Development of a Condition Monitoring Algorithm for Industrial Robots based on Artificial Intelligence and Signal Processing Techniques

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 8, No. 2, April 2018, pp. 996~1009
ISSN: 2088-8708, DOI: 10.11591/ijece.v8i2.pp996-1009  996
Journal homepage: http://iaescore.com/journals/index.php/IJECE
Development of a Condition Monitoring Algorithm for
Industrial Robots based on Artificial Intelligence and Signal
Processing Techniques
Alaa Abdulhady Jaber1
, Robert Bicker2
1
Mechanical Engineering Departement, University of Technology, Iraq
2
School of Mechanical and Systems Engineering, Newcastle University, UK
Article Info ABSTRACT
Article history:
Received Oct 1, 2017
Revised Dec 22, 2017
Accepted Jan 8, 2018
Signal processing plays a significant role in building any condition
monitoring system. Many types of signals can be used for condition
monitoring of machines, such as vibration signals, as in this research; and
processing these signals in an appropriate way is crucial in extracting the
most salient features related to different fault types. A number of signal
processing techniques can fulfil this purpose, and the nature of the captured
signal is a significant factor in the selection of the appropriate technique.
This chapter starts with a discussion of the proposed robot condition
monitoring algorithm. Then, a consideration of the signal processing
techniques which can be applied in condition monitoring is carried out to
identify their advantages and disadvantages, from which the time-domain
and discrete wavelet transform signal analysis are selected.
Keyword:
Condition monitoring
Discrete wavelet analysis
Industrial robot
Time-domain signal analysis
fourier transform Copyright © 2018 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Alaa Abdulhady Jaber,
Mechanical Engineering Departement,
University of Technology,
Baghdad/Iraq.
Email: 20039@uotechnology.edu.iq
1. INTRODUCTION
Industrial robots are extremely complex mechanism and hence the application of condition
monitoring for them differs from that of ‘simple’ rotating machinery. This is basically due to the
instantaneous change of geometrical configuration of the robot arm. However, there are two approaches to
condition monitoring, which are model-based and model-free. Either of these approaches or a combination of
both has been adapted in industrial robot condition monitoring. Filaretov, et al. [1] used a nonlinear model to
address problems of fault detection and isolation in complex systems, such as in robot manipulators.
Algebraic functions were implemented to design the nonlinear diagnostic observer, which was able to
dispense with the linearization in nonlinear models to avoid model errors. The robot modeling was conducted
using Matlab in discrete time. It was shown that, despite the fact that the use of this model dispenses with
linearization, it does not allow some faults to be isolated. In another paper, a model-based fault detection and
isolation (FDI) scheme for rigid manipulators was designed which depends on a suboptimal second-order
sliding-mode (SOSM) algorithm [2]. In order to make the procedure of FDI possible, an input signal
estimator and output observers were adopted and SOSM was used to design the input laws for the observers.
Experimental work and theoretical simulations were accomplished with a COMAU SMART3-S2 robot
manipulator, and the results showed that the scheme has a good ability to detect and identify faults. On the
other hand, the proposed scheme was not able to deal with multiple faults in more than one actuator or
sensor, and is also neglected elastic effects in the robot. However, because precise mathematical models for
complex systems like a robot are difficult to obtain, model-free methods based on AI or statistical approaches

Int J Elec & Comp Eng ISSN: 2088-8708 
Development of a Condition Monitoring Algorithm for Industrial Robots based …. (Alaa Abdulhady Jaber)
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have become prevalent choices for robot health monitoring. The backlash and looseness in the power
transmission system of a robot may cause torque variations. The electric motor itself generates what is known
as a back electromotive force (EMF) when subjected to mechanical load making them acting as a torque
transducer [3]. The torque variations measurements via current fluctuations on robotic actuators have been
applied for robot monitoring [3], [4]. The advantage of this technique, as early mentioned, to robot health
monitoring is that the motor current can remotely be measured along the power cables utilizing standard
current sensors without supplementary instrumentation on the robot.
