Fault Diagnosis Using Bond Graphs in an Expert System

Abstract

A fault diagnosis method using bond graphs in an expert system is proposed for a reactor coolant system. Firstly, the time causality graph and the variable relationship graph are derived from the bond graph. Secondly, the fault signature matrix is obtained by combining the change relationship of fault parameters. Finally, the fault signature matrix is used as the rule of the inference engine design in the expert system for fault diagnosis. In this paper, the key equipment of the reactor coolant system is used to verify the fault diagnosis method of the bond graph expert system, and the path reasoning relationship between alarms is obtained, which can accurately obtain the deep knowledge required by the operators. A new idea for fault diagnosis in a nuclear power plant’s expert system is provided by this method.

1. Introduction

The safety of nuclear power systems is regarded as the focus of nuclear power application. Fault diagnosis technology is highly valued in nuclear power plants. As a branch of artificial intelligence, expert systems have been widely used with high efficiency and accuracy. A nuclear power plant system is complex, which produces a large amount of data during its life, and the coupling relationship between various components is strong. Therefore, it is difficult to acquire expert knowledge, and it is impossible to quantitatively describe the fault degree and state of the system.

Bond graph theory is a graphical representation used to describe the energy structure and power transfer in engineering systems. It was proposed by H. M. Paynter of Massachusetts Institute of Technology in 1959. Subsequently, D. C. Karnopp and others further developed and improved it to form a systematic theoretical system [1]. Generally, a bond graph is used alone or in combination with other graphical models, functional observers, a statistical decision procedure, etc., to realize the fault diagnosis of mechanical components used in intermediary cooling systems of power plants [2], DC motors [3], stringing machines [4], six-tank systems [5], among others. In addition to using bond graph theory to establish the system fault model to realize equipment state identification and fault diagnosis, Sellami et al. established bond graph linear fractional transformation models of an accelerometer based on fault detection and isolation algorithms to minimize false alarms and delays in fault detection [6]. Lounici et al. proposed a hybrid bond graph model based on interval uncertainty, which overcomes the limitations of existing methods and improves the robustness of fault diagnosis for a controlled two-tank hybrid system [7]. In recent years, some scholars have combined bond graph theory with Gaussian mixture models, similarity techniques, finite state machine, optimized extreme learning machine, and other intelligent algorithms to realize the function of state and failure prediction [8,9]. These applications of the bond graph are based on the establishment of the analytical model of the system. However, for systems with complex dynamic models, it is difficult to establish analytical models, so it is impossible to establish quantitative bond graph models, which is also its shortcoming.

An expert system is a structured computer program with a large amount of knowledge and experience. It solves complex problems that need human experts to solve through reasoning and judgment [10]. In order to solve various problems, such as excessive manpower input, high risk of human failure, time-consuming data processing, and low information level of test means, an intelligent expert system for a cold functional test of an open reactor vessel was developed by Liao et al. The results have been successfully applied to several CPR1000 nuclear power plants and are of great significance [11]. Zhang et al. studied the fault diagnosis method for a pneumatic control valve. A fault diagnosis approach for pneumatic control valves based on a modified expert system was proposed by combining the particle swarm optimization (PSO) algorithm with expert rules. The modified method improves the accuracy and effectively reduces the false negative rate [12]. Xiao et al. propose a new intelligent fault diagnosis method for rapier looms based on the fusion of an expert system and a fault tree. Compared with the current intelligent diagnosis algorithm, the algorithm structure is simplified, which provides a theoretical basis for the broad application of intelligent fault diagnosis on rapier looms [13]. An expert system methodology based on a decision tree is proposed by Tahi et al., who exploit the information provided by the vibration signal time indicators. The methodology has been validated on an experimental test bench with five types of operating states (the good condition of the machine, the misalignment, the bearing defects, the unbalance, and the combination between the bearings and the unbalance) [14]. The acquisition of expert knowledge, however, is the inherent bottleneck of an expert system. Therefore, in the research on the application of expert systems described above, much work has been done in expert knowledge.

The characteristics of faults can be identified and diagnosed by knowledge-based diagnostic methods, but the composition of a knowledge system in an expert system is often the shallow knowledge in expert consciousness, that is, the knowledge fed back according to the phenomenon of the equipment or system. Therefore, the physical process inside each equipment component and the transfer and conversion relationship between variables cannot be reflected. It can only diagnose the faults contained in shallow knowledge, and cannot accurately describe fault phenomena invisible to human perception. These problems can be solved by using the bond graph method for inference engine modeling. In this paper, the inference engine of an expert system is designed by using a qualitative bond graph model to realize fault inference and diagnosis for reactor coolant systems. It can not only avoid the establishment of an accurate analytical model of the system, but it also reflects changes in the parameters, which is the deep knowledge of the system. This approach also provides a new way of acquiring knowledge for expert systems.

2. Materials and Methods

2.1. Bond Graph Model

In this paper, the zero junctions and one junctions of bond graphs were used to characterize the energy transfer process inside the equipment. The 0-junction is shown in Figure 1a and the relationship between variables in the 0-junction is shown in Formula (1). The 1-junction is shown in Figure 1b and the relationship between variables in the 1-junction is given in Formula (2). A two-port transformer is shown in Figure 1c and the relationship between variables in a two-port transformer is given in Formula (3). A two-port gyrator is shown in Figure 1d, and the relationship between variables in the two-port gyrator is given in Formula (4):

e₁ = e₂ = ⋯ = e_n
 f₁ = f₂ + ⋯ + f_n

(1)

e₁ = e₂ + ⋯ + e_n
 f₁ = f₂ = ⋯ = f_n

(2)

e₁ = m × e₂
 f₂ = m × f₁

(3)

e₁ = γ × f₂
 e₂ = γ × f₁

(4)

where m and γ are two non-negative real parameters.

Causal stroke is shown in Figure 2.

Figure 2a shows that the effort variable is the cause and the flow variable is the result. Figure 2b shows that the effort variable is the result and the flow variable is the cause.

For other basic knowledge of bond graphs, please refer to reference [15].

2.2. Research Method

The reactor coolant system is shown in Figure 3. The time causality graph and variable relationship graph are extracted, and the fault signature matrix (FSM) for each equipment component of the system is obtained. Then, the expert system inference engine is designed by combining the fault signature matrix and variable relationship graph to diagnose typical faults of the reactor coolant system. The proposed methodology structure is shown in Figure 4.

The qualitative bond graph fault diagnosis method for nuclear power systems proposed in this paper can analyze the internal characteristics of each fault, provide a deeper understanding for fault diagnosis, and solve the problem that only specific faults can be diagnosed in the expert system. At the same time, a novel way of knowledge acquisition is also proposed. The analysis of the impact of faults on equipment or the system provides a new idea to avoid or mitigate the harm of faults.

