Method for constructing vulnerable curved surface of power distribution tower wire system under wind and rain coupling condition

Abstract

The invention discloses a vulnerability curved surface construction method for a power distribution tower wire system under a wind and rain coupling condition, and the method comprises the steps: constructing a vulnerability function through employing a probability demand analysis method; deriving a conditional failure probability calculation formula for reaching a specified limit state; and constructing a wind-rain coupling load model based on given double-strength measurement parameter combinations, and calculating the failure probability of the power distribution tower-lead system reaching a specified limit state for any double-strength measurement parameter combination according to the constructed vulnerability function, the wind-rain coupling load model and the failure probability calculation formula. And a vulnerability curved surface model under the wind-rain coupling disaster is constructed, and the probabilistic vulnerability evaluation of the power distribution tower-lead system under the wind-rain coupling disaster is realized. According to the vulnerability analysis method based on double-strength measurement, the failure probability evaluation precision of a power distribution tower-lead system under a wind-rain coupling disaster is remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of power system risk assessment and operation and maintenance early warning technology, and in particular to a method for constructing a vulnerability surface of a distribution tower conductor system under wind and rain coupling conditions. It is applicable to the vulnerability modeling and rapid identification of the tower-conductor system in overhead distribution lines based on dual strength measurement and probabilistic demand analysis (PDA) under extreme weather conditions of wind and rain. Background Technology

[0002] With the intensification of global climate change, extreme weather disasters, especially wind-rain coupled disasters such as typhoons and torrential rains, have become one of the major threats to power system operation. In the distribution network, the distribution tower-conductor system is a critical infrastructure, and its stability directly affects the reliability of power supply. In recent years, power system failures caused by extreme weather, especially the collapse of distribution towers and damage to conductors, have occurred frequently, causing serious losses to the socio-economic situation.

[0003] Currently, most safety assessment methods for power distribution systems focus on the analysis of single disaster factors, such as the impact of wind speed or rainfall intensity. However, these traditional methods fail to fully consider the combined effects of wind-rain and other combined disasters on the power distribution tower-conductor system, thus their assessment results cannot accurately reflect the actual situation and have certain limitations. For risk assessment of wind-rain coupled disasters, some studies have proposed vulnerability analysis models based on dual intensity measures of wind speed and rainfall intensity to more comprehensively assess the impact of disasters on the structure.

[0004] Vulnerability analysis is a crucial method for assessing the probability of structural or system failure under specific disaster intensities. Traditional vulnerability analysis primarily evaluates the impact of disasters on structures using a single intensity metric (such as wind speed or rainfall intensity). However, this method neglects the coupling effects between different disaster factors, making it difficult to accurately describe the combined effects of multiple disasters on power distribution tower-conductor systems. To address this issue, recent studies have introduced "dual intensity metric" models, which simultaneously consider wind speed and rainfall intensity to construct vulnerability surfaces under combined disaster scenarios, thereby improving the accuracy of disaster risk prediction.

[0005] Furthermore, existing vulnerability analysis methods often neglect uncertainties on both the load and structural sides. Variations in structural parameters such as material properties, geometric dimensions, and wind pressure coefficients can significantly affect structural response and failure probability. Therefore, recent research has gradually incorporated uncertainty analysis, proposing vulnerability assessment methods based on structural and load uncertainties. These studies demonstrate that systematically considering uncertainty factors helps improve the accuracy of vulnerability analysis and the feasibility of engineering applications.

[0006] Although some studies have been conducted on vulnerability analysis under wind-rain coupled disasters, most have focused on transmission tower-conductor systems, while vulnerability analysis of distribution tower-conductor systems under wind-rain coupled disasters remains relatively lacking. Therefore, developing a vulnerability analysis method that comprehensively considers dual strength metrics and systematically incorporates load and structural uncertainties has significant theoretical value and application prospects for disaster risk assessment and safety improvement of power distribution systems. Summary of the Invention

[0007] The purpose of this invention is to overcome the deficiencies of existing technologies and provide a method for constructing a vulnerable surface for a power distribution tower conductor system under wind-rain coupling conditions, which can be used to evaluate the failure probability of the power distribution tower-conductor system under wind-rain coupling disasters.

[0008] This invention solves the following technical problems:

[0009] 1. Inability to effectively assess the combined impact of wind-rain coupled disasters

[0010] Existing vulnerability analysis methods often focus on analyzing single disaster factors, such as wind speed or rainfall intensity, neglecting the combined effects of wind-rain combined disasters. Since the combined effects of wind speed and rainfall intensity have a significant impact on the power distribution tower-conductor system, traditional methods cannot accurately reflect the risk of multiple concurrent disasters. To address this issue, this invention proposes a dual-intensity measurement model, combining basic wind speed and rainfall intensity as two intensity measurement factors to construct a vulnerability surface under wind-rain coupled conditions, thus more accurately assessing the risk of power distribution systems under combined meteorological disasters.

[0011] 2. Lack of consideration for uncertainties in structural and load parameters

[0012] Existing methods often neglect the randomness between structural parameters (such as material strength, elastic modulus, and geometric dimensions) and load parameters (such as wind pressure coefficient and drag coefficient), leading to potential biases in vulnerability analysis results. This invention introduces probabilistic demand analysis (PDA) to systematically consider load and structural uncertainties, and employs Latin hypercube sampling to generate different sample sets, thereby conducting analysis within a unified probabilistic framework and significantly improving the accuracy and reliability of vulnerability analysis.

[0013] 3. Insufficient assessment of failure probability under wind-rain coupled disaster scenarios

[0014] Most current vulnerability analysis methods lack a quantitative model for failure probability based on dual intensity measures of wind speed and rainfall intensity, and fail to provide effective real-time disaster risk assessment tools. To address this issue, this invention proposes a method based on dual-intensity vulnerability surfaces, which can quantitatively describe the structural failure probability under different combinations of wind speed and rainfall intensity, providing support for the safe operation and emergency dispatch of power distribution systems.

[0015] In summary, the present invention aims to provide a vulnerability analysis method for wind-rain coupled disasters that comprehensively considers both wind speed and rainfall intensity as dual strength measures and systematically considers load and structural uncertainties, thereby achieving accurate quantification and risk assessment of the failure probability of power distribution tower-conductor systems under combined disaster scenarios.

