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By Daming Lin
Senior Technical
Officer, Optimal Maintenance Decisions (OMDEC) Inc.
Extracted from
Chapter 12 of “Reliability-centered Knowledge”
In previous chapters
we learned that Condition-based Maintenance recommends actions based on
information acquired through observation and analysis. We noted, moreover,
that the CBM process, itself contains
three sub-processes or steps: data acquisiton, signal processing, and
maintenance decision making.
Figure
12‑1 The three CBM
steps
Chapter
5. Case based reasoning
(page 70) pointed out, in regard to complex systems, that
prognostics are often indistinguishable from diagnostics, where both aim to
identify the occurance of a potential failure.
Hundreds of theoretical
and practical research papers on CBM appear every year in scientific journals,
conference procedings and technical reports. In this chapter we provide an
overview of recent developments in the diagnostics and prognostics of systems.
We will mention a number of models, algorithms, and technologies for signal
processing and maintenance decision making. Given the increased use of multiple
sensors, we will also discuss various techniques for data fusion. The chapter
is concluded with a brief discussion on current practices and possible future
trends in CBM. The
purpose of this survey of advanced methods of signal processing and decision
making is not to instruct the reader in the the use of these new techniques,
but merely to provide the maintenance professional with references to the
source material so that he or she can investigate alternatives when
encountering various situations where a CBM solution is proposed.
Reliability
has always been an important criterion in the selection of industrial equipment.
Good equipment design is essential for processes requiring high reliability.
However, no amount of design effort will prevent deterioration over time.
Machinery and systems operate under stress in an environment that is
characterized by randomness. Maintenance is the major way in which we assure
the user of the asset a satisfactory level of reliability. Physical asset
managers look towards CBM as an efficient form of maintenance, which, they
expect will assist them in the avoidance or reduction of risk. That is, they
seek to reduce, to an acceptable level, the combined impact of the probability
of failure and its consequences. A CBM program, if properly established and
effectively implemented, can significantly reduce overall cost by reducing the
number and/or extent of unnecessary preventive maintenance operations, while
still achieving the desired
reliability.
Let us
begin by reviewing, briefly, the first CBM step, data acquisition.
Data acquisition, the essential first step in the
CBM task, is a process for collecting and storing useful information that
emanates from operating physical assets. Data collected in a CBM program is of
two main types: “event” data and condition monitoring (CM) data. Event data
tells us what happened, for example, an installation, a breakdown, or an
overhaul. Event data also tells us what was done, for example, a minor
repair, a preventive maintenance action, an oil change, and so on. CM data
consists of observational measurements that we believe are, in some way,
related to the deteriorating health or state of the physical asset.
CM data can include vibration data, acoustics data,
oil analysis data, temperature, pressure, moisture, humidity, and any other
physical observations, including visual clues, that relate to to the condition
of an operating physical asset in its environment. A variety of sensors
(microsensors, ultrasonic sensors, acoustic emission sensors, thermographic
imagers, etc) have been designed to collect different types of data [11,12]. Wireless
technologies such as Bluetooth have provided an alternative to more expensive
hard wired data communication. Information systems such as Computerized
Maintenance Management Systems (CMMS), Enterprise Resource Planning (ERP)
systems, control system historians, and CBM databases have been developed for
data storage and handling [13]. With the rapid
development of computer and advanced sensor technologies, data acquisition
technologies have become more powerful and less expensive, resulting in
exponentially growing databases of CM data.
Event data and CM data are equally important in
CBM. In practice, however, engineers and managers tend to place more emphasis
on the latter and sometimes neglect the former. Overlooking event data may have
grown from the mistaken belief that it is not valuable to fault prediction as
long as the condition monitoring data seems to be working well. We tend
to overlook event data, in part, because we lack the knowledge and methods to
use it. Event data is at least as helpful as CM data in assessing machine
health. It augments our ability to judge the significance of CM data with
respect to specific failure modes. The use of event data is discouraged by the
fact that its collection usually implies manual data entry. Once a human
is involved, everything becomes more complicated and error-prone. Choosing the
“simple” solution, that of removing the human element, is hasty and
ill-advised. Rather, as we discovered in Chapter
11. Information Procedures
for Optimized CBM Policies (page 155), it is preferable to equip humans with tools and
procedures with which to capture event data accurately, in a meaningful format,
and in sufficient detail.
Under the topic of signal processing we include a
necessary preliminary step - data cleaning. Data, especially event data,
particularly when it is entered manually, always contains errors. Data cleaning
is meant to ensure that clean (error-free) data is used for subsequent analysis
and modeling. Data errors are caused by many factors, including the human
factor mentioned previously. Errors in CM data may be caused by sensor faults,
which are handled by sensor fault isolation [14]. In general, there is no
simple, single method to clean data. Sometimes manual examination is required.
Graphical tools are helpful in finding and removing data errors. Data cleaning
is indeed a vast subject area. In Example 2 Data validation on page 129 (Chapter
10. ) we touched upon various aspects of data cleaning.
The next step in signal processing is data
analysis. A variety of models, algorithms and tools are described in the
technical literature. Their purpose is to analyze data in order to better
understand and interpret it. The choice of which model, algorithm, or tool to
use for data analysis depends primarily
on the type of data collected.
Condition monitoring data falls into three principal types:
Value: Data
collected at a specific time epoch as single valued variables. For example, oil
analysis data, temperature, pressure, humidity are all value type data.
Waveform: Data
collected at a specific time epoch as a time series of values. For
example, vibration data and acoustic data are or the waveform type.
Multi-dimension: Data
collected at a specific time epoch as multi-dimensional values. The most common
multi-dimensional data is image data, for example infrared thermographs, X-ray
images, visual images, etc.
Although we have been using the term more broadly
to describe the entire data analysis phase of CBM, “signal processing” usually
refers most specifically to waveform and multi-dimension data analysis. A large
variety of signal processing techniques have been developed to analyze and
interpret these types of data. Their purpose is to extract useful information
from the raw signal in order to perform diagnostics and prognostics. The signal
processing procedure for extracting information relevant to targeted failure
modes is often called “feature
extraction”.
There are numerous signal
processing techniques and algorithms in the literature for diagnostics and
prognostics of mechanical systems. Case-dependent knowledge and investigation
are required to select appropriate the signal processing tools from among a
large number of possibilities.
The most common waveform data in condition
monitoring are vibration signals and acoustic emissions. Other waveform data
include ultrasonic signals, motor current, partial discharge, and others. In the literature, there are
three main categories of waveform data analysis: time-domain analysis,
frequency-domain analysis and time-frequency analysis.
Time-domain analysis is directly based on the time
waveform itself. Traditional time-domain analysis calculates characteristic
features from time waveform signals as descriptive statistics. For example:
mean, peak, peak-to-peak interval, standard deviation, crest factor, high order
statistics: RMS (root mean square), skewness, kurtosis, etc. These features are
usually called time-domain features. A popular time-domain analysis approach is
time synchronous average (TSA). The idea of TSA is to use the ensemble average
of the raw signal over a number of evolutions in an attempt to remove or reduce
noise and effects from other sources, so as to enhance the signal components of
interest. A brief review of TSA was given by Dalpiaz [15] and some drawbacks of TSA
were pointed out by Miller [16]. Most of the references
on TSA can be found in [15,16].
