CN103617350B

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Publication number: CN103617350B
Application number: CN201310578506.6A
Authority: CN
Inventors: 侯平智; 徐晓滨; 张镇; 刘征
Original assignee: Hangzhou Dianzi University
Current assignee: Hangzhou Dianzi University
Priority date: 2013-11-15
Filing date: 2013-11-15
Publication date: 2016-09-28
Anticipated expiration: 2033-11-15
Also published as: CN103617350A

Abstract

Description

Translated fromChinese

一种基于诊断证据平滑更新的旋转机械设备故障诊断方法A Fault Diagnosis Method for Rotating Machinery Equipment Based on Smooth Update of Diagnosis Evidence

技术领域technical field

本发明涉及一种基于诊断证据平滑更新的旋转机械设备故障诊断方法，属于旋转机械设备故障检测与诊断技术领域。The invention relates to a fault diagnosis method for rotating mechanical equipment based on smooth update of diagnostic evidence, and belongs to the technical field of fault detection and diagnosis of rotating mechanical equipment.

背景技术Background technique

在线故障诊断技术是保障旋转机械设备安全生产和高效运行的有力手段，但是目前情况下，该技术才刚刚起步，在实施过程中还面临诸多挑战。由于故障模式及其特征的复杂性和多样性，传统的基于单传感器的信息处理方法已不能胜任故障的检测和诊断，要想实现实时诊断并提高故障确诊率，采用多传感器增大诊断信息量势在必行。信息融合中的证据理论及方法以其在不确定性的表示、量测和融合等方面具有的优势，成为故障诊断领域中逐步被重视的一种方法。在已有的基于证据理论的各种融合诊断方法，如文献《基于模糊故障特征信息的随机集度量信息融合诊断方法，电子与信息学报》中提出的诊断证据获取及融合方法，由于只采用当前诊断证据判定故障，没有考虑当前诊断证据与历史及未来诊断证据之间的变化趋势及关系，必将使得最终的诊断决策缺乏足够的准确性和可靠性。Online fault diagnosis technology is a powerful means to ensure the safe production and efficient operation of rotating machinery equipment, but under the current circumstances, this technology has just started, and there are still many challenges in the implementation process. Due to the complexity and diversity of fault modes and their characteristics, the traditional information processing method based on a single sensor is no longer competent for fault detection and diagnosis. In order to achieve real-time diagnosis and improve the fault diagnosis rate, multi-sensors are used to increase the amount of diagnostic information. It is imperative. The evidence theory and method in information fusion has become a method that has gradually been paid attention to in the field of fault diagnosis because of its advantages in uncertainty representation, measurement and fusion. In the existing various fusion diagnosis methods based on evidence theory, such as the diagnostic evidence acquisition and fusion method proposed in the literature "Random Set Metric Information Fusion Diagnosis Method Based on Fuzzy Fault Feature Information, Journal of Electronics and Information Technology", because only the current Diagnostic evidence determines faults without considering the trend and relationship between current diagnostic evidence and historical and future diagnostic evidence, which will inevitably make the final diagnostic decision lack sufficient accuracy and reliability.

发明内容Contents of the invention

本发明的目的在于，所提出的一种基于诊断证据平滑更新的旋转机械设备故障诊断方法，将当前时刻诊断证据、历史及未来时刻诊断证据进行更新融合，利用得到的当前时刻更新后的诊断证据做出诊断决策，从而使得诊断结果更加准确与可靠。The object of the present invention is to propose a fault diagnosis method for rotating machinery equipment based on smooth update of diagnostic evidence, update and fuse current diagnostic evidence, historical and future diagnostic evidence, and use the updated diagnostic evidence obtained at current time Make diagnostic decisions, so that the diagnostic results are more accurate and reliable.

本发明提出的一种基于诊断证据平滑更新的旋转机械设备故障诊断方法，包括以下各步骤：A fault diagnosis method for rotating mechanical equipment based on smooth update of diagnostic evidence proposed by the present invention includes the following steps:

（1）设定旋转机械设备的故障集合为Θ＝{F₀,F₁,…,F_j,…,F_N}，F_j代表旋转机械设备的第j种故障(j＝0,1,…,N)，则共有N+1种故障。(1) Set the fault set of rotating mechanical equipment as Θ={F₀ ,F₁ ,…,F_j ,…,F_N }, F_j represents the jth type of fault of rotating mechanical equipment (j=0,1, ...,N), then there are N+1 types of faults.

（2）通过诊断证据生成方法，可在第k个时刻(k=1,2,3,…)，获得旋转机械设备的诊断证据为E_k＝(m_k(F₀),m_k(F₁),…,m_k(F_j),…,m_k(F_N),m_k(Θ))，其中m_k(F_j)表示在k时刻，对第j种故障发生的信度赋值，m_k(Θ)表示对故障集合的信度赋值，则E_k为这些信度赋值构成的一个信度赋值向量，并有1-(m_k(F₀)+m_k(F₁)+…+m_k(F_j)+…+m_k(F_N))＝m_k(Θ)。(2) Through the diagnostic evidence generation method, at the kth moment (k=1,2,3,…), the diagnostic evidence of rotating mechanical equipment can be obtained as E_k ＝(m_k (F₀ ),m_k (F₁ ),…,m_k (F_j ),…,m_k (F_N ),m_k (Θ)), where m_k (F_j ) represents the reliability assignment for the occurrence of the jth fault at time k , m_k (Θ) represents the reliability assignment to the fault set, then E_k is a reliability assignment vector formed by these reliability assignments, and there is 1-(m_k (F₀ )+m_k (F₁ )+ ...+m_k (F_j )+...+m_k (F_N ))=m_k (Θ).

