CN111144002B - Method for predicting pipe burst of grey cast iron pipe of water supply pipe network - Google Patents
Method for predicting pipe burst of grey cast iron pipe of water supply pipe network Download PDFInfo
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- 229910001060 Gray iron Inorganic materials 0.000 title claims abstract description 51
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- 239000000463 material Substances 0.000 claims description 13
- 238000004210 cathodic protection Methods 0.000 claims description 12
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Abstract
The invention discloses a method for predicting pipe explosion of a grey cast iron pipe of a water supply pipe network, which comprises the following steps of firstly, determining pipe explosion influence factors, and acquiring and arranging pipe explosion information and pipeline basic data; secondly, performing variable descriptive statistics on the sorted sample data and performing discrete inspection on statistical results; thirdly, modeling the counting record of pipe explosion by adopting a ZIP model, carrying out parameter estimation and analysis on the estimation result, and rechecking zero expansion; then, obtaining the expected value of single pipe burst of the grey cast iron pipe of the water supply pipe network by using the parameter estimation result; and finally, obtaining the total number of the detonating tubes in the area prediction period according to the probability calculated by the corresponding ZIP model and the total number of the detonating tubes model. The method is beneficial to operation management personnel of the water supply network to predict the possibility of pipe explosion of the grey cast iron pipes in different areas and different periods, and is beneficial to early warning pipe explosion and making maintenance planning on the urban underground water supply network, so that the maintenance planning of urban infrastructure is facilitated.
Description
Technical Field
The invention relates to the technical field of water supply network pipe burst prediction, in particular to a method for predicting pipe burst of a grey cast iron pipe of a water supply network.
Background
The urban underground water supply pipe network is related to water consumption of residents, is an extremely important ring in urban infrastructure, is high in leakage rate and pipe explosion rate of urban pipe networks in China at present, seriously threatens water supply safety, and influences normal production and life, so that the problem of pipe explosion of water supply pipes is predicted and solved, and the problem is urgently needed to be solved by the industry.
When the previous research on the pipe burst prediction method is consulted, the statistical model is one of the main types of the existing prediction of the pipe burst phenomenon of the urban water supply pipeline and comprises a linear or exponential model, a generalized linear model and a risk proportion model, and when a large amount of pipe burst historical data and pipeline performance data exist, the statistical model can be applied to the pipe burst prediction. The counting data with the observation value of zero are found from counting data of a large number of water supply network grey cast iron pipes, and the ZIP model is applied to various industries and has not been introduced to prediction of water supply network pipe explosion. The influence of various factors on pipe explosion can be better known in the research of pipe explosion of the grey cast iron pipe of the water supply network, and early warning of pipe explosion and maintenance planning are facilitated to be carried out on the urban underground water supply network in advance, so that maintenance planning of urban infrastructure is facilitated.
Disclosure of Invention
The invention provides a method for predicting pipe explosion of a grey cast iron pipe of a water supply network, which can be used for predicting the total times of pipe explosion of the grey cast iron pipe of the water supply network in a certain period in a certain area and is beneficial to establishing a strategy for repairing and renewing the urban water supply network.
A method for predicting pipe explosion of a grey cast iron pipe of a water supply pipe network comprises the following steps:
1) acquiring pipeline basic data of the grey cast iron pipe according to pipe explosion influence factors, collecting pipe explosion information, and taking the collected pipe explosion information as sample data after the pipe explosion information is arranged;
2) carrying out covariate descriptive statistics on the pipe explosion influence factors on the sample data obtained in the step 1) according to the requirements of a zero-expansion Poisson (ZIP) model, detecting the dispersion phenomenon, if the dispersion phenomenon is met, conforming to the requirements of the zero-expansion Poisson (ZIP) model, carrying out parameter estimation, and entering the step 3);
3) analyzing the influence of various factors on the tube explosion times of the grey cast iron tube according to the parameter estimation result value obtained in the step 2), and determining alpha0、α1、α2、β1、β2、β3、γ1Obtaining a calculation formula (1) of the pipe explosion expected value of the single grey cast iron pipe;
