**Seungdeog Choi Ph.D.**

*Toshiba International*

**Bilal Akin Ph.D.**

*Texas Instruments, Inc.*

Within the last decade many studies have been conducted to detect electric machine faults prior to possible catastrophic failure [1–9]. One of the most popular methods for fault diagnosis is motor current signature analysis (MCSA) as it is more practical and less costly. Thanks to recent digital signal processor (DSP) technology developments, motor fault diagnosis can now be done in real-time based on the stator line current [10–17] allowing precise and low-cost motor fault detection. Beyond this, once simple and efficient fault detection algorithms are employed, it is possible to control the motor and detect the fault at very early stages simultaneously using the same DSP [12,17]. Typically, implementing a comprehensive fault diagnosis algorithm taking all the details into account like the decision-making stage is a long and complicated procedure. Therefore, in order to not violate CPU utilization and degrade motor control performance, the priorities of the DSP-based fault algorithms need to be carefully determined based on practical issues, including limited memory occupancy and computation complexity.

Among widely used traditional algorithms, spectrum analysis has been applied in fault diagnosis such as the fast Fourier transform (FFT), which is one of the most popular signal processing algorithms in motor fault detection applications. However, in real-time applications, (*N*/2) × log (*N*) complexity of FFT-radix 2 brings an overwhelming burden to the DSP where significant amounts of data need to be processed to produce sufficiently high resolution. Many of conventional FFT type or time-frequency analysis techniques have a similar problem in a DSP implementation. Using some of the recently proposed signal processing algorithms as alternatives to traditional methods [16–18] gives good real-time performance and satisfactory results when implemented by a committed high-speed DSP. On the other hand, a specific fault signature analysis technique instead of wide spectral analysis such as a phase locking loop, matched filtering, reference frame theory, and other relevant techniques have lower computational complexity for processing a large amount of data. Cruz et al. successfully implemented a simple algorithm based on multiple reference frame theory on a DSP used for direct torque control (DTC) of an induction machine [17]. The complexity order of a basic phase locking loop function is *N*, which is log(*N*)/2 times less than that of an FFT algorithm while occupying negligible memory. Instead of scanning the whole spectrum, a phase locking loop concentrates only on the expected fault frequencies that improve resolution and noise immunization [12].

While performing motor fault detection, it is important to have a noise suppression capability where high-energy noise content dominates the low amplitude fault signatures. As an effective tool, the matched filter is often pronounced as one of the best candidates [19] in an additive white Gaussian noise (AWGN) channel. The matched filter is known as an optimal detector that maximizes the signal-to-noise ratio (SNR) in the AWGN channel. A typical filter is expressed by

$${y}_{n}={\displaystyle \sum _{k=1}^{N}{h}_{n-k}{S}_{k}}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.1\right)$$

where *n* = 1,2,…*N*, *h*_{n} represent the impulse response of the filter, and *s*_{k} is the input signal. The output SNR of the filter can be written as

$$SNR={\left({H}^{T}S\right)}^{2}/E\left[{\left({H}^{T}W\right)}^{2}\right]={\left({H}^{T}S\right)}^{2}/\left({\text{\sigma}}^{2}{H}^{T}H\right)\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.2\right)$$

where *H* = [*h*_{N}*,h*_{N-1,…}*h*_{1}], *S* = [*s*_{1}*s*_{2}⋯*s*_{N}],*W* = [*w*_{1}, *w*_{2},⋯*w*_{N}], *w*_{n}is the sampled Gaussian noise with variance σ^{2}, and *T* is the vector transpose. Through the Cauchy-Schwarz inequality, the denominator in Equation (9.2) is maximized as

$${\left({H}^{T}S\right)}^{2}\le \left({H}^{T}H\right)\left({S}^{T}S\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}when\text{\hspace{0.17em}}H=cS\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.3\right)$$

where *c* is constant. It is obvious from Equation (9.3) that the SNR of filtering is maximized when *h*_{n} = *s*_{N−n}, which is called the matched filter.