（3）基于步骤（2）获得的诊断证据，通过线性加权诊断证据融合规则，用第k个时刻诊断证据对历史诊断证据进行平滑更新，从而获得k时刻更新后的诊断证据E_1:k＝(m_1:k(F₀),m_1:k(F₁),…,m_1:k(F_j),…,m_1:k(F_N),m_1:k(Θ))，其中1:k表示E_1:k是融合从1到k时刻所有的诊断证据得到的，具体步骤如下：(3) Based on the diagnostic evidence obtained in step (2), through the linear weighted diagnostic evidence fusion rule, the diagnostic evidence at the kth moment is used to smoothly update the historical diagnostic evidence, so as to obtain the updated diagnostic evidence E_1:k = (m_1:k (F₀ ),m_1:k (F₁ ),…,m_1:k (F_j ),…,m_1:k (F_N ),m_1:k (Θ)), Among them, 1:k means E._1:k is obtained by fusing all the diagnostic evidence from 1 to k. The specific steps are as follows:

（3-1）当k＝1时，更新后的诊断证据为(3-1) When k=1, the updated diagnostic evidence is

E_1:1＝E₁E_1:1 = E₁

亦即更新后的诊断证据即为该时刻获得的诊断证据；That is to say, the updated diagnostic evidence is the diagnostic evidence obtained at that time;

（3-2）当k≥2时，更新后的诊断证据向量E_1:k，其各元素取值由以下式(1)和(2)给出(3-2) When k≥2, the updated diagnostic evidence vector E_1:k , the value of each element is given by the following formulas (1) and (2)

m_1:k(A)＝α_km_1:k-1(A)+β_km_k(A|B) A,B∈Θ (1)m_1:k (A)＝α_k m_1:k-1 (A)+β_k m_k (A|B) A,B∈Θ (1)

m_1:k(Θ)＝1-Σ_A∈Θm_1:k(A) (2)m_1:k (Θ)＝1-Σ_A∈Θ m_1:k (A) (2)

其中，式(1)中的m_1:k-1(A)表示k-1时刻更新后诊断证据E_1:k-1对故障A的信度赋值；m_k(A|B)表示第k个时刻获得的关于故障A的条件化信度赋值，当A＝F_j时，若k时刻的诊断证据E_k＝(m_k(F₀),m_k(F₁),…,m_k(F_j),…,m_k(F_N),m_k(Θ))中，m_k(F_j)大于其他所有的m_k(F₀),m_k(F₁),…,m_k(F_j-1),…,m_k(F_j+1),…,m_k(F_N)，则B＝F_j，m_k(A|B)＝1；否则，m_k(A|B)＝0；Among them, m_1:k-1 (A) in formula (1) represents the reliability assignment of diagnostic evidence E_1:k-1 to fault A after updating at time k-1; m_k (A|B) represents the k-th The conditional reliability assignment about the fault A obtained at a moment, when A=F_j , if the diagnostic evidence E_{k at time k} =(m_k (F₀ ),m_k (F₁ ),…,m_k ( F_j ),…,m_k (F_N ),m_k (Θ)), m_k (F_j ) is greater than all other m_k (F₀ ),m_k (F₁ ),…,m_k ( F_j-1 ),…,m_k (F_j+1 ),…,m_k (F_N ), then B=F_j , m_k (A|B)=1; otherwise, m_k (A|B )=0;

α_k和β_k为线性融合平滑权重，求解步骤如下：α_k and β_k are linear fusion smoothing weights, and the solution steps are as follows:

（a）在获得k-1时刻更新后诊断证据E_1:k-1、k时刻诊断证据E_k和k+1时刻诊断证据E_k+1之后，利用公式(3)计算向量E_1:k-1与向量E_k之间的距离d(E_1:k-1,E_k)为(a) After obtaining the updated diagnostic evidence E_1:k-1 at time k-1, diagnostic evidence E k at time_k and diagnostic evidence E k+1 at time_k+1 , use formula (3) to calculate the vector E_1:k The distance d(E_1:k-1 ,E_k ) between_-1 and vector E_k is

$d d (({E E.}_{11 : : k k - - 11},, {E E.}_{k k})) = = \sqrt{\frac{11}{22} (({E E.}_{11 : : k k - - 11} - - {E E.}_{k k})) \underset{= =}{D D.} {(({E E.}_{11 : : k k - - 11} - - {E E.}_{k k}))}^{T T}} - - - - - - ((33))$

式中E_1:k-1-E_k为两向量对应元素相减后得到的向量，T表示向量的转置，为一个(N+2)×(N+2)的矩阵，它的对角线元素取值为1，其第N+2列的第1行至第N+1行的元素取值，以及第N+2行的第1列至第N+1列的元素取值均为1/(N+1)，其他元素取值为0;In the formula, E_1:k-1- E_k is the vector obtained after subtracting the corresponding elements of the two vectors, and T represents the transposition of the vector, It is a (N+2)×(N+2) matrix, its diagonal elements take the value 1, the elements of the N+2th column from the 1st row to the N+1th row take the value, and the The values of the elements from column 1 to column N+1 of row N+2 are all 1/(N+1), and the values of other elements are 0;

同理，由式(4)获得向量E_1:k-1与向量E_k+1之间的距离d(E_1:k-1,E_k+1)为Similarly, the distance d(E_1:k-1 ,E_k+1 ) between vector E_1:k-1 and vector E_k+1 is obtained from formula (4):

$d d (({E E.}_{11 : : k k - - 11},, {E E.}_{k k + + 11})) = = \sqrt{\frac{11}{22} (({E E.}_{11 : : k k - - 11} - - {E E.}_{k k + + 11})) \underset{= =}{D D.} {(({E E.}_{11 : : k k - - 11} - - {E E.}_{k k + + 11}))}^{T T}} - - - - - - ((44))$

由式(5)获得向量E_k与向量E_k+1之间的距离d(E_k,E_k+1)为The distance d(E_k ,E_k+1 ) between the vector E_k and the vector E_k+1 is obtained from formula (5) as

$d d (({E E.}_{k k},, {E E.}_{k k + + 11})) = = \sqrt{\frac{11}{22} (({E E.}_{k k} - - {E E.}_{k k + + 11})) \underset{= =}{D D.} {(({E E.}_{k k} - - {E E.}_{k k + + 11}))}^{T T}} - - - - - - ((55))$

（b）由上述步骤（a）求得距离d(E_1:k-1,E_k)、d(E_1:k-1,E_k+1)和d(E_k,E_k+1)后，计算k时刻E_1:k-1、E_k和E_k+1两两之间的相似度：(b) Calculate the distances d(E_1:k-1 ,E_k ), d(E_1:k-1 ,E_k+1 ) and d(E_k ,E_k+1 ) from the above step (a) Finally, calculate the similarity between E_1:k-1 , E_k and E_k+1 at time k:

