A method for obtaining a wind disaster vulnerability curve of a power transmission tower based on failure probability
By establishing a probability distribution model of the extreme response to wind load and the structural bearing capacity of transmission towers, and combining Latin hypercube sampling and engineering estimates, the vulnerability curve of transmission towers is obtained. This solves the problems of complexity and insufficient applicability of existing methods, and realizes an efficient quantitative assessment of the wind-induced vulnerability of transmission towers.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- WUHAN UNIV OF TECH
- Filing Date
- 2026-03-04
- Publication Date
- 2026-07-10
AI Technical Summary
Existing methods for studying the wind vulnerability of transmission towers are complex, fail to effectively analyze loss rates, and are not applicable enough in engineering applications.
By establishing a probability distribution model of the extreme response of transmission towers to wind loads, a probability distribution model of structural bearing capacity is constructed. Vulnerability analysis is performed using the Latin hypercube sampling method to obtain the failure probability. In conjunction with the engineering budget, a vulnerability curve is plotted, taking into account wind speed, failure probability, and loss rate.
This paper presents an efficient method for analyzing the wind-induced vulnerability of transmission towers, which can quantitatively assess the loss rate under wind disasters and is applicable to the analysis of transmission tower failure probability and loss rate in engineering contexts.
Smart Images
Figure CN122365801A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to structural engineering technology, and more particularly to a method for obtaining the wind damage vulnerability curve of transmission towers based on failure probability. Background Technology
[0002] Power transmission networks are highly vulnerable to damage from windstorms. As the carriers of electrical energy, the damage to transmission towers not only causes economic losses themselves, but the resulting large-scale power outages can also cause serious damage to society and people's property.
[0003] Transmission tower vulnerability refers to the probability of structural damage or reaching a certain limit state under different wind speeds. It is typically calculated quantitatively in probabilistic terms, relating wind load intensity to the degree of structural damage. Vulnerability studies, on the other hand, primarily consider the loss rate of the structure under wind loads in engineering economics. Existing methods for studying transmission tower vulnerability are complex. Traditional methods mainly rely on dynamic analysis to determine the uncertainty of wind loads or use integral methods to establish probabilistic models, but these methods have low engineering applicability. Furthermore, existing vulnerability studies mostly consider the probability of structural damage, without addressing the core issue of loss rate. Therefore, there is an urgent need to develop a wind-damage vulnerability analysis method for transmission towers. Summary of the Invention
[0004] The technical problem to be solved by the present invention is to provide a method for obtaining the wind damage vulnerability curve of transmission towers based on failure probability, in order to address the deficiencies in the existing technology.
[0005] The technical solution adopted by this invention to solve its technical problem is: a method for obtaining the wind damage vulnerability curve of transmission towers based on failure probability, comprising the following steps: Step 1) Establish a probability distribution model of the extreme response of the transmission tower under wind load; Step 2) Construct a probability distribution model of the load-bearing capacity of the transmission tower structure; Step 3) Based on Latin hypercube sampling, vulnerability analysis is performed to obtain the failure probability; Step 4) Plot vulnerability curves; plot the curves under different failure criteria with wind speed as the horizontal axis and failure probability as the vertical axis to obtain vulnerability curves based on failure probability. Step 5) Conduct a fragility analysis based on the project budget to obtain the loss rate; Step 6) Plot the vulnerability curve; plot the curve with wind speed on the horizontal axis and loss rate on the vertical axis to obtain the vulnerability curve based on the engineering estimate.
[0006] According to the above scheme, step 1) specifically includes the following: 1.1) Calculate the wind load effect on conductors and transmission towers under different wind speeds and wind direction angles; 1.2) Using the base shear force as the evaluation index for the extreme effect of wind load on transmission towers, for a given basic wind speed, based on the first exceedance probability theory, the average crossing rate is used to evaluate the effect. Sampling duration T, mean response With variance The probability distribution of obtaining the extreme value of the base shear force by the peak factor g.
