CN110516323B - Pressure pipeline damage prediction method based on time sequence analysis - Google Patents
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Abstract
The invention relates to a pressure pipeline damage prediction method based on time sequence analysis. The method comprises the steps of firstly calculating a first-order difference of monitored stress values, predicting the stress value difference in a plurality of day periods in the future by extracting stationarity information and combining an autoregressive moving average time sequence analysis (ARMA) model, further calculating the stress values in the plurality of day periods in the future, and finally analyzing and predicting the development trend of the stress values by a weighted moving average method (EWMA) so as to perform damage early warning. The invention can realize real-time early warning on the running pipeline, has the characteristics of timely and accurate early warning, and provides technical support for long-period safe running of the pipeline.
Description
Technical Field
The invention belongs to the technical field of process industry safety operation guarantee, and particularly relates to a pressure pipeline damage prediction method based on time sequence analysis.
Background
The pressure pipeline is an important component in the process industry, and the safe operation level of the pressure pipeline directly determines the safe operation level of the petrochemical enterprise. With the enlargement of petrochemical enterprises, the limitations of conventional detection means are becoming more and more obvious, such as: the daily manpower consumption is too much, the special position has certain danger, and the detection dead angle is easy to exist; the equipment safety evaluation can only be based on test data in a shutdown state, cannot reflect the real situation in a service state, cannot detect the structural state of the equipment in service in real time, and whether the safety is safe during two detection periods can only be estimated according to the previous detection result, but the estimation often has great errors due to the influence of a plurality of uncertain factors in the pipeline running environment.
In order to guarantee the safe operation level of the pipeline, researchers at home and abroad propose to monitor the stress state of the pipeline in real time, and consider that the pipeline is damaged when the monitored value exceeds a stress threshold value. In practical engineering application, damage development trends of all positions are different, and once a stress threshold is exceeded, the damage trend is too fast to develop, so that emergency plans are not ready. The published data shows that relevant researchers predict future stress values based on monitored data through an autoregressive moving average time sequence analysis method (ARMA (p, q)), but the stress value stability fluctuation caused by the change of the pipeline working condition can cause the distortion of the predicted value.
Disclosure of Invention
In order to solve the technical problem, the invention provides a pressure pipeline damage prediction method based on time sequence analysis. The method provides technical support for long-period safe operation of the pipeline.
In order to realize the purpose of the invention, the invention adopts the following technical scheme:
a pressure pipeline damage prediction method based on time sequence analysis comprises the following steps:
and 2, recording the stress value sequence accumulated in M days of the time history as follows:
{τ t }＝{τ 1 ,τ 2 ,...,τ M×f } (1)
assuming that the stress value sequence is a quasi-steady state sequence, namely the stress value fluctuates around a certain constant value in a small range, and the fluctuation amplitude of the stress value accords with normal distribution;
step 3, obtaining the stress value of the pressure pipeline in the next N days through time sequence analysis;
step 3-1, extracting stationarity information based on a difference method;
selecting first-order difference to extract stationarity information of the stress value trend to be monitored, and obtaining a zero-mean stationary random stress difference sequence as follows:
{Δτ t }＝{Δτ 2 ,Δτ 3 ,…Δτ M×f } (2)
in the formula (2), Δ τ t ＝τ t -τ t-1 Wherein t =2,3, \8230;, M × f;
step 3-2, stress difference sequence { Δ τ } t Auto-regressive moving average time series analysis (ARMA) (p, q) model parameter estimation;
sequence of stress differences { Δ τ t The internal data relationships are expressed in the ARMA (p, q) model as:
formula (3) in
Referred to as autoregressive model parameters; theta 1 ，θ 2 ，…，θ q Referred to as the moving average model parameters;
