement repeatability which is required for a reliable and robust structural health monitoring system. For this reason, the feasibility of automatic embedding of the advanced thinner FBGs in composite material is explored by extending existing automatic fibre placement strategies, developed for composite manufacturing such as Automated Fibre Placement technology (AFP).

In this paper, the development, processing, and characterization of a 60 µm diameter DTG® prototype is presented. First results of AFP using the 60 µm prototypes are shown, proving the controllability and repeatability of this embedding strategy.

DESIGN AND PROCESSING OF THE 60µM DRAW TOWER FBG

During previous R&D work at FBGS-technologies GmbH it has been shown that it is feasible to produce DTG®s with a cladding diameter of 80 µm. These fibres are commercially available today [START_REF]Trademark of FBGS-technologies GmbH[END_REF], however from experience gained during previous research during fibre drawing it is known that once the fibre is that thin the smallest misalignment and process instability can cause early failure and end of the process. In the next subsections, the manufacturing and characterization of 60 µm prototype draw tower FBGs is elaborated.

Production of 60µm Silica optical fibre

During preliminary trials, the limits of the current fibre drawing installation in terms of fibre diameter were tested. It is found that between a fibre cladding diameter of 60 µm and 40 µm large fluctuations (~5-10 µm) occur in the outer diameter of the optical fibre, which, on its turn, lead to undesirable effects such as fibre vibrations, fibre pinching in the coating applicator and fibre breakage during the process. With the fibre cladding diameter set to 60 µm, we have been able to draw successfully a few hundred meters of pure silica (dummy) fibre resulting in a stable cladding diameter of approximately 62 µm and an outer diameter with ORMOCER® coating of approximately 106 µm (Figure 1, left). This latter dimension is already very close to the thickness of a commonly used composite reinforcement layer (e.g. carbon prepregs or yarns) or smaller than commonly used glass fibre bundles, which improves the integration of the fibre optic sensors in between the reinforcement fibres. An important factor with respect to testing and first read-out of the sensors is the splicing or connectorisation of the thinner fibre to a standard fibre pigtail. Splicing tests of the 62 µm fibre to standard 125 µm telecom fibre were successful with normal splice losses (Figure 1, right). However, it must be noted that only manual splicing tests were possible by using adapted splice programs. Additionally coating removal and cleaving of the fibre end facet is not common and needs some extra handling because standard commercial tools are not yet available for fibre diameters below 80µm.

Production of the first 60µm Draw Tower FBGs

In a second stage, using in this case a photosensitive fibre preform, we have succeeded in drawing fibre with a cladding of approximately 63 µm and an outer diameter with ORMOCER® coating of approximately 106 µm (Figure 2, left). This is similar to the result we obtained for the dummy fibre drawing using a pure silica preform. A small coating non-concentricity exists of approximately 2.5µm caused by a small misalignment between the fibre and centre of the coating applicator. Extra attention is needed to minimize this effect in future runs to avoid possible negative effects on the FBG response once embedded. Similar to the dummy fibre, a manual splicing program is used to successfully splice 63 µm fibre with DTG®s to a standard 125 µm single mode fibre pigtail with FC/APC connector to be able to read out the sensors (Figure 2, right). During fibre drawing, several single DTG®s (Figure 3, left) and DTG® arrays (Figure 3, right) are inscribed. It is found that the spectral shape and FWHM (120pm) of all 63 µm versions is identical to that of standard DTG®s. More information regarding the assessment of the quality of these prototype DTG®s is found in Section 1.3, where the mechanical, opto-mechanical and thermo-optic sensor properties are determined. 1.3 Characterization of the first prototype 60µm Draw Tower FBGs.

Fibre tensile strength

Tensile tests are performed on dummy and sensor fibre to define their ultimate fibre stress (ε ult ) and ultimate strain at breakage (ε ult ). In Table 1, it is shown that the ultimate tensile properties of the 60 µm versions are excellent compared to the commercially available 125 µm and 80 µm DTG®s.

Strain gauge parameter:

In this research, we are defining the logarithmic relationship between the wavelength shift and applied longitudinal strain by determining a wavelength independent gauge factor, S  which is defined as ), with n the effective refractive index of the fibre and  the period of the grating. In contrary to the linear strain sensitivity commonly used in literature (typical 1.2pm/µε for 1550nm range), the gauge factor, S  according to Equation ( 1) is applicable for gratings at any given wavelength, moreover it can be used for large wavelength shifts (i.e. for high strain levels). The individual S  factor is determined for several DTG® arrays with multiple gratings in series. The fibre is fixed to translation stages and strained up to more than 0.5% in steps of approximately 800 µε. The DTG® its wavelength is recorded and plotted as a logarithmic, and divided by its initial Bragg wavelength at zero loading, ,0 B  , against the applied strain (Figure 4). In total two arrays with ten 63 µm DTG®s were calibrated. The average strain gauge factor is found S ε , 63 = 0.777±0.0027. This value matches very well the strain gauge factors of commercially available 80 µm and 125 µm DTG®s. The S ε -factor will be used further to estimate the strain during automated fibre placement (see Section 2).

,0 3 1 ln B B S       , (1) with

Temperature sensitivity:

According to literature [START_REF] Pal | Non-linear temperature dependence of Bragg gratings written in different fibres, optimised for sensor applications over a wide range of temperatures[END_REF], best fits of the temperature calibration curves for FBGs are obtained using second order polynomials. For the fits of the calibrations performed on the 63µm DTG®s the following quadratic function is used:  is the measured wavelength at the actual temperature T. The temperature sensitivities, S T1 and S T2 , are determined by performing a temperature calibration and fitting the calibration curve by using a second order polynomial. Three samples were prepared for the temperature calibration. The coating of the is removed to avoid humidity effects during calibration and each sensor is protected using a quartz capillary which is fixated and sealed using small drops of adhesive. The temperature calibration is performed using a Fluke 9170 metrology well calibrator. The metrology well has a temperature stability of ± 0.005°C and an accuracy of approximately ± 0.014°C. The temperature is cycled twice from -22.5°C up to 135°C in steps of 22.5°C, see Figure 5, left. The second cycle is used to calibrate the sensors. Each temperature level is kept constant for approximately 30 minutes and the peak wavelength of all samples is continuously recorded. An example of the experimental calibration curve is shown in Figure 5, right. A polynomial (Equation ( 2)) is fitted to the data points to determine S T1 and S T2 . The calibrated average temperature sensitivity is found to be S T1 =6.37E-6 and S T2 =7.3E-9. Again the values match very well the temperature sensitivities of commercial available 125 µm and 80 µm DTG®s. These parameters can be used to perform temperature compensation techniques or even be used to calculate temperature using the inverse of Equation (2).