More
advanced approaches to time-domain analysis apply time series models to
waveform data. The main idea of time series modeling is to fit the waveform
data to a parametric time series model and extract features based on this
parametric model. The popular models used in the literature are AR
(autoregressive) model and ARMA (autoregressive moving average) model. An ARMA
model of order 
, denoted by ARMA(
), is expressed by
where 
is the waveform
signal, 
’s are independent normally distributed with mean 0 and
constant variance 
, and 
are model
coefficients. An AR model of order 
is a special case of
ARMA(
) with 
. Poyhonen et al [17] applied AR model to
vibration signals collected from an induction motor and used the AR model
coefficients as extracted features. Baillie and Mathew [18] compared the performance
of three autoregressive time series modeling techniques: AR model, back
propagation neural networks and radial basis function networks, to bearing
fault diagnostics. Garga [19] proposed using AR
modeling followed by dimension reduction for machinery fault diagnostics.
Recently, Zhan [20] used a state space model
representation of an AR model to analyze vibration signals for fault detection.
There are many other time-domain
analysis techniques to analyze waveform data for machinery fault diagnostics.
Some of them are briefly described as follows. Wang et al [21]
introduced three nonlinear diagnostic methods for rotating machine fault
diagnosis. These three methods are pseudo-phase portrait, singular spectrum
analysis and correlation dimension. Pseudo-phase portrait is simple for
computer execution and is sensitive to some fault types. Wang and Lin [22] used a statistical
approach known as singular value decomposition to obtain the pseudo-phase
portrait. Singular spectrum analysis can reveal the complexity of a signal and
reduce the noise. Correlation dimension can provide some intrinsic information
of an underlying dynamical system. Koizumi [23] also considered application
of correlation dimension to fault diagnosis. Wang et al [24] applied both correlation
dimension and bispectrum for rotating machine fault diagnosis. Zhuge and Lu [25] proposed a modified least
mean square algorithm to model the non-stationary impulse-like signals for
reciprocating machine fault diagnosis. Baydar et al
investigated the use of a multivariate statistical technique known as principal
component analysis (PCA) in gear fault diagnostics [26].
Frequency-domain analysis is based on the transformed
signal in the frequency domain. The advantage of frequency-domain analysis over
time-domain analysis is its ability to easily identify and isolate certain
frequency components of interest. The most widely used conventional analysis is
spectrum analysis by means of FFT (fast Fourier transform). The main idea of
spectrum analysis is to either look at the whole spectrum or look closely at
certain frequency components of interest and thus extract features from the
signal (see, e.g. [27-29]). The most commonly used
tool in spectrum analysis is the power spectrum. It is defined as 
, where (and throughout this section) 
is the Fourier
transform of signal 
, E denotes expectation and “
” denotes complex conjugate. Some useful auxiliary tools for
spectrum analysis are graphical presentation of the spectrum, frequency
filters, envelope analysis (also called amplitude demodulation) [30-32], side band structure
analysis [33], etc. Descriptions of the
above mentioned techniques for FFT based spectrum can be found in textbooks
such as [34,35] and will not be discussed
in detail here. Another useful transform, Hilbert transform, has also been used
for machine fault detection and diagnostics [30,36].
Despite
the wide acceptance of the power spectrum, other useful spectra for signal
processing have been developed and have been shown to have their own advantages
over the FFT spectrum in certain cases. Cepstrum has the capability to detect
harmonics and sideband patterns in the power spectrum. There are several versions or definitions of
cepstrum [35]. Among them, the power
cepstrum, which is defined as the inverse Fourier transform of the logarithmic
power spectrum, is the most commonly used. A modified cepstrum analysis was
proposed in [37]. A high order spectrum,
i.e. bispectrum or trispectrum, can provide more diagnostic information than
the power spectrum for non-Gaussian signals. In the literature, high order
spectrum is also called high order statistics [38]. This name comes from the
fact that bispectrum and trispectrum are actually the Fourier transforms of the
third- and fourth-order statistics of the time waveform, respectively. But this
name could be confused with the time-domain high order statistics. Bispectrum
and trispectrum are defined as
and
respectively.
Bispectrum and trispectrum can be normalized to obtain bicoherence and
tricoherence as
and
respectively.
Bispectrum analysis has been shown to have wide application in machinery
diagnostics for various mechanical systems such as gears [39], bearings [40], rotating machines [41,42] and induction machines [43,24]. Li [44] investigated the
application of bispectrum diagonal slice 
to gear fault
diagnostics. Yang [40] used both bispectrum
diagonal slice and bicoherence diagonal slice 
, summed bispectrum, and summed bicoherence for bearing fault
diagnostics. Application of both bispectrum and trispectrum to bearing fault
diagnostics was discussed in [45]. A new technique called
holospectrum was introduced by Qu [46] to integrate all the
information of phase, amplitude and frequency of a waveform signal. Application
of holospectrum to machine fault diagnostics was studied in [47,48]. A review on holospectrum
and its applications was given by Qu [49] (in Chinese).
Generally
speaking, there are two classes of approaches for power spectrum
estimation. The first covers the
non-parametric approaches that estimate the autocorrelation sequence of the
signal and subsequently apply a Fourier transform to the estimated
autocorrelation sequence. For details, see [50]. The second class
includes the parametric approaches that build a parametric model for the signal
and then estimate power spectrum based on the fitted model. Among them, AR
spectrum [51-53] and ARMA spectrum [54] based on AR model and
ARMA model respectively are the two most commonly used parametric spectra for
machinery fault diagnostics.
One
limitation of frequency-domain analysis is its inability to handle
non-stationary waveform signals, which are very common when machinery faults
occur. Thus, time-frequency analysis,
which investigates waveform signals in both time and frequency domain, has been
developed for non-stationary waveform signals. Traditional time-frequency
analysis uses time-frequency distributions, which represents the energy or
power of waveform signals in two-dimensional functions of both time and
frequency. Short-time Fourier transform (STFT, and also called spectrogram) [55,56] and Wigner-Ville
distribution [57-60] are the most popular
time-frequency distributions. Cohen [61] reviewed a class of
time-frequency distributions which include spectrogram, Wigner-Ville
distribution, Choi-Williams and others. The idea of spectrogram is to divide
the whole waveform signal into segments with a short time window and then apply
a Fourier transform to each segment. Spectrogram has some limitations in
time-frequency resolution due to signal segmentation. It can be applied only to
non-stationary signals with slow change in their dynamics. Bilinear transforms
such as Wigner-Ville distribution are not based on signal segmentation and thus
overcome the time-frequency resolution limitation of spectrogram. However,
there is one main disadvantage of bilinear transforms, which is due to
interference terms formed by the transformation itself. These interference
terms make interpretation of the estimated distribution difficult [62]. Improved transforms such
as the Choi-Williams distribution have been developed to overcome this
difficulty. Gu et al [63] applied singular value
decomposition to extract features from the time-frequency distribution.
Loughlin [64] used a set of conditional
time-frequency moments as characteristic features for fault diagnosis.
