CN111144002B - Method for predicting pipe burst of grey cast iron pipe of water supply pipe network - Google Patents

Abstract

The invention discloses a method for predicting pipe bursting of gray cast iron pipes in a water supply pipe network. First, the influencing factors of pipe bursting are determined, and pipe bursting information and basic pipeline data are acquired and sorted; Statistics and discrete tests were done on the statistical results; thirdly, the ZIP model was used to model the pipe burst count records, the parameters were estimated and analyzed, and the estimated results were re-examined for zero expansion; then, the above parameter estimation results were used to obtain the grey outlet of the water supply pipe network. The expected value of a single pipe burst of the cast iron pipe; finally, the total number of pipe bursts in the forecast period in the region is obtained according to the probability calculated by the corresponding ZIP model and the total number of burst pipes. The use of the invention helps the operation and management personnel of the water supply pipe network to predict the possibility of the pipe bursting of the gray cast iron pipes in different periods in different regions, and is helpful for the early warning of pipe bursting and the formulation of maintenance plans for the urban underground water supply pipe network, which is helpful for Urban infrastructure maintenance planning.

Description

A method for predicting the bursting of gray cast iron pipes in water supply network

technical field

The invention relates to the technical field of pipe burst prediction of a water supply pipe network, in particular to a method for pipe burst prediction of gray cast iron pipes of a water supply pipe network.

Background technique

The urban underground water supply pipe network is related to the water consumption of residents and is an extremely important part of the urban infrastructure. At present, the leakage rate and pipe burst rate of the urban pipe network in my country are high, which seriously threatens the safety of water supply and affects normal production and life. Therefore, predict and solve the problem. The problem of water supply pipeline bursting has become an urgent problem for the industry.

When reviewing the previous studies on pipe burst prediction methods, it was found that statistical models are one of the main types of existing pipe bursts in urban water supply pipelines, including linear or exponential models, generalized linear models, and risk proportional models. When a large amount of historical data of pipe burst and pipeline performance data are available, statistical models can be applied to predict pipe burst. From a large number of water supply pipe network gray cast iron pipe burst count data, it is found that the count data with zero observation value accounts for the vast majority, and the ZIP model is used in all walks of life and has not been used in water supply pipe network pipe burst prediction. Studying the bursting of gray cast iron pipes in water supply network can better understand the impact of various factors on bursting, and it is helpful for early warning and maintenance planning of urban underground water supply network, which is helpful for urban infrastructure Maintenance planning.

SUMMARY OF THE INVENTION

The invention provides a method for predicting the bursting of gray cast iron pipes in a water supply pipe network. The method can be used to predict the total number of bursts of gray cast iron pipes in a water supply pipe network in a certain period in a certain area, which is helpful for formulating an urban water supply pipe network. Repair and refurbishment strategies.

A method for predicting pipe bursting of gray cast iron pipes in a water supply pipe network, comprising the following steps:

1) Obtain the pipe burst information of the basic data set of gray cast iron pipes according to the influencing factors of pipe burst, and use them as sample data after sorting;

2) According to the requirements of the zero-inflated Poisson (ZIP) model, the sample data obtained in step 1) are subjected to covariate descriptive statistics of the influencing factors of the pipe burst, and the over-dispersion phenomenon is tested. Poisson (ZIP) model requirements and parameter estimation, then go to step 3);

3) According to the parameter estimation results obtained in 2), analyze the influence of various factors on the number of bursts of gray cast iron pipes, and determine α ₀ , α ₁ , α ₂ , β ₁ , β ₂ , β ₃ , γ ₁ , and obtain a single Calculation formula (1) for the expected burst value of a gray cast iron pipe;