[0016] This invention is achieved through the following technical solution:

[0017] A method for constructing vulnerable curved surfaces of a power distribution tower conductor system under wind and rain coupling conditions, specifically including the following steps:

[0018] S1. Using the probabilistic demand analysis method, regression fitting is performed on the relationship between the engineering demand parameter EDP and the dual intensity measurement parameters in the logarithmic domain to construct a vulnerability function. The dual intensity measurement parameters are the basic wind speed and rainfall intensity.

[0019] S2. Assuming that the vulnerability function follows a log-normal distribution under a given combination of dual strength metric parameters, derive the formula for calculating the conditional failure probability of reaching the specified limit state.

[0020] S3. Construct a wind-rain coupled load model based on a given combination of dual intensity metric parameters. The wind-rain coupled load model includes a wind load calculation sub-model and a rain load calculation sub-model. The wind load calculation sub-model is obtained by superimposing the average wind and the time history of the spatiotemporally correlated fluctuating wind speed generated by the harmonic superposition method. The rain load calculation sub-model is obtained by integrally calculating the collision force of raindrops of different diameters on the windward projection surface of the structure under given rainfall intensity and basic wind speed conditions.

[0021] S4. Based on the constructed vulnerability function, wind-rain coupled load model, and failure probability calculation formula, calculate the failure probability of the distribution tower-conductor system reaching the specified limit state for any combination of dual strength measurement parameters. Using the failure probability as the vertical coordinate of the surface and the dual strength measurement parameters as the horizontal and vertical coordinates of the surface, construct a vulnerability surface model under wind-rain coupled disasters to realize the probabilistic vulnerability assessment of the distribution tower-conductor system under wind-rain coupled disasters.

[0022] The specific details of step S1 are as follows:

[0023] In the case of a single strength metric parameter IM, the relationship between the engineering requirement parameter EDP and the strength metric parameter IM can be represented by a log-linear model as follows:

[0024] (1)

[0025] In the formula and These are the regression coefficients;

[0026] When considering the two strength metrics, the log-linear model, i.e., the vulnerability function, is:

[0027] (2)

[0028] In the formula , , For regression coefficients, The base wind speed, This refers to the intensity of rainfall.

[0029] The specific details of step S2 are as follows:

[0030] Assuming that, given a combination of two strength metrics, the engineering requirement parameter EDP follows a log-normal distribution, the conditional failure probability of reaching a certain limit state LS is expressed as:

[0031] (3)

[0032] In the formula It is the standard normal distribution function. ; This indicates that the Engineering Requirements Parameter (EDP) is defined in a given combination of two strength metrics. The logarithmic domain dispersion under the given conditions is calculated from the root mean square of the regression residuals, as follows:

[0033] (4)

[0034] In the formula For sample size, The number of regression parameters, The sample number. For the first Sample project requirement parameters, and The first Individual weather intensity parameters, , , is the regression coefficient.

[0035] The wind load calculation sub-model described in step S3 is as follows: To accurately reflect the wind characteristics of the power distribution tower-conductor system under typhoon conditions, a spatiotemporally related dynamic wind field is applied to the structure at any height. With time The total wind speed is expressed as

[0036] (5)

[0037] In the formula The average wind speed, For pulsating wind speed, Indicates the total wind speed;

[0038] 1) Average wind speed: The average wind speed is expressed using a power-law profile as follows:

[0039] (6)

[0040] In the formula, The average wind speed at a height of 10 m over 10 minutes. This is the ground roughness correction factor. For height;

[0041] 2) Fluctuating wind speed: The statistical characteristics of fluctuating wind speed are described by both the velocity power spectral density and the spatial coherence function. For the near-surface layer of typhoons, the Davenport spectrum is used, and its scalar spectrum is expressed as follows:

[0042] (7)

[0043] In the formula For frequency, This is an empirical coefficient for surface resistance;

[0044] 3) Numerical synthesis of wind field: The time history of fluctuating wind speed is generated using the harmonic superposition method. According to Shinozuka theory, when the frequency division number... At that time, the first The pulsating wind speed at each observation point is

[0045] (8)

[0046] In the formula For discrete angular frequencies, , The lowest frequency, For the maximum frequency, Independent random phase; To calculate the number of points; The frequency of pulsating wind is divided into several categories; and For serial numbers; For time; From the target cross-spectral density matrix Obtained by Cholesky decomposition, satisfying , for The complex conjugate, Argument angle;

[0047] 4) Wind load: The nominal wind load acting on a structural member in a free wind field is expressed as...

[0048] (9)

[0049] In the formula air density; For structural coefficients; This refers to the drag coefficient; The wind pressure coefficient varies with altitude; The projected area facing the wind; The wind speed at the reference height is the total wind speed.

[0050] The rain load calculation sub-model described in step S3 is as follows:

[0051] Suppose a raindrop of diameter D is incident on the surface of a structure with a relative velocity, and its incident pressure per unit area is expressed as:

[0052] (10)

[0053] In the formula, This is an empirical coefficient; The density of water; The raindrop spectrum, i.e., the number of raindrops per unit volume as a function of... Distribution; The normalized curve of single-droplet collision force in The integral area of ​​the range; For the speed ratio, a segmented empirical formula is used.

[0054] (11)

[0055] In the formula The height is the center height of the component. This is the ground roughness correction factor; Effective action time of a single drop Pick

[0056] (12)

[0057] The total number of raindrops per unit volume; considering the upper limit of raindrop diameter in nature. have

[0058] (13)

[0059] Raindrop spectrum adopts an exponential model

[0060] (14)

[0061] In the formula Rainfall intensity, ;

[0062] At the specified wind speed With rainfall intensity Below, the effect on the windward projection of the component. The equivalent rain load is obtained by integrating over the raindrop size:

[0063] (15).

[0064] A vulnerable surface construction system for a power distribution tower conductor system under wind and rain coupling conditions includes:

[0065] Vulnerability function construction module: Using the probabilistic demand analysis method, the relationship between the engineering demand parameter EDP and the dual intensity metric parameters is regressed and fitted in the logarithmic domain to construct the vulnerability function. The dual intensity metric parameters are the basic wind speed and rainfall intensity.