Assuming *Sn* is the reference signal of the inspected fault signature and *x*_{k} is the input current signal, the output of matched filter is rewritten in the form of cross-correlation as given in Equation (9.4), which is supposed to suppress noise optimally for fault signature detection. Hence, cross-cor-relation can be proposed as one of the best signal detectors for the systems distorted by Gaussian noise.

$${y}_{n}={\displaystyle \sum _{k=1}^{N}{h}_{n-k}{S}_{k}}={\displaystyle \sum _{k=1}^{N}{h}_{n-k}{x}_{k}}={\displaystyle \sum _{k=1}^{N}{S}_{N-(n-k)}{x}_{k}\Rightarrow {y}_{N}={\displaystyle \sum _{k=1}^{N}{S}_{k}{x}_{k}}}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.4\right)$$

The analysis of a matched filter in continuous time can be derived in a similar manner through integration instead of summation in Equations (9.1) to (9.4) [19]. The matched filter output in continuous time can also be expressed as the cross-correlation in Equation (9.4) by replacing the summation to integration. The details of continuous-time matched filters are not covered since the implementation is based on discrete time processing.

Implementation of an algorithm on DSP is commonly limited by the memory and computing capacity of the system. The memory occupancy for cross-correlation operation is assumed negligible because it is performed in the sample sequence order of the input signal *x*_{k} in Equation (9.4), which does not need an additional signal memory buffer. The computing complexity of the cross-correlation is shown as *N* in Equation (9.4), which is low enough as each multiplication occurs only one time in each interrupt in normal operation of a DSP system. For the FFT-based scheme, which has been popularly used in fault diagnosis, all the signals should be inherently stored in a memory buffer for computation and the number of multiplication required is (*N*/2) × log(*N*), which is assumed not acceptable due to the overwhelming burden on DSP, especially for low cost on-line fault diagnosis systems. The inherent optimal performance in noise suppression, low memory occupation, and low computing complexity makes the cross-correlation based detection an attractive tool for on-line fault diagnosis of a motor.

Most of the specific fault signal detection schemes in literature utilize the optimal property of the matched filtering such as reference frame theory, phase sensitive detection, and any other relevant cross-correlation methods. In this chapter, the implementation of reference frame theory and phasesensitive detection as an example in an embedded DSP system is presented.

The topic of phase transformations and reference frame theory [12] constitutes an essential aspect of machine analysis and control. In this chapter, apart from the conventional applications, it is reported that the reference frame theory can also be successfully applied to fault diagnosis of electric machinery systems as a powerful toolbox to find the magnitude and phase quantities of fault signatures. The basic idea is to convert the associated fault signature to direct current (DC) quantity, followed by the computation of the signal's average in the new reference frame to filter out the rest of the signal harmonics, that is, its alternating current (AC) components. Because the rotor and stator fault signature frequencies are well known, the presented method focuses only on the fault signatures in the current spectrum, depending on the examined motor fault.

The introduction of reference frame theory in the analysis of electrical machine systems has turned out not only to be useful in their control and analysis, but also has provided a powerful tool for condition monitoring. By judiciously choosing the reference frame, it is possible to monitor any kind of motor fault whose effects are reflected to the line current as shown in the following section. The rotating reference frame module in the software used for fault analysis can work separately and independently than the one used for motor control, which is synchronized to the fundamental harmonic vector.

The commonly used transformation is the polyphase to orthogonal two-phase transformation. The complex current harmonic vector describes a circular trajectory in the space vector plane as shown in Figure 9.1. Therefore, a multiphase system in phase variables transforms to a circular locus in the equivalent two-axis representation. In Figure 9.1, the radius of the circle around the origin is the peak magnitude of the inspected harmonic quantities, and the vector rotational frequency is equal to the angular frequency of phase harmonic quantities. Note that the drawings in Figure 9.1 are exag-gerated to explain the basis of the theory explicitly; indeed the magnitude of fundamental harmonic is several times higher than all line and fault har-monics. If the new rotating reference frame is defined where the axes are made to rotate at the same rate as the angular frequency of the inspected harmonic, a stationary current space vector results, where its orthogonal components are DC quantities.