利用公式(6)计算向量E_1:k-1与向量E_k之间的相似度c(E_1:k-1,E_k)为Use formula (6) to calculate the similarity c(E_1:k-1 ,E_k ) between vector E_1:k-1 and vector E_k as

c(E_1:k-1,E_k)＝1-d(E_1:k-1,E_k) (6)相似度c(E_1:k-1,E_k)是衡量向量E_1:k-1与向量E_k的相近程度，亦即两个证据一致的程度，且有c(E_1:k-1,E_k)＝c(E_k,E_1:k-1)，即向量E_1:k-1与向量E_k的相似度等于向量E_k与向量E_1:k-1的相似度；c(E_1:k-1 ,E_k )＝1-d(E_1:k-1 ,E_k ) (6) similarity c(E_1:k-1 ,E_k ) is the measure vector E_1: The similarity between_k-1 and vector E_k is the degree of consistency between the two evidences, and c(E_1:k-1 ,E_k )=c(E_k ,E_1:k-1 ), that is, the vector The similarity between E_1:k-1 and vector E_k is equal to the similarity between vector E_k and vector E_1:k-1 ;

同理，由式(7)获得向量E_1:k-1与向量E_k+1之间的相似度c(E_1:k-1,E_k+1)为Similarly, the similarity c(E_1:k-1 , E_k+1 ) between vector E_1:k-1 and vector E_k+1 is obtained from formula (7):

c(E_1:k-1,E_k+1)＝1-d(E_1:k-1,E_k+1) (7)c(E_1:k-1 ,E_k+1 )＝1-d(E_1:k-1 ,E_k+1 ) (7)

由式(8)获得向量E_k与向量E_k+1之间的相似度c(E_k,E_k+1)为The similarity c(E_k ,E_k+1 ) between the vector E_k and the vector E_k+1 is obtained from formula (8) as

c(E_k,E_k+1)＝1-d(E_k,E_k+1) (8)c(E_k ,E_k+1 )＝1-d(E_k ,E_k+1 ) (8)

（c）按照上述步骤（b）获得在k时刻诊断证据向量E_1:k-1、E_k和E_k+1两两相似度c(E_1:k-1,E_k)，c(E_1:k-1,E_k+1)及c(E_k,E_k+1)之后，计算每个证据向量被其他两个证据向量所支持的支持度：(c) Obtain the pairwise similarity c(E_1:k-1 ,E_k ) of the diagnostic evidence vector E_1:k-1 , E_k and E_k+1 at time k according to the above step (b), c(E_1:k-1 ,E_k+1 ) and c(E_k ,E_k+1 ), calculate the support degree of each evidence vector supported by the other two evidence vectors:

利用式(9)计算证据向量E_1:k-1被证据向量E_k和E_k+1所支持的支持度s(E_1:k-1)为Use formula (9) to calculate the support degree s(E_1:k-1 ) of evidence vector E_1:k-1 supported by evidence vector E_k and E_k+1 as

s(E_1:k-1)＝c(E_1:k-1,E_k)+c(E_1:k-1,E_k+1) (9)s(E_1:k-1 )=c(E_1:k-1 ,E_k )+c(E_1:k-1 ,E_k+1 ) (9)

支持度s是相似性度量的函数，表示该证据被其他证据所支持的程度，s(E_1:k-1)值越高，则说明证据向量E_1:k-1与证据向量E_k和E_k+1之间的相似性越高；The support degree s is a function of the similarity measure, which indicates the extent to which the evidence is supported by other evidence. The higher the value of s(E_1:k-1 ), it means that the evidence vector E_1:k-1 is consistent with the evidence vector E_k and The higher the similarity between E_k+1 ;

同理，由公式(10)计算证据向量E_k被证据向量E_1:k-1和E_k+1所支持的支持度s(E_k)为Similarly, the support degree s(E_k ) of evidence vector E_k supported by evidence vector E_1:k-1 and E_k+1 calculated by formula (10) is

s(E_k)＝c(E_1:k-1,E_k)+c(E_k,E_k+1) (10)s(E_k )=c(E_1:k-1 ,E_k )+c(E_k ,E_k+1 ) (10)

由公式(11)计算证据向量E_k+1被证据向量E_1:k-1和E_k所支持的支持度s(E_k+1)为Calculate the support degree s(E_k+1 ) of the evidence vector E_k+1 supported by the evidence vector E_1:k-1 and E_k by the formula (11):

s(E_k+1)＝c(E_1:k-1,E_k+1)+c(E_k,E_k+1) (11)s(E_k+1 )=c(E_1:k-1 ,E_k+1 )+c(E_k ,E_k+1 ) (11)

（d）基于步骤（c）依次求出诊断证据向量E_1:k-1、E_k和E_k+1在k时刻的可靠度K：利用公式(12)计算证据向量E_1:k-1在k时刻的可靠度K(E_1:k-1)为(d) Calculate the reliability K of diagnostic evidence vectors E_1:k-1 , E_k and E_k+1 at time k based on step (c): calculate the evidence vector E_1:k-1 using formula (12) The reliability K(E_1:k-1 ) at time k is

$K K (({E E.}_{11 : : k k - - 11})) = = \frac{s the s (({E E.}_{11 : : k k - - 11}))}{s the s (({E E.}_{11 : : k k - - 11})) + + s the s (({E E.}_{k k})) + + s the s (({E E.}_{k k + + 11}))} - - - - - - ((1212))$

同理，由公式(13)计算证据向量E_k在k时刻的可靠度K(E_k)为Similarly, the reliability K(E_k ) of the evidence vector E_k at time k is calculated by formula (13) as

$K K (({E E.}_{k k})) = = \frac{s the s (({E E.}_{k k}))}{s the s (({E E.}_{11 : : k k - - 11})) + + s the s (({E E.}_{k k})) + + s the s (({E E.}_{k k + + 11}))} - - - - - - ((1313))$

由公式(14)计算证据向量E_k+1在k时刻的可靠度K(E_k+1)为Calculate the reliability K(E_k+1 ) of the evidence vector E_k+1 at time k by formula (14) as

$K K (({E E.}_{k k + + 11})) = = \frac{s the s (({E E.}_{k k + + 11}))}{s the s (({E E.}_{11 : : k k - - 11})) + + s the s (({E E.}_{k k})) + + s the s (({E E.}_{k k + + 11}))} - - - - - - ((1414))$

有K(E_1:k-1)+K(E_k)+K(E_k+1)=1，一个证据向量的可靠度K越高，说明该证据与其他证据的相似性越高，该证据越可靠，反之亦然；There is K(E_1:k-1 )+K(E_k )+K(E_k+1 )=1, the higher the reliability K of an evidence vector, the higher the similarity between the evidence and other evidence, the The more reliable the evidence, and vice versa;

