The Effects of Signal Processing Techniques in Damage Detection and Structural Health Monitoring

This work focuses on the application of the well-known signal processing techniques such as the time series models, Fourier transform, and wavelet transform in visualizing peaks of vibration and their pattern that are used in structural health monitoring. The primary objective of this study is to compare the ability of the continuous wavelet transform (CWT) series and the Fast Fourier Transform (FFT) series in detecting mechanical faults, specifically looseness and bearing condition, in an electrical motor simulator through the visualization of vibration peak changes. By utilizing these two signal processing techniques, the frequency peaks caused by alterations in the structure have been compared. It is done on a vibration experiment under different bearing conditions such as normal condition, looseness of bearing mountings at the mid of the shaft and loose end condition, bearing damage at mid and end condition. These defects are performed using two different speeds. The vibrations were measured with a Dytran Triaxial Accelerometer with three different axis which were X, Y and Z axis. Then, the raw data obtained in acceleration transformed into time series, Fourier transform and finally wavelet transform using Matlab software. As the raw data was collected in time series, they are transformed to frequency spectrum using the Fourier transform. The frequency data have been chosen by the comparison of the X, Y and Z axis in time series based on the most significant amplitudes in respective to the three-axis stated. Finally, continuous wavelet transform (CWT) series are compared with the frequency peaks obtained using the Fast Fourier Transform (FFT). CWT used to plot the data by using magnitude scalogram method. It is shown that this method has provided a better way to visualize and identify the vibration peaks through all frequency ranges with respect to time and magnitude of vibration. One notable advantage of employing CWT is the simultaneous display of magnitude and time measurements alongside color-scaled frequency peaks on the plot. This scalogram visualization permits more precise detection of the fluctuation of vibration peaks than the FFT, which can be laborious. Therefore, CWT has the better effective techniques in detection of high vibration in scope of this work.


Introduction
Nowadays, various methods are employed to detect damage in new structures such as buildings, aircraft structures, bridges, and others.Signal processing techniques, such as fast Fourier transform (FFT), time series, and wavelet transform, are the most commonly used methods for detecting damage.Accurate frequency evaluation is a crucial component of damage detection as it enables early observation of modal parameter changes.However, conventional frequency estimation has limitations in boosting the accuracy of research due to the quick decay of higher-order modes.The frequency resolution enhancement, which is attained by extending the time period of the analysis, is the key to overcoming this limitation.The Fast Fourier Transform (FFT) is one of the widely used and most useful tools in the field of signal processing, having been published in 1965.Wavelet analysis has also proven to be a helpful approach for identifying damage in structures in recent years [1][2].
Wavelet transform has a strong capacity to reassemble the decomposed signal and can tackle time domain-frequency domain issues more successfully.Therefore, the most effective signal processing techniques are to be determined in these studies to achieve the most practical way of detecting high acceleration of vibration.It has been demonstrated that these methods work well for identifying deterioration in a variety of mechanical and civil engineering structures, including electrical motors, aircraft structures, wind turbine and bridges [3][4][5].Improving comprehension of field structural behavior, cutting down on inspection and repair times, and creating logical management and maintenance plans are just a few advantages of SHM.
This study aims to identify the changes in vibration characteristics due to different conditions of the operating motor.To achieve this objective, three models, namely time series models, Fourier Transform, and Wavelet Transform, will be researched.After collecting the vibration data, the next step is to process the data using different signal processing techniques.These techniques will be compared to identify the best way to visualize the vibration peaks and their features in the presence of bearing damage and bolt looseness in comparison to the normal condition of the shaft whirling motor.The objectives of this project are: • To produce and measure the vibration signal in different bearing conditions.

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To apply time series models, Fourier Transform, and Wavelet Transform on the data to identify the changes of vibration characteristics due to different conditions of the operating motor.

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To compare and identify the three signal processing techniques for optimal visualization of vibration features in vibration-based structural health monitoring (SHM).

Methodology 2.1 Wavelet transform (WT)
The Wavelet transform (WT) is a mathematical technique used to analyze signals in the frequency domain as well as the time domain.The WT decomposes a signal into its constituent frequencies and time intervals.The integral wavelet transform is defined as: where f(t) is the signal being analyzed, ψ(t) is the analyzing wavelet, a is the scale parameter, and b is the translation parameter [2].The wavelet transform can be computed using a discrete version of the integral transform, known as the discrete wavelet transform (DWT).The DWT is a fast algorithm that computes the wavelet transform of a signal using a series of filters and subsampling operations (1).

