Tugas Metodologi Penelitian Bedah Jurnal 2
Tugas Metodologi Penelitian Bedah Jurnal
“Damage Detection in Vibration Signals Using Non
Parametric Time Frequency Representations”
Nama : Iqbal Bayu Kurniawan
Kelas : 3IC05
NPM : 22417948
Damage Detection in Vibration Signals Using Non
Parametric Time Frequency Representations
O. Cardona-Morales, A. Orozco-Ángel, G. Castellanos-Domínguez
Department
Electrical, Electronical and Computing Engineering, Manizales, Colombia
Universidad
Tecnológica de Pereira, Pereira, Colombia
Abstrak :
Analisis getaran adalah alat yang paling sering digunakan
untuk mendeteksi kesalahan pada mesin yang berputar, sehingga biayanya lebih
rendah dibandingkan dengan alat lain seperti ultrasonik. Alat ini menyelesaikan
pemrosesan sinyal digital sangat kuat untuk membuat keputusan dan identifikasi
kesalahan. Representasi frekuensi-waktu (TF) adalah salah satu metode
karakterisasi yang paling populer untuk sinyal getaran non-stasioner. Terlepas
dari potensi keuntungan mereka, representasi ini menderita sejumlah besar data
yang berlebihan dan tidak relevan yang membuatnya sulit digunakan untuk tujuan
klasifikasi. Dalam karya ini, metodologi untuk reduksi data yang tidak relevan
dan berlebihan dieksplorasi. Pendekatan ini terdiri dari menghilangkan data
yang tidak relevan, menerapkan ukuran relevansi pada bidang t-f yang mengukur
ketergantungan setiap titik t-f dengan label kelas. Hasil menunjukkan bahwa
langkah-langkah relevansi meningkatkan klasifikasi kinerja dan kesalahan
sepenuhnya dapat dibedakan.
Experimental Setup
dan Prosedur :
The
shaft unbalance and coupling misalignment are important faults of rotating
machines. The unbalance is characterized by a mass excess in a portion of the
shaft, causing rubbing with the rolling element bearings. The coupling
misalignment generates damage by the non-alignment between the rotation center
of the shaft and the rotor. These faults are common in industry and their
presences in the machines are the main source of other damages as rub, defect
roller element bearing, among others.
The
Figure 1 shows the experimental setup, where it is possible to study the
behavior of the damages mentioned above. The experimental setup is composed by
a DC electromotor of 2HP, with a maximum speed of 1800 rpm, and the behavior
analysis when a speed change makes clear the importance of this work. The
unbalance is generated inserting a mass of 5g inside the drilling wheels and
three possible malfunctions are obtained: one mass in the left-wheel (UBL), one
mass on the right-wheel (UBR), and one mass in both-wheels (UBB), at same
position to raise the vibration level. In the coupling misalignment case, the
rotor is displaced in vertical position (with 0.0025 and 0.007in, VM1 and VM2
respectively) and horizontal position (with 0.002 to left- and 0.004in right-shaft,
HML and HMR respectively). Additionally, the without damage signal, WD, was
record too, having a classification problem with eight classes.
Estimation of TF Representation :
TF analysis is really important
when the signal modeling is invaluable. Therefore, the time variable is
introduced in a Fourier based analysis to achieve an appropriate description of
the spectral content changes as a
function of the time [4]. The use of time-frequency representations (TFR)
supposes that the mapping is generated by frames and, in non-stationary
acceleration signals, it redistribute the fundamental frequency components in
the TF plane, as its harmonics (see Figure 2). The TF plane frames are obtained
by the operation between the base function ∅t,f(τ)
and the time signal x(τ). These base functions have finite energy, ∅t,f (τ) ∈ L2(ℝ). The spectrogram,
as time-frequency representation, allows to obtain the energy density of the
signal x(τ), which can be calculated as:
Where the term with x(v) is the base function ∅t,f(v). The signal in time is resampled each 8 points to get
the low frequency information. The window function m(v − t), is a 1024-points Hamming
window and the time-frequency representation, X(t, ƒ), has
256 frequency points
and 25000 time
instants. It is possible
to downsample X(t, ƒ) to 2.5% loosing
no information aiming
to reduce the computational cost.