[0066] Failure probability calculation formula derivation module: Assuming that the vulnerability function follows a log-normal distribution under a given combination of dual strength measurement parameters, derive the conditional failure probability calculation formula for reaching the specified limit state;

[0067] Wind-Rain Coupled Load Model Construction Module: Based on a given combination of dual strength metric parameters, a wind-rain coupled load model is constructed. The wind-rain coupled load model includes a wind load calculation sub-model and a rain load calculation sub-model. The wind load calculation sub-model is obtained by superimposing the average wind and the time history of the spatiotemporally correlated fluctuating wind speed generated using the harmonic superposition method. The rain load calculation sub-model is obtained by integrally calculating the collision force of raindrops of different diameters on the windward projection surface of the structure under given rainfall intensity and basic wind speed conditions.

[0068] Vulnerability Surface Model Construction Module: Based on the constructed vulnerability function, wind-rain coupled load model, and failure probability calculation formula, for any combination of dual strength metric parameters, the failure probability of the distribution tower-conductor system reaching the specified limit state is calculated. Using the failure probability as the vertical coordinate of the surface and the dual strength metric parameters as the horizontal and vertical coordinates of the surface, a vulnerability surface model under wind-rain coupled disaster is constructed to realize the probabilistic vulnerability assessment of the distribution tower-conductor system under wind-rain coupled disaster.

[0069] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps of the method for constructing a vulnerable surface of a power distribution tower conductor system under wind and rain coupling conditions.

[0070] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the method for constructing a vulnerable surface of a power distribution tower conductor system under wind and rain coupling conditions.

[0071] The advantages of this invention are: Based on a vulnerability analysis method using dual strength metrics, this invention significantly improves the accuracy of failure probability assessment for power distribution tower-conductor systems under wind-rain coupled disasters, and has the following main effects:

[0072] 1. Improved assessment accuracy: Compared with the traditional single intensity measurement method, this invention, by considering both basic wind speed and rainfall intensity, can more accurately reflect the impact of wind-rain combined disasters, thereby improving the accuracy of risk assessment.

[0073] 2. Considering structural and load uncertainties: This invention comprehensively considers the uncertainties of load and structural parameters by introducing probabilistic demand analysis (PDA) and Latin hypercube sampling (LHS) methods, thereby improving the reliability of vulnerability analysis and the accuracy of practical applications.

[0074] 3. Improve the resilience of power distribution systems: This invention helps to optimize the risk management strategy of power distribution systems. By accurately assessing the failure probability under different combinations of wind speed and rainfall intensity, it guides decisions on reinforcement, maintenance, etc., thereby improving the resilience of power distribution systems in disasters. Attached Figure Description

[0075] Figure 1 This is a schematic diagram of wind speed time history for this invention;

[0076] Figure 2 This is a comparison diagram of the simulated spectrum and the target power spectrum of the present invention;

[0077] Figure 3 This is a schematic diagram of the normalized curve of the present invention;

[0078] Figure 4 This is a typical "three-bar four-wire" finite element model of the present invention;

[0079] Figure 5 This is a time history diagram of the conductor tension force of the present invention;

[0080] Figure 6 This is the time history diagram of the bending moment at the bottom of the pole according to the present invention;

[0081] Figure 7 This is a graph showing the statistical results of the parameters under different sample sizes in this invention;

[0082] Figure 8 This is a histogram of the conductors per unit weight of the present invention;

[0083] Figure 9 This is a schematic diagram of the load application point of the present invention;

[0084] Figure 10 This is a regression analysis diagram of conductor faults in this invention;

[0085] Figure 11 This is a regression analysis diagram of tower collapse according to the present invention;

[0086] Figure 12 This is a surface diagram illustrating the fault vulnerability of the conductor in this invention.

[0087] Figure 13 This is a surface diagram illustrating the vulnerability of towers to collapse according to the present invention. Detailed Implementation

[0088] A method for constructing vulnerable curved surfaces of a power distribution tower conductor system under wind and rain coupling conditions, specifically including the following steps:

[0089] S1. Using the probabilistic demand analysis method, regression fitting is performed on the relationship between the engineering demand parameter EDP and the dual intensity measurement parameters in the logarithmic domain to construct a vulnerability function. The dual intensity measurement parameters are the basic wind speed and rainfall intensity.

[0090] S2. Assuming that the vulnerability function follows a log-normal distribution under a given combination of dual strength metric parameters, derive the formula for calculating the conditional failure probability of reaching the specified limit state.

[0091] S3. Construct a wind-rain coupled load model based on a given combination of dual intensity metric parameters. The wind-rain coupled load model includes a wind load calculation sub-model and a rain load calculation sub-model. The wind load calculation sub-model is obtained by superimposing the average wind and the time history of the spatiotemporally correlated fluctuating wind speed generated by the harmonic superposition method. The rain load calculation sub-model is obtained by integrally calculating the collision force of raindrops of different diameters on the windward projection surface of the structure under given rainfall intensity and basic wind speed conditions.

[0092] S4. Based on the constructed vulnerability function, wind-rain coupled load model, and failure probability calculation formula, calculate the failure probability of the distribution tower-conductor system reaching the specified limit state for any combination of dual strength measurement parameters. Using the failure probability as the vertical coordinate of the surface and the dual strength measurement parameters as the horizontal and vertical coordinates of the surface, construct a vulnerability surface model under wind-rain coupled disasters to realize the probabilistic vulnerability assessment of the distribution tower-conductor system under wind-rain coupled disasters.

[0093] 1. Probabilistic Demand Analysis (PDA)

[0094] This invention employs a probabilistic demand analysis method, performing regression fitting on the relationship between engineering demand parameters and strength metrics in the logarithmic domain, and constructing a vulnerability function accordingly. In the case of a single IM, the relationship between EDP and IM can be represented by a log-linear model as follows:

[0095] (1)

[0096] In the formula and is the regression coefficient.