in the formula (1), lambdai,tRepresents the pipe burst expected value, alpha, of the ith pipeline at time t0Is a constant term of a regression equation, alpha1Of pipe diameterValue z of the parameter1Parameter estimation, alpha, by zero-expansion Poisson (ZIP) model2Value z of the tube length2Parameter estimation, alpha, by zero-expansion Poisson (ZIP) model3Parameter value z for tubular material3Parameter estimation by zero-expansion Poisson (ZIP) model, z1As value of the pipe diameter, z2Value of tube length, z3Is the parameter value of the material of the pipe, beta1Parameter value p for tube age1Parameter estimation, beta, by zero-expansion Poisson (ZIP) model2Parameter value p being temperature influence index2Parameter estimation, beta, by zero-expansion Poisson (ZIP) model3As parameter value p of rainfall3Parameter estimation, beta, by zero-expansion Poisson (ZIP) model4For the value p of the traffic load4Parameter estimation by zero-expansion Poisson (ZIP) model, p1As a parameter value of the age of the tube, p2As a parameter value of the temperature influence index, p3As a parameter value of rainfall, p4As a parameter value of traffic load, gamma1Parameter value q of historical total times of pipe explosion1Parameter estimation by zero-expansion Poisson (ZIP) model, gamma2Parameter value q for cathodic protection2Parameter estimation by zero-expansion Poisson (ZIP) model, q1Parameter value, q, of the historical total number of pipe bursts2Are the values of the cathodic protection parameters. Due to z3、p4、q2All take zero value, the parameter estimation result value is alpha in formula0、α1、α2、β1、β2、β3、γ1。
4) Substituting the sample data obtained in the step 1) into the tube explosion expected value calculation formula (1) in the step 3) to calculate to obtain a tube explosion expected value result;
5) and (4) calculating the pipe explosion probability of the single grey cast iron pipe according to the pipe explosion expected value result obtained in the step (4), and further obtaining the estimated total times of pipe explosion in the prediction period in the region.
In step 1), the pipeline basic data set pipe explosion information comprises: pipe diameter, pipe length, pipe material, pipe age, temperature influence index, rainfall, traffic load, total times of pipe explosion history and whether cathodic protection is adopted.
The arrangement specifically comprises:
a) pipe diameter: and (3) generating variables in the model, directly considering the prediction of the explosion tube, selecting a trunk tube with the range of DN100 to DN300, recording the variables as DIA, and the parameter values as z1；
b) Length of the tube: the Length of the trunk in the sample, the variable is recorded as Length, and the parameter value is z2；
c) Pipe material: the grey cast iron pipe is made of the same material for different pipelines, and the parameter value is z3(ii) a Single pipe prediction can be 0;
d) the tube age is as follows: selecting the construction period of more than 5 years, recording the variable as Age and the parameter value as p1；
e) Temperature influence index: the daily average temperature is obtained according to the obtained daily average temperature, the daily average temperature is lower than 5 ℃ and higher than 30 ℃ in one year, the sum of the daily average temperature and the days is a temperature influence index, the variable is recorded as TI, and the parameter value is p2(ii) a The values of the temperature influence index TI among the above influencing factors are as follows:
p2＝TI5+TI30
in the formula, p2Is a temperature impact index parameter value; TI5The number of days that the average daily temperature is lower than 5 ℃ in one year; TI30Is the number of days in which the average daily temperature is higher than 30 ℃ in one year.
f) Rainfall: the total annual rainfall is recorded as Rain, the variable is recorded as Rain, and the parameter value is p3Showing the influence of the soil moisture content on the pipe burst;
g) traffic load: the traffic load borne by the urban underground water supply pipeline is transmitted through the soil body, the variable is recorded as TL, and the parameter value is p4If the traffic load borne by the urban underground water supply pipeline is the same or similar, the traffic load can be 0;
h) total historical times of pipe bursting: the sum of the times of pipe explosion occurring before the t year after the self-construction of a certain pipeline i is completed is recorded as NOKPF, the variable is q1；
i) And (3) cathodic protection: considering whether there is cathodic protection, variableDenoted CP, parameter value q2。
And 2) if the over-dispersion phenomenon is met, meeting the requirement of a zero-expansion Poisson (ZIP) model, and performing parameter estimation according to a log-likelihood function of the ZIP model.
In the step 4), the parameters of the unknown variables in the prediction period are specially processed by using the ZIP model and the determination of the variable parameters in the prediction period, and then the pipe explosion expected value of the single grey cast iron pipe is calculated.
