**2.3 Signal processing with a priori information**

Next, consider the processing of vibration signals received from the stand SP-180 M (**Figure 10**). This bench allows you to test all sizes and types of modern and advanced bearings used in aircraft gas turbine engines. The rotational speed at the maximum mode of the inter-rotor and inter-shaft bearings installed between the shafts of the rotors of high and low pressure of the engine, rotating in the parallel direction, is 3000 rpm. Therefore, on the stand, the operation of the bearings is modeled at speeds from 0 to 3000 rpm [13].

Stand SP-180 M allows us to place sensors directly on the outer or inner rings of the bearing [14]. As a rule, it is installed by gluing on a non-rotating outer ring. The results obtained make it possible to judge the condition of the bearings by the generated vibrations measured by the vibration sensors (**Figure 11**).

GTE tests are also being carried out on the high-pressure rotor of which was prepared with additional vibration sensors on the high-pressure compressor support. The results obtained are compared with information from vibration sensors located on the outer casing of the engine (**Figure 12**).

**Figure 10.** *External view of the stand SP-180 M.*

*Principles of Diagnosing: The Technical Condition of the Bearings of the Gas Turbine… DOI: http://dx.doi.org/10.5772/intechopen.108400*

#### **Figure 12.**

*Scheme and appearance of vibration sensors installed inside the engine, on the support of the GTE high-pressure compressor.*

**Figure 13** shows the fragments of vibration signals of the bearings received from SP-180 M. One bearing is good and the other two are defective. We will process the vibration signals using the above method.

From a priori information about the signals *S*1ð Þ*t* , *S*2ð Þ*t* , and *S*3ð Þ*t* **,** it is known that the rotation frequency of the separator is 23 Hz, the frequency of rotation of the rolling elements is 329 Hz, the frequency of rolling of the rolling elements along the outer ring is 529 Hz, and the frequency of rolling of the rolling elements along the inner ring is 612 Hz. In this regard, before selecting the standard, we will perform a preliminary filtering according to the scheme, which is shown in **Figure 14**.

In accordance with the scheme of **Figure 14**, the signal *S*1ð Þ*t* of a healthy bearing is prefiltered, and each of the filters is a bandpass filter with the center frequency of the

#### **Figure 13.**

*Recordings of vibration signal of bearings: a) correct operation, b) damage—medium risk, and c) damage—point large and small.*

passband corresponding to the frequency component from the prior knowledge. It is also worth noting that the filtering procedure is performed separately, and the signal is summed at the output of each of the filters. The transfer coefficients of the bandpass filters are shown in **Figure 15**.

Next, a filter was designed according to the formula (7), the frequency response of which is shown in **Figure 16**. The frequency response peaks at the given a priori frequencies.

As a result, we have the following rhythmograms and scatterograms (**Figures 17** and **18**) and statistical evaluation **Table 2.**

**Table 2** shows that the standard deviation value of the rhythmogram of a serviceable bearing is more than one and a half times lower than the standard deviation value of bearings with defects, which, in turn, can be an additional diagnostic feature. *Principles of Diagnosing: The Technical Condition of the Bearings of the Gas Turbine… DOI: http://dx.doi.org/10.5772/intechopen.108400*

**Figure 15.**

**Figure 16.** *Quasi-matched filter and Fourier spectrum of a good bearing.*

The median of the signal *S*1ð Þ*t* record has a slight deviation from the numerical value of the mathematical expectation, while the deviation of the median from the average value for signals *S*2ð Þ*t* and *S*3ð Þ*t* above. An approximately similar picture is observed in the analysis of modes. This indicates that the distribution of outliers relative to the mean value is close to symmetric for *S*1ð Þ*t* . For signals *S*2ð Þ*t* and *S*3ð Þ*t* emissions down (jerks and bumps) prevail [15].