**FIGURE 9.1**

Harmonic space vector with other harmonic vectors in the stationary and rotating reference frames.

If a reference frame is synchronized to a particular frequency, in the new reference frame all harmonics other than the inspected one remain as AC. The average of these AC harmonics converge to zero and have a negligible effect on the average after a sufficient time. In other words, the reference frame synchronized with fault harmonic shifts the frequency spectrum of the phase current by frequency of the fault component. The rotating frame converts only the associated fault harmonic vector to a stationary vector at zero Hertz whose projection on orthogonal base vectors are DC and the averages are nonzero in time. Thus, when the resultant fault vector modulation is normalized with respect to the fundamental vector that is computed at the synchronously rotating reference frame, the ratio gives the relative magnitude of the fault harmonic as

$$\left|\frac{{I}_{fault}}{{I}_{1}}\right|=20\mathrm{log}{\left[\frac{\left({\left({\displaystyle \sum _{k}{i}_{dk}}\right)}^{2}+{\left({\displaystyle \sum _{k}{i}_{qk}}\right)}^{2}\right){|}_{{\text{\theta}}_{h}{\text{=\theta}}_{fault}}}{\left({\left({\displaystyle \sum _{k}{i}_{dk}}\right)}^{2}+{\left({\displaystyle \sum _{k}{i}_{qk}}\right)}^{2}\right){|}_{{\text{\theta}}_{h}{\text{=\theta}}_{1}}}\right]}^{1/2}(\text{db})\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.5\right)$$

where *i*_{dk} and *i*_{qk} are the dq components of phase current in the rotating frame, θ_{1} is the angular position of the stator reference frame, and *I*_{1} and *I*_{fault} are the relative magnitudes of the fundamental and fault harmonic vectors, respectively. The fundamental operation of detection in Equation (9.5) constitutes multiple cross-correlation operation (matched filtering). In addition to fault harmonic magnitude calculation, the phase angle information of associated harmonic vector can also be found using the direct (d) and quadrature (q) components obtained by the proposed technique. The dq components of the harmonic vectors decouple depending on the phase angle between the rotating frame and the vector as shown in Figure 9.1. Therefore, the phase angle is formulated as

$$\text{\phi}{\text{\hspace{0.17em}}}_{fault}={\mathrm{tan}}^{-1}\left(\frac{{\displaystyle \sum _{k}{i}_{hqk}}|{\text{\theta}}_{h}={\text{\theta}}_{fault}}{{\displaystyle \sum _{k}{i}_{hdk}}|{\text{\theta}}_{h}={\text{\theta}}_{fault}}\right)\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.6\right)$$

One must note that the notations, indexes, and axes of the frames might change depending on how they are defined by the user. In the literature there are different representations of reference frame theory, but the basics are the same. So reference frame theory can be further simplified for single-phase signal-based detection, which can be derived without loss of generality.

Experiments are done on-line using the TMS320F2812 DSP, which is employed both for inverter control and fault signature detection. Several experiments are realized under various conditions such as different rotor speeds, slip, load conditions, switching frequencies, sampling frequency, and the number of data processed.

When using DSP core for both control and fault purposes, the fault code is embedded into the main control algorithm as a subroutine that processes the instantaneously measured current data for both fundamental component and fault signature frequency. The same experiments are also repeated for line-driven motors where the DSP is responsible only for fault analysis rather than control issues. Although undersampling and oversampling are possible, generally switching frequency is accepted to be the sampling frequency of the current data to synchronize the fault subroutine with the main control. The number of data is chosen to be the same as the sampling frequency, which can be adjusted between 4K and 20K depending on the applications. The stator frequency can either be calculated or equated to the reference value depending on the control type, and the rotor speed can either be measured using encoder or estimated to update the signature frequencies in real time. Though the DSP of the inverter is used in this experiment, the very simple algorithm of reference frame theory can be implemented using a simpler microcon-troller as well.

