Transmission Tower Collapse Risk Prediction Method Considering Cumulative Damage during Typhoon

Abstract

The present invention discloses a method for predicting the collapse risk of transmission towers considering the cumulative damage during typhoon processes, including: modeling the time-varying risk assessment process of transmission towers as a Markov process, establishing a transfer probability matrix of transmission towers and determining the corresponding relationship between the vulnerability curve and each element in the transfer probability matrix; based on multi-state vulnerability, according to the established risk prediction model, using finite element numerical analysis, performing limit state definition, wind-induced response analysis and statistical analysis fitting to obtain a multi-state transmission tower vulnerability curve library; combining the time-varying wind field prediction information, obtaining the transfer probabilities between various states of the transmission tower from the vulnerability curve library, and filling the transfer probabilities between various states of the transmission tower into the transfer probability matrix to realize the time-varying prediction of the collapse probability of the transmission tower and the failure probability of the transmission line. The present invention considers the possible initial damage of the transmission tower during the prediction process and realizes a more reliable prediction of the collapse risk of the transmission tower.

Description

Technical Field

[0001] The present invention relates to the technical field of power system disaster risk warning, and particularly relates to a method for predicting the collapse risk of transmission towers considering the cumulative damage during typhoon processes. Background Technique

[0002] Electric energy is one of the most important energy sources in modern society. The functions of key infrastructures such as transportation, water conservancy, healthcare, and information technology highly depend on the supply of electric energy. Currently, high-voltage transmission lines supported by transmission towers are usually used to transmit a large amount of electric power. Strong winds caused by typhoons can lead to the collapse of transmission towers, resulting in a large-scale power grid paralysis. The power interruption caused by the wind-induced damage of transmission towers under typhoons will also affect the operation of various infrastructures, as well as disaster assistance and subsequent construction, resulting in serious secondary disasters and social and economic losses. Different from other sudden disasters, typhoons are predictable, and the duration of a typhoon is usually about 3 to 10 days. Its predictability and persistence allow people to have a relatively long time for pre-disaster and in-disaster emergency responses, especially providing a valuable time window for the risk assessment of transmission towers. The prediction of the risk of transmission towers can not only provide decision-making support for power management in disaster scenarios, thereby narrowing the spatio-temporal scope of power failures, shortening the post-disaster repair time, and reducing the social and economic losses caused by power outages.

[0003] The vulnerability model of transmission towers is an important tool for studying the performance and risk of regional power infrastructures under strong wind disasters. It pre-positions a large number of mechanical analyses and complicated finite element processes, and can conveniently and quickly give the probability of damage or failure of transmission towers at a given wind speed, and predict the damage points before the transmission towers collapse. Compared with some statistical prediction methods based on disaster damage data, the vulnerability model of transmission towers has the advantage of considering physical mechanisms and is applicable to situations where there is no large amount of disaster damage data. Based on the vulnerability model of transmission towers and combined with time-varying wind speed and wind direction information, the collapse probability of transmission towers at future corresponding moments can be obtained, realizing the real-time risk assessment of the transmission system during typhoon processes.

[0004] According to full-scale tests, numerical simulations, and engineering practices, it has been found that during a continuous typhoon process, transmission towers may exist in three states: intact state, collapsed state, and intermediate damage state. Among them, the damage state of the tower refers to the state where component failures occur in the transmission tower, but this failure will not cause overall collapse and will not affect the power transmission of the transmission line. Instead, it may be that some members break or residual deformation remains, leaving the transmission tower in a state of being damaged but not collapsed. During the typhoon process, in addition to the collapse damage of the transmission tower, attention also needs to be paid to the damage of the transmission tower. For slightly or moderately damaged transmission towers that are damaged but not collapsed, although they can still temporarily undertake the task of power transmission, a typhoon is a continuous process, and the damage caused by the deformation of members and node failures in the structure will reduce the reliability of the transmission tower under the action of continuous strong winds. However, currently, when applying vulnerability to predict the risk of transmission towers during the typhoon process, only the probability of the transmission tower changing from the intact state to the damaged or collapsed state is considered at each time point, while the probability of the transmission tower changing from the damaged state to the collapsed state during the typhoon process is not considered. Ignoring this cumulative damage of the transmission tower during the typhoon process may lead to a systematic underestimation of the collapse risk of the transmission tower, non-conservatively affecting the analysis of subsequent power grid states and the assessment of the resources and time required for power transmission restoration. Summary of the Invention

[0005] In order to overcome the above technical deficiencies, the present invention provides a method for predicting the collapse risk of transmission towers considering cumulative damage during the typhoon process.