（e）基于上述步骤（b）所求得的E_1:k-1与E_k+1之间的相似度c(E_1:k-1,E_k+1)、E_k与E_k+1之间的相似度c(E_k,E_k+1)，通过判断二者之间的大小确定α_k，β_k的取值：(e) Based on the similarity c(E_1:k-1 ,E_k+1 ) between E_1:k-1 and E_k+1 obtained in the above step (b), E_k and E_k+ The similarity c(E_k ,E_k+1₎ between 1, determine the value of α_k and β_k by judging the size between them:

若c(E_1:k-1,E_k+1)≥c(E_k,E_k+1)， $\{\begin{matrix} α_{k} = K (E_{1 : k - 1}) + K (E_{k + 1}) \\ β_{k} = K (E_{k}) \end{matrix}$ If c(E_1:k-1 ,E_k+1 )≥c(E_k ,E_k+1 ), $\{\begin{matrix} α_{k} = K ({E.}_{1 : k - 1}) + K ({E.}_{k + 1}) \\ β_{k} = K ({E.}_{k}) \end{matrix}$

若c(E_1:k-1,E_k+1)＜c(E_k,E_k+1)， $\{\begin{matrix} α_{k} = K (E_{1 : k - 1}) \\ β_{k} = K (E_{k}) + K (E_{k + 1}) \end{matrix}$ If c(E_1:k-1 ,E_k+1 )<c(E_k ,E_k+1 ), $\{\begin{matrix} α_{k} = K ({E.}_{1 : k - 1}) \\ β_{k} = K ({E.}_{k}) + K ({E.}_{k + 1}) \end{matrix}$

求得α_k，β_k的取值后将其代入步骤（3-2）的(1)式中，通过递归计算即可获得各个时刻更新后的诊断证据。After obtaining the values of α_k and β_k , they are substituted into the formula (1) in step (3-2), and the updated diagnostic evidence at each moment can be obtained through recursive calculation.

（4）根据上述步骤（3）在k时刻获得的更新后诊断证据E_1:k＝(m_1:k(F₀),m_1:k(F₁),…,m_1:k(F_j),…,m_1:k(F_N),m_1:k(Θ))，对旋转机械设备的故障进行诊断：若m_1:k(F_j)的取值大于其他m_1:k(F₀),m_1:k(F₁),…,m_1:k(F_j-1),…,m_1:k(F_j+1),…,m_1:k(F_N)，则判定故障F_j发生。(4) The updated diagnostic evidence E_1:k ＝(m_1:k (F₀ ),m_1:k (F₁ ),…,m_1: k (F 1 ) obtained at time k according to the above step (3)._j ),…,m_1:k (F_N ),m_1:k (Θ)), diagnose the faults of rotating mechanical equipment: if the value of m_1:k (F_j ) is greater than other m_1:k (F₀ ),m_1:k (F₁ ),…,m_1:k (F_j-1 ),…,m_1:k (F_j+1 ),…,m_1:k (F_N ) , then it is judged that the fault F_j occurs.

上述方法的关键技术在于：步骤（3-2）中求解的线性融合平滑权重α_k，β_k，综合考虑了当前、历史及未来时刻诊断证据之间的变化趋势及关系，克服了以往诊断证据融合方法，在做出诊断决策时未考虑历史及未来时刻的诊断信息对当前时刻诊断证据的影响，所引起的诊断决策不准确和可靠性低的缺点。The key technology of the above method is: the linear fusion smoothing weights α_k and β_k solved in step (3-2) comprehensively consider the changing trend and relationship among the current, historical and future diagnostic evidence, and overcome the previous diagnostic evidence. The fusion method does not consider the impact of historical and future diagnostic information on the current diagnostic evidence when making diagnostic decisions, resulting in inaccurate diagnostic decisions and low reliability.

本发明提出的基于诊断证据平滑更新的旋转机械设备故障诊断方法，能实现旋转机械设备的在线故障诊断，有效地监控设备的运行状态，在发生紧急状况时能够及时提醒操作人员进行检修处理，大幅度地提升诊断的可靠性和准确性。而且本发明对故障演变的趋势进行了跟踪，在某种程度上对故障的发生也起到一定的预测作用。在诊断证据没有发生大的波动时，更新后的诊断证据可以与未更新诊断证据基本上保持一致且有利于对设备运行状态做出准确的判断；当诊断证据发生急剧的变化时，更新后的诊断证据能够反映出这种变化，并能快速跟踪故障信度的变化趋势，从而实现更快、更准的诊断决策。根据本发明方法编制的程序（编译环境LabVIEW，C++等）可以在监控计算机上运行，并联合传感器、数据采集器等硬件组成在线监测系统，进行实时的旋转机械设备故障的检测与诊断。The fault diagnosis method for rotating machinery equipment based on the smooth update of diagnostic evidence proposed by the present invention can realize online fault diagnosis of rotating machinery equipment, effectively monitor the operating status of the equipment, and promptly remind the operator to perform maintenance in case of an emergency. Significantly improve the reliability and accuracy of diagnosis. Moreover, the present invention tracks the trend of fault evolution, and to some extent also plays a role in predicting the occurrence of faults. When the diagnostic evidence does not fluctuate greatly, the updated diagnostic evidence can be basically consistent with the non-updated diagnostic evidence and is conducive to making an accurate judgment on the equipment operating status; when the diagnostic evidence changes sharply, the updated diagnostic evidence Diagnostic evidence can reflect this change, and can quickly track the changing trend of fault reliability, so as to achieve faster and more accurate diagnostic decisions. The program compiled according to the method of the present invention (compilation environment LabVIEW, C++, etc.) can run on the monitoring computer, and combine sensors, data collectors and other hardware to form an online monitoring system to detect and diagnose the faults of rotating mechanical equipment in real time.

附图说明Description of drawings

图1是本发明方法的流程框图。Fig. 1 is a block flow diagram of the method of the present invention.

图2本发明方法的实施例中电机转子故障诊断系统结构图。Fig. 2 is a structural diagram of a motor rotor fault diagnosis system in an embodiment of the method of the present invention.