[0007] According to the above scheme, in step 1.2), the probability distribution of the extreme value of the base shear force is... for:
[0008] in, Indicates the extreme value response. , The total load effect calculated according to the load code; The average crossing rate is represented by the following formula:
[0009] in, This is the peak factor.
[0010] According to the above scheme, in step 2), a probability distribution model of the load-bearing capacity of the transmission tower structure is constructed, as follows: 2.1) Select the elastic modulus and yield strength of the transmission tower material as uncertainties, and obtain the material distribution pattern, distribution parameters and coefficient of variation of the transmission tower; 2.2) Structural samples were generated using the Latin hypercube sampling method; 2.3) Apply conductor wind loads and segmented wind loads to each sample, and conduct nonlinear pushover analysis to determine the tower top displacement and base shear force under different failure states: 2.4) Statistical analysis of different destruction criteria Logarithmic mean of lower base shear force Sum of logarithmic variance Construct a probability distribution model of bearing capacity;
[0011] In the formula, A distribution model of structural bearing capacity; The cumulative distribution function representing the standard normal distribution; Different destruction criteria The structural bearing capacity below; The logarithmic mean of the load-bearing capacity; The standard deviation of the load-bearing capacity; subscript These represent different criteria for destruction.
[0012] According to the above scheme, in step 2.4), the failure criterion is defined as follows: Minor damage: The main material reaches its yield strength; Severe damage: Both the diagonal member and the main member reached their yield strength; Collapse: The overall base shear force reaches its peak.
[0013] According to the above scheme, step 3) specifically includes the following: 3.1) Function construction; The extreme value effect and structural bearing capacity probability distribution under a given wind speed are randomly sampled using the Latin hypercube sampling method. The sample size is n, and the function is defined as follows: ; in, Different destruction criteria The structural bearing capacity below; Indicates extreme value response; 3.2) Calculate the failure probability; By changing the base wind speed value, different structural responses are obtained. The function Z is used to determine whether the structure fails at a given base wind speed (Z<0 indicates structural failure). The number of failure samples is then counted. The failure probability is: ; This represents the failure probability corresponding to the damage criterion and wind speed. According to the above scheme, in step 5), the loss rate is calculated as follows: The probability intervals of failure probability are mapped to different loss states, and the loss rate is calculated using the failure probability: each interval corresponds to a different loss state probability, and the expression for the loss rate is: ; In the formula, Loss rate at wind speed V; loss ratio This represents the ratio of the repair to the replacement value for different loss states.
[0014] According to the above scheme, in step 5), the loss ratio The possible values are as follows: The loss ratio of transmission towers in plain areas is the average loss ratio; The loss ratio of transmission towers in complex terrain is based on the maximum loss ratio; When only considering the cost of raw materials and construction, the minimum loss ratio is used.
[0015] The beneficial effects of this invention are: This invention proposes a vulnerability analysis method that considers the uncertainty of wind load and structural parameters. It combines the repair value and replacement value of the transmission tower to draw a vulnerability curve. This method has the characteristics of high efficiency in analysis and calculation and is suitable for the analysis of the failure probability and loss rate of transmission towers in engineering contexts. Attached Figure Description
[0016] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the failure criterion in the structural bearing capacity probability distribution model of this invention. Detailed Implementation
[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0018] like Figure 1 As shown, a method for obtaining the wind-induced vulnerability curve of transmission towers based on failure probability includes the following steps: 1) Establish a probability distribution model for the extreme response of transmission towers to wind loads; 1.1) Calculate the wind load effect on conductors and transmission towers under different wind speeds and wind direction angles; 1.2) Using the base shear force as the evaluation index for the extreme effect of wind load on transmission towers, for a given basic wind speed, based on the first exceedance probability theory, the average crossing rate is used to evaluate the effect. Sampling duration T, mean response With variance The probability distribution of obtaining the extreme value of the base shear force by the peak factor g. for:
[0019] in, Indicates the extreme value response. , The total load effect calculated according to the load code; The average crossing rate is represented by the following formula:
[0020] in, Peak factor; 2) Establish a probability distribution model of the load-bearing capacity of the transmission tower structure; 2.1) The elastic modulus and yield strength of the transmission tower material are selected as uncertainties. Based on the data released by the Joint Commission on International Security, their distribution form, distribution parameters and coefficient of variation are obtained. 2.2) Structural samples were generated using the Latin hypercube sampling method (≥20 samples per group); 2.3) Apply conductor wind load (at the end of the crossarm) and segmental wind load to each sample, and conduct nonlinear pushover analysis to determine the tower top displacement and base shear force under different failure states: like Figure 2 The failure criterion in the structural bearing capacity probability distribution model of this invention is as follows: Minor damage: The main material reaches its yield strength; Severe damage: Both the diagonal member and the main member reached their yield strength; Collapse: The overall base shear force reaches its peak.