The eccentricity and broken rotor bar tests are repeated using TMS320F2812 DSP controlled inverter where *ω*_{rref}*=* 0.99 per unit. The motor is run at no load and at full load for eccentricity tests and broken rotor bar tests, respectively. As shown in Figure 9.2, both the eccentricity and broken rotor bar sidebands found by DSP microprocessor are very close to ones observed by FFT spectrum analyzer at (*f*_{s} ± *f*_{r}) and (1 ± 2*s*)*f*_{s}, respectively. The time spent to process 5K to 20K data and detect these signatures is 1 second, which is sufficiently short for fault monitoring where there is no strict time limitation. Depending on the resolution requirements and the system control parameters, execution time might be shortened or extended.

**FIGURE 9.2**

Experimentally obtained v/f controlled inverter-fed motor single-phase harmonic analysis result: (a) eccentricity signatures detected by DSP using rotating frame theory, (b) FFT spectrum analyzer output of eccentric motor line current, (c) broken rotor bar signatures detected by DSP using rotating frame theory, (d) FFT spectrum analyzer output of broken rotor bar motor line current.

In Figure 9.3, the same experiments are repeated running the motor with closed-loop field-oriented control algorithm at various operating points. The results obtained by industry purpose processor and 12-bit analogue-to-digital converter (ADC) are very close to FFT spectrum analyzer outputs, which have two DSP core and 16-bit ADC with a sampling rate of 256 kHz. These on-line experimental results confirm that the presented method can be successfully adapted to the real-time applications.

A stationary motor line current signal repeats into infinity with the same periodicity. However, this assumption is not realistic for most of the industrial applications where the duty cycle profile of the motor cannot be guaranteed to operate at steady state and at a single operating point. Instead, duty cycle involves various operating points at different load and speed combinations for an unknown time period.

**FIGURE 9.3**

Experimentally obtained FOC controlled inverter-fed motor single-phase harmonic analysis result: (a) eccentricity signatures detected by DSP using rotating frame theory, (b) FFT spectrum analyzer output of eccentric motor line current, (c) broken rotor bar signatures detected by DSP using rotating frame theory, (d) FFT spectrum analyzer output of broken rotor bar motor line current.

On the other hand, the motor current spectrum analyses done using Fourier transform assumes that the current signal is stationary. The Fourier transform performs poorly when this is not the case. Furthermore, the Fourier transform gives the frequency information of the signal, but it does not tell us when in time these frequency components exist. The information provided by the integral corresponds to all time instances because the integration is done for all time intervals. It means that no matter where in time the frequency appears, it will affect the result of the integration equally. This is why traditional application of Fourier transform is not suitable for nonstationary signals.

As stated earlier, continuous stator frequency and shaft speed information are available and are used to update fault signature frequencies at all operating points. The updated fault signature frequency is utilized to synchronize the reference frame and associated fault vector component of the line current. Therefore, even though the motor supply frequency or rotor shaft speed change due to acceleration, deceleration, loading, and so forth, the normalized fault signature magnitude is instantaneously and continuously monitored without using additional algorithms. In brief, this advantage provides real-time tracing of fault signature components in the frequency domain. In Figure 9.4a,b, the right eccentricity sideband magnitude and rotor speed are shown, respectively. The dynamic characteristics of the right eccentricity sideband at transients and different rotor speeds are traced experimentally by the DSP in real-time as shown in Figure 9.4a. A similar test is done under load when the motor is driven by the voltage-to-frequency (v/f) open loop control at 0.4 pu speed as shown in Figure 9.4c,d. In Figure 9.4c, the eccentricity right sideband track in real time is shown when the motor is loaded while running at no-load, and in Figure 9.4d the phase-A current vector magnitude is shown to identify the load characteristics.

