技术领域technical field
本发明提供一种基于DM分解的测点优选方法，属于故障诊断与检测领域。The invention provides a method for optimizing measuring points based on DM decomposition, which belongs to the field of fault diagnosis and detection.
背景技术Background technique
基于模型的故障诊断过程包含三个步骤：观测、比较和诊断。这种方法建立系统的模型来预测系统状态，在此基础上通过比较系统观测状态与预测状态从而确定系统中出现的故障。其中，为实现对系统的观测，需要在系统中安置传感器来进行状态变量的测量。考虑到传感器的安装难度以及其本身可能出现问题，研究如何选择测点设置传感器是非常必要的。测点优选的目的，就是以最小的传感器集合，实现系统的完全诊断能力。系统的完全诊断能力是说所有在建模时假设的故障能被发现并隔离。对于任何一个传感器设置问题，都能被分解为两个问题(a)故障模型或系统因果效应的预测，即产生一个在故障发生时，数值会变化的参数集合；(b)基于多种准则，使用产生的集合来确定传感器位置，例如可观测性，解决性，可靠性等。The process of model-based fault diagnosis consists of three steps: observation, comparison and diagnosis. This method establishes a model of the system to predict the state of the system, on this basis, by comparing the observed state of the system with the predicted state to determine the faults in the system. Among them, in order to realize the observation of the system, it is necessary to install sensors in the system to measure the state variables. Considering the difficulty of installing the sensor and its possible problems, it is very necessary to study how to select the measuring point to set up the sensor. The purpose of measuring point optimization is to realize the complete diagnosis capability of the system with the smallest set of sensors. Full diagnostic capability of the system means that all faults assumed during modeling can be found and isolated. For any sensor setting problem, it can be decomposed into two problems: (a) prediction of fault model or system causal effect, that is, generating a parameter set whose value will change when a fault occurs; (b) based on multiple criteria, Use the resulting collection to determine sensor locations such as observability, resolveability, reliability, etc.
基于分析方式的不同发展出了不同的传感器设置算法：基于有向图(DirectedGraph，DG)、基于带符号有向图(SignedDirectedGraph，SDG)、基于可靠性准则、基于DM(Dulmage-Mendelsohn)分解、基于A*搜索等等。其中，基于DM分解的传感器设置算法是2008年由KrysanderM提出的一种有效算法。这种算法在系统状态方程的基础上，通过DM分解对系统状态方程进行分析，从而得到能够实现系统最大诊断能力的系统传感器集合。其中，DM分解算法是1958年由A.L.Dulmage和NathanMendelsohn提出的一种在图论中使用的算法，能够按照一定规律将二分图中的顶点分割为不同的集合，并且不同集合之间满足一定的偏序关系。Based on different analysis methods, different sensor setting algorithms have been developed: based on directed graph (Directed Graph, DG), based on signed directed graph (Signed Directed Graph, SDG), based on reliability criterion, based on DM (Dulmage-Mendelsohn) decomposition, Based on A* search and more. Among them, the sensor setting algorithm based on DM decomposition is an effective algorithm proposed by KrysanderM in 2008. Based on the system state equation, this algorithm analyzes the system state equation through DM decomposition, so as to obtain the system sensor set that can realize the maximum diagnosis ability of the system. Among them, the DM decomposition algorithm is an algorithm used in graph theory proposed by A.L. Dulmage and Nathan Mendelsohn in 1958. It can divide the vertices in the bipartite graph into different sets according to certain rules, and the different sets satisfy certain partiality. sequence relationship.
发明内容Contents of the invention
发明目的purpose of invention
本发明的目的是提供一种基于DM分解的测点优选方法,它针对某特定系统，为实现基于模型的故障诊断，找到一个最小的传感器集合，最大化实现系统的诊断能力。The purpose of the present invention is to provide a method for optimizing measuring points based on DM decomposition, which aims at a specific system, in order to realize model-based fault diagnosis, find a minimum set of sensors, and maximize the diagnostic ability of the system.