Relevance Analysis :
Obtained TF
representations contain a large quantity of irrelevant and redundant
information which degrades quality and enlarges the computational load for
linear decomposition approaches. In order to determine the best set of t-f points a variable selection stage is
proposed. Variable selection consists on finding the minimum subset Xr such
that P(c|X) ≅ P(c|Xr), where P(c|X) is the probability distribution function of the classes c given the complete dataset
X and P(c|Xr) is the
probability distribution function of c
given the feature subset Xr. An approach to find this subset is using filtering
techniques, where variable are selected according to some relevance measure
assigned to each variable. Relevance measure evaluates the prediction quality
of each variable in relation with the classes.
Result Jurnal :
The
procedure of relevant features estimation was carried class by class, it
supposes that each class is an objective function and others are a big group.
Figure 4 shows the relevance values for WD database. It is possible to find out
that the TF features are inversely correlated with the acceleration segment
(see Figure 4-a), and such regions correspond to the most relevant
characteristics of this class. In Figure 4-b) the relevant features obtained
with the information measure correspond to a small portion of the TF plane,
which indicates that the percentage of relevant variables is low.
Figure
5 shows the measures sorted from the highest score to the lowest score from
each class database. It can be seen that linear correlation, Figure 5-a), is
more selective than symmetrical uncertainty, Figure 4- b), as the measure
decays faster and are most uniform between classes. This behavior strongly
affects the classification process, due to the high relevance level that a few
quantity of features has per class.
Concerning
to the symmetrical uncertainty measure, the difference of relevance is more
notorious, and the classification process thus is more affected by the high
variability between different relevance values. Final classification outcomes
are summarized in Table 1. Results are shown as mean and standard deviation of
accuracy, sensitivity and specificity figures after cross-validation test.
Direct comparison of relevance measures (PCA weights, linear correlation and
symmetrical uncertainty) can be made for each kind of signal. Comparison with
TF maps is required to show the advantages that the relevance measures present.
It is important to emphasize that the used relevance percentage to achieve the
maximum performance, as well as the dimensionality reduction (Dm Red.) achieved
with the proposed feature selection measures.
Results
show that linear correlation measure overcomes symmetrical uncertainty by 0.6%
in precision, and 8.1% in dimensionality reduction, which is reflected in lower
computational cost and higher classifier generalization. The proposed relevance
measures are compared with the TF map and PCA without relevance measure, the
performance improvement is highly clear and the computational cost is reduced,
which shows that this methodology is adequate for this detection problem.
CONCLUSIONS
:
In
this work, a method of feature extraction on TF representation of vibration
signal in non stationary process for classification is proposed. The method
directly deals with highly redundant and irrelevant data contained in TFRs,
combining a first stage of irrelevant data removing by variable selection with
a relevance measure, with a second stage of redundancy reduction by linear
transform methods. Results show high performance improvement compared with
other methodologies which do not take into account the presence of irrelevant
and redundant data. As relevance measure, two measures of dependence of the
features with class labels are used, linear correlation and symmetrical
uncertainty. Both measures show significant improvement in comparison with the
case when no relevance measure is used, with slightly better performance of
linear correlation.
As a
future work, the proposed methodology will be used in other class of vibration
signals, in order to generalize the achieved results in other classes of signal
dynamics. Also, other relevance measures will be taken into account, to compare
with those studied in this work.
REFERENCES :
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[3] M. Timuska, M. Lipsett, C. K. Mechefske, Deteksi kesalahan menggunakan sinyal mesin transient,Sistem Mekanik dan Pemrosesan Sinyal, Vol. 22, (2008), hlm. 1724–1749.
[4] E. Sejdic, I. Djurovic, J. Jiang, Representasi fitur waktu-frekuensi menggunakan konsentrasi energi:Ikhtisar kemajuan terkini, Pemrosesan Sinyal Digital, Vol. 19, (2009), hlm 153–183.[5] Yu L., Liu H., Seleksi Fitur yang Efisien melalui Analisis Relevansi dan Redundansi, JurnalMachine Learning Research, Vol 5, (2004), hlm 1205-1224.
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