3. Bond Graph Model of Key Equipment in the Reactor Coolant System

The reactor coolant system consists of the reactor, a pressurizer, two steam generators, four reactor coolant pumps, and pipelines and valves between equipment components. The processes for bond graph modeling of the system’s components follow.

3.1. Pressurizer

3.1.1. Simplified Conditions

In the modeling process, the pressurizer is divided into three control volumes. Among them, the first control volume is the fluctuation zone; the coolant has just entered the pressurizer. The second control volume is a saturated liquid region; the coolant has been fully mixed with the liquid inside the pressurizer. The third control volume is the gaseous zone, and it is also the key area for the pressurizer to control the pressure. The modeling process is simplified as follows:

• Water is treated as incompressible fluid;
• The pressure inside the liquid zone is the same throughout, and the pressure inside the gas zone is the same throughout;
• The volume in the pressurizer remains unchanged;
• Heat dissipation through the pressurizer wall is not considered;
• The instantaneous transfer of matter between regions becomes a parameter that controls volume after the transfer;
• Volume change in vapor space inside the pressurizer is caused by pressure change, while liquid-space pressure change is mainly caused by coolant parameter change.

3.1.2. Schematic Diagram and Simplification

The internal energy and mass transfer principle and simplification of the pressurizer are shown in Figure 5 [16].

As can be seen from Figure 5b, the input of control volume 1 is coolant flow (positive at inflow, negative at outflow, as follows), and coolant flows through control volume 1 to control volume 2. The input of control volume 2 includes the gas–liquid mixture brought by control volume 1, the mass flow of condensate on the inner surface of the pressurizer with control volume 3 entering control volume 2, the mass flow of condensate on the external surface of the spray droplet, and the flow of spray water. The input of control volume 3 is the interface mass transfer flow of control volume 2, and the output is the mass flow of condensate on the inner surface of the pressurizer released to control volume 2, the mass flow of condensate on the external surface of the spray droplet, and the flow released to the atmospheric environment through the safety valve.

3.1.3. Drawing Bond Graphs

The effort and flow variables are determined as pressure and mass flow. The bond graph model of each control volume is shown in Figure 6a–c [16].

Since e₇, e₉, and f₇, f₉ do not increase in multiples, “TF” is only used in Figure 6c to indicate that the parameter values in control volume 2 and 3 are different in the process of dynamic change, and there is no meaning of multiples.

The meaning of the physical quantities shown in Figure 6 is given in

Table 1. The meaning of the physical quantities shown in Figure 6.

	Codes	Physical Quantities	Unit	Paraphrasing
Control volume 1	e1	PSU	MPa	Fluctuating water pressure into the pressurizer
	e2	P1	MPa	Pressure in control volume 1
	e3	PBW	MPa	Pressure of bubbles and water leaving control volume 1
	f1	WSU	kg/s	Fluctuating water flow
	f2	W1	kg/s	Flow rate variation in control volume 1
	f3	WBW	kg/s	Flow of air bubbles and water leaving control volume 1
	Q1	Q1	kW	Heat of electric heater in control volume 1
Control volume 2	e4	PSC	MPa	Condensate pressure on the outer surface of spray droplets
	e5	PWC	MPa	Condensate pressure on inner surface of pressurizer
	e6	P2	MPa	Pressure in control volume 2
	e7	PFL	MPa	Interface mass transfer pressure in control volume 2
	e8	PSP	MPa	Sprinkling water pressure in control volume 2
	f4	WSC	kg/s	Mass flow rate of condensate on external surface of spray droplets
	f5	WWC	kg/s	Condensate mass flow rate on inner surface of pressurizer
	f6	W2	kg/s	Flow rate variation in control volume 2
	f7	WFL	kg/s	Interface mass transfer flow in control volume 2
	f8	WSP	kg/s	Spray water flow in control volume 2
	Q2	Q2	kW	Heat of electric heater in control volume 2
Control volume 3	e9	P’FL	MPa	Interface mass transfer pressure in control volume 3
	e10	P’WC	MPa	Condensate outflow control volume 3 pressure on internal surface of pressurizer
	e11	P’SC	MPa	Condensate outflow control volume 3 pressure on external surface of spray droplets
	e12	Prsv	MPa	Safety valve release pressure
	e13	P3	MPa	Pressure in control volume 3
	f9	W’FL	kg/s	Interface mass transfer flow in control volume 3
	f10	W’WC	kg/s	Condensate outflow control volume 3 mass flow rate on internal surface of pressurizer
	f11	W’SC	kg/s	Condensate outflow control volume 3 mass flow of spray droplet
	f12	Wrsv	kg/s	Safety valve flow
	f13	W3	kg/s	Flow rate variation in control volume 3

.

3.2. Steam Generator

3.2.1. Simplified Conditions

In the modeling process, the secondary side of the steam generator is divided into three control volumes. Among them, V_D control volume is the steam space above the liquid level, Vs control volume is the steam space below the liquid level, and V_W control volume is the water space below the liquid level. Simplifications in the modeling process follow:

• Heat transfer across heat transfer tubes is assumed uniform;
• The pressure in the steam generator is the same throughout;
• Both tube-side and shell-side are incompressible fluid;
• Only radial heat transfer is considered;
• Thermophysical parameters for each control volume are stored at the central node.

3.2.2. Schematic Diagram and Simplification

The principle and simplified diagram of mass and energy flow in the steam generator are shown in Figure 7.

It can be seen from Figure 7c that the input of the V_W control volume is the secondary-side water flow, and the output is the discharge flow of the steam generator and the vaporization rate of the liquid water under the liquid level. The input of the Vs control volume is the vaporization rate of liquid water under the liquid level, and the output is the amount of steam entering the steam space per unit time through the liquid level. The input of the V_D control volume is the amount of steam entering the steam space through the liquid level during unit time, and the output is the steam yield.

The mass exchange and energy transfer of the steam generator coexist. Figure 7d and Figure 7e show a section of the steam generator tube. The heat is transferred to the inner wall of the steam generator tube through convective heat transfer, and the heat conduction of the tube wall is transferred to the outer wall, and then transferred to the secondary fluid of the steam generator through convective heat transfer. Variables h_i, λ, and h₀ refer to the convective heat transfer coefficient inside the steam generator tube, the thermal conductivity of the steam generator tube, and the convective heat transfer coefficient outside the steam generator tube, respectively. The physical process of the primary side of the steam generator is shown in Figure 7b.

3.2.3. Drawing Bond Graphs

The effort variable and flow variable were determined as pressure and mass flow, respectively. The bond graph model of each control volume is shown in Figure 8.