AUTOMATED FIBRE PLACEMENT

The scope of this part of the workpackage within the SMARTFIBER project is to study automated fibre placement (AFP) using a robot cell of Airborne Technology Centre with a dedicated AFP head and the newly developed 63 µm DTG®-fibre described in this paper. Specific sensor arrays with a double DTG® configuraton are produced for the tests. The distance between the two DTG® sensors is 40mm. The aim is to determine the reproducibility of the AFP process. Multiple tests are performed to investigate the impact on the fibre during placement and the strain development is monitored during lay-down of the fibre onto prepreg material and during composite curing.

AFP straight on prepreg

In this test, the optical fibre is manually spooled on the OF reel and then automatically laid down on a GFRP prepreg using the AFP robot with dedicated AFP head (Figure 6, left). A nominal compaction pressure of 1.75bar is used to press the fibre into the prepreg (Figure 6, right). The strains of both sensors are simultaneously monitored during lay-down. The different sequences during the test are clearly shown in Figure 7, the strain develops I) during manually spooling, II) during automated placement and III) during lay-down. The two DTG®s measure a pre-strain of approximately 400µstrain after lay-down. Two different tests were then performed, each repeated three times: "short traject tests" with a fibre length of ~0.2m and "long traject tests" with a fibre length of ~1.5m. All test show that the sensors measure maximum approximately 400 -600µstrain during lay-down.

The value is acceptable and far below the limit of 7% strain at breakage, so these tests show that with the present AFP setup the risk of breaking the optical fibre is very low. In addition, this small pre-strain is beneficiary for keeping the fibres straight after placement. Examples of the results for both tests are shown in Figure 8: We see that for shorter fibre the pre-strain developed during lay-down decreases faster than in the case of longer fibre. We also notice that the strain difference between the first and second sensor is higher for the shorter fibre length. As a consequence, to ensure and control similar pre-strain levels for the sensors and to keep the initial pre-strain after lay-down, the length of the fibre after the sensors should be taken long enough. Results of further tests show that both sensors have exactly the same pre-strain and that the drop of pre-strain evolves much slower if compaction pressure is increased to 6bar. The work performed up to now has only focused on placement of straight fibres.

In a second stage a curved path will be envisaged.

Strain measurements during lay-down, lay-up, curing and after consolidation

In a final test, two fibres, having 1 DTG®, are embedded in a GFRP composite (0.6m x 1.5m) with lay-up [0,90] s . The laminate was oven cured at 120°C and vacuum is applied during curing. Both sensors were monitored at several stages during the embedding and production process, starting from fibre lay-down using AFP (compaction 6bar), after final lay-up, during application of vacuum, and finally after curing (Figure 9). A very similar response is found for fibre 1 and 2. The strain values of fibre 1 at different time stamps during the production process, is shown in Figure 9, right. A small decrease is noticed after composite lay-up, which is caused by a release of pre-strain during the time between AFP and finalization of the bagging material (~15minutes). More than 90% and 75% of pre-strain is left for fibre 1 and fibre 2, respectively. The strain after application of vacuum has dropped as well, which is probably a combination of compaction of the layers and drop in temperature because of air flow. Note that the strain level after debagging compared to the strain level measured at the start of the cure cycle (T=25°C), are found to be very similar. This could indicate that for this specific GFRP material no significant residual strain is built up during its production process.

CONCLUSIONS

In general it can be concluded that the newly developed smaller diameter fibre and draw tower FBG prototype with cladding 63 µm and coating outer diameter 106 µm, has identical sensor properties compared to the commercial available DTG®s. Moreover the strain at breakage is found excellent and the fibre copes very well with the AFP process. The induced strains are very small and form no risk to fibre breakage and fibre placement tests show to be very repeatable. We are able to control the pre-strain during embedding and assure straight fibre alignment. Result of these test prove that automated fibre embedding is feasible, even with very thin optical fibre sensors.

Figure 1 :

 1 Figure 1: Pure silica fibre with a cladding diameter of 62 µm and coating diameter of 106µm (left), Example of a spliced 62 µm "dummy" fibre to a standard 125µm fibre (right).

Figure 2 :

 2 Figure 2: Cross section of the 63 µm DTG® fibre with ORMOCER® coating of approximately 106µm (left), Example of a spliced 63 µm DTG® fibre to a standard 125µm fibre (right).

Figure 3 :

 3 Figure 3: Reflection spectrum (in dB) of a single 63 µm DTG® (left), and 63 µm DTG® array of ten gratings in series (right).

  initial Bragg wavelength (e.g. at zero load) and B  , the wavelength at any given time. Equation (1) is derived from the well-known standard Bragg condition (

Figure 4 :

 4 Figure 4: Typical strain calibration curves of ten 63µm DTG®s with the average gauge factor.

  between the reference temperature and actual temperature, S T1 and S T2 the wavelength independent linear and quadratic temperature sensitivities, respectively, , B ref  the Bragg wavelength at the reference temperature, T ref , and B

Figure 5 :

 5 Figure 5: Temperature calibration cycles from -22.5°C -135°C (left), calibration curve for three 63 µm DTG®s fitted polynomial, with T 0 = 22.5°C (right).

Figure 6 :

 6 Figure 6: Robot with AFP head and monitoring system (left), close-up of the compaction wheel and optical fibre on prepreg layer after lay-down (right).

