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Review of prognostic problem in condition-based
maintenance.
Otilia Elena Dragomir, Rafael Gouriveau, Florin Dragomir, Eugénia Minca,
Noureddine Zerhouni
To cite this version:
Otilia Elena Dragomir, Rafael Gouriveau, Florin Dragomir, Eugénia Minca, Noureddine Zerhouni. Re-
view of prognostic problem in condition-based maintenance.. European Control Conference, ECC’09.,
Aug 2009, Budapest, Hungary. pp.1585-1592. �hal-00418761�
Abstract— Prognostic is nowadays recognized as a key
feature in maintenance strategies as it should allow avoiding
inopportune maintenance spending. Real prognostic systems are
however scarce in industry. That can be explained from
different aspects, on of them being the difficulty of choosing an
efficient technology: many approaches to support the prognostic
process exist, whose applicability is highly dependent on
industrial constraints. Thus, the general purpose of the paper is
to explore the way of performing failure prognostics so that
manager can act consequently. Different aspects of prognostic
are discussed. The prognostic process is (re)defined and an
overview of prognostic metrics is given. Following that, the
"prognostic approaches" are described. The whole aims at
giving an overview of the prognostic area, both from the
academic and industrial points of views.
I. I
NTRODUCTION
aintenance activity combines different methods, tools
and techniques to reduce maintenance costs while
increasing reliability, availability and security of equipments.
Thus, one usually speaks about fault detection, failures
diagnostic, response development (choice of management
actions - preventive and/or corrective) and scheduling of
these actions. Briefly these steps correspond to the need,
firstly, of "perceiving" phenomena, next, of "understanding"
them, and finally, of "acting" consequently. However, rather
than understanding a phenomenon which has just appeared
like a failure (a posteriori comprehension), it seems
convenient to "anticipate" it's manifestation in order to
consequently and, as soon as possible, resort to protective
actions. This is what could be defined as the "prognostic
process" and which the object of this paper is.
Prognostic reveals to be a very promising maintenance
activity as it should permit to improve safety, plan successful
missions, schedule maintenance, reduce maintenance cost
and down time [1]. Also, industrials show a growing interest
in this thematic which becomes a major research framework;
see recent papers dedicated to "CBM", condition-based
maintenance [2], [3] and [4]. However, considering the
benefits that such technology may bring to the security,
economics and resource management fields, the research
Otilia E. Dragomir, Florin Dragomir and Eugenia Mincă are with
Valahia University of Târgoviste, Electrical Engineering Faculty,
Automation and Information Department, Unirii Avenue 18-20, Târgoviste,
Romania; {drg_otilia, drg_florin, minca}@yahoo.com.
Rafael Gouriveau and Noureddine Zerhouni are with FEMTO-ST
Institute, CNRS - UFC / ENSMM / UTBM, Automatic Control and Micro-
Mechatronic Systems Department, 24 rue Alain Savary, 25000 Besançon,
France; {rgourive, zerhouni}@ens2m.fr.
community still doesn't propose a formal framework to
instrument the prognostic process and real prognostic
systems are scarce in industry. That can be explained from
different aspects. Firstly, "prognostic" still is not a stabilized
concept: there is no consensual way of understanding it
which makes harder the definition of tools to support it in
real applications. Secondly, many approaches for prediction
exist whose applicability is highly dependent of the available
knowledge on the monitored system. Thirdly, the vagueness
of prognostic process definition impedes to point out the
inherent challenges for scientists. Thus, the purpose of this
paper is to analyze and discuss the prognostic process from
different points of view: the concept, the measures and the
tools. The whole aims at giving a frame to perform (and
develop) real prognostic systems.
The paper is organized as follows. First of all, the concept
of "prognostic" is briefly defined and positioned within the
maintenance strategies. Some developments have been led to
improve the proactive capacities of maintainers. So, the next
part is dedicated to the analysis of the tools used in
prognostic and prediction. At this stage, the advantages and
the drawbacks of the identified research approaches for
prognostic's purpose are pointed out.
