Large-span steel beam failure probability calculation method, safety optimization method and system

Abstract

The invention provides a large-span steel beam failure probability calculation method and a safety optimization method and system, and belongs to the technical field of reliability engineering. The method comprises the following steps: establishing a fault tree of a large-span steel beam, solving a minimum cut set, reasonably optimizing a distribution function and parameters of each bottom event, analyzing the fault tree by utilizing a Monte Carlo simulation method to obtain the change condition of the failure probability of the large-span steel beam along with time, researching safety optimization measures, and quantitatively analyzing the improvement effect of the safety optimization measures on the safety of the steel beam. The method is short in research period and clear and understandable in logic, covers the whole process from design to maintenance of the large-span steel beam, overcomes the defects of an existing analysis method, and can simply and clearly analyze the failure probability of the large-span steel beam in each time period, so that an owner can formulate a safety optimization scheme according to engineering economic conditions, and the safety of the large-span steel beam is improved. And adjusting parameters for quantitative analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability engineering, and particularly to a method for calculating the failure probability of a long-span steel beam, a safety optimization method and a system thereof. Background Art

[0002] A long-span steel beam refers to a steel beam member with a relatively large span used in engineering structures such as large-span buildings or bridges, usually made of high-strength steel. The processes of design, construction, maintenance, etc. will all affect the safety of the steel beam. At present, the research on the calculation of the failure probability of long-span steel beams and safety optimization methods mainly includes fatigue test technology, theoretical analysis technology, monitoring technology, etc. Existing research methods have specific problems. The fatigue test technology has a long cycle and high cost. The theoretical analysis technology requires a high academic level for researchers. The monitoring technology has a limited monitoring range. These methods all evaluate the safety of long-span steel beams unilaterally, without establishing a reliability analysis framework for the whole process from the design to the maintenance of the steel beam, nor quantitatively analyzing the improvement of the reliability of the steel beam by safety optimization measures. Summary of the Invention

[0003] To solve the technical problems existing in the prior art, the present invention provides a method for calculating the failure probability of a long-span steel beam, a safety optimization method and a system thereof. By establishing a fault tree of the long-span steel beam, finding the minimum cut sets, reasonably optimizing the distribution functions and parameters of each bottom event, and using the Monte Carlo simulation method to analyze the fault tree, the change of the failure probability of the long-span steel beam over time is obtained, and the safety optimization measures are studied and their improvement effects on the safety of the steel beam are quantitatively analyzed. The research cycle of the present invention is short, the logic is clear and easy to understand, covering the whole process from the design to the maintenance of the long-span steel beam, making up for the shortcomings of the existing analysis methods, and being able to simply and clearly analyze the failure probability of the long-span steel beam at each time period. The owner can formulate a safety optimization plan according to the project economic situation and adjust the parameters for quantitative analysis.

[0004] The present invention provides a method for calculating the failure probability of a long-span steel beam, including the following steps:

[0005] Construct a fault tree of the long-span steel beam, including a top event, intermediate events and bottom events, and the top event is the failure of the long-span steel beam;

[0006] Solve the minimum cut sets of the fault tree of the long-span steel beam;

[0007] Define the failure probability distribution function and related parameters of the bottom events of the fault tree of the long-span steel beam;

[0008] According to the Monte Carlo simulation method, perform large data sampling and calculate the change of the failure probability of the long-span steel beam over time.

[0009] Preferably, the intermediate events include material failure, structural instability, connection failure, and overloading.

[0010] Preferably, the basic events of material failure include corrosion, fatigue cracks, and material defects.

[0011] Preferably, the probability of corrosion failure increases exponentially with time. The expression of the probability distribution function P1(t) of corrosion failure is: P1(t) = 1 - exp(-λ1×t), where t is the time in years and λ1 is a set parameter.

[0012] Preferably, the probability of fatigue crack failure increases exponentially with time. The expression of the probability distribution function P2(t) of fatigue crack failure is: P2(t) = 1 - exp(-λ2×t), where t is the time in years and λ2 is a set parameter.