图3是本发明方法的实施例中电机转子处于正常运行模式（F₀）下各故障信度赋值的走势图（k=1,2,…,10时刻）。Fig. 3 is a trend diagram (moment k=1, 2, ..., 10) of each fault reliability assignment when the motor rotor is in the normal operation mode (F₀ ) in the embodiment of the method of the present invention.

图4是本发明方法的实施例中电机转子在k=7时刻由正常运行模式（F₀）逐渐转变为不平衡故障（F₁）时各故障信度赋值的走势图（k=1,2,…,10时刻）。Fig. 4 is a trend diagram of each fault reliability assignment when the motor rotor gradually changes from the normal operation mode (F₀ ) to the unbalanced fault (F₁ ) at k=7 in the embodiment of the method of the present invention (k=1,2 ,...,10 moments).

图5是本发明实施例中电机转子在k=6时刻由正常运行模式（F₀）突然转变为不平衡故障（F₁）时各故障信度赋值的走势图（k=1,2,…,10时刻）。Fig. 5 is a trend diagram of each fault reliability assignment (k₌_1,2 ,... ,10 moments).

图6是本发明实施例中电机转子开始时处于正常运行模式（F₀），在k=6时刻受到干扰（表现为不平衡故障F₁）又恢复正常状态时各故障信度赋值的走势图（k=1,2,…,10时刻）。Fig. 6 is a trend chart of the assignment of each fault reliability when the rotor of the motor in the embodiment of the present invention is in the normal operation mode (F₀ ) at the beginning, and is disturbed at k=6 (expressed as an unbalanced fault F₁ ) and returns to the normal state (k=1,2,...,10 moments).

图7是本发明实施例中电机转子开始时处于正常运行模式（F₀），在k=6和k=7时刻分别受到干扰（分别表现为不平衡故障F₁和不对中故障F₂）时各故障信度赋值的走势图（k=1,2,…,10时刻）。Fig. 7 shows that the rotor of the motor in the embodiment of the present invention is in the normal operation mode (F₀ ) at the beginning, and is disturbed at k=6 and k=7 (expressed as unbalance fault F₁ and misalignment fault F₂ , respectively). The trend chart of each fault reliability assignment (k=1, 2,..., 10 moments).

图8是本发明实施例中电机转子开始时处于正常运行模式（F₀），在k=5时刻突然受到干扰（表现为不平衡故障F₁）又恢复正常状态，然后，在k=7时刻又受到干扰（表现不对中故障F₂）时各故障信度赋值的走势图（k=1,2,…,10时刻）。Figure 8 shows that the rotor of the motor in the embodiment of the present invention was in the normal operation mode (F₀ ) at the beginning, and was suddenly disturbed at k=5 (expressed as an unbalanced fault F₁ ) and returned to the normal state, and then at k=7 The trend chart of the reliability assignment of each fault (moment k=1,2,...,10) when it is disturbed again (representing misalignment fault F₂ ).

具体实施方式detailed description

本发明提出的基于诊断证据平滑更新的旋转机械设备故障诊断方法，其流程框图如图1所示，包括以下各步骤：The fault diagnosis method for rotating mechanical equipment based on the smooth update of diagnostic evidence proposed by the present invention has a flow chart as shown in Figure 1, including the following steps:

（1）设定旋转机械设备的故障集合为Θ＝{F₀,F₁,…,F_j,…,F_N}，F_j代表旋转机械设备的第j种故障(j＝0,1,…,N)，则共有N+1种故障；(1) Set the fault set of rotating mechanical equipment as Θ={F₀ ,F₁ ,…,F_j ,…,F_N }, F_j represents the jth type of fault of rotating mechanical equipment (j=0,1, …,N), then there are N+1 types of faults;

（2）通过诊断证据生成方法，可在第k个时刻(k=1,2,3,…)，获得旋转机械设备的诊断证据为E_k＝(m_k(F₀),m_k(F₁),…,m_k(F_j),…,m_k(F_N),m_k(Θ))，其中m_k(F_j)表示在k时刻，对第j种故障发生的信度赋值，m_k(Θ)表示对故障集合的信度赋值，则E_k为这些信度赋值构成的一个信度赋值向量，并有1-(m_k(F₀)+m_k(F₁)+…+m_k(F_j)+…+m_k(F_N))＝m_k(Θ)；(2) Through the diagnostic evidence generation method, at the kth moment (k=1,2,3,…), the diagnostic evidence of rotating mechanical equipment can be obtained as E_k ＝(m_k (F₀ ),m_k (F₁ ),…,m_k (F_j ),…,m_k (F_N ),m_k (Θ)), where m_k (F_j ) represents the reliability assignment for the occurrence of the jth fault at time k , m_k (Θ) represents the reliability assignment to the fault set, then E_k is a reliability assignment vector formed by these reliability assignments, and there is 1-(m_k (F₀ )+m_k (F₁ )+ ...+m_k (F_j )+...+m_k (F_N ))=m_k (Θ);

E_1:1＝E₁E_1:1 = E₁

m_1:k(Θ)＝1-Σ_A∈Θm_1:k(A) (2)m_1:k (Θ)＝1-Σ_A∈Θ m_1:k (A) (2)

为了加深对诊断证据向量距离的理解，这里举例加以说明：假设已获得故障诊断证据E_k＝(m_k(F₀),m_k(F₁),…,m_k(F_j),…,m_k(F_N),m_k(Θ))，这里取k=1,2,3，N=2。各时刻诊断证据所对应的信度赋值如表1所示，其中，k表示各时刻，m表示信度赋值。In order to deepen the understanding of the distance of the diagnostic evidence vector, here is an example to illustrate: Suppose the fault diagnosis evidence E_k =(m_k (F₀ ),m_k (F₁ ),…,m_k (F_j ),…, m_k (F_N ), m_k (Θ)), where k=1,2,3, N=2. The reliability assignment corresponding to the diagnostic evidence at each moment is shown in Table 1, where k represents each moment, and m represents the reliability assignment.