The bond graph model of the steam generator is developed based on its internal physical process, which is mainly manifest as the transmission and change in pressure and mass flow in each control volume. Heat transfer is also involved in the steam generator. The temperature is set as an effort variable, and the heat flow is set as a flow variable. The bond graph model of the heat transfer process of the steam generator is shown in Figure 9. Because there are few faults that can be diagnosed in the process of heat transfer (just related to thermal resistance), only the bond graph model of the heat transfer process is established, which shows that this method is suitable for the heat transfer process of the steam generator; it is not designed into the inference engine.

The meaning of the physical quantities shown in Figure 8 and Figure 9 is given in

Table 2. The meaning of physical quantities shown in Figure 8 and Figure 9.

	Codes		Physical Quantities	Unit	Paraphrasing
Primary side of steam generator	e14		Pin	MPa	Primary inlet pressure
	e15		ΔP	MPa	Primary side average pressure
	e16		Pout	MPa	Primary outlet pressure
	f14		Win	kg/s	Primary inlet flow
	f15		ΔW	kg/s	Primary side flow changes
	f16		Wout	kg/s	Primary outlet flow
Secondary side of steam generator	VW control volume	e17	P1	MPa	Feedwater pressure
		e18	ΔP’	MPa	Pressure difference between feedwater and steam generator
		e19	P2	MPa	Steam generator pressure
		e20	PVW	MPa	VW control volume pressure
		e21	PS	MPa	Evaporation of liquid water into steam pressure
		e22	Pξ	MPa	Steam generator blowdown pressure
		f17	W1	kg/s	Feedwater flow in tube
		f18	W’	kg/s	Flow rate corresponding to ΔP’ pressure difference
		f19	W2	kg/s	Feedwater flow in steam generator
		f20	WVW	kg/s	VW control volume flow rate variation
		f21	WS	kg/s	Evaporation rate of liquid water into steam
		f22	Wξ	kg/s	Steam generator blowdown flow
		f*	W*	kg/s	Primary side into VW control volume flow
		E1	E1	kW	VW control volume primary side transfer to secondary side energy
	VS control volume	e23	PVS	MPa	VS control volume pressure
		e24	PD	MPa	Steam pressure per unit time into vapor space above liquid level
		f23	WVS	kg/s	VS control volume flow rate variation
		f24	WD	kg/s	Steam flow per unit time into vapor space above liquid level
		E2	E2	kW	VS control volume primary side transfer to secondary side energy
	VD control volume	e25	PVD	MPa	VD control volume pressure
		e26	Pfh	MPa	Steam pressure
		f25	WVD	kg/s	VD control volume flow rate variation
		f26	Wfh	kg/s	Steam production
Steam generator heat transfer process	e27		Tp	K	Primary side fluid temperature of steam generator
	e28		Thi	K	Temperature loss of convection heat transfer in inner wall of steam generator tube
	e29		Tin	K	Internal wall temperature of steam generator tube
	e30		Tλ	K	Temperature loss through steam generator tube
	e31		Tout	K	Outer wall temperature of steam generator tube
	e32		Tho	K	Temperature loss of convection heat transfer in outer wall of steam generator tube
	e33		Ts	K	Secondary side fluid temperature of steam generator
	e34		Tall	K	Total temperature loss in heat transfer process
	f27		qp	J/s	Primary side heat flow
	f28		qhi	J/s	Heat flow in convection heat transfer process of steam generator tube inner wall
	f29		qin	J/s	Heat flow through inner wall of steam generator tube
	f30		qλ	J/s	Heat conduction flow of steam generator tube
	f31		qout	J/s	Heat flow through the outer wall of steam generator tube
	f32		qho	J/s	Heat flow in convection heat transfer process of steam generator tube outer wall
	f33		qs	J/s	Secondary side heat flow
	f34		qall	J/s	Total heat flow in heat transfer process

.

3.3. Reactor Coolant Pump

3.3.1. Simplified Conditions

In the modeling process, the reactor coolant pump is divided into three parts, namely, the motor module, mechanical module, and hydraulic module. Each module is modeled separately and then connected into a complete bond graph model for the reactor coolant pump. The simplified conditions in the modeling process follow:

• Resistance and inductance are considered in the circuit of the reactor coolant pump motor;
• The change in potential energy in the reactor coolant pump is not considered;
• The medium fault of rotor misalignment is uniformly attributed to mechanical friction.

3.3.2. Schematic Diagram and Simplification

The principle and simplified diagram of internal mass and energy flow of the reactor coolant pump are shown in Figure 10.

In Figure 10a, A is the reactor coolant pump inlet and B is the reactor coolant pump outlet.

As can be seen from Figure 10b, the reactor coolant pump is divided into three modules: motor module, mechanical module, and hydraulic module. The motor module includes the resistance and inductance connection with the reactor coolant pump circuit. The mechanical module includes the idler flywheel, motor rotor and stator, and shaft seal. The hydraulic module includes the inlet fluid, impeller, and outlet fluid.

3.3.3. Drawing Bond Graphs

The effort and flow variables of the motor module are voltage and current, the effort and flow variables of the mechanical module are torque and angular velocity, and the effort and flow variables of the hydraulic module are pressure and mass flow. The bond graph of each module is shown in Figure 11.

The meaning of physical quantities shown in Figure 11 is given in

Table 3. The meaning of physical quantities shown in Figure 11.

	Codes	Physical Quantities	Unit	Paraphrasing
Motor part	e35	Ua	V	Supply voltage
	e36	UR7	V	Resistance voltage
	e37	Ue	V	Motor voltage
	e52	UL	V	Induction voltage
	f35	Ia	A	Loop current
	f36	IR7	A	Resistance current
	f37	Ie	A	Motor current
	f52	IL	A	Inductor current
mechanical part	e38	Me	Nm	Motor torque
	e39	MR	Nm	Mechanical friction dissipation torque
	e40	M	Nm	Effective torque of hydraulic part
	e51	MI	Nm	Inertia flywheel torque
	f38	ωe	rad/s	Motor angular velocity
	f39	ωR	rad/s	Mechanical friction angular velocity
	f40	ω	rad/s	Angular velocity of hydraulic part
	f51	ωI	rad/s	Inertia flywheel angular velocity
Hydraulic part	e41	Pe	MPa	Pressure provided by motor
	e42	PR9	MPa	Loss pressure of shaft seal
	e43	Pl	MPa	Applied to fluid pressure
	e44	Plo	MPa	Pressure of fluid leaving impeller
	e45	Pout	MPa	Pressure of fluid leaving pump
	e46	PR12	MPa	Pump outlet loss pressure
	e47	PR11	MPa	Loss pressure of impeller
	e48	PR10	MPa	Pump inlet loss pressure
	e49	Pin	MPa	Pressure of fluid entering pump
	e50	Pli	MPa	Pressure of fluid entering impeller
	f41	We	kg/s	Flow provided by motor
	f42	WR9	kg/s	Loss flow of shaft seal
	f43	Wl	kg/s	Applied to fluid flow
	f44	Wlo	kg/s	Flow of fluid leaving impeller
	f45	Wout	kg/s	Flow of fluid leaving pump
	f46	WR12	kg/s	Pump outlet loss flow
	f47	WR11	kg/s	Loss flow of impeller
	f48	WR10	kg/s	Pump inlet loss flow
	f49	Win	kg/s	Flow of fluid entering pump
	f50	Wli	kg/s	Flow of fluid entering impeller

.