Figure 7 :

 7 Figure 7: Strain development of two 63µm DTG®s (Δ d=4cm) during AFP.

Figure 8 :

 8 Figure 8: Strain development during lay-down of a 63µm DTG® pair (Δ d=4cm) for a short traject (left) and longer traject (right).

Figure 9 :

 9 Figure 9: Optical fibre egress points with PTFE tubes in final lay-up (left), lay-up in vacuum bag (right)

Table 1 :

 1 Statistics on the maximal applied force, the calculated tensile strain and tensile strength of the 63 µm DTG®-fibre in comparison with the commercial 125 µm and 82 µm DTG®-fibre and dummy 62 µm fibre.

	Fibre	F max [N]	ε ULT [%]	 f,ULT [MPa]
				(mean)
	125 / 190 µm (DTG®) (N=5)	58.0 ± 4.6	6.3 ± 0.50	4566 ± 362
	82 / 114 µm (DTG®) (N=15)	25.3 ± 0.8	6.5 ± 0.21	4667 ± 150
	62 / 106 µm (dummy) (N=14)	16.9 ± 0.3	7.4 ± 0.14	5316 ± 99
	63 / 106 µm (DTG®) (N=15)	17 ± 0.3	7.4 ± 0.11	5349 ± 78

July 8-11, 2014. La Cité, Nantes, France Copyright © Inria (2014)

EWSHM 2014 -Nantes, France

ACKNOWLEDGEMENT

The research leading to these results has received funding from the European Union Seventh Framework Programme FP7/2007-2013 under grant agreement n° 257733 (SmartFiber)


Dinh Dong Doan
email: dinhdong.doan@femto-st.fr

Emmanuel Ramasso

Vincent Placet

Lamine Boubakar

Noureddine Zerhouni

An unsupervised pattern recognition approach for AE data originating from fatigue tests on polymer-composite materials

Keywords: organic-matrix composites, acoustic emission, data clustering, noise reduction, feature selection

Acoustic Emission (AE) technique is gaining more and more interest for structural health monitoring (SHM) in polymer-composite materials. Recent literature has shown that using appropriate pattern recognition techniques (PRT), the identification of the natural clusters of acoustic emission data can be obtained. This work investigates acoustic emission generated during tension fatigue tests carried out on a carbon fiber reinforced polymer (CFRP) composite specimen. Since fatigue data processing, especially noise reduction remains an important challenge in AE data analysis, a noise modeling has been proposed in the present work to tackle this problem. A Davies-Bouldin-index-based progressive feature selection has been implemented to reduce high dimensional fatigue dataset. A classifier offline-learned from quasi-static data is then used to classify the processed data to different AE sources. An adaptation has been studied to enable the classifier to generate new class, i.e. AE source, for unidentified AE events. With efficient proposed noise removal and automatic separation of AE events, the results of this work provide an insight into fatigue damage development in composites and then ability to health assessment which is necessary for residual life prediction.

INTRODUCTION

AE testing has become a recognized nondestructive test (NDT) method, commonly used to detect and locate faults in mechanically loaded structures and components. AE could provide comprehensive information on the origination of a discontinuity (flaw) in a stressed component and also provide information pertaining to the development of this flaw as the component is subjected to continuous or repetitive stress [START_REF] Anastassopoulos | Clustering methodology for the evaluation of acoustic emission from composites[END_REF][START_REF] Johnson | Waveform based clustering and classification of AE transients in composite laminates using principal component analysis[END_REF]. Moreover, the method has been developed and applied in numerous structural components, such as steam pipes and pressure vessels, and in the research areas of rocks, composite materials, and metals.

Acoustic emissions (AE) are the stress waves produced by the sudden internal stress redistribution of the materials caused by the changes in the internal structure. Possible causes of the internal-structure changes are crack initiation and growth, crack opening and closure, dislocation movement, twinning, and phase transformation in monolithic materials and fiber breakage and fiber-matrix debonding in composites. Most of the sources of AE are damage-related; thus, the detection and monitoring of these emissions are commonly used to predict material failure.

With a huge noisy amount of data originating from fatigue loading tests, a major challenge in the use of AE technique is to associate each signal to a specific AE source related to noise or a damage mechanism. This analysis is a non-trivial task for two main reasons. First, AE signals are complex objects that must be characterized by multiple relevant features. Second, there is no a priori knowledge of the acoustic signatures of damage events and these are assumed rather scattered.

In the literature, dealing with the challenge of big data due to high sensitivity of AE sensors and to long-term fatigue loading experiments, several processing approaches have been proposed by [START_REF] Henry | Suivi de lendommagement en fatigue dun composite renfort interlock carbone/poxy par mission acoustique[END_REF][START_REF] Jianguo | Signal identification in acoustic emission monitoring of fatigue cracking in steel bridges[END_REF][START_REF] Yu | Quantification of fatigue cracking in CT specimens with passive and active piezoelectric sensing[END_REF][START_REF] Calabrese | Noise removal by cluster analysis after long time AE corrosion monitoring of steel reinforcement in concrete[END_REF]. In [START_REF] Henry | Suivi de lendommagement en fatigue dun composite renfort interlock carbone/poxy par mission acoustique[END_REF][START_REF] Jianguo | Signal identification in acoustic emission monitoring of fatigue cracking in steel bridges[END_REF], it is considered that only signals with amplitude higher than 70 dB or recorded above 80% of peak load contain information related to damage mechanisms. This filtering is subjectively supposed to be efficient in terms of quantitative reduction but it could take a serious risk at missing low and medium energy AE sources that condition the onset of more severe damage mode. In [START_REF] Yu | Quantification of fatigue cracking in CT specimens with passive and active piezoelectric sensing[END_REF], "friction emission" tests in which the maximum cyclic load was decreased to a level that was insufficient to generate crack growth were performed to understand the AE signal characteristics arising from hydraulics, machine start and stop, slippage, grating between fracture surfaces (also referred to as "fretting"), and abrasion of load train. All of the AE events at this lower peak load were therefore assumed to be due to friction emission. Emission having the characteristics of friction emission was then filtered. Friction emission testing was useful and did provide reference waveforms to aid in the differentiation of noise from cracking. However, it did not provide all-inclusive reference parameters for data filtering. This is because the loads were lower than those in the formal fatigue tests. Besides, this specialized kind of test requires a specific load level mentioned above that is not always easily determined. A more complex denoising process developed by [START_REF] Calabrese | Noise removal by cluster analysis after long time AE corrosion monitoring of steel reinforcement in concrete[END_REF] that combines PCA and K-means and several validation techniques was presented to be able to classify more than 60% of the detected signals as noise, before the application of a SOM algorithm to separate AE events from the residual noise in the remaining dataset recorded during long time corrosion monitoring of a pre-damaged post tensioned concrete beam.

