CN105740989B - A kind of water supply network anomalous event method for detecting based on VARX model - Google Patents
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Abstract
The invention discloses a kind of water supply network anomalous event method for detecting based on VARX model.The present invention carries out measuring point grouping first, determines input sample.Secondly VARX model is established by grouping.Then it carries out pressure prediction and calculates difference, and calculate the average and standard deviation of difference.Finally anomalous event is detected according to anomalous event decision rule.The present invention is based on the water supply network anomalous event method for detecting that VARX model uses variance analysis, have the features such as strong interference immunity, detecting ability is strong.
Description
Technical field
The invention belongs to urban water supply field, specifically a kind of water supply network anomalous event detecting side based on VARX model
Method.
Background technique
Dark leakage and booster are two kinds of common anomalous events of public supply mains, the former have the time persistently length, small scale,
Not noticeable feature, and the latter is then exactly the opposite, has sudden, uncertain, sweeping feature.Discovery is supplied water in time
Leakage loss event present in pipe network is accurately positioned venue location point, takes measures to prevent the state of affairs from deteriorating rapidly, to water supply network
It is particularly important for safe operation.
Water supply network anomalous event detecting at present is based primarily upon microcosmic hydraulic model and two kinds of macro-data model.Wherein
Micromodel needs the particulars of known pipe network system, such as the topological structure of pipe network, the material of pipeline section, length, diameter, frictional resistance
Equal specifying informations, the domestic application study based on micromodel are less.Research based on macromodel is broadly divided into marginal analysis
With two methods of variance analysis, marginal analysis method vulnerable to noise interference and difference analysis method anti-interference ability is stronger.
In view of this, can preferably be detected to water supply network anomalous event using difference analysis method.The present invention
Discriminant analysis, which is carried out, based on VARX model high-precision forecast detects water supply network anomalous event.
Summary of the invention
The water supply network anomalous event detecting based on VARX model that in view of the deficiencies of the prior art, the present invention provides a kind of
Method.Wherein VARX (a Vector Auto-Regressive with eXogenous variables) model by it is unidirectional because
The variable of fruit relationship is added in VAR model as exogenous variable, can effectively enhance the disturbance rejection of model, while the model
Precision with higher.
In order to achieve the above object, the present invention takes following steps:
The grouping of step 1. measuring point, determines input sample
Establish water supply network forecast database.Wherein input data includes: measurement point pressure, flow value etc.；Output data
It include: forecast pressure, flow value etc..
(1) monitoring point is grouped
Monitoring point is grouped by correlation, correlation calculations formula is as follows:
Illustrate: x, y are two groups of time series datas；Ex, Ey are the desired values of corresponding two groups of time series datas；Dx,
Dy is the variance of corresponding two groups of time serieses；Corr (x, y) is then the related coefficient of corresponding two groups of time series datas, is used
To characterize correlation.The value range of related coefficient indicates uncorrelated 0~1,0, otherwise 1 indicates that correlation is obvious, will be related
The apparent monitoring point of property is classified as one kind.
(2) input sample is determined
It is grouped according to monitoring point and determines that input sample is { xt,yt}i, wherein xtExogenous variable, y are tieed up for dtTo change in k dimension
Amount, i.e., the monitoring point of the endogenous variable of monitoring point k of d exogenous variable, t are chronomere, and i indicates i-th group of monitoring point.
Step 2. establishes VARX model by grouping
VARX model is established in prediction each time for each group of monitoring point, according to input sample data { xt,yt}iCarry out mould
Type determines rank and establishes model.
(1) VARX model order
Using AIC (Akaike Information Criterion) order selection criteria.It is defined as follows:
WhereinFor residual error, T is sample cycle, and p is that model lags item, and p value when AIC value is minimized is that model is best
Selective value.
(2) VARX model is established
The expression formula of VARX model are as follows:
Wherein: xtExogenous variable is tieed up for d；ΘjCoefficient matrix to be estimated is tieed up for k × d.ytFor the endogenous variable of k dimension；C is
The constant term of k dimension；ΦiCoefficient matrix to be estimated is tieed up for k × k；P1, q1 are lag order；{εtIt is that k ties up white noise sequence.