Another
transform for time-frequency analysis is the wavelet transform. Wavelet theory
has been rapidly developed in the past decade and has wide application [65]. A continuous wavelet
transform is defined as
where 
is the waveform
signal, 
is the scale
parameter, 
is the time parameter
and 
is a wavelet, which
is a zero average oscillatory function centered around zero with a finite
energy, and “
” denotes complex conjugate. Commonly used wavelets are
Morlet, Mexican hat, Haar, etc. Similar to Fourier transform, the wavelet
transform has its discrete form, which is obtained by discretizing 
and 
, and expressing 
in discrete form.
Similar to FFT, a fast wavelet transform is likewise available for the
calculation.
Wavelet analysis of a waveform
signal expresses the signal in a series of oscillatory functions with different
frequencies at different times by dilations via the scale parameter 
and translations via
the time parameter 
. Similar to the power spectrum and the phase spectrum in
Fourier analysis, a scalogram defined as 
and a wavelet phase
spectrum defined as the phase angle of the complex variable 
are used to interpret
the signal. Wavelet transformation has been successfully applied to fault
diagnostics of gears [66,67], bearings [68,69] and other mechanical
systems [70,71]. Dalpiaz and Rivola [72] assessed and compared the
effectiveness and reliability of wavelet transform to other vibration signal
analysis techniques for fault detection and diagnostics. Baydar and Ball [73] applied wavelet transform
to both acoustic signals and vibration signals for gear tooth fault diagnostic.
Addison et al [74] investigated the use of
low-oscillation complex wavelets, Mexican hat and Morlet wavelets, as feature
detection tools. Wavelet analysis using Haar wavelet was considered in [75,76]. Miller [77] used a wavelet basis as a
comb filter to decompose vibration signals for gear fault diagnostics. A
graphical tool called wavelet polar maps to display wavelet amplitude and phase
was proposed in [78] and was applied to gear
fault diagnostics in [79]. Wavelet transform
combined with Fourier transform to enhance feature extraction capability was
proposed in [80]. A more advanced
transform, known as wavelet packet transform, was studied and applied to
machinery fault diagnostics in [81-83]. A new technique know as
basis pursuit based on a general wavelet packet dictionary was applied to
rolling element bearing fault diagnostics in [84]. It was shown that basis
pursuit has some advantages over other commonly used wavelet analysis
approaches. A recent review with more references on the applications of wavelet
transform in machine condition monitoring and fault diagnostics was given in [85].
Image processing is similar to but more complicated
than waveform signal processing due to one more dimension involved. In
practice, raw images are usually very complicated and immediate information for
fault detection is unavailable. In these cases, image processing techniques
must be powerful enough to extract useful features from raw images for fault
diagnosis — see [86,87] for descriptions and
discussions on image processing tools and algorithms. Image processing seems unnecessary
when raw images provide sufficient and clear information under visual
examination to identify patterns and detect faults. However, image processing
can still help in extracting features for automatic fault detection in such
situations. In addition to raw images obtained via data acquisition, some
waveform processing techniques such as time-frequency analysis also produce
images. In these situations, image processing can be combined with waveform
processing to obtain better results.
A few examples of applying image processing
techniques in condition monitoring and fault diagnosis and prognosis are as
follows. Wang and MacFadden [88] applied image processing
techniques to spectrograms for early gear fault detection and diagnostics.
Utsumi et al [89] used a wavelet transform
to analyze ferrographic images for bearing diagnosis. Heger and Pandit [90] considered a wavelet-based segmentation approach to image processing for the
condition monitoring and fault diagnostics of grinding tools. Ellwein
et al [91] combined image processing
techniques with waveform power spectrum density to identify a region of
interest (ROI) for fault discrimination enhancement.
Value
type data includes both raw data obtained via data acquisition and feature
values extracted from raw signals via signal processing. Value type data looks
much simpler than waveform and image data. However, complexity lies in the
correlation structure when the number of variables is large. Multivariate
analysis techniques such as PCA and independent component analysis (ICA) are
very useful to handle data with complicated correlation structure. For example,
Stellman et al [92] applied PCA to
spectroscopic data to monitor the condition of a lubricant in helicopter rotary
gearboxes. Allgood and Upadhyaya [93] performed PCA on certain
descriptive statistics for DC motor diagnostics and prognostics. ICA is an
extension of PCA and will be discussed later. When the number of variables is
large, dimension reduction techniques such as PCA and project pursuit can be
used for data reduction. For a review on dimension reduction techniques, see [94]. An example of applying
dimension reduction techniques for machine fault diagnostics is given in [19].
Trend analysis techniques such as regression
analysis and time series model are commonly used techniques for analyzing value
type data. For example, Grimmelius et al [95] developed a prototype
condition monitoring and diagnostics system for compression refrigeration
plants using a regression analysis model to predict healthy system behavior.
Yang et al [96] established an ARMA
model to extract features from on-line data for power equipment diagnosis.
Sinha [97] applied both polynomial
regression and an ARMA model to predict the trend of vibration peak amplitude
for turbine fault diagnostics and prognostics.
Data analysis for event data only is well known as
“reliability analysis”, which fits the event data to a time between events
probability distribution and uses the fitted distribution for further analysis.
In condition-based maintenance, however, additional information — condition
monitoring data, is available. It is beneficial to analyze event data and
condition monitoring data together. This combined data analysis can be
accomplished by building a mathematical model that describes the underlying
mechanism of a fault or a failure. The model built on both event and condition
monitoring data is the basis for maintenance decision support — diagnostics and
prognostics, which will be discussed in the next section.
A time-dependent proportional hazards model (PHM)
is suitable for analyzing both event and condition monitoring data together. It
has a hazard function of the form
where 
is a baseline hazard
function, 
are covariates which
are functions of time, and 
are coefficients. The
baseline hazard function 
can be in
non-parametric or parametric form. A commonly used parametric baseline hazard
function is the Weibull hazard function, which is the hazard function of the
Weibull distribution. A PHM with Weibull baseline hazard function is called
Weibull PHM. Jardine et al [98] proposed using a Weibull
PHM to analyze the aircraft and marine engine failure data together with the
metal concentration measurements of the engine oil. An extension of PHM is the
proportional intensity model (PIM), which adopts a stochastic process setting
and assumes a similar form to the intensity function of the stochastic process.
Vlok et al [99] studied the application
of PIM to analyze failure and diagnostic measurement data from bearings.
In reliability centered maintenance (RCM) [100], the concept known as the
“P-F interval” is used to describe failure patterns in condition monitoring. A
P-F interval is the time interval between a potential failure (P), which is
identified by a condition indicator, and a functional failure (F). A P-F
interval is a useful concept with which to determine an appropriate interval
for periodic condition monitoring. A condition monitoring interval is usually
set to the P-F interval divided by an integer. In practice, however, it is
usually difficult to quantify the P-F interval (see Chapter 9. The Elusive P-F Curve page 102). Goode et al [101] assumed two Weibull
distributions for the P-F interval and the I-P interval, i.e. from machine
installation to a potential failure. Using the statistical process control
(SPC) methods on historical data, they separated each machine life cycle into
two zones: a stable zone and a failure zone. They used the stable zone duration
times to fit a Weibull distribution for the I-P interval. Similarly, they used
the failure zone duration times to fit the Weibull distribution for the P-F
interval. Based on these two fitted distributions combined with the condition monitoring
process, machine prognosis was derived.