[0097] When considering two strength measures and (When the basic wind speed and rainfall intensity are taken respectively in this invention), the model can be expanded to:

[0098] (2)

[0099] In the formula , , is the regression coefficient.

[0100] If we assume that, under a given IM condition, the EDP follows a log-normal distribution, then the conditional failure probability of reaching a certain limit state (LS) can be expressed as:

[0101] (3)

[0102] In the formula It is the standard normal distribution function. . This represents the logarithmic domain dispersion of the EDP under given IM conditions. This parameter can be calculated from the root mean square of the regression residuals:

[0103] (4)

[0104] In the formula For sample size, The number of regression parameters, The sample number. For the first Sample project requirement parameters, and The first Individual weather intensity parameters, , , is the regression coefficient.

[0105] From equations (2) to (4), we can further obtain the following: The vulnerable surface model is used as the independent variable. For any wind speed-rain intensity combination, equation (3) can give the failure probability of reaching the specified limit state, realizing the probabilistic characterization of the structure under the condition of dual strength measurement.

[0106] 2. Wind and rain load

[0107] To characterize the coupling effect of strong winds and rainfall during typhoons on the power distribution tower-conductor system, this invention establishes separate calculation models for wind load and rain load, and standardizes the relevant parameters, units, and numerical values. The wind field is composed of the superposition of mean wind and pulsating wind; the rain load is obtained by integrating the windward projected area of ​​raindrops on the tower and conductor.

[0108] 2.1 Wind Load Model

[0109] To accurately reflect the wind characteristics of the tower-conductor system under typhoon conditions, this invention applies a spatiotemporally correlated dynamic wind field to the structure. (Arbitrary height) With time The total wind speed can be expressed as

[0110] (5)

[0111] In the formula The average wind speed, This refers to the pulsating wind speed.

[0112] 1) Mean wind profile: The mean wind is represented using a power-law profile (Davenport power law) as follows:

[0113] (6)

[0114] In the formula, The average wind speed at a height of 10 m over 10 minutes. This is the ground roughness correction factor. For height.

[0115] 2) Pulsating Wind Spectrum: The statistical characteristics of pulsating wind are described by both the velocity power spectral density and the spatial coherence function. This invention uses the Davenport spectrum for the near-surface layer of typhoons, and its scalar spectrum can be expressed as follows:

[0116] (7)

[0117] In the formula For frequency, This is an empirical coefficient for surface resistance.

[0118] 3) Numerical synthesis of wind field: The time history of fluctuating wind speed is generated using the harmonic superposition method. According to Shinozuka theory, when the frequency division number... At that time, the first The fluctuating wind speed at each observation point can be written as:

[0119] (8)

[0120] In the formula For discrete angular frequencies, , The lowest frequency, For the maximum frequency, Independent random phase; To calculate the number of points; The frequency of pulsating wind is divided into several categories; and For serial numbers; For time; From the target cross-spectral density matrix Obtained by Cholesky decomposition, satisfying , for The complex conjugate, Argument angle;

[0121] 4) Simulation verification: using the average wind speed at a height of 10 m For example, take Time step Generate wind speed time history, such as Figure 1 As shown. To verify the rationality of the simulation, the generated time-history power spectrum was compared with the Davenport target spectrum, see... Figure 2 The results show that the variation trends of the two in the main energy frequency bands are consistent, indicating that the pulsating wind speed simulation of the present invention has high statistical fidelity and meets the accuracy requirements of subsequent dynamic analysis.

[0122] 5) Wind load: The nominal wind load acting on a structural member in a free wind field can be expressed as...

[0123] (9)

[0124] In the formula air density; For structural coefficients; This refers to the drag coefficient; The wind pressure coefficient varies with altitude; The projected area facing the wind; The wind speed at the reference height is the total wind speed. This is used in the calculations of this invention. , , Values ​​should be taken according to the specifications and listed item by item in the example section.

[0125] 2.2 Rain Load Model

[0126] Suppose a raindrop of diameter D is incident on the surface of a structure with a relative velocity, its incident pressure per unit area can be expressed as:

[0127] (10)

[0128] In the formula, This is an empirical coefficient; The density of water; Raindrop spectrum (number of raindrops per unit volume varies) (distribution) The normalized curve of single-droplet collision force in The integral area of ​​the range, the normalized curve of the single droplet collision force is as follows: Figure 3 ; For speed ratios, a segmented empirical formula is typically used.

[0129] (11)

[0130] In the formula The height is the center height of the component. This is the ground roughness correction factor; Effective action time of a single drop Pick

[0131] (12)

[0132] This represents the total number of raindrops per unit volume. It considers the upper limit of raindrop diameter in nature. have

[0133] (13)

[0134] Raindrop spectrum adopts an exponential model

[0135] (14)

[0136] In the formula Rainfall intensity (unit) ), .

[0137] At the specified wind speed With Yuqiang Below, the effect on the windward projection of the component. The equivalent rain load is obtained by integrating over the raindrop size:

[0138] (15).

[0139] The best embodiment of the specific application of the present invention:

[0140] 1. Nonlinear dynamic time history analysis using a three-dimensional finite element analysis model.

[0141] Considering that poles and conductors are the most critical and vulnerable components of power distribution networks under extreme wind and rain, this invention selects them as the main objects for modeling and vulnerability assessment. The research background is a typical power distribution line project in Anhui Province, China. Taking a 10 kV single-circuit overhead line with a span of 80 m as an example, a three-dimensional finite element model of a typical "three-pole, four-wire" overhead power distribution line is established, as follows... Figure 4 As shown.

[0142] First, the model was created using ANSYS software to model the power distribution tower-conductor system. The power distribution poles were C30 prestressed concrete conical hollow poles (top diameter...). Bottom diameter Wall thickness ), total height burial depth Design overturning resistance threshold The conductor type is JKLGYJ-185 / 10, with a diameter of... Line quality Design tensile strength During installation, the tension of the conductor is perpendicular to the horizontal. Included angle. The surface roughness coefficient of the site environment is taken as 0.16.