High dimensional feature space reduction is a remaining challenge to statistical processing and classification of AE data. In the literature, many approaches for AE data processing [START_REF] Anastassopoulos | Clustering methodology for the evaluation of acoustic emission from composites[END_REF][START_REF] Johnson | Waveform based clustering and classification of AE transients in composite laminates using principal component analysis[END_REF][START_REF] Godin | Clustering of acoustic emission signals collected during tensile tests on unidirectional glass/polyester composite using supervised and unsupervised classifiers[END_REF] are conditioned by Principal Component Analysis (PCA). The latter provides a feature space reduction as well as extraction of relevant components subset from the original features set. This algorithm assumes that 1) the linear combination of features improves the relevancy of the principal components and 2) a large variance implies meaningfulness. Other approaches [START_REF] Gutkin | On acoustic emission for failure investigation in CFRP: pattern recognition and peak frequency analyses[END_REF][START_REF] Moevus | Analysis of damage mechanisms and associated acoustic emission in two SiCf/[SiBC] composites exhibiting different tensile behaviours. part II: unsupervised acoustic emission data clustering[END_REF][START_REF] Sause | Pattern recognition approach to identify natural clusters of acoustic emission signals[END_REF] rely on a specific subset of features such as energy, rise time, duration, amplitude [START_REF] Gutkin | On acoustic emission for failure investigation in CFRP: pattern recognition and peak frequency analyses[END_REF] or reduce feature dimension space by using complete link hierarchical clustering in order to merge the correlated features into groups [START_REF] Moevus | Analysis of damage mechanisms and associated acoustic emission in two SiCf/[SiBC] composites exhibiting different tensile behaviours. part II: unsupervised acoustic emission data clustering[END_REF]. Those apply a greedy approach that generates all possible feature combinations and then selects the one which optimizes a given criterion [START_REF] Sause | Pattern recognition approach to identify natural clusters of acoustic emission signals[END_REF][START_REF] Halkidi | On clustering validation techniques[END_REF]. The goal of the criterion is generally to evaluate the quality of the partition provided by the clustering. Most of criteria are based on the Euclidean distance to assess the membership of an AE hit to a given cluster. Thus the applicability of this approach is limited to clustering algorithms which are based on the Euclidean distance. The PCA and K-means are theoretically related to each other as shown in [START_REF] Ding | K-means clustering via principal component analysis[END_REF]. The main reason to account for the performance of this couple is actually due to the link between both tools. An alternative approach based on the Gustafson-Kessel algorithm (GK) [START_REF] Gustafson | Fuzzy clustering with a fuzzy covariance matrix[END_REF] was proposed in [START_REF] Placet | Online segmentation of acoustic emission data streams for detection of damages in composite structures in unconstrained environments[END_REF] which used a modified Mahalanobis distance for each cluster which is iteratively adapted to fit ellipse-shaped clusters. The use of hyperellipses instead of hyper-spheres is more appropriate for AE clustering in presence of low density and high scattering. In the GK algorithm, the covariance between each pair of features is estimated so that possible redundancy or complementarity between features can be taken into account.

In this paper we propose a methodology to estimate the partition of AE data obtained in fatigue loading in presence of noise sources. The methodology includes an automated filtering step and a progressive feature selection. The algorithm proposed in [START_REF] Placet | Online segmentation of acoustic emission data streams for detection of damages in composite structures in unconstrained environments[END_REF] for quasi-static tests is adapted to be applied on fatigue tests. The next section is dedicated to presentation of the proposed methodology.

UNSUPERVISED PATTERN RECOGNITION METHODOLOGY

The flow chart of the methodology is shown on Figure 1.

Progressive selection algorithm of AE features

The goal of this section is to propose an automated technique to detect relevant feature subsets for clustering of AE events. In contrast to feature reduction procedures (e.g. based on correlation dendrogram in [START_REF] Anastassopoulos | Clustering methodology for the evaluation of acoustic emission from composites[END_REF]) or exhaustive search of global optimal feature combinations in [START_REF] Sause | Pattern recognition approach to identify natural clusters of acoustic emission signals[END_REF], the principle of the presented approach is to combine gradually each feature from an available feature space with an initial feature subset. The feature selection is achieved by minimizing the value of Davies and Bouldin (DB) index [START_REF] Davies | A cluster separation measure[END_REF] presented on Equation (1) :

DB = 1 k k ∑ i=1 max i = j d i + d j D i j (1)
where d i and d j are the average within-class distances of clusters i and j respectively, and D i j denotes the distance between the two clusters i and j. This clustering validity index has been used by several authors in order to select optimal cluster number [START_REF] Moevus | Analysis of damage mechanisms and associated acoustic emission in two SiCf/[SiBC] composites exhibiting different tensile behaviours. part II: unsupervised acoustic emission data clustering[END_REF] or to evaluate feature subset partition [START_REF] Sause | Pattern recognition approach to identify natural clusters of acoustic emission signals[END_REF]. Due to the way it is defined, as a function of the ratio of the within cluster scatter and the between-cluster separation, a lower value of this criterion means a good compactness and a good separation of dataset partition. The Figure 2 shows the diagram of the proposed algorithm based on a feature filtering approach [START_REF] John | Irrelevant features and the subset selection problem[END_REF]. Considering an initial selected feature set denoted S (empty by default), the algorithm will take each of available features from F to create a new subset with S. This subset is then partitioned by the clustering algorithm proposed in [START_REF] Placet | Online segmentation of acoustic emission data streams for detection of damages in composite structures in unconstrained environments[END_REF]. At the k th iteration, a feature f i ∈ F is added to the current subset of features S k , and the DB index DB i of the partition obtained by the GK algorithm is computed. The subset of features S k+1 for the next iteration is given by S k ∪ f i * with i * = arg min i DB i and the partition is then evaluated by the DB criterion. The additional feature of subset that minimizes the value of DB index is selected as the relevant one. Thus, this feature will be removed from F to S. At each iteration, the procedure generates k new subsets if the number of features remaining in F is k, because each new subset contains the features from S plus a new one taken from the remaining ones in F. The algorithm stops when no new subsets can improve the DB criterion. For each iteration i, an improvement rate is calculated by Equation (2) :