表1k=1,2,3时刻获得的诊断证据Table 1k=Diagnostic evidence obtained at time 1,2,3

由步骤（3-1）得到：k=1时刻更新后的诊断证据E_1:1为Obtained from step (3-1): the updated diagnostic evidence E_1:1 at time k=1 is

E_1:1=E₁=(0.9 0.04 0.03 0.03)E_1:1 =E₁ =(0.9 0.04 0.03 0.03)

根据步骤（a）知，为一个4×4的对角矩阵，表示如下：According to step (a), is a 4×4 diagonal matrix expressed as follows:

$\underset{= =}{D D.} = = [\begin{matrix} 11 & 00 & 00 & \frac{11}{33} \\ 00 & 11 & 00 & \frac{11}{33} \\ 00 & 00 & 11 & \frac{11}{33} \\ \frac{11}{33} & \frac{11}{33} & \frac{11}{33} & 11 \end{matrix}]$

矩阵中元素计算仅列出予以说明， ${\underset{=}{D}}_{2,4} = D ({F_{0}}, Θ) = | F_{0} | / | Θ | = 1 / 3$ matrix Element calculations only list be explained, ${\underset{=}{D.}}_{2,4} = D. ({f_{0}}, Θ) = | f_{0} | / | Θ | = 1 / 3$

由表1和公式(3)可以得到诊断证据向量E_1:1与向量E₂之间的距离d(E_1:1,E₂)为From Table 1 and formula (3), the distance d(E_1:1 , E₂ ) between the diagnostic evidence vector E_1:1 and the vector E₂ can be obtained as

E_1:1-E₂=（0.05 -0.02 -0.02 -0.01）E_1:1 -E₂ = (0.05 -0.02 -0.02 -0.01)

$d d (({E E.}_{11 : : 11},, {E E.}_{22})) = = \sqrt{\frac{11}{22} (({E E.}_{11 : : 11} - - {E E.}_{22})) \underset{= =}{D D.} {(({E E.}_{11 : : 11} - - {E E.}_{22}))}^{T T}} = = 0.0577 0.0577$

同理，根据公式(4)和(5)可以求出d(E_1:1,E₃)和d(E₂,E₃)为d(E_1:1,E₃)＝0.1871，Similarly, according to formulas (4) and (5), d(E_1:1 , E₃ ) and d(E₂ , E₃ ) can be calculated as d(E_1:1 , E₃ )=0.1871,

d(E₂,E₃)＝0.1354d(E₂ ,E₃ )=0.1354

c(E_1:k-1,E_k)＝1-d(E_1:k-1,E_k) (6)c(E_1:k-1 ,E_k )=1-d(E_1:k-1 ,E_k ) (6)

相似度c(E_1:k-1,E_k)是衡量向量E_1:k-1与向量E_k的相近程度，亦即两个证据一致的程度，且有c(E_1:k-1,E_k)＝c(E_k,E_1:k-1)，即向量E_1:k-1与向量E_k的相似度等于向量E_k与向量E_1:k-1的相似度；Similarity c(E_1:k-1 ,E_k ) is a measure of the similarity between vector E_1:k-1 and vector E_k , that is, the degree of consistency between the two evidences, and c(E_1:k-1 ,E_k )=c(E_k ,E_1:k-1 ), that is, the similarity between vector E_1:k-1 and vector E_k is equal to the similarity between vector E_k and vector E_1:k-1 ;

c(E_k,E_k+1)＝1-d(E_k,E_k+1) (8)c(E_k ,E_k+1 )＝1-d(E_k ,E_k+1 ) (8)

求得α_k，β_k的取值后将其代入步骤（3-2）的(1)式中，通过递归计算即可获得各个时刻的更新后的诊断证据；After obtaining the values of α_k and β_k , substitute them into the formula (1) in step (3-2), and obtain the updated diagnostic evidence at each moment through recursive calculation;

为了便于理解，这里给出具体实例，基于上例，求k=2时诊断证据的更新结果：For ease of understanding, a specific example is given here. Based on the above example, the update result of the diagnostic evidence when k=2 is obtained:

基于上例求得的诊断证据向量之间的距离，由公式(6)可以求出向量E_1:1与向量E₂之间的相似度c(E_1:1,E₂)＝1-d(E_1:1,E₂)＝0.9423Based on the distance between the diagnostic evidence vectors obtained in the above example, the similarity c(E_1:1 , E₂ )=1-d between the vector E_1:1 and the vector E₂ can be obtained by the formula (6) (E_1:1 ,E₂ )＝0.9423

同理，由公式(7)和(8)得到c(E_1:1,E₃)＝0.8129，c(E₂,E₃)＝0.8646Similarly, c(E_1:1 ,E₃ )=0.8129, c(E₂ ,E₃ )=0.8646 are obtained from formulas (7) and (8)

根据公式(9)～(14)可以依次计算出诊断证据向量E_1:1、E₂及E₃在k=2时刻的可靠度分别为K(E_1:1)＝0.3350，K(E₂)＝0.3449，K(E₃)＝0.3202According to formulas (9)-(14), the reliability of diagnostic evidence vectors E_1:1 , E₂ and E₃ at time k=2 can be calculated as K(E_1:1 )=0.3350, K(E₂ )=0.3449, K(E₃ )=0.3202

根据步骤（e）确定α₂，β₂的取值如下：Determine α₂ according to step (e), and the value of β₂ is as follows:

因为c(E_1:1,E₃)＜c(E₂,E₃)，故 $\{\begin{matrix} α_{1} = K (E_{1 : 1}) = 0.3350 \\ β_{2} = K (E_{2}) + K (E_{3}) = 0.6650 \end{matrix}$ Since c(E_1:1 ,E₃ )<c(E₂ ,E₃ ), so $\{\begin{matrix} α_{1} = K ({E.}_{1 : 1}) = 0.3350 \\ β_{2} = K ({E.}_{2}) + K ({E.}_{3}) = 0.6650 \end{matrix}$

由公式(1)和(2)对k=2时刻的诊断证据进行更新，因为在k=2时刻时，m(F₀)取值最大，故在确定条件化信度赋值时，B=F₀；当A=F₀时，m₂(F₀|F₀)＝1；否则，m₂(A|F₀)＝0（A=F₁、F₂、Θ），更新结果如表2The diagnostic evidence at time k=2 is updated by formulas (1) and (2), because m(F₀ ) takes the largest value at time k=2, so when determining the conditional reliability assignment, B=F₀ ; when A=F₀ , m₂ (F₀ |F₀ )＝1; otherwise, m₂ (A|F₀ )＝0 (A=F₁ , F₂ , Θ), the updated results are shown in Table 2

表2k=2时刻时更新后的诊断证据Table 2 The updated diagnostic evidence at time k=2

以下结合附图，详细介绍本发明方法的实施例：Below in conjunction with accompanying drawing, introduce the embodiment of the inventive method in detail:

本发明方法的流程框图如图1所示，核心部分是：通过求解历史、当前及未来相邻三个时刻诊断证据向量之间的距离，得到两两向量之间的相似度，继而得到线性加权诊断证据融合时的线性融合平滑权重，从而实现对历史诊断证据的更新，得到准确可靠的诊断结果。The flow chart of the method of the present invention is shown in Figure 1. The core part is: by solving the distance between the diagnostic evidence vectors at three adjacent moments in history, current and future, the similarity between two vectors is obtained, and then the linear weighting is obtained. The linear fusion smoothing weight in the fusion of diagnostic evidence can realize the update of historical diagnostic evidence and obtain accurate and reliable diagnostic results.

