CN110516323A - A kind of pressure pipeline damage forecast method based on Time-Series analysis - Google Patents
A kind of pressure pipeline damage forecast method based on Time-Series analysis Download PDFInfo
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Abstract
The pressure pipeline damage forecast method based on Time-Series analysis that the present invention relates to a kind of.The present invention calculates the first-order difference of monitor stress value first, by extracting stationarity information, the stress value difference in the following several days periods is predicted in conjunction with autoregressive moving average Time-Series analysis arma modeling, and then calculate the stress value in the following several days periods, finally by the development trend of the method for weighted moving average (EWMA) analysis predicted stresses value, to carry out damage alarming.The present invention may be implemented to carry out real-time early warning in in-service pipeline, have the characteristics that early warning is timely, accurate, this provides technical support for the safe operation of pipeline long period.
Description
Technical field
The invention belongs to process industries to be safely operated safeguards technique field, be specifically related to a kind of based on Time-Series analysis
Pressure pipeline damage forecast method.
Background technique
Pressure pipeline is the important component in process industry, and safety operation level directly determines petroleum chemical enterprise
Safety operation level.With the expansion of petroleum chemical enterprise's scale, the limitation of conventional detection means is also increasingly apparent, such as: day
Often consumption manpower is too many, and specific position has certain risk, is easy the presence of detection dead angle；It can only for equipment safety evaluation
Based on the test data under shutdown status, it can not reflect the truth under service state, it can not be to in-service device structure state
Be measured in real time, twice detect during whether safety can only be estimated according to testing result before, but it is this estimate usually by
The influence of many uncertain factors in pipeline performance environment and there is very big error.
In order to ensure its safety operation level, domestic and international researcher proposes to carry out real-time monitoring to pipe stress state,
Pipeline damages when thinking monitor value beyond stress threshold.In practical engineering application, each position lesion development trend is different,
Once beyond damaging after stress threshold, trend development is too fast to be often led to have little time to prepare emergency preplan.Open source information shows phase
It closes researcher and the following stress of monitoring data prediction is based on by autoregressive moving average Time Series Analysis Method (ARMA (p, q))
Value, but the fluctuation of stress value stationarity caused by pipeline operating condition changes, will lead to predicted value distortion.
Summary of the invention
In order to solve the above technical problem, the present invention provides a kind of pressure pipeline damage forecast side based on Time-Series analysis
Method.This method provides technical support for the safe operation of pipeline long period.
In order to achieve the object of the present invention, the invention adopts the following technical scheme:
A kind of pressure pipeline damage forecast method based on Time-Series analysis, comprising the following steps:
Step 1, pressure pipeline stress value is obtained by sensor unit, the stress value frequency acquisition is f times/day；
Step 2, the stress value sequence accumulated in time history M days is denoted as:
{τt}={ τ1,τ2,...,τM×f} (1)
Assuming that steady sequency subject to the stress value sequence, i.e., the described stress value is fluctuated around a certain steady state value small range,
Its fluctuation amplitude meets normal distribution；
Step 3, the stress value of the following N days pressure pipelines is obtained by Time-Series analysis；
Step 3-1 extracts stationarity information based on calculus of finite differences；
It selects first-order difference to extract the stationarity information of monitor stress value trend, it is poor to obtain the steady random stress of zero-mean
Sub-sequence, as follows:
{Δτt}={ Δ τ2,Δτ3,…ΔτM×f} (2)
In formula (2), Δ τt=τt-τt-1, wherein t=2,3 ..., M × f；
Step 3-2, stress difference sequence { Δ τtAutoregressive moving average Time-Series analysis ARMA (p, q) model parameter estimates
Meter；