In formula (1), λ _{i, t} represents the expected value of the pipe burst at time t of the i-th pipe, α ₀ is the constant term of the regression equation, α ₁ is the parameter value of the pipe diameter z ₁ through the zero expansion Poisson (ZIP) model , α ₂ is the parameter value of the pipe length, z ₂ is the parameter estimated value of the zero-inflation Poisson (ZIP) model, α ₃ is the parameter value of the pipe material, z ₃ is the parameter of the zero-inflation Poisson (ZIP) model. The estimated value, z ₁ is the parameter value of the pipe diameter, z ₂ is the parameter value of the pipe length, z ₃ is the parameter value of the pipe material, β ₁ is the parameter value of the pipe age, p ₁ is calculated by the zero expansion Poisson (ZIP) model. Parameter estimates, β ₂ is the parameter value of the temperature influence index p ₂ Parameter estimates through the zero-inflated Poisson (ZIP) model, β ₃ is the parameter value of the rainfall p ₃ Parameter through the zero-inflated Poisson (ZIP) model Estimated value, _β4 is the parameter value of the traffic load _p4 is the parameter estimated value through the zero expansion Poisson (ZIP) model, p1 is the parameter value _of the pipe age, _p2 is the parameter value _of the temperature influence index, p3 is the rainfall The parameter value of the traffic load, p ₄ is the parameter value of the traffic load, γ ₁ is the parameter value of the total number of pipe bursts in history, q ₁ is the parameter estimated value through the zero expansion Poisson (ZIP) model, and γ ₂ is the parameter value q of the cathodic protection ₂ Through the parameter estimation value of the zero-inflated Poisson (ZIP) model, q ₁ is the parameter value of the total number of pipe bursts in history, and q ₂ is the parameter value of cathodic protection. Since z ₃ , p ₄ , and q ₂ all take zero values, the parameter estimation result values are α ₀ , α ₁ , α ₂ , β ₁ , β ₂ , β ₃ , and γ ₁ in the formula.

4) The sample data obtained in step 1) is brought into step 3) the expected value calculation formula (1) of the burst pipe is calculated to obtain the result of the expected value of the burst pipe;

5) Calculate the burst probability of a single gray cast iron pipe according to the result of the expected value of pipe burst obtained in 4), and then obtain the estimated total number of pipe bursts in the forecast period in the region.

In step 1), the pipe burst information in the pipeline basic data set includes: pipe diameter, pipe length, pipe material, pipe age, temperature influence index, rainfall, traffic load, the total number of pipe bursts in history, and whether cathodic protection is used.

The arrangement specifically includes:

a) Pipe diameter: the model endogenous variable, directly consider the explosion pipe prediction, select the main pipe ranging from DN100 to DN300, the variable is recorded as DIA, and the parameter value is z ₁ ;

b) Pipe length: the length of the main pipe in the sample, the variable is denoted as Length, and the parameter value is z ₂ ;

c) Pipe material: gray cast iron pipe, for different pipes are of the same material, the parameter value is z ₃ ; for single pipe material prediction, the value can be 0;

d) management age: selected as having been constructed for more than 5 years, the variable is denoted as Age, and the parameter value is p ₁ ;

e) Temperature influence index: According to the obtained daily average temperature, the number of days when the daily average temperature is lower than 5 degrees Celsius and higher than 30 degrees Celsius in a year, the sum of the two is the temperature influence index, the variable is recorded as TI, and the parameter value is p ₂ ; The value of the temperature influence index TI in the above influencing factors is as follows:

p ₂ =TI ₅ +TI ₃₀

In the formula, p ₂ is the parameter value of the temperature influence index; TI ₅ is the number of days in which the daily average temperature is lower than 5 degrees Celsius in a year; TI ₃₀ is the number of days in which the daily average temperature is higher than 30 degrees Celsius in a year.

f) Rainfall: the total amount of annual rainfall, the variable is denoted as Rain, and the parameter value is p ₃ , which indicates the influence of soil moisture content on pipe bursting;

g) Traffic load: The traffic load on the urban underground water supply pipeline is transmitted through the soil. The variable is recorded as TL, and the parameter value is p ₄ . If the traffic load on the urban underground water supply pipeline is the same or similar, it can be taken as 0;

h) The total number of pipe bursts in history: the total number of pipe bursts that occurred in a certain pipeline i from the completion of construction to the predicted t-th year, the variable is recorded as NOKPF, and the parameter value is q ₁ ;

i) Cathodic protection: considering whether there is cathodic protection, the variable is recorded as CP, and the parameter value is q ₂ .

In step 2), if the overdispersion phenomenon is satisfied, the requirements of the zero-inflated Poisson (ZIP) model are met, and the parameters are estimated according to the log-likelihood function of the ZIP model.

In step 4), the ZIP model and the determination of variable parameter values in the forecast period are used, and the parameter values of the unknown variables in the forecast period are specially processed, and then the expected value of the pipe burst of a single gray cast iron pipe is calculated.

