Turbofan Engine Fault Prediction Based on Evidential Reasoning and Belief Rule Base

doi:10.16182/j.issn1004731x.joss.21-0396

Abstract

Abstract:

Aiming at the fault prediction problem of a turbofan engine, a fault prediction model based on evidential reasoning (ER) and belief rule base (BRB) is proposed. In order to describe the health state of turbofan engine, ER algorithm is adopted to fuse the state information. Combined with prior knowledge, a hybrid driven simulation prediction of BRB model is established. Projection covariance matrix adaptive evolution strategy (P-CMA-ES) is used to optimize the model parameters. The validity of the model is verified by experiments. Experimental results show that the proposed method not only accurately predicts the probability of failure risk of the turbofan engine, but also provides strong support for fault diagnosis and maintenance support.

Key words: turbofan, evidential reasoning (ER), belief rule base (BRB), projection covariance matrix adaptive evolution strategy (P-CMA-ES), fault prediction

CLC Number:

Hailong Zhu, Ruxia Jia, Liang Zhang, Wei He. Turbofan Engine Fault Prediction Based on Evidential Reasoning and Belief Rule Base[J]. Journal of System Simulation, 2022, 34(09): 2074-2086.

Figures/Tables 15

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Table 1

Table 2

Table 3

Table 4

Fig. 5

Table 5

Fig. 6

Table 6

Optimized BRB confidence

θ_l	ϑ_rϑ_s	{(S,β_1,l),(A,β_2,l),(B,β_3,l),(C,β_4,l),(D,β_5,l),(E,β_6,l),}
1	SS	{(S,0.160 8),(A, 0.056 9),(B,0.221 7),(C,0.0181),(D,0.378 7),(E,0.163 7)}
1	AS	{(S,0.390 8),(A,0.138 7),(B,0.147 8),(C,0.039 9),(D,0.045 0),(E,0.237 6)}
1	BS	{(S,0.430 1),(A,0.006 7),(B,0.042 6),(C,0.054 6),(D,0.094 4),(E,0.371 6)}
1	CS	{(S,0.092 0),(A,0.276 2),(B,0.108 9),(C,0.189 7),(D,0.083 5),(E,0.249 7)}
1	DS	{(S,0.181 3),(A,0.172 1),(B,0.360 2),(C,0.244 8),(D,0.017 9),(E,0.023 6)}
1	ES	{(S,0.227 7),(A,0.126 7),(B,0.180 4),(C,0.245 4),(D,0.110 4),(E,0.109 4)}
1	SA	{(S,0.232 9),(A,0.094 5),(B,0.3718),(C,0.076 1),(D,0.224 5),(E,0.000 1)}
1	AA	{(S,0.192 1),(A,0.1381),(B,0.436 3),(C,0.036 1),(D,0.135 2),(E,0.062 2)}
1	BA	{(S,0.161 9),(A,0.034 0),(B,0.054 6),(C,0.214 9),(D,0.084 5),(E,0.450 1)}
1	CA	{(S,0.5281),(A,0.0431),(B,0.114 8),(C,0.192 1),(D,0.021 4),(E,0.100 4)}
1	DA	{(S,0.081 0),(A,0.064 4),(B,0.425 5),(C,0.082 6),(D,0.306 2),(E,0.040 3)}
1	EA	{(S,0.1051),(A,0.292 4),(B,0.050 1),(C,0.087 0),(D,0.383 9),(E,0.081 5)}
1	SB	{(S,0.377 6),(A,0.105 6),(B,0.241 0),(C,0.064 2),(D,0.181 9),(E,0.029 8)}
1	AB	{(S,0.119 9),(A,0.171 0),(B,0.037 5),(C,0.1951),(D,0.115 7),(E,0.360 7)}
1	BB	{(S,0.046 2),(A,0.215 6),(B,0.097 4),(C,0.442 7),(D,0.137 0),(E,0.0611)}
1	CB	{(S,0.037 4),(A,0.104 6),(B,0.069 7),(C,0.074 9),(D,0.127 6),(E,0.585 9)}
1	DB	{(S,0.323 4),(A,0.036 4),(B,0.134 4),(C,0.081 7),(D,0.177 0),(E,0.247 1)}
1	EB	{(S,0.147 5),(A,0.103 6),(B,0.040 5),(C,0.315 8),(D,0.100 0),(E,0.292 5)}
1	SC	{(S,0.131 4),(A,0.278 3),(B,0.315 9),(C,0.157 4),(D,0.089 5),(E,0.027 5)}
1	AC	{(S,0.236 3),(A,0.051 7),(B,0.121 6),(C,0.231 0),(D,0.344 8),(E,0.014 6)}
1	BC	{(S,0.019 1),(A,0.076 3),(B,0.029 8),(C,0.072 0),(D,0.053 8),(E,0.749 0)}
1	CC	{(S,0.227 8),(A,0.0418),(B,0.009 3),(C,0.021 5),(D,0.000 0),(E,0.699 5)}
1	DC	{(S,0),(A,0.005 4),(B,0.016 8),(C,0),(D,0.000 4),(E,0.979 2)}
1	EC	{(S,0.303 6),(A,0.142 7),(B,0.087 6),(C,0.023 9),(D,0.088 6),(E,0.353 6)}
1	SD	{(S,0.2470),(A,0.1759),(B, 0.2034),(C,0.2412),(D,0.0949),(E,0.0375)}