3.4. Reactor

3.4.1. Simplified Conditions

In the reactor, the main form of energy transfer is heat transfer. Therefore, only the temperature transfer is considered in the reactor modeling process, which can be applied to most reactor failure processes. The specific simplified conditions follow:

• The fuel pellets are considered as cylinder heat conduction with an internal heat source;
• The coolant temperature in the reactor is considered as the average coolant temperature;
• Heat flow is constant in the process of heat transfer.

3.4.2. Schematic Diagram and Simplification

The simplified section diagram of the reactor fuel rod is shown in Figure 12.

Figure 12 shows that the internal structure of the fuel rod consists of the fuel pellet, air gap, and cladding. The fuel pellet is a cylinder with an internal heat source, which transmits heat to the inner surface of the cladding through air-gap heat conduction, and the cladding heat is transmitted by conduction to the reactor coolant.

3.4.3. Drawing Bond Graphs

According to Figure 12, the bond graph model of the reactor heat transfer process is established by setting the effort and flow variables as temperature and heat flow, as shown in Figure 13.

The meaning of physical quantities shown in Figure 13 is given in

Table 4. The meaning of physical quantities shown in Figure 13.

Codes	Physical Quantities	Unit	Paraphrasing
e53	Tri	K	Center temperature inside fuel pellets
e54	Trod	K	Conduction loss temperature of fuel pellets
e55	Tro	K	Surface temperature of fuel pellets
e56	Tg	K	Conduction loss temperature of air gap heat
e57	Tci	K	Internal surface temperature of fuel rod cladding
e58	Tc	K	Conduction loss temperature of fuel rod cladding
e59	Tco	K	External surface temperature of fuel rod cladding
e60	Tl	K	Convective heat transfer loss temperature
e61	Tavg	K	Coolant average temperature
f53	qri	W	Internal heat flow of fuel pellets
f54	qrod	W	Conduction heat flow of fuel pellets
f55	qro	W	Surface heat flow of fuel pellets
f56	qg	W	Conduction heat flow of air gap heat
f57	qci	W	Internal surface heat flow of fuel rod cladding
f58	qc	W	Conduction heat flow of fuel rod cladding
f59	qco	W	External surface heat flow of fuel rod cladding
f60	ql	W	Convective heat transfer heat flow
f61	qavg	W	Coolant heat flow

.

4. Time Causality Graph and Variable Relationship Graph of the Reactor Coolant System

A time causality graph (TCG) is a directed graph with system variables as nodes, which can characterize the relationship between variables in the system. The path from one variable to another in the TCG corresponds to a causal path in the bond graph. The causal path of the bond graph refers to a group of keys in the same direction through which the fault signature matrix of the system can be obtained [17]. Usually, the TCG is used to derive the fault hypothesis set in qualitative fault diagnosis [18,19,20].

The time causality graph is the pretreatment of a bond graph, and the variable relationship graph is obtained on the basis of the time causality graph. Although the time causal graph can represent the causal relationship between variables, and it is easy to extract key information from the bond graph, its representation method is not easy to distinguish in the modeling process. Therefore, transforming the time causality graph, which is not easy to distinguish, into the variable relationship graph can reflect the relationship between the variables and provide a theoretical basis for the variation in the coefficients in the fault signature matrix.

Through the bond graph, the input and output of each control volume are determined, and the corresponding TCG is drawn. Through the TCG, the mutual influence of each parameter can be determined, and then the variable relationship graph between parameters can be drawn.

The time causality graph and the variable relationship graph represent the influence relationship between coefficients: “+1” represents a positive correlation, “−1” represents a negative correlation, “=” represents an equality, C_iS (i = 1,2,3) represents the influence-of-effort variable on the flow variable caused by volume change, C_iS⁻¹ (i = 1,2,3) represents the influence of the flow variable on the effort variable caused by volume change, and R_i (i = 1,2,3) represents the resistance component, which refers to the effect of resistance on the system.

4.1. Pressurizer

Referring to Figure 6, the TCG of the pressurizer is obtained, as shown in Figure 14 [16].

The variable relationship graph for the pressurizer is shown in Figure 15.

4.2. Steam Generator

Since the physical process of the primary side of the steam generator is simpler than the secondary side, it is of no practical significance to list the time causality graph. Therefore, this paper only shows the time causality graph for the secondary side of the steam generator.

Referring to Figure 8, the TCG and the variable relationship graph of the steam generator are obtained, as shown in Figure 16 and Figure 17.

4.3. Reactor Coolant Pump

Referring to Figure 11, the TCG and the variable relationship graph of the reactor coolant pump are obtained, as shown in Figure 18 and Figure 19. LS represents the differential relationship between the inductive current and the voltage in the motor system. The relationship is shown in Formula (5). JS represents the differential relationship between the flywheel angular velocity and the torque in the mechanical system. The relationship is shown in Formula (6).

$$U\left(t\right)=L\frac{di\left(t\right)}{dt}$$

(5)

$$M\left(t\right)=J\frac{d\omega \left(t\right)}{dt}$$

(6)

where U(t) is voltage, L is the inductance coefficient, i(t) is current, M(t) is torque, J is rotational inertia, and ω(t) is angular velocity.

4.4. Reactor

Referring to Figure 13, the TCG and the variable relationship graph of the reactor are obtained, as shown in Figure 20 and Figure 21.

5. Fault Signature Matrix

5.1. Typical Faults in the Reactor Coolant System

Typical faults of the reactor coolant system’s equipment are shown in

Table 5. Typical faults of the reactor coolant system’s equipment.