**FIGURE 9.4**

Experimentally obtained v/f controlled inverter-fed motor single-phase harmonic analysis result: (a) normalized eccentricity sideband variation detected by DSP using rotating frame theory, (b) motor speed in pu, (c) normalized eccentricity sideband variation detected by DSP using rotating frame theory, (d) motor line current in amps.

This chapter has presented the experimental and the analytical validation of the reference frame theory application to electric motor fault diagnosis. The presented method has many advantages over existing fault diagnosis methods using external hardware and powerful software tools. The experimental test results are compared with FFT spectrum analyzer results to confirm the accuracy of this method. It is experimentally shown that this simple fault diagnosis algorithm can be embedded in the main control subroutine and run by the motor drive processor in real-time without affecting control performance of the inverter. Therefore, it can be considered as a no-cost application, which is highly promising for fault diagnosis products.

This section presents DSP-based phase-sensitive motor fault signature detection [21]. The implemented method has a powerful line current noise suppression capability while detecting the fault signatures. Because the line current of inverter-fed motors involves low order harmonics, high frequency switching disturbances, and the noise generated by harsh industrial environment, the real-time fault analyses yield erroneous or fluctuating fault signatures. This situation becomes a significant problem when SNR of the fault signature is quite low. It is theoretically and experimentally shown that the method can determine the normalized magnitude and phase information of the fault signatures even in the presence of noise, where the noise amplitude is several times higher than the signal itself.

Phase-sensitive detection is based on correlation of two signals. In the correlation process, the input signal is compared with a reference signal and similarity between these signals is determined. Similarly, a lock-in detector takes a periodic reference signal and a noisy input signal, and then extracts only that part of the output signal whose frequency and phase match the reference. To see how the phase-sensitive detector works, consider a reference signal, *I*_{ref}, which is a pure sine wave with frequency of *w*_{ref},

$${I}_{ref}(t)={I}_{ref}\text{\hspace{0.17em}}\text{COS}({w}_{ref}t+{\varphi}_{ref})\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.7\right)$$

and the noisy fault signal,

$${I}_{in}(t)={I}_{fault}\text{COS}({w}_{fault}t+{\text{\phi}}_{fault})+{\displaystyle \sum {I}_{noise}\text{COS}({w}_{noise}t+{\text{\phi}}_{noise})}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.8\right)$$

The correlation between these two signals is given by

$$\begin{array}{l}{I}_{II}(\text{\phi})={I}_{ref}\mathrm{cos}({w}_{ref}t+{\text{\phi}}_{ref}){I}_{fault}\mathrm{cos}({w}_{fault}t+{\text{\phi}}_{fault})\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{I}_{ref}\mathrm{cos}({w}_{ref}t+{\text{\phi}}_{ref}){\displaystyle \sum {I}_{noise}}\mathrm{cos}({w}_{noise}t+{\text{\phi}}_{noise})\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}={I}_{ref}{I}_{fault}\mathrm{cos}({w}_{ref}t-{w}_{fault}t{\text{+\phi}}_{ref}-{\text{\phi}}_{fault})\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{I}_{ref}{I}_{fault}({w}_{ref}t+{w}_{fault}t+{\text{\phi}}_{ref}+{\text{\phi}}_{fault})\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{I}_{ref}{I}_{noise}{\displaystyle \sum \mathrm{cos}({w}_{ref}t-{w}_{noise}t+{\text{\phi}}_{ref}-{\text{\phi}}_{noise})}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{+}_{ref}{I}_{noise}{\displaystyle \sum \mathrm{cos}({w}_{ref}t+{w}_{noise}t+{\text{\phi}}_{ref}+{\text{\phi}}_{noise})}\end{array}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.9\right)$$