Table 6

Table 7

Fig. 7

Fig. 8

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主要参数	具体信息
收录时间	2008-05-18
收录库名称	Prognostics CoE at NASA
数据收集系统	Commercial Modular Aero-Propulsion System Simulation
发动机推力	90 000磅
环境条件	海平面
数据集大小	4.01 MB

名称	权重	参考值1	参考值2	参考值3	参考值4	参考值5	参考值6
低压压气机出口总温度/ºR	0.10	645	644	643	642	641	640
高压压气机出口总温度/ºR	0.05	1 616	1 600	1 592	1 584	1 573	1 562
低压涡轮出口总温度/ºR	0.10	1 442	1 433	1 421	1 409	1 397	1 377
高压压气机出口静压/psia	0.04	571	568	564	559	554	548
物理风扇转速/(rpm)	0.10	2 389.80	2 389.40	2 389.00	2 388.20	2 387.00	2 386.00
高压涡轮冷气流量/(lbm/s)	0.10	9 235	9 200	9 162	9 120	9 052	9 017
低压涡轮冷气流量/(lbm/s)	0.04	48.5	48.2	47.9	47.5	47.1	46.6
风扇换算转速/(rpm)	0.10	538	535	532	527	523	518
核心机换算转速/(rpm)	0.04	2 389.00	2 388.50	2 388.00	2 387.40	2 386.60	2 386.00
需求风扇转速/(rpm)	0.04	8 290	8 257	8 216	8 183	8 155	8 099
需求风扇换算转速/(rpm)	0.04	8.58	8.50	8.43	8.33	8.21	8.15
燃油油量与高压压气机出口静压的比率/(pps/psi)	0.10	400	398	396	394	391	388
涵道比	0.10	39.90	39.80	39.60	39.40	38.80	38.10
抽气焓	0.05	24.00	23.80	23.70	23.50	23.20	22.80