Equipment Type	Typical Failure
Pressurizer	Immersion-type heater inadvertent turned off or failure
	Immersion-type heater inadvertent turned on
	Spray valve inadvertent turned off or failure
	Spray valve inadvertent turned on
	Safety valve inadvertent turned off
	Safety valve inadvertent turned on (depressurization accident)
Steam generator	Steam generator tube rupture
	Feedwater regulating valve inadvertent open
	Feedwater regulating valve inadvertent close
Reactor coolant pump	Motor damage
	Mechanical friction
	Shaft seal failure
	Vapor corrosion
Reactor	Cladding damage
	Inadvertent CR rod insertion
	Inadvertent CR rod withdrawal

.

The reason why these faults are selected for diagnosis is that these faults are typical faults that may occur in various parts of the reactor coolant system with high frequency and great influence, so modeling and diagnosis are of engineering significance. The variable causality graph obtained by the bond graph can clearly determine the occurrence conditions of each fault and the impact on the internal equipment after the occurrence.

5.2. Establishment of the Fault Signature Matrix

The variable relationship graph reflects the relationship between the variables, while the fault signature matrix reflects the changes in the parameters under the fault condition. When a fault occurs, one or more typical signatures are selected as input, and the changes in other fault signatures can be found by the variable relationship graph. The change trend of this signature is developed into the fault signature matrix, which is the ultimate goal of fault analysis using the bond graph.

It can be seen from the variable causality graph that the relationship between variables is very complex. In the huge reactor coolant system of a nuclear power plant, it may occur that several parameters change at the same time, and it is impossible to determine the resulting change in the parameters. Therefore, this paper used “*” to represent the main change parameters in the fault signature matrix. Only focusing on the main influence of parameters can judge their changes. First, the variables directly affected by the fault are judged. Then, the change trend of a certain variable is marked. Finally, the change trends of other related variables are determined by referring to the corresponding variable relationship graphs (Figure 15, Figure 17, Figure 19 and Figure 21). The fault signature matrix for each equipment component is shown in

Table 6. The fault signature matrix of the pressurizer.

Failure Modes	f9	f10	f11	f12
Immersion-type heater inadvertently turned off or failure	0	—	—	—
Immersion-type heater inadvertently turned on	+1	—	—	—
Spray valve inadvertently turned off or failure	—	0	0	—
Spray valve inadvertently turned on	—	+1	+1	—
Safety valve inadvertently turned off	—	+1	+1	0
Safety valve inadvertently turned on (depressurization accident)	—	+1	+1	+1

,

Table 7. The fault signature matrix of the steam generator.

Failure Modes	e17	e18	e19	f17	f18	f19	f20	f21	f22	f *	f23	f24	f25	f26
Steam generator tube rupture	—	—	—	—	—	—	+1	+1 *	—	+1 *	+1	+1 *	−1	+1
Feedwater regulating valve inadvertently open	—	—	—	+1	+1	+1	+1 *	−1 *	—	—	−1	−1 *	−1	−1
Feedwater regulating valve inadvertently close	—	—	—	−1	−1	−1	−1 *	+1 *	—	—	+1	+1 *	+1	+1
High feedwater pressure	+1	+1	—	+1	+1	+1	+1 *	−1 *	—	—	−1	−1 *	−1	−1
Low feedwater pressure	−1	−1	—	−1	−1	−1	−1 *	+1 *	—	—	+1	+1 *	+1	+1

,

Table 8. The fault signature matrix of the reactor coolant pump.

Failure Modes	e38		e39	e40		e51	f38	f39	f40	f51
Motor damage	−1 *		−1	−1		−1	−1 *	−1	−1	−1
Mechanical friction	—		—	−1		—	—	—	—	—
Failure modes	e41	e42	e43	e44	e45	e46	e47	e48	e49	e50
Shaft seal failure	—	+1 *	−1	−1	−1	−1	—	—	—	—
Vapor corrosion	—	—	—	−1	−1	−1	+1 *	—	—	—
Failure modes	f41	f42	f43	f44	f45	f46	f47	f48	f49	f50
Shaft seal failure	—	—	—	—	+1′	−1′	—	—	—	—
Vapor corrosion	—	—	—	—	+1′	−1′	—	—	—	—

and

Table 9. The fault signature matrix of the reactor.

Failure Modes	e53	e54	e55	e56	e57	e58	e59	e60	e61
Inadvertent CR rod insertion	−1 *	—	−1	—	−1	—	−1	—	−1
Inadvertent CR rod withdrawal	+1 *	—	+1	—	+1	—	+1	—	+1
Cladding damage	—	—	—	—	—	−1 *	+1	—	+1

. The symbol “—” represents faults that are independent of this variable, “0” represents parameters that remain unchanged. The symbol “+1” represents an increase in the parameter under the specific fault, and “−1” represents a decrease in the parameter under the specific fault.

6. Combination of Bond Graph and Expert System Inference Engine

6.1. Introduction of the Expert System

The expert system G2, produced by Gensym Corporation, is used in this paper. It is a real-time intelligent expert system development platform with a graphical interface and is object-oriented [21]. It has advanced knowledge representation and a reasoning engine, so that designers and developers are free from the heavy technical implementation and can focus on solving industry problems. For original equipment manufacturers, value-added service providers, system integrators, and end users, G2 is an excellent development platform.

6.1.1. Event

The basic unit of G2 reasoning is an event, which includes six types: OR-AND, AND-AND, IF-AND, N/M-AND, N/M-N/M, OR-N/M, and event view. The OR-AND and AND-AND events are used in this article.

6.1.2. Event Type

For a single event, there are three different types, namely, root cause, alert, and unspecified. The root cause event represents the root cause of the fault, which is also the purpose of fault diagnosis. It is expressed in yellow in the inference engine, as shown in Figure 22a. An alert event indicates an alert caused by a failure, expressed in purple in the inference engine. Alarm and fault cause can be inferred from each other. The alert event is shown in Figure 22b. The unspecified event is represented by gray, representing an undefined event, as shown in Figure 22c.

6.1.3. Value of Event

There are four kinds of event values in G2:

• True: the event must happen;
• False: the event will not happen;
• Suspect: the event may happen;
• Unknown: the event is uncertain.

For an OR-AND event, as long as one of the inputs is true, the output must be true; For an AND-AND event, the output is true only when all inputs are true.

6.1.4. Diagnostic Procedure

The input and output of expert system G2 are shown in

Table 10. The input and output of expert system G2.

Input	Middle Process	Output
Domain map	Specific fault models	Root causes
Rules		Alarms
Generic fault models		Advice

.

After determining the input and output, G2 can be used for diagnosis.

6.2. Inference Engine Design

The design of an inference engine for the expert system is the core of fault diagnosis. The occurrence of faults is often accompanied by the change in corresponding parameters. To judge the fault, we should not only consider the changes in corresponding parameters, but also consider the data types that can be provided by the simulator or the actual system. The following sections describe the typical fault modeling for each system component.