II. P
ROGNOSTIC
C
ONCEPT
(RE) D
EFINITION
A. Concept of prognostic
The European Standard on maintenance terminology does
not define "prognostic" [5]. It doesn't appear either on the
IFAC keywords list. This reveals that prognostic is a quite
new area of interest.
Prognostic is traditionally related to fracture mechanics
and fatigue. It started to be brought up by the modal analysis
community as a field of interest [6]. In this "meaning",
prognostic is called the prediction of a system’s lifetime and
corresponds to the last level of the classification of damage
detection methods introduced by [7]. Prognostic can also be
defined as a probability measure: a way to quantify the
chance that a machine operates without a fault or failure up
to some future time. This "probabilistic prognostic value" is
all the more an interesting indication as the fault or failure
can have catastrophic consequences (e.g. nuclear power
plant) and maintenance manager need to know if inspection
intervals are appropriate. However, a small number of papers
address this acceptation for prognostic [6], [8].
Finally, although there are some divergences in literature,
prognostic can be defined as recently proposed by the
Review of Prognostic Problem in Condition-Based Maintenance
Otilia Elena DRAGOMIR, Rafael GOURIVEAU, Florin DRAGOMIR,
Eugenia MINCA, Noureddine ZERHOUNI
M
International Organization for Standardization: "prognostic
is the estimation of time to failure and risk for one or more
existing and future failure modes" [9]. In this acceptation,
prognostic is also called the "prediction of a system's
lifetime" as it is a process whose objective is to predict the
remaining useful life (RUL) before a failure occurs given the
current machine condition and past operation profile [2].
All definitions proposed here before assimilate prognostic
to a "prediction process": a future situation must be caught.
In addition, this obviously supposes that the current situation
can be grasped (practically, it's the synthesis of a detection
process and of measured data of the system). More over,
these approaches are grounded on the failure notion
("termination of the ability to perform a required function
[5]"), which implies that the "prognostic activity" is
associated with a degree of acceptability. Following that and
according to previous works, prognostic should be based on
assessment criteria, whose limits depend on the system itself
and on performance objectives [10], [11], and prognostic
could be split into 2 sub-activities: a first one to predict the
evolution of a situation at a given time, and a second one to
assess this predicted situation with regards to an evaluation
referential (Fig. 1.). A central problem can be pointed out:
the accuracy of a prognostic system is related to its ability to
approximate and predict the degradation of equipment; the
prediction phase is a critical one. A look at prognostic
metrics enables to point it out.
B. Prognostic metrics
There is no general agreement as to an appropriate and
acceptable set of metrics that can be employed in prognostic
applications, and researchers and maintenance practitioners
are still working on this [12]. Various measures emerge
however from literature: as for any industrial task, prognostic
can be evaluated at least in two ways: 1) the main objective
of prognostic is to provide the efficient information that
enables the underlying decision process, i.e., the choice of
maintenance actions. Also, a first set of metrics are those that
quantify the risks incurred by the monitored system. This
kind of metrics can be called the prognostic measures, 2)
assuming that prognostic is in essence an uncertain process,
it is useful to be able to judge from its "quality" in order to
imagine more suitable actions. In this way, prognostic
system performance measures can be constructed.
Prognostic measures
The main prognostic measure pursued is the predicted time
to failure (TTF), also called the remaining useful life (RUL).
In addition, a confidence measure can be built to indicate the
degree of certitude of the future predicted failure time. By
extension, and considering that practitioners can be
interested on assessing the system with regard to any
performance limit, RUL and confidence can be generalized:
in Fig. 2a, TTxx refers to the remaining time to overpass the
performance limit Perf/xx, and Conf/xxT is the confidence
with which can be taken the asset TTxx > T.
Prognostic system performance measures
The timeliness of the predicted time to failure (TTF) is
the relative position of the probability density function (pdf)
of the prediction model along the time axis with respect to
the occurrence of the failure event. This measure evolves as
more data are available and reveals the expected time to
perform preventive actions [12] (Fig. 2b). According to [13],
one has to define two different boundaries for the maximum
acceptable late and early predictions. Accuracy measures
the closeness of the predicted value to the actual one. It has
an exponential form and is as higher as the error between the
predicted value of TTF and the real one is smaller. Precision
reveals how close predictions are clustered together and is a
measure of the narrowness of the interval in which the
remaining life falls. Precision follows from the variance of
the predicted results for many experiments. Complementary
of accuracy and precision is illustrated in Fig. 2c.