参考点	参考值	参考点	参考值
S	0	C	0.70
A	0.30	D	0.80
B	0.55	E	1

θ_l	ϑ_rϑ_s	{(S,β_1,l),(A,β_2,l),(B,β_3,l), {(C,β_4,l),(D,β_5,l),(E,β_6,l)}
1	SS	{(S,1),(A,0),(B,0),(C,0),(D,0),(E,0)}
1	AS	{(S,0),(A,1),(B,0),(C,0),(D,0),(E,0)}
1	BS	{(S,0),(A,0),(B,1),(C,0),(D,0),(E,0)}
1	CS	{(S,0),(A,0),(B,0),(C,1),(D,0),(E,0)}
1	DS	{(S,0),(A,0),(B,0),(C,0),(D,1),(E,0)}
1	ES	{(S,0),(A,0),(B,0),(C,0),(D,0),(E,1)}
1	SA	{(S,1),(A,0),(B,0),(C,0),(D,0),(E,0)}
1	AA	{(S,0),(A,1),(B,0),(C,0),(D,0),(E,0)}
1	BA	{(S,0),(A,0),(B,1),(C,0),(D,0),(E,0)}
1	CA	{(S,0),(A,0),(B,0),(C,1),(D,0),(E,0)}
1	DA	{(S,0),(A,0),(B,0),(C,0),(D,1),(E,0)}
1	EA	{(S,0),(A,0),(B,0),(C,0),(D,0),(E,1)}
1	SB	{(S,1),(A,0),(B,0),(C,0),(D,0),(E,0)}
1	AB	{(S,0),(A,1),(B,0),(C,0),(D,0),(E,0)}
1	BB	{(S,0),(A,0),(B,1),(C,0),(D,0),(E,0)}
1	CB	{(S,0),(A,0),(B,0),(C,1),(D,0),(E,0)}
1	DB	{(S,0),(A,0),(B,0),(C,0),(D,1),(E,0)}
1	EB	{(S,0),(A,0),(B,0),(C,0),(D,0),(E,1)}
1	SC	{(S,1),(A,0),(B,0),(C,0),(D,0),(E,0)}
1	AC	{(S,0),(A,1),(B,0),(C,0),(D,0),(E,0)}
1	BC	{(S,0),(A,0),(B,1),(C,0),(D,0),(E,0)}
1	CC	{(S,0),(A,0),(B,0),(C,1),(D,0),(E,0)}
1	DC	{(S,0),(A,0),(B,0),(C,0),(D,1),(E,0)}
1	EC	{(S,0),(A,0),(B,0),(C,0),(D,0),(E,1)}
1	SD	{(S,1),(A,0),(B,0),(C,0),(D,0),(E,0)}
1	AD	{(S,0),(A,1),(B,0),(C,0),(D,0),(E,0)}
1	BD	{(S,0),(A,0),(B,1),(C,0),(D,0),(E,0)}
1	CD	{(S,0),(A,0),(B,0),(C,1),(D,0),(E,0)}
1	DD	{(S,0),(A,0),(B,0),(C,0),(D,1),(E,0)}
1	ED	{(S,0),(A,0),(B,0),(C,0),(D,0),(E,1)}
1	SE	{(S,1),(A,0),(B,0),(C,0),(D,0),(E,0)}
1	AE	{(S,0),(A,1),(B,0),(C,0),(D,0),(E,0)}
1	BE	{(S,0),(A,0),(B,1),(C,0),(D,0),(E,0)}
1	CE	{(S,0),(A,0),(B,0),(C,1),(D,0),(E,0)}

规则状态	匹配度
规则状态	t=334时刻	t=335时刻
S&S	0	0
S&A	0	0.358 4
S&B	0	0.641 6
S&C	0	0
S&D	0	0
S&E	0	0
A&S	0.370 4	0
A&A	0.370 4	0.358 4
A&B	0.370 4	0.641 6
A&C	0.370 4	0
A&D	0.370 4	0
A&E	0.370 4	0
B&S	0.629 6	0
B&A	0.629 6	0.358 4
B&B	0.629 6	0.641 6
B&C	0.629 6	0
B&D	0.629 6	0
B&E	0.629 6	0
C&S	0	0
C&A	0	0.358 4
C&B	0	0.641 6
C&C	0	0
C&D	0	0
C&E	0	0
D&S	0	0
D&A	0	0.358 4
D&B	0	0.641 6
D&C	0	0
D&D	0	0
D&E	0	0
E&S	0	0
E&A	0	0.358 4
E&B	0	0.641 6
E&C	0	0
E&D	0	0
E&E	0	0