The Fault Location Method Research of Three-Layer Network System

The fault location technology research of three-layer network system structure dynamic has important theoretic value and apparent engineering application value on exploring the fault detection and localization of the complex structure dynamic system. In this article, the method of failure propagation and adverse inference are adopted, the fault location algorithm of the three-layer structure dynamic network system is established on the basis of the concept of association matrix and the calculating method are proposed, and the simulation calculation confirmed the reliability of this paper. The results of the research can be used for the fault diagnosis of the hierarchical control system、 testing of the engineering software and the analysis of the failure effects of layered network of all kinds and other different fields. I. INTRODUCTION Nearly half a century, the automation technology of system during operating process has developed along two general directions as a whole. One is the optimization and intelligent of the system in normal conditions, the other is fault monitoring and safety of the system in failure. Especially the latter, since the 1970s, Berd put forward a control system which is based on the analytic redundant fault detection and diagnosis, it was widely valued by the international and domestic academic industry and the engineering application industry, successively proposed and developed a series of fault detection and diagnosis methods that are novel and practical( FDD: Fault Detection and Diagnosis), such as FDD method based on signal processing、FDD method based on data-driven、FDD method based on structural redundancy、FDD method based on information redundancy、 method based on equivalent space and FDD method based on system simulation etc. The concerns of the research have developed from early static equipment or the single fault of the system to the concurrent malfunction of the complex structure system and the continual failure of the system during running process. For the fault monitoring and security of a complicated structure dynamic system, it has been the focus and difficulty that how to use the anomaly information monitored by all sorts of sensing/sensors or other measuring equipment to fault location accurately. Complex structure dynamic system has a complex relationship between relevant components, the difficulty of the fault location become higher and higher, in order to overcome the technology difficulty of the develop of the fault diagnosis expert system and the technical problems of familiar reasoning process conflicts which are based on rule reasoning or cases, this paper develops a practical and concise fault location algorithm based on mathematical operation, which can locate the fault point fastly, it also solves the difficult problems of fault location of the complex structure system and proves the effectiveness of the new method through the simulation results. , 1 1 n i v V i    2 n i v V i   


INTRODUCTION
Nearly half a century, the automation technology of system during operating process has developed along two general directions as a whole.One is the optimization and intelligent of the system in normal conditions, the other is fault monitoring and safety of the system in failure.Especially the latter, since the 1970s, Berd put forward a control system which is based on the analytic redundant fault detection and diagnosis, it was widely valued by the international and domestic academic industry and the engineering application industry, successively proposed and developed a series of fault detection and diagnosis methods that are novel and practical ( FDD ： Fault Detection and Diagnosis), such as FDD method based on signal processing、FDD method based on data-driven、FDD method based on structural redundancy、FDD method based on information redundancy 、 method based on equivalent space and FDD method based on system simulation etc.The concerns of the research have developed from early static equipment or the single fault of the system to the concurrent malfunction of the complex structure system and the continual failure of the system during running process.
For the fault monitoring and security of a complicated structure dynamic system, it has been the focus and difficulty that how to use the anomaly information monitored by all sorts of sensing/sensors or other measuring equipment to fault location accurately.Complex structure dynamic system has a complex relationship between relevant components, the difficulty of the fault location become higher and higher, in order to overcome the technology difficulty of the develop of the fault diagnosis expert system and the technical problems of familiar reasoning process conflicts which are based on rule reasoning or cases, this paper develops a practical and concise fault location algorithm based on mathematical operation, which can locate the fault point fastly, it also solves the difficult problems of fault location of the complex structure system and proves the effectiveness of the new method through the simulation results.