技术方案Technical solutions
本发明一种基于DM分解的测点优选方法，其步骤如下:A kind of measuring point optimization method based on DM decomposition of the present invention, its steps are as follows:
步骤一、对目标系统建模，获得系统状态方程组；Step 1. Model the target system and obtain the system state equations;
步骤二、将系统状态方程组转化为二分图，中顶点对应状态方程和状态变量，二分图中边对应状态方程含有状态变量；Step 2. Transform the system state equations into a bipartite graph, the middle vertices correspond to state equations and state variables, and the edges in the bipartite graph correspond to state equations containing state variables;
步骤三、求解实现系统故障可探测性的传感器集合：Step 3. Solve the sensor set to realize the detectability of system faults:
1)对二分图进行DM分解，得到强连通分量以及其中的偏序关系；1) Perform DM decomposition on the bipartite graph to obtain strongly connected components and the partial order relationship;
2)根据偏序关系求解可探测故障fi的传感器集合D[fi]，i＝1...n(系统中共有n个故障)；2) Solve the sensor set D[fi ] that can detect the fault fi according to the partial order relationship, i=1...n (there are n faults in the system);
3)求集合D[f1],D[f2]...,D[fn]的碰集，为系统故障可探测性求解结果；3) Find the collision set of the set D[f1 ], D[f2 ]...,D[fn ], which is the solution result of the system fault detectability;
步骤四、求解实现系统故障可隔离性的传感器集合：Step 4. Solve the sensor set to realize the system fault isolation:
1)根据强连通分量和其间的偏序关系构建子系统；1) Construct the subsystem according to the strongly connected components and the partial order relationship between them;
2)对于每个子系统计算实现故障隔离性的传感器集合I[Mi]；2) Calculate the sensor set I[Mi ] to achieve fault isolation for each subsystem;
3)整合I[M1],I[M2],...,I[Mk](子系统数目为k个)中结果，为系统故障可隔离性3) Integrating the results of I[M1 ], I[M2 ],...,I[Mk ] (the number of subsystems is k) is the fault isolation of the system
求解结果。Solve the result.
其中，在步骤一中所述的“对目标系统建模”，其建模的作法如下：使用在故障诊断中常用的键合图方法，根据能量转换将系统中部件抽象为储能元件、耗能元件，功能元件等，并用能量键连接构成键合图，从中能够直接得到系统的状态方程。Among them, in the "modeling of the target system" described in step 1, the modeling method is as follows: using the bond graph method commonly used in fault diagnosis, the components in the system are abstracted into energy storage elements, energy consumption components according to energy conversion energy components, functional components, etc., and connect them with energy bonds to form a bond graph, from which the state equation of the system can be directly obtained.
其中，在步骤二中所述的“将系统状态方程组转化为二分图”，其作法如下：二分图中一组点对应方程，一组点对应状态变量，当方程含有变量时，对应点间有一条边存在。Among them, the method of "converting the system state equations into a bipartite graph" described in step 2 is as follows: a set of points in the bipartite graph corresponds to an equation, and a set of points corresponds to a state variable. When the equation contains variables, the distance between the corresponding points There is an edge.
其中，在步骤三中所述的“对二分图进行DM分解”，其作法如下：使用图论中分析图中关联性的DM分解算法，得到图中强连通变量和其间的偏序关系。Among them, the "DM decomposition of the bipartite graph" described in step 3 is performed as follows: use the DM decomposition algorithm for analyzing the correlation in the graph in graph theory to obtain the strongly connected variables in the graph and the partial order relationship between them.
其中，在步骤三中所述的“求解可探测故障fi的传感器集合D[fi]”，其作法如下：DM分解后，故障fi所在的强连通变量为Vi，找到所有和Vi有偏序关系的强连通变量，这些强连通变量中含有的代表系统状态变量的点，构成D[fi]。Among them, in step 3, "solve the sensor set D[fi ] for the detectable fault fi ", the method is as follows: after DM decomposition, the strongly connected variable where the fault fi is located is Vi , find all sums Vi is a strongly connected variable with a partial order relationship, and the points representing the system state variables contained in these strongly connected variables constitute D[fi ].
其中，在步骤三中所述的“求集合D[f1],D[f2]...,D[fn]的碰集”，其做法如下：使用任意一种常用碰集求解算法即可。Among them, the method of "finding the collision set of the set D[f1 ], D[f2 ]...,D[fn ]" described in step three is as follows: use any common algorithm for solving the collision set That's it.
