Data Processing

A major issue confronting condition monitoring is ability to handle the col- lected data in terms of measurable machinery conditions. Data processing is the most critical stage in CBM because it is not always clear during the col- lection and manipulation of raw data from different sensors when meaningful information useful to lifetime estimations is being produced (Vatani, 2013).

Condition monitoring data collected from the data acquisition stage is versatile and falls into various categories such as value type (single value collected at a specific time epoch ), waveform type (time series of a condition monitoring variable) and multidimension type (multidimensional time series acquired from multiple operating conditions) (Jardine et al., 2006b) .

In the case of complex systems under dynamic operating regimes, special attention is given to multidimension type data as it requires more processing and many techniques have been developed for its analysis and interpretation. Raw multidimensional data acquired from sensors providing information under multiple operating conditions are almost always processed before it is used for further analysis.

A typical complex system is made of different interacting components in which the collective actions are hard to deduce from those of the individ-

ual components, system predictability is limited, and the responses do not scale linearly (Bar-Yam, 2003). Additionally, the technological advancements have resulted in easy and efficient generation of data sets, most of which are multidimensional and/or multivariate (Seo, 2005).

A multidimensional database is composed of sets of vectors on rela- tional elements constructed from hierarchies of dimension levels (Vassiliadis, 1998). Considering Ωas the space of all dimensions andΨas the space of all dimension levels, for each dimension D there exist a set of regime levels and there is a set of values belonging to it. Accordingly, a basic multidimensional data set,Cb, can be defined as a 3-tuple <Db,Lb,Rb > (Vassiliadis, 1998),

where

Db=< D1, D2,· · ·Dn, M > (2.1)

is a list of dimensions (Di, M ∈Ω) andM is a dimension that represents

the measure of Cb.

Lb=< DLb1, DLb2,· · ·DLbn,∗M L > (2.2)

is a list of regime levels (DLbi,∗M L ∈ Ψ). M L is the multi-valued

dimension level of the measure of Cb. Rb is a set of cell data and formed of

x= [x1, x2,· · · , xn] (2.3)

Having specified this cell data, there is a possibility to assess the system breakdown time,θb, by using the life dependence of observed sensor readings, R, in terms of a function of some simplified health measure,H (Cempel, 2003).

H= t

tb

where t is the current system life time and tb is the anticipated breakdown

time. A single observed sensor of order n points dependent on the health

measure, H, is expressed as:

Rn(t) =Rn t tb ·θ =Rn(H·t), (2.5) n = 1,2,· · · , r (2.6)

Usually, the signal observations are over some life distance, ∆θ, in which the condition of the operating system, hence the values of observed signals, may substantially change (Cempel, 2003).

Rn(tm) = Rn(m∆t) =Rmn, (2.7)

n = 1,2,· · ·, r, m = 1,2,· · · , p (2.8)

Condition monitoring data in such a multidimensional and multivariate form needs to be processed to produce meaningful information. Appropriate data characteristics are required to be calculated, selected and/or extracted for effective life estimations of the monitored systems (Heng, 2009). In this respect, data processing module carries out the functions of signal processing, feature extraction and selection (Tran and Yang, 2012). The data in these steps is processed to remove distortions and re-establish the actual form of signals.

Raw signals received from sensors are also generally very noisy, have very low signal-to-noise ratios and can be biased. Referring to equation 2.5, the noise in data needs to be added to the single observed sensor dependent on the health measure.

whereε is a random variable accounting for noise and/or the measure- ment uncertainties. Since the values in the term ε are identically distributed and statistically independent (and hence uncorrelated), it is commonly as-

sumed that ε is drawn from a Gaussian white noise (It is called white in

analogy to white light which has uniform emissions at all frequencies in the visible spectrum) (Li et al., 2000; Menezes and Barreto, 2008; Lam et al., 2014). The probability density function (p) of such a Gaussian noise (ε) is given by the normal distribution.

pG(ε) =

1 σ√2πe

−(ε−µ)2

2σ2 _(2.10)

where µ and σ represent the mean value and the standard deviation

respectively (Cattin, 2013). The relative power of ε in the channel of Rn is

typically described by the measure of “signal-to-noise ratio” (SNR) per sample which is defined as the ratio of the power of a signal to the unwanted signal (Ede et al., 2010).

SNR = Psignal Pnoise

(2.11)

where P is average power. Both the power of signals and noise are

measured at the same points, and within the same bandwidth.

To extract useful information from the data where theεis high and SNR is low, various signal processing methods have been developed to evaluate and analyse the characteristics of noisy and multidimensional raw data (Jardine et al., 2006a).

The common techniques used those of Fourier Transform (Schoen and Habetler, 1993; De Almeida et al., 2002; Liu et al., 2004) and Wavelets Trans- form (Staszewski and Tomlinson, 1994; Wang and McFadden, 1996; Rubini and Meneghetti, 2001) are studied for signal processing. Typically, these meth-

ods transform a time-domain signal into another domain, with an attempt to extract the useful information embedded within the time series that is other- wise not readily understandable in its raw form. Although these techniques are widely applied in the waveform type time series, further signal processing methods are needed to extract information from multidimensional data.

In later signal processing studies, Kalman filter (Peng et al., 2012a), principal component analysis (Liao and Sun, 2011) and Gaussian kernel smooth- ing (Wang, 2010) are used to perform dimension reduction and data filtering. The main advantage of these methods is the ability to reduce noise in raw signals; however, when a common data source is available and different oper- ational trajectories are included, the population of the entire dataset should be considered for signal processing. To that end, Wang et al. (2008) and Peel (2008) introduced the multi-regime data normalisation technique, which per- forms a standardisation method based on the population parameters of the entire dataset. Different operational trajectories can be filtered into a com- mon range with respect to their initial wear levels and failure points. The main drawback in such dimension reduction methods is the introduction of novel tra- jectories that change the population characteristics and force the repetition of dataset standardisation.

Alternatively, the neural network based prognostic approaches are pro- posed (Heimes, 2008; Greitzer et al., 1999; Fink et al., 2014; Wu et al., 2016; Loutas et al., 2017; Elforjani, 2016; Yang et al., 2016; Zheng et al., 2017) and these could filter the data sets even though novel trajectories are introduced. The network function is able to standardise various trajectories without re- quiring population characteristics but these trajectories have distinct initial wear levels which should be considered with the entire dataset. Taking into account the associated merits and drawbacks, multi-regime data normalisa- tion and neural network filtering can be merged to provide a signal processing

method that can produce desired outcomes with due consideration to dataset population parameters and wear-level characteristics.