The sample data obtained in step 1) is brought into step 3) the expected value calculation formula (1) of the burst pipe is calculated to obtain the expected value result of the burst pipe, which specifically includes:

z ₁ is the parameter value of the pipe diameter in the sample data, z ₂ is the parameter value of the pipe length in the sample data, p ₁ is the parameter value of the pipe age in the sample data, q ₁ is the parameter of the total number of pipe bursts in the history of the sample data value;

Use the correction value p _2,t of the temperature influence index as the parameter value p ₂ of the temperature influence index and the correction value p _3,t of the rainfall as the parameter value p ₃ of the rainfall, and bring it into the formula for calculating the expected value of the pipe burst (1 ) to calculate the expected value λ _i,t of the squib.

The correction value p _2,t of the temperature influence index is calculated according to the day:

①When the day is in December of the current year, predict the number of pipe bursts in the next year, and calculate the average value of the temperature influence index for the three years before the next year according to formula (2), and obtain the correction value p _2,t of the temperature influence index;

In formula (2), p _2,t-1 , p _2,t-2 , p _2,t-3 are in turn 1 year before the next year (ie this year), 2 years before the next year, and 3 years before the next year. temperature influence index;

② When the day is from January to November of the current year, predict the number of pipe bursts in the current year, and calculate the sum of the average values of the data in the time period according to formula (3) to obtain the correction value p _2,t of the temperature influence index;

In formula (3), p' _2,t is the sum of the days when the daily average temperature of the known months is lower than 5℃ and higher than 30℃ in the current year, p' _2,t-1 , p' _2,t-2 , p' _{2, t-3} are the sum of the number of days when the daily average temperature is lower than 5℃ and higher than 30℃ in the first year, 2 years, and 3 years of the current year, respectively. That is, p' _{2, t-1} is the sum of the number of days when the daily average temperature is lower than 5℃ and higher than 30℃ in the unknown month in the previous year.

For example, when the day is in June of the current year, p' _2,t is the sum of the number of days when the daily average temperature is lower than 5°C and higher than 30°C in the known months from January to June in the current year t, p' _{2 , t-1} , p' _{2, t-2} , p' _{2, t-3} are the corresponding daily average temperatures from July to December in the first year, 2 years, and 3 years of the current year when the temperature is lower than 5℃ and higher than Sum of days at 30°C. p' _2,t-1 is the sum of the number of days when the daily average temperature is lower than 5℃ and higher than 30℃ from July to December in the year before t.

The corrected value of rainfall p _{3, t} is calculated separately according to the day:

① The day is in December of the current year. When predicting the number of pipe bursts in the following year, calculate the average rainfall of the previous three years according to formula (4), and obtain the corrected value of rainfall p _3,t ;

In formula (4), p _3,t-1 , p _3,t-2 , p _3,t-3 are the rainfall values in the previous year, 2 years, and 3 years in turn.

②When the day is from January to November of the current year, predict the number of pipe bursts in the current year, calculate the sum of the average values of rainfall data in the time period according to formula (5), and obtain the corrected value of rainfall p _3,t ;

In formula (5), p' _{3, t} is the total rainfall of the known months in the current year, p' _{3, t-1} , p' _{3, t-2} , p' _{3, t-3} are the first 1 of the current year. The corresponding total rainfall values for the unknown months of the year, 2 years, and 3 years.

For example, when the day is in June of the current year, p' _3,t is the total rainfall from January to June in the known months of the year, p' _3,t-1 , p' _3,t-2 , p'' _{3, t-3} are the corresponding total rainfall values of the unknown months from July to December in the first year, two years, and three years of the current year. p' _{3, t-1} is the corresponding total rainfall value of the unknown month July to December in the previous year.

In step 5), the pipe burst probability of a single gray cast iron pipe is calculated according to the result of the expected value of pipe burst obtained in 4), and then the estimated total number of pipe bursts in the forecast period in the region is obtained, specifically including:

A) Calculate the burst probability p(k _i,t ) of a single gray cast iron pipe. When k _i,t ≠0, the model is as follows:

表示爆管次数k_i,t对应的爆管期望值，k_i,t！表示对爆管次数k_i,t进行阶乘运算；Among them, ki _,t represents the number of pipe bursts of the ith gray cast iron pipe in the time t, p(ki _,t ) represents the probability of the number of pipe bursts _ki,t , and G _i,t represents the ith gray cast iron pipe The probability of zero-expansion Poisson (ZIP) model structure of the cast-iron pipe at time t,

Indicates the expected value of the pipe burst corresponding to the number of pipe bursts _ki,t , ki _,t ! Indicates that the factorial operation is performed on the number of pipe bursts _{ki, t} ;

B) Calculate the estimated total number of pipe bursts N _t during the forecast period in the area, and N _t is modeled as follows:

N _t =∑ki _,t p(ki _,t ).