[0143] In numerical modeling, the pole body was discretized using SOLID45 solid elements; the internal longitudinal reinforcement and stirrups were simulated using LINK8 tension / compression elements; the crossarms and insulators were simulated using BEAM188 beam elements; and the conductors were modeled using LINK10 cable elements, arranged in a three-loop configuration (front-middle-rear). Approximately 20 elements were discretized along the line direction for each span to fully capture the conductor sag and its dynamic response characteristics. Material parameters were set as follows: concrete elastic modulus... Poisson's ratio ,density ;wire , The crossarm is rigidly coupled to the top of the pole, and a fully constrained boundary condition is applied to the bottom of the pole. The initial tension of the conductor is converted into the initial strain of the element based on the installation tension, while also considering the influence of its own weight and the weight of auxiliary components.

[0144] The solution process employs static large deformation analysis and utilizes the initial stress stiffening effect to obtain the true initial sag and internal force distribution of the tower-conductor system under the combined action of self-weight and initial tension. This initial equilibrium state is used as the benchmark condition for wind and rain dynamic time history analysis to ensure consistency and comparability between the input load and the structural response.

[0145] 2 Response Analysis

[0146] After inputting wind and rain loads, a nonlinear dynamic time history analysis was performed on the "three poles and four wires" finite element model. The calculation duration was set to 600 s, and the time step was [missing information]. For each "sample" "The combination extracts the peak statistics of engineering demand parameters from the output time history and uses them as the representative response of this intensity metric combination for subsequent probabilistic demand analysis regression. In this analysis, combined with wind and rain coupled loads, a dynamic time history analysis method is used to simulate the response of the power distribution tower-conductor system over time. Wind field and rain load are input into the model, with wind speed and precipitation intensity acting on the structure through corresponding load functions. Wind load is simulated using a pulsating wind field generated by the Davenport spectrum and harmonic superposition method, while rain load is calculated based on raindrop spectrum integrals. The load forces generated by these methods change over time, accurately reflecting the dynamic characteristics of wind speed and rainfall intensity."

[0147] In the nonlinear dynamic time-history analysis, to comprehensively consider the impact of different wind speeds and rainfall intensities on the power distribution tower-conductor system, discrete grids for the design wind speed and rainfall intensity are introduced into the analysis. Specifically, the design wind speed range is 0 to 60 m / s, divided into 10 levels, each level representing a wind speed interval. For example, the wind speed range from 0 m / s to 60 m / s is divided into 10 levels, each level representing a wind speed interval of 6 m / s. Thus, the discrete grid for wind speed includes ranges from 0 m / s to 6 m / s, 6 m / s to 12 m / s, and so on, up to 60 m / s.

[0148] Similarly, the design range for rainfall intensity is 0 to 160 mm / h, divided into eight levels, each representing a rainfall intensity interval. Each rainfall intensity level spans 20 mm / h; specifically, the discrete grid of rainfall intensity includes 0 mm / h to 20 mm / h, 20 mm / h to 40 mm / h, and up to 160 mm / h. These discrete rainfall intensity levels cover different meteorological conditions ranging from no rainfall to extreme rainfall.

[0149] During the analysis, different combinations of wind speed and rainfall intensity are applied as input loads to the finite element model of the power distribution tower-conductor system. For each combination of wind speed and rainfall intensity, a corresponding load time history is generated. Next, nonlinear dynamic time history analyses are performed for each of these combinations of wind speed and rainfall intensity. This means that for each combination of wind speed and rainfall intensity, a separate dynamic simulation is conducted to analyze the structural response of the power distribution tower-conductor system under that combination of conditions, including the tower's bending moment, the conductor's tension, sag, and vibration.

[0150] In this way, the various impacts of wind speed and rainfall intensity on the power distribution system can be comprehensively considered, thereby accurately predicting and assessing the system's disaster resistance capability under various wind and rain disaster conditions.

[0151] In summary, the three-dimensional finite element analysis model for nonlinear dynamic time history analysis accurately simulates the dynamic response of the power distribution tower-conductor system, considering the nonlinear characteristics of loads, structure, and materials. This allows for the effective assessment of structural failure risks under wind and rain loads. Through this method, this invention provides a reliable computational tool for assessing the wind-rain coupling disaster risk of power distribution systems, improving the accuracy and practicality of the assessment results.

[0152] This invention selects two types of EDP: pole base bending moment. Axial tension of the conductor . Figure 5 and Figure 6 Each of the following is given in a typical wind and rain scenario: and Time history response. Taking this working condition as an example, the peak bending moment at the bottom of the pole is... Its relationship with the design overturning limit bending moment The comparison is marked with dashed lines in the figure; the peak tension of the conductor is Corresponding to the design tensile strength threshold Also represented by dashed lines. As can be seen from the figure, under this wind and rain condition, both types of EDP exhibited instantaneous exceedance of the limit state, indicating that both the tower and the conductor are likely to fail under this combined load condition.

[0153] Repeating the above process for all samples and dual-IM combinations yields the peak records of the response dataset used for log-linear regression with dual intensity measures. Based on this dataset, a vulnerability function for the "wind-rain-tower / conductor" system is further constructed to achieve a quantitative assessment of the structural failure probability under wind and rain conditions.

[0154] 3 Uncertain parameters

[0155] The key to vulnerability analysis lies in the systematic and standardized incorporation of various uncertainty sources. Combining existing research findings with practical engineering conditions, this invention selects random variables that are sensitive to structural response and have relatively complete statistical information for modeling. Randomness mainly originates from two aspects: load and structure. On the load side, uncertainties such as wind pressure coefficient, wind resistance coefficient, and structural coefficients are considered; on the structural side, randomness is introduced in factors such as conductor unit weight, conductor diameter, conductor elastic modulus, concrete density, concrete elastic modulus, tower wall thickness, and tower height. The probability distribution type, mean, and coefficient of variation (COV) of each random variable are listed in Table 1. The above settings fully reflect the uncertainty characteristics of both the "load-structure" sides under typhoon conditions, achieving a coordinated characterization of system randomness within a unified probabilistic framework, and providing a solid statistical foundation for subsequent vulnerability analysis.

