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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|贝叶斯网络代写Bayesian network代考|Mapping the Operators in GO-FLOW Method into BNs

Generally, three types of signals are used to connect to an operator: the main input signal $S(t)$, subinput signal $P(t)$, and an output signal $R(t)$. Different operators have different logics for combining the inputs and producing the outputs. The equivalent BNs of the fourteen operators are proposed in this paper. As the equations of output signal intensity are complicated and time variant, it is hard to develop a complete equivalent DBN or BN for a GO-FLOW model. A GO-FLOW model involves with several discrete time points and some signals change at different time points. But the GO-FLOW model at one time point is a static system, it is able to be described with BN. Therefore, the developed $\mathrm{BN}$ with the proposed method in this paper is equivalent to GO-FLOW model at one time point. Defining the parameters of $\mathrm{BN}$ based on the analysis of GO-FLOW model, an equivalent $\mathrm{BN}$ can be developed at all time points. In the following, each of those fourteen different types of operators is introduced and its equivalent $\mathrm{BNs}$ is presented.

Type-21 operator describes a “good/bad” component, which has one input and one output signal line. The output signal will be present when the input signal is present and the operator is in good state. $P_{g}$ is the probability for the good state of a component that the operator describes. So, $1-P_{g}$ is the probability for the bad state of a component. Hence, the intensity of the output signal is obtained by
$$R(t)=P_{g} \cdot S(t)$$
Its equivalent $\mathrm{BN}$ is shown in Fig. 2. Node $\mathrm{S}$ denotes the input signal $\mathrm{S}$, and node $\mathrm{R}$ represents the output signal. For node $\mathrm{S}$, “Yes” and “No” denote the presence and absence of input signal, respectively. For node R, “Yes” and “No” denote the presence and absence of output signal, respectively. Conditional probability of node $\mathrm{R}$ is given in Fig. 2. According to the Bayesian inference,
$$P(R=\text { Yes })=\sum P(S) \cdot P(R=\operatorname{Yes} \mid S)=S(t) \cdot P_{g}$$

## 统计代写|贝叶斯网络代写Bayesian network代考|Auxiliary Feedwater System and Its GO-FLOW Model

To illustrate the mapping method based on the developed BNs of the operators, a case of auxiliary feedwater system of a pressurized water reactor has been selected.

As one of the engineered safety facilities, the auxiliary feedwater system acts as a heat sink to remove the decay heat from the reactor core during accident scenarios [29]. It cools down the steam generator secondary side and eventually removes the decay heat from the reactor core by a natural circulation mechanism, for example, condensing steam in nearly horizontal U-tubes submerged inside a pool [30]. Its simplified scheme is shown in Fig. 16. The system consists of two motor pumps, which take suction from a common condensate storage tank and provide auxiliary feedwater flow to steam generators. A normally closed valve is employed between the supply tank and pumps. Two identical motor pumps are used for redundancy. The outlet of each pump is connected with a normally closed check valve. Each motor pump can provide flow through successful valve opening to the steam generator. Therefore, two pumps compose a parallel system. For the successful operation of the system, it needs to supply flow to at least one steam generator.

A total of five time points are defined in the case. Time point 1 is an initial time, and no actions are taken. At time point 2 , the system starts to work and motor pump A is activated. Time point 3 is $3 \mathrm{~h}$ later than time point 2 , and time point 4 immediately succeeds time point 4 . At time point 4 , motor pump $B$ is also activated. Time point 5 is $12 \mathrm{~h}$ later than time point 4 .

According to the function and structure of the system, GO-FLOW model of the case is shown in Fig. 17. A total of 15 operators in total are used, and the sequence number is labeled in each operator. The model initiates from operator 1 , and the output line of the final operator 15 corresponds to the probability of the successful operation of the system. As shown in Fig. 17, type-25 operators are used to generate input signals at different time points. The supply tank is denoted by type- 21 operator. Control valve and two check valves are denoted by type-21 operators. For the motor pump, Type-26 operator is used to describe the motor, while type-35 operator is used to model the pump. Parameters of the all the operators are given in Table 1 .

# 贝叶斯网络代考

## 统计代写|贝叶斯网络代写Bayesian network代考|Mapping the Operators in GO-FLOW Method into BNs

Type-21 运算符描述了一个“好/坏“组件，它有一个输入和一个输出信号线。当输入信号存在且操作者处于良好状态时，输出信号将存在。 $P_{g}$ 是算子描述的组件良好状 态的概率。所以， $1-P_{g}$ 是组件不良状态的概率。因此，输出信号的强度由下式获得
$$R(t)=P_{g} \cdot S(t)$$

$$P(R=\text { Yes })=\sum P(S) \cdot P(R=\text { Yes } \mid S)=S(t) \cdot P_{g}$$

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## MATLAB代写

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