其中，在步骤四中所述的“根据强连通分量和其间的偏序关系构建子系统”，其做法如下：根据DM分解的结果对系统进行分割建立子系统，对于任一强连通分量Vi均构建一个子系统，如果有偏序关系Vi＜Vj，则将Vj转化为其中的一个公式，该公式是否有故障视Vj中是否有故障而定，如果有偏序关系Vj＜Vi，则将Vj转化为其中的一个不带有故障的公式。Among them, the method of "constructing subsystems based on strongly connected components and the partial order relationship" described in step 4 is as follows: according to the results of DM decomposition, the system is divided to establish subsystems, and for any strongly connected component Vi Each constructs a subsystem. If there is a partial order relationship Vi < Vj , then convert Vj into one of the formulas. Whether the formula is faulty or not depends on whether there is a fault in Vj . If there is a partial order relationship Vj < Vi , then convert Vj into one of the formulas without faults.
其中，在步骤四中所述的“计算实现故障隔离性的传感器集合I[Mi]”，其做法如下：针对系统中的每个故障，通过删除该故障所在的方程，构建一个新的模型计算其故障探测性集合，得到结构后，求解这些集合的碰集。Among them, the method of "calculating the sensor set I[Mi ] to achieve fault isolation" described in step 4 is as follows: for each fault in the system, a new model is constructed by deleting the equation where the fault is located Calculate its fault detection set, and after obtaining the structure, solve the collision set of these sets.
其中，在步骤四中所述的“整合I[M1],I[M2],...,I[Mk](子系统数目为k个)中结果”，其做法如下：为求I[M1],I[M2],...,I[Mk]的并集。Among them, in step 4, "integrate the results in I[M1 ], I[M2 ],...,I[Mk ] (the number of subsystems is k), the method is as follows: The union of I[M1 ], I[M2 ],...,I[Mk ].
通过以上步骤，能够解决和实现在带诊断系统中安置最少的传感器最大化该系统故障诊断能力的问题。Through the above steps, the problem of arranging the fewest sensors in the belt diagnostic system and maximizing the fault diagnosis capability of the system can be solved and realized.
发明优点Advantages of the invention
本发明的优点是能够用流程化方式解决故障诊断中传感器设置的问题；The advantage of the present invention is that it can solve the problem of sensor setting in fault diagnosis in a process-based manner;
能够通过将系统分解为较小子系统的方式，降低算法复杂度，更快求解问题。It can reduce the complexity of the algorithm and solve the problem faster by decomposing the system into smaller subsystems.
附图说明Description of drawings
图1四水箱模型。Figure 1 Four tank model.
图2系统二分图矩阵。Figure 2 System bipartite graph matrix.
图3DM分解后系统二分图矩阵。Figure 3. System bipartite graph matrix after DM decomposition.
图4系统子系统(一)。Figure 4 System Subsystem (1).
图5系统子系统(二)。Figure 5 System Subsystem (2).
图6本发明所述方法流程图。Fig. 6 is a flowchart of the method of the present invention.
代号说明Code Description
Sf1流量源Sf1 flow source
Ci能量存储元件参数Ci energy storage element parameters
Ri能量消耗元件参数Ri energy consumption component parameters
qi流量qi traffic
pi压强pi pressure
Ei方程Ei equation
fi故障fi failure
具体实施方式detailed description
方法实施对象为一水箱模型，假设四个水箱内的压强p1、p2、p3、p4；从每个水箱中经管道流出的流量大小q1、q2、q3、q4。见图1所示。The object of the method is a water tank model, assuming the pressures p1 , p2 , p3 , p4 in the four water tanks; the flow sizes q1 , q2 , q3 , q4 flowing out of each water tank through the pipeline. See Figure 1.