The parameter Estimation of VARX model is obtained using maximum-likelihood method, setting: β=vec ([c Φ1...Φp1Θ1...
Θq1]),Then above formula may be expressed as:
yt=Wt-1β+εt
Then had according to maximum likelihood algorithm:
From β andAspect we can to derive model parameter as follows:
Step 3. pressure prediction simultaneously calculates difference
The predicted value of each monitoring point is obtained according to sample data and established model, and is calculated every in monitoring point n days
The difference of one moment predicted value and observation.Wherein VARX model predication value is (Y '1j,Y′2j,...,Y′ij), observation is
(x1j,x2j,...,xij), i=1...k (k indicates monitoring point pressure data number), j=1...n, then difference may be expressed as:
Δyij=(x1j-Y′1j,x2j-Y′2j,...,xij-Y′ij)
The average and standard deviation of step 4. calculating difference
Calculate the average and standard deviation of each monitoring point difference in M days.The sample frequency of assumed stress time series
It is u min/ times, M days difference can be indicated such as step 3, then the average value of one day differenceIt can be by following
Formula be calculated, wherein q=1...u...1440/u.
Standard deviation (σ1,σ2,...,σq) can be calculate by the following formula to obtain:
Step 5. detects anomalous event
According to following anomalous event decision rules, the abnormal conditions of detecting real-time water supply network:
A. any time point pressure, Flow Observation value are lower than -4 boundaries σ；
B. continuous 2 time point pressures, Flow Observation value are lower than -3 boundaries σ；
C. continuous 4 time point pressures, Flow Observation value are lower than -2 boundaries σ；
D. continuous 8 time point pressures, Flow Observation value are lower than -1 boundary σ.
Once observation touches decision rule, then assert that pipe network anomalous event occurs, the moment occurs for record, and triggers corresponding
Early warning.
Beneficial effects of the present invention: the present invention is based on VARX models using the water supply network anomalous event detecting of variance analysis
Method has the features such as strong interference immunity, detecting ability is strong.
Detailed description of the invention
Fig. 1: DMA 10, area monitoring point distribution map；
Specific embodiment
To make the technological means realized of the present invention be easy to express with creation characteristic, with reference to the accompanying drawing and example, to this hair
Bright real-time mode is described in further detail.
Certain area DMA (District Metering Area) is considered in this example, there are 10 effective pressure measuring points, it is geographical
Position such as Fig. 1.Three water inlet pressure spots (respectively with P1, P2, P3 expression) are introduced simultaneously and the area DMA water consumption is used as and changes outside
Amount.Pressure data time range is from X March 20 to X April 3, wherein establishing mould using March 20 to data on April 2
Type detects April 3 " 5 simulation booster tests " anomalous event.Here, it is only illustrated with pressure value, but this
Inventive method is equally applicable to flow value.
Step 1. determines input data
Establish water supply network forecast database.Wherein input data includes: measurement point pressure value, flow value etc.；Export number
According to including: forecast pressure value etc..
(1) monitoring point is grouped
Pressure monitoring point and water inlet pressure spot are grouped by correlation, correlation calculations formula is as follows:
Illustrate: x, y are two groups of time series datas；Ex, Ey are the desired values of corresponding two groups of time series datas；Dx,
Dy is the variance of corresponding two groups of time serieses；Corr (x, y) is then the related coefficient of corresponding two groups of time series datas.?
Table 1 is grouped as follows to pressure monitoring point.
Table 1: monitoring point is grouped situation table
| Group number | Monitoring point member |
| First group | No.3、No.5、No.6、No.7、No.10、P2 |
| Second group | No.1、No.8、No.9、P3 |
| Third group | No.2、No.4、P1 |
(2) input sample is determined
It is grouped according to monitoring point and determines that input sample is { xt,yt}i, wherein xtExogenous variable, y are tieed up for dtTo change in k dimension
Amount, t are chronomere, and i indicates i-th group of monitoring point.The input sample of first group of monitoring point is 2 dimension exogenous variables, including P2 enters
The endogenous variable of mouth of a river pressure-measuring-point and the area DMA water consumption, 5 dimensions is 5 pressure monitoring points, can similarly obtain remaining two groups of input
Sample situation, sample frequency are 5min/ times.