[0156] To obtain a representative sample set with limited computational cost, this invention employs Latin hypercube sampling (LHS) to generate random samples. Compared to the direct Monte Carlo method, LHS achieves better sample coverage and statistical convergence with the same sample size. To determine a reasonable sample size... This invention conducts convergence analysis: under different sample size conditions, the sample mean and sample standard deviation of each random variable are calculated as follows: The curve of change was analyzed, and it was determined whether it was stable within the target confidence interval. The results are as follows: Figure 7 As shown. Analysis indicates that when the sample size At this point, the mean and standard deviation of each variable tend to stabilize, and further increasing the sample size has limited effect on improving the statistical characteristics, while significantly increasing the computational cost. Based on this, the present invention adopts... As a benchmark sample size.

[0157] Furthermore, to verify the matching between the distribution setting and the sampling implementation, this invention uses the unit weight of the conductor as a representative variable, plots a sample histogram, and overlays the probability density function of the target distribution, such as... Figure 8 As shown in the figure. The results show that the sample frequency distribution is in good agreement with the log-normal target distribution, indicating that the random variable distribution setting, parameter calibration and LHS implementation process are consistent and reliable, and can meet the requirements of subsequent nonlinear dynamic time history and PDA regression analysis for input statistical consistency.

[0158] Table 1 Uncertain Parameters

[0159] parameter Probabilistic Model mean COV conductor unit weight (kg / m) Log-normal 0.55 0.03 Wire diameter (m) Log-normal 0.016 0.03 Elastic modulus of conductor (GPa) Log-normal 70.5 0.05 Concrete density (kg / m³) Log-normal 2400 0.02 Elastic modulus of concrete (GPa) Log-normal 35 0.05 Tower wall thickness (m) Log-normal 0.06 0.03 Tower height (m) normal distribution 12 0.03 Tower structural coefficient normal distribution 0.9 0.12 Conductor structure coefficient normal distribution 1.0 0.12 Tower drag coefficient normal distribution 0.85 0.11 conductor drag coefficient normal distribution 0.93 0.11 Tower wind pressure coefficient normal distribution 1.0 0.16 Conductor wind pressure coefficient normal distribution 1.0 0.16

[0160] Latin hypercube sampling (LHS) method generates sample sets:

[0161] Latin hypercube sampling (LHS) is a statistical method commonly used for multidimensional parameter sampling. It effectively improves sample coverage and sampling efficiency, and is widely applied in scenarios requiring Monte Carlo simulations, particularly in risk analysis involving multiple uncertain parameters. In this invention, the LHS method is used to generate a sample set to account for multiple uncertainties in loads and structures in subsequent finite element analysis and vulnerability analysis.

[0162] The principle of the LHS method: The core idea of ​​LHS is to rationally partition the parameter space and extract a sample point from each dimension, so that the generated samples can uniformly cover the entire parameter space. Compared with traditional random sampling methods, LHS has better sample distribution characteristics, especially when dealing with high-dimensional problems, and can significantly improve sample effectiveness and reduce computational costs.

[0163] The steps of generating a sample set using the LHS method in this invention are as follows:

[0164] 1) Selecting uncertainty parameters

[0165] Uncertainty parameters related to the structure and loads were selected, including wind pressure coefficient, drag coefficient, wind speed, rainfall intensity, conductor unit weight, conductor diameter, conductor elastic modulus, tower height, and tower wall thickness. These parameters are stochastic in actual engineering, therefore requiring modeling using probability distributions. Each parameter has a known probability distribution type, typically derived from historical data or theoretical derivation. For example, wind speed and wind pressure coefficient may follow a normal distribution, while conductor unit weight and tower wall thickness may follow a log-normal distribution. Next, for each selected parameter, its value range is determined based on its probability distribution, and this range is uniformly divided into several intervals. The size and number of each interval are determined according to the parameter's distribution characteristics, with the aim of ensuring that each interval has an equal probability density, guaranteeing uniform sample coverage for each parameter within its range.

[0166] 2) Generate a sample set

[0167] After dividing the parameter intervals, the LHS method randomly selects one sample point within each interval. Unlike traditional simple random sampling, LHS ensures that only one sample is selected from each interval, thus avoiding duplication of sample points and guaranteeing the uniformity of the parameter space. This method reduces sampling error and improves the statistical validity and computational efficiency of the samples by effectively covering the independent samples of each dimension. Each sampled parameter is then combined with samples of other parameters to form a complete sample set. In this process, each sample represents a different load and structural configuration. In this way, the LHS method can fully represent the entire parameter space with a limited sample size, thereby providing more accurate analysis results.

[0168] The generated sample set was then input into a three-dimensional finite element analysis model. In this model, nonlinear dynamic time history analysis was performed to simulate the dynamic response of the power distribution tower-conductor system under different wind speeds, rainfall intensities, and structural configurations. By generating the sample set using the LHS method, this invention effectively considers the randomness of load and structural parameters, providing an accurate model and analytical framework for the vulnerability analysis of power distribution systems under wind-rain coupled disasters.

[0169] 4. Vulnerability Analysis

[0170] Nonlinear dynamic time history analysis was performed on the "three rods and four wires" finite element model. The calculation duration was 600 s, and the time step was [missing information]. According to equations (5) to (9), the fluctuating wind speed time histories satisfying the target spectrum and spatial coherence characteristics are generated at the selected spatial discrete points; subsequently, the equivalent surface pressure obtained by wind-rain coupling is discretized into nodal concentrated forces and applied to the numerical model, with the load application points as follows: Figure 9 As shown. This example assumes the wind direction is perpendicular to the line, and constructs accordingly. Combine and conduct time history analysis; apply fixed boundaries at both ends of the conductor and at the insulator-crossarm connection to reflect the anchorage constraint conditions.

[0171] This invention selects the middle pole-mid span conductor as the stress observation section on the line side, and simultaneously uses the base of the middle pole as the bending moment observation point on the tower side. The above process is repeated for all "sample" combinations to extract the peak values ​​of each engineering requirement parameter, which are then used for subsequent PDA regression and vulnerability surface construction.

[0172] Based on each The nonlinear dynamic time history results under the combination are substituted into Equation (2) to perform a log-linear model regression with dual intensity measures. Figure 10 and Figure 11 The scatter plots and fitting planes for the conductor tension and tower bending moment are given respectively. The goodness of fit for the two types of models are as follows: and This indicates that the first-order bivariate plane model in the logarithmic domain can explain the sample variation well and has high fitting accuracy.