a in formula (3) t-1 ，a t-2 ，…，a t-q Called the first q-step interference term, independent of each other and subject to a mean value of 0, said a t-1 ，a t-2 ，…，a t-q According to variance of
Normal distribution of (d) is recorded as:
in the formula (4), i = t-q, \ 8230;, t-2, t-1, t
Step 3-3, determining the order of an autoregressive moving average time sequence analysis (ARMA) (p, q) model;
multiplying both sides of equation (3) by Δ τ t-k And solving for a mathematical expectation to yield:
in the formula: r k ＝E[Δτ t Δτ t-k ]，R i-k ＝E[Δτ t-i Δτ t-k ]，
And:
because R is k Is an even function, so when taking k = q +1, q +2, \8230;, q + p, taking advantage of the property of equation (6), equation (5) is obtained after unfolding:
the following matrix is obtained according to equation (7):
the autoregressive model parameter can be obtained by the formula (8)
Taking the autoregressive model parameters into equation (5) and taking k =0,1,2, \ 8230;, q at the same time, and using the properties of equation (6), the following equation is obtained:
in formula (9):
the moving average model parameter theta can be obtained by the equation (9) 1 ，θ 2 ，…，θ q ；
Step 3-4, determining the order of an autoregressive moving average time sequence analysis ARMA (p, q) model;
extraction of sequences { Δ τ) using information criterion t Maximum information quantity in the data, the information criterion function is:
selecting p and q < 5 for the pipeline structure, calculating the values of all combinations of p and q, and taking the p and q combination which enables the AIC (p and q) value to be minimum as the ARMA (p and q) model order;
step 3-5, calculating the stress value of the future N days:
after determining the order of the ARMA (p, q) model, calculating the stress value of the future N days, and the steps are as follows:
the stress difference of the future N days is calculated, and t = M xf +1, M xf +2, \ 8230is taken by using the formula (3), and f stress differences of the future 1 day are obtained by (M + 1) × f as follows:
by using the same method, the stress difference of the future N days can be obtained, and the stress difference sequence is constructed by combining the formula (2)
Further determining the stress sequence
For the pipeline structure, in order to ensure the solving precision, M is generally less than or equal to 100, and N is less than or equal to 20;
and 4, analyzing the stress development trend by a weighted moving average method (EWMA):
expected μ and variance σ of pre-M day stress values 2 Expressed as the maximum likelihood estimate:
sequence of opposite stresses { tau t Carrying out weighted moving average analysis, wherein the control variable of the ith stress value in the sequence is represented as:
in formula (17), take Z 0 λ is a smoothing parameter, and 0 < λ < 1, for a pipeline configuration a generally straight pipe is taken as λ =0.6;
according to the statistic distribution characteristics of the EWMA control chart, the statistical characteristics and the control variable Z can be obtained i The expectation of (2):
in formula (20):
controlled variable Z i The variance of (c) is:
and according to the stress value of the previous M days, solving the control limit of the EWMA control chart as follows:
wherein UCL is the upper control limit, and LCL is the lower control limit;
step 5, early warning of damage:
calculating the control variable Z of the stress value in the next N days according to the formula (17) i Trend of value as the variable Z is controlled i If the value gradually deviates and exceeds the control limit, the damage is considered to occur in the next N days; when the development trend is within the control limit, the damage is not considered to occur, and the updated stress time history data sequence is as follows:
{τ t }＝{τ f+1 ,...,τ M×f ,...,τ (M+1)×f-1 ,τ (M+1)×f } (23)
repeating the steps 3 and 4, and continuing to control the control variable Z of the stress value in the next N days i And judging the development trend.
The invention has the beneficial effects that:
the method comprises the steps of firstly calculating the first-order difference of the monitored stress values, predicting the stress value difference in a plurality of future day periods by extracting stationarity information and combining an autoregressive moving average time sequence analysis (ARMA) model, further calculating the stress values in the plurality of future day periods, and finally analyzing and predicting the development trend of the stress values by a weighted moving average method (EWMA) so as to carry out damage early warning. The invention can realize real-time early warning of the running pipeline, has the characteristics of timely and accurate early warning, and provides technical support for long-period safe running of the pipeline.