Compared with the prior art, the present invention has beneficial effects:

When analyzing the number of pipe bursts in the pipe network, the method analyzes the influencing factors of the gray cast iron pipe water supply pipe network affecting pipe bursts, and predicts the results of the total burst times. Compared with the prior art, the same burst rate is set. The probability of occurrence of pipe bursts is determined. The Poisson model, the Logistics model and the ZIP model are used to estimate the parameters of the sample data respectively. The ZIP pipe burst prediction model has the best prediction accuracy when the total number of pipe bursts in each year during the forecast period, and the Poisson pipe burst prediction model tends to overshoot. High predicted burst numbers, while the Logistics burst prediction model tends to underestimate annual burst numbers. In this method, when analyzing the number of pipe bursts in the pipe network, it is divided into two processes for analysis, and it is determined that the observed value of pipe bursts in a larger proportion of pipes is zero, and the number of pipe bursts follows the Poisson distribution, which improves the accuracy of the analysis. .

The use of the invention helps the operation and management personnel of the water supply pipe network to predict the possibility of the pipe bursting of the gray cast iron pipes in different periods in different regions, and is helpful for the early warning of pipe bursting and the formulation of maintenance plans for the urban underground water supply pipe network, which is helpful for Urban infrastructure maintenance planning.

Description of drawings

Fig. 1 is the schematic flow sheet of the method for predicting the pipe burst of gray cast iron pipe of water supply pipe network of the present invention;

Fig. 2 is the comparison diagram of the total number of predicted pipe bursts and the actual number of pipe bursts in the present invention;

Detailed ways

The method for predicting the pipe burst of a gray cast iron pipe in a water supply pipe network of the present invention will be further described below with reference to the accompanying drawings.

The method for predicting the explosion of gray cast iron pipes in a water supply pipe network of the present invention comprises the following steps:

(1) Obtain the pipe burst information of the gray cast iron pipe in a certain area in a certain period of time according to the influencing factors of pipe burst, and arrange it as sample data;

(2) According to the requirements of the zero-inflated Poisson (ZIP) model, descriptive statistics of the factors (covariates) of the final sample data are carried out, and the overdispersion phenomenon is tested;

(3) Divide the burst records of gray cast iron pipes in a certain area into two states, one is the structural zero satisfying the Logistic model, and the other is the burst count value that satisfies the Poisson model, where the obtained zero burst value is sampling zero. Parameter estimation according to the log-likelihood function of the ZIP model;

(4) According to the parameter estimation results obtained in (3), the influence of various factors on the number of bursts of gray cast iron pipes is analyzed, and the calculation formula for the expected burst value of a single gray cast iron pipe is obtained;

(5) According to the data in (3) and the analysis results in (4), use the ZIP model and the determination of variable parameter values during the forecast period, especially deal with the parameter values of unknown variables during the forecast period, and then calculate the value of a single gray cast iron pipe. Burst expectations.

(6) Calculate the burst probability of a single gray cast iron pipe according to the result in (5), and then obtain the estimated total number of pipe bursts in the forecast period in the region.

The pipe burst information and basic pipeline data mentioned in step (1) mainly include: the number of pipe bursts within the sample period and a) static variables: pipe diameter, pipe length, pipe material; b) dynamic variables: pipe age, temperature influence index, Rainfall, traffic load; c) Dynamic and static variables: the total number of historical pipe bursts, cathodic protection. The factors affecting the final selection of pipe bursts include: pipe diameter, pipe length, pipe material, pipe age, temperature influence index, rainfall, traffic load, the total number of historical pipe bursts and cathodic protection. in:

1) Pipe diameter: the model endogenous variable, directly considering the explosion pipe prediction, select the main pipe ranging from DN100 to DN300, the variable is recorded as DIA, and the parameter value is z ₁ ;

2) Pipe length: the length of the main pipe in the sample, the variable is denoted as Length, and the parameter value is z ₂ ;

3) Pipe material: gray cast iron pipe, for different pipes are of the same material, the parameter value is z ₃ ; for single pipe material prediction, the value can be 0;

