基于递归图和张量分解的故障可诊断性评价方法

doi:10.12382/bgxb.2021.0790

摘要/Abstract

摘要：

可诊断性反映了系统故障诊断的难易程度，对系统进行可诊断性评价是开展故障诊断工作的前提条件。针对可诊断性评价问题，将测点信号考虑在内，提出了一种基于递归图和张量分解的故障可诊断性评价方法。利用相空间重构技术对装备在不同状态下的测点信号进行图形化表示，形成递归图；对递归图进行分析以提取其中的特征，并将该特征视为原信号特征；通过张量分解的方法，计算不同状态下信号特征之间的相似程度，作为故障诊断难易程度的基本度量。通过仿真实验对所提出的方法与仅考虑系统模型的D矩阵的可诊断性评价方法进行对比，结果表明该方法在评价可诊断性方面具有准确性和客观性。

关键词: 可诊断性评价, 递归图, 张量分解, 相空间重构

Abstract:

Diagnosability reflects the difficulty of diagnosing system faults, so diagnosability evaluation of the system is a prerequisite for fault diagnosis. Taking the signals of test points into consideration, a fault diagnosability evaluation method based on a recurrence plot and tensor decomposition is proposed. The phase space reconstruction technique is used to graphically represent the signals of measured points in different states to form a recurrence plot. Features are extracted through analyzing the recurrence plot, which are then regarded as the original signal features. Through tensor decomposition, the similarity between signal features in different states is calculated as a basic measure of fault diagnosis difficulty. Simulation experiments show that, compared with the previous D-matrix diagnosability evaluation method that only considers the system model, the newly proposed method has effectiveness and objectivity.

Key words: fault diagnosability evaluation, recurrence plot, tensor decomposition, phase space reconstruction

吕佳朋, 史贤俊, 聂新华, 秦玉峰, 龙玉峰. 基于递归图和张量分解的故障可诊断性评价方法[J]. 兵工学报, 2023, 44(3): 763-772.

LÜ Jiapeng, SHI Xianjun, NIE Xinhua, QIN Yufeng, LONG Yufeng. Evaluation Method of Fault Diagnosability Based on Recursive Plot and Tensor Decomposition[J]. Acta Armamentarii, 2023, 44(3): 763-772.

图/表 15

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指标	计算方法	物理含义
递归率	$RR=\frac{\sum\limits_{i=1}^{{{N}_{m}}}{\sum\limits_{j=1}^{{{N}_{m}}}{{{R}_{ij}}}}}{N_{m}^{2}}$	描述了递归图中递归点的密度，反映了一个特定状态出现的概率
确定性	$DET=\frac{\sum\limits_{l={{l}_{\min }}}^{{{l}_{\max }}}{lp(l)}}{\sum\limits_{i=1}^{{{N}_{m}}}{\sum\limits_{j=1}^{{{N}_{m}}}{{{R}_{ij}}}}}$	描述了对角线结构的递归点数与所有递归点数的比例，反映了系统的可预测性
层流性	$LAM=\frac{\sum\limits_{v={{v}_{\min }}}^{{{v}_{\max }}}{vp(v)}}{\sum\limits_{v=1}^{{{v}_{\max }}}{vp(v)}}$	描述了递归图中垂直线结构的递归点数量，反映了系统的间歇性和层次性
递归熵	$ENTER = -\sum_{l=l_{\min }}^{N_{m}} p(l) \ln p(l)$	基于对角线长度频率分布的香农熵，描述了动力学系统种确定性结构和复杂度，反映了系统的动力学信息量或随机性程度

指标	计算方法	物理含义
递归率	$RR=\frac{\sum\limits_{i=1}^{{{N}_{m}}}{\sum\limits_{j=1}^{{{N}_{m}}}{{{R}_{ij}}}}}{N_{m}^{2}}$	描述了递归图中递归点的密度，反映了一个特定状态出现的概率
确定性	$DET=\frac{\sum\limits_{l={{l}_{\min }}}^{{{l}_{\max }}}{lp(l)}}{\sum\limits_{i=1}^{{{N}_{m}}}{\sum\limits_{j=1}^{{{N}_{m}}}{{{R}_{ij}}}}}$	描述了对角线结构的递归点数与所有递归点数的比例，反映了系统的可预测性
层流性	$LAM=\frac{\sum\limits_{v={{v}_{\min }}}^{{{v}_{\max }}}{vp(v)}}{\sum\limits_{v=1}^{{{v}_{\max }}}{vp(v)}}$	描述了递归图中垂直线结构的递归点数量，反映了系统的间歇性和层次性
递归熵	$ENTER = -\sum_{l=l_{\min }}^{N_{m}} p(l) \ln p(l)$	基于对角线长度频率分布的香农熵，描述了动力学系统种确定性结构和复杂度，反映了系统的动力学信息量或随机性程度

故障	释义
f₀	正常状态
f₁	电阻R₁开路
f₂	电阻R₃开路
f₃	电容C₁被击穿
f₄	电容C₁漏电

故障	释义
f₀	正常状态
f₁	电阻R₁开路
f₂	电阻R₃开路
f₃	电容C₁被击穿
f₄	电容C₁漏电

故障	f₀	f₁	f₂	f₃	f₄
f₀	0	0.017 8	0.101 0	0.386 3	0.039 2
f₁	0.017 8	0	0.056 0	0.182 1	0.006 6
f₂	0.101 0	0.056 0	0	0.164 9	0.025 2
f₃	0.386 3	0.182 1	0.164 9	0	0.142 7
f₄	0.039 2	0.006 6	0.025 2	0.142 7	0