III. P
ROGNOSTIC
A
PPROACHES
A. Overview
Various approaches to prognostics have been developed
that range in fidelity from simple historical failure rate
degradation rate (%)
t
100 %
0
Perf/xx
Failure
xx %
t
0
TTxx
TTF = RUL
prediction
prediction limits
curves
T
90%
t
t
0
pdf
Conf/xxT: "TTxx > T
with 90% of confidence"
TTxx pdf
too early prediction
t
failure
occurrence
acceptable
bounds
prediction
TTF pdf
too late prediction
t
failure
occurrence
prediction
TTF pdf
good prediction
t
pdf
time
failure occurrence
Accuracy of pred 1 > Accuracy of pred 2
Precision of pred 1 < Precision of pred 2
pred. 1 pdf
pred. 2 pdf
accuracy curve
-a-
-b-
-c-
degradation rate (%)
t
100 %
0
Perf/xx
Failure
xx %
t
0
TTxx
TTF = RUL
prediction
prediction limits
curves
T
90%
t
t
0
pdf
Conf/xxT: "TTxx > T
with 90% of confidence"
TTxx pdf
degradation rate (%)
t
100 %
0
Perf/xx
Failure
xx %
t
0
TTxx
TTF = RUL
prediction
prediction limits
curves
degradation rate (%)
t
100 %
0
Perf/xx
FailureFailure
xx %
t
0
TTxx
TTF = RUL
prediction
prediction limits
curves
T
90%
t
t
0
pdf
Conf/xxT: "TTxx > T
with 90% of confidence"
TTxx pdf
T
90%
t
t
0
pdf
Conf/xxT: "TTxx > T
with 90% of confidence"
TTxx pdf
too early prediction
t
failure
occurrence
acceptable
bounds
prediction
TTF pdf
too late prediction
t
failure
occurrence
prediction
TTF pdf
good prediction
t
too early prediction
t
failure
occurrence
acceptable
bounds
prediction
TTF pdf
too early prediction
t
failure
occurrence
acceptable
bounds
prediction
TTF pdf
too late prediction
t
failure
occurrence
prediction
TTF pdf
too late prediction
t
failure
occurrence
prediction
TTF pdf
good prediction
t
good prediction
t
pdf
time
failure occurrence
Accuracy of pred 1 > Accuracy of pred 2
Precision of pred 1 < Precision of pred 2
pred. 1 pdf
pred. 2 pdf
accuracy curve
pdf
time
failure occurrence
Accuracy of pred 1 > Accuracy of pred 2
Precision of pred 1 < Precision of pred 2
pred. 1 pdf
pred. 2 pdf
accuracy curve
pred. 1 pdfpred. 1 pdf
pred. 2 pdfpred. 2 pdf
accuracy curveaccuracy curve
-a-
-b-
-c-
Fig. 2. Some prognostic metrics.
prediction /
forecasting
performance
assessment
evaluation
referential
assessment
p
rediction
prognostic
Perf(t)
situation(t)
Predicted(t+dt)
Perf(t+dt)
Fig. 1. Prognostic as a prediction and assessment process [10].
models to high-fidelity physics-based models [14]. The
required information (depending on the type of prognostics
approach) include: engineering model and data, failure
history, past operating conditions, current conditions,
identified fault patterns, transitional failure trajectories,
maintenance history, system degradation and failure modes.
Let's have a first view of prognostics approaches that have
successfully been applied on different types of problems.
- Experience-Based Prognostics. Use statistical reliability
to predict probability of failure at any time.
- Evolutionary/Statistical Trending Prognostics. Multi-
variable analysis of system response and error patterns
compared to known fault patterns.
- Artificial Intelligence Based Prognostics. Mechanical
failure prediction using reasoners trained with failure data.
- State Estimator Prognostics. System degradation or
diagnostic feature tracking using Kalman filters and other
predictor-corrector schemes.
