Part 3 - Future Development of State Of The Art Statistical Method in Signal Analysis

‘Rivers of Statistic’

M-Z-N

•       Mesokurtosis-Zonal-Nonparametric (M-Z-N) is the latest signal analysis to be developed.

•       In M-Z-N method, the signal data will be divided into desired number of segment, M

Example divison a of signal data

•       RMS value for each segment will be calculated.

•       M-Z-N coefficient is defined as :-

where x_i is the discrete data values ​​ of i-th sample in a segment, rms is the root mean square value for a segment, M is the number of segments, and N is the number of data in a segment.

•       M-Z-N method had been applied in study of acoustic signal characteristic in impact testing.(Hilmi 2011)

•       The structure borne ultrasonic and air borne ultrasonic signal of a low carbon steel 1050 is analyzed by M-Z-N method.

M-Z-N coefficient for SBU and ABU of low carbon steel 1050

•       From this study, we had discover that M-Z-N coefficient increase with increment of impact magnitude.

MoZAK

•       Generally, in translational motion, as the camera approaches an object, the degree of complexity of the edges of the object image will change.

•       This principle can be used to estimate the distance to a targeted object.

•       This work introduces a novel statistical method, named Moment of Zoomed-Algorithm Kurtosis (MoZAK), which is based on the I-kaz method, as an indicator for controlling the motion system.

•       Generally, Mozak coefficient is defined as :-

x  =    coentroid to edge distance data

k  =   kurtosis

std =  standard deviation

c  = analysis order 

•       The MoZAK parameter, ʓ_c which represents the degree of complexity of image edges, is used to indicate if further actuation of the motor, or otherwise, is required.

•       This study is done using two approach to get a effective method to estimate motor motor movement so that no collision will occur between camera and targeted object. The approaches are:

                                I.            Comparison of conventional statistical methods (standard deviation and kurtosis) with MoZAK method.

                             II.            Varying order of statistical analysis and MoZAK method.

• •      Results indicate that the MoZAK method presents a viable distance estimator compared to conventional statistical methods.
• •      Generally, 4th moment statistical analysis at the 2nd order able to give coefficient changes that is proportional to image sequence.

End

Part 2 - Advance DEVELOPMENT OF I-KAZ ™ family

I-KAZ™ FAMILY

• Under the I-kaz ™ family, there are I-kaz™ derivative   methods to   diversify the application of this method in signal analysis.
• Each method has its own special application.

I-KAZ 2D  

• In the study using I-kaz 2D, two channels signal is used. This method was developed for signal analysis in two axes.
• Different from the  I-Kaz ™ method, the signal does not need to be decomposed to three different frequency ranges.
• For example, the analysis of vibration signals of which the vibration signal measured on the x axes and y axes.
• I-kaz 2D coefficient can  be defined as :- 

What is I-kaz 2D?

•      I-kaz 2D analysis is consist of two components I-kaz 2D graphical representation and I-kaz 2D coefficient, Z_∞² .

•      Axis of I-kaz 2D graphical representation:

o   x-axis : Data from channel I

o   y-axis : Data from channel II

•      I-kaz 2D coefficient, Z₂^{∞ :-} 

Application

•      I-kaz 2D technique had been used in development of online tool wear measurement and monitoring system. ( J.A. Ghani 2010)

•      A two-channel strain gauge is mounted at the tool holder to measure the deflection in both tangential direction and feed direction.

•      The signal is transmitted to the signal conditioning device, then to data acquisition, and finally to the computer system.

•    Comparison of predicted and actual tool wear magnitude measured with different sets of cutting parameters:

•            (a) Vc = 180 m/min and feed rate = 0.2 mm/rev

•            (b) Vc = 230 m/min and feed rate = 0.25 mm/rev

•            (c) Vc = 270 m/min and feed rate = 0.15 mm/rev

and all with a depth of cut of 1 mm.

•      From the analysis and calculation of I-kaz 2D coefficient, the relationship is obtained between the I-kaz 2D coefficient and the flank wear value, and is given by:-

Where a and n are coefficient that the value depend on cutting condition that are cutting speed, feed rate and depth of cut.

•      A new correlation has been developed between the I-kaz™ coefficient of the raw signal and flank wear data. The regression trend of its correlation shows a power-law curve with the R-square values of the regression coefficient between 0.938 and 0.991.

•      Therefore, this system is able to give an early warning of flank wear in the cutting tool, and assists the smooth operation of the machining process in order to produce a part of acceptable quality. 

I-KAZ 3D 

•      I-kaz 3D method is developed to measure the degree of dispersion for 3 axes signals and it plays an important role in the clustering process of the statistical analysis parameters ( Nuawi et al. 2008).

•      It is used in the application requiring measurement in x-axis, y-axes and z-axes.

•      The I-kaz 3D coefficient can be defined as: 

What is I-kaz 3D?

•       I-kaz 3D analysis is consist of two components I-kaz 3D graphical representation and I-kaz 3D coefficient, Z^∞₃ .