Substituting the sample data obtained in the step 1) into the pipe explosion expected value calculation formula (1) in the step 3) to calculate to obtain a pipe explosion expected value result, and specifically comprising the following steps:
z1is the parameter value of the pipe diameter in the sample data, z2As a parameter value of the tube length in the sample data, p1Parameter values of tube ages in sample data, q1The parameter value of the total historical times of tube explosion in sample data is obtained;
using correction values p for temperature-influencing indices2,tParameter value p as temperature influence index2And using the correction value p for the amount of rainfall3,tParameter value p as rainfall3Substituting the formula into the formula to calculate the expected value of the pipe explosion by the formula (1) to obtain the expected value lambda of the pipe explosioni,t。
Correction value p for temperature influence index2,tRespectively calculating according to the days:
firstly, when the day is in the 12 months of the current year, predicting the tube explosion times of the next year, calculating the average value by adopting the temperature influence indexes of three years before the next year according to the formula (2), and obtaining the correction value p of the temperature influence indexes2,t；
In the formula (2), p2,t-1、p2,t-2、p2,t-3The temperature influence indexes are sequentially 1 year before the next year (namely the year), 2 years before the next year and 3 years before the next year;
② when the day is in the 1-11 months of the current year, predicting the tube explosion times of the current year, when calculating according to the formula (3)The sum of the average values of the data in the time interval is used for obtaining the correction value p of the temperature influence index2,t；
In the formula (3), p'2,tP 'is the sum of days with the average temperature per day of the known month below 5 ℃ and above 30 ℃ in the year'2,t-1、p’2,t-2、p’2,t-3The average daily temperature is the sum of days of being lower than 5 ℃ and higher than 30 ℃ corresponding to unknown months of 1 year, 2 years and 3 years before the current year. I.e. p'2,t-1Is the sum of days with the average temperature below 5 ℃ and above 30 ℃ in the day corresponding to the unknown month 1 year before the current year.
For example, when the day is in the 6 months, p 'of the year'2,tP 'is the sum of days with the average temperature of the day being lower than 5 ℃ and higher than 30 ℃ in known months from 1 to 6 in the current year t'2,t-1、p’2,t-2、p’2,t-3The average daily temperature is the sum of days with the average daily temperature lower than 5 ℃ and the average daily temperature higher than 30 ℃ which correspond to 1 year, 2 years and 3 years from 7 months to 12 months before t in the current year. p'2,t-1Is the sum of days with the average daily temperature of less than 5 ℃ and more than 30 ℃ corresponding to the period from 7 months to 12 months in 1 year before t in the current year.
Corrected value p of rainfall3,tRespectively calculating according to the days:
firstly, when the day of the year is in 12 months of the year and the pipe explosion times of the next year are predicted, calculating the average rainfall of the previous three years according to the formula (4) to obtain the corrected value p of the rainfall3,t；
In the formula (4), p3,t-1、p3,t-2、p3,t-3The rainfall values of 1 year, 2 years and 3 years before the next year are sequentially obtained.
Secondly, when the day is in 1-11 months of the current year, predicting the tube explosion times of the current year, calculating the sum of the average values of rainfall data in a time period according to the formula (5),obtaining a correction value p for rainfall3,t；
In the formula (5), p'3,tIs the total rainfall, p 'of the known month in the year'3,t-1、p’3,t-2、p’3,t-3The corresponding total rainfall values of the unknown months of 1 year, 2 years and 3 years before the current year are sequentially obtained.
For example, when the day is in the 6 months, p 'of the year'3,tIs the total rainfall, p ', of the known months from 1 month to 6 months of the year'3,t-1、p’3,t-2、p’3,t-3The corresponding total rainfall values of the unknown months from 7 months to 12 months in the previous 1 year, 2 years and 3 years of the current year are sequentially obtained. p'3,t-1The corresponding total rainfall amount for the unknown months of 7 to 12 months 1 year prior to the current year.
In the step 5), calculating to obtain the pipe explosion probability of the single grey cast iron pipe according to the pipe explosion expected value result obtained in the step 4), and further obtaining the estimated total times of pipe explosion in the prediction period in the region, wherein the method specifically comprises the following steps:
A) calculating the pipe explosion probability p (k) of a single grey cast iron pipei,t) When k isi,tWhen not equal to 0, the model is as follows:
wherein k isi,tRepresents the tube explosion times of the ith grey cast iron tube in t time, p (k)i,t) Indicates the number of pipe bursts ki,tProbability of (G)i,tThe probability of zero generation of a zero-expansion Poisson (ZIP) model structure of the ith gray cast iron pipe in t time is shown,
indicates the number of pipe bursts ki,tCorresponding expected value of detonation, ki,t| A Indicates the number of opposite detonating tubes ki,tPerforming factorial operation;
B) computing intra-region predictionsEstimated total number of times N for pipe explosion in periodt，NtThe modeling is as follows:
Nt＝∑ki,tp(ki,t)。
compared with the prior art, the invention has the beneficial effects that:
when the pipe network pipe explosion times are analyzed, influence factors influencing pipe explosion of a grey cast iron pipe water supply pipe network are analyzed, and the total pipe explosion time result condition is predicted. According to the method, when the pipe network pipe explosion times are analyzed, the pipe network pipe explosion times are divided into two processes for analysis, the pipe explosion observation value of a pipeline with a large proportion is determined to be zero, the pipe explosion times follow the Poisson distribution state, and the analysis accuracy is improved.
