Method for calculating failure probabilities of single unit pipe length long-distance pipeline, single multi-section pipe length oil conveying pipeline and oil conveying pipe network

Abstract

The invention relates to the technical field of reliability engineering, in particular to a method for calculating the failure probability of a single unit-pipe-length long-distance pipeline, a single multi-section-pipe-length oil conveying pipeline and an oil conveying pipeline network, which comprises the following steps of: taking'failure of a single unit-pipe-length oil conveying pipeline 'as a top event of a fault tree; constructing a fault tree of the single oil pipeline with the unit pipe length; extracting a minimum cut set from the fault tree according to a downlink method; all underlying events of the fault tree are regarded as not having memorability, and the distribution type of the underlying event life satisfies exponential distribution; and according to a Monte Carlo algorithm, adopting matlab programming to calculate the probability of occurrence of the top event. According to the method, accurate simulation of the failure probability of the single multi-section pipe length oil pipeline system is realized, the obtained statistical data is more scientific and accurate, and reference is provided for the maintenance period of the long-distance multi-section pipe length pipeline.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability engineering, and in particular to a calculation method for the failure probability of a single-unit-length long-distance oil pipeline, a single multi-segment-length long-distance oil pipeline, and an oil pipeline network. Background Art

[0002] Resources such as petroleum and natural gas are generally transported through pipelines. A long-distance oil and gas pipeline refers to a pipeline used for transporting oil and gas between the place of origin, storage depot, and user unit.

[0003] The long-distance pipeline is buried deep underground. As time goes by, the pipeline gradually ages underground and enters the aging period, and pipeline accidents are likely to occur. Therefore, it is necessary to analyze and calculate the failure probability of the oil pipeline, and replace the pipeline that is about to fail in a timely manner.

[0004] Currently, for the analysis of the failure probability of oil pipelines, methods such as data statistics, expert scoring, and fault tree analysis are mostly used. In the analysis process, due to the large amount of manual participation, there are disadvantages such as strong subjectivity, small application range, and easy to be interfered, resulting in a large error between the final result and the actual failure probability. Summary of the Invention

[0005] In order to reduce the manual participation in the process of analyzing the failure of oil pipelines, the present invention provides a calculation method for the failure probability of a single-unit-length long-distance oil pipeline, a single multi-segment-length long-distance oil pipeline, and an oil pipeline network.

[0006] The present invention provides a calculation method for the failure probability of a single-unit-length long-distance oil pipeline, and adopts the following technical solutions:

[0007] A calculation method for the failure probability of a single-unit-length long-distance oil pipeline includes the following steps:

[0008] Taking the failure of a single-unit-length long-distance oil pipeline as the top event of the fault tree, and constructing a fault tree for the single-unit-length long-distance oil pipeline;

[0009] According to the downward method, extracting the minimum cut sets from the fault tree;

[0010] Regarding all the bottom events of the fault tree as not having memory, and the distribution type of the bottom event life satisfies the exponential distribution;

[0011] According to the Monte Carlo algorithm, using matlab programming to calculate the probability of the top event occurring.

[0012] In a specific feasible implementation, the method for constructing the fault tree is:

[0013] The main causes leading to the top event are used as intermediate events. All undesirable events are arranged from top to bottom according to the causal logic relationship, and the undesirable events are connected using logic gates to form a fault tree.

[0014] In a specific implementable embodiment, the main causes of the top event include defects in design and construction, corrosion, third-party damage, natural disasters, and misoperations.

[0015] In a specific implementable embodiment, when extracting the minimum cut sets from the fault tree, when encountering an "AND" gate, the capacity of the events included in the cut set is expanded, and when encountering an "OR" gate, the number of events included in the cut set is expanded until all logic gates are replaced with basic events.

[0016] In a specific implementable embodiment, the distribution type of the basic event life satisfies the formula:

[0017]

[0018] P(X<x)=F(x)=1 - e -λx x>0

[0019] In the above formula, x is the time variable;

[0020] e is the base of the natural logarithm;

[0021] λ refers to the failure rate, that is, the probability of failure occurring per unit time;

[0022] F(x) is the probability of the oil pipeline failing before time x.

[0023] In a specific implementable embodiment, according to the Monte Carlo algorithm, calculating the probability of the top event using matlab programming includes the following steps:

[0024] Input the number of simulation times M, initialize, set m = 1, m ∈ [1, M], M>1 and M ∈ R;

[0025] Generate uniformly distributed random numbers {ε i |i = 1, 2, …, n} that are the same as the number of basic events n, and 0 < ε i <1;

[0026] Through Calculate the total working time of the basic events and sort them to generate [t1, t2, …, tn];

[0027] Define the function TOP = φ(X);

[0028] Check TOP one by one in the order of [t1, t2, …, tn];

[0029] When TOP = 0, advance the time ti to t(i + 1), and re - execute step A5 to check TOP one by one; when TOP = 1, store the system working time t of this simulation into T(w) and end this simulation.

[0030] Let m = m + 1, and start executing from step A2 again, looping until m = M to end the simulation.

[0031] In a specific feasible implementation, after the simulation is completed, a curve of the occurrence probability of the top event changing with time is generated.

[0032] The present invention also provides a method for calculating the failure probability of a single - root multi - section long - distance oil pipeline, adopting the following technical solution:

[0033] A method for calculating the failure probability of a single - root multi - section long - distance oil pipeline includes the following steps:

[0034] Construct a fault tree for a single - root unit - length oil pipeline, and take the failure of the single - root unit - length oil pipeline as the top event of the fault tree of the single - root unit - length oil pipeline.