Robots are required to perform a variety of different repetitive tasks and are as designed
programmable and configurable machines; and consequently the joints are subjected to continuously varying
loads and speeds. Therefore, designing a CM system for a robot being adaptable for different robot tasks is
challenging. In this work, to achieve this, it was decided to conduct the robot CM using two stages, as shown
in Figure 1. The first stage is only responsible for detection the fault and is performed during the robot
movement for accomplishing whatever the task. The vibration signals are captured and features are extracted
using time-domain signal analysis technique (as explained later). Then, the features are analysed in order to
select the most fault-sensitive one. From the extracted features that are related to the robot healthy state,
threshold values are calculated, in order to be used as a baseline reference, using the statistical control chart
(SCC) approach, a technique by which a plant (or process) is monitored to investigate whether or not the
plant remains in control. The above mentioned steps have to be done offline, before running the monitoring
system and the purpose is to compute the threshold values. If the robot is reprogrammed for a different task
than the previous, the same steps are needed to be followed, in order to establish different threshold values
for the new task. During the online operation the selected (most) fault-sensitive feature will be calculated and
compared to the reference thresholds. The result of the fault detection stage will report either the robot is
healthy or a fault is developing. If a fault is detected, the robot should be stopped and the second stage of the
CM system conducted. In the first stage, the time-domain signal analysis and SCC have been selected
because they are relatively computationally easy to implement and the fault category is not needed to be
known at this stage.
The aim of the second stage of the monitoring algorithm is to accurately identify in which joint the
fault has occurred and what is its type exactly, for example, backlash, gear tooth wear or bearing fault. To
achieve this, the robot will be programmed to move each joint independently in a cyclic movement. The
vibration signals are captured and analysed, but this time using multi-resolution signal analysis technique
based on the discrete wavelet transform (DWT), since it has been found very appropriate for non-stationary
vibration signal analysis, which is the case in industrial robots in which the speed and load on each joint is
continuously changing, and can assist in the precise diagnosis of faults. Then, the features related to the
healthy state and different fault conditions are determined and used for design and training an artificial fault
classification system using the artificial neural network (ANN). The established ANN is then employed for
online fault diagnosis.
Figure 1. Descriptive flowchart for the proposed intelligent condition monitoring algorithm

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2. BASIC CONCEPTS OF SIGNAL
A signal can be defined as a function that describes a physical variable as it evolves over time.
Analogue signals, such as sound, noise, light and heat, represent the majority of signals in nature. Variations
in these signals are continuous over time and the processing of analogue signals is called analogue signal
processing (ASP). By sampling such continuous signals at repeated time intervals using data acquisition
equipment, they can be converted into discrete format, and the processing of the digital (discrete) signal is
named digital signal processing. A discrete signal, on the other hand, has values only at specific time periods.
The benefits of converting signals from analogue to discrete (digital) form are that it can avoid the
degradation and corruption of the signals. Knowing the type of signal to be analyzed has a significant
influence on the type of analytic technique chosen. Subsequently, it is necessary to carefully inspect the
various types of signal that are encountered in practice. Thus, signals can be classified as shown in Figure 2
below.
Figure 2. Schematic diagram of signal classification
Deterministic signal: If, after a suitable number of measurements, the signal can be described by an
analytical expression and its values can be predicted at any time in the past and future, then it is called a
deterministic signal, such as a sinusoid. A deterministic signal may be classified as a periodic signal if the
change in the magnitude of the signal repeated at regular time intervals, and if not it is termed an aperiodic
signal [Figliola and Beasley, 2011].
Non-deterministic: Conversely, non-deterministic or random signals cannot be described by a
deterministic mathematical expression and they are more complex than deterministic signals. By determining
their statistical properties, random signals can be broken down into stationary and non-stationary parts.
Therefore, if the statistical properties of the random signal do not change with time, then it can be called a
stationary signal, otherwise, it is named non-stationary [Wilkinson, 2008]. However, a majority of the signals
emitted from industrial machines are non-deterministic. And when a fault starts to appear in a machine the
signals monitored tend to non-stationary in nature. Therefore, a suitable signal processing technique has to be
applied to analyse this type of signal, as discussed in the coming sections.
3. SIGNAL ANALYSIS TECHNIQUES
After a signal is being captured, a large number of signal processing techniques can be utilized to
extract the most sensitive and interesting features concerning defects. As a matter of fact, choosing the most
suitable method for each specific task represents a major challenge in condition monitoring. Signal
processing techniques are classified as using time domain, frequency domain, and time-frequency domain
methods. These methods are not totally independent, and in many situations they complement each other.