Drawings
FIG. 1 is a graph of stress time course for the first 70 days.
Fig. 2 is a stress differential time course curve for the first 70 days.
FIG. 3 is a differential time course plot of stress at the first 70 days and predicted stress at the next 15 days.
FIG. 4 is a time course plot of stress at the first 70 days versus predicted stress at the next 15 days.
FIG. 5 is a controlled variable trend curve of stress at the first 70 days and predicted stress at the next 15 days.
FIG. 6 is a trend curve of the manipulated variables for predicting stress 15 days into the future after 1025 days.
Detailed Description
The technical scheme of the invention is more specifically explained by combining the following embodiments:
a pressure pipeline damage prediction method based on time sequence analysis comprises the following steps:
{τ t }＝{τ 1 ,τ 2 ,…τ 140 } (1)
the stress value sequence time history curve is shown in fig. 1;
assuming that the stress value sequence is a quasi-steady state sequence, that is, the stress value fluctuates around a certain constant value in a small range, and the fluctuation amplitude conforms to normal distribution, and the time history curve of the stress value sequence is shown in fig. 1;
step 3, obtaining the stress value of the pressure pipeline in the next 15 days through time sequence analysis;
step 3-1, extracting stationarity information based on a difference method;
selecting first-order difference to extract stationarity information of the stress value trend to be monitored, and obtaining a zero-mean stationary random stress difference sequence as follows:
{Δτ t }＝{Δτ 2 ,Δτ 3 ,…,Δτ 140 } (2)
in the formula (2), Δ τ t ＝τ t -τ t-1 Wherein t =2,3, \ 8230;, 140;
the stress differential time history curve is shown in fig. 2;
step 3-2, stress difference sequence { Δ τ } t Autoregressive moving average time sequence analysis ARMA (p, q) model parameter estimation;
sequence of stress differences { Δ τ t The internal data relationships are expressed in the ARMA (p, q) model as:
in the formula (3)
Referred to as autoregressive model parameters; theta 1 ，θ 2 ，…，θ q Referred to as the moving average model parameters; />
A in formula (3) t-1 ，a t-2 ，…，a t-q Called the first q-step interference term, independent of each other and subject to a mean value of 0, said a t-1 ，a t-2 ，…，a t-q According to variance of
Normal distribution of (d) is recorded as:
in the formula (4), i = t-q, \ 8230;, t-2, t-1, t
Step 3-3, determining the order of an autoregressive moving average time sequence analysis ARMA (p, q) model;
multiplying both sides of equation (3) by Δ τ t-k And solving for a mathematical expectation to yield:
in the formula: r k ＝E[Δτ t Δτ t-k ]，R i-k ＝E[Δτ t-i Δτ t-k ]，
And:
because R is k The reason for the even function is as follows:
R k ＝E[Δτ t Δτ t-k ]＝E[Δτ t-k Δτ t ]＝E[Δτ t-k Δτ t-k+k ]
＝E[Δτ s Δτ s-(-k) ]＝E[Δτ t Δτ t-(-k) ]＝R -k
so when taking k = q +1, q +2, \ 8230;, q + p, equation (5) is developed using the properties of equation (6) to obtain:
the following matrix is obtained according to equation (7):
the autoregressive model parameter can be obtained by the formula (8)
Taking the autoregressive model parameters into equation (5) and taking k =0,1,2, \ 8230;, q at the same time, and using the properties of equation (6), the following equation is obtained:
namely:
in formula (9):
the moving average model parameter theta can be obtained by the equation (9) 1 ，θ 2 ，…，θ q And σ a ；
Step 3-4, determining the order of an autoregressive moving average time sequence analysis ARMA (p, q) model;