4) Management age: selected as having been constructed for more than 5 years, the variable is denoted as Age, and the parameter value is p ₁ ;

5) Temperature influence index: the sum of the days when the average daily temperature is lower than 5 degrees Celsius and higher than 30 degrees Celsius within a year, the variable is denoted as TI, and the parameter value is p ₂ ; the value of the temperature influence index TI in the above influencing factors is as follows:

p ₂ =TI ₅ +TI ₃₀

In the formula, p ₂ is the parameter value of the temperature influence index; TI ₅ is the number of days in which the daily average temperature is lower than 5 degrees Celsius in a year; TI ₃₀ is the number of days in which the daily average temperature is higher than 30 degrees Celsius in a year.

6) Precipitation: the total annual rainfall, the variable is denoted as Rain, and the parameter value is p ₃ , which indicates the influence of soil moisture content on pipe bursting;

7) Traffic load: The traffic load on the urban underground water supply pipeline is transmitted through the soil. The variable is recorded as TL, and the parameter value is p ₄ . If the traffic load on the urban underground water supply pipeline is the same or similar, it can be taken as 0;

8) The total number of pipe bursts in history: the total number of pipe bursts that occurred in a certain pipeline i from the completion of construction to the predicted t-th year, the variable is recorded as NOKPF, and the parameter value is q ₁ ;

9) Cathodic protection: consider whether there is cathodic protection, the variable is recorded as CP, and the parameter value is q ₂ .

In step (2), descriptive statistics of variables are performed to obtain the mean, standard deviation, minimum and maximum values of each variable of the sample data. The O statistic for the overdispersion test model is as follows:

为样本均值。In the formula, n is the number of samples; S2 is the sample variance;

is the sample mean.

Step (3) is modeled as follows:

Among them, λ _{i,t is} the predicted value of pipe burst for pipeline i in the next year t; N is the total number of pipes in the sample; T is the record period of pipe burst; 0,1].

Among them, g ₀ is the parameter to be estimated in the ZIP model.

The log-likelihood function of the ZIP model is:

According to the log-likelihood function, the estimated value of each parameter in the ZIP model can be obtained by using the Newton-Raphson iteration method.

Based on the above estimates, zero-inflated count data were retested, and SC statistic was used. The SC statistic follows a chi-square distribution χ ² with 1 degree of freedom, which is modeled as follows:

为根据ZIP模型算得的爆管预测值；X为影响因素变量向量。Where n is the number of pipes, T is the record period;

is the predicted value of pipe burst calculated according to the ZIP model; X is the variable vector of influencing factors.

Step (4) The calculation and modeling of the expected burst value of a single gray cast iron pipe during the forecast period is as follows:

为待拟合的系数向量；

为静态变量，如管径、管长、管材；

为动态变量，如管龄、温度影响指数、降雨量、交通荷载；

为动静态变量，如历史爆管总次数、阴极保护；由于z₃、p₄、q₂均取零值，参数估计结果值即式中的α₀、α₁、α₂、β₁、β₂、β₃、γ₁。where α ₀ is the constant term of the regression equation,

is the coefficient vector to be fitted;

are static variables, such as pipe diameter, pipe length, and pipe material;

are dynamic variables, such as pipe age, temperature influence index, rainfall, traffic load;

are dynamic and static variables, such as the total number of pipe bursts in history, cathodic protection; since z ₃ , p ₄ , and q ₂ all take zero values, the parameter estimation results are α ₀ , α ₁ , α ₂ , β ₁ , β in the formula ₂ , β ₃ , γ ₁ .

Step (5) utilizes the ZIP model and the determination of variable parameter values in the forecast period, especially handles the parameter values of unknown variables in the forecast period, and then calculates the expected value of a single gray cast iron pipe burst. The known variables in the influencing factors during the forecast period are pipe diameter, pipe age, the total number of pipe bursts in history, and pipe length, while there are unknown variables, temperature influence index and rainfall. in:

₁ ) The pipe diameter z ₁ and the pipe length z ₂ can be known from the basic data of the pipeline; the pipe age p ₁ is accumulated on the basis of the year of the pipeline data estimated by the model parameters;

2) Temperature influence index p ₂ :

①When predicting the number of pipe bursts in the next year at the end of the year (December), the average value of the temperature impact index in the first three years of the forecast period t is used;

In the formula, p _2,t is the value of the temperature influence index in the forecast period t, p _2,t-1 , p _2,t-2 , p _2,t-3 are the first year, two years, 3-year temperature impact index.