The generated reference signal frequency is set to be the same as the fault signal frequency; therefore some of the terms in Equation (9.9) are converted to DC as given by Equation (9.10):

$$\begin{array}{l}{I}_{II}(\text{\phi})={I}_{ref}{I}_{fault}\mathrm{cos}({\text{\phi}}_{ref}-{\text{\phi}}_{fault})+{I}_{ref}{I}_{fault}(2{w}_{ref}t+{\text{\phi}}_{ref}+{\text{\phi}}_{fault})\hfill \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{I}_{ref}{I}_{noise}{\displaystyle \sum \mathrm{cos}({w}_{ref}t-{w}_{noise}t+{\text{\phi}}_{ref}-{\text{\phi}}_{noise})}\hfill \\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+{I}_{ref}{I}_{noise}{\displaystyle \sum \mathrm{cos}({w}_{ref}t+{w}_{noise}t+{\text{\phi}}_{ref}+{\text{\phi}}_{noise})}\hfill \end{array}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.10\right)$$

If the correlation output is low pass filtered simply by averaging, only two terms survive: the DC term due to the output of the system and the noise component with frequency near the reference signal. The rest of the noise and low order harmonics disappear as shown in Equation (9.11):

$${I}_{II\_\text{\hspace{0.17em}}filtered}(\text{\phi})\approx {K}_{1}\mathrm{cos}({\text{\phi}}_{ref}-{\text{\phi}}_{fault})+{K}_{2}{\displaystyle \sum \mathrm{cos}({\text{\phi}}_{ref}-{\text{\phi}}_{noise})}\phantom{\rule[-0.0ex]{1.0em}{0.0ex}}\left(9.11\right)$$

The phase of the noise signal varies randomly. In order to minimize the effects of noise content at the same frequency, the phase angle difference between the reference signal and the fault signals should be minimized. There are some alternatives to maximize the low pass filtered portion of the autocorrelation function. One alternative is to track the autocorrelation function and detect the peak point where the phase angles of the reference signal and the fault signal are the same. The second and more efficient method is examining both the correlation of cosinusoidal and sinusoidal reference signals to the same phase angle instantaneously. The arctangent of the correlation ratio results in the phase angle difference between the reference signal and the fault signal. The maximum correlation degree and minimum noise effect are observed when the phase angles are equated to each other by simply adjusting the reference signal's phase angle. The similar processes are repeated for the fundamental component to calculate the correlation ratio between the fundamental and fault components to find the normalized magnitude of the fault signature.

The characteristic frequencies of the well-known motor faults are given in the literature [22–25]. The most commonly reported faults in electric machines are bearing faults, eccentricity, broken rotor bar, and stator faults. All of these faults are modeled as functions of both stator frequency and rotor speed. These two variables are mostly observed by drive systems to control the motor effectively. Therefore, the reference signals are generated according to the fault equations using the rotor speed and the supply frequency to precisely capture the associated fault signatures.

Tests are repeated on-line using the TMS320F2812 DSP, which is employed both for inverter control and fault signature detection. When using DSP core for both control and fault purposes, the fault code is embedded into the main control algorithm as a subroutine that processes the instantaneously measured current data. The number of data is chosen to be the same as the sampling frequency, which can be adjusted between 4k and 20k depending on the applications. The stator frequency is equated to the reference value depending on the control type. The rotor speed can either be measured using the encoder or estimated to update the signature frequencies in real time. Because the embedded ADC in TMS320F2812 has 12-bit, the quantization constraints prevent sensing signals less than −65 dB. The experiments are carried out by testing broken rotor bar and eccentric motors.

The results obtained in Figure 9.5 using the DSP with 12-bit ADCs are very close to results obtained from the FFT spectrum analyzer that has a two-DSP core and a 16-bit ADC with a sampling rate of 256 kHz. The left sideband signature of an eccentric motor is measured to be −39.24 dB and −38.98 dB using the FFT analyzer and the DSP, respectively. It is reported that the fault signature magnitude is not strongly affected by the switching frequency of the inverter. Since this measurement is taken when the motor is running at the steady state, the ratio of the number of data to the switching frequency is mostly taken as unity, which provides sufficient resolution. The correlation of the fault component and the fundamental component with respect to the reference signals generated by the DSP are given in Figure 9.5c,d. It is possible to obtain smoother waveforms simply by processing more data. These on-line experimental results confirm that the method can be adapted to the real-time applications.

