Power transmission tower line system loss assessment method considering influence of seismic oscillation incidence angle

Abstract

The invention discloses a power transmission tower line system loss assessment method considering the influence of a seismic oscillation incident angle, and relates to the technical field of power transmission tower safety assessment. According to an actual engineering drawing, a power transmission tower line system structure finite element analysis model is established, modal information of a power transmission tower structure is calculated, and the power transmission tower line system loss is assessed under a selected seismic oscillation intensity level; performing repeated operation on all generated space seismic oscillation of different seismic oscillation incident angles to analyze the structural response of each seismic oscillation incident angle; calculating a vulnerability curve of the structure to obtain a vulnerability curve of the power transmission tower line system structure under the action of a space earthquake considering different seismic oscillation incidence angles, and evaluating the anti-seismic performance of the power transmission tower structure; analyzing earthquake dangerousness under different earthquake motion incidence angles; and analyzing the seismic economic loss based on directivity. According to the evaluation method, the precision, comprehensiveness and engineering practicability of seismic loss evaluation of the power transmission tower line system are remarkably improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power transmission tower safety evaluation, and particularly relates to a power transmission tower line system loss evaluation method considering the influence of seismic motion incidence angle. BACKGROUND

[0002] The power transmission tower system undertakes the activities of power transmission and distribution from the power plant to the end user, plays a vital role in modern society, and is widely regarded as an important part of critical infrastructure, making an important contribution to the high-quality development of economy and society. However, the power transmission tower line system has the characteristics of large flexibility and large span, and due to the strong nonlinearity of the power transmission line, once the power transmission line fails or is damaged, it will directly lead to large-area power outage of the power grid, causing huge economic losses and affecting post-disaster recovery work. Therefore, the power transmission tower structure will inevitably be invaded by earthquake disasters in its whole life cycle, and even may be destroyed under the action of earthquake. The destruction of the power transmission tower structure will not only affect the normal use of the structure and cause great economic losses, but also seriously affect the post-disaster rescue work and cause adverse social impact.

[0003] At present, the seismic analysis and research of the power transmission tower are mostly to input the two horizontal orthogonal components of the seismic motion along the two horizontal principal axes of the structure respectively, and the relevant seismic design specifications also do not make corresponding description on the influence of the seismic motion incidence direction on the seismic performance of the structure. In actual situation, the seismic motion may excite the power transmission tower structure in different directions, therefore, the real seismic motion incidence direction has high uncertainty and is difficult to estimate. At present, the seismic design of the submarine suspension pipeline is basically through the seismic performance of the structure under 0-degree seismic incidence angle, completely ignoring the influence of the seismic motion incidence direction on the whole life seismic performance of the suspension pipeline structure. However, the time, intensity and incidence direction of the earthquake are difficult to predict. Therefore, it is important to provide a power transmission tower line system loss evaluation method considering the influence of seismic motion incidence angle to ensure its safety and functionality. SUMMARY

[0004] The purpose of the present application is to provide a power transmission tower line system loss evaluation method considering the influence of seismic motion incidence angle to solve the problems in the background art.

[0005] To achieve the above-mentioned purpose, the present application provides the following technical scheme: a power transmission tower line system loss evaluation method considering the influence of seismic motion incidence angle, the evaluation method comprising the following steps:

[0006] Step 1: analyze the structural response under different seismic motion incidence angles;

[0007] According to the actual engineering drawings, a finite element analysis model of the transmission tower-line system structure is established, modal information of the transmission tower structure is calculated, and spatial seismic motions of different seismic motion incidence angles are repeatedly generated under selected seismic intensity levels to analyze structural responses at each seismic motion incidence angle;

[0008] Step two: analysis of seismic vulnerability under different seismic motion incidence angles;

[0009] Calculating the vulnerability curve of the structure, obtaining the vulnerability curve of the transmission tower-line system structure under spatial seismic action considering different seismic motion incidence angles, and performing seismic performance evaluation of the transmission tower structure;

[0010] Step three: analysis of seismic risk under different seismic motion incidence angles;

[0011] Step four: analysis of directional seismic economic loss;

[0012] The expected annual loss and life cycle loss indicators are used to evaluate the seismic economic loss of the pile-supported transmission tower-line system.