Step 2. establishes VARX model
Model order and model are determined according to input sample, and the number of one day pressure monitoring point is predicted using five days data
According to so needing to establish 3 × 10 models, i.e. three groups of monitoring points do not need to establish the VARX pressure of prediction 10 days on the 3.25th~4.3
Power prediction model.
(1) VARX model order
Using AIC (Akaike Information Criterion) order selection criteria.It is defined as follows:
WhereinFor residual error, T is sample cycle, and p is that model lags item, and p value when AIC value is minimized is that model is best
Selective value.It is p=4 that model order, which is calculated,.
(2) VARX model is established
The expression formula of VARX model are as follows:
Wherein: xtExogenous variable is tieed up for d；ΘjCoefficient matrix to be estimated is tieed up for k × d.ytFor the endogenous variable of k dimension；C is
The constant term of k dimension；ΦiCoefficient matrix to be estimated is tieed up for k × k；P1, q1 are lag order；{εtIt is that k ties up white noise sequence.
The parameter Estimation of VARX model is obtained using maximum-likelihood method, setting: β=vec ([c Φ1...Φp1Θ1...
Θq1]),Then above formula may be expressed as:
yt=Wt-1β+εt
Then had according to maximum likelihood algorithm:
From β andAspect we can to derive model parameter as follows:
Step 3. pressure prediction simultaneously calculates difference
The predicted value of each monitoring point is obtained according to sample data and established model, and is calculated every in monitoring point n days
The difference of one moment predicted value and observation.Obtain prediction data VARX model predication value (Y '1j,Y′2j,...,Y′ij), observation
Value is (x1j,x2j,...,xij), wherein (k indicates monitoring point pressure data number, first group of k=5, second group of k=to i=1...k
3, third group k=2), j=1:10, then difference may be expressed as:
Δyij=(x1j-Y′1j,x2j-Y′2j,...,xij-Y′ij)
The average and standard deviation of step 4. calculating difference
Calculate the average and standard deviation of each monitoring point each sampled point in 9 days.Sample frequency is 5min/ times, then 9
It pressure data is represented by (x1j,x2j,...,xij), wherein i=1:k (first group of k=5, second group of k=3, third group k
=2), j=1:9, then the average value of one day differenceIt can be calculated by following formula, wherein q=
1...5...288, M=9.
Standard deviation (σ1,σ2,...,σq) can be calculate by the following formula to obtain:
Step 5. abnormity detecting
To the pressure observed value of 10 monitoring points on April 3, according to following anomalous event decision rules:
A. any time point pressure observation is lower than -4 boundaries σ；
B. continuous 2 time points pressure observation value is lower than -3 boundaries σ；
C. continuous 4 time points pressure observation value is lower than -2 boundaries σ；
D. continuous 8 time points pressure observation value is lower than -1 boundary σ.
For this sentences No. 2 monitoring points, the anomalous event detected such as table 2,5 simulation booster test situations of coincideing.