•       Axis of I-kaz 3D graphical representation:

o   x-axis : Data from channel I

o   y-axis : Data from channel II

o   z-axis : Data from channel III

•      I-kaz 3D coefficient, Z^∞_{3 :-}

Introduction

•       Both descriptive and inferential statistics was comprised in the I-kaz 3D method

•       Descriptive statistics

o   to summarize the data, either numerically or graphically

o   to describe the sample

o   the numerical descriptor of I-kaz 3D is the I-kaz 3D coefficient

•       Inferential statistics

o   to model patterns in the data, accounting for randomness and drawing inferences about the larger population

Application I

Study of A Novel Analysis (I-kaz 3D) for Three Axial Vibration Signal in Bearing Condition Monitoring 

Methodology

Results & Discussions

Conclusion

•     The I-kaz 3D and I-kaz 3D coefficient (dBz∞) are tested on their performance in bearing condition monitoring

•       Statistical analysis is very useful and sensitive to the minor defects and provides both inferential and descriptive statistic

•     Defect bearings will display high scatteration in I-kaz 3D and the value of I-kaz 3D coefficient is normally higher compare to healthy bearing

Application II

•       I-kaz 3D method had also been applied to in study of observation of cutting tool wear. (J.A Ghani et al 2009)

•       From the analysis and calculation of I-kaz 3D coefficient, the relationship is obtained between the I-kaz 3D coefficient and the flank wear value, and is given by:

o   where a and n are coefficient that the value depend on cutting condition that are cutting speed, feed rate and depth of cut.

I-KAZ HYBRID

•       I-kaz Hybrid method is a derivative of the I-kaz ™ method that is developed to measure the degree of  data scattering for two different types of  signals that is strain signal and vibration signal. Correlation between vibration signal and strain signal can also be obtained by using the I-kaz Hybrid method (Abdullah 2010).

•       I-kaz Hybrid and I-kaz™ method differ in terms of the input signal  analyzed.  

•       I-Kaz ™ method analyze only one type of data while Kaz Hybrid-I method analyze two types of data at the same time.

•       For two types of signals, I-Kaz™ method will give two different coefficients; I-Kaz Hybrid method will give only one coefficient for two different types of signals.

•       I-kaz Hybrid coefficient is defined as:-

•       I-kaz Hybrid analysis had been applied in durability analysis of an automobile coil spring. ( N. Ismail et al. 2010)

•       An experiment has been performed on an automotive suspension system machine.

•       This study considered the test signal which is excited based on ten different frequencies that are 1 Hz to 10 Hz.

•       The time domain fatigue signal and vibration signal was then analysed based on Coffin-Manson model for fatigue damage assessment and I-kaz Hybrid method.

I-KAZ OCTAVE

•       In the I-kaz Octave method, only the frequency in the octave band will be analyzed.

•       Octave band frequency covers a certain range of frequencies and exclude others. 

•       Octave is a musical terminology in which it is a series of eight music note. The ratio of frequency of the highest note to the lowest note is 2:1.

•       The I-kaz Octave coefficient on respective  frequency range is defined as:

•       I-kaz Octave analysis had been used to analyse characteristic of sound absorption ( Lee Yau Weng 2010).

•       Noise source of 1/3 Otave is applied to fiber coconut and egg cartoon which is differ in characteristics.

•       Value of coefficient absorption for those material will compared with I-kaz Octave coefficient.

•       Result shows an inverse correlation between absorption sound coefficient and I-kaz Octave coefficient.

•       Therefore, by knowing the I-kaz Octave coefficient, we can predict and monitor acoustic absorption characteristic of a material.

I-KAZ Z-PFD

• In the I-kaz Z-Pascal Frequency Decomposition (Z-PFD) method, each frequency components is decomposes into different frequencies ranges by applying the concept of Pascal's triangle. 

•       The frequency range is determined by the level selected in the Pascal triangle. If, level 3 is selected, then the order chosen is 1-2-1. Thus, the low frequency(LF) range is ¼ of the entire range, high-frequency range (HF) is ½ of the entire range and very high frequency(VF) range and is ¼ of the entire range.

•       I-kaz Z-PFD coefficient can be defined as:

•    I-kaz Z-PFD analysis had been applied in condition–based monitoring using ultrasound structural propagation signal on journal bearing (Sivachidambaram 2010).

•       In this study, journal bearing was rotated in the range of 500 rpm till 2500 rpm with 1 kg, 2 kg and 3 kg of mass applied to it. 

•      Coefficient of I-kaz Z-PFD will decline from the rate of rotation of 500 rpm to 1500 rpm then will increase at 2000 rpm onwards. 

•       When ​​the coefficients are plotted according to the criterion of the rate of rotation (rpm) and loading, the pattern obtained is in quadratic shape. 

I-KAZ Z-FFD

•       I-kaz Z-Fibonacci Frequency Decomposition (Z-FFD) is one of derivative analysis of I-kaz™ where the data is decomposes into frequency ranges based on the Fibonacci triangles.

•       Fibonacci Triangle is a geometric arrangement built based on the Fibonacci numbers.

•       The Fibonacci numbers are the sequence of numbers  defined by the linear recurrence equation that is :-

•       The frequency range is determined by the level selected in the Pascal triangle. If, level 3 is selected, then the order chosen is 2-3-2. Thus, the low frequency(LF) range is 2/7 of the entire range, high-frequency range (HF) is 3/7 of the entire range and very high frequency(VF) range and is 2/7 of the entire range.

•       I-kaz Z-FFD coefficient is defined as:

End of Part 2