[0013] Preferably, step one: analysis of structural responses under different seismic motion incidence angles, including the following steps:

[0014] A finite element analysis model of the transmission tower-line system structure is established, and modal information of the transmission tower structure is calculated;

[0015] According to the site information and seismic fortification level of the transmission tower structure, seismic waves that meet the conditions are simulated, and the seismic waves are adjusted to different seismic intensity levels;

[0016] The seismic motion applied to the transmission tower-line system is divided into directions, with an interval of counterclockwise, and the seismic motion incidence angle is calculated;

[0017] The probability of each seismic motion incidence angle occurring within a statistical period, the power spectral density function of seismic motion at different soil depths, and the bidirectional coherence loss function of seismic motion at different site depths are calculated;

[0018] By constructing the site power spectral density function, the transfer function, and the coherence loss function, spatial seismic motions of different seismic motion incidence angles input into the transmission tower-line system are randomly generated using spectral representation method;

[0019] The simulated spatial seismic motions of different seismic motion incidence angles are applied to the finite element model of the transmission tower structure for nonlinear time-history analysis, and the structural responses of the transmission tower-line system to be evaluated are obtained.

[0020] Preferably, the power spectral density function of seismic motion at different soil depths is calculated as follows: , For the first The modulus of a ground motion site transfer function Let be the power spectral density function of the bedrock, and , and yes And the damping ratio of the high-pass filter, and It is the corresponding center frequency. Scaling factor Represents angular frequency, and Equal to 2π times the frequency f, the vertical motion on the bedrock is simulated using the same PSD function, with an amplitude that is 2 / 3 of the horizontal amplitude.

[0021] Preferably, the formula for calculating the bidirectional coherence loss function of seismic motion at different site depths is as follows:

[0022] ; In the formula, i is the imaginary unit. Angular frequency, The horizontal distance between sites A and B is [missing information]. The vertical distance between sites A and B is [missing information]. , It is an attenuation coefficient related to site characteristics and seismic wave propagation. It is a coefficient related to the propagation characteristics of seismic waves. It is a coefficient related to the propagation characteristics of seismic waves. Visual wave velocity;

[0023] , In the formula It is a piecewise function. , , It is a coefficient related to the frequency characteristics of seismic waves. and These are two frequency intervals of a piecewise function, and different coefficients are used depending on the frequency range.

[0024] Preferably, spatial ground motions with simulated incident angles at different ground motions are applied to a finite element model of the transmission tower structure for nonlinear time history analysis to obtain the structural response of the transmission tower-line system to be evaluated, i.e., the peak engineering demand parameters. , It is the first The peak engineering demand parameter values ​​related to damage simulation in the transmission tower are as follows: The first ground motion intensity level Angle of incidence of seismic motion Excited by secondary ground motion It represents the total number of all transmission towers in the transmission tower system under study.

[0025] Preferred, the first The incident angle of each ground motion is expressed as: In the formula, For the first An incident angle of the earthquake;

[0026] The probability of each ground motion incident angle occurring within a statistical period is calculated and expressed as: In the formula, For the first The probability of a seismic event occurring at a given incident angle. Indicates the number of directions of earthquake motion.

[0027] Preferably, step two: analyzing seismic vulnerability under the influence of different ground motion incident angles, including the following steps:

[0028] The damage status of transmission towers is classified into different levels based on the displacement of the tower top;

[0029] Calculate the vulnerability curve of the structure, for the first The first transmission tower is at the Calculate the damage state of the first damage state. Damage probability under a given incident angle of seismic motion;

[0030] By substituting the calculated structural response into the damage probability formula, the vulnerability curves of the transmission tower system structure under spatial seismic action with different ground motion incident angles are obtained.

[0031] Preferably, step three involves analyzing the seismic hazard under different incident angles of ground motion, including the following steps:

[0032] Calculate for a given = When the incident angle of the earthquake is The probability of occurrence, i.e. For the first Each transmission tower is designated Probability of occurrence;

[0033] For the The first transmission tower, in the... At the incident angle of the secondary seismic event, calculations exceeding... average annual probability and in the time interval Below, calculations exceed probability .

[0034] Preferably, the calculation is performed for a given = When the incident angle of the earthquake is The probability of occurrence, i.e. For the first Each transmission tower is designated The probability of occurrence is expressed as:

[0035] ; in, The intensity of the ground motion. The incident angle of the earthquake. It is in a damaged state. Represents probability symbols. This refers to the actual damage condition. The engineering requirement parameters are the response parameters of the structure under seismic loading. This indicates that on the k-th transmission tower, when the strength index is... = And the incident angle of the earthquake is The corresponding engineering requirement parameter values ​​at that time.

