This chapter describes a new diagnosis approach, the Root-MUSIC (RM) method, for identification of the progressive cracking in the rotor of induction motors. This method used initially in the domain of RADAR for localizing mobile targets is being applied to the domain of induction motors diagnosis. This approach has several advantages compared to the conventional power spectral density estimation (PSD) by periodogram technique. Indeed, the main advantage of this approach is its very good frequency resolution for a very short acquisition time, something impossible to achieve with the conventional method. However, in order to reduce the computation time which is the main drawback of the RM method, this method will be applied to only a specified frequency band: one that carries information about the sought fault.
TopIntroduction
The induction motor is the most common electric machine in the industry. Its main advantage is the absence of sliding electrical contacts, which leads to a simple and robust structure easy to build with low cost. However, various faults can appear on the induction motor making the fault detection procedure necessary to prevent the interruption of the industrial process (Toliyat et al., 2013).
In order to diagnose these faults, several techniques have been developed, depending on the type of physical quantity measured. The most widespread is that based on the vibration analysis. Moreover, the analysis of the stator current is a very promising approach, since its main advantages lie in the instrumentation used, the ease of its implementation as well as the richness of information provided on the existence or not of the fault and its severity. To reveal this richness of information, several methods of signal processing have been developed.
Among these methods, the spectral analysis is the most approach used. In general, spectral analysis involves estimating the power spectrum of a signal from a limited number of samples. If the signal to be analyzed is deterministic, the main tool is the Fourier Transform (FT). But, if the signal to be processed is random as is the case for the stator current, the FT of a single measurement is often insufficient. For this reason, one must calculate or rather estimate the Power Spectral Density (PSD). The PSD thus makes it possible to recognize the nature of a signal, to possibly identify its origin and to detect the variations of its characteristics. To estimate this PSD, several techniques and algorithms have been developed, which can be classified in two main approaches:
The methods belonging to the non-parametric approach, are relatively simple to implement, they provide excellent results provided that the duration of the observed signal is not too limited. In the opposite case, parametric methods are generally more efficient. Their implementation is, however, much more complex and their success depends on the adequacy of the chosen method to the type of signal to be analyzed.
Amongst the existing analysis methods, the PSD by Periodogram of the stator current, is considered as a very popular technique and is widely used in industry. Several studies (Boudinar et al., 2016; El Bouchikhi et al., 2012) have demonstrated the reasons for its durability in the field of diagnosis and its preference to other recent methods. The main reasons are:
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Independent of the signal physical nature to be analyzed (vibration or electrical), provided that this signal is stationary.
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Simple to program.
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Fast calculation time due to the use of Fast Fourier Transform (FFT) algorithm.
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Easy to implement on FPGA cards for a real-time use.
However, this method presents two major drawbacks:
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Frequency resolution conditioned by the acquisition time: Indeed, in order to have an efficient diagnosis, one must increase the acquisition time to be able to distinguish two close harmonics from each other, which is not always easy.
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Identification for low harmonics quasi impossible: Indeed, the presence of side-lobes related to the type of the window function used in the PSD estimation by Periodogram (Boudinar et al., 2015) risks masking the frequency signatures of incipient faults. Unfortunately, even an adequate choice of this window does not improve the diagnosis for certain operating modes of the motor, such as the rotor faults diagnosis at very low load. Indeed, in this case, the incipient fault signature is embedded in that of the fundamental.
To eliminate this effect from the fundamental, some studies use the combined information found in the current and voltage, in order to calculate the instantaneous power (Ibrahim et al., 2008; Dzwonkowski & Swędrowski, 2012). However, this solution is not always accurate and, in addition, it is expensive, because it requires the use of sensors of currents and voltages.