本发明一种基于DM分解的测点优选方法，见图6所示，其步骤如下:A kind of measuring point optimization method based on DM decomposition of the present invention, as shown in Figure 6, its steps are as follows:
步骤一、对目标系统建模，获得系统状态方程组；Step 1. Model the target system and obtain the system state equations;
步骤二、将系统状态方程组转化为二分图，中顶点对应状态方程和状态变量，二分图中边对应状态方程含有状态变量；Step 2. Transform the system state equations into a bipartite graph, the middle vertices correspond to state equations and state variables, and the edges in the bipartite graph correspond to state equations containing state variables;
步骤三、求解实现系统故障可探测性的传感器集合Step 3. Solve the sensor set to realize the detectability of system faults
4)对二分图进行DM分解，得到强连通分量以及其中的偏序关系；4) Perform DM decomposition on the bipartite graph to obtain strongly connected components and the partial order relationship;
5)根据偏序关系求解可探测故障fi的传感器集合D[fi]，i＝1...n(系统中共有n个故障)；5) Solve the sensor set D[fi ] that can detect the fault fi according to the partial order relationship, i=1...n (there are n faults in the system);
6)求集合D[f1],D[f2]...,D[fn]的碰集，为系统故障可探测性求解结果步骤四、求解实现系统故障可隔离性的传感器集合6) Find the collision set of the set D[f1 ], D[f2 ]...,D[fn ], and solve the result for the system fault detectability Step 4: Solve the sensor set to realize the system fault isolateability
4)根据强连通分量和其间的偏序关系构建子系统；4) Construct the subsystem according to the strongly connected components and the partial order relationship between them;
5)对于每个子系统计算实现故障隔离性的传感器集合I[Mi]；5) Calculate the sensor set I[Mi ] to achieve fault isolation for each subsystem;
6)求集合I[M1],I[M2],...,I[Mk](子系统数目为k个)的并集，为系统故障可隔离性求解结果。6) Calculate the union of the sets I[M1 ], I[M2 ],...,I[Mk ] (the number of subsystems is k), which is the result of the system fault isolation.
其中，在步骤一中所述的“对目标系统建模”，其建模的作法如下：使用在故障诊断中常用的键合图方法，根据能量转换将系统中部件抽象为储能元件、耗能元件，功能元件等，并用能量键连接构成键合图。从中能够直接得到系统的状态方程。图1系统对应状态方程如下：Among them, in the "modeling of the target system" described in step 1, the modeling method is as follows: using the bond graph method commonly used in fault diagnosis, the components in the system are abstracted into energy storage elements, energy consumption components according to energy conversion energy components, functional components, etc., and connect them with energy bonds to form a bond graph. The state equation of the system can be obtained directly from it. The corresponding state equation of the system in Figure 1 is as follows:
其中，在步骤二中所述的“将系统状态方程组转化为二分图”，其作法如下：二分图中一组点对应方程，一组点对应状态变量，当方程含有变量时，对应点间有一条边存在。为方便理解，将二分图以矩阵形式表示，见图2所示。其中行代表公式，列代表变量，空白方格表示二分矩阵在该处值为0，对应公式不含对应变量，斜线方格表示二分矩阵在该处值为1，对应公式含有对应变量。其中除方程3、6、9、12以外，其他方程都有可能由于参数变化引入故障，用符号表示为F＝{f1,f2,f3,f4,f5,f6,f7,f8}对应参数C1～C4,R1～R4。Among them, the method of "converting the system state equations into a bipartite graph" described in step 2 is as follows: a set of points in the bipartite graph corresponds to an equation, and a set of points corresponds to a state variable. When the equation contains variables, the distance between the corresponding points There is an edge. For the convenience of understanding, the bipartite graph is expressed in matrix form, as shown in Figure 2. Among them, the row represents the formula, and the column represents the variable. The blank square indicates that the value of the binary matrix is 0 at this position, and the corresponding formula does not contain the corresponding variable. The diagonal line indicates that the value of the binary matrix at this position is 1, and the corresponding formula contains the corresponding variable. Except for equations 3, 6, 9, and 12, other equations may introduce faults due to parameter changes, which are expressed as F={f1 ,f2 ,f3 ,f4 ,f5 ,f6 ,f7 , f8 } corresponds to parameters C1 -C4 , R1 -R4 .
其中，在步骤三中所述的“对二分图进行DM分解”，其作法如下：使用图论中分析图中关联性的DM分解算法，得到图中强连通变量和其间的偏序关系，见图3所示。Among them, the "DM decomposition of the bipartite graph" described in step 3 is done as follows: use the DM decomposition algorithm for analyzing the correlation in the graph in graph theory to obtain the strongly connected variables in the graph and the partial order relationship between them, see Figure 3 shows.