[0036] Preferred, the first Directional transmission tower The calculation is as follows:

[0037]

[0038] Based on directionality It can be calculated as follows: , For the first Directional-based expected annual loss of a transmission tower This represents the normalized loss rate under the damaged state. This represents the damage state i and direction of the k-th transmission tower. A certain energy related to loss, This represents the damage state i+1 and direction of the k-th transmission tower. A certain energy related to loss, For the first Each transmission tower is designated probability of occurrence This represents the expected annual loss of the entire power transmission system based on directionality. This indicates the total number of transmission towers;

[0039] No. Directional transmission tower and system From the corresponding Conversion: In the formula For the first Directional-based expected annual loss of a transmission tower This represents the expected annual loss of the entire power transmission system based on directionality. For the first Directional lifecycle loss of a transmission tower This represents the lifecycle loss of the entire power transmission system based on directionality. Lifespan The discount rate.

[0040] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0041] This application establishes a detailed finite element model and calculates modal information. Combined with spatial seismic inputs at different incident angles, it can comprehensively obtain the response characteristics of the structure under various seismic motion directions, revealing the intrinsic relationship between the seismic incident angle and the structural response, and laying a reliable data foundation for subsequent vulnerability and loss assessment.

[0042] Based on the structural response under different incident angles, this application calculates the seismic vulnerability curves that take into account the directional effect, making the seismic performance assessment of transmission tower structures under different seismic motion directions more accurate and scientific, and helping to identify the weak links of the structure in specific seismic motion directions.

[0043] This application analyzes the seismic hazard under different incident angles, so that the overall seismic risk assessment is no longer limited to a single or average ground motion input, but fully considers the actual influence of the direction of seismic wave propagation, thus improving the authenticity and applicability of seismic hazard analysis.

[0044] This application introduces expected annual loss and life cycle loss indicators to quantify the potential losses of transmission tower systems based on seismic motion directionality from an economic perspective. This provides an important basis for seismic fortification decisions, insurance assessments, and post-disaster economic loss predictions, and enhances the resilience management and economic evaluation capabilities of transmission tower structures under earthquake disasters. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0046] Figure 1 This is a flowchart of the evaluation method of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] Example: This example provides a method for assessing the losses of a transmission tower system that considers the influence of the incident angle of seismic motion. Please refer to [link / reference]. Figure 1 As shown, the evaluation method includes the following steps:

[0049] Step 1: Structural response analysis under different incident angles of seismic motion;

[0050] (1) Based on the actual engineering drawings, establish a finite element analysis model of the transmission tower system structure and calculate the modal information of the transmission tower structure;

[0051] (2) Based on the site information and seismic design level of the transmission tower structure, simulate seismic waves that meet the conditions; adjust the seismic waves to different ground motion intensities ( )level;

[0052] (3) Dielectric motions applied to the transmission tower system are divided into There are 1 direction, with a counter-clockwise interval of 1. , No. The incident angle of each ground motion is expressed as: In the formula, For the first An incident angle of the earthquake, Indicates the number of directions of earthquake motion;

[0053] (4) Calculate the probability of each ground motion incident angle occurring within the statistical period, assuming that the probability of all ground motion incident angles occurring is equal, expressed as: In the formula, For the first The probability of a seismic event occurring at a given incident angle. Indicates the number of directions of earthquake motion.

[0054] (5) Calculate the power spectral density (PSD) function of seismic motion at different soil depths. The following formula can be used to calculate it: , For the first The modulus of a ground motion site transfer function This represents the power spectral density function of the bedrock, reflecting the energy distribution characteristics of bedrock seismic motions in the frequency domain. , and yes And the damping ratio of the high-pass filter, and It is the corresponding center frequency. Scaling factor Represents angular frequency, and It is equal to 2π times the frequency f, where frequency f is the conventional frequency measured in Hz. It is a physical quantity that describes the number of repetitions of periodic phenomena (such as earthquake vibrations) per unit time, i.e., the number of vibrations per second. Furthermore, the vertical motion on the bedrock is also simulated using the same PSD function, with an amplitude of 2 / 3 of the horizontal amplitude.