6.2.1. Pressurizer

According to the fault signature matrix of the pressurizer in Table 6, the inference engine is designed as shown in Figure 23.

• Immersion-type heater inadvertently turned on

The condition for this failure is that the immersion-type heater was not closed when it should have been closed, so two conditions are required:

• Immersion-type heater had power;
• The pressure was not in the operating range of the immersion-type heater.

Since the pressurizer mainly functions through the steam space, the change after component action can be reflected only through the variable relationship graph of the steam space. The two conditions noted above could extract the corresponding data from PCTRAN, which is a reactor simulation software program developed by IAEA. The power of the immersion-type heater is directly related to the mass transfer flow at the gas–liquid interface (f₉). If it had power, the mass transfer flow at the gas–liquid interface (f₉) would increase. As can be seen from Figure 15b, the increase in f₉ directly leads to the increase in flow for control volume 3 (f₁₃); this leads to the rise of steam-space pressure (e_{9 ~ 13}).

2.

Immersion-type heater inadvertently turned off or failed

The condition for this failure is that the immersion-type heater was not turned on when it should have been turned on, so two conditions are required:

• Immersion-type heater had no power;
• The pressure was in the operating range of the immersion-type heater.

The two conditions above could also extract the corresponding data from the simulator. Mass transfer flow at the gas–liquid interface (f₉) is relatively stable due to no power of the immersion-type heater. According to Figure 15b, flow stability in control volume 3 (f₁₃) could be obtained, and then the pressure stabilizes, so pressure is not affected by the immersion-type heater.

3.

Spray valve inadvertently turned on

The condition for this failure is that the spray valve was not closed when it should have been closed, so two conditions are required:

• Spray valve had flow;
• The pressure was not in the operating range of the spray valve.

The flow of the spray valve causes condensing liquid mass flow rate on the inside surface of the pressurizer (f₁₀), and the mass flow rate of condensate on external surface of spray droplets (f₁₁) increases at the same time. According to Figure 15b, the flow rate in control volume 3 (f₁₃) decreases, and finally the pressure (e₁₃) decreases.

4.

Spray valve inadvertently turned off or failure

The condition for this failure is that the spray valve was not turned on when it should have been turned on, so two conditions are required:

• Spray valve had no flow;
• The pressure was in the operating range of the spray valve.

No flow of the spray valve causes condensing liquid mass flow rate on the inside surface of the pressurizer (f₁₀), and mass flow rate of condensate on external surface of spray droplets (f₁₁) is stable. According to Figure 15b, the flow rate in control volume 3 (f₁₃) is stable, and finally, the pressure (e₁₃) is not affected by spray.

5.

Safety valve inadvertently turned off

The condition for this failure is that the safety valve was not turned on when it should have been turned on, so two conditions are required:

• Safety valve had no flow;
• The pressure was in the operating range of the safety valve.

According to Figure 15b, no flow of the safety valve (f₁₂) leads to flow stability in control volume 3 (f₁₃), and the pressure (e₁₃) is unchanged.

6.

Safety valve inadvertently turned on (depressurization accident)

The condition for this failure is that the safety valve was not closed when it should have been closed, so two conditions are required:

• Safety valve had flow;
• The pressure was not in the operating range of the safety valve.

According to Figure 15b, the flow of the safety valve (f₁₂) leads to decrease in the flow for control volume 3 (f₁₃) and continuous decrease in the pressure (e₁₃).

6.2.2. Steam Generator

According to the fault signature matrix of the steam generator given in Table 7, the inference engine is designed as shown in Figure 24.

• Steam generator tube rupture

The condition of the fault is that the water level of the steam generator rose and radioactivity was detected when the feedwater flow was constant, so three conditions are required:

• Feedwater flow was stable or reduced;
• Water level in steam generator was high;
• Radioactivity was detected inside the steam generator.

According to Figure 17, steam generator tube rupture leads to primary side into V_W control volume flow (f^*) increase, which leads to the increase in evaporation rate of liquid water into steam (f₂₁), steam flow per unit time into vapor space above the liquid level (f₂₄), and steam production (f₂₆).

2.

Feedwater regulating valve inadvertently opened

The condition of this fault is that the feedwater flow was still increasing under the condition of high water level, so two conditions are required:

• High feedwater flow;
• High water level in the steam generator.

According to Figure 17, high feedwater flow (f₁₇) is the increase in flow rate corresponding to ΔP’ pressure difference (f₁₈) and feedwater flow in the steam generator (f₁₉). Since the feedwater is supercooled water, under the premise of a constant heat source, the increase in supercooled water leads to a decrease in evaporation rate of liquid water into steam (f₂₁), thus causing decreases in steam flow per unit time into the vapor space above the liquid level (f₂₄) and steam production (f₂₆).

3.

Feedwater regulating valve inadvertently closed

The condition of this fault is that the feedwater flow was still decreasing under the condition of low water level, so two conditions are required:

• Low feedwater flow;
• Low water level in steam generator.

According to Figure 17, low feedwater flow (f₁₇) is the decrease in flow rate corresponding to ΔP’ pressure difference (f₁₈) and feedwater flow in steam generator (f₁₉). Owing to the lack of feedwater, the supercooled water on the secondary side of the steam generator becomes smaller, resulting in the decrease in V_W control volume flow rate variation (f₂₀). At the same time, the evaporation rate of liquid water into steam (f₂₁) increases, resulting in the increases of steam flow per unit time into vapor space above the liquid level (f₂₄) and steam production (f₂₆). However, during the simulation, it was found that the feedwater was automatically closed when the reactor was shut down, and the root cause of the feedwater regulating valve inadvertently closed was also triggered. Therefore, the signal that the reactor was not shut down is added here to judge this fault.

6.2.3. Reactor Coolant Pump

According to the fault signature matrix of the reactor coolant pump given in Table 8, the inference engine is designed as shown in Figure 25.

Since the fault data of the reactor coolant pump cannot be obtained in the simulator, only the speed data are available. Therefore, in contrast to the inference engine design of other equipment, the reduction in reactor coolant pump speed may lead to the following four faults, but the specific fault cannot be determined through the simulator data. The diagnosis of the main pump can be analyzed by vibration signal, and the accuracy of diagnosis is relatively high.

• Motor damage

The fault of motor damage can be detected and diagnosed by detecting the power module of the reactor coolant pump. The most intuitive impact follows:

• Low motor torque (e₃₈);
• Low motor angular velocity (f_38–41);
• Low flow reactor coolant loop.

