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摘要:
针对故障本身构建量子贝叶斯Petri网模型算法，并利用该子网模型进行Petri网系统故障分析。对于部分可观Petri网模型中的不可观故障，根据可达标识图分析变迁点火路径不能判断系统状态，建立量子贝叶斯子网模型，通过不确定路径引起的量子干涉重新标定变迁的条件概率表得到量子概率振幅表。根据故障变迁的前置集合并结合量子贝叶斯推理计算变迁触发的先验概率，由后置集合中的可观变迁修正后验概率，由最大后验概率估计系统所处状态，当故障变迁不唯一时，选取最大概率的故障作为故障源。以实际故障系统建立部分可观Petri网模型，结合可观标签概率序列信息和量子贝叶斯概率估计，对系统不可观部分进行故障诊断验证算法的有效性。
Abstract:This paper proposes an algorithm to construct a quantum Bayesian Petri nets model for the fault, and uses the sub net model to analyze the fault of Petri net system. According to the reachability identification diagram, which is the transition firing path can not judge the system state, establish the quantum Bayesian Petri nets subnet model to tackle the unobservable faults in partial observable Petri model. Through the quantum interference caused by the uncertain path, recalibrate the conditional probability table of the transition to obtain the quantum probability amplitude table. According to the pre-set of fault transition and quantum Bayesian reasoning, calculates the firing prior probability of transition. The posterior probability is modified by the observable transition in the post-set, and the state of the system is estimated by the maximum posterior probability. When the fault transition is not unique, the fault with the maximum probability is selected as the fault source. Finally, establishes a partial observable Petri nets model of a real fault system. Combined with the probability sequence information of observable label and quantum Bayesian probability estimation, the fault diagnosis of the unobservable parts of the system is carried out to verify the effectiveness of the algorithm with the data in simulation experiment.
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Key words:
- fault diagnosis /
- Petri nets /
- partially observed /
- quantum Bayesian /
- quantum interference
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图 6 经典贝叶斯和量子贝叶斯概率
Figure 6. Classical Bayesian probability and quantum Bayesian probability
图 7 t5条件下t14的量子贝叶斯概率值变化曲线
Figure 7. Change of quantum Bayesian probability value of t14 under the condition of t5
图 8 t5条件下
Figure 8. Change of quantum Bayesian probability value of
图 10 干涉角{θ1, θ2}引起t3条件下t8点火概率变化
Figure 10. Interference angle {θ1, θ2} causes the change of firing probability of t8 under the condition of t3
图 11 干涉角{θ3, θ4}引起t3条件下t8点火概率变化
Figure 11. Interference angle {θ3, θ4} causes the change of firing probability of t8 under the condition of t3
图 14 BPN算法和QBPN算法故障诊断概率比较
Figure 14. Comparison of fault diagnosis probability between BPN algorithm and QBPN algorithm
表 1 总概率情况和量子贝叶斯情况的概率估计比较
Table 1. Comparison of probability estimates between total probability and quantum Bayesian
概率估计 概率值 Pr(t8|t5) 0.81 φ(t8|t5) 
Pr(t10|t5) 0.19 φ(t10|t5) 
Pr(t14|t8) 0.63 φ(t14|t8) 
Pr(t14|t10) 0.43 φ(t14|t10) 
总概率下Pr(t14|t5) 0.592 量子贝叶斯Pr(t14|t5) 0.795 5 总概率下Pr(t14|t5) 0.408 量子贝叶斯Pr(t14|t5) 0.204 5 
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表 2 基于POPN的量子贝叶斯故障算法故障诊断结果
Table 2. Fault diagnosis results of quantum Bayesian fault algorithm based on POPN
可观概率序列σo 故障变迁Tfi触发概率 干涉角θ/rad QB函数结果 置信度Fb 系统故障概率Pr(σo, ψ, Tfi) 系统状态估计W 系统实际状态 (t0, 1)(t4, 0.883)(t3, 0.926) Pr(tf10|t0, t4, t3) π/2 0 0 0 N 无故障 (t0, 1)(t4, 0.883)
(t3, 0.926)(t15, 0.879)Pr(tf10|t0, t4, t3) π/2 0.162 1 0.4 0.047 1 N 无故障 Pr(tf10|t0, t4, t3, t15) 0 0.047 1 Pr(tf11|t0, t4, t3) π/2 0.158 6 Pr(tf11|t0, t4, t3, t15) 0 0.007 6 (t0, 1)(t4, 0.883)
(t3, 0.926)(t14, 0.851)
(t15, 0.879)(t12, 0.463)Pr(tf10|t0, t4, t3) π/2 0.162 1 0.6 0.966 8 F 故障 Pr(tf10|t0, t4, t3, t14) 0 0.756 9 Pr(tf10|t0, t4, t3, t14, t15) 0 0.926 3 Pr(tf10|t0, t4, t3, t14, t15, t12) 0 0.966 8 Pr(tf11|t0, t4, t3) π/2 0.158 6 Pr(tf11|t0, t4, t3, t14, t15, t12) 0 0.000 6 (t0, 1)(t3, 0.907)
(t13, 0.736)Pr(tf11|t0, t3, t13) π/2 1 1 1 F 故障
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表 3 QBPN算法与BPN算法比较
Table 3. Comparison of QBPN algorithm and BPN algorithm
算法 响应时间/ms 诊断正确率/% BPN 300 93.70 QBPN 230 98.74
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