The method is beneficial to operation management personnel of the water supply network to predict the possibility of pipe explosion of the grey cast iron pipes in different areas and different periods, and is beneficial to early warning pipe explosion and making maintenance planning on the urban underground water supply network, so that the maintenance planning of urban infrastructure is facilitated.
Drawings
FIG. 1 is a schematic flow chart of a method for predicting pipe burst of a grey cast iron pipe of a water supply pipe network according to the invention;
FIG. 2 is a comparison of annual predicted total number of detonators and actual total number of detonators in accordance with the present invention;
Detailed Description
The method for predicting pipe burst of the gray cast iron pipe of the water supply pipe network is further described by combining the attached drawings of the specification.
The invention discloses a method for predicting pipe burst of a grey cast iron pipe of a water supply pipe network, which comprises the following steps of:
(1) acquiring pipeline basic data set pipe explosion information of the grey cast iron pipe in a certain area in a certain time period according to pipe explosion influence factors, and finishing the pipe explosion information as sample data;
(2) performing pipe explosion influence factor (covariate) descriptive statistics on final sample data according to the requirements of a zero expansion Poisson (ZIP) model, and detecting a dispersion phenomenon;
(3) and dividing the tube explosion record of the grey cast iron tube in a certain period of a certain area into two states, wherein one state is the structural zero meeting the Logistic model, the count value of the tube explosion meets the Poisson model, and the obtained zero tube explosion value is sampling zero. Performing parameter estimation according to the log likelihood function of the ZIP model;
(4) analyzing the influence of various factors on the pipe burst frequency of the grey cast iron pipe according to the parameter estimation result value obtained in the step (3) to obtain a pipe burst expected value calculation formula of the single grey cast iron pipe;
(5) and (4) determining variable parameter values in a prediction period by using a ZIP model according to the data in the step (3) and the analysis result in the step (4), particularly processing the parameter values of unknown variables in the prediction period, and calculating the pipe explosion expected value of the single grey cast iron pipe.
(6) And (5) calculating to obtain the tube explosion probability of the single grey cast iron tube according to the result in the step (5), and further obtaining the estimated total times of tube explosion in the prediction period in the region.
The pipe explosion information and pipeline basic data mentioned in the step (1) mainly comprise: number of bursts within a sample period and a) static variables: pipe diameter, pipe length, pipe material; b) dynamic variables: pipe age, temperature influence index, rainfall and traffic load; c) dynamic and static variables: historical total times of tube explosion and cathode protection. The final selected booster influencing factors include: pipe diameter, pipe length, pipe material, pipe age, temperature influence index, rainfall, traffic load, total times of pipe explosion history and cathodic protection. Wherein:
1) pipe diameter: and (3) generating variables in the model, directly considering the prediction of the explosion tube, selecting a trunk tube with the range of DN100 to DN300, recording the variables as DIA, and the parameter values as z1；
2) Length of the tube: the Length of the trunk in the sample, the variable is recorded as Length, and the parameter value is z2；
3) Pipe material: the grey cast iron pipe is made of the same material for different pipelines, and the parameter value is z3(ii) a SheetPredicting a pipe, wherein the value can be 0;
4) the tube age is as follows: selecting the construction period of more than 5 years, recording the variable as Age and the parameter value as p1；
5) Temperature influence index: the sum of days with the average daily temperature of less than 5 ℃ and more than 30 ℃ in one year, the variable is recorded as TI, and the parameter value is p2(ii) a The values of the temperature influence index TI among the above influencing factors are as follows:
p2＝TI5+TI30
in the formula, p2Is a temperature impact index parameter value; TI5The number of days that the average daily temperature is lower than 5 ℃ in one year; TI30Is the number of days in which the average daily temperature is higher than 30 ℃ in one year.