[0021] 2.4) Statistical analysis of different destruction criteria Logarithmic mean of lower base shear force Sum of logarithmic variance Construct a probability distribution model of bearing capacity;
[0022] In the formula, A distribution model of structural bearing capacity; The cumulative distribution function representing the standard normal distribution; For structural bearing capacity; The logarithmic mean of the load-bearing capacity; The standard deviation of the load-bearing capacity; subscript Indicates different criteria for destruction; 3) Vulnerability analysis based on Latin hypercube sampling to obtain the failure probability; 3.1) Function construction; The extreme value effect and structural bearing capacity probability distribution under a given wind speed are randomly sampled using the Latin hypercube sampling method. The sample size is n, and the function is defined as follows: ; 3.2) Calculate the failure probability by changing the base wind speed value and obtaining different structural responses. Use the function Z to determine whether the structure fails at a given base wind speed (Z<0 indicates structural failure). Count the number of failure samples. The failure probability is: ; To determine the failure probability corresponding to the failure criteria and wind speed; consider the failure probability of various failure criteria at different wind speeds. 4) Plot vulnerability curves with wind speed on the horizontal axis and failure probability on the vertical axis. Plot curves under different failure criteria to obtain vulnerability curves based on failure probability.
[0023] 5) Conduct a vulnerability analysis based on the project budget (obtain the loss rate). Define the loss ratio: Referring to the budget standards for power engineering construction, and considering factors such as the damage status of components, geographical conditions, and construction costs, the loss ratio is... Defined as the ratio of repair value to reset value: The loss ratio of transmission towers in plains areas: average loss ratio; Complex terrain: maximum loss ratio; Considering only the cost of raw materials and construction: minimum loss ratio; The distribution of various loss ratios is described using a Beta distribution with upper and lower bounds.
[0024] The loss rate is calculated by mapping probability intervals to different loss states, and deriving the loss rate from the failure probability: each interval corresponds to a different loss state probability, and the loss rate expression is:
[0025] In the formula, The loss rate at wind speed V; 6) Plot the vulnerability curve with wind speed on the horizontal axis and loss rate on the vertical axis to obtain the vulnerability curve based on the engineering estimate.
[0026] Through the above steps, wind damage vulnerability curves of transmission towers based on failure probability and engineering estimates are obtained respectively, thereby achieving a quantitative assessment of wind damage vulnerability.
[0027] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.
Claims
1. A method for obtaining the wind-induced vulnerability curve of transmission towers based on failure probability, characterized in that, Includes the following steps: Step 1) Establish a probability distribution model of the extreme response of the transmission tower under wind load; Step 2) Construct a probability distribution model of the load-bearing capacity of the transmission tower structure; Step 3) Based on Latin hypercube sampling, vulnerability analysis is performed to obtain the failure probability; Step 4) Plot vulnerability curves; plot the curves under different failure criteria with wind speed as the horizontal axis and failure probability as the vertical axis to obtain vulnerability curves based on failure probability. Step 5) Conduct a fragility analysis based on the project budget to obtain the loss rate; Step 6) Plot the vulnerability curve; plot the curve with wind speed on the horizontal axis and loss rate on the vertical axis to obtain the vulnerability curve based on the engineering estimate.