A hidden Markov model (HMM) [102,103] is another model for
analyzing event and condition monitoring data together. A HMM consists of two
stochastic processes: a Markov chain with a finite number of states describing
an underlying failure mechanism, and an observation process that depends on the
hidden state. Bunks et al [104] applied a HMM to analyze
Westland helicopter data which consists of gearbox fault class information and
vibration measurements surrounding the occurance of various faults. The fault classes were treated as states in the
hidden Markov chain, whereas the vibration measurements were treated as
realizations of the observation process. The trained HMM using lab test data
was then applied to fault classification for a data set from an operating
gearbox. Dong and He [105] proposed a more general
model, hidden semi-Markov model (HSMM), for hydraulic pump diagnostics. It was
shown that HSMM outperforms HMM in pump diagnostics.
Lin and
Makis [106] proposed using a
partially observable stochastic model to describe the underlying failure
mechanism of a system undergoing condition monitoring. The proposed model is
similar to that of a HMM but it has some distinguishing characteristics. One
(failure) state is observable, whle the partially hidden state process is
continuous in time. The observation process, however, is in discrete in time.
These characteristics are more realistic in relation to actual condition
monitoring processes. The model parameters were estimated using both event and
condition monitoring data. The fitted model is used for subsequent diagnostics
and prognostics. A fast recursive parameter estimation procedure for a
partially observable stochastic model was given in [107].
Other models in the literature that can be used to
analyze both event and condition monitoring data are models using the delay
time concept [108] and stochastic process
models such as a gamma process [109].
The
ultimate goal and final step of a CBM program is maintenance decision making.
Sufficient and efficient decision support will result in maintenance
personnel’s taking the “right” maintenance actions given the current known
information. Jardine [110] reviewed and compared
several commonly used CBM decision strategies. They included trend analysis
that is rooted in statistical process control, expert systems, and neural
networks. Wang and Sharp [111] discussed the decision
aspect of CBM and reviewed the recent development in modeling CBM decision
support.
Machine
fault diagnostics is a discovery procedure based on mapping information in the
measurement space and/or features in the feature space to machine faults in the
fault space. From an “RCM” perspective, a machine fault may or may not have
immediate consequences. If a fault does not have immediate consequences, other
than those necessary to diagnose and repair it, it is a potential failure.
The diagnostic action following the detection of a potential failure will be a proactive
activity, initiated, often, by a condition based maintenance process. A common
example is an alarm generated by a “rule” applied to the data in a control
system historian. Besides a potential failure, a diagnostic alarm may also
expose an otherwise hidden functional failure, usually the failure of a
protective or backup device. The failure of a hidden function has the immediate
consequence that a “multiple” failure is, from that moment on, highly probable.
This topic was developed in Failure Finding
Intervals of Chapter
3. on page 38.
The
diagnostic mapping process is also called pattern recognition. Traditionally,
pattern recognition was a manual exercise, performed with the assistance of
graphical tools such as a power spectrum graph, a phase spectrum graph, a
cepstrum graph, an AR spectrum graph, a spectrogram, a wavelet scalogram, a
wavelet phase graph, and so on. However, manual pattern recognition requires
expertise in the specific area of the diagnostic application. It is slow and
expensive requiring highly trained and skilled personnel. Therefore, automatic
pattern recognition is highly desirable. This can be achieved by classification
of signals based on the information and/or features extracted from the signals.
In the following sections, different machine fault diagnostic approaches are
discussed with emphasis on statistical approaches and artificial intelligent
approaches. Machine diagnostics with emphasis on practical issues was discussed
in [112]. Various topics in fault
diagnosis with emphasis on model-based and artificial intelligence approaches
were covered in a recent co-authored book [113].
A common
method of fault diagnostics is to detect whether a specific fault is present or
not based on the available condition monitoring information without intrusive
inspection of the machine. This fault detection problem can be described as a
hypothesis test problem with null hypothesis H0: Fault A is present,
against alternative hypothesis H1: Fault A is not present. In a concrete
fault diagnostic problem, hypotheses H0 and H1 are
interpreted into an expression using specific models or distributions, or the
parameters of a specific model or distribution. Test statistics are then
constructed to summarize the condition monitoring information so as to be able
to decide whether to accept the null hypothesis H0 or reject it. See
[114-116] for some examples of
using hypothesis testing for fault diagnosis. Recently, a framework for fault
diagnosis, called structured hypothesis tests, was proposed for conveniently
handling complicated multiple faults of different types [117].
A
conventional approach, statistical process control, which was originally
developed in quality control theory, has been well developed and widely used in
fault detection and diagnostics. The principle of SPC is to measure the
deviation of the current signal from a reference signal representing the normal
condition to see whether the current signal is within the control limits or
not. An example of using SPC for damage detection was discussed in [118].
Cluster
analysis, as a multivariate statistical analysis method, is a statistical
classification approach that groups signals into different fault categories on
the basis of the similarity of the characteristics or features they possess. It
seeks to minimize within-group variance and maximize between-group
variance. The result of cluster
analysis is a number of heterogeneous groups with homogeneous contents. There
are substantial differences between the groups, but the signals within a single
group are similar. Application of cluster analysis in machinery fault diagnosis
was discussed in [119,120]. A natural way of signal
grouping is based on certain distance measures or similarity
measures between two signals. These measures are usually derived from certain
discriminant functions in statistical pattern recognition [121]. Commonly used distance
measures are Euclidean distance, Mahalanobis distance, Kullback-Leibler
distance and Bayesian distance. See [122-125] for some examples of using these distance metrics for fault
diagnostics. Ding et al [122] introduced a new distance
metric called quotient distance for engine fault diagnosis. Pan et al [126] proposed an extended
symmetric, the Itakura distance, for signals in time-frequency representations,
for example the Wigner-Ville distributions. In addition to distance measures,
the feature vector correlation coefficient is a similarity measure
commonly used for signal classification in machinery fault diagnosis [125]. Many clustering
algorithms are available for distinguishing the signal groups [127]. A commonly used
algorithm in machine fault classification is the nearest neighbour algorithm
that fuses the two closest groups into a new group and calculates the distance
between two groups as the distance of the nearest neighbour in the two separate
groups [128]. The boundary between two
adjacent groups is determined by the discriminant function used. A piecewise
linear discriminant function was used and thus piecewise linear boundaries
were obtained for bearing condition classification in [129]. A technique called support vector machine
(SVM) is usually employed to optimize a boundary curve in the sense that the
distance of the closest point to the boundary curve is maximized. The support
vector machine approach applied to machine fault diagnosis was considered in [17,130].
The
hidden Markov model (HMM) described earlier can also be used for fault classification.
Early applications of HMM in fault classification and diagnostics treated the
real machine faulty states and the machine normal state as the hidden states of
the HMM [104,131]. Two recent applications
of HMM in fault classification assumed a HMM with hidden states having no
physical meaning for two machine conditions (normal and faulty) [132,133]. The trained HMMs are
then used to decode an observation for fault classification in a machine whose
condition is unknown. Xu and Ge [134] presented an intelligent
fault diagnosis system based on a hidden Markov model. Ye et al [135] considered the
application of 2-dimension HMM based on time-frequency analysis for fault
diagnosis.