以下结合图2中电机转子故障诊断系统的最佳实施例，详细介绍本发明方法的各个步骤，并通过实际结果验证本发明提出的基于诊断证据平滑更新的故障诊断方法优于其他方法。Below in conjunction with the best embodiment of the motor rotor fault diagnosis system in Fig. 2, each step of the method of the present invention is introduced in detail, and the actual results verify that the fault diagnosis method based on the smooth update of diagnostic evidence proposed by the present invention is superior to other methods.

1、电机转子故障诊断系统设置实例1. Setting example of motor rotor fault diagnosis system

实验设备如图2中的ZHS-2型多功能电机柔性转子系统，将振动位移传感器和加速度传感器分别安置在转子支撑座的水平和垂直方向采集转子振动信号，经HG-8902采集箱将信号传输至计算机，然后利用Labview环境下的HG-8902数据分析软件得到转子振动加速度频谱以及时域振动位移平均幅值作为故障特征信号。The experimental equipment is the ZHS-2 multifunctional motor flexible rotor system shown in Figure 2. The vibration displacement sensor and the acceleration sensor are respectively placed in the horizontal and vertical directions of the rotor support seat to collect the rotor vibration signal, and the signal is transmitted through the HG-8902 acquisition box. Then use the HG-8902 data analysis software in the Labview environment to obtain the rotor vibration acceleration spectrum and the average amplitude of the vibration displacement in the time domain as the fault characteristic signal.

2、电机转子故障设置及故障特征参数的选取2. Motor rotor fault setting and selection of fault characteristic parameters

分别在试验台上对电机转子设置了故障F₀={正常运行}、F₁={不平衡}、F₂={不对中}和F₃={基座松动}，则故障集合即辨识框架为Θ＝{F₀,F₁,F₂,F₃}。通过监测设备的运行状况，得到传感器在不同情况下连续10个时刻的证据。The faults F₀ = {normal operation}, F₁ = {unbalanced}, F₂ = {misalignment} and F₃ = {loose base} are set for the motor rotor on the test bench, then the fault set is the identification framework is Θ={F₀ , F₁ , F₂ , F₃ }. By monitoring the operating status of the equipment, the evidence of the sensor in different situations for 10 consecutive moments is obtained.

结合最佳实施例图3到图8中描述的六个诊断实验（三种情况），将本发明方法与传统的线性组合方法进行对比，以凸显本发明方法的优势，具体分析如下：In conjunction with the six diagnostic experiments (three situations) described in Fig. 3 to Fig. 8 of the best embodiment, the method of the present invention is compared with the traditional linear combination method to highlight the advantages of the method of the present invention. The specific analysis is as follows:

2-1）情况一：电机转子在第k（k=1,2,…,10）时刻一直保持正常运行状态，不同时刻获得的诊断证据（图3中“--◇--”表示）如表3所示：2-1) Situation 1: The motor rotor keeps running normally at the kth time (k=1,2,...,10), and the diagnostic evidence obtained at different times (indicated by "--◇--" in Figure 3) is as follows Table 3 shows:

由表3知，在设备正常运行时，各不同时刻诊断证据向量之间差异不明显时，用本发明方法与线性组合方法获得的各个故障信度赋值的走势图如图3所示：这里之所以没有给出m_k(Θ)的走势图，是因为m_k(Θ)经过融合之后会变得非常小以至于几乎不影响故障的诊断和决策。It is known from Table 3 that when the equipment is in normal operation, when the difference between the diagnostic evidence vectors at different times is not obvious, the trend diagram of each fault reliability assignment obtained by the method of the present invention and the linear combination method is shown in Figure 3: Therefore, the trend chart of m_k (Θ) is not given, because m_k (Θ) will become so small after fusion that it will hardly affect the fault diagnosis and decision-making.

在这种情况下，因为系统总是保持正常运行，故m_k(F₀)始终保持最大。因此，更新后诊断证据中对F₀的信度赋值一直最大，从图3可以明显地看出本发明方法计算出的F₀的信度赋值（图3中“--◇--”表示），要比线性组合方法计算出的信度赋值（图3中“--*--”表示）更大，更有利于可靠地判定设备此时处于F₀，并且通过F₁、F₂、F₃的走势图分析，不难得知到本发明还可以有效地降低其他故障的信度赋值，避免决策中受到这些不确定信度的干扰。In this case, m_k (F₀ ) always remains maximum because the system always keeps running normally. Therefore, the reliability assignment of F₀ in the updated diagnostic evidence has always been the largest, and it can be clearly seen from Figure 3 that the reliability assignment of F₀ calculated by the method of the present invention (indicated by "--◇--" in Figure 3) , is larger than the reliability assignment calculated by the linear combination method (indicated by "--*--" in Figure 3), and is more conducive to reliably determine that the equipment is at F₀ at this time, and through F₁ , F₂ , F₃ , it is not difficult to know that the present invention can also effectively reduce the reliability assignment of other faults, and avoid the interference of these uncertain reliability in decision-making.

表3各个时刻获得的诊断证据Table 3 Diagnosis evidence obtained at each moment

2-2）情况二：电机转子由正常运行状态过渡到故障状态时，此时过渡态又可以分渐变（图4）和突变（图5）两种情况。2-2) Situation 2: When the motor rotor transitions from the normal operation state to the fault state, the transition state can be divided into two cases: gradual change (Figure 4) and sudden change (Figure 5).

（a）电机转子在k=1时刻至k=7时刻处于正常运行状态，之后逐渐发生故障F₁。图4中给出了更新融合前的诊断证据，以及两种方法得到的更新后诊断证据走势图。(a) The rotor of the motor is in normal operation from time k=1 to time k=7, and then the fault F₁ gradually occurs. Figure 4 shows the diagnostic evidence before the update fusion, and the trend chart of the updated diagnostic evidence obtained by the two methods.