[0035] Extract the minimum cut sets from the fault tree of the single - root unit - length oil pipeline according to the downward method.

[0036] Regard all the bottom - layer events of the fault tree of the single - root unit - length oil pipeline as having no memory, and the distribution type of the bottom - layer event lifetimes satisfies the exponential distribution.

[0037] According to the Monte Carlo algorithm, use matlab programming to calculate the occurrence probability of the top event.

[0038] Establish a model of a single - root multi - section long - distance oil pipeline.

[0039] Construct a fault tree for a single - root multi - section long - distance oil pipeline, and take the inability of the pipeline to transport oil as the top event of the fault tree of the single - root multi - section long - distance oil pipeline.

[0040] Determine the lifetime distribution and parameters of the bottom - layer events of the fault tree of the single - root multi - section long - distance oil pipeline.

[0041] Calculate the occurrence probability of the top event of the fault tree of the multi - section long - distance oil pipeline through the Monte Carlo method.

[0042] In a specific feasible implementation, when determining the lifetime distribution and parameters of the bottom - layer events of the fault tree of the single - root multi - section long - distance oil pipeline, the number of damages λ occurring per 10 kilometers per month is 0.01497.

[0043] The present invention also provides a method for calculating the failure probability of an oil pipeline network, adopting the following technical solution:

[0044] A method for calculating the failure probability of an oil pipeline network includes the following steps:

[0045] Construct a fault tree for a single - unit - length oil pipeline. Take "failure of a single - unit - length oil pipeline" as the top event of the fault tree for a single - unit - length oil pipeline.

[0046] According to the downward method, extract the minimal cut sets from the fault tree of the single - unit - length oil pipeline.

[0047] Regard all the bottom - layer events of the fault tree of the single - unit - length oil pipeline as having no memory, and the distribution type of the bottom - layer event lifetimes satisfies the exponential distribution.

[0048] According to the Monte Carlo algorithm, use Matlab programming to calculate the occurrence probability of the top event.

[0049] Establish a model of a single - root multi - section - length oil pipeline.

[0050] Construct a fault tree for a single - root multi - section - length oil pipeline. Take the inability of this pipeline to transport oil as the top event of the fault tree for a single - root multi - section - length oil pipeline.

[0051] Determine the lifetime distribution and parameters of the bottom - layer events of the fault tree for a single - root multi - section - length oil pipeline.

[0052] Calculate the occurrence probability of the top event of the fault tree for the multi - section - length oil pipeline through the Monte Carlo method.

[0053] Construct an oil pipeline network model.

[0054] Construct a fault tree for the oil pipeline network. Take the failure of a small - scale pipeline network as the top event of the fault tree for the oil pipeline network.

[0055] Determine the lifetime distribution and parameters of the bottom - layer events of the fault tree for the oil pipeline network.

[0056] Calculate the occurrence probability of the top event of the fault tree for the oil pipeline network through the Monte Carlo method.

[0057] In summary, the present invention has the following beneficial effects:

[0058] 1. By establishing a long - distance oil pipeline model with a simplified and clear structure and reasonable assumptions, a fault tree for a single - unit - length long - distance oil pipeline is established. Using the Monte Carlo method to conduct a large number of sampling simulations on the fault tree, the accurate simulation of the failure probability of the single - unit - length long - distance oil pipeline system is realized. The obtained statistical data is more scientific and accurate, providing a reference for the maintenance cycle of long - distance oil pipelines.

[0059] 2. By establishing a long - distance multi - section - length oil pipeline model with a simplified and clear structure and reasonable assumptions, a fault tree for a single - root multi - section - length oil pipeline is constructed. Using the Monte Carlo method to conduct a large number of sampling simulations on the fault tree, the accurate simulation of the failure probability of the single - root multi - section - length oil pipeline system is realized.

[0060] 3. By establishing a simple small-scale oil pipeline network model and making reasonable assumptions, a fault tree for the small-scale oil pipeline network is constructed. Using the Monte Carlo method to conduct a large number of sampling simulations on the fault tree, the precise simulation of the failure probability of the small-scale oil pipeline network system is realized, and the obtained statistical data is more intuitive and accurate. The large and complex oil pipeline network system is reasonably simplified, and the change of the failure probability of the small-scale oil pipeline network over time is simulated, providing a reference for the investment construction and maintenance cycle of the small-scale oil pipeline network. Description of the Drawings

[0061] Figure 1 It is a flowchart of the calculation method for the failure probability of a single-unit-length long oil pipeline.

[0062] Figure 2 It is a fault tree diagram of a single-unit-length oil pipeline.

[0063] Figure 3 It is a flowchart of matlab programming.

[0064] Figure 4 It is a diagram of the occurrence probability of the top event in Example 1.

[0065] Figure 5 It is a flowchart of the calculation method for the failure probability of a single multi-unit-length oil pipeline.

[0066] Figure 6 It is a schematic diagram of the model of the long oil pipeline a.

[0067] Figure 7 It is a fault tree diagram for constructing a single multi-unit-length long oil pipeline.

[0068] Figure 8 It is a diagram of the occurrence probability of the top event in Example 2.

[0069] Figure 9 It is a flowchart of the calculation method for the failure probability of the oil pipeline network.

[0070] Figure 10 It is a schematic diagram of the oil pipeline network model.

[0071] Figure 11 It is a fault tree diagram of the oil pipeline network.

[0072] Figure 12 It is a diagram of the occurrence probability of the top event in Example 3

[0073] Figure 13 It is a schematic diagram of the oil pipeline network model in the example.

[0074] Figure 14 It is a probability diagram of the failure probability of a single-unit-length long oil pipeline in the example.