Stress difference sequence { Δ τtInternal data relationship is expressed as with ARMA (p, q) model:
In formula (3) formulaReferred to as Parameters of Autoregressive Models；θ1, θ2..., θqReferred to as sliding average mould
Shape parameter；
A in formula (3)t-1, at-2..., at-qReferred to as preceding q walks distracter, and mutually indepedent and obedience mean value is 0, at-1,
at-2..., at-qMeeting variance isNormal distribution, be denoted as:
I=t-q in formula (4) ..., t-2, t-1, t
Step 3-3 determines autoregressive moving average Time-Series analysis ARMA (p, q) model order；
To formula (3) two sides respectively multiplied by Δ τt-kAnd mathematic expectaion is sought, it obtains:
In formula: Rk=E [Δ τtΔτt-k], Ri-k=E [Δ τt-iΔτt-k],And:
Because of RkFor even function, k=q+1, q+2 ..., q+p are taken so working as, using formula (6) property, after formula (5) expansion
It obtains:
Following matrix is obtained according to formula (7):
Parameters of Autoregressive Models can be acquired by formula (8)
It brings the Parameters of Autoregressive Models into formula (5), while taking k=0,1,2 ..., q, and obtained using formula (6) property
To following equation:
In formula (9):
By the way that moving average model parameter θ can be found out in formula (9)1, θ2..., θq；
Step 3-4 determines autoregressive moving average Time-Series analysis ARMA (p, q) model order；
Using information criterion abstraction sequence { Δ τtIn maximum fault information, information criterion function are as follows:
P, q < 5 are selected for pipeline configuration, calculate p, all combined values of q take so that AIC (p, q) value the smallest p, q
Group is combined into ARMA (p, q) model order；
Step 3-5 calculates the following N days stress values:
After determining ARMA (p, q) model order, the following N days stress values can be calculated, steps are as follows:
It calculates the following N days stress difference and takes t=M × f+1, M × f+2 ... using formula (3), (M+1) × f obtains future
F stress difference is as follows within 1 day:
Using same method, then the available following N days stress difference, convolution (2) construct stress difference sequence
Further acquire stress sequence
M≤100, N≤20 are generally taken in order to ensure solving precision for pipeline configuration；
Step 4, stress development trend is analyzed by the method for weighted moving average (EWMA):
The expectation μ and variances sigma of preceding M days stress values2It is indicated with maximal possibility estimation are as follows:
To stress sequence { τtWeighted moving average analysis is done, the control variable of i-th of stress value is expressed as in sequence:
In formula (17), Z is taken0=μ, λ are smoothing parameter, and 0 < λ < 1, for pipeline architecture, general straight tube take λ=
0.6；
According to EWMA control figure statistics distribution feature, variable Z can be controlled in the hope of its statistical natureiExpectation:
In formula (20):
Control variable ZiVariance are as follows:
According to preceding M days stress values, the control for acquiring EWMA control figure is limited to:
Wherein UCL is upper control limit, and LCL is lower control limit；
Step 5, damage alarming:
The control variable Z of stress value in N days following is calculated according to formula (17)iThe development trend of value, as control variable ZiValue
It is gradually deviated from and is more than that control is prescribed a time limit, then it is assumed that will damage within following N days；When development trend is in above-mentioned control limit, it is believed that
There is no updating Stressing history data sequence at this time for damage are as follows:
{τt}={ τf+1,...,τM×f,...,τ(M+1)×f-1,τ(M+1)×f} (23)
Step 3,4 are repeated, the control variable Z to stress value in following N days is continuediDevelopment trend is judged.
The beneficial effects of the present invention are:
The present invention calculates the first-order difference of monitor stress value first, by extracting stationarity information, slides in conjunction with autoregression
Average Time-Series analysis arma modeling predicts the stress value difference in the following several days periods, and then calculates the following several days weeks
Stress value in phase, finally by the development trend of the method for weighted moving average (EWMA) analysis predicted stresses value, to be damaged
Early warning.The present invention may be implemented to carry out real-time early warning in in-service pipeline, have the characteristics that early warning is timely, accurate, this is pipeline
Long period safe operation provides technical support.