②If the number of pipe bursts in the year is predicted in the middle of the year (January to November), according to the known data and the unknown time period, the sum of the data averages in the previous three years is corresponding.

In the formula, p _2,t is the value of the temperature influence index in the forecast period t, p' _2,t is the sum of the number of days when the daily average temperature of the known months in the forecast period t is lower than 5°C and higher than 30°C, p' _2,t-1 , p' _2,t-2 , p' _2,t-3 are the corresponding daily average temperatures of the unknown months 1 year, 2 years, and 3 years before the forecast period. Sum of days at 30°C.

3) Rainfall p ₃ :

①When predicting the number of pipe bursts in the next year at the end of the year (December), the average rainfall of the three years before the forecast period t is used;

In the formula, p _3,t is the value of rainfall in the forecast period t, p _{3, t-1} , p _{3, t-2} , p _{3, t-3} are 1 year, 2 years, 3 years before the forecast period. annual rainfall value.

②If the number of pipe bursts in the year is predicted in the middle of the year (January to November), according to the known rainfall of the year and the unknown time period, it corresponds to the sum of the average rainfall data in the previous three years.

In the formula, p _3,t is the value of the rainfall in the forecast period t, p' _3,t is the total rainfall of the known months in the forecast period t, p' _3,t-1 , p' _{3,t- 2} , p' _{3 , t-3} are the corresponding total rainfall values of unknown months in the first year, two years, and three years before the forecast period.

Step (6) The burst probability of a single gray cast iron pipe, when ki _,t ≠ 0, the model is as follows:

The total number of pipe bursts N _t during the forecast period is modeled as follows:

N _t =∑ki _,t p(ki _,t ),k=1,2,...n

Specifically, the pipe burst information and basic data of gray cast iron pipes in the water supply network are obtained, including: pipe diameter, pipe length, pipe age, daily average temperature, rainfall, and the total number of historical pipe bursts.

The total sample data is preprocessed, and the final sample data is selected:

1) The pipe diameter is an endogenous variable in the model. In the prediction of the blast pipe, the main pipe in the range of DN100 to DN300 is selected, the variable is denoted as DIA, and the parameter value is z ₁ ;

2) The pipe length is the length of the main pipe in the sample, the variable is recorded as Length, and the parameter value is z2

3) The management age is selected as having been constructed for more than 5 years, the variable is denoted as Age, and the parameter value is p ₁ ;

4) According to the daily average temperature, the temperature influence index is obtained, which is the sum of the days when the daily average temperature is lower than 5 degrees Celsius and higher than 30 degrees Celsius in one year. The variable is recorded as TI, and the parameter value is p ₂ , as follows:

p ₂ =TI ₅ +TI ₃₀

In the formula, p ₂ is the parameter value of the temperature influence index; TI ₅ is the number of days in which the daily average temperature is lower than 5 degrees Celsius in a year; TI ₃₀ is the number of days in which the daily average temperature is higher than 30 degrees Celsius in a year.

5) The rainfall is the total annual rainfall, the variable is denoted as Rain, and the parameter value is p ₃ , which indicates the influence of soil moisture content on pipe bursting;

6) The total number of historical pipe bursts that have occurred in pipeline i before t is used to represent the impact of pipe burst history on pipe bursting. The sum of the number of pipe bursts, the variable is recorded as NOKPF, and the parameter value is q ₁ .

Perform variable descriptive statistics on the final sample data, and test the overdispersion phenomenon, using O statistics to model:

为样本均值。In the formula, n is the number of samples; S ² is the sample variance;

is the sample mean.

For parameter estimation, use the Newton-Raphson iteration method to solve the log-likelihood function of the following ZIP model:

Retest zero inflation and use SC statistic to model as follows:

为根据ZIP模型算得的爆管预测值；X为影响因素变量向量。Where n is the number of pipes, T is the record period;

is the predicted value of pipe burst calculated according to the ZIP model; X is the variable vector of influencing factors.

