文章快速检索 高级检索

1. 兰州理工大学 电气工程与信息工程学院, 兰州 730050;
2. 兰州理工大学 甘肃省工业过程先进控制重点实验室, 兰州 730050

Fault diagnosis of particle filter nonlinear systems based on adaptive threshold
JIANG Dongnian1,2 , LI Wei1,2
1. College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou 730050, China ;
2. Key Laboratory of Gansu Advanced Control for Industrial Processes, Lanzhou University of Technology, Lanzhou 730050, China
Received: 2015-09-17; Accepted: 2015-11-27; Published online: 2016-01-04 10:04
Foundation item: National Natural Science Foundation of China (61364011); Natural Science Foundation of Gansu Province of China (2015GS05221)
Corresponding author. Tel.:0931-2976020, E-mail:liwei@lut.cn
Abstract: In view of the problem of actual nonlinear system that the traditional method is difficult to obtain reliable fault diagnosis, this paper uses the particle filter method and applies the logarithm likelihood function as evaluation index to study the nonlinear non-Gaussian system fault detection and fault isolation with the aid of adaptive threshold design. The selection of threshold value is the criterion for accurately judging system failure. This paper analyzes the statistical properties of residual error, determines the residual error statistical property of normal distribution, and designs an adaptive threshold method based on particle filter fault diagnosis, which reduce the miss alarm and false alarm ratios of fault diagnosis. Through the simulation example of non-constant temperature continuous stirred tank reactor, the accuracy and feasibility of this method in fault diagnosis are verified.
Key words: adaptive threshold     particle filter     fault diagnosis     false alarm ratio     miss alarm ratio     normal distribution     nonlinear system

1 问题描述

 (1)

 (2)

 (3)

 (4)

2 粒子滤波算法

1) 预测

 (5)

2) 更新

 (6)
 (7)

 (8)

 (9)

 (10)

3 故障诊断方法设计

3.1 故障检测

H0θ=θ0原假设，系统无故障

H1θ≠θ0备择假设，系统有故障

 (11)

 (12)

 (13)

 (14)

3.2 自适应阈值设计

 图 1 残差随随时间分布图 Fig. 1 Distribution of residual error versus time

 (15)
 (16)

 (17)

 (18)

 阈值偏差 u1 u2 u3 u4 φ1 -0.0000 -0.0047 -0.0101 -0.0092 φ2 0.0303 0.4441 0.9822 0.9300 φ3 0.0019 -7.2248 -18.4420 -16.0660

 (19)

3.3 故障隔离

 图 2 故障诊断原理图 Fig. 2 Principle of fault diagnosis
3.4 故障误报率和漏报率

 (20)
 (21)

4 仿真分析

 图 3 非恒温连续搅拌水箱式反应堆 Fig. 3 Non-constant temperature continuous stirred tank reactor
 (22)

 参数 数值 L0/(m3·h-1) 4.998 L1/(m3·h-1) 4.998 L3/(m3·h-1) 8 V1 /m3 1 V2 /m3 3 R /(kJ·kmol-1) 8.314 T0 /K 280 T03 /K 280 CA0s /(kmol·m-3) 2.4 CA03s /(kmol·m-3) 2.6 Q1s /(kJ·h-1) 0.7×106 Q2s /(kJ·h-1) 0.3×106 Δ H1 /(kJ·kmol-1) -1.00×105 Δ H2 /(kJ·kmol-1) -1.04×105 Δ H3 /(kJ·kmol-1) -1.08×105 k10 /h-1 3.0×106 k20 /h-1 3.0×105 k30 /h-1 3.0×105 E1 /(kJ·kmol-1) 5.0×104 E2 /(kJ·kmol-1) 7.53×104 E3 /(kJ·kmol-1) 7.53×104 ρ /(kg·m-3) 2000 cp /(kJ·kg-1) 0.731 T1s/K 424.4 T2s /K 444.5 CA1s/(kmol·m-3) 1.69 CA2s/(kmol·m-3) 0.89

 故障 稳态值 故障值 F1:温度传感器偏差T0 /℃ 280 295~311 F2:流量传感器偏差L0 / (m3·h-1) 4.998 5.25~5.5 F3:温度传感器偏差T03 /℃ 280 295~311 F4:流量传感器渐变故障L1 / (m3·h-1) 4.998 4.998(1-β) 注：β—传感器失效率。

 图 4 故障模式F1、F2、F3和F4检测 Fig. 4 Detection of failure mode F1, F2, F3 and F4

 故障 漏报率 阈值δ=65 自适应阈值 F1:温度传感器偏差T0 0.1287 0.0865 F2:流量传感器偏差L0 0.1043 0.0887 F3:温度传感器偏差T03 0.1276 0.0564 F4:流量传感器渐变故障L1 0.2190 0.1007