[0075] Figure 15 It is the fault tree diagram of a single multi-segment long-distance oil pipeline in the example.

[0076] Figure 16 It is the probability diagram of the failure probability of a single multi-segment pipe long-distance oil pipeline in the example.

[0077] Figure 17 It is the fault tree diagram of the oil pipeline network in the example.

[0078] Figure 18 It is the probability diagram of the failure probability of the oil pipeline network in the example. Specific implementation manners

[0079] The following further elaborates on the present invention in conjunction with the attached Figures 1 - 18 drawings.

[0080] Example 1:

[0081] Referring to Figure 1 , a calculation method for the failure probability of a single unit-length long-distance oil pipeline includes the following steps:

[0082] S100. Construct a fault tree for a single unit-length long-distance oil pipeline.

[0083] There are often many undesirable events in a system. According to the tree-building purpose and the final target result, "failure of a single unit-length long-distance oil pipeline" is used as the top event of the fault tree. Further analyzing the top event, the main reasons for the failure of a single unit-length long-distance oil pipeline are mainly defects in design and construction, corrosion, third-party damage, natural disasters, and misoperation. These five aspects are used as intermediate events. All undesirable events are arranged from top to bottom according to the causal logic relationship, and all undesirable events are connected using the correct logic gates, that is, the intermediate events and the bottom events are connected using the correct logic gates to form a fault tree. Exemplarily, after normalizing and logically simplifying the fault tree, the fault tree diagram as shown in Figure 2 can be obtained. Table 1 shows the correspondence between the codes and events in Figure 2 .

[0084] Table 1

[0085]

[0086]

[0087] S200. Analyze the minimal cut sets of the fault tree.

[0088] According to the downward method, that is, starting from the top event of the fault tree and analyzing downward. When encountering an "AND gate", the capacity of the events included in the cut set is expanded; when encountering an "OR gate", the number of events included in the cut set is expanded until all logical gates are replaced by basic events. Simplify and absorb the results output by the downward method according to the set operation rules, and extract all minimal cut sets from the final results. Table 3 is based on Figure 2 The list of minimal cut sets extracted from the fault tree.

[0089] Table 2

[0090]

[0091]

[0092] S300, for the quantitative analysis of the fault tree, find the life distribution type and parameters of the basic events.

[0093] Analyzing the basic events of the fault tree, it is found that some events have great ambiguity, such as the influence of X2 debris flow, etc.; some basic events have memory, that is, after working for a period of time, the life distribution of the event is different from the life distribution parameters when it was not working before and is difficult to determine. The uncertainty of the basic events makes it difficult to accurately determine the life fraction and parameters of the basic events.

[0094] To simplify the calculation and improve the calculation accuracy, each basic event is regarded as having no memory. According to the characteristics of the exponential distribution, the physical meaning of the formula is regarded as: the probability that the product fails within a given time ≤ the established time. To further simplify the calculation, it is approximately considered that the life distributions of the basic events of the fault tree all conform to the exponential distribution, and the following formula can be obtained:

[0095]

[0096] P(X < x) = F(x) = 1 - e -λx x > 0

[0097] In the above formula, x is the time variable;

[0098] e is the base of the natural logarithm;

[0099] λ refers to the failure rate, that is, the probability of failure per unit time;

[0100] F(x) is the probability that the oil pipeline fails before time x.

[0101] By considering all basic events as having no memory, the probability of a basic event occurring does not depend on past history but only on the current state. Moreover, each basic event can be regarded as an independent variable, and the outcome of one basic event does not affect the outcome of another, eliminating the need to consider complex temporal dependencies and thus greatly simplifying the analysis process. Relying on the characteristics of basic events having no memory and following an exponential distribution, the exponential distribution can be directly used instead of constructing a complex temporal model to calculate the probability of basic events occurring, further simplifying the calculation process.

[0102] In traditional fault tree analysis, due to a large amount of manual participation, some subjective judgments and empirical parameters may be introduced. By virtue of the fact that basic events have no memory and the objective failure rate λ, the influence of subjective factors is reduced, making the results more reliable.

[0103] Exemplarily, by making reasonable assumptions about the parameters in the formula, λ is defined as the number of damages occurring per 10 kilometers per month, and assuming a month has 30 days, the life distribution of each bottom event in the fault tree is shown in Table 3.

[0104] Table 3

[0105]

[0106]

[0107] S400, calculate the probability of the top event occurring.

[0108] Combined with Figure 3 , based on the Monte Carlo algorithm simulation, using matlab programming for analysis, the probability of the top event occurring is calculated. Monte Carlo is a statistical method for estimating system performance through random sampling. After combining with fault tree analysis, the Monte Carlo method can be used to simulate the occurrence of basic events and evaluate the reliability of the entire system. Through a large number of simulation runs, an approximate value of the system failure probability can be obtained, and statistical methods are used to compensate for or correct potential errors.

[0109] The specific steps are as follows:

[0110] A1, input the number of simulation times M, initialize, set m = 1, m ∈ [1, M], M > 1 and M ∈ R;

[0111] A2, generate uniformly distributed random numbers {ε i |i = 1, 2, …, n} that are the same in number as the number of bottom events, and 0 < ε i < 1.

[0112] A3, calculate the total working time of the bottom events through and sort them to generate [t1, t2, …, tn].

[0113] A4. Define the function TOP = φ(X).

[0114] A5. Check TOP one by one in the order of [t1, t2, …, tn].

[0115] A6. When TOP = 0, advance the time ti to t(i + 1), and re - execute step A5 to check TOP one by one. When TOP = 1, store the system working time t of this simulation into T(w), and end this simulation.

