## 4 Quantitative Identification and Abnormality Alarm Strategy for Blade Crack Faults
### The Proposed Quantitative Identification Method
#### 4.1.2 Relative Energy Ratio at Second Harmonic Frequency Component  
According to the previous section, we know that when a breathing crack appears, the rotor stiffness changes twice from large to small in one rotation cycle [33; 34]. The amplitude of the second harmonic increases obviously and the phase also changed significantly [35; 36]. Hence, a quantitative identification method for blade crack fault and a new index are proposed to describe the degree of damage accurately when cracks grow. The new index is called relative energy ratio at second harmonic frequency component and expressed as \(K_{2f}\):  
\[K_{2f}=\frac{\left[A_{2f}\right]^{2}}{\sum\limits_{i=1}^{j}\left[A_{if}\right] ^{2}}\quad i=1\sim j \tag{5}\]  
Figure 11: The LLE value of the A fan No. 2H sensor.  
where \(A_{f}\) means the amplitude of the rotating frequency and \(A_{2f}\) means the amplitude of the second harmonic. Moreover, we can find that the energy of the first six order harmonic accounts for more than 98% of the total energy, so based on the amplitude of the frequency spectrum, the parameter \(j\) is selected as \(j=6\).  
The value of \(K_{2f}\) can be used to judge the degree of the damage, where \(a\) and \(b\) are thresholds that need to be decided:  
(1) \(0\leqslant K_{2f}<a:\) Normal condition, the rotor works well;  
(2) \(a\leqslant K_{2f}\leqslant b\): Incipient fault, a crack appears, but is small;  
(3) \(K_{2f}>b\): Serious fault, many cracks appear.  
During the period of August 2010 to December 2010, the rotor worked normally and we can think the reliability of this fan remained at the normal level of 0.9 during this time. The values of \(K_{2f}\) calculated from the bearing data in the horizontal direction are shown in Figure 12. According to the LLE value in Figure 11, a non-linear condition appeared after 9 December 2010. Moreover, according to the value of \(K_{2f}\) in December 2010 to March 2011 as shown in the Figure 12, the threshold value of \(a\) is preliminarily determined as 0.02. On 20 July 2011, the rotor broke apart during the process of switching from low speed to high speed (from 744 r/min to 993 r/min) and we can think that the reliability of this fan has decreased to 0 at this time. Based on the lowest reliability requirement the steel-making plant requires for safe running and the value of \(K_{2f}\) in bearing 2 from June 2011 to July 2011, the value of \(b\) is determined as 0.25 for safety's sake and the reliability of this fan has decreased below 0.5 at this time by linear mapping relationship analysis, so the parameters are determined completely.  
\[\begin{array}{l}a=0.02\\ b=0.25\end{array} \tag{6}\]  
The new index \(K_{2f}\) is introduced into the testing system and works well in the condition monitoring of the centrifugal booster fan. The results in Figure 12 could be employed to analyze the condition of No. A fan.  
Based on the proposed quantitative identification method, the abnormality alarm strategy can be obtained, and then the condition-based maintenance actions can be arranged reasonably to ensure safe and reliable operation. To sum up, the proposed quantitative identification and abnormality alarm strategy procedure of using sensor-dependent vibration data for blade crack identification in centrifugal booster fans can be summarized by the flow chart displayed in Figure 13.  
Figure 12: The results by the quantitative identification index on A fan No. 2H sensor.  
Meanwhile, the process of the proposed method and strategy for the mentioned engineering tasks in the power station can be summarized as follows:  
1. Collect the sensor-dependent running condition vibration data;
2. Pre-process this vibration data using the discrete spectrum interpolation method and STFT;
3. Compute the LLE and the relative energy ratio \(K_{2f}\).
4. Confirm the degree of blade crack fault(s) of the centrifugal booster fan;
5. Conduct the corresponding maintenance management activities based on the fault degree.