[0013] Preferably, the probability of material defect failure P3(t) is a constant, where t is the time in years;

[0014] Preferably, the probability distribution function P3(t) of material defect failure is: P3(t) = 0.01, where t is the time in years.

[0015] Preferably, the basic events of structural instability include buckling load overrun and insufficient material strength.

[0016] Preferably, the probability of buckling load overrun failure P4(t) is set as a constant, where t is the time in years;

[0017] Preferably, the probability distribution function P4(t) of buckling load overrun failure is: P4(t) = 0.005×t, where t is the time in years.

[0018] Preferably, the probability distribution function P5(t) of failure caused by insufficient material strength is: P5(t) = 0.001×t, where t is the time in years.

[0019] Preferably, the basic events of connection failure include bolt loosening and welding defects.

[0020] Preferably, the probability distribution function P6(t) of bolt loosening failure is: P6(t) = 1 - exp(-λ6×t), where t is the time in years and λ6 is a set parameter.

[0021] Preferably, the probability distribution function P7(t) of welding defect failure is: P7(t) = 0.02×(1 - exp(-0.1×t)), where t is the time in years.

[0022] Preferably, the basic events of overloading include insufficient design load and accidental load.

[0023] Preferably, the failure probability P8(t) caused by insufficient design load is: P8(t) = 0.001, where t is time in years.

[0024] Preferably, the probability distribution function P9-1(t) of accidental load occurring annually is: P9-1(t) = 0.005, and the cumulative probability distribution function P9-2(t) of accidental load is: P9-2(t) = 1 - exp(-ν × t), where ν is the annual occurrence rate and t is time in years.

[0025] Preferably, by analyzing the fault tree, the logical expression of the top event is obtained, and the minimum cut sets of the long-span steel beam fault tree are solved according to the logical expression of the top event.

[0026] Preferably, the specific steps of calculating the failure probability of a long-span steel beam by the Monte Carlo method include:

[0027] Set the number of simulations;

[0028] Calculate the failure time of each bottom event;

[0029] Statistically determine the minimum value of the failure time in each cut set;

[0030] Calculate the cumulative failure probability of the steel beam.

[0031] The present invention also provides a safety optimization method for long-span steel beams. The failure probability of the steel beam is calculated using the above-mentioned failure probability calculation method for long-span steel beams, and the safety of the long-span steel beam is optimized based on the calculated failure probability of the steel beam.

[0032] The present invention also provides a safety optimization system for long-span steel beams, including a processor that can execute the steps of the above-mentioned failure probability calculation method for long-span steel beams.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] The present invention uses the fault tree analysis method to build a whole-process model for the design - construction - maintenance of long-span steel beams. The research scope covers the entire life cycle. Using the Monte Carlo simulation method and programming with matlab, the change of the failure probability of long-span steel beams over time during the design cycle is analyzed through large data sampling simulation, and the obtained analysis results have high accuracy. Researchers can quickly and low-costly build a research model for the failure probability of long-span steel beams through the method of the present invention. At the same time, referring to the safety optimization measures proposed by the present invention, the safety optimization plan can be selected according to the engineering economy situation and safety requirements. Description of the Drawings

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on the structures shown in these drawings.

[0036] Figure 1 Schematic diagram of the fault tree of a long - span steel beam constructed for an embodiment of the present invention;

[0037] Figure 2 Matlab programming flowchart for an embodiment of the present invention;

[0038] Figure 3 Graph showing the variation of the occurrence probability of the top event of the fault tree calculated by the Monte Carlo method with time for an embodiment of the present invention;

[0039] Figure 4 Long - span steel grid diagram of the Daxing office building project for an embodiment of the present invention;

[0040] Figure 5 Graph showing the variation of the failure probability of the long - span steel beam in the office building with time calculated for an embodiment of the present invention. Detailed implementation manners

[0041] The following will make a detailed description of the specific implementation manners of the present invention.