Detailed description of the invention
Fig. 1 is preceding 70 days stress time-history curves.
Fig. 2 is that preceding 70 days stress differences divide time-history curves.
Fig. 3 is the difference time-history curves of preceding 70 days stress and following 15 days predicted stresses.
Fig. 4 is the time-history curves of preceding 70 days stress and following 15 days predicted stresses.
Fig. 5 is the control variable trends curve of preceding 70 days stress and following 15 days predicted stresses.
Fig. 6 is the control variable trends curve of following 15 days predicted stresses after 1025 days.
Specific embodiment
More specific detail is made to technical solution of the present invention below with reference to embodiment:
A kind of pressure pipeline damage forecast method based on Time-Series analysis, comprising the following steps:
Step 1, pressure pipeline stress value being obtained by sensor unit, the stress value frequency acquisition is f=2 times/
It；
Step 2, the stress value sequence accumulated in time history 70 days is denoted as:
{τt}={ τ1,τ2,…τ140} (1)
Above-mentioned stress value sequence time history curve is as shown in Figure 1；
Assuming that steady sequency subject to the stress value sequence, i.e., the described stress value is fluctuated around a certain steady state value small range,
Its fluctuation amplitude meets normal distribution, and above-mentioned stress value sequence time history curve is as shown in Figure 1；
Step 3, the stress value of following 15 days pressure pipelines is obtained by Time-Series analysis；
Step 3-1 extracts stationarity information based on calculus of finite differences；
It selects first-order difference to extract the stationarity information of monitor stress value trend, it is poor to obtain the steady random stress of zero-mean
Sub-sequence, as follows:
{Δτt}={ Δ τ2,Δτ3,…,Δτ140} (2)
In formula (2), Δ τt=τt-τt-1, wherein t=2,3 ..., 140；
Above-mentioned stress Differential time course curve is as shown in Figure 2；
Step 3-2, stress difference sequence { Δ τtAutoregressive moving average Time-Series analysis ARMA (p, q) model parameter estimates
Meter；
Stress difference sequence { Δ τtInternal data relationship is expressed as with ARMA (p, q) model:
In formula (3) formulaReferred to as Parameters of Autoregressive Models；θ1, θ2..., θqReferred to as sliding average mould
Shape parameter；
A in formula (3)t-1, at-2..., at-qReferred to as preceding q walks distracter, and mutually indepedent and obedience mean value is 0, at-1,
at-2..., at-qMeeting variance isNormal distribution, be denoted as:
I=t-q in formula (4) ..., t-2, t-1, t
Step 3-3 determines autoregressive moving average Time-Series analysis ARMA (p, q) model order；
To formula (3) two sides respectively multiplied by Δ τt-kAnd mathematic expectaion is sought, it obtains:
In formula: Rk=E [Δ τtΔτt-k], Ri-k=E [Δ τt-iΔτt-k],And:
Because of RkFor even function, reason is as follows:
Rk=E [Δ τtΔτt-k]=E [Δ τt-kΔτt]=E [Δ τt-kΔτt-k+k]
=E [Δ τsΔτs-(-k)]=E [Δ τtΔτt-(-k)]=R-k
So, using formula (6) property, will be obtained after formula (5) expansion when taking k=q+1, q+2 ..., q+p:
Following matrix is obtained according to formula (7):
Parameters of Autoregressive Models can be acquired by formula (8)
It brings the Parameters of Autoregressive Models into formula (5), while taking k=0,1,2 ..., q, and obtained using formula (6) property
To following equation:
That is:
In formula (9):
By the way that moving average model parameter θ can be found out in formula (9)1, θ2..., θqAnd σa；