The anomalous event that table 2:2 is detected monitoring point
| Serial number | Abnormal time section | Duration (min) | Worst error (σ) |
| 1 | 9:25 | <5 | -5.946 |
| 2 | 9:40 | <5 | -4.242 |
| 3 | 10:05 | <5 | -5.339 |
| 4 | 12:25 | <5 | -9.326 |
| 5 | 19:50 | <5 | -4.493 |
Claims (1)
1. a kind of water supply network anomalous event method for detecting based on VARX model, it is characterised in that this method includes following step
It is rapid:
The grouping of step 1. measuring point, determines input sample, specifically:
Establish water supply network forecast database；Wherein input data includes: measurement point pressure, flow value；Output data includes: pre-
Measuring pressure, flow value；
(1) monitoring point is grouped
Monitoring point is grouped by correlation, correlation calculations formula is as follows:
Wherein x, y are two groups of time series datas；Ex, Ey are the desired values of corresponding two groups of time series datas；Dx, Dy are pair
The variance for the two groups of time serieses answered；Corr (x, y) is then the related coefficient of corresponding two groups of time series datas, for characterizing
Correlation；The value range of related coefficient indicates uncorrelated 0~1,0, otherwise 1 indicates that correlation is obvious；
(2) input sample is determined
It is grouped according to monitoring point and determines that input sample is { xt,yt}i, wherein xtExogenous variable, y are tieed up for dtEndogenous variable is tieed up for k, i.e.,
The monitoring point of the endogenous variable of monitoring point k of d exogenous variable, t are chronomere, and i indicates i-th group of monitoring point；
Step 2. establishes VARX model by grouping
VARX model is established in prediction each time for each group of monitoring point, according to input sample data { xt,yt}iIt is fixed to carry out model
Rank simultaneously establishes model；
(1) VARX model order
Using AIC order selection criteria；It is defined as follows:
WhereinFor residual error, T is sample cycle, and p is that model lags item, and p value when AIC value is minimized is model optimal selection
Value；
(2) VARX model is established
The expression formula of VARX model are as follows:
Wherein: xtExogenous variable is tieed up for d；ΘjCoefficient matrix to be estimated is tieed up for k × d；ytFor the endogenous variable of k dimension；C is k dimension
Constant term；ΦiCoefficient matrix to be estimated is tieed up for k × k；P1, q1 are lag order；{εtIt is that k ties up white noise sequence；
The parameter Estimation of VARX model is obtained using maximum-likelihood method, setting: β=vec ([c Φ1...Φp1 Θ1...
Θq1]),Then above formula may be expressed as:
yt=Wt-1β+εt
Then had according to maximum likelihood algorithm:
From β andIt is as follows that aspect can derive model parameter:
Step 3. pressure prediction simultaneously calculates difference
The predicted value of each monitoring point is obtained according to sample data and established model, and calculates per a period of time in monitoring point n days
Carve the difference of predicted value and observation；Wherein VARX model predication value is (Y1'j,Y2'j,...,Yij'), observation is (x1j,
x2j,...,xij), i=1...k, j=1...n, k indicate monitoring point pressure data number, then difference may be expressed as:
Δyij=(x1j-Y′1j,x2j-Y′2j,...,xij-Y′ij)
The average and standard deviation of step 4. calculating difference
Calculate the average and standard deviation of each monitoring point difference in M days；The sample frequency of assumed stress time series is u
Min/ times, M days difference can be indicated such as step 3, then the average value of one day differenceIt can be by following public affairs
Formula is calculated, wherein q=1...u...1440/u；
Standard deviation (σ1,σ2,...,σq) can be calculate by the following formula to obtain:
Step 5. detects anomalous event
According to following anomalous event decision rules, the abnormal conditions of detecting real-time water supply network:
A. any time point pressure, Flow Observation value are lower than -4 boundaries σ；
B. continuous 2 time point pressures, Flow Observation value are lower than -3 boundaries σ；
C. continuous 4 time point pressures, Flow Observation value are lower than -2 boundaries σ；
D. continuous 8 time point pressures, Flow Observation value are lower than -1 boundary σ；
Once observation touches decision rule, then assert that pipe network anomalous event occurs, the moment occurs for record, and triggers corresponding pre-
It is alert.
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| CN106287233B (en) * | 2016-08-11 | 2018-04-10 | 中国科学院生态环境研究中心 | A kind of pipe network leakage method for early warning and system |
| CN106872657B (en) * | 2017-01-05 | 2018-12-14 | 河海大学 | A kind of multivariable water quality parameter time series data accident detection method |
| CN109344708B (en) * | 2018-08-29 | 2021-10-22 | 昆明理工大学 | Water supply pipe network pipe burst signal abnormity analysis method |
| CN109930658B (en) * | 2019-03-27 | 2021-02-05 | 杭州电子科技大学 | Water supply network monitoring point arrangement method based on system visibility |
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Application publication date: 20160706 Assignee: CHITIC CONTROL ENGINEERING Co.,Ltd. Assignor: HANGZHOU DIANZI University Contract record no.: X2021330000072 Denomination of invention: An abnormal event detection method of water supply network based on varX model Granted publication date: 20190927 License type: Common License Record date: 20210817 |