[0042] As Figures 1 - 5 shown, the present invention provides a method for calculating the failure probability of a long - span steel beam, including the following steps:

[0043] Construct a fault tree for the long - span steel beam, including a top - level event, intermediate events, and bottom - level events. The top - level event is the failure of the long - span steel beam;

[0044] Solve the minimal cut sets of the fault tree of the long - span steel beam;

[0045] Define the failure probability distribution function and related parameters of the bottom - level events of the fault tree of the long - span steel beam;

[0046] According to the Monte Carlo simulation method, conduct large - data sampling to calculate the variation of the failure probability of the long - span steel beam with time.

[0047] Furthermore, the intermediate events include material failure, structural instability, connection failure, and overloading.

[0048] Even further, the basic events of material failure include corrosion, fatigue cracks, and material defects.

[0049] Furthermore, the corrosion failure probability increases exponentially with time. The expression of the probability distribution function P1(t) of corrosion failure is: P1(t) = 1 - exp(-λ1×t), where t is the time in years and λ1 is a set parameter.

[0050] Furthermore, the fatigue crack failure probability increases exponentially with time. The expression of the probability distribution function P2(t) of fatigue crack failure is: P2(t) = 1 - exp(-λ2×t), where t is the time in years and λ2 is a set parameter.

[0051] Furthermore, the probability P3(t) of material defect failure is a constant, where t is the time in years;

[0052] Furthermore, the probability distribution function P3(t) of material defect failure is: P3(t) = 0.01, where t is the time in years.

[0053] Furthermore, the basic events of structural instability include buckling load exceeding the limit and insufficient material strength.

[0054] Furthermore, the probability P4(t) of buckling load exceeding the limit failure is set as a constant, where t is the time in years;

[0055] Furthermore, the probability distribution function P4(t) of buckling load exceeding the limit failure is: P4(t) = 0.005×t, where t is the time in years.

[0056] Furthermore, the probability distribution function P5(t) of failure caused by insufficient material strength is: P5(t) = 0.001×t, where t is the time in years.

[0057] Furthermore, the basic events of connection failure include bolt loosening and welding defects.

[0058] Furthermore, the probability distribution function P6(t) of bolt loosening failure is: P6(t) = 1 - exp(-λ6×t), where t is the time in years and λ6 is a set parameter.

[0059] Furthermore, the probability distribution function P7(t) of welding defect failure is: P7(t) = 0.02×(1 - exp(-0.1×t)), where t is the time in years.

[0060] Furthermore, the basic events of overloading include insufficient design load and accidental load.

[0061] Furthermore, the probability P8(t) of failure caused by insufficient design load is: P8(t) = 0.001, where t is the time in years.

[0062] Furthermore, the probability distribution function P9-1(t) of accidental loads occurring annually is: P9-1(t) = 0.005, and the cumulative probability distribution function P9-2(t) of accidental loads is: P9-2(t) = 1 - exp(-ν×t), where ν is the annual occurrence rate and t is the time in years.

[0063] Furthermore, by analyzing the fault tree, the logical expression of the top event is obtained, and the minimum cut sets of the long-span steel beam fault tree are solved according to the logical expression of the top event.

[0064] Furthermore, the specific steps of calculating the failure probability of the long-span steel beam by the Monte Carlo method include:

[0065] Set the number of simulations;

[0066] Calculate the failure time of each bottom event;

[0067] Statistically find the minimum value of the failure time in each cut set;

[0068] Calculate the cumulative failure probability of the steel beam.

[0069] The present invention also provides a safety optimization method for long-span steel beams. The failure probability of the long-span steel beam is calculated by using the above-mentioned failure probability calculation method of the long-span steel beam, and the safety of the long-span steel beam is optimized according to the calculated failure probability of the long-span steel beam.

[0070] The present invention also provides a safety optimization system for long-span steel beams, including a processor that can execute the steps of the above-mentioned failure probability calculation method of the long-span steel beam.