IR(i) = DB(S i ) -DB(S i-1 ) DB(S i-1 ) (2)
where IR(i) is the improvement rate in the i th iteration, DB(S i ) and DB(S i-1 ) are value of DB index of the best feature selection for the i th and (i -1) th iteration. The sign of IR indicates if the DB criterion is improved (negative) or not (positive). In the last iteration j, i.e. IR( j) > 0, if IR( j) < min i = j |IR(i)| then the best-DB-index feature can be added to S to establish the final selected feature set.

AE source classification

Quasi-static tests are first applied to obtain a relatively low amount of data compared to fatigue by assuming that damage sources are similar from quasi-static to fatigue. The GK algorithm as proposed in [START_REF] Placet | Online segmentation of acoustic emission data streams for detection of damages in composite structures in unconstrained environments[END_REF] is applied to estimate the parameters of a given set of k clusters. An additional k + 1 th cluster is estimated during fatigue to include all feature vectors located far from the previous k clusters. The average Mahalanobis-like distance (used in GK) in each cluster representing its radius is estimated after the quasi-static data partitioning. A feature vector obtained during fatigue belongs to the k + 1 th cluster if its distance to nearest cluster is above the corresponding radius. Figure 3 resumes the developed procedure used for AE data analysis, showing its main steps.

Data preprocessing:

- were recorded during test at the material surface using a multi-channels data acquisition system from EPA (Euro Physical Acoustics) corporation (MISTRAS Group). The system is made up of miniature piezoelectric sensors (micro-80) with a range of resonance of 250 -325 kHz, preamplifiers with a gain of 40dB and a 20 -1000 kHz filter, a PCI card with a sampling rate of 1MHz and the AEWin software. The sensors were coupled on the specimen faces using silicon grease. The calibration of the system was performed after installation of the transducers on the specimen and before each test using a pencil lead break procedure. A part of the ambient noise was filtered using a threshold of 40dB. The acquisition parameters: PDT (Peak Definition Time) = 60 µsec; HDT (Hit Definition Time) = 120 µsec and HLT (Hit Lock Time) = 300 µsec were identified using preliminary measurements. Many features such as absolute energy, counts, hits, amplitude, duration, frequency centroid were calculated from recorded waves.

RESULTS AND DISCUSSION

Two AE datasets A1 and A2 recorded during quasi-static and fatigue tests respectively are now used to present the proposed methodology.

Noise reduction

Noise modeling has been made from AE data recorded before application of load, i.e. during the first 320s of quasi-static test. Noise during loading is then filtered by this model. Figure 4(a) represents the whole A1 dataset made of 52,832 AE hits, in the duration-amplitude space, segmented into three populations: noise before loading, noise during loading and denoised data after application of noise model. The two first populations possess the same characteristics, the same location and the same scattering. This observation is justified by the graphic of AE cumulated energy on Figure 4(b). Indeed, the level of AE cumulated energy of noise before and during loading is negligible and the total energy is conserved within denoised data while the latter occupies only 12% of the whole dataset in terms of quantity (Figure 4(c)). Application of the noise model to fatigue dataset A2 made of 1,682,434 AE hits leads to the similar separation between noise and denoised data (Figure 5(a)). In spite of 93% of AE hits recorded associated to noise (Figure 5(c)), this highest population represents negligible AE cumulated energy level in comparison with that of denoised data (Figure 5(b)).

Feature selection

Many energy-based approaches of damage characterization or identification have been studied since AE energy provides a good correlation with damage mechanisms. Thus, in this work, absolute energy numbered by n • 22 (Figure 6) is used to initialize the subset of relevant features. As the number of clusters is unknown, 3 cases were addressed to verify the stability of the selection algorithm by considering 4, 5 and 6 clusters. Applying the latter to quasi-static dataset A1 with 4 clusters, at

AE source detection

The denoised and selected feature subset in previous sections is now used to estimate the parameters of the clusters in quasi-static dataset A1 using the GK clustering algorithm proposed in [START_REF] Placet | Online segmentation of acoustic emission data streams for detection of damages in composite structures in unconstrained environments[END_REF]. Afterwards, testing directly this classifier with fatigue dataset A2 does not carry out a good separation (Figure 7(a)).

In fact, overlapping zones between clusters can be observed due to a new AE source that did not exist in the case of quasi-static testing. Consequently, according to this hypothesis, by creating a new class, a better segmentation is obtained (Figure 7(b)). In Figure 7(b), amplitude range of 5 detected AE-sources is clearly different. This can be explained by the evolution of AE cumulated energy of each source (Figure 7(c)). Despite its smallest population, AE source 2 is dominant in term of energy at the end of test. It could be associated to severe damage mechanisms such as fiber rupture, fiber bundle rupture, fiber pullout. AE source 1 is the most scattered and populated but represents negligible contribution energy to the total one. It could be friction between the specimen and the testing devices or very small cracks of matrix. AE source 5 generates long duration and high energy events that seem to be macro-matrix cracking or damage related to interfaces. It has been also observed in the Figure 8(a) that during the first 600s appears an high concentration of AE hits including all modes, followed by a steady state where all activities due to damage slow down. This stage corresponds to accommodation phase of composite material subjected to fatigue loading. Again, until 3500s, an acceleration and accumulation of high energy AE hits occurs up to the ruine of the specimen. Concerning AE sources 3 and 4, they have an interesting interpretation: according to their apparition following loading and unloading, a repetitive phenomenon takes place all along of the test that AE source 4 locates mainly in loading phase and AE source 3 in unloading phase (Figure 8(b)). The latter could correspond to internal friction or fretting between the faces of the previously developed matrix cracks that could be associated to AE source 4. Again, this dissimilarity justifies the good capacity of cluster detection approach presented in this paper.

