We undertook this study as a result of repeated breakdowns in turbochargers on some power generating sets, to early detect causes of the breakdowns. Chief among them is the wear of turbine blades. During the normal functioning of the turbocharger the blades are likely to wear out over time. If the worn-out blades are not replaced in time breakdowns can occur on the turbocharger, which led us to determine the global vibration level of the turbochargers under investigation. The global vibration level is measured according to a standardized threshold, or obtained experimentally . The wear of turbine blades occurs in global vibration level above the reference threshold. To detect the defect, the signals are interpreted with the help of signal processing methods . The signals collected from the turbochargers are stationary . There are many methods for signal processing. For the purposes of this study, Fast Fourier Transform (FFT) has been selected, for it is easy to implement and can be efficiently applied for processing stationary signals. Thus, we determined a vibration signature corresponding to the wear of the turbine blades. We found that the explosion frequency of the diesel engine does not disturb the spectra collected on the turbochargers.
Signals collected on diesel generating sets are mostly cyclostationary  . The first studies on cyclostationary signals can be traced back to the 1950s. In telecommunications, cyclostationarity received much attention, in particular since the 1980s; its use in mechanics appeared more recently, though . A power generating set is characterised by the frequency of a rotating crankshaft and the frequency of explosions in the diesel engine cylinders. Disruptions may occur when the two frequencies are overlaid. These result in random cyclic signals; in other words, these are cyclostationary signals.
A random process is strictly cyclostationary with period T, if its probability density being periodic of period T.
Period T is called cyclic period.
A random process is solely stationary, if its probability density is invariant by time translation.
Turbochargers on a diesel generator are insulated from mechanic shocks resulting from explosions in the diesel engine cylinders, which explains why the signals produced by the turbochargers are stationary. These signals can be properly processed using Fast Fourier Transform method. This method is obtained from discrete Fourier transform. Fast Fourier Transform (FFT) is an algorithm for calculating discrete Fourier transform (DFT). We selected this algorithm for its efficiency. On the one hand, it is an algorithm that makes possible filtering by altering the spectrum, and using the inverse transform (finite impulse response filter), on the other hand. A discrete Fourier transform of T size (number of samples) is given by the formula:
For example, t = 2n if t is even and t = 2n + 1 if t is odd. We arrive at the rapid Fourier transform (FFT). X(k) is then written   :
2.1. Determining Explosion Frequency in Diesel Engine
Explosion frequency is an important parameter for diesel generators since the primary source of vibration is related to this frequency. It is determined based on the crankshaft positioning and the number of cylinders in diesel engine. The frequency of explosion is given by the following formula:
with : rotation frequency of the diesel engine.
The diesel engine under study has 18 cylinders (Table 1). Explosion occurs 2 by 2, or 9 explosions per cycle. Following the formula (7), explosion frequency is 45 Hz.
Measurements were carried out on a diesel power generator at Balingue plant, belonging to the public energy utility of Mali. The instruments that have been used for measurements included a 100 mv/g-sensitivity accelerometer, a signal collector with 12,800 line capacity, and signal processing software. Measurements were made at standard measurement points (Figure 1) by fitting the
Table 1. Characteristics of the power generating set investigated.
Figure 1. Configuration of measurement points.
accelerometer at these points, while the generator was running at full capacity (11 MW). We selected 6 measurement points on the turbochargers 8 measurement points on the diesel engine, and 8 measurement points on the alternator. On each measurement point, 3 measures were performed following 3 directions: axial, radial vertical and radial horizontal.
3.1. Global Vibration Level Analysis
Tables 2(a)-7(a) show the global vibration level of the turbocharger with worn-out blades. Tables 2(b)-7(b) show the global vibration level of the turbocharger with healthy blades.
It has been noted that the whole range of the diesel engine vibration levels are below the permissible limit of 45 mm/s for the diesel side (Table 2 and Table 3). As for the alternator, the limit is 20 mm/s. All the measurements on the alternators are below this limit (Table 4 and Table 5).