- Model-Based or Physics of Failure Based Prognostics.
Fully developed functional and physics-of-failure models to
predict degradation rates given loads and conditions.
Similar to diagnosis, prognostic methods can be classified
as being associated with one of the following two
approaches: model-based and data-driven. Each one of these
approaches has its own advantages and disadvantages, and,
consequently, they are often used in combination in many
applications. Next paragraphs present a synthesis of it.
B. Model based approaches
The model-based methods assume that an accurate
mathematical model can be constructed from first principles.
As an example, physics-based fatigue models have been
extensively employed to represent the initiation and
propagation of structural anomalies. These methods often
use residuals as features, where the residuals are the
outcomes of consistency checks between the sensed
measurements of a real system and the outputs of a
mathematical model. The premise is that the residuals are
large in the presence of malfunctions, and small in the
presence of normal disturbances, noise and modeling errors.
Statistical techniques are used to define thresholds to detect
the presence of faults. Several techniques are proposed in the
literature to generate residuals: parity space, parameters
estimation, observers, bond graph, etc.
Model-based literature. Model-based approaches to
prognostic require specific failure mechanism knowledge
and theory relevant to the monitored machine. The existing
papers propose different model based solution for the
industrial problems.
Bartelmus and Zimroz [15] estimated through a
demodulation process, the vibration signal for a planetary
gearbox in good and bad conditions.
Kacprzynski et al. [16] proposed fusing the physics of
failure modeling with relevant diagnostic information for
helicopter gear prognostic.
Chelidze and Cusumano [17] proposed a general method
for tracking the evolution of a hidden damage process given
a situation where a slowly evolving damage process is
related to a fast, directly observable dynamic system.
Luo et al. [18] introduced an integrated prognostic process
based on data from model-based simulations under nominal
and degraded conditions.
Oppenheimer and Loparo [19] applied a physical model
for predicting the machine condition in combination with a
fault strengths-to-life model, based on a crack growth law, to
estimate the RUL.
Adams [20] proposed to model damage accumulation in a
structural dynamic system as first/second order nonlinear
differential equations.
Chelidze [21] modeled degradation as a "slow-time"
process, which is coupled with a "fast-lime", observable
subsystem. The model was used to track battery degradation
(voltage) of a vibrating beam system.
Li et al. [22] and [23] introduced two defect propagation
models via failure mechanism modeling for RUL estimation
of bearings.
Ray and Tangirala [24] used a nonlinear stochastic model
of fatigue crack dynamics for real-time computation of the
time-dependent damage rate and accumulation in mechanical
structures.
A different way of applying model-based approaches to
prognostic is to derive the explicit relationship between the
condition variables and the lifetimes (current lifetime and
failure lifetime) via failure mechanism modeling. Two
examples of research along this line are [25] for machines
considered as energy processors subject to vibration
monitoring and [26] for bearings with vibration monitoring.
In [27] and [28] the problem of forecasting machine failure
is illustrated for a high power fan bearing and a railroad
diesel engine.
Engel et al. [29] discussed some practical issues regarding
accuracy, precision and confidence of the RUL estimates.
Lesieutre et al. [30] developed a hierarchical modeling
approach for system simulation to assess the RUL.
Advantage and drawback. The main advantage of model-
based approaches is their ability to incorporate physical
understanding of the monitored system. In addition, in many
situations, the changes in feature vector are closely related to
model parameters [21]. and a functional mapping between
the drifting parameters and the selected prognostic features
can be established [31]. Moreover, if the understanding of
the system degradation improves, the model can be adapted
to increase its accuracy and to address subtle performance
problems. Consequently, they can significantly outperform
data-driven approaches (next section). But, this closed
relation with a mathematical model may also be a strong
weakness: it can be difficult, even impossible to catch the
system's behavior. Further, some authors think that the
monitoring and prognostic tools must evolve as the system
does…
C. Data driven approaches
Data-driven approaches use real data (like on-line
gathered with sensors or operator measures) to approximate
and track features revealing the degradation of components
and to forecast the global behavior of a system. Indeed, in
many applications, measured input/output data is the major
source for a deeper understanding of the system degradation.
