## 2 Dynamic Health Intelligent Evaluation Model
### Component Failure Probability Fuzzy Modeling
#### 2.3.1 Fuzzy Reasoning  
Fuzzy reasoning goes through three basic processes: fuzziness, fuzzy reasoning, and clearness. Fuzzification--compare input variables and membership functions to obtain membership values of each language identifier; Fuzzy reasoning--performs union operation (usually multiplication or minimization) on the membership function of the initial part to obtain the activation right of each rule, and relies on the activation right to produce the effective result of each rule; Clarity--overlay all valid results to produce a clear output. The failure probability of unit is related not only to temperature but also to the rate of change of unit time temperature. Therefore, the intelligent evaluation model algorithm proposed in this paper adopts the fuzzy reasoning decision structure with double input and single output. The double inputs are the temperature and the rate of change of temperature per unit time, and the output is the failure probability of component units. The fuzzy reasoning decision system is shown in Figure 2.  
Figure 2 shows the fuzzy reasoning system consisting of a fuzzifier, a fuzzy inference engine, a defuzzifier, and a fuzzy rule base. The double inputs to the fuzzifier are the temperature \(T^{*}\) and its difference \(\left(\frac{\Delta T}{\Delta T}\right)^{*}\) normalized by the factors \(K_{A}\) and \(K_{B}\). Considering that the actual variation range of the theoretical domain of different component elements may be different, in order to normalize the model, we uniformly adopt the standardized theoretical domain [-1, 1] and use different transformation factors to transform the practical theoretical domain. Similarly, the output \(\xi\) scaled by the factor \(K_{c}\). The transformation factor satisfies the following equation:  
\[\left\{ \begin{array}{c}T^{*}=K_{A}\Big{(}T-\frac{T_{\max}+T_{\min}}{2}\Big{)} \\ (dT/dt)^{*}=K_{B}\Big{[}(dT/dt)-\frac{(dT/dt)_{\max}+(dT/dt)_{\min}}{2}\Big{]} \end{array} \right.\]  
\[\left\{ \begin{array}{c}K_{A}=\frac{2}{T_{\max}-T_{\min}}\\ K_{B}=\frac{(dT/dt)_{\max}-(dT/dt)_{\min}}{}\end{array} \right. \tag{5}\]  
The input and output variables to the fuzzy reasoning system are characterized by the fuzzy sets, linguistic values, and associated analytical ranks shown in Table 1. In order to facilitate the formulation of fuzzy rule table, each fuzzy set is divided into 9 element levels. The subscript of the fuzzy set represents which element level the language value is related to. Each fuzzy set is defined by a Gaussian membership function shown in Figure 3. The membership functions have an overlap with each other to provide a smooth output transition between the regions. The input of fuzzy logic (temperature, temperature change rate per unit time) is not completely attributed to a certain class (fuzzy set). That is to say, there is no strict boundary between higher and higher temperatures, and fuzzy theory uses membership degree to measure the degree of attribution of variables to each set. The process of transforming the input of logic into the membership of each fuzzy set is called fuzzification. Figure 2: Fuzzy reasoning system. The failure probability of a component is not only related to temperature, but also related to electrical stress, mechanical stress, fatigue and other factors. Some component failure probabilities are mainly affected by temperature, while some component temperatures have less influence on their failure probability. Therefore, the specific dependence of the failure probability of components of different functions on temperature determines the range of failure probability of the actual component. We also use the standardization domain for generalization transformation. Considering the non-negative nature of failure probability, the corresponding failure probability uses the standardization domain [0, 1], its fuzzy set and fuzzy language as Table 1(b).