[0116] A7. Let m = m + 1, and re - execute from step A2, loop until m = M, and end the simulation.

[0117] A8. Generate the curve of the top - event occurrence probability changing with time according to the results of M simulations.

[0118] Exemplarily, set the number of simulations to 1000 and perform Monte Carlo algorithm simulation, then the top - event occurrence probability table and the top - event occurrence probability graph can be obtained, namely Table 4 and Figure 4 .

[0119] Table 4

[0120]

[0121]

[0122] Using the combination of fault tree and Monte Carlo for research not only retains the logical rigor of the fault tree but also breaks through the static limitations of traditional methods through random sampling. In high - dimensional and dynamic complex systems such as oil pipelines, it can more realistically reflect the overall risk picture, thereby improving the accuracy.

[0123] Example 2:

[0124] The long - distance oil pipeline is an extremely complex system. The components in multiple pipeline segments are interrelated and affected by each other, and at the same time, it is affected by various factors such as design, construction, natural disasters, and misoperations, making it extremely difficult to study the failure probability of a single multi - segment long - distance oil pipeline. At present, for the failure probability analysis of oil pipelines at home and abroad, methods such as data statistics, expert scoring, and fault tree analysis are mostly used, but there is a lack of research methods for refined analysis, resulting in large deviations in the research results of the failure probability of long - distance oil pipelines.

[0125] Therefore, Example 2 provides a calculation method for the failure probability of a single multi - segment long - distance oil pipeline, including the following specific steps:

[0126] M100. Construct a fault tree for a single unit - length oil pipeline.

[0127] There are often many undesirable events in a system. According to the tree-building purpose and the final target result, "the failure of a single-unit-length oil pipeline" is taken as the top event of the fault tree. Further analysis of the top event shows that the main reasons for the failure of a single-unit-length oil pipeline are mainly defects in design and construction, corrosion, third-party damage, natural disasters, and misoperations. These five aspects are used as intermediate events. All undesirable events are arranged from top to bottom according to the causal logic relationship, and all undesirable events are connected using the correct logic gates, that is, the intermediate events and the bottom events are connected using the correct logic gates to form a fault tree.

[0128] M200, analyze the minimal cut sets of the fault tree.

[0129] According to the downward method, that is, starting from the top event of the fault tree and analyzing downward, when encountering an "AND gate", expand the capacity of the events included in the cut set, and when encountering an "OR gate", expand the number of events included in the cut set until all logic gates are replaced by bottom events. Simplify and absorb the results output by the downward method according to the set operation rules, and extract all minimal cut sets from the final results.

[0130] M300, quantitatively analyze the fault tree to obtain the life distribution type and parameters of the bottom events.

[0131] Analysis of the bottom events of the fault tree reveals that some events have great ambiguity, such as the impact of debris flows, etc.; some bottom events have memory, that is, after working for a period of time, the life distribution of the event is different from the life distribution parameters when it was not working before and is difficult to determine. The uncertainty of the bottom events makes it difficult to accurately determine the life fraction and parameters of the bottom events.

[0132] To simplify the calculation and improve the calculation accuracy, each bottom event is regarded as not having memory. According to the characteristics of the exponential distribution, the physical meaning of the formula is regarded as: the probability that the product fails within a given time ≤ the established time. To further simplify the calculation, it is approximately considered that the life distributions of the bottom events of the fault tree all conform to the exponential distribution, and the following formula can be obtained:

[0133]

[0134] P(X < x) = F(x) = 1 - e -λx x > 0

[0135] In the above formula, x is the time variable;

[0136] e is the base of the natural logarithm;

[0137] λ refers to the failure rate, that is, the probability of failure per unit time;

[0138] F(x) is the probability that the oil pipeline fails before time x.

[0139] M400, calculate the occurrence probability of the top event.

[0140] Based on the Monte Carlo algorithm simulation and using Matlab programming for analysis, the specific steps are as follows:

[0141] B1, input the number of simulations M, initialize, set m = 1, m ∈ [1, M], M > 1 and M ∈ R;

[0142] B2, generate uniformly distributed random numbers {ε i |i = 1, 2, …, n} that are the same in number as the number of basic events, and 0 < ε i < 1.

[0143] B3, calculate the total working time of the basic events and sort them to generate [t1, t2, …, tn]. Calculate the total working time of the basic events and sort them to generate [t1, t2, …, tn].

[0144] B4, define the function TOP = φ(X).

[0145] B5, check TOP one by one in the order of [t1, t2, …, tn].

[0146] B6, when TOP = 0, advance the time ti to t(i + 1), and re - execute step A5 to check TOP one by one. When TOP = 1, store the system working time t of this simulation into T(w), and end this simulation.

[0147] B7, let m = m + 1, and start from step A2 again to execute, loop until m = M, and end the simulation.

[0148] B8, generate the curve of the occurrence probability of the top event changing with time according to the results of M simulations.

[0149] M500, establish a model of a single - root multi - segment long - distance oil pipeline.

[0150] Establish a model of the long - distance pipeline between two destinations. Divide the long - distance pipeline into multiple segments according to the preset unit length. For the sake of illustration, set two destinations A and B. The total length of the long - distance pipeline a between A and B is 70 km, and the unit length is set to 10 km. Therefore, the long - distance pipeline a is evenly divided into 7 small segments, and the 7 small segments are numbered in the order from A to B as No. 1 - No. 7.

[0151] M600, construct a fault tree for a single - root multi - segment long - distance oil pipeline.