Some of the widely used signals processing techniques are discussed in the following sub-sections to
establish their suitability for robot fault detection and diagnosis.
3.1. Time-Domain Signal Analysis Technique
The technique used in processing the signal can be classified as a time-domain method if it
processes a raw signal directly in the time domain without being transformed into another domain, such as
the frequency domain [5]. It is considered one of the cheapest and simplest approaches to implement for fault
detection. The purpose of time-domain analysis is to determine the statistical features of the original signal

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by manipulating the series of discrete numbers. With this technique, however, only the fault can be detected
without diagnosing its source. Statistical parameters such as peak value (PK), which represents the maximum
amplitude in the signal regardless of sign, can be used to give useful information about the hidden defects
represented in the time domain signal. Some of these parameters are illustrated as shown:
Root-mean-square (RMS) is defined as the square root of the average of the sum of the squares of
the signal samples, (Equation (1)). RMS can be used for measuring the overall level of average power in the
vibration signal [6], [7].
√ [∑ [ (1)
where [ is the original sampled signal, is the total number of samples, and is the sample
index.
Crest factor (CF) is a non-dimensional parameters defined as the ratio of maximum absolute value
(or PK value) to the RMS value of the signal, and is given by [6], [7]
(2)
CF is a normalized measurement of the amplitude of the signal which increases in the presence of a
small number of high amplitude peaks, such as in the case for some types of local tooth damage in a gearbox.
The sensitivity of CF to the changes in the sharpness of the signal is much higher than the RMS value, and it
is much less likely to give false alarms than using the (PK) on its own [8].
Skewness (Sk) and Kurtosis (Ku) are also dimensionless parameters and denote the statistical
moments of the signal [9]. The distribution shape of the signal can be described using the 3rd
moment or
skewness, which is a gauge of symmetry of the probability density function (PDF) around its mean. If the
distribution is symmetric, its value is zero. The skewness becomes negative if the distribution develops a
longer tail left of the mean, and positive if the other way around, indicating that something is going wrong in
the monitored system, as shown in Figure 3 [10]. The 4th
moment or kurtosis represents a measure of the
relative flatness or spikiness of a signal compared to its normal state. Skewness and Kurtosis can be
calculated using the following equations:
∑ [ ̅
(3)
∑ [ ̅
(4)
where ̅ and are the signal mean and standard deviation, which represent the first and second
moment of the signal respectively, as given by:
̅ ∑ [ (5)
√ ∑ [ ̅ (6)
Every signal distribution has different kurtosis values as shown in the Table 1 [11]. The monitored
signal usually shows a normal pattern with a kurtosis value of approximately 3 if it is healthy. When a fault is
developed in the system, the kurtosis value increases indicating that the signal is no longer normally
distributed, and therefore, it is useful in identifying the machine nature [12].
Figure 3. Positive and negative skewness [10]

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Table 1. Kurtosis values for different signal distribution
Type of signal distribution Ku
Normal-peak 3
Flatter than normal 3
Sharper 3
A substantial number of papers have employed time-domain technique to identify defects in many
applications. Zhen and Zhang [13] and Li and Frogley [14] utilized time-domain analysis to detect faults in
wind turbine bearings and gears respectively. Piezoelectric accelerometers and capacitive sensors were used
to acquire vibration signals from healthy and faulty bearings. Statistical parameters include peak value,
average, variance, RMS and kurtosis have been calculated for the bearings and by comparing their results,
the status of bearing has been found easily. Although time-domain analysis has many advantages, including
straightforward signal processing and simple calculations, it is relatively insensitive tool for early stage fault
detection and severely distributed defects if used without being combined with other machine health
evaluation techniques [15]. This was verified in two other papers on bearing health monitoring [16], [17],
who concluded that most of the bearing fatigue time is consumed during the development of material
accumulative damage, whereas the period of crack propagation and development is comparatively short. The
time available for initiating a maintenance action before a catastrophic failure after confirming a defect will
be very short if this traditional technique is used. In contrast, Tseng, et al. [18] and Kamiel, et al. [19] have
shown that utilizing the statistical process control (or statistical control chart) techniques combined with the
time-domain features have effectively improved the fault detection process, but could not diagnose it. Thus,
as it was mentioned previously that the first stage is in charge of only detecting the fault, so the combination
of time-domain signal analysis with SCC will be applied at this stage.