[0055] (6) The bidirectional coherence loss function of seismic motion at different site depths can be calculated using the following formula: ; i is the imaginary unit. Angular frequency, The horizontal distance between sites A and B is [missing information]. The vertical distance between sites A and B is [missing information]. , It is an attenuation coefficient related to factors such as site characteristics and seismic wave propagation. It is a coefficient related to the propagation characteristics of seismic waves. It is a coefficient related to the propagation characteristics of seismic waves. , This mainly describes the influencing factors of seismic wave propagation attenuation or phase changes at different site depths and propagation paths. It is usually related to a specific propagation mechanism of seismic waves (such as the propagation of body waves, surface waves, or reflection and refraction at the interface between different media). Yes Supplementary corrections, , It is closely related to site conditions (such as soil type, overburden thickness, and geotechnical parameters), seismic wave type (such as P-wave, S-wave, and surface wave), and propagation path (horizontal / vertical distance, and media stratification). For example, in a homogeneous hard rock site, , The values ​​are relatively small (e.g., on the order of 0.1 to 0.5); however, in soft soil or complex stratified sites, the values ​​are larger (e.g., on the order of 0.5 to 2.0). The specific value needs to be determined based on site investigation, seismic observation, or numerical simulation results. Visual wave velocity;

[0056] , It is a piecewise function. , , These are coefficients related to the frequency characteristics of seismic waves. Different segments correspond to different coefficient values, used to fit the patterns of coherence changes within different frequency ranges to reflect the differences in the propagation characteristics of seismic waves in the low-frequency and high-frequency bands (such as energy attenuation and phase changes). These coefficients are usually obtained through statistical analysis of seismic ground motion observation data (such as fitting coherence functions to a large number of actual earthquake records), theoretical model derivation (based on wave theory of seismic wave propagation and medium response models), or empirical formula calibration. They need to be adjusted in conjunction with specific site conditions (such as soil layer type and overburden thickness), seismic wave type (such as P-wave, S-wave, and surface wave), and regional geological background (such as seismic zone characteristics). Their values ​​generally do not have fixed universal values ​​and need to be determined based on the seismic ground motion characteristics of the study area, site classification, or numerical simulation results. For example, in a homogeneous hard rock site, the coefficients may take smaller values ​​(such as 0.1 to 1.0), while in soft soil or complex stratified sites, the values ​​may be larger (such as 1.0 to 5.0). Therefore, the values ​​need to be determined through data fitting or literature reference. and These are two frequency intervals of a piecewise function, and different coefficients are used depending on the frequency range.

[0057] (7) By constructing the site power spectral density (PSD) function, transfer function and coherence loss function, a series of spatial ground motions with different incident angles can be randomly generated by using the spectral representation method and input into the transmission tower-line system;

[0058] (8) The simulated spatial ground motions with different incident angles are applied to the finite element model of the transmission tower structure for nonlinear time history analysis to obtain the structural response of the transmission tower line system to be evaluated, namely a series of peak engineering demand parameters. . It is the first Peak engineering demand parameters related to damage simulation in a transmission tower (e.g., tower top displacement, inter-node displacement, and inter-node damage) are calculated in the _th_ ... The first ground motion intensity level Angle of incidence of seismic motion Excited by secondary ground motion It refers to the total number of all transmission towers in the transmission tower line system under study;

[0059] (9) Under the selected seismic intensity level, repeat the above operation for all generated spatial seismic motions with different incident angles to successfully achieve structural response analysis for each seismic motion incident angle.

[0060] Step 2: Seismic vulnerability analysis under the influence of different incident angles of ground motion;

[0061] (10) Determine the damage status of the transmission tower ( Based on the displacement of the tower top, it is divided into basically intact ( Minor injury ), moderate injury ( ), serious injury ( ) and complete collapse ( Four categories;

[0062] (11) The vulnerability curve of the structure is calculated using the following formula: For the first The first transmission tower is at the Each damage state ( ) below, in the Damage probability under a specific earthquake incidence angle The estimate is:

[0063] ;

[0064] ; ; In the formula, This indicates the angle of incidence of the k-th transmission tower during the j-th seismic motion. The structural response parameters (such as strain, displacement, and other damage-related indicators of a certain part of the structure) when a certain damage state is reached under action. This indicates that the k-th transmission tower is in the l-th damage state ( At the j-th incident angle of the ground motion The structural response parameters of the critical state corresponding to the action. The intensity of the ground motion. for A specific value of is used for calculating conditional probability. The cumulative distribution function of the standard normal distribution. and They are respectively and The natural logarithm, and These are linear regression coefficients. To be related to the incident angle of the k-th transmission tower at the j-th seismic motion Under the influence of the action, the standard deviation parameter related to the damage state, For the k-th transmission tower at the j-th seismic incident angle Simulated values ​​of engineering requirement parameters under the action, For the incident angle corresponding to the j-th ground motion The number of samples.