extraction of sequences { Δ τ) using information criterion t Maximum information quantity in the data, the information criterion function is:
selecting p and q < 5 for the pipeline structure, calculating the values of all combinations of p and q, and taking the p and q combination which enables the AIC (p and q) value to be minimum as the ARMA (p and q) model order;
to obtain
TABLE 1 AIC (p, q) values for different p, q combinations
| 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 |
Determining the ARMA (p, q) model order, p =3, q =2; at this time, the autoregressive model parameters are:
σ a =0.12; moving average model parameter θ 1 ＝0.53，θ 2 ＝-0.79；
Step 3-5, calculating stress values of 1-15 days in the future:
after determining the order of the ARMA (p, q) model, the stress value of the future N days can be calculated, and the steps are as follows:
calculating stress difference of 1 day in the future, and taking t =141,142 to obtain 2 stress differences of 1 day in the future by using formula (3) as follows:
in the formula a 141 ，a 142 Subject to NID = (0, sigma) a ) The random number of (2); by the same method, taking t =142,143, \ 8230;, 168,169,170, the stress difference value of the future 15 days can be obtained, and the stress difference sequence is constructed by combining the formula (2):
the time history curve of the stress difference sequence is shown in fig. 3;
further determining the stress sequence
The time history curve of the stress value sequence is shown in fig. 4;
for the pipeline structure, in order to ensure the solving precision, M is generally less than or equal to 100, and N is less than or equal to 20;
and 4, analyzing the stress development trend by a weighted moving average method (EWMA):
expected μ and variance σ of stress values for the first 70 days 2 Expressed as the maximum likelihood estimate:
sequence of corresponding stresses { tau } t Carrying out weighted moving average analysis, wherein the control variable of the ith stress value in the sequence is represented as:
in formula (17), take Z 0 λ is a smoothing parameter and 0 < λ < 1, for a pipeline structure a generally straight pipe is taken as λ =0.6;
according to the statistic distribution characteristics of the EWMA control chart, the statistical characteristics and the control variable Z can be obtained i The expectation of (2):
in formula (20):
controlled variable Z i The variance of (c) is:
and according to the stress value of the previous M days, solving the control limit of the EWMA control chart as follows:
wherein UCL is the upper control limit, and LCL is the lower control limit;
step 5, early warning of damage:
calculating the control variable Z of the stress value in the next N days according to the formula (17) i A trend of values;
as shown in fig. 5, given the control limit and the change of the control variable, it can be seen that the control variable is within the control limit in the first 70 days, and it can be seen from the predicted value in the next 15 days, the control variable is within the control limit in the next 15 days, the structure will not be damaged, and the data sequence of the time history of the updated stress value in the 2 nd to 71 th days is:
{τ t }＝{τ 3 ,τ 4 ,…,τ 140 ,τ 141 ,τ 142 } (23)
repeating the steps 3 and 4, and continuing to control the control variable Z of the stress value in the next N days i And judging the development trend. After data is collected on day 1025, as shown in FIG. 6, it is predicted that the control variables will exceed the control limits on the next 15 days, and the pipeline will be damaged on the next 15 days.