II. THE STATUS ANALYSIS OF COMPLEX STRUCTURE SYSTEM AND CAUSAL MODELING
Any complex structure dynamic system is usually composed of several functional subsystem, each subsystem includes several components.Similarly, each subsystem can also be further broken down into some functional subsystem in level 2 and each subsystem in level 2 also includes several small parts.
Whether the systems or the subsystems or the components, only when it transfer information to the outside system directly or indirectly, can we perceive or judge whether it runs normal or not.In other words, whether the state of work is normal or not is unknown to the outside world without any way to transform subsystems or components to the outside system directly or indirectly.For this kind of system that cannot transfer parts of information or subsystems to the outside system, we call it a "black hole".
For this kind of system, when malfunction happened, how to locate fault source becomes difficult, considering the complexity of the system, causal modeling method is adopted in this paper, namely layered network modeling method, it sets up the correlation matrix through the top and the bottom of the association.So, the changes of the bottom can find the changes of the top source through the incidence matrix.

III. THE DESIGN AND CALCULATION OF THE TOP -BOTTOM RELATING MATRIX
For the three layer network in figure 1, simple to set the top nodes as , to set the middle nodes as ,to set the bottom nodes as For the bottom nodes And the joint strength between adjacent layer contacts nodes Thus, using operator "and"  and operator "or"  of Borel algebra, we can calculate the flag values of the middle layer nodes Similarly, defining the flag values of the bottom nodes , so either every top layer node does not broke down or the node which brokes down does not spread into the middle layer node , so the top layer has at least one node broke down, and the failure influence spread into the middle layer nodes  , so for all the top layer nodes , it means that either this node does not broke down or there is no united way between this node and the middle layer node.
, so there must be 1 0 Thus, the top layer node , so there is at least one top middle node is abnormal and its fault influence transfer to the bottom layer node Proof.It is familiar with proposition 1, so omit the proof process here.Making flag vector )) ( , ), ( ( According to the definition of the formula (6) and the proving process of propoistion1 and proposition 2, we can easily derive the next conclusion:  (6) shows the numbers of paths that top layer node uses to transfer its fault form different middle layer nodes to the bottom layer nodes.
According to the proposition 3, the fault of the first k layer node can not be transferred and can not effect the bottom layer node.We called these top layer nodes isolated points.
For the three-layer network system without isolated points, we can eastablish a top-bottom associated matrix by calculating the numbers of the paths ) (k s i that the top layer node uses to transfer its fault to the bottom layer nodes.
In the formula ( Obviously, the matrix M 3 1 has the next qualities: ( , it means every elements of the associated matrix is a nonnegative number that is not exceeding 1. ( , it means that all elements in each row of the matrix added to 1 .

IV. ALGORRTHM OF THE FAULT LOCATION
Bringing all different groups of the formular (5) into the formular k v d into the formular (4), after the above process, we can calculate the state flag matrix: Obviously, the flag value ) ( , According to the analysis above, we can establish the fault location algorithm: we supposed that every bottom layer node is installed with a sensor, so we can achieve the fault omen information of the layer node directly.According to the state information of the bottom layer of the system, we can demarcate the state of the bottom layer nodes Calculating the weighting indicator: . When

Figure 1 .
Figure 1.The structure schematic drawing of three layer network

Proof.
By formula (4) and the operation rule of Borel operator middle layer node either works properly or the influence of the abnormal node do not transfer to the bottom layer node 3 , 3 numbers of the propagation paths that the top layer node uses to transfer the fault to the bottom layer node.

1 , 1 and v 3 , 1 ,.
the fault omens of the bottom layer nodes are not caused by the top layer node i v , 1 ).In practical operation, considering the fault omen or the sensitivity of the detection sensor, the similar judge as above.V.SIMULATION CALCULATIONFor the three-layer network as the figure1shows, we use 4 to express all the groups of the formula (5), comparing the matrix D1, we assume the fault nodes are v according to the figure1, we can calculate the flag matrix of the bottom layer www.ijacsa.thesai.org the state flag matrix when the top layer nodes transfer its faults to the bottom layer nodes by the formulae (3) and (4) the weighting matrix, it is also the top-bottom associated matrix can get the weighting indicator matrix of the top layer nodes by using the formula (10) We can make the conclusion from the simulation result of matlab that g(1,1) and g(1,3) satisfy the condition nodes, it proves the accuracy of the algorithm.
showing that the top layer node