Artificial
intelligence (AI) techniques have been increasingly applied to machine diagnosis
and have shown improved performance over conventional approaches. In the
literature, two popular AI techniques for machine diagnosis are artificial
neural networks (ANN) and expert systems (ES). Other AI techniques include
fuzzy logic systems (FLS), fuzzy-neural networks (FNN), neural-fuzzy systems
(NFS), and evolutionary algorithms (EA). A review of recent developments in
applications of AI techniques for induction machine stator fault diagnostics
was given by Siddique et al [136].
An
artificial neural network is a computational model that mimics the human brain.
It consists of simple
processing elements connected together in a complex layer structure. The model
approximates a complex nonlinear function with multi-input and multi-output.
One processing element comprises a node and a weight. The artificial neural
network learns the unknown function by adjusting its weights with observations
of input and output. This process is usually called training of an
artificial neural network. There are various neural network models. The
feedforward neural network (FFNN) is the most widely used neural network
structure in machine fault diagnosis [137-140]. A special FFNN, mulitlayer perceptron (MLP) with the back
propagation (BP) training algorithm, is the most commonly used neural network
model for pattern recognition and classification. Hence it is popular in
machine fault diagnostics as well [140,141,142]. The BP neural networks,
however, have two main limitations: 1) difficulty of determining the
appropriate network structure and the number of nodes; 2) slow convergence of
the training process.
A cascade
correlation neural network (CCNN) does not require initial determination of the
network structure and the number of nodes. CCNN can be used in cases where
on-line training is preferable. Spoerre [143] applied CCNN to bearing
fault classification and showed that CCNN can result in utilizing the minimum
network structure for fault recognition with satisfactory accuracy. Other neural network models applied in machine
diagnostics are radial basis function neural networks [18], recurrent neural
networks [144,145] and counter propagation
neural networks (CPNN) [146]. The above ANN models
usually use supervised learning algorithms which require external input such as
a priori knowledge about the target
or desired output. For example, a common practice of training a neural network
model is to use a set of experimental data with known (seeded) faults. This
training process is supervised learning. In contrast to supervised learning,
unsupervised learning does not require external input. An unsupervised neural
network learns by itself using new information available. Wang and Too [38] applied unsupervised
neural networks, a self-organizing map (SOM), and learning vector quantization
(LVQ) to the detection of rotating machine faults. Tallam et al [147] proposed several
self-commissioning and on-line training algorithms for FFNN applied
particularly to electric machine fault diagnostics. Sohn et al [116] used an autoassociative
neural network to separate the effect of damage on the extracted features from
those caused by the environmental and vibration variations of the system. Then
a sequential probability ratio test was performed on the normalized features
for damage classification.
In
contrast to neural networks, which acquire knowledge by training on observed
data with known inputs and outputs, expert systems utilize domain expert
knowledge in a computer program with an automated inference engine to perform
reasoning for problem solving. Three main reasoning methods for ES used in the
area of machinery diagnostics are rule-based reasoning [148-150], case-based reasoning [151,152] and model-based reasoning
[153]. Another reasoning
method, negative reasoning, was introduced to mechanical diagnosis by Hall et
al [154]. Stanek et al [155] compared case-based and
model-based reasoning and proposed to combine them for a lower cost solution to
machine condition assessment and diagnosis. Unlike other reasoning methods,
negative reasoning deals with negative information, which by its absence or
lack of symptoms is indicative of meaningful inferences.
Expert
systems and neural networks have known limitations. A significant limitation of
rule-based expert systems is combinatorial explosion, which refers to
the computation problem caused when the number rules increases exponentially as
the number of variables increases. Another important limitation is consistency
maintenance, which refers to the process by which
the system decides when some of the variables need to be recomputed in response
to changes in other values. Two important limitations of neural networks are the difficulty to
have physical explanations of the trained model and the difficulty of the
training process. It is natural then to attempt a combination of both techniques in order to combine their
respective advantages thus improving performance in a hybrid system. For
instance, Silva et al [156] used two neural networks,
SOM and adaptive resonance theory (ART), combined with an expert system based
on Taylor's tool life equation to classify tool wear state. DePold and Gass [157] studied the applications
of neural networks and expert systems in a modular intelligent and adaptive
system for gas turbine diagnostics and prognostics. Yang et al [158] presented an approach for
integrating case-based reasoning ES with an ART-Kohonen neural network to
enhance fault diagnosis. It was shown that the proposed approach outperforms
the self-organizing feature map (SOFM) based system with respect to
classification rate.
In
condition monitoring practice, knowledge from domain specific experts is
usually inexact. Therefore expert system reasoning on domain knowledge is often
imprecise. Measures of the uncertainties in knowledge and reasoning are required
in order that an ES may provide more robust problem solving capability.
Commonly used uncertainty measures are probability, fuzzy member functions in
fuzzy logic theory, and belief functions in belief networks theory. An example
of applying fuzzy logic to machine fault classification was given in [159] to classify frequency
spectra representing various rolling element bearing faults. A comparison
between conventional rule-based expert systems and belief networks applied to
machine diagnostics was given in [160]. Du and Yeung [161] introduced an approach
called fuzzy transition probability, which combines transition probability
(Markov process) as well as the fuzzy set, to monitoring progressive faults.
The application of fuzzy logic is usually incorporated with other techniques such
as neural networks and expert systems. For example, Zhang et al [162] developed a fuzzy neural
network for fault diagnosis of rotary machines to improve the recognition rate
of pattern recognition, especially in the case when sample data are similar.
Lou and Loparo [125] employed an adaptive
neural-fuzzy inference system as a diagnostic classifier for bearing fault
diagnosis. Liu et al [163] applied fuzzy logic and
expert systems to build a fuzzy expert system for bearing fault detection.
Chang et al [164] built a system for
decision making support in a power plant using both a rule-based ES and fuzzy
logic.
Neural
networks and expert systems have also been combined with other AI techniques to
enhance machine diagnostic systems. Garga et al [165] proposed a hybrid
reasoning approach combining neural network, fuzzy logic and expert systems to
integrate domain knowledge and test operational data. Evolutionary algorithms [166], which mimic the natural
evolution process of a population, have also been shown to have merit when
applied to machine diagnostics. Genetic algorithms (GA) are the most widely
used type of EA. Sampath et al [167] proposed a GA-based
optimization approach to gas turbine diagnostics. Several examples of ANN
incorporating GA and other EA algorithms for machine fault classification and
diagnostics are [168-170].
Another
class of machine fault diagnostic approaches are the model-based approaches [171,172]. These approaches utilize
physics specific, explicit mathematical models of the monitored machine. Based
on this explicit model, residual generation methods such as Kalman filter,
parameter estimation (or system identification), and parity relations are used
to obtain signals, called residuals, which indicate fault presence in the machine.
The residuals are evaluated to detect, isolate and identify the faut(s). This
general procedure is illustrated in Figure 12‑2 . Model-based approaches can be more effective than
other approaches if a correct and
accurate model is built. However, explicit mathematical modeling may not be
feasible for complex systems.
Figure 12‑2: General flowchart of a model-based approach
Various
model-based diagnostic approaches have been applied to fault diagnosis of a
variety of mechanical systems such as gearboxes [173,174],
bearings [175-177], rotors [178,179], and cutting tools [180]. Bartelmus [181,182] used mathematical
modeling and computer simulation to aid signal processing and interpretation.