Step 3-4 determines autoregressive moving average Time-Series analysis ARMA (p, q) model order；
Using information criterion abstraction sequence { Δ τtIn maximum fault information, information criterion function are as follows:
P, q < 5 are selected for pipeline configuration, calculate p, all combined values of q take so that AIC (p, q) value the smallest p, q
Group is combined into ARMA (p, q) model order；
It acquires
Table 1 difference p, q combine corresponding AIC (p, q) value
| p | q | AIC(p,q) |
| 0 | 1 | 3.37 |
| 0 | 2 | 3.11 |
| … | … | … |
| 3 | 2 | 1.95 |
| … | … | … |
| 4 | 3 | 2.67 |
| 4 | 4 | 2.74 |
Determine ARMA (p, q) model order, p=3, q=2；At this point, Parameters of Autoregressive Models are as follows: σa=0.12；Moving average model parameter θ1=0.53, θ2=-0.79；
Step 3-5 calculates the following 1-15 days stress values:
After determining ARMA (p, q) model order, the following N days stress values can be calculated, steps are as follows:
Following 1 day stress difference is calculated, using formula (3), takes t=141,142 obtain following 1 day 2 stress difference such as
Under:
A in formula141, a142To obey NID=(0, σa) random number；Using same method, t=142 is taken, 143 ...,
168,169,170 available following 15 days stress difference values, convolution (2) construct stress difference sequence:
Above-mentioned stress difference sequence time history curve is as shown in Figure 3；
Further acquire stress sequence
Above-mentioned stress value sequence time course curve is as shown in Figure 4；
M≤100, N≤20 are generally taken in order to ensure solving precision for pipeline configuration；
Step 4, stress development trend is analyzed by the method for weighted moving average (EWMA):
The expectation μ and variances sigma of preceding 70 days stress values2It is indicated with maximal possibility estimation are as follows:
To stress sequence { τtWeighted moving average analysis is done, the control variable of i-th of stress value is expressed as in sequence:
In formula (17), Z is taken0=μ, λ are smoothing parameter, and 0 < λ < 1, for pipeline architecture, general straight tube take λ=
0.6；
According to EWMA control figure statistics distribution feature, variable Z can be controlled in the hope of its statistical natureiExpectation:
In formula (20):
Control variable ZiVariance are as follows:
According to preceding M days stress values, the control for acquiring EWMA control figure is limited to:
Wherein UCL is upper control limit, and LCL is lower control limit；
Step 5, damage alarming:
The control variable Z of stress value in N days following is calculated according to formula (17)iThe development trend of value；
As shown in figure 5, providing control limit and control variable change situation, it can be seen that control variable is controlling within first 70 days
In limit, 15 days futures can be seen that according to 15 days predicted values of future, in control limit, structure will not damage control variable
Wound updates data sequence of the stress value in the 2nd~71 day time history at this time are as follows:
{τt}={ τ3,τ4,…,τ140,τ141,τ142} (23)
Step 3,4 are repeated, the control variable Z to stress value in following N days is continuediDevelopment trend is judged.Work as acquisition
After 1025th day data, as shown in Figure 6, it is predicted that following 15 days control variables will exceed control limit, it is believed that following 15 days pipelines
It will damage.