3.2. Frequency-Domain Signal Analysis Technique
In most applications, signal representation in the time domain is not the most appropriate, since
much of the relevant information is hidden in the frequency content of the signal. Frequency or spectral
analysis provides additional information about time series data, and can be used to explain the spectra of
frequencies which exist in the signal. The parameters of frequency domain analysis are more reliable in
damage diagnosis than time domain parameters. However, time-domain signals can be represented by a
family of complex exponents with infinite time duration using Fourier transforms (FTs). Additionally, any
given time-domain signal can be written as a function of all of the frequencies present within it using Fourier
transforms, which allows analysts to concentrate on all or specific frequencies. This is achieved by
representing a time-domain signal by sinusoidal components with infinite time duration [20], [21],
which are given by:
∫ (7)
where is the transformed signal, is frequency, and is time. To regenerate the time domain
signal back from the frequency domain signal, an inverse Fourier transform has to be applied:
∫ (8)
However, the continuous-time Fourier transform can only be applied to signals of continuous time
and infinite duration. Additionally, in most applications, signals are commonly acquired and sampled at a
specific frequency, which is called the sampling frequency ( ), and converted into a set of digital data points,
and therefore it is necessary to use the discrete version of the Fourier transform (DFT) [20], [21], which is:
[ ∑ [ ( ⁄ )
(9)
[ ∑ [ ( ⁄ )
(10)
where [ and [ denote discrete frequency and time signal respectively, k and n represent the
frequency and time indices, and represents the total number of points that are equally spaced.To perform

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the DFT, a large number of complex computations are involved. This is a computationally intensive process
and not practical when performing real-time signal analysis. Thus, an algorithm that is able to perform rapid
calculation of the DFT by greatly reducing the number of computations was developed in the early 1960s
[22]. This algorithm is known as the fast Fourier transform (FFT) and commonly used in industry for
analyzing the data. The FFT algorithm requires the time domain sequence [ to have a length of data
points equal to the power of 2; which means that samples are required where is a positive integer [22].
Generally speaking, the FFT is a useful technique for transforming difficult operations into very simple ones,
and for analyzing stationary signals, which have spectral content that does not change over time. Also, in
many signal processing applications, the Fourier transform represents an adequate analytic method.
However, the Fourier technique can become less effective and inefficient if the analyzed signal is
non-stationary and transitory, with characteristics that change over time, due to its constant time and
frequency resolutions [23], [24]. Furthermore, it has a major drawback that when it is used in transforming
the signal from the time domain to the frequency domain, all of the information belonging to time will be lost
[24]. Nevertheless, provided that the signals are stationary, the task of distinguishing faulty from normal
conditions based on the FFT can be accurately achieved. This is performed by investigating particular
estimated frequencies related to some component in the machine, such as gears or bearings. If a fault has
developed in these components, the amplitude of these particular frequencies will change or some sideband
frequencies will be distributed around them. Therefore, many fault diagnosis studies using this technique
have been published, having been successfully applied for the condition monitoring of electrical motors,
cutting tools, bearings and gears [25-27].
Industrial robots, on the other hand, are required to function under a wide range of joint speeds and
variable loading within a large working area and varying joint articulation. Also, the typical cycle of robot
motion starts with an acceleration from the initial position, then moving at constant speed, and finally
deceleration towards the end position, which means movement at a time-varying speed [28], [29]. This
motion makes the robot a highly non-linear dynamic system and introduces the non-stationary phenomenon
in the captured vibration signal, and this will be more complicated if a fault is progressed in the robot. Using
a conventional FFT signal analysis technique to process such signals with transiently nature is not feasible for
accurate robot fault diagnosis in second stage. Therefore, several methods of signal processing have been
developed to cope with this category of signals, such as joint time-frequency techniques, as discussed in the
following section.