[0152] To standardize and simplify the calculations, the following assumptions are made: 1. The probability of failure of the oil pipeline is proportional to the length of the intercepted pipeline and is independent of the time and location of the intercepted pipeline. That is, the failure rate of the intercepted pipeline is constant with respect to time and location; 2. Whether failures occur between the intercepted unit pipelines are mutually independent; 3. If one unit length pipeline in multiple sections of pipelines is damaged, the system is considered to have failed.

[0153] Select "the 'a' line pipeline cannot transport oil" as the top event of the fault tree for the long-distance oil pipeline with a single multi-section pipeline. Since the 7 small sections in the long-distance pipeline 'a' are connected in series in sequence, the failure of each small section will cause the top event to occur. Therefore, "pipeline No. 1 fails", "pipeline No. 2 fails"... "pipeline No. 7 fails" are both basic events and minimal cut sets simultaneously, as shown in Table 5 and Table 6.

[0154] Table 5

[0155] Code Event Code Event P The pipeline of line a cannot transport oil X4 Pipeline No. 4 fails X1 Pipeline No. 1 fails X5 Pipeline No. 5 fails X2 Pipeline No. 2 fails X6 Pipeline No. 6 fails X3 Pipeline No. 3 fails X7 Pipeline No. 7 fails

[0156] Table 6

[0157] Serial number Minimum cut set Serial number Minimum cut set 1 X1 5 X5 2 X2 6 X6 3 X3 7 X7 4 X4

[0158] M700, determination of the life distribution and parameters of the basic events of the fault tree.

[0159] Assume that the life distribution of the basic events of the fault tree for the unit length pipeline follows an exponential distribution. Further assume that the life distributions of each unit length pipeline all follow an exponential distribution and have the same parameters. Define the physical meaning of λ as the number of damages per 10 kilometers per month. Assuming there are 30 days in a month, λ can also be obtained based on the historical statistical data of specific pipelines. The life distribution types and parameters of the basic events of the fault tree for the 'a' line oil pipeline are shown in Table 7, and λ is approximately 0.01497.

[0160] Table 7

[0161]

[0162] M800, calculating the occurrence probability of the top event of the fault tree through the Monte Carlo method.

[0163] The process and steps of calculating the occurrence probability of the top event of the fault tree by the Monte Carlo method are similar to those of Step B1 - Step B7, with the only difference being the transformation of parameters and objectives. Therefore, it will not be elaborated here. Set the number of simulation times to 2000 times, and the calculation results as shown in Table 8 and Figure 8 can be obtained.

[0164] Table 8

[0165]

[0166] It is easy to understand that there is no necessary sequence between step M100 and step M800. The step numbers are only used for distinction, and the sequence can be adjusted according to the actual situation.

[0167] In steps M600 and M700, some assumptions are made to simplify the calculation. These assumptions may lead to a reduction in the accuracy of the calculation results. However, through the fault tree, various failure factors such as design, construction, and corrosion can be comprehensively considered. The complex system failure problem is decomposed into a combination of multiple simple events, and the overall failure situation can be grasped to make up for the accuracy loss caused by the assumptions. Similarly, through these assumptions, the basic events do not have memory, and combined with the objective failure rate λ, the influence of subjective factors can be reduced, making the results more reliable and improving the accuracy of the final calculation results.

[0168] Using the combination of the fault tree and Monte Carlo for research not only retains the logical rigor of the fault tree but also breaks through the static limitations of traditional methods through random sampling. Through a large number of simulation runs, an approximate value of the system failure probability can be obtained, and statistical methods can be used to compensate for or correct potential errors. In a high-dimensional and dynamic complex system such as an oil pipeline, it can more realistically reflect the overall risk, thereby improving the accuracy.

[0169] By establishing a long-distance multi-segment pipe oil pipeline model with a simplified and clear structure and reasonable assumptions, a fault tree for a single multi-segment pipe oil pipeline is established. Using the Monte Carlo method to conduct a large number of sampling simulations on the fault tree, the accurate simulation of the failure probability of the single multi-segment pipe oil pipeline system is realized. The obtained statistical data is more scientific and accurate, providing a reference for the maintenance cycle of long-distance multi-segment pipelines.

[0170] Embodiment 3:

[0171] An oil pipeline mainly consists of pipelines, pumping stations, valves, metering devices, oil storage tanks, etc. To improve the oil transportation efficiency and safety, multiple oil pipelines form an oil pipeline network. The oil pipeline network usually needs to cross various complex terrains, and various factors such as geological conditions, temperature, pressure, and pipeline corrosion will affect the pipeline, resulting in the failure of the pipeline network system. The complex composition and uncertainty of influencing factors make it extremely difficult to study the failure probability of the oil pipeline network. Currently, for the analysis of the failure probability of the oil pipeline network, methods such as the fault tree analysis method, Bayesian network analysis method, and reliability block diagram are mostly used. These methods have defects such as the oil pipeline network system and the fault tree being too complex, high calculation costs, and large deviations between the calculation results and the actual situation.

[0172] Therefore, Embodiment 3 proposes a calculation method for the failure probability of an oil pipeline network, and the specific steps are as follows:

[0173] N100, construct a fault tree for a single unit-length oil pipeline.

[0174] There are often many undesirable events in a system. According to the tree-building purpose and the final target result, "the failure of a single-unit-length oil pipeline" is taken as the top event of the fault tree. Further analysis of the top event shows that the main reasons for the failure of a single-unit-length oil pipeline are mainly defects in design and construction, corrosion, third-party damage, natural disasters, and misoperations. These five aspects are used as intermediate events. All undesirable events are arranged from top to bottom according to the causal logic relationship, and all undesirable events are connected using the correct logic gates, that is, the intermediate events and the bottom events are connected using the correct logic gates to form a fault tree.

