Prognostics of composite structures utilizing structural health
monitoring data fusion
Nick Eleftheroglou a, Dimitrios Zarouchas
b, Rene Alderliesten
c, Rinze Benedictus
d
Structural Integrity & Composites Group, Aerospace Engineering Faculty, Delft
University of Technology, 2629 HS Delft, the Netherlands [email protected],
Theodoros Loutas
Applied Mechanics Laboratory, Department of Mechanical Engineering & Aeronautics,
University of Patras, 26500 Rio, Greece
Abstract
A new structural health monitoring (SHM) data fusion methodology is proposed in
order to produce features with strong prognostic capability. The Non-Homogenous
Hidden Semi Markov model (NHHSMM) is utilized to estimate the remaining useful
life (RUL) of composite structures using conventional as well as fused SHM data. The
proposed data fusion methodology and NHHSMM are applied to open hole
carbon/epoxy specimens under fatigue loading. During the specimens’ lifetime, acoustic
emission (AE) and digital image correlation (DIC) techniques were used in order to
capture the inherently dynamic and multi-scale character of damage. This work
investigates the prognostic performance of the fused data in comparison to the
performance of the conventional AE and DIC data. Prognostic performance metrics
were used and as it was found fused data has potential to provide better prognostics.
1. Introduction
Damage accumulation of composite structures is a complex phenomenon of stochastic
nature and it depends on a number of parameters such as type and frequency of loading,
stacking sequence, material properties etc. As a result, specimens from the same
composite material, being manufactured under the same process and tested under the
same machine may fail in totally different times.
One of the main profits of modelling the damage accumulation phenomenon is the
capability to estimate the remaining useful life (RUL) of a component/structure, this
capability is called ‘prognostics’. The term RUL estimation usually implies to find the
probability density function (pdf) of RUL utilizing structural health monitoring (SHM)
data, which are collected during the composite structure’s lifetime. These data are
needed in order to estimate the parameters of the selected RUL model since they are
linked to the damage accumulation process.
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However, perfect SHM data in practical cases are not realistic since these kind of data
are corrupted by the uncertainty during the data acquisition process(1)
. Furthermore, it is
profitable to note that, in many cases, the phenomenon of damage accumulation cannot
be directly measured but is correlated in a hidden way to these data. SHM data should
be able to reflect the damage accumulation of the monitored composite structure(2-5)
.
Furthermore, in the SHM community(6,7)
, it has been long known that various SHM
techniques have different sensitivities to composite structures’ failure mechanisms.
Based on SHM community’s statement, the process of extracting information from
different monitoring techniques, which compose the so-called multisensory system, and
integrate them into a consistent, accurate and reliable data set is known as data fusion
and it has been already successfully applied to damage diagnostics(8-10)
. There are
numerous reasons why a multisensory system is more desirable. For example, this
system has a higher signal-to-noise ratio, extended coverage which offers a more
complete monitoring picture of the studied composite structure, robustness and
reliability since even if a subset of the sensors fails, the other subsets are still
available(11)
.
In principle, data fusion can be implemented in three levels; raw multi-sensor fusion,
feature-level fusion and decision-level data fusion. Raw data fusion should be treated
with caution since the data from two or more of the sensors are directly combined
before any pre-processing has been performed. As a result, sensor recordings may have
different acquisition, pre-filtering and amplification settings. In addition, raw data
fusion needs to have as input commensurate data. Therefore, feature-level and decision-
level fusion are more common(12)
in literature. In the current work the feature-level data
fusion is selected. As a consequence, two or more pre-processed sensor signals should
be combined to produce a single feature. This process can be as simple as concatenation
or can be as complex as a nonlinear mapping e.g. nonlinear principal component
analysis.
By combining features extracted from different sensors or SHM techniques and
integrating them into a single feature, is known to enhance the diagnostics
performance(12,13)
. Data fusion for structural prognostics purposes has never been
attempted according to the authors best knowledge. We hypothesize that the prognostic
performance improves when SHM fusion data are utilized. In order to quantify this
statement various prognostic performance metrics are employed for the comparison.