2. The method for obtaining the wind-induced vulnerability curve of transmission towers based on failure probability according to claim 1, characterized in that, In step 1), the specific details are as follows: 1.1) Calculate the wind load effect on conductors and transmission towers under different wind speeds and wind direction angles; 1.2) Using the base shear force as the evaluation index for the extreme effect of wind load on transmission towers, for a given basic wind speed, based on the first exceedance probability theory, the average crossing rate is used to evaluate the effect. Sampling duration T, mean response With variance The probability distribution of obtaining the extreme value of the base shear force by the peak factor g.
3. The method for obtaining the wind-induced vulnerability curve of transmission towers based on failure probability according to claim 2, characterized in that, In step 1.2), the probability distribution of the extreme value of the base shear force. for: in, Indicates the extreme value response. , The total load effect calculated according to the load code; The average crossing rate is represented by the following formula: in, This is the peak factor.
4. The method for obtaining the wind-induced vulnerability curve of transmission towers based on failure probability according to claim 1, characterized in that, In step 2), a probability distribution model of the load-bearing capacity of the transmission tower structure is constructed, as follows: 2.1) Select the elastic modulus and yield strength of the transmission tower material as uncertainties, and obtain the material distribution pattern, distribution parameters and coefficient of variation of the transmission tower; 2.2) Structural samples were generated using the Latin hypercube sampling method; 2.3) Apply conductor wind loads and segmented wind loads to each sample, and conduct nonlinear pushover analysis to determine the tower top displacement and base shear force under different failure states: 2.4) Statistical analysis of different destruction criteria Logarithmic mean of lower base shear force and logarithmic variance Construct a probability distribution model of bearing capacity; In the formula, A distribution model of structural bearing capacity; The cumulative distribution function representing the standard normal distribution; Different destruction criteria The structural bearing capacity below; The logarithmic mean of the load-bearing capacity; The standard deviation of the load-bearing capacity; subscript These represent different criteria for destruction.
5. The method for obtaining the wind-induced vulnerability curve of transmission towers based on failure probability according to claim 4, characterized in that, In step 2.4), the failure criterion is defined as follows: Minor damage: The main material reaches its yield strength; Severe damage: Both the diagonal member and the main member reached their yield strength; Collapse: The overall base shear force reaches its peak.
6. The method for obtaining the wind-induced vulnerability curve of transmission towers based on failure probability according to claim 1, characterized in that, In step 3), the specific details are as follows: 3.1) Function construction; The extreme value effect and structural bearing capacity probability distribution under a given wind speed are randomly sampled using the Latin hypercube sampling method. The sample size is n, and the function is defined as follows: ； in, Different destruction criteria The structural bearing capacity below; Indicates extreme value response; 3.2) Calculate the failure probability; By changing the base wind speed value, different structural responses are obtained. The function Z is used to determine whether the structure fails at a given base wind speed (Z < 0 indicates structural failure). The number of failure samples is then counted. The failure probability is: ; This represents the failure probability corresponding to the damage criterion and wind speed.
7. The method for obtaining the wind-induced vulnerability curve of transmission towers based on failure probability according to claim 1, characterized in that, In step 5), the loss rate is calculated as follows: The probability intervals of failure probability are mapped to different loss states, and the loss rate is calculated using the failure probability: each interval corresponds to a different loss state probability, and the expression for the loss rate is: ； In the formula, Loss rate at wind speed V; loss ratio This represents the ratio of the repair to the replacement value for different loss states.
8. The method for obtaining the wind-induced vulnerability curve of transmission towers based on failure probability according to claim 7, characterized in that, In step 5), the loss ratio The possible values are as follows: The loss ratio of transmission towers in plain areas is the average loss ratio; The loss ratio of transmission towers in complex terrain is based on the maximum loss ratio; When only considering the cost of raw materials and construction, the minimum loss ratio is used.
9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 8.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 8.