CN108682140B - Enhanced anomaly detection method based on compressed sensing and autoregressive model - Google Patents

Enhanced anomaly detection method based on compressed sensing and autoregressive model Download PDF

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CN108682140B
CN108682140B CN201810367791.XA CN201810367791A CN108682140B CN 108682140 B CN108682140 B CN 108682140B CN 201810367791 A CN201810367791 A CN 201810367791A CN 108682140 B CN108682140 B CN 108682140B
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李哲涛
王建辉
周仪璇
邓清勇
田淑娟
徐雁冰
张�杰
刘倩
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Xiangtan University
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Abstract

The invention provides an enhanced anomaly detection method based on compressed sensing and an autoregressive model. Firstly, carrying out primary anomaly detection on monitoring data of sensor nodes in a cluster at a certain moment by utilizing compressed sensing by a cluster head; then, accurately detecting abnormal monitoring data of the sensor nodes at a certain moment by utilizing the time correlation of the monitoring data of the sensor nodes and combining an autoregressive model; and finally, the sink node judges whether the abnormal monitoring data is caused by abnormal events or measurement errors by utilizing the spatial correlation of the monitoring data of the nodes in each cluster, and positions the occurrence area of the abnormal events. The invention can improve the accuracy of abnormal event detection in the wireless sensor network, reduce the false alarm rate and the incidence rate of misjudgment events, and has wide applicability.

Description

Enhanced anomaly detection method based on compressed sensing and autoregressive model
Technical Field
The invention relates to the field of abnormal event detection in a wireless sensor network.
Background
Abnormal event detection is an important application of wireless sensor networks. When an abnormal event (e.g., a chemical leakage, a fire, etc.) occurs, the sensor node should be able to detect an area where the event may occur as soon as possible and report to the sink node in time.
Compressed sensing opens up a new idea for data collection in distributed sensing networks. Firstly sampling sparse data, then carrying out compression measurement on the sampled data to obtain a measured value, and finally reconstructing the original data by the measured value. The theory reduces the sampling frequency of the signal and also reduces the data storage space and the network transmission amount. Since the abnormal event is a small probability occurrence event, the compressed sensing provides a thought for the detection of the abnormal event in the wireless sensor network. However, the node data is reconstructed by a reconstruction algorithm in compressed sensing, and whether the data sent by the node is abnormal is detected directly through a reconstruction result, so that the defects of inaccurate detection result and increased false alarm rate exist. In addition, the main problem faced by the wireless sensor network in event monitoring is that the detection accuracy is affected by environmental noise and equipment instability, if the event is judged only according to the perception data of a single node at a certain time point, the occurrence of misjudgment events in the wireless sensor network is easily caused, and the amount of calculation is large when the monitoring data of each node at each time is detected by using a time sequence method.
In summary, on the basis of primarily detecting abnormal events in the wireless sensor network nodes by using compressed sensing, how to improve the detection accuracy by combining with a node autoregressive model and how to identify and position measurement errors and abnormal events by using spatial correlation of nodes in a cluster do not have a scientific solution at present.
Disclosure of Invention
Aiming at the problems, an enhanced anomaly detection method based on compressed sensing and autoregressive models in a wireless sensor network is provided, and the method specifically comprises the following steps:
step one, the arrangement of a network scene and the initialization processing of a network:
1. randomly distributing N sensor nodes in a monitoring area; all sensor nodes have the same initial energy and transmission rate; all the sensor nodes can acquire self geographical position information by positioning methods such as a GPS (global positioning system) and the like;
2. according to the distribution of abnormal events, dividing the monitoring area of the whole wireless sensor network into C clusters, selecting cluster heads and sink nodes to form a clustering network, wherein the number of sensor nodes monitored by the jth cluster head is Nj，j＝1,2,...,C。
Step two, based on historical normal data, the cluster head establishes an autoregressive model for each sensor node in the monitoring area:
1. within a certain time range, the monitoring data of each sensor node is stable, namely the monitoring data of the ith node at the moment t
Figure BDA0001637749440000021
Monitoring data at time t +1
Figure BDA0001637749440000022
Have the same distribution;
2. the monitoring data of each sensor node meets a law of large numbers, namely for any T moments, the monitoring data value of each sensor node converges to the expected value of all the monitoring data, and the expected value is as follows:
Figure BDA0001637749440000023
3. constructing a p for the ith node by using normal historical data monitored by each node as prior informationiAutoregressive model of order:
Figure BDA0001637749440000024
wherein the content of the first and second substances,
Figure BDA0001637749440000025
the residual error of the model at the moment t is subjected to mean value muiVariance is
Figure BDA0001637749440000026
The normal distribution of (c),
Figure BDA0001637749440000027
respectively representing p before the ith node tiThe influence strength of the monitoring data at each moment on the monitoring data at the current t moment;
step three, at the moment t, sensing and binarizing the monitoring data by the node, and if the monitoring data is binarized according to a preset threshold value theta, determining that the monitoring data is not binary
Figure BDA0001637749440000028
Then
Figure BDA0001637749440000029
Otherwise
Figure BDA00016377494400000210
Obtaining the binaryzation monitoring data, wherein the node data vector in the ith cluster is
Figure BDA00016377494400000211
Wherein
Figure BDA00016377494400000212
Has a value of 0 or 1;
step four, the cluster head performs compression sampling on the node data vectors in the cluster at the time t, then the sampled data are routed to the sink node, the sink node reconstructs the node data vectors in each cluster to obtain a primary detection result, and finally the cluster head collects abnormal monitoring data:
1. generating a random observation matrix from a jth cluster head
Figure BDA00016377494400000213
Where M is the vector dimension obtained by compressed sensing, NjSensing for jth cluster head monitoringThe number of nodes of the device projects the monitoring data vector of the nodes in the cluster to an observation matrix
Figure BDA00016377494400000214
Obtaining a sensing data sequence, and routing the sensing data sequence to a sink node, wherein the sensing data sequence of the jth cluster head route is
Figure BDA00016377494400000215
Figure BDA00016377494400000216
2. The sink node reconstructs the node data vector in each cluster by utilizing an OMP algorithm according to the received sensing data sequence;
3. the sensor nodes with non-zero monitoring data obtained by reconstruction in each cluster send the original monitoring data to the cluster head, wherein the original monitoring data sent by the sensor node with the serial number i is
Figure BDA00016377494400000217
Step five, identifying the monitoring result of the sensor node (hereinafter referred to as target sensor node) with non-zero monitoring data obtained by reconstruction in each cluster at the time t by each cluster head according to the time-space correlation of the monitoring data in the cluster:
1. according to the autoregressive model previously established for each sensor node:
Figure BDA0001637749440000031
from its monitoring data at time t and its previous piThe residual error value of t moment can be calculated according to the model from the historical data of each moment
Figure BDA0001637749440000032
2. Judgment of
Figure BDA0001637749440000033
Whether the value of (D) falls within the interval [ mu ]i-3σi,μi+3σi]Within. If it is
Figure BDA0001637749440000034
Value of (D) falls in [ mu ]i-3σi,μi+3σi]If the time is within the range, the monitoring data of the target sensor node with the sequence number i at the time t is normal, otherwise, the monitoring data of the target sensor node with the sequence number i at the time t is abnormal;
3. at time t, each cluster head receives abnormal monitoring data sent by target sensor node with sequence number i
Figure BDA0001637749440000035
Then, sending data transmission requests to other sensor nodes in the cluster, and sending the current monitoring data of the other sensor nodes in the cluster to the cluster head; the monitoring data of all the sensor nodes are collected into
Figure BDA0001637749440000036
4. The cluster head sorts the monitoring data sent by all the nodes in the cluster to obtain a median Me (if there are even monitoring data, the mean value of the middle two is taken); the monitoring data of each node and the difference value of the median Me are collected into
Figure BDA0001637749440000037
Mean value
Figure BDA0001637749440000038
Standard deviation of
Figure BDA0001637749440000039
Monitoring data of ith node
Figure BDA00016377494400000310
Normalized value of
Figure BDA00016377494400000311
5. When in use
Figure BDA00016377494400000312
When the number of the nodes in the monitoring area is larger than a preset threshold α, the abnormal data sent by the ith node is caused by measurement errors, otherwise, the abnormal situation occurs in the area monitored by the ith node, and the node sends an early warning signal to the cluster head in the cluster where the ith node is located;
in summary, the advantages of the invention are as follows:
1. on the basis of carrying out preliminary detection on abnormal data by using a compressed sensing theory, the time correlation of the sensor node monitoring data is fully utilized to carry out more accurate detection on the abnormal data by establishing an autoregressive model, so that the false alarm rate in the network is reduced, and the detection result is more reliable.