Claims (1)
1. a kind of pressure pipeline damage forecast method based on Time-Series analysis, it is characterised in that the following steps are included:
Step 1, pressure pipeline stress value is obtained by sensor unit, the stress value frequency acquisition is f times/day；
Step 2, the stress value sequence accumulated in time history M days is denoted as:
{τt}={ τ1,τ2,...,τM×f} (1)
Assuming that steady sequency subject to the stress value sequence, i.e., the described stress value is fluctuated around a certain steady state value small range, wave
Dynamic amplitude meets normal distribution；
Step 3, the stress value of the following N days pressure pipelines is obtained by Time-Series analysis；
Step 3-1 extracts stationarity information based on calculus of finite differences；
It selects first-order difference to extract the stationarity information of monitor stress value trend, obtains the steady random stress difference sequence of zero-mean
Column, as follows:
{Δτt}={ Δ τ2,Δτ3,…ΔτM×f} (2)
In formula (2), Δ τt=τt-τt-1, wherein t=2,3 ..., M × f；
Step 3-2, stress difference sequence { Δ τtAutoregressive moving average Time-Series analysis ARMA (p, q) model parameter estimation；
Stress difference sequence { Δ τtInternal data relationship is expressed as with ARMA (p, q) model:
In formula (3) formulaReferred to as Parameters of Autoregressive Models；θ1, θ2..., θqReferred to as moving average model is joined
Number；
A in formula (3)t-1, at-2..., at-qReferred to as preceding q walks distracter, and mutually indepedent and obedience mean value is 0, at-1,
at-2..., at-qMeeting variance isNormal distribution, be denoted as:
I=t-q in formula (4) ..., t-2, t-1, t
Step 3-3 determines autoregressive moving average Time-Series analysis ARMA (p, q) model order；
To formula (3) two sides respectively multiplied by Δ τt-kAnd mathematic expectaion is sought, it obtains:
In formula: Rk=E [Δ τtΔτt-k], Ri-k=E [Δ τt-iΔτt-k],And:
Because of RkFor even function, k=q+1, q+2 ..., q+p are taken so working as, using formula (6) property, will be obtained after formula (5) expansion:
Following matrix is obtained according to formula (7):
Parameters of Autoregressive Models can be acquired by formula (8)
It brings the Parameters of Autoregressive Models into formula (5), while taking k=0,1,2 ..., q, and it is following to utilize formula (6) property to obtain
Equation:
In formula (9):
By the way that moving average model parameter θ can be found out in formula (9)1, θ2..., θq；
Step 3-4 determines autoregressive moving average Time-Series analysis ARMA (p, q) model order；
Using information criterion abstraction sequence { Δ τtIn maximum fault information, information criterion function are as follows:
P, q < 5 are selected for pipeline configuration, calculate p, all combined values of q take so that AIC (p, q) value the smallest p, q combination
For ARMA (p, q) model order；
Step 3-5 calculates the following N days stress values:
After determining ARMA (p, q) model order, the following N days stress values can be calculated, steps are as follows:
It calculates the following N days stress difference and takes t=M × f+1, M × f+2 ... using formula (3), (M+1) × f obtains 1 day f of future
A stress difference is as follows:
Using same method, then the available following N days stress difference, convolution (2) construct stress difference sequence:
Further acquire stress sequence:
M≤100, N≤20 are generally taken in order to ensure solving precision for pipeline configuration；
Step 4, stress development trend is analyzed by the method for weighted moving average (EWMA):
The expectation μ and variances sigma of preceding M days stress values2It is indicated with maximal possibility estimation are as follows:
To stress sequence { τtWeighted moving average analysis is done, the control variable of i-th of stress value is expressed as in sequence:
In formula (17), Z is taken0=μ, λ are smoothing parameter, and 0 < λ < 1, and for pipeline architecture, general straight tube takes λ=0.6；
According to EWMA control figure statistics distribution feature, variable Z can be controlled in the hope of its statistical natureiExpectation:
In formula (20):
Control variable ZiVariance are as follows:
According to preceding M days stress values, the control for acquiring EWMA control figure is limited to:
Wherein UCL is upper control limit, and LCL is lower control limit；
Step 5, damage alarming:
The control variable Z of stress value in N days following is calculated according to formula (17)iThe development trend of value, as control variable ZiIt is worth gradually inclined
It prescribes a time limit from and more than control, then it is assumed that will damage within following N days；When development trend is in above-mentioned control limit, it is believed that damage does not have
There is generation, update Stressing history data sequence at this time are as follows:
{τt}={ τf+1,...,τM×f,...,τ(M+1)×f-1,τ(M+1)×f} (23)
Step 3,4 are repeated, the control variable Z to stress value in following N days is continuediDevelopment trend is judged.
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