6) Rainfall: the total annual rainfall is recorded as Rain, the variable is recorded as Rain, and the parameter value is p3Showing the influence of the soil moisture content on the pipe burst;
7) traffic load: the traffic load borne by the urban underground water supply pipeline is transmitted through the soil body, the variable is recorded as TL, and the parameter value is p4If the traffic load borne by the urban underground water supply pipeline is the same or similar, the traffic load can be 0;
8) total historical times of pipe bursting: the sum of the times of pipe explosion occurring before the t year after the self-construction of a certain pipeline i is completed is recorded as NOKPF, the variable is q1；
9) And (3) cathodic protection: considering whether cathodic protection exists, the variable is marked as CP, and the parameter value is q2。
And (3) carrying out variable descriptive statistics in the step (2) to obtain the mean value, the standard deviation, the minimum value and the maximum value of each variable of the sample data. The over-dispersion test model O statistic is as follows:
in the formula, n is the number of samples; s2 is the sample variance;
is a sampleAnd (4) average value.
Modeling in the step (3) is as follows:
wherein λ isi,tThe pipe explosion prediction value of the pipeline i in the t year in the future is obtained; n is the total number of pipelines in the sample; t is the recording age of tube explosion; gi,tThe probability of zero generation is the structure, and the value range is [0,1 ]]。
Wherein, g0Parameters to be estimated for the ZIP model.
The log-likelihood function of the ZIP model is:
and obtaining the estimated value of each parameter in the ZIP model by utilizing a Newton-Raphson iteration method according to the log-likelihood function.
Performing zero-expansion review of the counting data according to the above estimated values, and using SC statistics. SC statistics obey chi-square distribution with degree of freedom of 12The modeling is as follows:
wherein n is the number of pipelines and T is the recording age;
calculating a pipe explosion predicted value according to a ZIP model; x is an influencing factor variable vector.
And (4) calculating and modeling the pipe explosion expected value of the single grey cast iron pipe in the prediction period as follows:
wherein alpha is0In order to be a constant term of the regression equation,
is the coefficient vector to be fitted;
static variables such as pipe diameter, pipe length, pipe material;
dynamic variables such as pipe age, temperature influence index, rainfall and traffic load;
dynamic and static variables such as historical total tube explosion times and cathodic protection; due to z3、p4、q2All take zero value, the parameter estimation result value is alpha in formula0、α1、α2、β1、β2、β3、γ1。
And (5) determining variable parameter values in a prediction period by using a ZIP model, particularly processing the parameter values of unknown variables in the prediction period, and calculating the pipe explosion expected value of the single grey cast iron pipe. Known variables in the influence factors in the prediction period are pipe diameter, pipe age, total pipe explosion history times and pipe length, and unknown variables, temperature influence indexes and rainfall exist. Wherein:
1) pipe diameter z1Length of tube z2The method is known according to pipeline basic data; age of pipe p1Accumulating on the basis of the pipeline data years estimated by the model parameters; total historical times q of pipe burst1: accumulating according to the pipe bursting information of the pipeline;
2) temperature influence index p2：
Firstly, when predicting the tube explosion times of the next year at the bottom of the year (12 months), adopting the average value of temperature influence indexes three years before the prediction period t;
in the formula, p2,tFor the evaluation of the temperature influence index, p, in the prediction period t2,t-1、p2,t-2、p2,t-3The temperature influence indexes are sequentially 1 year, 2 years and 3 years before the prediction period.
And if the number of pipe explosion times in the same year is predicted in the year (1 to 11 months), the sum of the average values of the data in the time period of the last three years corresponding to the known data and the unknown time period is used.
In the formula, p2,tIs taken as the temperature influence index value p 'in the prediction period t'2,tP 'is the sum of days with the average temperature per day of the known months in the prediction period t being lower than 5 ℃ and higher than 30℃'2,t-1、p’2,t-2、p’2,t-3The average daily temperature of the unknown months of 1 year, 2 years and 3 years before the prediction period is the sum of days with the average daily temperature lower than 5 ℃ and the average daily temperature higher than 30 ℃.
3) Amount of rainfall p3：
Firstly, when predicting the pipe explosion times of the next year at the bottom of the year (12 months), adopting the average rainfall of three years before the prediction period t;
in the formula, p3,tFor the rainfall value in the prediction period t, p3,t-1、p3,t-2、p3,t-3The rainfall values of 1 year, 2 years and 3 years before the forecast period are sequentially obtained.
If the number of times of pipe explosion in the same year is predicted in the year (1 to 11 months), the sum of the known rainfall and the average value of the rainfall data in the time period corresponding to the previous 3 years is calculated according to the known rainfall and the unknown time period in the same year.
In the formula, p3,tIs a rainfall value p 'in the prediction period t'3,tIs the total rainfall, p 'of the known months within the forecast period t'3,t-1、p’3,t-2、p’3,t-3The corresponding total rainfall values of the unknown months 1 year, 2 years and 3 years before the forecast period are sequentially obtained.