 图 5 故障模式F1、F2、F3和F4隔离 Fig. 5 Isolation of failure mode F1, F2, F3 and F4
5 结论

1) 粒子滤波是解决非线性系统故障诊断的一种有效手段，采用对数似然函数和作为评价指标，可以实现非线性系统的故障检测和故障隔离。

2) 阈值的设计是非线性系统故障诊断的基础，利用统计特性设计残差的阈值可以避免非线性系统模型中的复杂因素，且采用自适应阈值可有效地降低故障诊断的漏报率和误报率。

3) 本文通过统计方法得到残差特性满足正态分布特性，只要满足正态分布特性的残差，就可通过本文设计的方法实现自适应阈值的设计。

 [1] GERTLER J J. Fault detection and diagnosis in engineering systems[M]. New York: Marcel Dekker, Inc., 1998 : 36 -58. [2] GHANTASALA S, EL-FARRA N H. Robust actuator fault isolation and management in constrained uncertain parabolic PDE systems[J]. Automatica, 2009, 45 (10) : 2368 –2373. DOI:10.1016/j.automatica.2009.06.024 [3] FENG K, JIANG Z, HE W. Rolling element bearing fault detection based on optimal antisymmetric real Laplace wavelet[J]. Measurement, 2011, 44 (9) : 1582 –1591. DOI:10.1016/j.measurement.2011.06.011 [4] TAFAZOLI S, SUN X. Hybrid system state tracking and fault detection using particle filters[J]. IEEE Transactions on Control Systems Technology, 2006, 14 (6) : 1078 –1087. DOI:10.1109/TCST.2006.883193 [5] MICHELE C, PIERO B, PIETRO T, et al. Interacting multiple-models, state augmented particle filtering for fault diagnostics[J]. Probabilistic Engineering Mechanics, 2015, 40 : 12 –24. DOI:10.1016/j.probengmech.2015.01.001 [6] 杜京义, 殷梦鑫. 一种改进的粒子滤波算法应用于故障诊断[J]. 系统仿真学报, 2014, 26 (1) : 62 –66. DU J Y, YIN M X. Improved algorithm of particle filter applied to fault diagnosis[J]. Journal of System Simulation, 2014, 26 (1) : 62 –66. (in Chinese) [7] ZHANG B, SCONYERS C, BYINGTON C, et al. A probabilistic fault detection approach:Application to bearing fault detection[J]. IEEE Transactions on Industrial Electronics, 2011, 58 (5) : 2011 –2018. DOI:10.1109/TIE.2010.2058072 [8] WEI T, HUANG Y, CHEN C. Adaptive sensor fault detection and identification using particle filter algorithms[J]. IEEE Transactions on Systems, Man, and Cybernetics, Part C:Applications and Reviews, 2009, 39 (2) : 201 –213. DOI:10.1109/TSMCC.2008.2006759 [9] MICHAL Z. Online fault detection of a mobile robot with a parallelized particle filter[J]. Neurocomputing, 2014, 126 : 151 –165. DOI:10.1016/j.neucom.2012.11.049 [10] TADIC' P, DUROVIC' Z. Particle filtering for sensor fault diagnosis and identification in nonlinear plants[J]. Journal of Process Control, 2014, 24 (4) : 401 –409. DOI:10.1016/j.jprocont.2014.02.009 [11] CHEN C C, GEORGE V C, MARCOS E. Machine remaining useful life prediction:An integrated adaptive neuro-fuzzy and high-order particle filtering approach[J]. Mechanical Systems and Signal Processing, 2012, 28 : 597 –607. DOI:10.1016/j.ymssp.2011.10.009 [12] YU J. A particle filter driven dynamic Gaussian mixture model approach for complex process monitoring and fault diagnosis[J]. Journal of Process Control, 2012, 22 (4) : 778 –788. DOI:10.1016/j.jprocont.2012.02.012 [13] VICENC P, SAUL M D, JOAQUIM B. Adaptive threshold generation in robust fault detection using interval models:Time-domain and frequency-domain approaches[J]. Interational Journal of Adaptive Control and Signal Process, 2013, 27 (10) : 873 –901. [14] JOHNSON A L.A new algorithm for adaptive threshold generation in robust fault detection based on a sliding window and global optimization[C]//Proceedings of European Control Conference 1999, ECC'99. Piscataway, NJ:IEEE Press, 1999:1546-1551. [15] JOHANSSON A, BASK M, NORLANDER T. Dynamic threshold generators for robust fault detection in linear systems with parameter uncertainty[J]. Automatica, 2006, 42 (7) : 1095 –1106. DOI:10.1016/j.automatica.2006.02.009 [16] DING X, FRANK P M.Frequency domain approach and threshold selector for robust model-based fault detection and isolation[C]//IFAC/IMACS Symposium on Fault Detection, Supervision and Safety for Technical Processes-SAFEPROCESS'91. Tarrytown, NY:Pergamon Press Inc., 1992:271-276. [17] RAMBEAUX F, HAMELIN F, SAUTER D. Optimal thresholding for robust fault detection of uncertain systems[J]. International Journal of Robust and Nonlinear Control, 2000, 10 (4) : 1155 –1173. [18] GORDON N J, SALMOND D J, SMITH A F M. Novel approach to nonlinear/non-Gaussian Bayesian state estimation[J]. IEEE Proceedings on Radar and Signal Processing, 1993, 140 (2) : 107 –113. DOI:10.1049/ip-f-2.1993.0015 [19] ALROWAIE F, GOPALUNI R, KWOK K. Fault detection and isolation in stochastic non-linear state-space models using particle filters[J]. Control Engineering Practice, 2012, 20 (10) : 1016 –1032. DOI:10.1016/j.conengprac.2012.05.008 [20] BHATTACHARYA R, WAYMIRE E C. Stochastic processes with applications[M]. New York: Wiley, 1990 : 40 -55. [21] SHI Z, GU F, LENNOX B, et al. The development of an adaptive threshold for model-based fault detection of a nonlinear electro-hydraulic system[J]. Control Engineering Practice, 2005, 13 (11) : 1357 –1367. DOI:10.1016/j.conengprac.2004.11.014 [22] KADIRKAMANATHAN V. Particle filtering-based fault detection in non-linear stochastic systems[J]. International Journal of Systems Science, 2002, 33 (4) : 259 –265. DOI:10.1080/00207720110102566

#### 文章信息

JIANG Dongnian, LI Wei

Fault diagnosis of particle filter nonlinear systems based on adaptive threshold

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(10): 2099-2106
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0611