[0065] (12) Substitute the calculated structural response into the above formula to obtain the vulnerability curve of the transmission tower system under the spatial seismic action considering different ground motion incident angles, thereby conducting a seismic performance evaluation of the transmission tower structure.

[0066] Step 3: Seismic hazard analysis under different incident angles of ground motion;

[0067] (13) Calculate for a given = and the angle of incidence of earthquake motion ( )hour The probability of occurrence, i.e. For the first Each transmission tower is designated The probability of occurrence can be calculated using the following formula:

[0068] ; in, The intensity of the ground motion. The incident angle of the earthquake. It is in a damaged state. Represents probability symbols. This refers to the actual damage condition. Engineering requirements parameters are the response parameters of a structure under seismic loading, such as displacement, strain, and acceleration. This indicates that on the k-th transmission tower, when the strength index is... = And the incident angle of the earthquake is The corresponding engineering requirement parameter values ​​at that time.

[0069] (14) The purpose of earthquake risk analysis is to indicate the risk level within a reference time period (in years). Exceeding the given The probability of a magnitude 1 earthquake; for the 1st... The first transmission tower, in the... At the incident angle of the second seismic event, exceeding average annual probability and in the time interval Below, exceeding probability They can be defined as follows:

[0070] ,

[0071] , ; in, The intensity of the ground motion. The incident angle of the earthquake. This indicates the angle of incidence of the k-th transmission tower during the j-th seismic motion. The structural response parameters (such as strain, displacement, and other damage-related indicators of a certain part of the structure) when a certain damage state is reached under action. This indicates that the k-th transmission tower is in the l-th damage state ( At the j-th incident angle of the ground motion The structural response parameters of the critical state corresponding to the action. It is a site for the power transmission tower system. More than a specific The annual probability, This is a reference time period. and These are the scale and shape parameters of the ET-II distribution, respectively.

[0072] Through the above calculation process, the seismic hazard of the transmission tower system can be systematically analyzed.

[0073] Step 4: Directional earthquake economic loss analysis;

[0074] (15) Define the economic loss function as the expected normalized loss under the damaged state. ,when , No. When the incident angle of the ground motion is 1, the 2nd earthquake is 3. Expected normalized loss of each transmission tower It can be calculated using the following formula:

[0075]

[0076] In the formula, basically intact ( Minor damage () ), moderate damage ( ), severely damaged ( ) and complete collapse ( When ), the relevant The percentages were 3%, 11%, 26%, 46%, and 68%, respectively. Set it to 0.5. This represents the normalized loss rate under the damaged state. For the first Each transmission tower is designated The probability of occurrence is used to adjust the relationship between expected losses and earthquake intensity indices and incident angle. This represents a quantity related to economic loss when the k-th transmission tower is in the l-th damage state, such as the expected loss correction value in the l-th damage state.

[0077] (16) Two risk-based economic indicators are used to assess the seismic economic losses of pile-supported transmission tower systems, namely, the expected annual loss ( ) and lifecycle loss ( ).

[0078] No. Directional transmission tower It can be calculated as follows:

[0079]

[0080] Based on directionality It can be calculated as follows: , For the first Directional-based expected annual loss of a transmission tower This represents the normalized loss rate under the damaged state. This represents the damage state i and direction of the k-th transmission tower. A certain energy related to loss, This represents the damage state i+1 and direction of the k-th transmission tower. A certain energy related to loss, For the first Each transmission tower is designated probability of occurrence This represents the expected annual loss of the entire power transmission system based on directionality. This indicates the total number of transmission towers.

[0081] This energy refers to the energy generated by earthquakes and other forces on transmission towers under specific damage states (such as the degree of structural damage) and directions, which is related to structural failure and functional loss. Examples include structural vibration energy and energy dissipation due to material damage. This energy can be identified by analyzing the structural dynamic response of the transmission tower (such as strain energy and kinetic energy), damage evolution models (such as energy consumption in fatigue damage and brittle damage), or by referring to the definition of structural loss energy in similar projects (such as the relationship between energy dissipation and damage degree in an earthquake). The specific connotation of this energy can usually be determined by existing research results. For example, it can be the energy dissipation per unit time or per unit displacement of the transmission tower under the damage state and direction (such as damping energy dissipation and plastic energy dissipation), or the energy difference before and after structural damage (an energy index reflecting the degree of damage).