[0173] The coefficients obtained from regression identification are as follows:

[0174]

[0175]

[0176] Therefore, the conditional transcendence probability of the limiting state LS under any wind speed-rain intensity combination can be obtained:

[0177]

[0178]

[0179] The coefficient comparison shows that the two types of components affect the basic wind speed. The sensitivity of all parameters is significant. In the conductor model... much smaller This indicates that wind speed is the dominant factor within the studied rainfall intensity range; while in the tower model... and At the same magnitude, the amplification effect of wind and rain coupling on the base bending moment is more pronounced.

[0180] Design overturning moment limit With conductor breaking force limit By substituting the values ​​into the dual-IM regression models for both the conductor and the tower, the corresponding conditional exceedance probabilities can be calculated. Based on this, Draw the vulnerable surfaces of the conductors and towers on a plane, such as... Figure 12 and Figure 13 As shown: the longitudinal direction of the curved surface represents the failure probability, and the horizontal direction represents the basic wind speed and rainfall intensity.

[0181] As can be seen from the surface shape:

[0182] 1) The failure probability of the two types of components varies with the basic wind speed The rate of increase is monotonically determined, with wind speed being the dominant controlling factor.

[0183] 2) In the range of low to medium rainfall intensity ( The marginal sensitivity of the failure probability to rainfall intensity is significant, but gradually weakens thereafter, reflecting the influence of the regression coefficients. Compared The secondary importance is particularly evident in the conductor model;

[0184] 3) In the same Below, the overall surface of the tower is higher than that of the conductor, indicating that the base bending moment is more likely to reach the limit state. This pattern is consistent with the peak response transcendence relationship in time history analysis.

[0185] The core technical solution of this invention is a vulnerability analysis method based on dual strength metrics, used to assess the failure probability of power distribution tower-conductor systems under wind-rain coupled disasters. The key technical points of this solution are as follows:

[0186] 1. Dual Intensity Measurement Model: This invention introduces basic wind speed and rainfall intensity as dual intensity measurement factors, overcoming the shortcomings of traditional single intensity measurement methods that cannot accurately reflect the impact of wind-rain combined disasters. By simultaneously considering the impact of wind speed and rainfall intensity on the power distribution tower-conductor system, a more accurate risk assessment of wind-rain coupled disasters is achieved.

[0187] 2. Nonlinear dynamic time history analysis: A three-dimensional finite element analysis model is used to perform nonlinear dynamic time history analysis to simulate the wind-rain load under different wind speeds and rainfall intensities, and extract key engineering requirement parameters (such as conductor axial tension, pole bottom bending moment, etc.) for regression analysis.

[0188] 3. Probabilistic Demand Analysis (PDA): PDA is used to perform regression analysis on the relationship between wind speed and rainfall intensity and engineering demand parameters, constructing a vulnerability function and forming a dual-intensity vulnerability surface. This surface can quantify the failure probability under different disaster scenarios, providing quantitative support for risk assessment and decision-making in power distribution systems.

[0189] 4. Uncertainty Analysis of Load and Structural Parameters: This invention systematically considers the randomness of load and structural parameters, generates a sample set through Latin hypercube sampling (LHS), and comprehensively analyzes the impact of the uncertainty of load and structural parameters on the risk assessment results, thereby improving the reliability and engineering applicability of the assessment.

[0190] The protection points of this invention mainly include the following aspects:

[0191] 1. Dual Intensity Measurement Model: A technical method for assessing the combined impact of wind-rain coupled disasters on the power distribution tower-conductor system by using two intensity measurement factors: basic wind speed and rainfall intensity.

[0192] 2. Wind-rain load calculation method combining nonlinear dynamic time history analysis and finite element model: This section describes the technical steps for calculating loads and extracting key engineering requirements parameters using a finite element analysis model, especially under wind-rain coupling conditions.

[0193] 3. Construction of vulnerability function based on PDA method: This method protects the construction of vulnerability surface through regression analysis, which is used to quantify the probability of structural failure under different combinations of wind speed and rainfall intensity.

[0194] 4. Uncertainty Analysis Method: This method involves modeling the uncertainties of loads and structural parameters and combining them with the Latin hypercube sampling method to analyze their impact on the risk assessment results.

[0195] Through these technical solutions, this invention not only solves the problems of accuracy and uncertainty in wind-rain coupled disaster assessment, but also provides an efficient and real-time risk assessment tool for power distribution systems, which has significant engineering application value.

Claims

1. A method for constructing a vulnerable surface for a power distribution tower conductor system under wind and rain coupling conditions, characterized in that: Specifically, the steps include the following: S1. Using the probabilistic demand analysis method, regression fitting is performed on the relationship between the engineering demand parameter EDP and the dual intensity measurement parameters in the logarithmic domain to construct a vulnerability function. The dual intensity measurement parameters are the basic wind speed and rainfall intensity. S2. Assuming that the vulnerability function follows a log-normal distribution under a given combination of dual strength metric parameters, derive the formula for calculating the conditional failure probability of reaching the specified limit state. S3. Construct a wind-rain coupled load model based on a given combination of dual intensity metric parameters. The wind-rain coupled load model includes a wind load calculation sub-model and a rain load calculation sub-model. The wind load calculation sub-model is obtained by superimposing the average wind and the time history of the spatiotemporally correlated fluctuating wind speed generated by the harmonic superposition method. The rain load calculation sub-model is obtained by integrally calculating the collision force of raindrops of different diameters on the windward projection surface of the structure under given rainfall intensity and basic wind speed conditions. S4. Based on the constructed vulnerability function, wind-rain coupled load model, and failure probability calculation formula, calculate the failure probability of the distribution tower-conductor system reaching the specified limit state for any combination of dual strength measurement parameters. Using the failure probability as the vertical coordinate of the surface and the dual strength measurement parameters as the horizontal and vertical coordinates of the surface, construct a vulnerability surface model under wind-rain coupled disasters to realize the probabilistic vulnerability assessment of the distribution tower-conductor system under wind-rain coupled disasters.