**FIGURE 9.5**

Experimentally obtained (a) left eccentricity sideband in real time, (b) correlation degree between reference signal and the fault component, (c) correlation degree between reference signal and the fundamental component, and (d) FFT spectrum.

In order to realize on-line lock-in of the reference signal and fault signature, a few ways are possible. For instance, the phase angle difference between the reference signal and the fault signature can be calculated using the arctangent relation of the cross-correlation and the autocorrelation at each fault signature detection cycle. Next, the minimum phase angle difference point is chosen as the operating point that maximizes the correlation and minimizes the noise effects. Once this point is detected, the rest of the fault diagnosis process can be continued at this point or it can be updated at each phase difference zero crossings.

As shown in Figure 9.6a, the correlation degree of fault component is set to maximum at zero crossing of the phase difference and fixed at this point until the next zero crossing. A similar process is repeated for the fundamental component to normalize the fault component as shown in Figure 9.6b. Despite the decrease in precision, the phase angle scanning can be accelerated by increasing the reference signal phase angle increments in each drive control cycle. Since the period of phase angle scanning is in the range of minutes this method is appropriate for constant duty cycle steady-state operations.

In order to examine the motors, the duty cycles of which are continuously fluctuating, an alternative autotuning algorithm is developed. Apart from the previous method, the phase difference between the reference signal and the fault signature is continuously updated. Thanks to this method, it is possible to track fault signature not only at the steady state but during transients as well. Therefore, one can follow the dynamic characteristics of fault signatures during acceleration, deceleration, and loadings. The false error warnings can be minimized employing this method and previously determined operating point dependent on the adaptive threshold. If there are rare measurements to be made of a current magnitude that does not change significantly in time, it may be acceptable to process as many data as possible to enhance the precision of the result. However, if there are multiple measurements to be made particularly during transients, the number of processed data should be optimized. Typically, a few drive control cycles data processing time is enough at steady state and at most one or a half cycle will be sufficient during transients. It is reported that less than half a control cycle significantly degrades precision. Since the results are normalized, computation time will not affect the relative amplitude of the fault signature or the correlation degree.

**FIGURE 9.6**

Experimentally obtained (a) phase difference between reference signal and fault component, and normalized left eccentricity sideband correlation degree in real time, (b) phase difference between reference signal and fault component, and normalized left eccentricity sideband correlation degree in real time.

In Figure 9.7, continuous tracking of the right eccentricity sideband is given. The phase lock-in is achieved in each drive control cycle by the autotuning algorithm. Using the phase-sensitive detection, the right eccentricity sideband is measured as less than |1| dB error when compared to the FFT analyzer results.

**FIGURE 9.7**

Experimentally obtained (a) normalized fundamental and right eccentricity sideband correlation degree in real time, and (b) FFT analyzer output.

In Figure 9.8, the real-time fault signature tracks are given. In Figure 9.8a, the right eccentricity sideband variation is given from no-load to 0.33 pu load using the autotuned phase-sensitive lock-in detector. In Figure 9.8b, the broken rotor bar fault right sideband variation is given from 0.8 pu to 1.1 pu load. Because the supply frequency is already continuously available in the control algorithm and the rotor speed is measured or estimated, these parameters are used to update the fault signature frequencies in real time at various operating points. These results prove that the method has a powerful real-time fault signature tracking capability.

**FIGURE 9.8**

Experimentally obtained (a) normalized right eccentricity sideband correlation degree in real time under no load and 0.33 pu load, and (b) normalized broken rotor bar fault right sideband correlation degree in real time under 0.8 pu and 1.1 pu load.

In this chapter, a simple noise immune real-time fault signature detection tool is presented. Since this method can easily be implemented using general-purpose microcontrollers without any additional hardware, PC, filters, and large size memory, it can be adapted to single- and multiphase drive systems.

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