[0082] (17) No. Directional transmission tower and system , can be obtained from the corresponding The conversion is shown below: In the formula For the first Directional-based expected annual loss of a transmission tower This represents the expected annual loss of the entire power transmission system based on directionality. For the first Directional lifecycle loss of a transmission tower This represents the lifecycle loss of the entire power transmission system based on directionality. Lifespan The discount rate. and The values ​​are assumed to be 5% and 50 years, respectively.

[0083] (18) The expected annual loss of the transmission tower is calculated. ) and lifecycle loss ( This allows for the assessment of the economic losses from earthquakes affecting the transmission tower and line system.

[0084] Specifically:

[0085] 1) Assuming a new power transmission tower system is being constructed in an earthquake-prone area, traditional assessment methods do not consider the influence of the seismic incident angle. Conventional assessments often conclude that the transmission tower exhibits a relatively small structural response during an earthquake, thus assuming its structural safety. However, by establishing a finite element analysis model of this transmission tower system structure, the structural response under different seismic incident angles (e.g., 0°, 30°, 45°, 60°, 90°) is analyzed. The results show that when a 45° seismic incident angle is considered, the stress response of certain critical components of the transmission tower increases significantly, far exceeding the results of traditional assessments. This indicates that traditional methods are inaccurate due to neglecting the directionality of seismic motion, while the method presented in this application more accurately reflects the true structural response during an earthquake, improving the reliability of the assessment and providing engineers with a more accurate understanding of the transmission tower's safety.

[0086] 2) Taking a real-world power transmission tower system as an example, previous seismic assessments of this tower did not analyze different ground motion incident angles; the overall seismic performance of the tower was simply considered good. Analysis of the dynamic response under different incident angles revealed that when a ground motion occurred at a 60° angle, the maximum stress values ​​of the 4th and 6th main structural members on the upper part of the tower were significantly higher than at other angles. This clearly indicates that these two main structural members are the weak points of the tower under specific ground motion directions. Based on this, the power sector can specifically reinforce these two main structural members instead of unnecessarily reinforcing the entire tower, saving costs and improving the tower's seismic resistance.

[0087] 3) Enhancing disaster prevention decision support capabilities

[0088] In a large power grid, there are multiple transmission lines and numerous transmission towers. Suppose an earthquake is about to occur in a certain area, and the magnitude and epicenter location have been preliminarily determined. Traditional assessment methods can only roughly determine which areas of transmission towers are likely to be damaged, but cannot specify the exact extent and priority of damage. However, using the method proposed in this application, on the one hand, based on vulnerability analysis under different seismic incident angles, it is possible to predict in advance which transmission towers and poles are more susceptible to damage under the earthquake, providing a basis for precise pre-earthquake fortification, such as additional reinforcement or maintenance of these vulnerable transmission towers. On the other hand, after the earthquake, the power sector can use this method to quickly assess the damage to different lines and towers based on real-time earthquake information. For example, if analysis reveals that several transmission towers on a certain line have an extremely high risk of damage under the current seismic incident angle, the power sector can prioritize inspection teams to inspect these towers and promptly carry out emergency repairs, significantly shortening power restoration time and improving the resilience and rapid recovery capability of the power grid.

[0089] Application Scenario 1:

[0090] A high-voltage transmission line is planned and constructed in a seismically active plateau region. This region has historically experienced several moderate to strong earthquakes, and the direction of seismic wave propagation is complex and variable. Traditional seismic design typically only considers horizontal bidirectional seismic input, neglecting the directional influence of the seismic incident angle, which may lead to an overestimation of the actual seismic resistance of key components (such as the main tower structure and joint connections). By employing this assessment method, firstly, based on the topography, geology, and site conditions of the areas traversed by the transmission line, information on soil profiles, mechanical parameters, and structural layout is collected to establish a high-precision finite element model of the transmission tower system and calculate its modal characteristics. Subsequently, spatial ground motions at different incident angles (such as 0°, 30°, 45°, 60°, 90°, etc.) are simulated, and peak engineering demand parameters of the transmission tower at each angle (such as tower top displacement, key node stress, etc.) are obtained through nonlinear time history analysis. Furthermore, based on structural response data at different incident angles, vulnerability curves considering directional effects are calculated, identifying that the stress response of a certain main material of the tower body at a specific incident angle (such as 45°) is significantly higher than that in other directions, and the probability of exceeding the preset damage threshold (such as moderate or severe damage) is relatively high. Based on this result, designers can specifically strengthen the cross-sectional dimensions of the main material or optimize the node connection structure. At the same time, multi-directional seismic input requirements can be incorporated into the seismic fortification standards to improve the safety redundancy of the overall line in complex seismic environments, avoid structural failures caused by directional blind spots, and ensure the power grid's continuous power supply capability after an earthquake.

