## 1 Introduction  
Blast furnace gas (BFG) is a byproduct of iron-making. With the great expansion of the iron and steel industry, the production of BFG during iron-making has increased remarkably [1]. However, blast furnace gas is characterized in low calorific value, difficulty to burn and combustion instability as a power fuel [2], so how to deal effectively with blast furnace gas is a problem that puzzles iron and steel enterprises. In recent years, many enterprises have taken to use BFG to generate electricity in order to save energy and improve benefits. Centrifugal booster fans are important pieces of equipment which are used to pressurize BGF and make sure it can go into the furnace safely and combust stably. Faults occurring on the centrifugal booster fan may lead to accidents such as unstable combustion in the furnace, blow outs, downtime, and potentially huge economic losses. Blade crack faults (BCFs) are among the typical faults in centrifugal booster fans. Different cracks arise after long running due to the resonance, decreased anti-fatigue capability because of manufacture problems, installation issues or the work conditions [3]. This may result in blades breaking off and the unit being damaged. For a rotor system, the stiffness of the shaft would display cyclical behavior once blade cracks occur [4], and the dynamic response signal will show obvious non-stationary characteristics. Fault diagnosis for blade crack faults is a difficult problem that has drawn the attention of top scholars and outstanding engineers worldwide [5; 6; 7; 8]. Lots of related studies have been reported in important journals [9; 10; 11]. These researches place emphasis on the following aspects: first, the method based on finite element tries to model the cracked rotor and analyze the fracture mechanisms and the effect on the structural dynamic properties [12; 13; 14]. This method can provide a theoretical basis for the blade damage identification method based on vibration signals. Second, the method combining the finite element modeling with the signal processing makes use of the finite element method to analyze the dynamic responses of the cracked rotor [15]. Then a signal processing method such as the wavelet transform is applied to analyze the dynamic response and lock the position and size of the crack damage. However, the practical engineering of these methods, especially for blade crack fault detection under operation conditions, should be studied further. On-line and off-line condition monitoring systems have been widely used for important rotating machinery [16; 17; 18; 19; 20]. Vibration signals can be acquired effectively in various industrial fields [21; 22; 23; 24]. The key issue is how to extract the characteristics of the blade crack faults using appropriate signal analysis methods [25]. In this paper, operation condition information is monitored and collected in a timely way based on a condition monitoring and fault diagnosis system for centrifugal booster fans. Firstly, aiming at the problem of energy leak in FFT, amplitude and phase can be accurately estimated by an discrete spectrum interpolation method [26; 27]. The short time Fourier transform (STFT) can effectively pick out the non-stationary components in vibration signals [28]. The discrete spectrum interpolation method and STFT are integrated in the testing system. They are used to extract the features of the blade cracks of generator centrifugal booster fans in a certain iron and steel group's power plants. Finally, for the purpose of quantitative identification and abnormality alarm for blade crack faults, a quantitative identification and abnormality alarm strategy based on compound indexes including the largest Lyapunov exponent (LLE) [29; 30] and relative energy ratio at the second harmonic frequency component is proposed in this paper. The proposed method is applied to an accident caused by blade crack faults using historical data. The results demonstrate that this method could quantitatively identify blade cracks in booster fans successfully.