Model the expected burst value of a single grey cast iron pipe during the forecast period:

log(λ _i,t )=α ₀ +α ₁ z ₁ +α ₂ z ₂ +β ₁ p ₁ +β ₂ p ₂ +β ₃ p ₃ +γ ₁ q ₁

The total number of detonators N _t in the forecast period t is modeled as follows:

N _t =∑ki _,t p(ki _,t )

where k _i,t is the number of bursts of a single pipe, and p(ki _,t ) is the probability of the corresponding pipe burst. When ki _,t is non-zero, the probability of the corresponding pipe burst is modeled as follows:

Using the pipeline data and pipe burst records of gray cast iron main pipes with pipe diameters between DN100 and DN300 in a province M city from 2006 to 2013, the pipe burst data in 2014 was used as the comparison data for the prediction results. The construction period of gray cast iron pipes in the study area was between 1969 and 2000, including a total of 1789 pipes with a total length of 90.07km.

In this example, the two influencing factors of temperature influence index and precipitation are processed according to the given definitions, and then the required pipeline data table is obtained, and the ZIP model parameter estimation result table is obtained. The temperature impact index and precipitation data collation results are shown in Table 1, the pipeline data and pipe burst records of this example are shown in Table 2, and the ZIP model parameter estimation results are shown in Table 3.

Table 1 The temperature impact index and precipitation data collation results

Table 2 Pipeline data and pipe burst records of this example

pipe number Number of burst pipes 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 influencing factor by the ZIP model, a positive parameter indicates that the increase of the covariate is related to the increase of the expected value of the squib, which is a positive correlation, while the negative parameter indicates that the increase of the covariate is related to the decrease of the expected value of the squib. related. And the size of the P value reflects the significance of the parameter estimate. Therefore, it can be seen from the table that the pipe burst expectation is negatively correlated with the pipe diameter, that is, the smaller the pipe diameter, the greater the probability of pipe bursting, the smaller the pipe diameter can withstand, the smaller the stress, bending moment and torque. Small wall thickness also makes its corrosion resistance weaker, and P<0.0001, indicating that this parameter is highly estimated; the expectation of pipe bursting is positively correlated with pipe age, that is, the greater the pipe age, the greater the probability of pipe bursting, and P< 0.01, indicating that this parameter is estimated to be highly significant; the expectation of pipe bursting is negatively correlated with the temperature influence index and rainfall, that is, the smaller the temperature influence index and the less rainfall, the greater the probability of pipe bursting, but P>0.1, It shows that the estimation of this parameter is not significant. The reason may be that the pipeline in the study area is buried deep and is not sensitive to environmental factors, and the study area is in the subtropical zone, with a suitable climate and few extreme weather. The more times the pipe burst, the greater the probability of pipe burst, and P<0.01, indicating that the parameter estimation is highly significant; the pipe burst expectation is positively correlated with the pipe length, that is, the longer the pipe length, the higher the probability of the pipe burst. The possible reason is that the longer the pipeline, the greater the influence of uneven settlement, and P<0.0001, indicating that the parameter estimation is highly significant.

In this example, the expected value of a single gray cast iron pipe burst during the forecast period in this area is as follows:

log(λ _i,t )=α ₀ +α ₁ z ₁ +α ₂ z ₂ +β ₁ p ₁ +β ₂ p ₂ +β ₃ p ₃ +γ ₁ q ₁

=-1.5690-0.01001z ₁ +0.02525z ₂ +0.00708p ₁ -0.01021p ₂

-0.00103p ₃ +0.2311q ₁

Figure 2 shows the comparison of the total number of pipe bursts in the forecast year and the actual number of pipe bursts. The ZIP pipe burst prediction model of the present invention has the best prediction accuracy when the total number of pipe bursts in each year in the forecast period is the best.

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 indices_2,tParameter value p as temperature influence index₂And using the correction value p for the amount of rainfall_3,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 explosion_i,t；

Correction value p for temperature influence index_2,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 indexes_2,t；

In the formula (2), p_2,t-1、p_2,t-2、p_2,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 index_2,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 rainfall_3,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 rainfall_3,t；

In the formula (4), p_3,t-1、p_3,t-2、p_3,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 rainfall_3,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 pipe_i,t) When k is_i,tWhen not equal to 0, the model is as follows:

wherein k is_i,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 k_i,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 k_i,tCorresponding expected value of detonation, k_i,t| A Indicates the number of opposite detonating tubes k_i,tPerforming factorial operation;

B) calculating the estimated total times N of tube explosion in the prediction period in the region_t，N_tThe modeling is as follows:

N_t＝∑k_i,tp(k_i,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), λ_i,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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