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Rotating machinery such as induction motors and gears driven by shafts are widely used in industry. A variety of techniques have been employed over the past several decades for fault detection and identification in such machinery. However, there is no universally accepted set of practices with comprehensive diagnostic capabilities. This paper presents a new and sensitive approach, to detect faults in rotating machines; based on principal component techniques and residual matrix analysis (PCRMA) of the vibration measured signals. The residual matrix for machinery vibration is extracted using the PCA method, crest factors of this residual matrix is determined and then machinery condition is assessed based on comparing the crest factor amplitude with the base line (healthy) level. PCRMA method has been applied to vibration data sets collected from several kinds of rotating machinery: a wind turbine, a gearbox, and an induction motor. This approach successfully differentiated the signals from healthy system and systems containing gear tooth breakage, cracks in a turbine blade, and phase imbalance in induction motor currents. The achieved results show that the developed method is found very promising and Crest Factors levels were found very sensitive for machinery condition.

Detection of faults in rotating machinery remains a big challenge especially for complex mechanical systems. Despite substantial advances in sensing and signal processing technologies, many difficulties remain to the successful detection of faults at an early stage of their development to avoid catastrophic failure [

With wind turbines, Jüngert [

Parey et al. [

Induction motors are critical components for many industrial processes and frequently integrated in commercially available equipment and industrial processes. Early fault detection would eliminate consequential damages of motors and reduce outage time and costs of repairs.

Several diagnosis techniques for the identification and localisation of the faults have been proposed. Acosta et al. [

Multivariate statistical analysis (i.e., PCA) has been used in many areas of science and engineering to detect abnormalities in the structure of data sets. Its operation can be thought of as extracting from the data of those parameters which best explains the variability in the data. PCA works by computing a compact and optimal description of the observed or experimental data set, reducing the number of dimensions of the data set while retaining as much relevant information as possibleIt is assumed that the different parameters are uncorrelated with each other, that is, the signals from different faults can be discerned from each other. PCA is a useful technique for discerning variables that explain the observed trends in a process.

PCA describes the dispersion of an array of n points in p-dimensional space by introducing a set of principal components. The first principal component is chosen in such a way that accounts for as much of the variance in the data set as possible. The second principal component is in mathematical terms said to be orthogonal to the first, uncorrelated with it, that is, in reality it would be an independent fault. This second principal component is chosen to account for as much of the remaining variance as possible. The process then proceeds with each succeeding component accounting for as much of the remaining variance as possible. The process continues until a suitable termination is reached depending on the accuracy required or limits of computation.

Consider

The third step is to perform single-value decomposition (SVD) on

The elements of matrix

In (

The proposed novel technique is to determine rotating machinery faults based on the PCRMA algorithm shown graphically in Figure

Illustration of the PCA-based proposed technique.

The experimental work was carried out in the Mechanical Laboratory of the Manchester Metropolitan University using several different kinds of rotating machinery: a wind turbine, a gearbox, and an induction motor. The same instrumentation, for example, accelerometers and associated charge amplifiers were used to collect data from all three systems. The accelerometers were B and K type 4371 with sensitivity of 10 mV/g and suitable for vibration measurements within a range of 1 Hz to 12 kHz. Before the accelerometer signals were fed to the analogue-to-digital converter NI USB 9233 card, they passed through a B and K type 2635 charge amplifier to condition the signal. The charge amplifier converts the accelerometer high-impedance, low-charge (in the range of Pico-coulomb) signal into low impedance and high voltage (in the range of mV), and the cut-off frequency for initialising filter was set to 10 kHz. The developed Labview-based system allowed the user to monitor and store machine variables, and subsequently, a Matlab code was used for further signal processing. The accelerometer was mounted vertically on the gearbox housing, on the nacelle of the wind turbine, and on the induction motor.

Figure

Wind turbine test rig.

The gearbox used as a second machinery test consists of a two-stage, 11 kW, helical gearbox driven by a three-phase induction motor and connected to a DC generator and resistor banks as shown in Figure

Schematic layout of the gearbox test.

A third rotating machinery test used a 3 kW, 220 V induction motor, and a DC generator with a resistor bank to act as a load. A schematic diagram of the test rig is shown in Figure

Schematic diagram of induction motor test rig.

The collected vibration data from a wind turbine for the healthy blade case is shown in Figure

Healthy vibration signal from wind turbine.

Magnitude of kurtosis, RMS, and crest factor vibration signal from wind turbine with healthy blades and one faulty blade with the fault of three different degrees of severity.

PCA is a method for reducing what may be considered a contaminated signal into a series of manageable data sets. Every set contains its principal components (PCs), which are interpretations of the original data. Data were collected and analyzed using PCA method as shown in Figures

Eigenvalues as a function of Principal Component for healthy and faulty blade at wind speed of 4.7 m/s.

Score plot for healthy and faulty blade at wind speed of 4.7 m/s for the first principal component.

Residual error plot for healthy and faulty blade at wind speed 4.7 m/s.

As shown from the eigenvalues, plot healthy and faulty cases were studied for different fault conditions, but the change in shape of the curves is not sufficiently clear to detect and identify the seeded faults. Figure

The main use of PCA is to reduce the dimensionality of a data set, and it is assumed that the first few PCs contain most of, not all, the necessary relevant information contained with the original data. Thus, it follows that the remaining PCs should contain mostly noise from the original data. According to PCA theory, these PCs can be contained in a separate matrix called the residual matrix, which is constructed in the same way as the original data matrix except using only the irrelevant PCs and their respective weightings.

Actually, the relevant scores (PCs) are used to calculate the residual matrix. The residual matrix contains the information which has been removed from the analysis, and the errors are found using this matrix. The sum of the errors in each column of the matrix is calculated and squared to give a positive result which is plotted. The residual errors plots for healthy and faulty cases are showed in Figure

Developing a new way of thinking about this analysis could provide an effective method of evaluating the signals obtained from condition monitoring to determine incipient faults. A PCA-based technique was applied to the measured data for each of the three test systems. The CF was calculated for the residual signal for each of the three systems for each fault seeded into the system.

To test this novel approach, the proposed technique was applied to different data sets. Figures

Crest factor for healthy and faulty turbine blade at wind speeds of 4.7 m/s.

Crest factor for healthy and faulty turbine blade at wind speeds of 5.3 m/s.

Crest factor plot for healthy gearbox and gearbox with three tooth faults introduced (40% full load and 90% full speed).

Finally, the new technique was applied to data collected from an induction motor under different conditions. The motor was tested at 0%, 25%, 50%, 75%, and 100% load in a healthy condition and then under two different single-phase imbalance voltages of 20 and 40 V.

In this case, the CF was also used as a statistical feature extracted from the raw vibration signal, but no adequate, reliable information related to the condition of the motor was observed. To detect the phase imbalance, the PCA method was applied to the measured vibration signals. Crest factor values for the residual error based on PCA were calculated, and in Figure

Crest factor of residual error for healthy and faulty induction motor.

The vibration signals collected from rotating machinery are often so contaminated that simple statistical parameters are not sufficient for fault detection. This study has introduced a promising new approach to detect faults in different rotating machines. PCA was used to extract the residual matrix which contains the information removed from the analysis and the errors from the vibration signal. Then the crest factor was applied to the residual matrix. It has been found that such a technique has shown great promise in detecting voltage imbalance in an induction motor, gear teeth breakage in a gearbox, and cracked blades on a wind turbine.