[0175] N200, analyze the minimal cut sets of the fault tree.

[0176] According to the downward method, that is, starting from the top event of the fault tree and analyzing downward, when encountering an "AND gate", the capacity of the events included in the cut set is expanded, and when encountering an "OR gate", the number of events included in the cut set is expanded until all logic gates are replaced by bottom events. Simplify and absorb the results output by the downward method according to the set operation rules, and extract all minimal cut sets from the final results.

[0177] N300, quantitatively analyze the fault tree to obtain the life distribution type and parameters of the bottom events.

[0178] Analysis of the bottom events of the fault tree reveals that some events have great ambiguity, such as the impact of debris flows, etc.; some bottom events have memory, that is, after working for a period of time, the life distribution of the event is different from the life distribution parameters when it was not working before and is difficult to determine. The uncertainty of the bottom events makes it difficult to accurately determine the life fraction and parameters of the bottom events.

[0179] To simplify the calculation and improve the calculation accuracy, each bottom event is regarded as not having memory. According to the exponential distribution characteristics, the physical meaning of the formula is regarded as: the probability that the time when the product fails ≤ the established time. To further simplify the calculation, it is approximately considered that the life distributions of the bottom events of the fault tree all conform to the exponential distribution, and the following formula can be obtained:

[0180]

[0181] P(X<x)=F(x)=1 - e -λx x>0

[0182] In the above formula, x is the time variable;

[0183] e is the base of the natural logarithm;

[0184] λ refers to the failure rate, that is, the probability of failure per unit time;

[0185] F(x) is the probability that the oil pipeline fails before time x.

[0186] M400, calculate the probability of the top event occurring.

[0187] Based on the Monte Carlo algorithm simulation, using matlab programming for analysis, the specific steps are as follows:

[0188] C1, input the number of simulations M, initialize, set m = 1, m ∈ [1, M], M > 1 and M ∈ R;

[0189] C2, generate uniformly distributed random numbers {ε i | i = 1, 2, …, n}, and 0 < ε i < 1.

[0190] C3, through Calculate the total working time of the basic events and sort them to generate [t1, t2, …, tn].

[0191] C4, define the function TOP = φ(X).

[0192] C5, check TOP one by one in the order of [t1, t2, …, tn].

[0193] C6, when TOP = 0, advance the time ti to t(i + 1), and re - execute step A5 to check TOP one by one. When TOP = 1, store the system working time t of this simulation into T(w), and end this simulation.

[0194] C7, let m = m + 1, and re - execute from step A2, loop until m = M, and end the simulation.

[0195] C8, generate the curve of the probability of the top event occurring changing with time according to the M - time simulation results.

[0196] N500, establish a model of a single - root multi - segment long - distance oil pipeline.

[0197] Establish a model of the long - distance pipeline between two destinations. Divide the long - distance pipeline into multiple segments according to the preset unit length. For the sake of easy explanation, set up two destinations A and B. The total length of the long - distance pipeline a between A and B is 70 km, and the unit length is set to 10 km. Therefore, the long - distance pipeline a is evenly divided into 7 small segments, and the 7 small segments are numbered in the order from A to B, numbered 1 - 7.

[0198] N600, construct a fault tree for a single - root multi - segment long - distance oil pipeline.

[0199] To standardize and simplify the calculations, the following assumptions are made: 1. The probability of failure of the oil pipeline is proportional to the length of the intercepted pipeline and is independent of the time and location of the intercepted pipeline. That is, the failure rate of the intercepted pipeline is constant with respect to time and location. 2. Whether failures occur between the intercepted unit pipelines are mutually independent. 3. If one unit-length pipeline in multiple sections of pipelines is damaged, the system is considered to have failed.

[0200] Select "the a-line pipeline cannot transport oil" as the top event of the fault tree of a single multi-section long-distance oil pipeline. Since the 7 small sections in the long-distance pipeline a are connected in series in sequence, the failure of each small section will cause the top event to occur. Therefore, "the failure of pipeline No. 1", "the failure of pipeline No. 2",... "the failure of pipeline No. 7" are both basic events and minimal cut sets at the same time.

[0201] N700, determination of the life distribution and parameters of the bottom events of the fault tree of a single multi-section long-distance oil pipeline.

[0202] Assume that the life distribution of the bottom events of the fault tree of the unit-length pipeline is an exponential distribution, and further assume that the life distributions of each unit-length pipeline all follow an exponential distribution and have the same parameters. Define the physical meaning of λ as the number of damages occurring per 10 kilometers per month. Assuming a month has 30 days, λ can also be obtained based on the historical statistical data of specific pipelines, and λ is approximately 0.01497.

[0203] N800, calculating the occurrence probability of the top event of the fault tree by the Monte Carlo method.

[0204] The process and steps of calculating the occurrence probability of the top event of the fault tree by the Monte Carlo method are similar to those of steps C1 - C7, with the difference only being the transformation of parameters and objectives, so it will not be elaborated here.

[0205] N900, constructing an oil pipeline network model.

[0206] Establish a model of the oil pipeline network between two destinations, and segment each oil pipeline in the oil pipeline network according to the preset unit length. For the sake of easy explanation, set up two destinations A and B. There are three oil pipelines a, b, and c between destination A and destination B. Among them, the lengths of oil pipelines a and c are 70 km, and the length of oil pipeline b is 50 km. For each oil pipeline, it is segmented according to a unit length of 10 km, forming as Figure 10 the model shown.

[0207] N1000, constructing the fault tree of the oil pipeline network.