[0071] Example 1

[0072] The present invention provides a failure probability calculation method for long-span steel beams, including the following steps:

[0073] Construct a long-span steel beam fault tree, including a top event, intermediate events, and bottom events. The top event is the failure of the long-span steel beam;

[0074] Solve the minimum cut sets of the long-span steel beam fault tree;

[0075] Define the failure probability distribution function and related parameters of the bottom events of the long-span steel beam fault tree;

[0076] According to the Monte Carlo simulation method, large data sampling is carried out, and the change of the failure probability of the long-span steel beam with time is calculated.

[0077] Example 2

[0078] The present invention provides a failure probability calculation method for long-span steel beams, including the following steps:

[0079] Construct a fault tree for long-span steel beams, including top events, intermediate events, and bottom events. The top event is the failure of long-span steel beams;

[0080] Among them, as shown in Table 1, the intermediate events include material failure, structural instability, connection failure, and overloading.

[0081] Table 1. Event table of the fault tree for long-span steel beams

[0082] Code Event Code Event P Failure of long - span steel beam E3 Material defect X1 Material failure E4 Exceeding of buckling load X2 Structural instability E5 Insufficient material strength X3 Connection failure E6 Bolt loosening X4 Overload E7 Welding defect E1 Corrosion E8 Insufficient design load E2 Fatigue crack E9 Accidental load

[0083] Furthermore, the basic events of material failure include corrosion E1, fatigue crack E2, and material defect E3.

[0084] Furthermore, the corrosion failure probability increases exponentially with time. The expression of the probability distribution function P1(t) of corrosion failure is: P1(t) = 1 - exp(-λ1×t), where t is time in years and λ1 is a set parameter.

[0085] Furthermore, the fatigue crack failure probability increases exponentially with time. The expression of the probability distribution function P2(t) of fatigue crack failure is: P2(t) = 1 - exp(-λ2×t), where t is time in years and λ2 is a set parameter.

[0086] Furthermore, the material defect failure probability P3(t) is a constant, where t is time in years;

[0087] Furthermore, the probability distribution function P3(t) of material defect failure is: P3(t) = 0.01, where t is time in years.

[0088] Furthermore, the basic events of structural instability include buckling load overrun E4 and insufficient material strength E5.

[0089] Furthermore, the buckling load overrun failure probability P4(t) is set as a constant, where t is time in years;

[0090] Furthermore, the probability distribution function P4(t) of buckling load overrun failure is: P4(t) = 0.005×t, where t is time in years.

[0091] Furthermore, the probability function P5(t) of failure caused by insufficient material strength is: P5(t) = 0.001×t, where t is time in years.

[0092] Furthermore, the basic events of connection failure include bolt loosening E6 and welding defect E7.

[0093] Furthermore, the probability distribution function P6(t) of bolt loosening failure is: P6(t) = 1 - exp(-λ6×t), where t is time in years and λ6 is a set parameter.

[0094] Furthermore, the probability distribution function P7(t) of welding defect failure is: P7(t) = 0.02×(1 - exp(-0.1×t)), where t is time in years.

[0095] Further, the basic time events of overloading include insufficient design load E8 and accidental load E9.

[0096] Furthermore, the failure probability P8(t) caused by insufficient design load is: P8(t) = 0.001, where t is time in years.

[0097] Furthermore, the probability distribution function P9-1(t) of accidental load occurring per year is: P9-1(t) = 0.005, and the cumulative probability distribution function P9-2(t) of accidental load is: P9-2(t) = 1 - exp(-ν×t), where ν is the annual occurrence rate and t is time in years.

[0098] Define the failure probability distribution function and related parameters of the bottom events of the long-span steel beam fault tree. The specific probability distribution functions and set parameter values are shown in Table 2.