（b）电机转子k=1时刻至k=6时刻处于正常运行状态，k=7时刻突然发生故障F₁直至k=10时刻。此时诊断证据的更新结果如图5所示：(b) The motor rotor is in normal operation from time k=1 to time k=6, and a fault F₁ occurs suddenly at time k=7 until time k=10. At this time, the update results of the diagnostic evidence are shown in Figure 5:

从图4故障信度赋值发生渐变的情况可以看出，在k=8时刻，当故障F₁的信度赋值逐渐变大时，本发明方法给出的更新后诊断证据中，对F₁的信度赋值增大明显（取值0.75）而线性组合方法给出的更新后诊断证据中，对F₁的信度赋值只有0.48，此时该方法误判为F₀。随着时间的推移，本发明方法对F₁的信度赋值一直保持最大，而线性组合方法对F₁的信度赋值增长缓慢，且与原始诊断证据差距较小，说明其更新融合的作用不大。从图5故障信度赋值发生突变的情况可以看出，在k=7时刻，原始诊断证据对F₁的信度赋值突然增大，之后一直保持高位，说明F₁突然发生，此时本发明方法给出的更新后诊断证据中对F₁的信度赋值增大明显（取值0.78）而线性组合方法给出的更新后诊断证据中，对F₁的信度赋值只有0.21，此时该方法误判为F₀。随着时间的推移，本发明方法对F₁的信度赋值一直保持最大，而线性组合方法对F₁的信度赋值增长缓慢，且与原始诊断证据差距较小，说明其更新融合的作用不大。综合比较可以看出，本发明方法给出的更新后诊断证据，对所发生故障的信度赋值一直高于线性组合方法给出的结果且稳定保持，有利于给出更为可靠的诊断结果。It can be seen from the gradual change of the fault reliability assignment in Figure 4 that at k=8, when the reliability assignment of the fault F₁ gradually becomes larger, in the updated diagnostic evidence given by the method of the present invention, the F₁ The reliability assignment increased significantly (value 0.75), but in the updated diagnostic evidence given by the linear combination method, the reliability assignment for F₁ was only 0.48, and the method misjudged F₀ at this time. As time goes by, the method of the present invention maintains the largest reliability assignment to F₁ all the time, while the reliability assignment of the linear combination method to F₁ grows slowly, and the gap with the original diagnostic evidence is small, indicating that its update fusion effect is not significant. Big. It can be seen from the sudden change in the assignment of fault reliability in Fig. 5 that at k=7, the reliability assignment of the original diagnostic evidence to F₁ suddenly increases, and then remains high, indicating that F₁ occurs suddenly. At this time, the present invention In the updated diagnostic evidence given by the method, the reliability assignment to F₁ increased significantly (value 0.78), while in the updated diagnostic evidence given by the linear combination method, the reliability assignment to F₁ was only 0.21. The method misjudged F₀ . As time goes by, the method of the present invention maintains the largest reliability assignment to F₁ all the time, while the reliability assignment of the linear combination method to F₁ grows slowly, and the gap with the original diagnostic evidence is small, indicating that its update fusion effect is not significant. Big. From a comprehensive comparison, it can be seen that the updated diagnostic evidence given by the method of the present invention has always been higher than the result given by the linear combination method and remains stable, which is conducive to giving more reliable diagnostic results.

2-3）情况三：电机转子正常运行过程中不同时刻受到了外界干扰，一旦干扰消失，转子又重新恢复到正常运行状态，此时系统状态又可细分为三种子情况：2-3) Situation 3: The motor rotor is subjected to external interference at different times during normal operation. Once the interference disappears, the rotor returns to normal operation again. At this time, the system state can be subdivided into three sub-cases:

（a）电机转子仅在k=6时刻受到干扰（表现为不平衡故障F₁），此时诊断证据的更新结果如图6所示：(a) The rotor of the motor is disturbed only at time k=6 (expressed as an unbalanced fault F₁ ), and the update results of the diagnostic evidence at this time are shown in Figure 6:

（b）电机转子在k=6和k=7时刻连续受到干扰（分别表现为故障F₁及故障F₂），此时诊断证据的更新结果如图7所示：(b) The rotor of the motor is continuously disturbed at the time k=6 and k=7 (shown as fault F₁ and fault F₂ respectively), and the update results of the diagnostic evidence at this time are shown in Figure 7:

（c）电机转子受到间歇扰动，在k=5时刻受到干扰（表现为故障F₁），在k=7时刻又受到干扰（表现为故障F₂），此时诊断证据的更新结果如图8所示：(c) The rotor of the motor is disturbed intermittently. It is disturbed at time k=5 (shown as fault F₁ ), and disturbed again at time k=7 (shown as fault F₂ ). At this time, the update result of the diagnostic evidence is shown in Figure 8 Shown:

一个理想的故障诊断系统对外来的干扰应该具有一定的免疫作用，即系统运行过程中即便受到某种干扰，也不会对诊断结果造成恶劣的影响。从图6、图7及图8可以看出，本发明和线性组合方法都能在一定程度上削减故障的干扰（亦即在干扰发生时刻，干扰所表现出来的故障状态的信度赋值不高于F₀的信度赋值），虽然当干扰发生时线性组合对干扰表现出的故障状态的赋值略微小于本发明方法给出的赋值，但是当干扰消失后，本发明方法对F₀的信度赋值迅速走高，从而更有利于故障的诊断，在都能够做出准确决策的同时，本发明无疑是更好的、更为可靠的选择。An ideal fault diagnosis system should have a certain immunity to external interference, that is, even if some interference is encountered during the system operation, it will not have a bad influence on the diagnosis results. As can be seen from Fig. 6, Fig. 7 and Fig. 8, both the present invention and the linear combination method can reduce the interference of faults to a certain extent (that is, at the moment when the interference occurs, the reliability assignment of the fault state shown by the interference is not high Based on the reliability assignment of F₀ ), although the assignment of the fault state shown by the linear combination to the disturbance is slightly smaller than the assignment given by the method of the present invention when the disturbance occurs, but when the disturbance disappears, the reliability of the method of the present invention to F₀ The assigned value increases rapidly, which is more conducive to fault diagnosis, and while making accurate decisions, the present invention is undoubtedly a better and more reliable choice.