[0208] To standardize and simplify the calculations, the following assumptions are made: 1. The probability of failure of the oil pipeline is proportional to the length of the intercepted pipeline and is independent of the time and location of the intercepted pipeline, that is, the failure rate of the intercepted pipeline is a constant with respect to time and location; 2. Whether failures occur between the intercepted unit pipelines are mutually independent; 3. The failure probability of a unit pipe length is P1, and the failure probability of the oil pipeline network is P si , where i = 1, 2,..., n, and n is the total number of oil pipeline networks. For the sake of convenience of explanation, the failure probabilities of the three oil pipelines a, b, and c are represented as Pa, Pb, and Pc respectively. 4. The probability that all oil pipelines fail simultaneously is extremely low and almost impossible. Therefore, when calculating the failure probability of the oil pipeline network, it is assumed that the oil pipeline network fails only when at least two oil pipeline networks fail, and the failure probability of the oil pipeline network is P.

[0209] Take "small pipeline network failure" as the top event of the fault tree of the oil pipeline network. Since the top event will occur only when two pipelines fail simultaneously, there are three cases: oil pipeline a and oil pipeline b fail, oil pipeline a and oil pipeline c fail, and oil pipeline b and oil pipeline c fail. Deduce downward based on these three cases, establish a fault tree, and generate the minimum cut sets, as shown in Table 9, Table 10, and Figure 11 .

[0210] Table 9

[0211] Code Event Code Event P Small - scale pipe network fails X1 Pipeline of line a fails B1 Pipelines of line a and line b fail X2 Pipeline of line b fails B2 Pipelines of line a and line c fail X3 Pipeline of line c fails B3 Pipelines of line b and line c fail

[0212] Table 10

[0213] Serial number Minimum cut set 1 X1X2 2 X1X3 3 X2X3

[0214] N1100, determining the life distribution and parameters of the bottom events of the fault tree of the oil pipeline network.

[0215] Calculate the failure probability P1 of the unit pipe length through steps N100 - N400, calculate the failure probabilities Pa, Pb, and Pc of the oil pipelines a, b, and c through steps N500 - N800, and generate a curve of the failure probability changing with time. Define the physical meaning of λ as the number of damages occurring per 10 kilometers per month. Assuming a month has 30 days, λ can also be obtained based on the historical data of specific pipelines. The values of λ are shown in Table 11.

[0216] Table 11

[0217] Code Event Distribution type Parameter λ (times / 10km·month) X1 Pipeline of line a fails Exponential distribution 0.106 X2 Pipeline of line b fails Exponential distribution 0.0729 X3 Pipeline of line c fails Exponential distribution 0.106

[0218] N1200, calculating the occurrence probability of the top event of the fault tree of the oil pipeline network through the Monte Carlo method.

[0219] The process and steps C1 - C7 for calculating the occurrence probability of the top event of the fault tree using the Monte Carlo method are similar, with the only difference being the transformation of parameters and objectives, so it will not be elaborated further. Setting the number of simulations to 2000 times, the calculation results as shown in Table 12 and Figure 12 can be obtained.

[0220] Table 12

[0221]

[0222] It is easy to understand that there is no necessary sequence between steps N100 - N1200. The step numbers are only used for distinction and the order can be adjusted according to the actual situation.

[0223] By establishing a simple small - scale oil pipeline network model and reasonable assumptions, a fault tree for the small - scale oil pipeline network was established; using the Monte Carlo method to conduct a large number of sampling simulations on the fault tree, the accurate simulation of the failure probability of the small - scale oil pipeline network system was achieved, and the obtained statistical data is more intuitive and accurate. The large and complex oil pipeline network system was reasonably simplified, and the variation of the failure probability of the small - scale oil pipeline network over time was simulated, providing a reference for the investment construction and maintenance cycle of the small - scale oil pipeline network.

[0224] Exemplarily, take the crude oil pipeline in a certain city as an example for illustration. There are four destinations A, B, C, and D along the whole line of the crude oil pipeline. Among them, the crude oil flows from points A, B, and C to point D, which are set as line a, line b, and line c respectively. The unit pipe length is 1 km, and when it is less than 1 km, it is rounded up. The length of line A is about 13 km, the length of line b is about 18 km, and the length of line c is about 38 km. Construct a pipeline network model as Figure 13 shown.

[0225] Taking 1 km of pipe length as the research object, first calculate the change graph and probability table of the failure probability of 1 km of pipe length over time through the calculation method of the failure probability of a single - unit - length long - distance pipeline. See Table 13 and Figure 14 shown.

[0226] Table 13

[0227]

[0228]

[0229] Then, take line a as the analysis object. Therefore, line a is divided into 13 sections of unit pipelines and numbered from 1 - 13. The failure numbers are X1 - X13. Construct a model as Figure 15The fault tree of line a. According to the calculation method of the failure probability of a single-unit-length long-distance pipeline, the change diagram of the failure probability obtained is used to determine the failure rate parameter λ. By calculating the change diagram and probability table of the failure probability of line a changing with time through steps N500 - N800, see Table 14 and Figure 16 .

[0230] Table 14

[0231]

[0232] According to the calculation method of the failure probability of the oil pipeline network in Embodiment 3, an event table (Table 15) and a fault tree as Figure 17 are constructed. The λ values of line a, line b, and line c are determined to be 0.129, 0.2022, and 0.3689 respectively, where λ is the number of damages per kilometer per month. And further calculate the change diagram and probability table of the failure probability of the oil pipeline network changing with time, see Table 16 and Figure 18 .

