# Multi-Source Information Fusion Diagnosis Method for Aero Engine
## 3 Case Study
### Information Fusion Diagnosis Analysis  
#### 3.3.1 Information Fusion Based on Bayesian Network  
Bayesian network parameter tuning is divided into two parts: DAG and CPT. The Bayesian network used in this case is constructed as shown in Figure 7. The failures of different components are regarded as independent events. The child nodes of the network are eight fault characteristic nodes, and the parent nodes are three fault cause nodes. The structure of Bayesian networks is derived from prior knowledge. Because the fault in this case occurred at the fan component, HPC and LPC are selected as the system components that indicate the cause of the fault. To simplify the modeling process, only one vibration feature and the gas path degradation parameters related to these components are included as child nodes in the diagnostic layer. Figure 5: The vibration amplitude of the four measuring points. (**a**) Amplitude of the measuring point V\({}_{11}\). (**b**) Amplitude of the measuring point V\({}_{12}\). (**c**) Amplitude of the measuring point V\({}_{ic1}\). (**d**) Amplitude of the measuring point V\({}_{ic2}\). Figure 6: The results of the degradation of each component. (**a**) Fan degradation; (**b**) low-pressure compressor degradation; (**c**) high-pressure compressor degradation; (**d**) high-pressure turbine degradation; (**e**) low-pressure turbine degradation. Figure 7: Bayesian network structure. The construction of CPT is critical to the Bayesian network. Reference [29] provides the construction method of CPT, including two cases without prior information and with prior information. First, the prior conditional probability should be defined, that is, the probability of occurrence of nodes A1, A2, and A3. Reference [30] provided a probabilistic failure analysis method, which can obtain the probability of failure of each component according to the probability of the occurrence of the bottom events. These bottom events can be regarded as the class of failure that occurs in the component. The resulting prior probabilities for the parent nodes are listed in Table 3.  
The child node parameters in Figure 7 represent continuous variables rather than discrete binary values (0 or 1). These continuous variables are modeled using Gaussian distributions to characterize their conditional probability distributions. This hybrid approach combining discrete and continuous variables constitutes what is formally termed a hybrid Bayesian network (HBN). In this paper, a Gaussian distribution is used for nodes X1-X7 to represent their continuous distribution probabilities. Considering that this case is mainly a fan failure, the relevant Gaussian distribution functions are listed as shown in Table 4. The vibration signal uses the amplitude as input, and the gas path uses the degradation parameter as input. According to the fault criteria knowledge from previous works [31; 32; 33], the mean value of flow rate degradation in a gas path system can be set as \(-\)0.05, which means a 5% increase in flow rate is considered a failure. As for vibration systems, in order to improve the speed of solutions, the amplitude of vibration in the time domain can be used as evidence of the need for fusion. Based on the existing research [34; 35], blade failure can greatly affect the time domain characteristics of vibration. The mean value of the child node probability distribution of the vibration system is set to 220 \(\upmu\)m according to the existing research results and the data characteristics of the sensor. According to reference [30], without considering prior knowledge, the same standard deviation (0.5) is obtained when the A1 state is 0 or 1. When the prior knowledge is taken into account, the probability distribution function is adjusted, enlarging the standard deviation at A1 = 0 and shrinking the standard deviation at A1 = 1. The purpose of this adjustment is to obtain the result of the component failure only if the parameter is very close to the mean value of A1 = 1.