其中，在步骤三中所述的“求解可探测故障fi的传感器集合D[fi]”，其作法如下：DM分解后，故障fi所在的强连通变量为Vi，找到所有和Vi有偏序关系的强连通变量，这些强连通变量中含有的代表系统状态变量的点，构成D[fi]。结果如下：Among them, in step 3, "solve the sensor set D[fi ] for the detectable fault fi ", the method is as follows: after DM decomposition, the strongly connected variable where the fault fi is located is Vi , find all sums Vi is a strongly connected variable with a partial order relationship, and the points representing the system state variables contained in these strongly connected variables constitute D[fi ]. The result is as follows:
D[f1]＝{q1,p1,q3,p3,q4,p4}D[f5]＝{q1,p1,q3,p3,q4,p4}D[f1 ]={q1 ,p1 ,q3 ,p3 ,q4 ,p4 }D[f5 ]={q1 ,p1 ,q3 ,p3 ,q4 ,p4 }
D[f2]＝{q2,p2,q3,p3,q4,p4}D[f6]＝{q2,p2,q3,p3,q4,p4}D[f2 ]={q2 ,p2 ,q3 ,p3 ,q4 ,p4 }D[f6 ]={q2 ,p2 ,q3 ,p3 ,q4 ,p4 }
D[f3]＝{q3,p3,q4,p4}D[f7]＝{q3,p3,q4,p4}D[f3 ]={q3 ,p3 ,q4 ,p4 }D[f7 ]={q3 ,p3 ,q4 ,p4 }
D[f4]＝{q3,p3,q4,p4}D[f8]＝{q3,p3,q4,p4}D[f4 ]={q3 ,p3 ,q4 ,p4 }D[f8 ]={q3 ,p3 ,q4 ,p4 }
其中，在步骤三中所述的“求集合D[f1],D[f2]...,D[fn]的碰集”，其做法如下：使用任意一种常用碰集求解算法即可。对上述8个集合的的碰集，为系统故障可探测性求解结果{q3}、{q4}、{p3}、{p4}。Among them, the method of "finding the collision set of the set D[f1 ], D[f2 ]...,D[fn ]" described in step three is as follows: use any common algorithm for solving the collision set That's it. The collision set of the above 8 sets is the solution result {q3 }, {q4 }, {p3 }, {p4 } of the system fault detectability.
其中，在步骤四中所述的“构建子系统”，其做法如下：根据DM分解的结果对系统进行分割建立子系统，对于任一强连通分量Vi均构建一个子系统，如果有偏序关系Vi＜Vj，则将Vj转化为其中的一个公式，该公式是否有故障视Vj中是否有故障而定，如果有偏序关系Vj＜Vi，则将Vj转化为其中的一个不带有故障的公式。强连通分量b1会被b2和b3影响，分别经由位置(1,7)和(4,10)上的元素。所以对于b1而言，b2和b3可以被视为两个能量源，并且由于故障集合{f1,f2,f5,f6}中的故障，这两个能量源会为b1带来故障，将b2和b3中的故障分别抽象为故障f9和f10。此外，由于添加传感器集合{q3}实现故障的可探测性，表现为一个含有故障的新公式。由此构建的子系统见图4所示。强连通分量b2和b3类似，以b2为例，构建子系统时，考虑强连通分量间的相互影响关系，将b1简化为一个新的公式E15引入，见图5所示。Among them, the method of "constructing subsystems" described in step 4 is as follows: according to the results of DM decomposition, the system is divided to establish subsystems, and a subsystem is constructed for any strongly connected component Vi . If there is a partial order Vi < Vj , then transform Vj into one of the formulas, whether the formula is faulty or not depends on whether there is a fault in Vj , if there is a partial order relation Vj < Vi , then transform Vj into One of those formulas that doesn't come with a glitch. The strongly connected component b1 will be affected by b2 and b3 via elements at positions (1,7) and (4,10) respectively. So for b1 , b2 and b3 can be regarded as two energy sources, and due to faults in the fault set {f1 , f2 , f5 , f6 }, these two energy sources will be b1 brings faults, and the faults in b2 and b3 are abstracted as faults f9 and f10 , respectively. Furthermore, due to the addition of the sensor set {q3 } to achieve the detectability of faults, it appears as a new formulation with faults. The subsystem thus built is shown in Figure 4. Strongly connected components b2 and b3 are similar. Taking b2 as an example, when constructing subsystems, considering the mutual influence relationship between strongly connected components, simplifying b1 into a new formula E15 is introduced, as shown in Figure 5.