CONCLUSION

An unsupervised pattern recognition approach for AE data originating from fatigue tests on polymercomposite materials has been presented to tackle different existing challenges of AE analysis and damage detection: 1) data pre-processing, especially noise reduction; 2) automatic and fast feature selection; 3) clustering of big data from fatigue tests with cluster adaptation. The proposed methodology permits to overcome problems related to computing approaches involving time consuming, computational cost and accuracy gain. The first results on real fatigue tests demonstrate that the proposed methodology allows to identify some relevant clusters in loading and unloading phases, some clusters of different levels of energy which seems important for structural health monitoring.

Figure 1 :Figure 2 :

 12 Figure 1: Unsupervised damage detection methodology

Figure 3 :Figure 4 :

 34 Figure 3: AE data analysis flow chart

Figure 5 :Figure 6 :

 56 Figure 5: Fatigue dataset A2: (a) Duration vs. Amplitude; (b) AE cumulated energy; (c) Percentage in terms of population

Figure 7 :Figure 8 :

 78 Figure 7: Testing phase: (a) direct classification without adaptation; (b) adaptive classification giving better separation; (c) evolution of AE cumulated energy of each AE source

EWSHM 2014 -Nantes, France

ACKNOWLEDGMENT

This work has been carried out in the framework of the Laboratory of Excellence ACTION through the program "Investments for the future" managed by the National Agency for Research (references ANR-11-LABX-01-01).


Sanne Sulejmani
email: ssulejma@b-phot.org

Camille Sonnenfeld

Thomas Geernaert

Geert Luyckx

Pawel Mergo

Waclaw Urbanczyk

Karima Chah

Hugo Thienpont

Francis Berghmans

ADHESIVE DISBOND MONITORING WITH MICROSTRUCTURED OPTICAL FIBER BRAGG GRATING SENSORS

Keywords: optical fiber sensor, fiber Bragg grating, microstructured optical fiber, adhesive bond, structural health monitoring, disbond monitoring

We present a sensing system that is based on a combination of 3 optical fiber sensors which are non-intrusively integrated in an adhesive layer, and that allows detecting the initiation and monitoring the growth of disbonds. The fiber sensors consist of fiber Bragg gratings fabricated in a dedicated microstructured optical fiber and feature an enhanced response to shear stress. The change in response of the sensors to tensile loading of the joint is used as a measure for the shear stress redistribution in the bond layer caused by disbonding. With our technique we can detect the initiation of disbonds as short as 100 µm, which corresponds to 0.4% of the overlap length. This is the first time, to the best of our knowledge, that an adhesive disbond on-line monitoring system is presented that can quantitatively evaluate even very short disbonds.

INTRODUCTION

Adhesive bonding is becoming an increasingly popular mechanical fastening technique for many applications [START_REF] Banea | Adhesively bonded joints in composite materials: an overview[END_REF]- [START_REF] Wahab | Fatigue in Adhesively Bonded Joints: A Review[END_REF]. More conventional techniques such as riveting, bolting or welding can weaken the structure locally. Furthermore, adhesive joints are lightweight, they allow for a more uniform stress transfer between different components, they can be used to join dissimilar materials, they do not affect the corrosion resistance of the material, and they have a smoother appearance. However, industry remains hesitant to rely entirely on adhesive bonds, and at present adhesive bonding is still mostly combined with another type of mechanical fastening. One reason is that no adequate technique is currently available to evaluate the manufacturing quality of an adhesive bond or to monitor its reliability during the lifetime of the structure. Results obtained with non-destructive evaluation techniques using acoustic emission, ultrasonic detection or even classical electrical strain gauges have been published, but none of these techniques allows reliable and accurate in-situ disbond monitoring [START_REF] Li | Debonding detection using a selfcalibration sensor network[END_REF]- [START_REF] Kumar | Evaluation of kissing bond in composite adhesive lap joints using digital image correlation: Preliminary studies[END_REF].

Optical fiber sensors, and in particular fiber Bragg grating sensors, have already been proposed several times for adhesive bond monitoring purposes. Optical fiber Bragg grating (FBG) sensors are light and flexible, they can be embedded non-intrusively in adhesive layers and multiple FBGs can be multiplexed into a chain of FBG sensors [START_REF] Berghmans | Optical fiber point sensors[END_REF]. So far most fiber optic based bond evaluation techniques either require complex read-out systems, feature a significant cross-sensitivity to temperature, or call for extensive calibration procedures [START_REF] Murayama | Strain Monitoring Technique For Bonded Joints By Fibre-Optic Distributed Sensors[END_REF]- [START_REF] Schulz | Health monitoring of an adhesive joint using a multiaxis fiber grating strain sensor system[END_REF]. Disbonding of the adhesive/adherend interface or cracks in the bond leads to a redistribution of the shear stress profile in the bond layer. Therefore, a method that allows continuously assessing the shear stress distribution in the adhesive bond will also return information about the bond quality. Our work relies on that principle and we propose a configuration of multiple dedicated Bragg grating based shear stress sensors that can measure the shear stress at different locations in the bond line, and that is able to monitor the initiation and growth of disbonds and to determine their length.