According to Figure 19a,b, the decrease in motor torque (e₃₈) directly leads to the decrease in flywheel torque (e₅₁) and effective torque of hydraulic module (e₄₀). The decrease in motor angular velocity (f₃₈) directly leads to the decrease in mechanical friction angular velocity (f₃₉), inertia flywheel angular velocity (f₅₁), and angular velocity of hydraulic module (f₄₀).

2.

Mechanical friction

Mechanical wear can be judged by two output parameters of the reactor coolant pump:

• Motor torque (e₃₈) stability;
• Effective torque of hydraulic module (e₄₀) decrease.

According to Figure 19b, mechanical friction directly leads to the increase in mechanical friction dissipation torque (e₃₉), the decrease in effective torque of hydraulic module (e₄₀), pressure provided by motor (e₄₁), and flow provided by motor (f₄₁).

3.

Shaft seal failure

Shaft seal failure can be detected by the pressure data of the shaft seal. According to Figure 19c, the impact of shaft seal failure follows: shaft seal failure (e₄₂) results in the decrease in applied fluid pressure (e₄₃), fluid leaving impeller pressure (e₄₄), fluid leaving pump pressure (e₄₅), and pump outlet loss pressure (e₄₆).

4.

Vapor corrosion

Vapor corrosion can be detected by external characterization such as vibration signal or sound, but there were no corresponding data in the simulator, so only the influence after cavitation is considered. According to Figure 19c, the impact of vapor corrosion follows: the increase in loss pressure of the impeller (e₄₇), resulting in the decrease in pressure of fluid leaving the impeller (e₄₄), pressure of fluid leaving the pump (e₄₅), and the pump outlet loss pressure (e₄₆).

The unified consequence of all these faults was that the flow of the reactor coolant pump was low, which is also the only physical quantity that can be reflected in the simulator.

6.2.4. Reactor

According to the fault signature matrix of the reactor given in Table 9, the inference engine is designed as shown in Figure 26.

• Cladding damage

Cladding damage can be reflected by the cladding damage rate in the simulator. However, in actual nuclear power plants, cladding damage is often detected by means of radioactivity. According to Figure 21, the damage of fuel cladding leads to the decrease in conduction loss temperature of the fuel rod cladding (e₅₈), the increase in external surface temperature of the fuel rod cladding (e₅₉), and coolant average temperature (e₆₁).

2.

Inadvertent rod insertion

Inadvertent rod insertion means that the rod position still drops when the reactivity total is low, so two conditions are required:

• Low reactivity total;
• Reactivity rod decrease.

According to Figure 21, the decrease in reactivity rod leads to decreases in center temperature inside the fuel pellets (e₅₃), surface temperature of fuel pellets (e₅₅), internal surface temperature of fuel rod cladding (e₅₇), external surface temperature of fuel rod cladding (e₅₉), and coolant average temperature (e₆₁).

3.

Inadvertent rod withdrawal

Inadvertent rod withdrawal means that the rod position still rises when the reactivity total is high, so two conditions are required:

• High reactivity total;
• Reactivity rod increase.

According to Figure 21, the increase in reactivity rod leads to the increases in center temperature inside fuel pellets (e₅₃), surface temperature of fuel pellets (e₅₅), internal surface temperature of fuel rod cladding (e₅₇), external surface temperature of fuel rod cladding (e₅₉), and coolant average temperature (e₆₁).

6.3. Threshold Setting of Expert System

Through multiple comparisons of simulator result data, the threshold settings for different events in each equipment component are shown in

Table 11. Threshold of different parameters.

Equipment	Parameters	Threshold Value
Pressurizer	Working pressure of immersion-type heater	<15.50 MPa
	Working pressure of spray valve	15.563 MPa~16.08 MPa
	Working pressure of safety valve	>16.08 MPa
Steam generator	Flow SG feedwater	1772.125 t/h~1774.8 t/h
	Level SG narrow range	49.9349%~50.00727%
Reactor coolant pump	Flow reactor coolant loop	>15.261 kt/h
Reactor	Level core water	>3.65 m
	Reactivity rod of all control rods inserted	−4.263%dk/k

.

7. Diagnostic Results and discussion

After the conditions described above were set, the established fault diagnosis system was verified by selecting immersion-type heater inadvertent turned off or failure, spray valve inadvertently turned off or failure, steam generator tube rupture, feedwater regulating valve inadvertently closed, low flow reactor coolant loop, cladding damage, inadvertent rod insertion, and inadvertent rod withdrawal. The diagnosis results are shown in Figure 27.

7.1. Pressurizer

In the fault diagnosis of the pressurizer, two faults were introduced through the simulator: immersion-type heater inadvertently turned off or failure, and spray valve inadvertently turned off or failure. Immersion-type heater inadvertently turned on, spray valve inadvertently turned on, safety valve inadvertently turned off, and safety valve inadvertently turned on (depressurization accident) were similar to the two failures shown, and so they were not repeated.

7.1.1. Immersion-Type Heater Inadvertent Turned Off or Failure

When the pressure in the pressurizer is within the working range of the immersion-type heater, and if the power of the immersion-type heater is still 0, it is judged that the immersion-type heater was inadvertently turned off or failed. At this time, through the bond graph model, analysis indicated that the immersion-type heater had no power, resulting in stability of mass transfer flow at the gas–liquid interface, and flow stability in control volume 3, steam-space flow stability, and the immersion-type heater did not cause the change in the current system pressure. Through the analysis of the process described above, the diagnosis results can be divided into two categories: shallow knowledge and deep knowledge. Shallow knowledge is that the immersion-type heater had no power and the current pressure was in the working range of the immersion-type heater. Deep knowledge refers to the mass flow at the gas–liquid interface, the flow in the steam space, and the resulting pressure change.

7.1.2. Spray Valve Inadvertent Turned Off or Failure

When the pressure in the pressurizer is in the working range of the spray valve, and if the spray flow is still 0, it is judged that the spray valve was inadvertently turned off or failed. At this time, through the bond graph model, analysis indicated that the spray valve had no flow, which did not cause excessive changes in the condensate rate on the inner wall of the pressurizer and the condensate rate on the outer surface of the droplets. The flow rate in the steam space was stable and did not cause pressure changes. No spray occurs when the pressure inside the pressurizer is high, and if no measures are taken to restore the pressure to normal, a more serious accident may occur in the reactor coolant system.

7.2. Steam Generator

7.2.1. Steam Generator Tube Rupture

When the feedwater of the steam generator remains unchanged or decreases, and if the water level rises, steam generator tube rupture is considered. In nuclear power plants, the radioactivity in the steam generator can be detected to judge whether the heat transfer tube is broken. In the simulator, there were data indicating steam generator tube rupture, so in this experiment water level and feedwater flow data were used to judge the rupture failure of the steam generator tube. Through the bond graph model, analysis indicated that after the rupture of the tube, the rate of water on the liquid surface turning into steam increased, which led to the increase in steam volume in the steam space and, finally, the increase in steam production.