The Fast Fourier Transform (FFT)
FFT is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT).The DFT is obtained by decomposing a sequence of values into components of different frequencies.The Fourier transform of a function f(x) is given by: where F(k) is the frequency variable and i is the imaginary unit 1.The inverse Fourier transform is given by: where F(k) is the Fourier transform of f(x).The FFT is a fast algorithm that computes the DFT of a sequence using a series of sparse factors.As a result, it manages to reduce the complexity of computing the DFT from, which arises if one simply applies the definition of DFT, to log O (nlogn), where n is the data size 1.The difference in speed can be enormous, especially for long data sets where n may be in the thousands or millions.The FFT is widely used for applications in engineering, music, science, and mathematics [3].
The test section is the outdoor unit of split air-conditioning system that is located outside of a building which close to the office area where it possibly yielding the annoyance and uncomfortable environment.The outdoor unit and its components are illustrated in Figure 1 (a) and (b) where it contains the compressor, condenser coil, expansion valve and fan.Knowledge of these components is important as it will describe the phenomenon that might take place in the noise evaluation.

Experimental set up
The first step of the experiment is to measure the vibration signal.The goal of this step is to gather and store vibration signal information before processing the data.To achieve this goal, a three-phase AC electric motor with a shaft and many masses is used for the experiment's setup.Instruments like an accelerometer and NI are selected to measure the vibration signal.The triaxial accelerometer that was utilized in this experiment is labeled Dytran.This accelerometer's triaxial code is 3023A2.Triaxial accelerometers were chosen as the preferred option because they can simultaneously create a dynamic output in three perpendicular planes-X, Y, and Z, which are also known as vertical, horizontal, and axial directions.The accelerometer is mounted on top of the motor next to the bearing to measure the vibration signal.To increase the accuracy of the data collected, the surface must be cleaned before mounting the accelerometer.The laptop that is running Matlab software and has an NI DAQ driver installed is where the accelerometer is linked.To start the measurement procedure, a code is entered into Matlab.Three variable factors, the motor's speed, the mass of the shaft, and the mass of the load, are used in these studies.Two speeds are chosen, and afterward, three distinct shaft masses are chosen  Loose conditions indicate that, during the experiment, the mounting bearing was loose at the midpoint and end section of the shaft.During the experiment, the damage bearing was used in the mid and end sections of the shaft for the damage condition.Every condition in the experiment ran for 20 seconds, with each condition operating at two distinct rates.Although each condition in this experiment took 20 seconds to complete, we only needed 1 second to obtain the time series model's figure.Thus, 2048 samples make up 1 second of data (40960 sample data divided by 20 seconds).In terms of the outcomes, there are 2048 samples row data for every experiment condition.There are 50 runs for each experiment condition.Because there were 5 conditions in the experiment with 2 different speeds, the total sample data was 500.Finally, to raise the weight of the electric motor and create artificial damage to the bearing, three different masses of load must be attached to the shaft.We run through each step fifty times.

Results and discussions
The FFT and WT results are shown in the following figures.While the FFT shows the frequencies and their magnitudes, WT is displayed in a magnitude scalogram that indicates information about frequency, time, and vibration strength.The following circumstances can be found by researchers using the WT in term magnitude scalogram: • The color scale's frequency and intensity • The moment at which the system behaves.

Conclusion
In this work, the most effective signal processing techniques is the wavelet transform which was choose based on the following criteria: • The frequency peaks of the vibration where it is shown a convenient way to locate the intensity of the vibration in complete frequency range.

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The frequency values (Hz), the magnitude and time period where the vibration peaks occur.

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Color intensity of the scalogram that easier to visualize.

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The practical way to detect high peaks of vibration with information of time period of these high peaks.After comparison with the FFT, it can be said that the continuous wavelet transform (CWT) is the suitable signal processing method that satisfies the aforementioned criteria.This is due to the fact that WT employs the magnitude scalogram technique, which is a more practical means of identifying alterations in motor health conditions in relation to variations in vibration peaks.It is crucial to remember that machine learning approaches are preferable for automatically detecting damage and classifying different problems without the need for visual inspection in order to detect these variations in vibration peaks caused by malfunction or bearing damage [3,6,8].

Figure 1 .
Figure 1.Experimental set up: Electric motor with indicated different bearing and accelerometers positions.

Figure 2 .
Figure 2. Locations of accelerometers 1, 2 and 3 (from the right) represented by the red circles that are placed on bearing mounting.

Figure 3 .
Figure 3. FFT and CWT under normal condition and first speed

Figure 4 .Figure 5 .Figure 7 .
Figure 4. FFT and CWT under normal condition and second speed