Claims (1)
1. A pressure pipeline damage prediction method based on time sequence analysis is characterized by comprising the following steps:
step 1, obtaining a stress value of a pressure pipeline through a sensor unit, wherein the acquisition frequency of the stress value is f times/day;
and 2, recording the stress value sequence accumulated in M days of the time history as follows:
{τ t }＝{τ 1 ,τ 2 ,...,τ M×f } (1)
assuming that the stress value sequence is a quasi-steady state sequence, namely the stress value fluctuates around a certain constant value in a small range, and the fluctuation amplitude of the stress value accords with normal distribution;
step 3, obtaining the stress value of the pressure pipeline in the next N days through time sequence analysis;
step 3-1, extracting stationarity information based on a difference method;
selecting first-order difference to extract stability information of the trend of the monitored stress value to obtain a zero-mean stationary random stress difference sequence as follows:
{Δτ t }＝{Δτ 2 ,Δτ 3 ,…Δτ M×f } (2)
in the formula (2), Δ τ t ＝τ t -τ t-1 Wherein t =2,3, \8230;, M × f;
step 3-2, stress difference sequence { Δ τ } t Autoregressive moving average time sequence analysis ARMA (p, q) model parameter estimation;
sequence of stress differences { Δ τ t The internal data relationships are expressed in the ARMA (p, q) model as:
in the formula (3)
Referred to as autoregressive model parameters; theta 1 ，θ 2 ，…，θ q Referred to as the moving average model parameters;
a in formula (3) t-1 ，a t-2 ，…，a t-q Called the first q-step interference term, independent of each other and subject to a mean value of 0, said a t-1 ，a t-2 ，…，a t-q Meet variance of
Normal distribution of (d) is recorded as:
in the formula (4), i = t-q, \ 8230;, t-2, t-1, t
Step 3-3, determining the order of an autoregressive moving average time sequence analysis ARMA (p, q) model;
multiplying both sides of equation (3) by Δ τ t-k And solving for a mathematical expectation to yield:
in the formula: r k ＝E[Δτ t Δτ t-k ]，R i-k ＝E[Δτ t-i Δτ t-k ]，
And:
because R is k Is an even function, so when taking k = q +1, q +2, \8230;, q + p, taking advantage of the property of equation (6), equation (5) is obtained after unfolding:
the following matrix is obtained according to equation (7):
by the formula (8)Evaluating parameters of an autoregressive model
Taking the autoregressive model parameters into equation (5) and taking k =0,1,2, \ 8230;, q at the same time, and using the properties of equation (6), the following equation is obtained:
in formula (9):
the moving average model parameter theta can be obtained by the equation (9) 1 ，θ 2 ，…，θ q ；
Step 3-4, determining the order of an autoregressive moving average time sequence analysis ARMA (p, q) model;
extraction of sequences { Δ τ) using information criterion t Maximum information quantity in the data, the information criterion function is:
selecting p and q < 5 for the pipeline structure, calculating the values of all combinations of p and q, and taking the p and q combination which enables the AIC (p and q) value to be minimum as the ARMA (p and q) model order;
step 3-5, calculating the stress value of the future N days:
after determining the order of the ARMA (p, q) model, calculating the stress value of the future N days, and the steps are as follows:
the stress difference of the future N days is calculated, and t = M xf +1, M xf +2, \ 8230is taken by using the formula (3), and f stress differences of the future 1 day are obtained by (M + 1) × f as follows:
by using the same method, the stress difference of the future N days can be obtained, and the stress difference sequence is constructed by combining the formula (2):
further finding a stress sequence:
for the pipeline structure, in order to ensure the solving precision, M is generally less than or equal to 100, and N is less than or equal to 20;
and 4, analyzing the stress development trend by a weighted moving average method (EWMA):
expected μ and variance σ of pre-M day stress values 2 Expressed as the maximum likelihood estimate:
sequence of opposite stresses { tau t Carrying out weighted moving average analysis, wherein the control variable of the ith stress value in the sequence is represented as:
in formula (17), take Z 0 λ is a smoothing parameter, and 0 < λ < 1, for pipeline structures, λ =0.6 is typically taken for straight pipes;
according to the statistic distribution characteristics of the EWMA control chart, the statistical characteristics and the control variable Z can be obtained i The expectation of (2):
in formula (20):
controlled variable Z i The variance of (c) is:
and according to the stress value of the previous M days, solving the control limit of the EWMA control chart as follows:
wherein UCL is the upper control limit, and LCL is the lower control limit;
step 5, damage early warning:
calculating the control variable Z of the stress value in the next N days according to the formula (17) i Trend of value as the control variable Z i If the value gradually deviates and exceeds the control limit, the damage is considered to occur in the next N days; when the development trend is within the control limit, the damage is not considered to occur, and the updated stress time history data sequence is as follows:
{τ t }＝{τ f+1 ,...,τ M×f ,...,τ (M+1)×f-1 ,τ (M+1)×f } (23)
repeating the steps 3 and 4, and continuing to control the control variable Z of the stress value in the next N days i And judging the development trend.
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