2. The spatial correlation among the monitoring data of the sensor nodes in each cluster is fully utilized, and the abnormal data monitored by a certain sensor node is compared with the data monitored by other sensor nodes in the cluster where the sensor node is located, so that whether the abnormal data is caused by abnormal events in the area monitored by the sensor node or caused by measurement errors can be identified.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of a process for further detecting and identifying anomalous monitoring data;
FIG. 3 is a schematic diagram of network model clustering in accordance with the present invention.
Detailed description of the invention
The invention designs an enhanced anomaly detection method based on compressed sensing and autoregressive models in a wireless sensor network, and with the combination of a figure 1, a specific implementation method for anomaly event detection is as follows:
step one, as shown in fig. 2, the arrangement of the network scenario and the initialization process of the network:
1. randomly distributing N sensor nodes in a monitoring area; all sensor nodes have the same initial energy and transmission rate; all the sensor nodes can acquire self geographical position information by positioning methods such as a GPS (global positioning system) and the like;
2. according to the distribution of abnormal events, dividing the monitoring area of the whole wireless sensor network into C clusters, selecting cluster heads and sink nodes to form a clustering network, wherein the number of sensor nodes monitored by the jth cluster head is Nj，j＝1,2,...,C。
Step two, based on historical normal data, the cluster head establishes an autoregressive model for each sensor node in the monitoring area:
1. it is assumed that the monitoring data of each sensor node is stable in a certain time range, namely the monitoring data of the ith node at the moment t
Figure BDA0001637749440000041
Monitoring data at time t +1
Figure BDA0001637749440000042
Have the same distribution;
2. the monitoring data of each sensor node meets a law of large numbers, namely for any T moments, the monitoring data value of each sensor node at a certain moment converges to the expected value of all the monitoring data values, and the expected value is as follows:
Figure BDA0001637749440000043
3. constructing a p for the ith node by using normal historical data monitored by each node as prior informationiAutoregressive model of order:
Figure BDA0001637749440000044
wherein the content of the first and second substances,
Figure BDA0001637749440000051
as residual error at model time tObey a mean value of μ i and a variance of
Figure BDA0001637749440000052
The normal distribution of (c),
Figure BDA0001637749440000053
respectively representing p before the ith node tiThe influence strength of the monitoring data at each moment on the monitoring data at the current t moment;
step three, at the moment t, sensing and binarizing the monitoring data by the node, and if the monitoring data is binarized according to a preset threshold value theta, determining that the monitoring data is not binary
Figure BDA0001637749440000054
Then
Figure BDA0001637749440000055
Otherwise
Figure BDA0001637749440000056
Obtaining the binaryzation monitoring data, wherein the node data vector in the ith cluster is
Figure BDA0001637749440000057
Wherein
Figure BDA0001637749440000058
Has a value of 0 or 1;
step four, the cluster head performs compression sampling on the node data vectors in the cluster at the time t, then the sampled data are routed to the sink node, the sink node performs reconstruction operation on the node data vectors in each cluster to obtain a primary detection result, and finally the cluster head collects abnormal monitoring data:
1. generating a random observation matrix from a jth cluster head
Figure BDA0001637749440000059
Where M is the vector dimension obtained by compressed sensing, NjProjecting the monitoring data vector of the node in the jth cluster to an observation matrix for the number of the sensor nodes monitored by the jth cluster head
Figure BDA00016377494400000510
Obtaining a sensing data sequence, and routing the sensing data sequence to a sink node, wherein the sensing data sequence of the jth cluster head route is
Figure BDA00016377494400000511
Figure BDA00016377494400000512
2. The sink node reconstructs the node data vector in each cluster by utilizing an OMP algorithm according to the received sensing data sequence;
the OMP algorithm pseudo code used in the present invention is as follows:
inputting: dictionary matrix phi, original signal y, sparsity K, index set T identifying positions of non-zero elements in signal to be reconstructed
And (3) outputting: reconstruction of the Signal x
Initialization: x is 0, r0Y, the cycle identifier k is 0, index set T0Is an empty collector
When the ending condition is not met, executing steps ① - ⑥ circularly
①k＝k+1
② find the index lambda of the residue r and the best matching atom in the sampling matrixkI.e. by
λk＝argmaxj＝1,2,...,N{|<rk-1,φk>|}
③ update index set Tk＝Tk-1∪{λkAnd updating the set of reconstructed atoms in the corresponding sampling matrix
Figure BDA0001637749440000061
④ are obtained by least squares
Figure BDA0001637749440000062
⑤ update the residual:
Figure BDA0001637749440000063
⑥ judging whether K > K is satisfied, if so, stopping iteration, if not, executing step ①
3. The sensor nodes with non-zero monitoring data obtained by reconstruction in each cluster send the original monitoring data to the cluster head, wherein the original monitoring data sent by the sensor node with the serial number i is
Figure BDA0001637749440000064
Step five, identifying the monitoring results of the sensor nodes (hereinafter referred to as target sensor nodes) with non-zero monitoring data obtained by reconstruction in each cluster at the time t by the cluster head according to the time-space correlation of the monitoring data:
1. according to the autoregressive model (2) established previously for each sensor node:
from its monitoring data at time t and its previous piThe residual error value of t moment can be calculated according to the model from the historical data of each moment
Figure BDA0001637749440000065
2. Judgment of
Figure BDA0001637749440000066
Whether the value of (D) falls within the interval [ mu ]i-3σi,μi+3σi]Within. If it is
Figure BDA0001637749440000067
Value of (D) falls in [ mu ]i-3σi,μi+3σi]If the time is within the range, the monitoring data of the target sensor node with the sequence number i at the time t is normal, otherwise, the monitoring data of the target sensor node with the sequence number i at the time t is abnormal;
3. at time t, each cluster head receives abnormal monitoring data sent by target sensor node with sequence number i
Figure BDA0001637749440000068
Then, sending data transmission requests to other sensor nodes in the cluster, and sending the current monitoring data of the other sensor nodes in the cluster to the cluster head; the monitoring data of all the sensor nodes are collected into
Figure BDA0001637749440000069
4. The cluster head sorts the monitoring data sent by all the nodes in the cluster to obtain a median Me (if there are even monitoring data, the mean value of the middle two is taken); the difference between the monitoring data of each node and the median Me is set as
Figure BDA00016377494400000610
Mean value
Figure BDA00016377494400000611
Standard deviation of
Figure BDA00016377494400000612
Figure BDA00016377494400000613
Normalized value of
Figure BDA00016377494400000614
The cluster head sorts the monitoring data sent by all the nodes in the cluster to obtain a median Me (if there are even monitoring data, the mean value of the middle two is taken); the monitoring data of each node and the difference value of the median Me are collected into
Figure BDA00016377494400000615
Mean value
Figure BDA00016377494400000616
Standard deviation of
Figure BDA0001637749440000071
Figure BDA0001637749440000072
Normalized value of
Figure BDA0001637749440000073
5. When in use
Figure BDA0001637749440000074
When the number of the nodes in the monitoring area is larger than a preset threshold α, the abnormal data sent by the ith node is caused by measurement errors, otherwise, the abnormal situation occurs in the area monitored by the ith node, the node sends an early warning signal to the cluster head in the cluster where the ith node is located, each cluster head sends the respective detection result to the sink node, namely, the node number of the abnormal situation occurs in the monitoring area is sent to the sink node, and finally, a global detection result is obtained.

Claims (2)

1. An enhanced anomaly detection method based on compressed sensing and autoregressive models, the method comprising the steps of:
step one, arrangement of a network scene and initialization processing of a network;
step two, using normal historical data monitored by each node as prior information, and establishing a p for each sensor node in a cluster by each cluster headiAutoregressive model of order:
Figure FDA0002538546520000011
wherein the content of the first and second substances,
Figure FDA0002538546520000012
the residual error of the model at the moment t is subjected to mean value muiVariance is
Figure FDA0002538546520000013
Normal distribution of (2);
Figure FDA0002538546520000014
respectively representing the ith node at and p before time tiA moment of timeThe monitoring data of (2) is obtained,
Figure FDA0002538546520000015
respectively representing p before the ith node tiThe influence strength of the monitoring data at each moment on the monitoring data at the current t moment;
step three, at the moment t, the ith node senses monitoring data
Figure FDA0002538546520000016
And binarizing the image according to a preset threshold value theta if
Figure FDA0002538546520000017
Then
Figure FDA0002538546520000018
Otherwise
Figure FDA0002538546520000019
Obtaining binarized monitoring data; at this time, the vector formed by the binarization monitoring data of each node in the ith cluster is
Figure FDA00025385465200000110
Wherein
Figure FDA00025385465200000111
Representing the monitoring data after the k sensor node in the ith cluster is binarized at the time t,
Figure FDA00025385465200000112
is 0 or 1, NiIs the number of sensor nodes in the ith cluster;