Hansen et al [183] proposed an approach to
more robust diagnosis based on the fusion of sensor-based and model-based
information. Vania and Pennacchi [184] developed some methods to
measure the accuracy of the results obtained with model-based techniques aimed
to identify faults in rotating machines. The information provided by these
methods was shown to be very helpful to precise fault identification as well as
an evaluation the confidence of the diagnostic decision.
Petri nets, as a general purpose graphical
tool for describing relations existing between conditions and events [185], have been applied
recently to machine fault detection and diagnostics. Propes [186] used a fuzzy Petri net to
describe operating mode transition and to detect a mode change event for fault
detection and diagnosis in complex systems. Yang [187] proposed a hybrid Petri-net modeling method
coupled with fault-tree analysis and Kalman filtering for early failure
detection and fault isolation. Yang et al [188] introduced an approach
for integrating case-based reasoning with Petri net for fault diagnosis of
induction motors. The integrated approach was shown to outperform the
conventional case-base reasoning expert system.
Compared with diagnostics,
the literature on prognostics is much smaller. There are two main prediction
types in machine prognostics. The most obvious and widely used is the
prediction of how much time is left before a failure occurs (or, one or more
faults or “potential failures”) given the current machine condition and the
past (and future) operating profile. The time left before observing a failure
is usually called “remaining useful life” or RUL.
In many situations,
especially when a fault or a failure has catastrophic consequences (e.g.
nuclear power plant), it is desirable to predict the chance that a machine
operates without a fault or a failure up to some future time (for example, the
next inspection), given the machine’s current condition and its past
operational profile. In the general maintenance context, the probability that a
machine operates without fault until next inspection interval is a good reference in helping to determine whether or
not the inspection interval is appropriate.
Most of the papers
in the literature of machine prognostics discuss only the former type of
prognostics, namely RUL estimation. Only a small number of papers address the
second type of prognostics [106,189]. In the following
sections, we discuss 1. RUL estimation,
2. prognostics that incorporate maintenance actions or policies, and 3.
the determination of the appropriate condition monitoring interval.
RUL, also called
remaining service life, residual life, or remnant life, refers to the time left
before observing a failure, given the current machine age, its condition, and
the past operation profile. Note here that the definition of failure is
crucial to the interpretation of RUL. Although there is some controversy in
current industrial practice, a formal definition of failure can be found in
many reliability textbooks.
Prognosis, requires
knowledge (or data) on the fault propagation process as well as knowledge (or
data) on the failure mechanism. The fault propagation process is usually
tracked by a trending or forecasting model for certain condition variables.
There are two ways of describing the failure. The first assumes that failure
depends on the condition variables (which reflect the actual fault level)and a
predetermined boundary. The most commonly used failure definition in this case
is simple: failure occurs when the fault reaches the predetermined level.
The second builds a
model for the failure mechanism using available historical data. Various
definitions of failure can be used. A failure can be defined as the event that
the machine is operating at an unsatisfactory level (a partial failure); or, it
can be a total functional failure when the machine cannot perform its intended
function at all; or it can be a breakdown when the machine stops operating; or
it can be the attainment of a potential failure condition defined in
terms of acceptable risk. Similar to diagnosis, the prognostic methods fall
into three main categories: statistical
approaches, artificial intelligent
approaches and model-based approaches.
Goode et al [101] used SPC to separate the
whole machine life into two intervals, the I-P (Installation-Potential failure)
interval in which the machine is running correctly and the P-F (Potential
failure-Functional failure) in which the machine is running with a problem.
Based on two Weibull distributions assumed for the I-P and P-F time intervals
respectively, failure prediction was derived in the two intervals and the RUL
was estimated. Yan et al [190] employed a logistic
regression model to calculate the probability of failure for given condition
variables and an ARMA time series model to trend the condition variables for
failure prediction. A predetermined level of failure probability was used to
estimate the RUL. Phelps et al [191] proposed to track
sensor-level test-failure probability vectors instead of the physical system or
sensor parameters for prognostics. A Kalman filter with an associated
interacting multiple model (IMM) was used to perform the tracking.
Two statistical
models in survival analysis, PHM and PIM, are useful tools for RUL estimation
in combination with a trending model for the fault propagation process.
Banjevic and Jardine [192] discussed RUL estimation
for a Markov failure time process which includes a joint model of PHM and a
Markov property for the covariate evolution as a special case. Vlok et al [99] applied PIM with
covariate extrapolation to estimate bearing residual life. HMM, a stochastic
process model discussed earlier, is also a powerful tool for RUL estimation [193,194]. Lin and Makis [195] introduced a partially
observable continuous-discrete stochastic process model to describe the hidden
evolution process of the machine state associated with the observation process.
RUL estimation, as one of the prediction tasks, was generated by the model.
Wang et al [109] proposed a stochastic
process, called a “gamma process”, with hazard rate as the the residual life
prediction criterion. The condition information considered was expert judgment
based on vibration analysis. Wang [108] used the residual delay
time concept and stochastic filtering theory to derive the residual life
distribution.
AI
techniques applied to RUL estimation have been considered by some researchers.
Zhang and Ganesan [196] used self-organizing
neural networks, for multivariable trending of the fault development, to
estimate the residual life of a bearing system. Wang and Vachtsevanos [197] applied dynamic wavelet
neural networks to predict the fault propagation process and estimate the RUL
as the time left before the fault reaches a given value. Yam et al [198] applied a recurrent
neural network for predicting the machine condition trend. Dong et al [199] utilized a grey model and
a BP neural network to predict machine condition. Wang et al [200] compared the results of
applying recurrent neural networks and neural-fuzzy inference systems to
predict the fault damage propagation trend. Chinnam and Baruah [201] presented a neural-fuzzy
approach to estimating 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.
Model-based
approaches to prognosis require specific failure mechanism knowledge and theory
relevant to the monitored machine. Ray and Tangirala [202] used a nonlinear
stochastic model of fatigue crack dynamics for real-time computation of the
time-dependent damage rate and accumulation in mechanical structures. Li et al [203,204] introduced two defect
propagation models via failure mechanism modeling for RUL estimation of
bearings. Oppenheimer and Loparo [178] 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 RUL. Chelidze
and Cusumano [205] 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 [206] introduced an integrated
prognostic process based on data from model-based simulations under nominal and
degraded conditions. Kacprzynski et al [207] proposed fusing the
physics of failure modeling with relevant diagnostic information for helicopter
gear prognosis.
A
different way of applying model-based approaches to prognosis 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 [208] for machines considered
as energy processors subject to vibration monitoring and [209] for bearings with
vibration monitoring. Lesieutre et al [210] developed a hierarchical
modeling approach for system simulation to assess RUL. Engel et al [211] discussed some practical
issues regarding accuracy, precision and confidence of the RUL estimates.
The aim
of machine prognosis is to provide decision support for maintenance actions. As
such, it is natural to include maintenance policies in the consideration of the
machine prognostic process. This makes the situation more complicated since
extra effort is needed to describe the nature of maintenance policies. We interest
ourselves particularly in policies governing in the broad class of maintenance actions
that we know as “CBM” and have set out to describe in this review. Compared to
conventional maintenance, mathematical
models applicable to the CBM scenario are much fewer [212]. See also [213] for more recent
references on maintenance modeling.