7.2.2. Feedwater Regulating Valve Inadvertently Closed (Loss of Feedwater)

Low feedwater flow and low steam generator water level could be used to determine when the steam generator lost feedwater. However, it was found in the simulator that the two alarms described above were also triggered after shutdown for other reasons. Therefore, the condition that the reactor did not shutdown was added to the inference engine. According to the bond graph model, the loss of feedwater reduced the flow change in the liquid phase area inside the steam generator. Since the feedwater is supercooled water, if the supercooled water became smaller, the amount of steam in the liquid phase increased, and the amount of steam entering the steam space increased, which eventually led to the increase in steam production.

7.3. Reactor Coolant Pump

Because the data regarding the reactor coolant pump in the simulator considered only the low flow, the reliability of judging the fault only through the low flow was not high. At the same time, there was no difference in the performance of the simulator after each fault occurred, so it was impossible to judge a specific fault. However, in monitoring the actual reactor coolant pump, special monitoring points were set. Therefore, one or several specific faults could be judged through these measuring points, and the corresponding consequence of the fault could be deduced. Through the bond graph model, it was detected that each fault of the reactor coolant pump was “suspect”, as shown in Figure 27e.

7.4. Reactor

7.4.1. Cladding Damage

The failure resulting from cladding damage was judged by the cladding damage rate in the simulator. In practical engineering, the radioactivity in the reactor is measured to judge whether the cladding is damaged and the degree of damage. Through the bond graph model, analysis indicated that the cladding damage reduced the heat conduction loss of the cladding; at the same time, the change in the central temperature of the fuel was not obvious, the temperature of the outer surface of the fuel cladding increased, and the average temperature of the coolant rose (the heat conduction effect of the fuel cladding was lost).

7.4.2. Inadvertent CR Rod Insertion

The fault of inadvertent rod insertion was judged by dropping the control rod to reduce the reactivity when the total reactivity was low. In engineering practice, the decline of control rod position and reactivity are used to judge this condition. Through the bond graph model, it was inferred that the control rod position decreased through the decrease in rod reactivity. At the same time, the fuel pellet center temperature decreased, the fuel pellet surface temperature decreased, the fuel rod cladding inner surface temperature decreased, and the fuel rod cladding outer surface temperature decreased, which finally led to the decrease in coolant temperature.

7.4.3. Inadvertent CR Rod Withdrawal

The fault of inadvertent rod withdrawal was judged by raising the control rod to increase the reactivity when the total reactivity was high. In practical engineering, the rise of the control rod position and excessive reactivity are used to judge this condition. Through the bond graph model, it was inferred that the control rod position rose. At the same time, the fuel pellet center temperature rose, the fuel peak temperature rose, the fuel pellet surface temperature rose, the fuel rod cladding inner surface temperature rose, the fuel rod cladding outer surface temperature rose, and finally the coolant temperature rose.

The reasoning results are shown in

Table 12. Reasoning results.

Diagnostic Results	Physical Quantity Variation
Immersion-type heater inadvertently turned off or failed	f9, f13
Spray valve inadvertently turned off or failed	f10, f13
Steam generator tube rupture	f*, f21, f24, f26
Feedwater regulating valve inadvertently closed	f17, f20, f21, f24, f26
Low flow reactor coolant loop	Suspect
Cladding damage	e53, e58, e59, e61
Inadvertent CR rod insertion	e53, e55, e57, e59, e61
Inadvertent CR rod withdrawal	e53, e55, e57, e59, e61

.

8. Conclusions

In this paper, the bond graph is used to model the equipment of a reactor coolant system. The signature matrix of typical faults is obtained by using the time causality graph and the variable relationship graph. Finally, the fault diagnosis is realized by using the expert system, and the diagnosis results are obtained. This paper proposes a fault diagnosis system based on the combination of the bond graph and expert system. After analyzing the fault diagnosis results, it is concluded that this method has the following advantages:

• A new idea for the expert system inference engine design is provided by the bond graph model.

The quality of inference engine is one of the important criteria to judge the quality of the expert system. The bond graph model can describe the physical relationships within the system and extracts the detailed logical relationship between parameters, so it can be used in the design of the expert system inference engine. This method is based on the internal mechanism of the system. More comprehensive information of the system is obtained through the time causality graph and the variable relationship graph, which can help operators and researchers carry out subsequent operations and research. A new idea for bond graph application is provided in this paper. In previous studies, a bond graph model was often used to describe the dynamic process of the system, but in this paper, it is used to find the variable characteristics of the system.

2.

The deep knowledge of faults can be interpreted by using the bond graph.

From the perspective of fault diagnosis, the use of the bond graph method can deeply analyze the fault characteristics, and provide a modeling method based on deep knowledge for fault diagnosis. In traditional knowledge-based modeling methods, knowledge acquisition is a bottleneck problem. In most nuclear power plants, the knowledge base of the expert system mostly uses shallow knowledge for modeling, which leads to problems such as not knowing the internal parameter state of the system. In this paper, the bond graph model is transformed into inference engine modeling with expert deep knowledge. This method can provide more useful information than the traditional inference engine modeling method, and can help the operator better realize fault diagnosis. At the same time, the operator can also identify the unknown faults in the system through deep knowledge, which solves the inherent bottleneck that the expert system cannot identify the unknown faults.

3.

The bond graph model can be used to analyze the impact of faults and mitigate their consequences.

From the perspective of the impact caused by the fault, the bond graph can be used to analyze the changes in internal parameters caused by the fault to the system or equipment, thus providing a theoretical basis for researchers to analyze the impact degree caused by the fault. At the same time, solutions can be considered according to the impact of the fault, to improve the safety of the reactor coolant system, and prevent major accidents. This method can provide researchers with a new idea to avoid or mitigate the harm of failure.

The follow-up work of fault diagnosis using bond graph models includes:

• Bond graph modeling of major accidents.

A loss-of-coolant accident (LOCA) is typical for reactor coolant systems. The judgment criteria of the accident and the impact after the accident are more complex, involving many changes in parameters, which lead to an excessive fault diagnosis system of the bond graph. However, it will be necessary to analyze these major accidents with bond graph models and put forward effective mitigation measures and methods.

2.

Quantification of the bond graph.

This paper is limited to the qualitative analysis of faults; however, the quantification of a bond graph model is another advantage. Therefore, the quantitative physical description of each component of the reactor coolant system and its modeling with a bond graph will give full play to its advantages and quantitatively describe the fault degree.