2. The method for constructing a vulnerable curved surface for a power distribution tower conductor system under wind and rain coupling conditions as described in claim 1, characterized in that: The specific details of step S1 are as follows: In the case of a single strength metric parameter IM, the relationship between the engineering requirement parameter EDP and the strength metric parameter IM can be represented by a log-linear model as follows: （1） In the formula and These are the regression coefficients; When considering the two strength metrics, the log-linear model, i.e., the vulnerability function, is: （2） In the formula , , For regression coefficients, The base wind speed, This refers to the intensity of rainfall.

3. The method for constructing a vulnerable surface for a power distribution tower conductor system under wind and rain coupling conditions as described in claim 2, characterized in that: The specific details of step S2 are as follows: Assuming that, given a combination of two strength metrics, the engineering requirement parameter EDP follows a log-normal distribution, the conditional failure probability of reaching a certain limit state LS is expressed as: （3） In the formula It is the standard normal distribution function. ; This indicates that the Engineering Requirements Parameter (EDP) is defined in a given combination of two strength metrics. The logarithmic domain dispersion under the given conditions is calculated from the root mean square of the regression residuals, as follows: (4) In the formula For the sample size, The number of regression parameters, The sample number. For the first Sample project requirement parameters, and The first Individual weather intensity parameters, , , is the regression coefficient.

4. The method for constructing a vulnerable curved surface for a power distribution tower conductor system under wind and rain coupling conditions as described in claim 1, characterized in that: The wind load calculation sub-model described in step S3 is as follows: To accurately reflect the wind characteristics of the power distribution tower-conductor system under typhoon conditions, a spatiotemporally related dynamic wind field is applied to the structure at any height. With time The total wind speed is expressed as （5） In the formula The average wind speed, For pulsating wind speed, Indicates the total wind speed; 1) Average wind speed: The average wind speed is expressed using a power-law profile as follows: （6） In the formula, The average wind speed at a height of 10 m over 10 minutes. This is the ground roughness correction factor. For height; 2) Fluctuating wind speed: The statistical characteristics of fluctuating wind speed are described by both the velocity power spectral density and the spatial coherence function. For the near-surface layer of typhoons, the Davenport spectrum is used, and its scalar spectrum is expressed as follows: （7） In the formula For frequency, This is an empirical coefficient for surface resistance; 3) Numerical synthesis of wind field: The time history of fluctuating wind speed is generated using the harmonic superposition method. According to Shinozuka theory, when the frequency division number... At that time, the first The pulsating wind speed at each observation point is （8） In the formula For discrete angular frequencies, , The lowest frequency, For the maximum frequency, Independent random phase; To calculate the number of points; The frequency of pulsating wind is divided into several categories; and For serial numbers; For time; From the target cross-spectral density matrix Obtained by Cholesky decomposition, Argument angle; 4) Wind load: The nominal wind load acting on a structural member in a free wind field is expressed as... （9） In the formula air density; For structural coefficients; This refers to the drag coefficient; The wind pressure coefficient varies with altitude; The projected area facing the wind; The wind speed at the reference height is the total wind speed.

5. The method for constructing a vulnerable curved surface for a power distribution tower conductor system under wind and rain coupling conditions according to claim 1, characterized in that: The rain load calculation sub-model described in step S3 is as follows: Suppose a raindrop of diameter D is incident on the surface of a structure with a relative velocity, and its incident pressure per unit area is expressed as: （10） In the formula, This is an empirical coefficient; The density of water; The raindrop spectrum, i.e., the number of raindrops per unit volume as a function of... Distribution; The normalized curve of single-droplet collision force in The integral area of ​​the range; For the speed ratio, a segmented empirical formula is used. （11） In the formula The height is the center height of the component. This is the surface roughness correction factor; Effective action time of a single drop Pick （12） The total number of raindrops per unit volume; considering the upper limit of raindrop diameter in nature. have （13） Raindrop spectrum adopts an exponential model （14） In the formula Rainfall intensity, ; At the specified wind speed With rainfall intensity Below, the effect on the windward projection of the component. The equivalent rain load is obtained by integrating over the raindrop size: （15）。 6. A vulnerable curved surface construction system for a power distribution tower conductor system under wind and rain coupling conditions, characterized in that: Including: Vulnerability function construction module: Using the probabilistic demand analysis method, the relationship between the engineering demand parameter EDP and the dual intensity metric parameters is regressed and fitted in the logarithmic domain to construct the vulnerability function. The dual intensity metric parameters are the basic wind speed and rainfall intensity. Failure probability calculation formula derivation module: Assuming that the vulnerability function follows a log-normal distribution under a given combination of dual strength measurement parameters, derive the conditional failure probability calculation formula for reaching the specified limit state; Wind-Rain Coupled Load Model Construction Module: Based on a given combination of dual strength metric parameters, a wind-rain coupled load model is constructed. The wind-rain coupled load model includes a wind load calculation sub-model and a rain load calculation sub-model. The wind load calculation sub-model is obtained by superimposing the average wind and the time history of the spatiotemporally correlated fluctuating wind speed generated using the harmonic superposition method. The rain load calculation sub-model is obtained by integrally calculating the collision force of raindrops of different diameters on the windward projection surface of the structure under given rainfall intensity and basic wind speed conditions. Vulnerability Surface Model Construction Module: Based on the constructed vulnerability function, wind-rain coupled load model, and failure probability calculation formula, for any combination of dual strength metric parameters, the failure probability of the distribution tower-conductor system reaching the specified limit state is calculated. Using the failure probability as the vertical coordinate of the surface and the dual strength metric parameters as the horizontal and vertical coordinates of the surface, a vulnerability surface model under wind-rain coupled disaster is constructed to realize the probabilistic vulnerability assessment of the distribution tower-conductor system under wind-rain coupled disaster.

7. 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 for constructing vulnerable curved surfaces of the power distribution tower conductor system under wind and rain coupling conditions as described in any one of claims 1-5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for constructing vulnerable curved surfaces of the power distribution tower conductor system under wind and rain coupling conditions as described in any one of claims 1-5.

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