Data-driven approaches can be divided into two categories:
articial intelligence (AI) techniques (neural networks, fuzzy
systems, decision trees, etc.), and statistical techniques
(multivariate statistical methods, linear and quadratic
discriminators, partial least squares, etc.). Case-based
Reasoning (CBR), intelligent decision-based models and
min-max graphs have been considered as potential
candidates for prognostic algorithms too.
- artificial intelligent techniques
- neural networks (multi-layers perceptron, probabilistic
neural networks, learning vector quantization, self-
organizing maps, etc.),
- fuzzy rule-based systems and neuro-fuzzy systems,
- decision trees,
- graphical models (Bayesian networks, hidden Markov
models).
- statistical techniques:
- multivariate statistical methods (static and dynamic
principle components (PCA),
- linear and quadratic discriminant,
- partial least squares (PLS),
- canonical variates analysis (CVA),
- signal analysis (niters, auto-regressive models, FFT,
etc.).
Artificial intelligence techniques.
Within the field of maintenance problems, Artificial
Neural Networks (ANNs) and neuro-fuzzy systems (NFs)
have successfully been used to support the detection,
diagnostic and prediction processes, and research works
emphasize on the interest of using it [32], [33], [34], [35],
[36]: ANNs and NFs are a general and flexible modeling
tool, especially for prediction problems. Let's point out the
principle arguments of this assumption (non exhaustive list).
1- Adaptable tools. ANNs are data-driven self-adaptive
methods in that they learn from examples and capture subtle
functional relationships among the data, even if the
underlying relationships are unknown. Thus, they are well
suited for problems whose solutions require knowledge that
is difficult to specify but for which there are enough data or
observations. As examples, Recurrent Radial Basis Neural
Networks (RRBF) have been used for time series prediction,
detection and prognostic of nonlinear systems states (gas
ovens) and for dynamic detection of breakdowns [37]. The
dynamic wavelet neural networks were applied by Wang and
Vachtsevanos [34] to predict the fault propagation process
and estimate the RUL as the time left before the fault reaches
a given value.
2- Robust tools. After the learning phase, ANNs can often
correctly infer the unseen part of a population even if the
sample data contain noisy information. Wang et al. [38]
proved the robustness of the ANN in his researches. He
compared the results of applying recurrent neural networks
and neural-fuzzy inference systems to predict the fault
damage propagation trend. Neuro-fuzzy networks have been
use in robust prognostic systems for real time industrial
applications like mechanical gears cracking by [39].
3- General tools. ANNs are capable of performing
nonlinear modeling which is a really interesting
characteristic as many real world systems are nonlinear too.
Recurrent neural network were applied by Yam et al. [35]
for predicting the machine condition trend. The dynamic
wavelet neural network (DWNN) was implemented to
transform sensor data to the time evolution of a fault pattern
and predict the remaining useful time of a bearing [40]: the
DWNN model was first trained by using vibration signals of
defective bearings with varying depth and width of cracks,
and then was used to predict the crack evolution until the
final failure. Self-organizing neural networks were used by
Zhang and Ganesan [36] for multivariable trending of the
fault development, to estimate the residual life of a bearing
system.
4- Open tools. In recent works, extensions of ANNs like
neuro-fuzzy systems (NFs) have been developed in order to
overpass the performance of classical neural networks, in
particular for prediction problems. See [39] and [3] for an
example. Chinnam and Baruah [41] presented a neuro-fuzzy
approach to estimate the RUL for the situation where neither
failure data nor a specific failure definition model is
available, but domain experts with strong experiential
knowledge are on hand.
Statistical techniques.
Statistical techniques require, due to the algorithms
involved, quantitative data measurements. This information
related to the sources is combined and the result is a
stochastic estimation of the future state. Following
paragraphs give a non exhaustive list of these techniques.
Yan et al. employed the logistic regression model to
calculate the probability of failure for given condition
variables [42]. A predetermined level of failure probability
![Fig. 1. Prognostic as a prediction and assessment process [10].](/figures/fig-1-prognostic-as-a-prediction-and-assessment-process-10-2j7euu4j.webp)