The main
idea of prognostics incorporating maintenance policies is to optimize the
maintenance policies according to certain criteria such as risk, cost,
reliability and availability. Risk is defined as the combination of failure probability
and consequence. Usually, consequence can be measured by cost. In this case, the
risk criterion is equivalent to the cost criterion. However, there are some
cases, for example, critical equipment in a power plant, in which consequence
cannot be estimated by cost. In these scenarios, probability or reliability
criterion would be more appropriate. Since the cost criterion applies to most
situations, it is not surprising that the literature in CBM optimization is
dominated by cost-based CBM optimization. The consequence analysis technique
discussed in [214] is a general risk
evaluation tool for CBM optimization based on various kinds of criteria.
In
condition monitoring, no matter what machines are monitored, they fall into two
categories: completely observable systems
and partially observable systems. For
a completely observable system, the machine state can be completely observed or
identified. The information collected from this system is called direct
information. For a partially observable system, the machine condition cannot be
fully observed or identified. The information obtained from this system is
called indirect information, which is somehow related to the real
machine state. In the text to follow, we discuss various models and methods for
evaluating, through modeling, these two types of systems.
First, we
consider completely observable systems. Wang [215] developed a CBM model
based on a random coefficient growth model where the coefficients of the
regression growth model are assumed to follow known distribution functions. The
model was used to determine the optimal critical level and inspection interval
in CBM in terms of a criterion of interest, which can be cost, downtime or
reliability. In a series of works [216-218], a stochastic model — gamma process, was used to
describe the deterioration process; the system was considered as failed if its
condition jumps above a pre-set failure level;
a sequential (or non-periodic) inspection interval was assumed. Grall et
al [216] went on to assume a
multi-level control-limit rule replacement policy and obtained the optimal
thresholds and inspection scheduling by minimizing the expected maintenance
cost per unit time. Castanier et al [217] assumed a multi-level
control-limit rule repair/replacement policy and obtained optimal thresholds
and inspection scheduling based on a cost criterion and an availability
criterion as well. Dieulle et al [218] assumed a one-level
replacement policy and a sequentially chosen inspection interval using a
maintenance scheduling function, and obtained the optimal threshold and
inspection scheduling by minimizing the global cost per unit time. Amari
and McLaughlin [219] utilized a Markov chain
to describe the CBM model for a deterioration system subject to periodic
inspection. The optimal inspection frequency and maintenance threshold were
found to maximize the system availability.
Berenguer
et al [220] presented a CBM structure
for continuously deteriorating multi-component systems, which allows cost
savings by performing simultaneous maintenance actions. Barata et al [221] used Monte-Carlo
simulation to model continuously monitored deteriorating systems,
non-repairable single components or multi-component repairable systems. Then
optimal degradation thresholds of maintenance intervention were found to
minimize the expected total system cost over a given mission time by a direct
search. Marseguerra et al [222] used GA to find the
optimal thresholds in the previous work by simultaneously optimizing two
typical objectives of interest, profit and availability. Hosseini et al [223] employed generalized
stochastic Petri nets to represent a CBM model for a system subject to
deterioration failures and Poisson failures. It was assumed that deterioration
failures are restored by major repair and Poisson failures are restored by
minimal repair. The optimal maintenance policy and inspection interval were
then found to maximize system throughput.
We turn
now to the consideration of partially observable systems. Ohnishi et al [224] applied a Markov decision
process model for a discrete-time deterioration system to find the optimal
replacement policy in which minimal repair is used to restore a failure if the
decision is not to replace. Hontelez et al [225] formulated the decision
process as a discrete Markov decision problem based on a continuous
deterioration process to find the optimum maintenance policy with respect to
cost. Aven [226] presented a counting
process approach to determining the replacement policy minimizing the long run
expected cost. Barbera et al [227] proposed a CBM model
assuming that exponential failures with failure rate depend on the condition
variables, and fixed inspection intervals. The optimal maintenance action was
then found to minimize the long-run average cost of maintenance actions and
failures. Barbera et al [228] extended the previous
work to the case of two-unit series systems. Christer et al [229] used a state space model
and the Kalman filter to predict the erosion condition of the inductors in an
induction furnace conditional on the indirect measurements to date. Then a
replacement cost model was developed to obtain the optimal replacement policy
given all available information. Kumar and Westberg [230] proposed a reliability
based approach for estimating the optimal maintenance time interval or the optimal
threshold of the maintenance policy to minimize the total cost per unit time.
The authors used PHM to identify the importance of monitored variables and a
total time on test (TTT) plot to find the optimal solution. Makis and Jardine [231] established a CBM model
using a Markov process to describe the evolution process of condition variables
and a PHM to describe the failure mechanism which depends both on age and
condition variables. This CBM model was further elaborated in [232]. The optimal replacement
policy of the hazard control limit type was then determined by minimizing the
long-run expected total cost per unit time. Makis et al [233] applied optimal stopping
theory to find the replacement policy maximizing the total expected profit
during the machine life where no assumption of monotonicity of the signal
process is made. Makis and Jiang [234] presented a framework for
CBM optimization based on a continuous-discrete stochastic model. The evolution
of the hidden machine state was described by a continuous-time Markov process,
and the condition monitoring process was described by a discrete-time
observation stochastic process which depends on the hidden machine state. Then
the optimal replacement policy was found to minimize the long run expected cost
per unit time using optimal stopping theory. Wang [235] applied a stochastic
recursive control model for CBM optimization based on the assumptions that the
item monitored follows a two-period failure process with the first period of a
normal life and the second, of a potential failure. A stochastic recursive
filtering model was used to predict the residual, and then a decision model was
established to recommend the optimal maintenance actions. The optimal condition
monitoring intervals were determined by a hybrid of simulation and analytical
analysis. Okumura and Okino [236] constructed a generalized
condition-based maintenance model, in which residual life loss and replacement
preparation lead-time are included. The optimal inspection time vector and
warning level of the target maintained system under a constraint preventive replacement
probability were obtained by minimizing the long-run average incurred cost per
unit time. Barros et al [237] considered an optimal CBM
policy for a two-unit parallel system of which unit-level monitoring
information is imperfect and/or partial.
There are
two broad types of condition monitoring: continuous and periodic. By continuous
monitoring one continuously monitor (usually by mounted sensors) a machine and
trigger a warning alarm whenever something wrong is detected. Two limitations
of continuous monitoring are: 1) it is often expensive; 2) the continuous
monitoring of raw signals produces large volumes of data, including noise,
leading to difficult and inaccurate diagnostics. Periodic monitoring,
therefore, is used due to its being more cost effective. Diagnostics from
periodic monitoring are often more accurate due to the use of filtered and/or
processed the data. Of course, the risk of periodic monitoring is the
possibility of missing some failure events that occur between successive
inspections ([34], p. 131).