3.3. Time–Frequency Signal Analysis Technique
The signals from faulty parts have a non-stationary nature. However, if the frequency component of
the non-stationary signals is calculated using the Fourier transform, the results will represent the frequency
composition averaged over the duration of the signal [30]. Consequently, the characteristics of the transient
signal cannot be described adequately using the Fourier transform, however, time-frequency analysis has
been investigated and applied for the fault diagnosis of machinery because of its capability of signal
representation in both the frequency and time domains [24], [30]. This unique feature of time-frequency
analysis techniques means that it is suitable for non-stationary signals. Moreover, time-frequency methods
can give interesting information with regard to energy distribution over frequency bands. A number of
techniques of time-frequency analysis, such as the short time Fourier transform and wavelet transforms, have
been used for fault detection and diagnosis. These techniques will now be discussed to identify the main
differences between them and select the best to be used at the diagnosis stage.
3.3.1. Short time Fourier Transforms
To overcome the limitations of the Fourier transform technique, Gabor introduced a windowing
technique in 1946 known as the short time Fourier transform (STFT). The STFT algorithm is based on the
division of the signal into small portions which are assumed to be stationary. Then, a window function is
located at the start of the signal and multiplied together. After that, the Fourier transform will be taken for the
result of this product. Next, this window function is moved to a new segment of the signal and the above-
mentioned process is repeated. This sequence is repeated until the end of the signal is reached [31]. As a
result, the STFT outlines the time-domain signal into a two-dimensional time-frequency representation. This
can be mathematically expressed and graphically revealed as follow.
∫ (11)
Figure 4 shows the signal analysed by STFT [32].

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Figure 4. Signal analysed by STFT [32]
is the Fourier transform of the signal which has already been windowed by the
window function with respect to the time shift variable 𝝉. Various window types, with each one
employed for a particular application, have been developed over the past decades. For instance, the Hann and
Hamming windows are utilized for analyzing random and narrowband signals [32], whereas a Gaussian
window is exploited for analyzing transient signals. Selection of the window function has a direct influence
on the time and frequency resolutions of the analyzed signal. Generally, superior separation of the essential
components within a signal can be achieved if high resolution in the time and frequency domains is used. To
illustrate the difference between FFT and STFT a LabVIEW programme, designed by Kehtarnavaz [21] was
used, in which three forms of signals were combined to produce a non-stationary signal with 512-input
points. The forms of the combined signals are a chirp signal with linearly decreasing frequency from 200 Hz
to 120 Hz, a sinusoidal signal of 75 Hz, and an impulse signal located at the 256th sample and having
amplitude of 2. The composite signal and its FFT and STFT are shown in the Figure 5.
Figure 5. The difference between FFT and STFT for a non-stationary signal
From Figure 5 it can be observed that in the FFT spectrum graph there is one major peak at 75 Hz,
and also there is an indication of presence of a signal from 120 Hz to 200 Hz. However, the impulse signal,
which has short time duration, cannot be recognized in the spectrum, although it can clearly be observed in
the STFT graph at 0.5 second, which shows the spectrogram for a time increment of 1 second and a
rectangular window of width 48 points. Although the STFT provides both the frequency spectrum and the
time evolution of the signal, it does have a major drawback: it has a fixed resolution with respect to the time
window size at all frequencies, and can be explained as follows. When the FFT is used it can be noticed that
there is no time resolution, but on the other hand the frequency resolution is very high. The reason for this

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high resolution is related to the fact that the window function used in FFT covers the entire time interval from
± ∞. Conversely, the frequency resolution when the STFT is implemented becomes poorer than the
resolution given in the FFT, since the window function has a finite length and therefore only a small segment
of the signal will be covered. In order to increase the frequency resolution, the window function has to be
wide enough, but that will lead to missing time information as well as violating the stationarity assumption
which requires the window to be very small. Accordingly, there is a trade-off relationship between time and
frequency in the STFT. A wide window gives good frequency resolution but poorer time resolution and vice
versa [33]. This is well illustrated in the Figure 6 below depending on the above analyzed signal.
Figure 6. STFT with different window widths
3.3.2. Wavelet Transforms
The wavelet transform (WT) was introduced to overcome the resolution limitation of the STFT. The
main difference between the WT and the STFT is that the former has varying window lengths, and represents
the signal as a sum of wavelets at different scales [34]. To clearly understand the differences among the time-
frequency resolution of the DFT, STFT and WT, their time-frequency mapping is compared in Figure 7, from
which it can be seen that, and as stated earlier, the DFT allows extraction only of the frequency content of a
signal and any information concerning time-localization of the frequency components is eliminated. The area
of each rectangular box in both STFT and WT has a fixed value [35]. However, in the STFT the window has
fixed dimensions in both time and frequency axes which offer a constant time-frequency resolution. In WT
the window dimensions are not constant, and when the height of the box is greater this corresponds to wide
frequency bandwidth, which leads to low frequency resolution, but on the other hand the time resolution is
improved. Similarly, if the width is greater, long time duration is covered providing coarser time resolution in
contrast to better frequency resolution. So, the WT behaves rather like a mathematical microscope, as
condensing the wavelet corresponds to increasing the magnification of the microscope, which increases more
of the signal detail [35].