In this study a data-driven approach is followed utilizing the Non-Homogeneous Hidden
Semi Markov model (NHHSMM), since the physics of composite structures’ damage
evolution is not yet fully explained by a mathematical model of global validity and
recent advances in SHM technologies enable us to continuously monitor composite
structures during their operation time(14)
. In addition, as it was shown in previous
studies, the NHHSMM provided accurate RUL estimations, using separately AE(15)
and
DIC(16)
data, and it outperformed Bayesian Neural Networks(17)
, the state-of-the-art in
data-driven models. Furthermore, we follow the feature-level data fusion strategy
combining features extracted from two different SHM techniques and introducing new
hyper-features of higher monotonicity that it is expected to improve the RUL
estimations. As already mentioned, AE and DIC techniques are employed to monitor the
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damage evolution during fatigue loading. The first provide data related to the failure
mechanisms that occur after energy release due to damage formulation in micro-scale
level and the latter measures surface strain fields, so macro-scale level. The main
objective of this paper is to investigate the potential of SHM data fusion for structural
prognostics of composite structures.
The remainder of this paper is organized as follows; in section 2, the selected data
fusion methodology is described. A case study analysis follows in section 3 and finally
conclusions are presented in section 4.
2. Data fusion methodology
A data fusion strategy on the feature-level is implemented in order to enhance the
prognostic performance of the available SHM data, a set of metrics has been proposed
in the relevant literature(18-21)
and consists of monotonicity, prognosability and
trendability. Monotonicity characterizes a parameter's general increasing or decreasing
trend, prognosability measures the spread of a parameter's failure value and finally,
trendability indicates whether degradation histories of a specific parameter have the
same underlying trend.
In this study, the proposed data fusion methodology is based on monotonicity since a
feature that is sensitive to the degradation process is desirable to have a monotonic
trend(19,20,22)
. Prognosability is excluded from the present data fusion process since
NHHSMM dictates that the last observation of the SHM data must be unique and
common for all the degradation histories(15,23)
.Furthermore, the data fusion methodology
does not take into account the influence of trendability because the aim of this work is
to identify monotonicity’s influence in prognostics.
The proposed methodology is a new hyper-feature data fusion scheme, which combines
AE and DIC features. The rationale behind that scheme is explained via introducing the
following equation.
(1)
where is the fused output feature, are constant coefficients that control the weight
of the exponential DIC and AE features’ product and M the maximum polynomial
degree power which these features have. The Modified Mann-Kendal (MMK) criterion
is adopted to enable the data fusion process and is expressed in equation(2). MMK is
used as an objective function to be maximized and thus determine which polynomial
degree M and constant coefficients aij give the most monotonic fused feature.
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(2)
where K is the number of available training degradation histories (e.g. the number of
tested specimens), fi(k) the fused feature value at time of measurement ti(k) for the kth
specimen, dk the number of the kth specimen’s measurements and
.
The constant polynomial coefficients , for each polynomial degree M, are based on
the optimization problem described in equation(3) with the monotonicity obtained by
the MMK criterion as the objective function. The unconstrained optimization problem is
formulated as:
(3)
In conclusion, the outputs of the proposed data fusion methodology are the optimum
polynomial degree M and the optimum constant coefficients aij based on the MMK
monotonicity, equation(3).
3. Case Study
3.1 Experimental campaign
Seven open-hole carbon/epoxy specimens with [0/±45/90]2s lay-up were manufactured
via the autoclave process with the following geometrical details: dimensions [300mm x
30mm] and a central hole of 6mm diameter. These specimens were subjected to fatigue
loading with maximum amplitude 90% of the static tensile strength (Sf =42.66kN), R=0
and f=10Hz.
A stereovision system was used to perform 3D full field DIC measurements in order to
measure strain distribution on the coupon surface during the entire fatigue test. Figure 1
presents the seven axial strain degradation histories.
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Figure 1. Axial strain degradation histories of seven open-hole specimens
Furthermore, an AE system was used in order to perform the AE measurements. 1/A
(1/amplitude) calculated cumulatively in periodic windows of 500 cycles, same with the
DIC measurements, for all tested specimens. 1/A is chosen since it produced more
monotonic observation sequences than other conventional AE features e.g. energy, hits,
RA (rise time/amplitude), as it was observed in paper(15)
. The AE degradation histories
for seven specimens are shown in Figure 2. The reader can refer to Eleftheroglou et
al.(24)
for a more detailed description of the experimental campaign.
Figure 2. AE degradation histories of seven open-hole specimens
3.2 SHM data fusion
For the aforementioned optimization data-fusion study, equation(3), different
optimization techniques were used i.e. Nelder-Mead, Neural Networks, Particle Swarm
Optimization (PSO), Genetic Algorithms and OptQuest/NLP (OQNLP). It was found
that OQNLP(25)
is the most efficient optimization technique regarding the computational
time of the parameters and M. The results are presented for various polynomial
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degrees M in Figure 3. The MMK monotonicity converges for a polynomial degree
M≥5. Therefore, the polynomial degree is selected as M = 5.