An
important issue relevant to periodic monitoring is the determination of the
condition monitoring interval. Optimal design of the condition monitoring
interval (or inspection interval) has been studied together with optimal
threshold design in some of the works discussed in the previous section [215-219,223,230,235,236]. The following research
works considered condition monitoring interval determination only. Christer and
Wang [238] derived a simple model to
find the optimal time for next inspection based upon the wear condition
obtained up to current inspection. The criterion is to minimize the expected
cost per unit time over the time interval between the current inspection and
the next inspection time. Okumura [239] used a delay-time model
to obtain the optimal sequential inspection intervals of a CBM policy for a
deteriorating system by minimizing the long-run average cost per unit time.
Goode et al [240] used the model developed
in [101] to determine the length of the next
condition monitoring interval for a given risk level. Wang [241] developed a model for
optimal condition monitoring intervals based on the failure delay time concept
and the conditional residual time concept. Condition monitoring is assumed to
be performed at a fixed condition monitoring interval over the whole life and
at a dynamic condition monitoring interval as well in the failure delay-time
period realizing that more frequent monitoring might be needed in this later
period. A hybrid of simulation and analytical procedure was used to find the
optimal intervals based on one of five cost criterion functions.
For a complex system, a single sensor is limited in
its capability of collecting enough data for accurate condition monitoring,
fault diagnosis and prognosis. Multiple sensors are needed in order to do a
better job. With the rapid development of computer science and advanced sensor
technology, there has been an increasing trend in the use of multiple sensors
for condition monitoring, fault diagnosis and prognosis. Data collected from
different sensors may contain dissimilar partial information on the same
machine’s condition. The problem is knowing how to combine all partial information
obtained from different sensors for accurate machine diagnosis and prognosis.
The solution to this problem is the subject of multisensor data fusion.
There
are many techniques to multisensor data fusion. They can be grouped into three
main approaches: (1) data-level fusion, (2) feature-level fusion, and (3)
decision-level fusion. For more discussion on these three approaches, see [242,243]. Heger and Pandit [90] used a data-level fusion
approach to fuse images obtained by multidirectional illumination to generate
an image with a high degree of relevant information for grinding tool condition monitoring and fault diagnostics. Liu and
Wang [244] briefly reviewed some
applications of these three multisensor data fusion approaches to machine
diagnosis and prognosis, and applied a feature-level fusion approach called
Cascade-Correlation neural network for rotating imbalance diagnosis.
Diagnostics based on the multisensor data fusion was shown to outperform
diagnostics based on a single sensor. Wang and Wang [245] used a decision-level
data fusion approach called Dempster-Shafer evidence theory for diesel engine
fault diagnosis. Kozlowski et al [246] proposed a model-based
approach to battery diagnostics using decision-level data fusion. Byington et
al [247] explored the methods to
fuse non-commensurate oil and vibration features for better gearbox fault
diagnostics and prognostics. Mannan et al [248] applied a radial basis function neural
network to fuse the features extracted from images of machined surfaces and
acoustic signals generated during the machining process. The results were
applied to the diagnostics of cutting tools. Hannah et al [249] discussed frameworks in
data fusion applications for condition monitoring and diagnostic engineering.
Data fusion combined with CBM optimization was studied in [250,251]. Assessment and
evaluation of data and information fusion strategies were discussed in [252,253]. Wang and Wang [254] discussed the reliability
and self-diagnosis of sensors in a multisensor data fusion diagnostic system.
In a
mechanical system with multiple sensors installed, data collected from each
sensor may be a complicated mixture of data from several sources. But only some
of the sources are related to a particular machine condition of interest. The
problem is to separate the various sources for better machine diagnosis and
prognosis by fusing the observed multisensor data. The technique for solving
this problem is known as blind source separation (BSS) [255]. Recently, BSS has received increasing
attention in the area of machine fault diagnostics and prognostics. The general
idea behind BSS is shown in Figure 12‑3. It is assumed that the source signals 
, generated from 
unknown independent
sources, and the noise signals 
, independent of the source signals, are combined together by
an unknown mixing process. The mixed result is observed at the channel output
as an 
-dimensional (
) signal 
. A formula for the mixing process can be written as
where 
is generally a
non-linear, time-dependent function. A commonly used form for the mixing
process separates the signal and noise, i.e., 
. The objective of BSS is to find a separating function that
is applied to the observed signals 
to obtain an estimate
of the source signals 
.
Figure 12‑3: General idea of BSS
In the literature, there are two
categories of mixing process: instantaneous and convolutive mixing process. A
mixing process is instantaneous if 
is a time-independent
(memoryless) function, and convolutive otherwise. The convolutive mixing process
is more common, especially for mechanical systems. The instantaneous mixing
model is also called an “independent component analysis” (ICA) model, which is
a natural extension of PCA. For a survey of ICA theory and methods, see [256]. Several authors applied
ICA together with other signal processing techniques for condition monitoring
and machine fault diagnosis [257-260]. Tian et al [261] used ICA in frequency
domain and wavelet filtering for gearbox fault diagnostics. Zhang et al [262] studied ICA for partially
blind source separation of diagnostic signals for bearing faults with prior
knowledge. For a convolutive mixing process, BSS is more complicated. Gelle et
al [263] compared two approaches,
namely a temporal approach and a frequency approach, to solving the BSS problem
of rotating machine signals for monitoring and diagnosis purposes. They further
studied the application of the temporal approach to bearing fault diagnostics [264]. Tse and Zhang [265] applied the BSS based
method of second order statistics to separate aggregated vibration signals
generated from a number of mechanical components for machine fault diagnostics.
Vilela et al [266] used the temporal
de-correlation approach to separate the mixed acoustic signals for machine
monitoring and fault diagnosis. Serviere et al [267] applied BSS to separate
noisy harmonic signals for rotating machine diagnostics on a semi-blind mixing
basis.
In this chapter, we have summarized recent research
and developments in machinery diagnostics and prognostics used in implementing
CBM. Various techniques, models and algorithms were reviewed. Of the three main
steps of a CBM program, namely, data acquisition, signal processing, and
maintenance decision making, we focused on the latter two. Finally we discussed
various techniques for multiple sensor data fusion.
Although
advanced maintenance techniques have been available in the literature, CBM, is
under-employed by maintenance departments. Commercial predictive maintenance
solution providers have not kept pace with recent advances in signal processing
and decision support despite many situations, especially where both maintenance
and failure are very costly, where well developed and managed condition-based
maintenance is absolutely a better choice than current time based, or
inadequate condition based, maintenance policies. Expert knowledge of both the
application field and of reliability
and maintenance theory are required for selecting and implementing effective
condition based maintenance policies in each operating context.
Among
the reasons that advanced maintenance technologies have not been well
implemented in industry are: 1) lack of data due to incorrect data collecting
approaches (see Chapter
11. page 155), 2) lack of efficient communication between theory
developers and practitioners in the area of reliability and maintenance; 3)
lack of efficient validation approaches; 4) difficulty of communication of the
principles of CBM to business policy makers and management executives.
With the
rapid development of the MEMS (micro-electro-mechanical systems) technology,
future trends in CBM research will include the design of intelligent devices
capable of continuously monitoring their own health (see, e.g. [268]). Fast and robust on-line
signal processing algorithms are crucial to the design of intelligent devices.
Such novel technology will, no doubt, stimulate increased research interest in
this area. Another trend in CBM research is a growing collaboration among
different, yet individually specialised, CBM research groups, for the joint
devlopment of integrated platforms for enhanced diagnostics and prognostics
(See [2] for an application of
this idea).
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