[0099] Table 2. Probability distribution functions and set parameter values of each event

[0100]

[0101] By analyzing the fault tree, the logical expression of the top event is obtained: T = (E1 ∪ E2 ∪ E3) ∪ (E4 ∩ E5) ∪ (E6 ∪ E7) ∪ (E8 ∪ E9). According to the logical expression of the top event, the minimum cut sets of the long-span steel beam fault tree are solved, as shown in Table 3, and 8 minimum cut sets are obtained, E1, E2, E3, E4E5, E6, E7, E8, and E9;

[0102] Table 3. Minimum cut set table of the constructed long-span steel beam fault tree

[0103] Serial number Minimum cut set Serial number Minimum cut set 1 E1 5 E6 2 E2 6 E7 3 E3 7 E8 4 E4E5 8 E9

[0104] According to the Monte Carlo simulation method for large data sampling, the variation of the failure probability of the long-span steel beam with time is calculated, as Figure 3 shown.

[0105] Further, programming is carried out using matlab. The specific algorithm flow is shown in Figure 2 , and the Monte Carlo method for calculating the failure probability of the long-span steel beam specifically includes:

[0106] Set the number of simulations and the time vector. The number of simulations is 100,000, and the time vector is t = 0:50;

[0107] Calculate the failure times of each basic event;

[0108] Statistically analyze the minimum value of the failure times in each cut set;

[0109] Calculate the cumulative failure probability of the steel beam.

[0110] Furthermore, by analyzing the fault tree, obtain the logical expression of the top event, and solve the minimum cut sets of the long-span steel beam fault tree according to the logical expression of the top event.

[0111] Example 3

[0112] As Figure 4 shown, Office Building No. 9, Plot 2-002A, 2nd Collective Operating Construction Land in Xihongmen Town, Daxing District, Beijing, has 10 above-ground floors and 2 underground floors, and adopts a steel frame structure form. Components such as frame columns, frame beams, and secondary beams are all steel components. The top floor of this single building is a long-span steel grid, and the design, construction, and maintenance are all very difficult. Now, one long-span steel beam (span 40m) is intercepted as the research object, and all the above engineering suggestions for reducing the failure probability are adopted: First, establish a failure fault tree for the long-span steel beam; according to the Monte Carlo simulation principle, use matlab programming to analyze the change of the failure probability of this long-span steel beam, as Figure 5 shown. The specific process refers to Example 1 and Example 2.

[0113] According to the calculation results, obtain the analysis results of the life cycle and failure factors, as shown in Table 4.

[0114] Table 4. Life Cycle and Failure Factors

[0115]

[0116] Engineering suggestions for specific safety optimization measures adopted;

[0117] (1) Use a corrosion-resistant coating (such as galvanizing) to reduce the corrosion rate of E1 (λ can be reduced to 0.02).

[0118] (2) Increase fatigue monitoring (such as strain sensors) and regularly repair cracks (λ of E2 can be reduced to 0.01)

[0119] (3) Strictly detect material defects (E3) and welding processes (E7), and reduce the initial defect probability from 1% to 0.1%.

[0120] (4) Select high-strength steel (the linear cumulative probability of E5 is reduced to 0.05% per year).

[0121] Through the analysis of the simulation results, it is concluded that the above-mentioned probability reduction suggestions can significantly reduce the failure probability of long-span steel beams, improve the safety of long-span steel beams, and provide references for design, construction and later maintenance.

[0122] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are all included within the protection scope of the present invention.

Claims

1. A method for calculating the failure probability of a long-span steel beam, characterized in that, It includes the following steps: Construct a fault tree for long-span steel beams, including top events, intermediate events, and bottom events. The top event is the failure of long-span steel beams; Solve the minimal cut sets of the fault tree for long-span steel beams; Define the failure probability distribution functions and related parameters of the bottom events of the fault tree for long-span steel beams; According to the Monte Carlo simulation method, conduct large data sampling and calculate the variation of the failure probability of long-span steel beams over time.