Figure 7. Time-Frequency signal mapping [21]

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Complex sinusoids are used in the Fourier transform for signal decomposing, whereas in wavelet
analysis a mother wavelet function is utilized. In Fourier analysis sines and cosines are used to fit the signal
in order to generate a set of coefficients, however, in wavelet analysis the mother wavelet is fitted on the
signal and then the inner product between the analyzed signal and a series of daughter wavelets is performed.
The daughter wavelets are generated by scaling and shifting the mother wavelet by controlling the scaling (s)
and shifting (τ) parameters. Scaling the mother wavelet is equivalent to stretching or dilating it; although the
wavelet is squashed in the vertical axis if it is stretched horizontally, this is to ensure that the energy content
in the scaled wavelet is equal to the original mother wavelet [36]. In the shifting step, the wavelet is moved
along the X-axis until it covers the analyzed signal entirely, which can be expressed mathematically as
follows [35]:
√
∫ ( ) (12)
Where is the wavelet transform of the signal and is the mother wavelet (or the
transforming function). The mother wavelet differs from the infinite sine and cosine functions, as it has a
finite start and finish. Mathematically, it can be said that the mother wavelet has "compact support" [37], the
importance of which appears in that when the mother wavelet fit to the signal, a localized result will be
obtained rather than a global result. A series of coefficients that vary with time will be extracted instead of
getting a single coefficient for each sine and cosine as in Fourier analysis, and consequently the wavelet
decomposition can accommodate the local and sharp changes in the monitored signal; thus it is suitable for
those signals whose spectral content changes over time. Accordingly, it represents the most appropriate
method that can be applied for analyzing the expected robot vibration signal for precise fault diagnosis and
hence it will be adopted in this study.
3.4. Discrete Wavelet Transform (DWT)
The above Equation (12) is called the continuous wavelet transform (CWT) and offers greater
accuracy in signal analysis; however, theoretically it is infinitely redundant, which means a significant
amount of unnecessary information is produced when it is implemented, and such it is impractical [38]. The
redundancy problem is a result of the continuous scaling and shifting of the mother wavelet. This increases
the required computational time, power and memory, making the CWT impractical in many situations,
particularly when applying real-time wavelet analysis on an embedded system which is the case here. To
reduce required power and time it is appropriate to remove any unnecessary information and reduce the
number of wavelets without loss of the essential information. The discrete wavelet transform (DWT) was
developed to achieve this, in which the mother wavelet is not continuously scaled and shifted, but is instead
only at discrete steps along the signals. By using DWT, the original signal is often decomposed into several
signals each with a specific frequency band each of which can be handled as an independent signal on which
separate analysis can be implemented. The strength of the DWT is that filters with different cut-off
frequencies are utilized to analyze the signal at different scales. First, the signal is passed through a high-pass
(HP) filter to analyze high frequencies, and then it is passed through a low-pass (LP) filter to analyses low
frequencies. Using digital techniques such as this, a time-scale representation of a digital signal can be
obtained. Another type of wavelet analysis called complex wavelet transform and is represented by the dual-
tree complex wavelet transform. It is an alternate, complex-valued extension and enhancement to the
standard DWT, and has important properties that provides multiresolution, sparse representation and the
capability to reduce the aliasing effects, which is caused by the overlap of opposing-frequency pass-bands of
the wavelet filters [39], [40]. Two parallel DWTs with different low-pass and high-pass filters in each scale
are used for decomposition and reconstruction in the dual-tree implementation. The two DWTs use two
different sets of filters, with each satisfying the perfect reconstruction condition. However, the drawback of
this transform is that it is exhibits redundancy compared to the standard DWT at the expense of extra
computational power; therefore, it was not considered in this study due to the expected computational
limitation of the embedded system.