Our FBG sensors are fabricated in highly birefringent microstructured optical fibers (MOF). MOFs have been proposed to overcome issues specifically related to conventional polarization maintaining fibers, such as for example their significant thermal cross sensitivity and rather low transverse strain sensitivity [START_REF] Martynkien | Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure[END_REF]. High birefringence in MOFs is induced by an asymmetric air hole geometry and only a small and low GeO2-doped region is needed to allow for Bragg grating inscription using conventional UV inscription techniques. Moreover, their transverse strain sensitivity can be enhanced by properly tuning the air hole geometry, i.e. by altering the number of air holes, their sizes and/or their positions in the cross-section of the fiber. Results of the 'butterfly' microstructured optical fiber Bragg grating (MOFBG) sensor demonstrate that by designing dedicated MOFs one can improve the transverse strain sensitivity by an order of magnitude compared to conventional polarization maintaining fibers [START_REF] Sonnenfeld | Microstructured Optical Fiber Sensors Embedded in a Laminate Composite for Smart Material Applications[END_REF]. We have shown recently that the butterfly MOFBG sensor can also be used for shear stress sensing [START_REF] Sulejmani | Shear stress sensing with Bragg grating-based sensors in microstructured optical fibers[END_REF]. By aligning the optical axes parallel with the directions of principal stress in a shear loaded material, the butterfly MOFBG sensor will detect the shear load induced transverse stress.

SHEAR STRESS SENSING WITH A BUTTERFLY MOFBG SENSOR

The sensing principle of the butterfly MOFBG sensor relies on the change of modal birefringence B mod caused by a mechanical load that is applied to the cladding of the fiber, or to the host material in which the sensor is embedded [START_REF] Martynkien | Highly birefringent microstructured fibers with enhanced sensitivity to hydrostatic pressure[END_REF]. Because of the asymmetric microstructure (Figure 1a), a radial load will induce an asymmetric mechanical stress distribution in the core of the fiber. The refractive indices n x and n y of the modes polarized along the x-and y-direction are therefore affected in a different manner. This is translated into a change of the separation Δ λ between the individual Bragg peak wavelengths λ i for each linearly polarized mode, which is directly linked to B mod as given by Δ λ = 2• B mod •Λ , with Λ the period of the FBG. We consider Δ λ as the sensor signal (Figure 1b), and the sensitivity of the butterfly MOFBG sensor corresponds to the rate of change of Δ λ when submitted to a specific mechanical or thermal load.

The butterfly MOFBG sensor has a sine-like dependence of the transverse strain sensitivity to the angular orientation of the microstructure with respect to the direction of the applied load [START_REF] Sonnenfeld | Microstructured Optical Fiber Sensors Embedded in a Laminate Composite for Smart Material Applications[END_REF]. It is most sensitive when the load is applied along α = 90°, which is indicated by the slow-axis or y'axis in Figure 1. However, when the sensor is embedded in a shear loaded material at an angular orientation α = +45° or α = -45°, it will detect the transverse strain that is induced by the shear load. By orienting the sensor at +45° or -45°, the fundamental optical axes are aligned parallel to the directions of principal strain in the material. We previously demonstrated that the shear stress sensitivity of a butterfly MOFBG sensor is 59.8 pm/MPa when embedded at α=-45° in a single lap adhesive joint that is tension loaded [START_REF] Sulejmani | Shear stress sensing with Bragg grating-based sensors in microstructured optical fibers[END_REF].

SHEAR STRESS SENSING IN AN ADHESIVE BOND LINE

To embed one or multiple optical fibers in the adhesive bond line of a single lap adhesive joint (SLJ), no modifications of the fabrication process are required. The overlap regions of the adherends are polished and degreased. The adhesive is applied to the lower adherend, and immediately afterwards the optical fiber sensors are placed in the adhesive line. The angular orientation α of the optical fibers, and their position x along the overlap length is controlled during integration. Finally, the top adherend is added and the sample is cured at room temperature for at least 24h. The instrumented joints are subjected to a static tensile load by gripping them at both ends in a hydraulic servo-controlled tensile test machine with a load capacity of max. 100 kN. During loading, the FBG sensor response is recorded using an FBG interrogator (FBG-scan 608 [16]). Linear regression analyses of the responses of the MOFBG sensors to tensile loading F result in sensor sensitivities expressed in pm/kN. The theoretical model of Goland-Reissner [17] is used to relate the applied load to the shear stress at the position of the sensor, while the low amount of peel stress present at the sensor location is neglected. This allows calculating the shear stress sensitivity, expressed in pm/MPa. After testing the samples up to failure, their sides are polished in order to determine the exact angular orientation of the embedded optical fibers with a microscope.

We first demonstrate experimentally that the shear stress sensitivity of the butterfly MOFBG sensor is comparable when embedded in various adhesive bond configurations. Three sensors have been embedded in SLJs, bonded by different types of adhesive; two types of epoxybased adhesives (Araldite 420 A/B and Araldite 2015) and one methyl methacrylate adhesive (Supergrip MMA 8105). This resulted in shear stress sensitivities of respectively 59.7 pm/MPa, 63.3 pm/MPa and 59.8 pm/MPa. These values demonstrate that the sensor response does not depend on the type of adhesive in which it is integrated. Since many different joint configurations are used in practical applications, we also test the shear stress sensitivity of the butterfly MOFBG sensor when integrated in a double lap joint (DLJ). Because of its symmetric configuration, the peel stress level in this bond type is much lower than that in a single lap joint. We obtain that a sensor sensitivity of 59.7 pm/MPa when embedded in a SLJ and a sensitivity of 52.9 pm/MPa when embedded in a DLJ. The small differences in shear stress sensitivity of the different configurations can be attributed to the uncertainties on the joint dimensions, on the material properties and on the location and angular orientation of the optical fiber sensors. The peak separation Δ λ is used as sensor signal to measure shear loading.

SHEAR STRESS MAPPING ALONG A BOND OVERLAP

We embed 3 shear stress sensors in a SLJ at the specific locations x where the magnitude of the peel stress is minimal (Figure 2). The SLJs are made of two aluminum laps bonded by a two-component epoxy adhesive (Huntsman Araldite® 2015, E = 1850 MPa, G = 650 MPa and ν = 0.42). We subject the sample to a cyclic tensile loading test to evaluate the shear stress sensitivity and the response of the sensors and their ability to detect disbond initiation and propagation by monitoring their response throughout the fatigue test. At regular intervals the loading frequency -following a haversine trend and using a displacement controlled tensile load -is decreased from 2Hz to 0.01 Hz. During these intervals, we record the Bragg peak wavelengths to determine the sensor sensitivity.

