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 an.eleftheroglou@tudelft.nl,

bd.zarouchas@tudelft.nl,

cr.c.alderliesten@tudelft.nl,

dr.benedictus@tudelft.nl

Theodoros Loutas

Applied Mechanics Laboratory, Department of Mechanical Engineering & Aeronautics,

University of Patras, 26500 Rio, Greece

loutas@mech.upatras.gr

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

9

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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