The tube explosion probability of the single grey cast iron tube in the step (6) is when ki,tWhen not equal to 0, the model is as follows:
total number of blast tubes N in prediction periodtThe modeling is as follows:
Nt＝∑ki,tp(ki,t),k＝1,2,...n
specifically, obtain the pipe burst information and the basic data of water supply pipe network grey cast iron pipe, mainly include: pipe diameter, pipe length, pipe age, daily average air temperature, rainfall and historical total pipe bursting times.
Preprocessing total sample data, selecting final sample data:
1) the pipe diameter is an endogenous variable of the model, a main trunk pipe with the range of DN100 to DN300 is selected in direct consideration of prediction of pipe feeding and explosion, the variable is marked as DIA, and the parameter value is z1；
2) The Length of the pipe is the Length of the main trunk pipe in the sample, the variable is recorded as Length, and the parameter value is z2
3) Selecting the Age of the pipe as the Age of the pipe which is constructed for more than 5 years, recording the variable as Age and the parameter value as p1；
4) Obtaining a temperature influence index according to the daily average temperature, wherein the temperature influence index is the sum of days with the daily average temperature lower than 5 ℃ and higher than 30 ℃ in one year, the variable is recorded as TI, and the parameter value is p2The following are:
p2＝TI5+TI30
in the formula, p2Is a temperature impact index parameter value; TI5Is the average daily temperature in one yearDays at a temperature below 5 ℃; TI30Is the number of days in which the average daily temperature is higher than 30 ℃ in one year.
5) The rainfall is the total annual rainfall, the variable is recorded as Rain, and the parameter value is p3Showing the influence of the soil moisture content on the pipe burst;
6) the total historical pipe explosion times of the pipeline i before t are adopted to represent the influence of pipe explosion history on pipe explosion, the total historical pipe explosion times are the sum of the pipe explosion times of the pipeline i after the pipeline i is built and before the predicted t year, variables are recorded as NOKPF, and parameter values are q1。
Performing variable descriptive statistics on final sample data, detecting a discrete phenomenon, and modeling by adopting O statistic:
in the formula, n is the number of samples; s2Is the sample variance;
is the sample mean.
And (3) performing parameter estimation, and solving the log likelihood function of the ZIP model by using a Newton-Raphson iteration method:
and (3) carrying out the zero expansion by a double test, and modeling by adopting SC statistics as follows:
wherein n is the number of pipelines and T is the recording age;
calculating a pipe explosion predicted value according to a ZIP model; x is an influencing factor variable vector.
Modeling the pipe explosion expected value of the single grey cast iron pipe in the prediction period:
log(λi,t)＝α0+α1z1+α2z2+β1p1+β2p2+β3p3+γ1q1
total number N of implosion tubes in prediction period ttThe modeling is as follows:
Nt＝∑ki,tp(ki,t)
wherein k isi,tFor single burst, p (k)i,t) When k is the probability of a corresponding pipe bursti,tWhen the time is not zero, the probability modeling of the corresponding tube explosion is as follows:
and (3) using pipeline data and pipe explosion records of the main trunk pipe of the grey cast iron pipe with the pipe diameter between DN100 and DN300 in 2006-2013 of a certain province M city, and using the pipe explosion data in 2014 as prediction result comparison data. The construction period of the gray cast iron pipes in the research area is between 1969 and 2000, the construction period comprises 1789 pipes, and the total length of the pipes is 90.07 km.
In the embodiment, two influence factors, namely the temperature influence index and the precipitation, are firstly processed according to given definitions, and then a required pipeline data table is obtained through sorting, so that a ZIP model parameter estimation result table is obtained. The temperature influence index and precipitation data arrangement results are shown in table 1, the pipeline data and the pipe bursting records of the example are shown in table 2, and the ZIP model parameter estimation results are shown in table 3.