step four, each cluster head conducts compressed sensing on vectors formed by the binarization monitoring data of each node in the cluster at the time t, then the sampled data are routed to a sink node, the sink node conducts reconstruction on the vectors formed by the binarization monitoring data in each cluster to obtain a preliminary detection result, and finally the cluster head collects abnormal monitoring data:
1) generating random observation matrix by jth cluster head
Figure FDA00025385465200000113
Where M is the vector dimension obtained by compressed sensing, NjProjecting the monitoring data vector of the node in the jth cluster to an observation matrix for the number of the sensor nodes monitored by the jth cluster head
Figure FDA00025385465200000114
Obtaining a sensing data sequence, and routing the sensing data sequence to a sink node, wherein the sensing data sequence of the jth cluster head route is
Figure FDA00025385465200000115
Figure FDA00025385465200000116
Wherein
Figure FDA00025385465200000117
A vector formed by the binarization monitoring data of all nodes in the jth cluster, wherein j is 1,2, …, and C is the number of cluster heads;
2) the sink node is based on the received compressed sensing sequence
Figure FDA0002538546520000021
Reconstructing the node data vector in each cluster by using an OMP algorithm;
3) the sensor nodes with non-zero monitoring data obtained by reconstruction in each cluster send the original detection data to the corresponding cluster heads, wherein the original monitoring data sent by the sensor node with the serial number i is
Figure FDA0002538546520000022
Step five, according to the section for sending abnormal dataPoint-based autoregressive model from current monitoring data of nodes
Figure FDA0002538546520000023
And historical monitoring data
Figure FDA0002538546520000024
Calculating the residual value of the current model
Figure FDA0002538546520000025
If it is
Figure FDA0002538546520000026
If the data fall in the target interval, the monitoring data are normal, and the preliminary detection result obtained by adopting compressed sensing is corrected:
1) according to the autoregressive model previously established for each sensor node:
Figure FDA0002538546520000027
thereby calculating the residual value at the time t
Figure FDA0002538546520000028
2) Judgment of
Figure FDA0002538546520000029
Whether the value of (D) falls within the interval [ mu ]i-3σi,μi+3σi]If the value falls within [ mu ]i-3σi,μi+3σi]If the time is within the range, the monitoring data of the target sensor node with the sequence number i at the time t is normal, otherwise, the monitoring data of the target sensor node with the sequence number i at the time t is abnormal;
and step six, identifying the detection result of the abnormal node of the monitoring data by each cluster head at the time t according to the space-time correlation of the monitoring data in the cluster, and finally sending the detection result of the abnormal event in the cluster by each cluster head, namely, numbering the abnormal event occurring node in the monitoring area to the sink node to obtain a global detection result:
1) at time t, each cluster head receives abnormal monitoring data sent by target sensor node with sequence number i
Figure FDA00025385465200000210
Then, sending a data transmission request to other sensor nodes in the cluster, and sending the monitoring data of the other sensor nodes in the cluster at the time t to a cluster head; setting the monitoring data set of all sensor nodes at the time t as
Figure FDA00025385465200000211
2) The cluster head sorts the monitoring data sent by all the nodes in the cluster to obtain a median Me (if there are even monitoring data, the mean value of the middle two is taken); the difference value set of the monitoring data of each node and the median Me is
Figure FDA00025385465200000212
Mean value
Figure FDA00025385465200000213
Standard deviation of
Figure FDA00025385465200000214
Figure FDA00025385465200000215
Normalized value of
Figure FDA00025385465200000216
3) When in use
Figure FDA00025385465200000217
When the value is larger than the preset threshold α, the abnormal data sent by the ith node is caused by the measurement error, otherwise, the abnormal condition occurs in the area monitored by the ith node, and the node sends the abnormal data to the area monitored by the ith nodeSending an early warning signal by a cluster head in a cluster; each cluster head sends respective detection results to the sink node, namely sends the node number of the abnormal condition of the monitoring area to the sink node, and finally obtains a global detection result.
2. The enhanced anomaly detection method based on compressive sensing and autoregressive models as claimed in claim 1, wherein the network scenario layout and network initialization process comprises the following steps:
1) randomly distributing N sensor nodes in a monitoring area; all sensor nodes have the same initial energy and transmission rate; all the sensor nodes can acquire self geographical position information by positioning methods such as a GPS (global positioning system) and the like;
2) according to the distribution of abnormal events, dividing the monitoring area of the whole wireless sensor network into C clusters, selecting cluster heads and sink nodes to form a clustering network, wherein the number of sensor nodes monitored by the jth cluster head is Nj，j＝1,2,...,C。
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