其中，在步骤四中所述的“计算实现故障隔离性的传感器集合I[Mi]”，其做法如下：针对系统中的每个故障，通过删除该故障所在的方程，构建一个新的模型计算其故障探测性集合，得到结构后，求解这些集合的碰集。以b1对应子系统为例，针对系统中的每个故障，通过删除该故障所在的方程，构建一个新的模型计算其故障探测性集合，得到结构后，求解这些集合的碰集，即可实现系统的故障隔离性，结果为{q3,q4}。另两个子系统的隔离性结果分别为{p1}和{p2}。Among them, the method of "calculating the sensor set I[Mi ] to achieve fault isolation" described in step 4 is as follows: for each fault in the system, a new model is constructed by deleting the equation where the fault is located Calculate its fault detection set, and after obtaining the structure, solve the collision set of these sets. Taking the subsystem corresponding to b1 as an example, for each fault in the system, by deleting the equation of the fault, construct a new model to calculate its fault detection set, after obtaining the structure, solve the collision set of these sets, then To achieve the fault isolation of the system, the result is {q3 ,q4 }. The isolation results of the other two subsystems are {p1 } and {p2 } respectively.
其中，在步骤四中所述的“整合I[M1],I[M2],...,I[Mk](子系统数目为k个)中结果”，其做法如下：求集合{q3,q4}、{p1}、{p2}的并集，最终结果为{q3,q4,p1,p2}。Wherein, in step 4, "integrate the results in I[M1 ], I[M2 ],..., I[Mk ] (the number of subsystems is k), the method is as follows: find the set The union of {q3 ,q4 }, {p1 }, {p2 }, the final result is {q3 ,q4 ,p1 ,p2 }.
通过以上步骤，能够解决和实现在带诊断系统中安置最少的传感器最大化该系统故障诊断能力的问题。Through the above steps, the problem of arranging the fewest sensors in the belt diagnostic system and maximizing the fault diagnosis capability of the system can be solved and realized.
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| CN201610127718.6ACN105808842B (en) | 2016-03-07 | 2016-03-07 | A kind of measuring point preferred method decomposed based on DM |
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| CN201610127718.6ACN105808842B (en) | 2016-03-07 | 2016-03-07 | A kind of measuring point preferred method decomposed based on DM |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102736616A (en)* | 2012-06-18 | 2012-10-17 | 北京控制工程研究所 | Dulmage-Mendelsohn (DM)-decomposition-based measuring point optimal configuration method for closed loop system |
| US20150106067A1 (en)* | 2013-10-14 | 2015-04-16 | Invensys Systems, Inc. | Model decomposing for optimizing |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102736616A (en)* | 2012-06-18 | 2012-10-17 | 北京控制工程研究所 | Dulmage-Mendelsohn (DM)-decomposition-based measuring point optimal configuration method for closed loop system |
| US20150106067A1 (en)* | 2013-10-14 | 2015-04-16 | Invensys Systems, Inc. | Model decomposing for optimizing |
| Title |
|---|
| MATTIAS KRYSANDER等: "Sensor placement for fault diagnosis", 《IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS》* |
| 刘文静等: "基于 DM 分解技术的传感器优化配置研究", 《第二十三届全国空间探测学术交流会论文》* |
| 刘文静等: "基于可诊断性约束的测点优化配置研究", 《空间控制技术与应用》* |
| 王冬等: "基于参数矩阵计算全体极小碰集的方法", 《北京航空航天大学》* |
| Publication number | Publication date |
|---|---|
| CN105808842B (en) | 2019-04-05 |
| Publication | Publication Date | Title |
|---|---|---|
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