TABLE 1 temperature influence index and precipitation data interpretation results
TABLE 2 pipe data and burst records for this example
| Pipeline numbering | Number of pipe bursts | DIA | Age | TI | Rain | NOKPE | Length |
| 1 | 0 | 200 | 9 | 13 | 1039 | 0 | 59.95 |
| 2 | 1 | 100 | 9 | 29 | 740 | 0 | 87.39 |
| 3 | 0 | 200 | 15 | 40 | 800 | 0 | 63.91 |
| 4 | 1 | 150 | 8 | 13 | 1039 | 0 | 48.47 |
| 5 | 2 | 150 | 10 | 15 | 782 | 1 | 43.88 |
| … | … | … | … | … | … | … | … |
| 1789 | 0 | 100 | 10 | 29 | 740 | 0 | 53.76 |
TABLE 3ZIP model parameter estimation results
In the parameter estimation of each influence factor by the ZIP model, a positive parameter indicates that the increase of the covariate is related to the increase of the detonation expectation value, namely positive correlation, and a negative parameter indicates that the increase of the covariate is related to the decrease of the detonation expectation value. And the magnitude of the P value reflects the significance of the parameter estimate. Therefore, as can be seen from the table, the pipe bursting is expected to be inversely related to the pipe diameter, that is, the smaller the pipe diameter is, the greater the probability of pipe bursting is, the smaller the stress, bending moment and torque which can be borne by the pipe with the small pipe diameter are, the smaller the wall thickness is, the weaker the corrosion resistance is, and P is less than 0.0001, which indicates that the estimated height of the parameter is significant; the pipe explosion expectation is positively correlated with the pipe age, namely the larger the pipe age is, the higher the probability of pipe explosion is, and P is less than 0.01, which shows that the parameter estimation height is obvious; the pipe explosion expectation is negatively correlated with both the temperature influence index and the rainfall, namely the smaller the temperature influence index is, the less the rainfall is, the higher the probability of pipe explosion is, but P is greater than 0.1, which indicates that the parameter estimation is not significant, and the reason may be that the pipeline in the research area is buried deeply and is not sensitive to environmental factors, and the research area is in a subtropical zone, and has proper climate and less extreme weather; the pipe explosion expectation is positively correlated with the pipe explosion history, namely the pipe explosion occurrence probability is higher when the pipe explosion times which occur historically are higher, and P is less than 0.01, which indicates that the parameter estimation height is obvious; pipe bursting is expected to be positively correlated with pipe length, namely the larger the pipe length is, the higher the probability of pipe bursting is, probably because the longer the pipeline is, the larger the influence of uneven settlement is, and P <0.0001 indicates that the parameter estimation is highly significant.
The pipe burst expectation for a single grey cast iron pipe during the prediction period of this zone in this example is as follows:
log(λi,t)＝α0+α1z1+α2z2+β1p1+β2p2+β3p3+γ1q1
＝-1.5690-0.01001z1+0.02525z2+0.00708p1-0.01021p2
-0.00103p3+0.2311q1
the finally obtained comparison graph of the annual prediction total number of pipe explosion and the actual total number of pipe explosion is shown in fig. 2, and the prediction accuracy of the ZIP pipe explosion prediction model is the best when the annual total number of pipe explosion is in the prediction period.
Claims (3)
1. A method for predicting pipe explosion of a grey cast iron pipe of a water supply pipe network is characterized by comprising the following steps:
1) acquiring pipeline basic data of the grey cast iron pipe according to pipe explosion influence factors, collecting pipe explosion information, and taking the collected pipe explosion information as sample data after the pipe explosion information is arranged;
2) carrying out covariate descriptive statistics on the pipe explosion influence factors on the sample data obtained in the step 1) according to the requirements of the zero-expansion Poisson model, detecting the dispersion phenomenon, if the dispersion phenomenon is met, conforming to the requirements of the zero-expansion Poisson model and carrying out parameter estimation, and then entering the step 3);
3) analyzing the influence of various factors on the tube explosion times of the grey cast iron tube according to the parameter estimation result value obtained in the step 2), and determining alpha0、α1、α2、β1、β2、β3、γ1Obtaining a calculation formula (1) of the pipe explosion expected value of the single grey cast iron pipe;
4) substituting the sample data obtained in the step 1) into the pipe explosion expected value calculation formula (1) in the step 3) to calculate to obtain a pipe explosion expected value result, and specifically comprising the following steps:
z1is the parameter value of the pipe diameter in the sample data, z2As a parameter value of the tube length in the sample data, p1Parameter values of tube ages in sample data, q1The parameter value of the total historical times of tube explosion in sample data is obtained;
using correction values p for temperature-influencing indices2,tParameter value p as temperature influence index2And using the correction value p for the amount of rainfall3,tParameter value p as rainfall3Substituting the formula into the formula to calculate the expected value of the pipe explosion by the formula (1) to obtain the expected value lambda of the pipe explosioni,t；
Correction value p for temperature influence index2,tRespectively calculating according to the days:
firstly, when the day is in the 12 months of the current year, predicting the tube explosion times of the next year, calculating the average value by adopting the temperature influence indexes of three years before the next year according to the formula (2), and obtaining the correction value p of the temperature influence indexes2,t；
In the formula (2), p2,t-1、p2,t-2、p2,t-3The temperature influence indexes are sequentially 1 year before the next year (namely the year), 2 years before the next year and 3 years before the next year;
secondly, when the day is in 1-11 months of the current year, predicting the tube explosion times of the current year, and calculating the sum of the average values of the data in the time period according to the formula (3) to obtain a corrected value p of the temperature influence index2,t
In the formula (3), p'2,tP 'is the sum of days with the average temperature per day of the known month below 5 ℃ and above 30 ℃ in the year'2,t-1、p’2,t-2、p’2,t-3The average daily temperature is lower than 5 ℃ and higher than 3 years before the current yearSum of days at 30 ℃;
corrected value p of rainfall3,tRespectively calculating according to the days:
firstly, when the day of the year is in 12 months of the year and the pipe explosion times of the next year are predicted, calculating the average rainfall of the previous three years according to the formula (4) to obtain the corrected value p of the rainfall3,t；
In the formula (4), p3,t-1、p3,t-2、p3,t-3The rainfall values of 1 year, 2 years and 3 years before the next year are sequentially obtained.