The cyclic test starts at a low frequency of 0.01 Hz and the responses of the 3 sensors are recorded. Linear regression analyses of the results show that sensor 2, which is located in the center of the overlap, has a sensor response of 51.1 pm/kN, while sensor 1 and sensor 3, both located towards opposite edges of the overlap, yield a sensor response of respectively 109.9 pm/kN and 141.5 pm/kN. Since shear stress increases towards the edges of the overlap, these sensors will experience more shear loading, resulting in a higher sensor response. When taking into account the lap joint dimensions, material properties, and fiber locations, we can use Goland-Reissner theory to calculate the shear stress at the particular location of the fibers [17]. When neglecting the much lower peel stress, the 'shear stress sensitivity' of the sensors can be derived. This results in 51.3 pm/MPa, 63.3 pm/MPa, and 60.5 pm/MPa for respectively sensor 1, sensor 2, and sensor 3. These values correspond well to values reported earlier, which also demonstrates that we can evaluate the shear stress at different positions along the length of the bond overlap.

DETECTION OF DISBOND INITIATION AND PROPAGATION

When the SLJ is submitted to a cyclic fatigue loading test, disbonds and cracks will be initiated and will propagate until failure of the sample. Due to these cracks, the shear stress distribution in the joint will change throughout the test. This continuous stress redistribution will result in changes of the sensor responses. These responses can therefore be used as a basis for detecting the occurrence of disbonding and for quantifying the disbonding length.

During the cyclic test, at regular intervals, we reduce the loading frequency of 2 Hz to 0.01 Hz. During these intervals, we determine the sensor response in a similar manner as discussed in section 3 for the first loading cycle. The evolution of the sensor response throughout the complete cyclic test is a measure of the redistribution of shear stress in the bond layer, which provides information on the initiation and propagation of cracks or disbonds.

Figure 3a shows the percentage of change in response of each of the 3 sensors with respect to their initial response. The evolution of the sensor responses throughout cyclic testing of the single lap joint displays distinct features which can be attributed to the initiation and growth of disbonds and that can help to predict the onset of lap failure. The trend of the sensor response is reconstructed by 2D FE analyses (Simulia Abaqus FEA [18]) of the sensor responses when static disbonds are present. A disbond is modeled by omitting a narrow row of mesh elements in the adhesive layer. In Figure 3a we show the very good agreement between results from experiments (solid scattered point) and modeling (empty scattered points). Figure 3b shows the disbond lengths or positions of the crack tip that lead to sensor responses that correspond best to those experimentally achieved and displayed in Figure 3a. The modeling results show that after 3 000 cycles, a disbond of 0.25mm is located at the left side of the overlap, resulting in an increase of the response of sensor 1 of 10%. At the right side a disbond of 0.75mm is present, leading to an increase of the sensor response of 25%.

Once the disbond has propagated that far that sensor 1 is no longer located in a high region with a high level of shear stress, its sensor response will decrease. This is characterized by the change in trend around 10 000 cycles for sensor 1. After 10 000 cycles, the responses of sensor 1 and sensor 3 decrease, while the response of sensor 2 increases steeply after 16 000 cycles. This increase can be attributed to the shorter overall overlap length of the bond, which generates a larger shear stress along the bond line.

Our results demonstrate that by monitoring the response of shear stress fiber optic sensors integrated in a SLJ, we can continuously assess the shear stress distribution and hence detect the initiation and propagation of disbonds. Moreover, we find that when a disbond is present with a length of 1% of the initial overlap length, the sensor response can already change by 10%. Additional FE modeling has demonstrated that the shortest disbond length that can be detected by our sensing system -considering a Bragg peak separation detection accuracy of 2 pm [16] -is 100 µm, which corresponds to 0.4% of the initial bond overlap length. 3a. The sensing system allows detecting disbonds at both sides of the overlap, when the single lap joint is subjected to a cyclic fatigue test. The shortest disbond that can be detected with our system using commercially available FBG sensor interrogators is 100 µm.

CONCLUSION

We have proposed to use uniform FBG sensors fabricated in highly birefringent microstructured optical fibers (MOF) to measure shear stress in adhesive bonds. . We embedded 3 sensors at different locations along the length of the overlap of a single lap adhesive joint. We managed to map the shear stress distribution in the adhesive by following the response of these sensors when the joint is tensile loaded. Whenever disbonds occur, the resulting redistribution of the shear stress modifies the sensor response. Using the ratio of the 3 sensor responses we determined the shear stress redistribution and we linked this to a specific disbond length. Considering the Bragg peak wavelength detection resolution of commercially available interrogators, we showed that we can detect disbonds of 100 µm, or 0.4% of the overlap length. Our experimental results have been verified using two dimensional finite element modeling.

Figure 1 :

 1 Figure 1: a. Cross sectional view of the 'butterfly' microstructured optical fiber Bragg grating (MOFBG) sensor. The specific asymmetric air hole topology results in a MOFBG sensor with unprecedented shear stress sensitivity. b. Optical reflection spectrum of a butterfly MOFBG sensor.The peak separation Δ λ is used as sensor signal to measure shear loading.

Figure 2 :

 2 Figure 2: Configuration of the sensing system, consisting of 3 FBG sensors fabricated in a butterfly MOF, with a microstructure oriented with an angle of 45° and embedded at different locations along the overlap length.

Figure 3 :

 3 Figure 3: a. Evolution of the procentual change with respect to the initial sensor response recorded during the low frequency cycles in the fatigue test. b. The disbond lengths or positions of the crack tip that lead tosensor responses that correspond best to those experimentally achieved and displayed in Figure3a. The sensing system allows detecting disbonds at both sides of the overlap, when the single lap joint is subjected to a cyclic fatigue test. The shortest disbond that can be detected with our system using commercially available FBG sensor interrogators is 100 µm.

EWSHM 2014 -Nantes, France