3.4.1. Multi-Resolution Analysis using DWT
Generally speaking, by using the DWT, a multi-resolution analysis can be performed at different
frequency bands with different resolutions by decomposing the time domain signal [30], [34]. Two sets of
functions are employed in the DWT, called the wavelet function and the scaling function, which are
associated with the HP and LP filters respectively. At the first level, the original signal [ is decomposed
by passing it through both of these filters and emerges as two signals, each one having the same number of
samples as the original signal, and are termed as coefficients. In order to keep the total number of coefficients

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in the produced filtered signals equal to the original signal samples they are then down-sampled by a factor of
2, by keeping only one sample out of two successive samples. Thus, the extracted signal coefficients from the
HP filter and after down sampling are called the detail coefficients of the first level . These coefficients
contain the high frequency information of the original signal, whilst, the coefficients that are extracted from
the LP filter and after the down sampling process are called the approximation coefficients of the first level
. The low frequency information of the signal is hidden in these coefficients. This can be expressed
mathematically as [41]:
[ ∑ [ [ (13)
[ ∑ [ [ (14)
where [ and [ are the high- and low-pass filters respectively. After obtaining the first level of
decomposition, the above procedure can be repeated again to decompose into another approximation and
detail coefficients, as articulated in Equations (15) and (16) [41]. This procedure can be continued
successively until a pre-defined certain level up to which the decomposition is required to be found.
[ ∑ [ [ (15)
[ ∑ [ [ (16)
where [ and [ are the DWT coefficients at level , and [ is the approximate
coefficient at level . At each decomposition level, the corresponding detail and approximation
coefficients have specific frequency bandwidths given by [ ⁄ for the approximation coefficients
and [ ⁄ ⁄ for the detailed one where is the sampling frequency [30], [41].
However, at every level, the filtering and down-sampling will result in half the number of samples (half the
time resolution) and half the frequency band (double the frequency resolution). Also, due to the consecutive
down sampling by 2, the total number of samples in the analysed signal must be a power of 2 [42]. By
concatenating all coefficients starting from the last level of decomposition, the DWT of the original signal is
then produced, and it will have the same number of samples as the original signal. A schematic diagram
illustrates how the multi-level decomposition is performed shown in Figure 8. The number of decomposition
levels is identified by the lowest frequency band needed to be traced, and a higher number of decomposition
levels are required if very low frequency band is investigated. However, the highest decomposition level that
can be achieved is up to that the individual details consist of a single sample [43].
Figure 8. Multi-level signal decomposition using DWT
Once the approximation and detail coefficients are computed to different levels of decomposition, it
becomes possible to reconstruct the approximation and detail signals at each level, in order to extract
features, such as standard deviation and mean, related to the frequency bands in each level. Each signal,
however, will have the same number of samples as the original signal but with a definite frequency band.
This can be achieved by up-sampling the approximation (or details) coefficients by two, since they were
produced previously by down sampling by 2, and then passing them through high- and low-pass synthesis

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filters. For instance, to reconstruct the approximation signal of the first level , just the approximation
coefficients at this level are required and a vector of zeros is feed in place of the detail coefficients. Similarly,
the first-level detail signal can be constructed using the analogous process. The concept of signal
synthesizing is illustrated in Figure 9.
Figure 9. Reconstruction the approximation and detail signals with zero padding
3.4.2. Selection the Optimum Mother Wavelet
There are available a number of commonly used wavelet families for performing the DWT. Any
discussion of wavelets starts with wavelet, which is the first, simplest, and resembles a step function.
However, to find the optimum wavelet function for this research, a survey has been conducted to uncover the
different types of mother wavelets researchers have used for the purpose of fault diagnosis. Some examples
of common wavelets families previously used are Daubechies (dbN), Coiflet (coifN) and Symlets (symN)
(Figure 10), where N is the order number in the wavelet family [30], [44]. The N value also identifies the
number of filter coefficients in each wavelet order; for instance, the wavelet dbN and symN have 2N
coefficients in each order. Generally, the use of different wavelets to analyze the same signal would lead to
different results, and to date no generic theoretical procedure has been published describing on how to select
the optimum wavelet family [39], [45],[ 46].