[0233] Table 15

[0234] P Small - scale pipe network fails X1 Pipeline of line a fails B1 Pipelines of line a and line b fail X2 Pipeline of line b fails B2 Pipelines of line a and line c fail X3 Pipeline of line c fails B3 Pipelines of line b and line c fail

[0235] Table 16

[0236]

[0237] The above are all the preferred embodiments of the present invention, and the protection scope of the present invention is not limited accordingly. Therefore, all equivalent changes made according to the structure, shape, and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for calculating the failure probability of a single unit length long-distance pipeline, characterized by: The steps include: Taking the failure of a single unit length oil pipeline as the top event of the fault tree, a single unit length oil pipeline fault tree is constructed; According to the descending method, the minimum cut set is extracted from the fault tree; All the bottom-level events of the fault tree are considered to have no memory, and the distribution type of the bottom-level event lifespan satisfies the exponential distribution; According to the Monte Carlo algorithm, the probability of top events is calculated using Matlab programming.

2. The method for calculating the failure probability of a single unit length long-distance pipeline according to claim 1 is characterized by: The method to construct a fault tree is: The main cause of the top event is taken as the intermediate event. All undesirable events are arranged from top to bottom according to the cause-effect logic relationship. The undesirable events are connected using logic gates to form a fault tree.

3. The method for calculating the failure probability of a single unit length long-distance pipeline according to claim 1 is characterized by: The main causes of roof failures include design and construction defects, corrosion, third-party damage, natural disasters, and misoperation.

4. The method for calculating the failure probability of a single unit length long-distance pipeline according to claim 1 is characterized by: When extracting the minimum cut set from the fault tree, when encountering an "AND gate", the capacity of the events included in the cut set is expanded, and when encountering an "OR gate", the number of events included in the cut set is expanded until all logic gates are replaced by underlying events.

5. The method for calculating the failure probability of a single unit length long-distance pipeline according to claim 1 is characterized by: The distribution type of the underlying event lifetime satisfies the formula: P(X<x)=F(x)=1-e -λx x>0 In the above formula, x is the time variable; e is the natural number base; λ refers to the failure rate, that is, the probability of failure occurring per unit time; F(x) is the probability that the oil pipeline fails before time x.

6. The method for calculating the failure probability of a single unit length long-distance pipeline according to claim 1 is characterized by: According to the Monte Carlo algorithm, the calculation of the probability of occurrence of the top event using Matlab programming includes the following steps: Input the number of simulations M, initialize it so that m=1, m∈[1,M], M>1 and M∈R; Generate a uniformly distributed random number {ε i |i=1,2,…,n}, and 0<ε i <1; pass Calculate the total working time of the underlying events and sort them to generate [t1, t2, …, tn]; Define function TOP = φ(X); Check TOP one by one in the order of [t1, t2, …, tn]; When TOP=0, advance time ti to t(i+1), re-execute step A5, and check TOP one by one; When TOP=1, the system working time t simulated in this simulation is stored in T(w), and the simulation ends; Let m=m+1, and start again from step A2, loop until m=M, and end the simulation.

7. The method for calculating the failure probability of a single unit length long-distance pipeline according to claim 6 is characterized by: After the simulation is completed, a curve showing the probability of occurrence of the top event changing with time is generated.

8. A method for calculating the failure probability of a single multi-section long oil pipeline, characterized by: The steps include: Construct a single unit length oil pipeline fault tree, and take the failure of the single unit length oil pipeline as the top event of the single unit length oil pipeline fault tree; According to the descending method, the minimum cut set is extracted from the fault tree of a single unit length oil pipeline; All the underlying events of the fault tree of a single unit length oil pipeline are considered to have no memory, and the distribution type of the underlying event life meets the exponential distribution; According to the Monte Carlo algorithm, the probability of occurrence of the top event is calculated using Matlab programming; Establish a single multi-section long oil pipeline model; Construct a single multi-section long oil pipeline fault tree, and take the failure of the pipeline to transport oil as the top event of the single multi-section long oil pipeline fault tree; Life distribution and parameter determination of bottom event of fault tree for single multi-section long oil pipeline; The probability of occurrence of top events in the fault tree of multi-section long oil pipelines is calculated by Monte Carlo method.

9. The method for calculating the failure probability of a single multi-section long oil pipeline according to claim 8 is characterized by: When the life distribution and parameters of the bottom event of the fault tree of a single multi-section long oil pipeline are determined, the number of damages per month per 10 kilometers is 0.01497.

10. A method for calculating the failure probability of an oil pipeline network, characterized in that: The steps include: Construct a single unit length oil pipeline fault tree, and take "single unit length oil pipeline failure" as the top event of the single unit length oil pipeline fault tree; According to the descending method, the minimum cut set is extracted from the fault tree of a single unit length oil pipeline; All the underlying events of the fault tree of a single unit length oil pipeline are considered to have no memory, and the distribution type of the underlying event life meets the exponential distribution; According to the Monte Carlo algorithm, the probability of occurrence of the top event is calculated using Matlab programming; Establish a single multi-section long oil pipeline model; Construct a single multi-section long oil pipeline fault tree, and take the failure of the pipeline to transport oil as the top event of the single multi-section long oil pipeline fault tree; Life distribution and parameter determination of bottom event of fault tree for single multi-section long oil pipeline; The probability of occurrence of top events in the fault tree of multiple long oil pipelines is calculated by Monte Carlo method; Construct an oil pipeline network model; Construct a fault tree for the oil pipeline network, and take the failure of a small pipeline network as the top event of the fault tree for the oil pipeline network; Fault tree bottom event life distribution and parameter determination for oil pipeline network; The Monte Carlo method is used to calculate the probability of occurrence of the top event in the fault tree of the oil pipeline network.

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