Figure 3. Modified Mann-Kendal value versus the polynomial degree
For determined polynomial degree M=5, Table 1 summarizes the optimization results
regarding the constant coefficients aij.
Table 1. Optimization results for M=5.
AE0 AE1 AE2 AE3 AE4 AE5
DIC0 -39,955 -953,757 -743,892 471,0798 882,5275 1,985843
DIC1 -783,606 1,989894 -746,044 381,3022 -344,348 0
DIC2 412,001 411,5522 271,9862 829,036 0 0
DIC3 -922,063 -183,044 -16,7071 0 0 0
DIC4 292,6789 906,5035 0 0 0 0
DIC5 336,2406 0 0 0 0 0
The fused features for polynomial degree M = 5 and the aforementioned polynomial
coefficients aij are depicted in Figure 4.
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Figure 4. Fused degradation histories of seven open-hole specimens
Figure 5 presents the MMK monotonicity for each SHM feature i.e. AE, DIC and fused
data and it is observed that the fused data has the highest monotonic rate.
Figure 5. Comparison between DIC, AE and Fusion MMK monotonicity.
3.3 Remaining useful life estimations
The procedure of damage accumulation in composite materials under fatigue loading is
modelled via the NHHSMM. The reader can refer to Moghadass and Zuo(23)
and
Eleftheroglou and Loutas(15)
for a more detailed description since the main contribution
of this study is to propose a new data fusion methodology independent on the selected
RUL prediction model.
8
Based on the aforementioned figures, i.e. Figure1,2 and 4, seven degradation histories
Y=[y(1)
,y(2
),…,y(7)
] were available. The parameter estimation process employed six
degradation histories for the training procedure and keeps the seventh degradation
history as the prognostic set. The RUL estimations of the three available SHM
techniques are presented in Figure 6 for specimen03. The choice of presenting the
results of specimen03 was random, similar results were obtained for the rest other
specimens.
Figure 6. Estimated mean RUL and 90% confidence intervals for specimen03
The RUL estimations converge quite satisfactorily with the actual RUL values. Based
on Figure 6 the strain data provides RUL estimations, which are closer to the actual
RUL than the AE and Fusion RUL estimations. In order to quantify these observations
some prognostic performance metrics are utilized in the following subsection 3.4.
3.4 Prognostic performance metrics implementation
Four prognostic performance metrics are employed in order to evaluate the predictive
performance of the three NHHSMMs trained with the different types of SHM features.
Mean square error (MSE), mean absolute percentage error (MAPE), median absolute
percentage error (MDAPE) and cumulative relative accuracy (CRA) were used as the
selected prognostic performance metrics(26,27)
. These metrics were calculated between
the predicted RUL and the actual RUL. MSE, MAPE, MDAP and CRA are defined as:
MSE = , MAPE = MdAPE = and
CRA=
Where
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is the mean value of error Em and Em(ti) = - and ti ε
[1,D] is the discrete time moment when the ith
SHM observation is recorded,
Emd(ti) = - and
RA(ti) = 1- .
In Figures 7-10 the results of the aforementioned performance metrics are presented.
Based on these results, it is confirmed that DIC data provides the best RUL estimations
since DIC RUL estimations score better in most of the prognostic performance metrics.
Figure 7. MSE prognostic performance metric of each specimen and SHM
technique (minimum value)
Figure 8. MAPE prognostic performance metric of each specimen and SHM
technique (minimum value)
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Figure 9. MDAPE prognostic performance metric of each specimen and SHM
technique (minimum value)
Figure 10. CRA prognostic performance metric of each specimen and SHM
technique (maximum value)
4. Conclusions
A new hyper-feature data fusion methodology that utilized two different heterogeneous
sources of SHM data were presented in this paper. Open-hole carbon/epoxy specimens
were subjected to constant amplitude fatigue loading up to failure and two SHM
techniques, i.e. DIC and AE, were employed to monitor the fatigue tests and provide the
required data regarding the data fusion process. In addition, four prognostic
performance metrics were employed in order to compare the performance of the
available RUL estimations.
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Although the degradation histories of the fused data had monotonicity higher than the
monotonicity of the degradation histories of DIC and AE features, the fused data didn’t
provide always better estimations, indicating that the requirement of monotonicity is not
enough and extra criteria should be involved. Nevertheless, the results demonstrate the
potential of the proposed data fusion methodology and its evolvement by adding extra
criteria i.e. trendability will enhance the performance of the fused data.
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