[0091] Application Scenario 2:

[0092] In a province prone to earthquakes, a power transmission line that had been in operation for many years showed abnormalities in some sections during a recent earthquake (such as tower tilting and conductor strand breakage), but the overall damage pattern was still unclear. Traditional assessment methods, which do not take into account the differences in the incident angle of the ground motion, make it difficult to accurately determine which tower locations or components were most severely damaged, which may lead to inefficient allocation of emergency resources (such as over-inspecting low-risk towers and neglecting high-risk towers). By applying this method, firstly, based on the original design drawings and on-site measured data (such as tower height, span, material properties, etc.), the finite element model of the line is reconstructed and the modal information of the current structure is determined. Combining the source mechanism and site conditions, the method simulates the multi-angle ground motion inputs that may exist in actual earthquake events (e.g., the main incident angle range is estimated to be 30°-60° based on the epicenter location), and adjusts the seismic waves to the intensity level actually observed. Nonlinear time history analysis is performed on the multi-angle ground motion input to the finite element model to obtain the structural response of each tower at different incident angles (such as tower top displacement, strain of key components, etc.). Further, based on predefined damage states (basically intact, minor damage, moderate damage, severe damage, complete collapse) and corresponding vulnerability curves, the damage probability of each tower within the incident angle range of this ground motion is calculated. Simultaneously, using directional expected annual loss (EAL) and life-cycle loss (LCL) indices, the potential economic losses (such as repair costs, power outage losses, etc.) caused by ground motions at specific incident angles are quantified for different tower locations. Ultimately, based on the assessment results, the power sector can prioritize on-site inspections and emergency reinforcement of towers with a high probability of damage (e.g., more than 60% reaching moderate or higher damage) or high economic loss (e.g., ranking in the top 10% of EAL), quickly identifying the "critical few" with the highest risk, avoiding the waste of resources caused by blind investigation, and providing data support for the development of scientific post-disaster recovery plans (e.g., prioritizing the restoration of power supply to high-risk lines), significantly improving the resilience management and emergency response efficiency of the power grid after the earthquake.

[0093] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0094] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion, characterized in that: The evaluation method includes the following steps: Step 1: Analyze the structural response under different incident angles of seismic motion; Based on the actual engineering drawings, a finite element analysis model of the transmission tower system structure was established, and the modal information of the transmission tower structure was calculated. Under the selected seismic intensity level, the spatial seismic motions with different incident angles were repeatedly run to analyze the structural response at each incident angle. Step 2: Analyze seismic vulnerability under the influence of different incident angles of ground motion; The vulnerability curve of the structure is calculated to obtain the vulnerability curve of the transmission tower system under the spatial seismic action considering different ground motion incident angles, and to evaluate the seismic performance of the transmission tower structure. Step 3: Analyze the seismic hazard under different incident angles of ground motion; Step 4: Analyze the economic losses from earthquakes based on directionality; The expected annual loss and life-cycle loss indices are used to assess the seismic economic losses of pile-supported transmission tower systems.

2. The method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion according to claim 1, characterized in that: Step 1: Analyze the structural response under different incident angles of seismic motion, including the following steps: A finite element analysis model of the transmission tower structure was established, and the modal information of the transmission tower structure was calculated. Based on the site information and seismic design level of the transmission tower structure, simulate seismic waves that meet the conditions and adjust the seismic waves to different ground motion intensity levels. The seismic motions applied to the transmission tower system are divided into... There are 1 direction, with a counter-clockwise interval of 1. Calculate the first An incident angle of the earthquake; Calculate the probability of each ground motion incident angle occurring within a statistical period, the power spectral density function of seismic motion at different soil depths, and the bidirectional coherence loss function of seismic motion at different site depths. By constructing the site power spectral density function, transfer function and coherence loss function, spatial ground motions with different incident angles of ground motions are randomly generated and input into the transmission tower-line system using spectral representation. The simulated spatial ground motions with different incident angles were applied to the finite element model of the transmission tower structure for nonlinear time history analysis, and the structural response of the transmission tower line system to be evaluated was obtained.