As no measurement on the diesel and alternator reaches these limits (45 mm/s and 20 mm/s), the vibration status of the diesel engine and alternator is sound  .
On the other side, the maximum vibration measured on the turbochargers was 20.8 mm/s in side A (Table 6) and 22.5 mm/s in side B (Table 7) compared to a limit of 18 mm/s in the first measurement campaign. That has led us to undertake investigations in an attempt to pinpoint what was causing this abnormal vibration. After the turbochargers have been repaired, we obtained a vibration of 16.5 mm/s, at the same measurement point (Table 7).
3.2. Spectral Analysis
We can see that on the faulty turbocharger where turbine blades are worn out [Figure 2(b)], the spectrum [Figure 2(a)] is different from the spectrum [Figure 3(a)] of the healthy turbocharger [Figure 3(b)]. These spectra are obtained in frequency domain. Their occurrence is linked to the state of the turbocharger . If a break occurs, it manifests itself in a separate spectral typology. This indicates
Table 2. Vibration level of the diesel engine side A.
Table 3. Vibration level of the diesel engine side B.
Table 4. Vibration level of the alternator side A.
Table 5. Vibration level of the alternator side B.
Table 6. Vibration level of the turbocharger side B.
Table 7. Vibration level of the turbocharger side A.
that turbochargers, while part of the diesel engine, are fully insulated from the mechanical shocks originating from the diesel engine cylinders. They work like a usual rotating machine. The Fast Fourier Transform method, in frequency domain, correctly applies to turbochargers for power generating set. As a consequence, the spectral analysis enabled us to obtain relevant results. High vibration at frequency C1:3478.51 Hz has been detected in the turbine wheel. It has 39 blades and turns at 349 Hz.
4C1:13.9 kHz corresponds to almost 39 times the rotation speed of the turbine wheel (13.6 kHz). This shows that 4 out of the 39 blades are worn out. On dismantling the turbocharger, we, indeed, found that out of the 39 blades in the turbine wheel 4 were worn-out. We found that the signals collected from the diesel engine and alternator are cyclostationary and carried by explosion frequency in the diesel engine cylinders. On the other hand, the signals collected from the turbochargers are stationary and insulated from explosion frequency, at 45 Hz. This frequency is no more the dominant one. In our previous studies, the spectra collected from the diesel engine and alternator of the diesel power generators
Figure 2. Defective turbine blade.
Figure 3. Healthy turbine blade.
The measurement points on the turbocharger part were in places where the temperature was very high. This constraint has led us to repeat the same measures several times to ensure the accuracy of these measures. We found relevant results from the Fast Fourier Transform method. However, it is possible to improve these results by testing other methods. In perspective, we intend to test the time-frequency method on high power diesel generators and compare these results with those found with the Fast Fourier Transform method (FFT).
The explosion frequency in diesel engine has no impacts on the turbochargers. They work as a usual rotating machine. Therefore, it was possible to analyse the
Figure 4. Spectra of diesel engine.
Figure 5. Spectra of alternator.
signals collected with the help of Fast Fourier Transform method in frequency domain. The vibration signature changes according to the sound health or the defect in the turbocharger. On the other hand, our previous studies have shown that the vibration signature of a power generating set along the diesel part and the alternator part does not change, even with a defect, in terms of frequency domain. This vibration signature was always born by the explosion frequency in the diesel engine.
The study found that explosion frequency in the diesel engine cylinders, which disrupted the vibration signals in the diesel engine and alternator, did not impact on the vibration signals in the turbocharger.
Through experiment, we determined a vibration signal corresponding to an actual defect in the turbocharger turbine, including detecting the defect, the cause of the defect, as well as the extent and severity of the given defect (wear of 4 blades).
 Metaga, J.S., Badié, D. and Lamissa, D. (2018) Vibration Analysis-Based Diagnosis of High-Power Diesel Generator Turbocharger. International Journal of Engineering and Advanced Technology (IJEAT), 8.