2. The method for calculating the failure probability of a long-span steel beam according to claim 1, characterized in that The intermediate events include material failure, structural instability, connection failure, and overloading.

3. The method for calculating the failure probability of a long-span steel beam according to claim 2, wherein The basic events of material failure include corrosion, fatigue cracks, and material defects.

4. The method for calculating the failure probability of a long-span steel beam according to claim 3, wherein, The corrosion failure probability increases exponentially with time. The expression of the probability distribution function P1(t) of corrosion failure is: P1(t) = 1 - exp(-λ1×t), where t is the time in years and λ1 is a set parameter.

5. The method for calculating the failure probability of a long-span steel beam according to claim 3, characterized in that The fatigue crack failure probability increases exponentially with time. The expression of the probability distribution function P2(t) of fatigue crack failure is: P2(t) = 1 - exp(-λ2×t), where t is the time in years and λ2 is a set parameter.

6. The method for calculating the failure probability of a long-span steel beam according to claim 3, characterized in that, The probability distribution function P3(t) of material defect failure is: P3(t) = 0.01, where t is the time in years.

7. The method for calculating the failure probability of a long-span steel beam according to claim 2, wherein, The basic events of structural instability include buckling load exceeding the limit and insufficient material strength.

8. The method for calculating the failure probability of a long-span steel beam according to claim 7, wherein The probability distribution function P4(t) of buckling load exceeding the limit failure is: P4(t) = 0.005×t, where t is the time in years.

9. The method for calculating the failure probability of a long-span steel beam according to claim 7, wherein, The probability distribution function P5(t) of failure caused by insufficient material strength is: P5(t) = 0.001×t, where t is the time in years.

10. The method for calculating the failure probability of a long-span steel beam according to claim 2, characterized in that The basic events of connection failure include bolt loosening and welding defects.

11. The method for calculating the failure probability of a long-span steel beam according to claim 10, wherein The probability distribution function P6(t) of bolt loosening failure is: P6(t) = 1 - exp(-λ6×t), where t is the time in years and λ6 is a set parameter.

12. The method for calculating the failure probability of a long-span steel beam according to claim 10, wherein The probability distribution function P7(t) of welding defect failure is: P7(t) = 0.02×(1 - exp(-0.1×t)), where t is the time in years.

13. The method for calculating the failure probability of a long-span steel beam according to claim 2, characterized in that, The basic events of overloading include insufficient design load and accidental load.

14. The method for calculating the failure probability of a long-span steel beam according to claim 13, wherein The failure probability P8(t) caused by insufficient design load is: P8(t) = 0.001, where t is the time in years.

15. The method for calculating the failure probability of a long-span steel beam according to claim 13, wherein The probability distribution function P9-1(t) of accidental load occurring annually is: P9-1(t) = 0.005, and the cumulative probability distribution function P9-2(t) of accidental load is: P9-2(t) = 1 - exp(-ν×t), where ν is the annual occurrence rate and t is the time in years.

16. The method for calculating the failure probability of a long-span steel beam according to any one of claims 1-15, characterized in that, By analyzing the fault tree, obtain the logical expression of the top event, and solve the minimal cut sets of the fault tree for long-span steel beams according to the logical expression of the top event.

17. The method for calculating the failure probability of a long-span steel beam according to claim 16, wherein The specific steps of calculating the failure probability of long-span steel beams by the Monte Carlo method include: Set the number of simulations; Calculate the failure time of each bottom event; Statistically find the minimum value of the failure time in each cut set; Calculate the cumulative failure probability of the steel beam.

18. A safety optimization method for long-span steel beams, characterized in that, Use the long-span steel beam failure probability calculation method described in any one of claims 1-17 to calculate the failure probability of the steel beam, and conduct safety optimization for the long-span steel beam according to the calculated failure probability of the steel beam.

19. A safety optimization system for long-span steel beams, characterized in that, Comprising a processor, the processor being capable of performing the steps of the method for calculating the failure probability of a long-span steel beam according to any one of claims 1-17.

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