Figure 10. Examples of mother wavelets
The selection in many cases is achieved by trial and error. Indeed, the wavelet function is
considered appropriate for analyzing the signal under study if there is a significant similarity between the
signal and mother wavelet [47], and based on this several quantitative methods have been proposed to
measure the similarity between the signal and the mother wavelet. For example, Bouzid [48] has proposed
calculating the cross correlation coefficient between the signal and the mother wavelet. The wavelet that
maximises this coefficient considered as the optimum mother wavelet. So, an important question now raised
is which wavelet family should be utilized for analyzing the robot vibration signals in the second stage.
From the reviewed work it has been observed that the majority of researchers are performing either off- or
on-line condition monitoring using PC platforms. In this case there is no need for concern about computers’
memory or processing power, since they are designed for conducting daunting tasks such as this. In this

1007
research, however, it is intended to achieve on chip wavelet analysis in conjunction with intelligent fault
classification system, and thus the above mentioned factors need to be carefully considered. Therefore, the
number of wavelet’s filters coefficients in each order of specific wavelet family has to be counted. Some
wavelet functions, such as db10 or sym7, have many coefficients in their filters, which will raise the
execution time required for real-time wavelet analysis because of the increased computational burden on the
embedded system. Also, higher order wavelet function will generate higher number of coefficients from the
analysed signals that may case exceed the available system memory [39], [49].
The mother wavelet selection has been limited to the lower order families and hence there is no
need to apply further quantitative methods as the remaining options are very few. Daubechies and Symelet
families are recognized as very effective in vibration signal analysis and have various wavelet orders, thus,
in this project Daubechies’s second order (db2), which is the same as Symelet’s second order (sym2), has
been selected. It has four filter coefficients and Figure 11 shows the low and high pass decomposition and
synthesis filters extracted from the Matlab software. Extracted features using this wavelet showed high
sensitivity to different robot faults, as will be explained later in Chapter 6.
Figure 11. Filter coefficients of Daubechies order 2 (db2) mother wavelet
4. SUMMARY
In this paper, an intelligent condition monitoring algorithm composed of two stages that can be
used for robot fault detection (first stage) and diagnosis (second stage) has been proposed. An outline of
three conventional signal analysis techniques that are commonly utilized in developing condition
monitoring systems has been provided, in order to choose the appropriate techniques for the robot fault
detection and diagnosis; these techniques are time-domain, frequency-domain and joined time-frequency
domain. The advantages and disadvantages along with a brief theoretical background for each method were
discussed. Time-domain analysis represents the simplest signal processing technique; it can provide an
efficient fault detection performance if it is used with other fault evaluation methods. Subsequently this will
be used in combination with statistical control chart (SCC) technique in the first stage for robot fault
detection. Frequency-domain signal analysis based on fast Fourier transform (FFT) is a valuable and widely
used technique for analysing signals that have spectral content that do not change over time (stationary
signals), but its effectiveness is reduced if applied for analysing signals that have characteristics which
change over time (non-stationary signals). The limitations in Fourier transform have been overcome by
using time-frequency signal analysis techniques such as short time Fourier transform (STFT) and wavelet
transform (WT). The main advantage of these techniques over the Fourier transform is their ability in
revealing the non-stationary and random components within the signals of interest. However, STFT is based
on fixed window size which means it has fixed resolution for all the frequencies in the signal, which is not
appropriate when a non-stationary signal is investigated. Wavelet transform represents an efficient method
of time-frequency analysis and was introduced to surmount the drawback of the STFT, since it uses variable
window size to get high frequency resolution at low frequencies and high time resolution at high
frequencies. By applying wavelet analysis, the signal can be analyzed down to its sub-band frequencies and
it is increasingly being utilized for fault diagnosis. Hence, it will be adapted in this thesis for analyzing the
robot transitory vibration signals in order to diagnose the fault in the second stage. Thus, more focus has

 ISSN: 2088-8708
1008
been placed on examining the practical use of the WT as an efficient signal processing technique for health
monitoring. The differences between the continuous wavelet transform (CWT) and the discrete wavelet
transform (DWT) are discussed and it was concluded that DWT is more appropriate to be implemented,
along the with intelligent classification system, using an embedded system. Before it is applied using the
embedded system a preliminary robot vibration analysis will be undertaken in Chapter 6, in order to extract
the salient signal features and use them for designing the intelligent embedded system.
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