Secondly, when the day is in 1-11 months of the current year, predicting the tube explosion times of the current year, and calculating the sum of the average values of rainfall data in the time period according to the formula (5) to obtain a corrected value p of the rainfall3,t；
In the formula (5), p'3,tIs the total rainfall, p 'of the known month in the year'3,t-1、p’3,t-2、p’3,t-3Sequentially obtaining the corresponding total rainfall values of unknown months in the previous 1 year, 2 years and 3 years of the current year;
5) calculating to obtain the tube explosion probability of the single grey cast iron tube according to the tube explosion expected value result obtained in the step 4), and further obtaining the estimated total times of tube explosion in the prediction period in the region, wherein the method specifically comprises the following steps:
A) calculating the pipe explosion probability p (k) of a single grey cast iron pipei,t) When k isi,tWhen not equal to 0, the model is as follows:
wherein k isi,tRepresents the tube explosion times of the ith grey cast iron tube in t time, p (k)i,t) Indicates the number of pipe bursts ki,tProbability of (G)i,tThe probability of zero generation of a zero-expansion Poisson (ZIP) model structure of the ith gray cast iron pipe in t time is shown,
indicates the number of pipe bursts ki,tCorresponding expected value of detonation, ki,t| A Indicates the number of opposite detonating tubes ki,tPerforming factorial operation;
B) calculating the estimated total times N of tube explosion in the prediction period in the regiont，NtThe modeling is as follows:
Nt＝∑ki,tp(ki,t)。
2. the method for predicting pipe explosion of the grey cast iron pipe of the water supply pipe network according to claim 1, wherein in the step 1), the pipe explosion information of the pipeline basic data set comprises: pipe diameter, pipe length, pipe material, pipe age, temperature influence index, rainfall, traffic load, total times of pipe explosion history and whether cathodic protection is adopted.
3. The method for predicting pipe burst of grey cast iron pipe of water supply pipe network according to claim 1, wherein in step 3), in formula (1), λi,tRepresents the pipe burst expected value, alpha, of the ith pipeline at time t0Is a constant term of a regression equation, alpha1Is the value z of the pipe diameter1Parameter estimation by zero-expansion Poisson model, alpha2Value z of the tube length2Parameter estimation by zero-expansion Poisson model, alpha3Parameter value z for tubular material3Parameter estimation by zero-expansion Poisson model, z1As value of the pipe diameter, z2Value of tube length, z3Is the parameter value of the material of the pipe, beta1Parameter value p for tube age1Parameter estimation by zero-expansion Poisson model, beta2Parameter value p being temperature influence index2Parameter estimation by zero-expansion Poisson model, beta3As parameter value p of rainfall3Passing through zeroParameter estimation, beta, of an expanded Poisson model4For the value p of the traffic load4Parameter estimation by zero-expansion Poisson model, p1As a parameter value of the age of the tube, p2As a parameter value of the temperature influence index, p3As a parameter value of rainfall, p4As a parameter value of traffic load, gamma1Parameter value q of historical total times of pipe explosion1Parameter estimation by zero-expansion Poisson model, gamma2Parameter value q for cathodic protection2Parameter estimation by zero-expansion Poisson model, q1Parameter value, q, of the historical total number of pipe bursts2Are the values of the cathodic protection parameters.
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