3. The method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion according to claim 2, characterized in that: The power spectral density function of seismic motion at different soil depths is calculated using the following expression: , For the first The modulus of the site transfer function of a seismic motion Let be the power spectral density function of the bedrock, and , and yes And the damping ratio of the high-pass filter, and It is the corresponding center frequency. Scaling factor Represents angular frequency, and Equal to 2π times the frequency f, the vertical motion on the bedrock is simulated using the same PSD function, with an amplitude that is 2 / 3 of the horizontal amplitude.

4. The method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion according to claim 3, characterized in that: The formula for calculating the bidirectional coherence loss function of seismic motion at different site depths is as follows: ； In the formula, i is the imaginary unit. Angular frequency, The horizontal distance between sites A and B is [missing information]. The vertical distance between sites A and B is [missing information]. , It is an attenuation coefficient related to site characteristics and seismic wave propagation. It is a coefficient related to the propagation characteristics of seismic waves. It is a coefficient related to the propagation characteristics of seismic waves. Visual wave velocity; ， In the formula It is a piecewise function. , , It is a coefficient related to the frequency characteristics of seismic waves. and These are two frequency intervals of a piecewise function, and different coefficients are used depending on the frequency range.

5. The method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion according to claim 3, characterized in that: Nonlinear time-history analysis was performed on a finite element model of the transmission tower structure by applying simulated spatial ground motions with different incident angles. This yielded the structural response of the transmission tower-line system under evaluation, i.e., the peak engineering demand parameters. , It is the first The peak engineering demand parameter values ​​related to damage simulation in the transmission tower are as follows: The first ground motion intensity level Angle of incidence of seismic motion Excited by secondary ground motion It represents the total number of all transmission towers in the transmission tower system under study.

6. The method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion according to claim 2, characterized in that: No. The incident angle of each ground motion is expressed as: In the formula, For the first An incident angle of the earthquake; The probability of each ground motion incident angle occurring within a statistical period is calculated and expressed as: In the formula, For the first The probability of a seismic event occurring at a given incident angle. Indicates the number of directions of earthquake motion.

7. The method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion according to claim 1, characterized in that: Step 2: Analyze seismic vulnerability under different incident angles of ground motion, including the following steps: The damage status of transmission towers is classified into different levels based on the displacement of the tower top; Calculate the vulnerability curve of the structure, for the first The first transmission tower is at the Calculate the damage state of the first damage state. Damage probability under a given incident angle of seismic motion; By substituting the calculated structural response into the damage probability formula, the vulnerability curves of the transmission tower system structure under spatial seismic action with different ground motion incident angles are obtained.

8. The method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion according to claim 1, characterized in that: Step 3: Analyze the seismic hazard under different incident angles of ground motion, including the following steps: Calculate for a given = When the incident angle of the earthquake is The probability of occurrence, i.e. For the first Designated for each transmission tower Probability of occurrence; For the The first transmission tower, in the... At the incident angle of the secondary seismic event, calculations exceeding... average annual probability and in the time interval Below, calculations exceed probability .

9. The method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion according to claim 8, characterized in that: Calculate for a given = When the incident angle of the earthquake is The probability of occurrence, i.e. For the first Designated for each transmission tower The probability of occurrence is expressed as: ； in, The intensity of the ground motion. The incident angle of the earthquake. It is in a damaged state. Represents probability symbols. This refers to the actual state of damage. The engineering requirement parameters are the response parameters of the structure under seismic loading. This indicates that for the k-th transmission tower, when the strength index is... = And the incident angle of the earthquake is The corresponding engineering requirement parameter values ​​at that time.

10. The method for assessing the loss of a transmission tower system considering the influence of the incident angle of seismic motion according to claim 1, characterized in that: No. Directional transmission tower The calculation is as follows: Based on directionality It can be calculated as follows: , For the first Directional-based expected annual loss of a transmission tower This represents the normalized loss rate under the damaged state. This represents the damage state i and direction of the k-th transmission tower. A certain energy related to loss, This represents the damage state i+1 and direction of the k-th transmission tower. A certain energy related to loss, For the first Designated for each transmission tower probability of occurrence This represents the expected annual loss of the entire power transmission system based on directionality. This indicates the total number of transmission towers; No. Directional transmission tower and system From the corresponding Conversion: In the formula For the first Directional-based expected annual loss of a transmission tower This represents the expected annual loss of the entire power transmission system based on directionality. For the first Directional lifecycle loss of a transmission tower This represents the lifecycle loss of the entire power transmission system based on directionality. Lifespan The discount rate.

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