[0006] Term Explanation:

[0007] 1. TPM: Transition Probability Matrix, the transition probability matrix.

[0008] 2. FEM: Finite Element Model, finite element modeling.

[0009] 3. Pushover analysis: Nonlinear static analysis.

[0010] 4. CDF: Cumulative Distribution Function, the cumulative distribution function.

[0011] The technical solution adopted by the present invention to overcome its technical problems is as follows:

[0012] A method for predicting the collapse risk of transmission towers considering cumulative damage during the typhoon process, comprising the following steps:

[0013] S1. Establish a risk prediction model based on Markov property: Assume that there are three states of transmission towers during typhoon processes, namely intact state, damaged state, and collapsed state. Model the time-varying risk assessment process of transmission towers as a Markov process, then establish a transition probability matrix for transmission towers and determine the corresponding relationship between the vulnerability curve and each element in the transition probability matrix;

[0014] S2. Establish a vulnerability curve library for multi-state transmission towers: Based on multi-state vulnerability, according to the risk prediction model based on Markov property established in step S1, use finite element numerical analysis to perform limit state definition, wind-induced response analysis, and statistical analysis fitting to obtain a vulnerability curve library for multi-state transmission towers;

[0015] S3. Combine the time-varying wind field prediction information, obtain the transition probabilities between various states of the transmission tower from the vulnerability curve library of multi-state transmission towers obtained in step S2, and then fill the transition probabilities between various states of the transmission tower into the transition probability matrix established in step S1, so as to realize the time-varying prediction of the collapse probability of the transmission tower and the failure probability of the transmission line.

[0016] Furthermore, step S1 includes:

[0017] S11. Assume that there are three states of transmission towers during typhoon processes, namely intact state, damaged state, and collapsed state;

[0018] S12. Assume that the probability of the transmission tower being in a certain state at the current moment only depends on the state of the transmission tower at the previous moment, and model the time-varying risk assessment process of the transmission tower as a Markov process;

[0019] S13. According to the total probability formula, establish a transition probability matrix for the transmission tower at any moment;

[0020] S14. Determine the corresponding relationship between the vulnerability curve and each element in the transition probability matrix.

[0021] Furthermore, step S1 specifically includes the following:

[0022] S11. Assume that there are three states of transmission towers during typhoon processes, namely intact state, damaged state, and collapsed state, denoted as 、 、 ;

[0023] S12. Assume that the probability of the transmission tower being in a certain state at the current moment only depends on the state of the transmission tower at the previous moment , and model the time-varying risk assessment process of the transmission tower as a Markov process:

[0024] (1)

[0025] In formula (1), is the probability that the transmission tower is in various states at time; is the probability that the transmission tower transfers from the state at the previous moment to the state at the current time. Among them, , ;

[0026] The probability that the transmission tower is damaged at time and collapses at time is expressed as: , and this probability is related to the wind load intensity at time. The influencing factors of the wind load include wind speed and wind direction. Then, let this probability be a function of wind speed and wind direction , expressed as:

[0027] (2)

[0028] In formula (2), is the predicted wind speed at time; is the predicted wind direction at time, abbreviated as , and its subscript

[0029] S13 means that the transmission tower is in a sound, damaged or collapsed state. Among them, the damaged state includes multiple types of damaged states, expressed as , represents the type of damaged state. Let represent the probability of being in state at time, that is . Among them, , then the state probability vector of the transmission tower at time is:

[0030] (3)

[0031] Among them, for any time, it satisfies , and the initial state probability vector of the transmission tower π 0 = [ π O 0 , π D 1 0 , π D 2 0 ,…, π D n 0 , π C 0 ] T For [1, 0,0,…,0, 0] T , assume that the initial state of the transmission tower is in a sound and undamaged state;

[0032] According to the total probability formula, establish the transition probability matrix of the transmission tower at any time to realize the multi-state risk prediction of the transmission tower at continuous times. Assume that there is no mutual transfer between various damage states of the transmission tower, then there are:

[0033] (4)

[0034] (5)

[0035] In formula (4), represents the probability that the transmission tower remains sound and undamaged at time while in the sound and undamaged state; represents the probability that the transmission tower suffers the th type of damage at time while in the sound state, ; represents the probability that the transmission tower collapses at time while in the sound state; represents the probability that the transmission tower remains in the th type of damage state at time while in the th type of damage state; represents the probability that the transmission tower collapses at time while in the th type of damage state; represents the probability that the transmission tower returns to the sound and undamaged state at time while in the th type of damage state; represents the probability that the transmission tower returns to the sound and undamaged state at time while in the collapsed state; represents the probability that the transmission tower remains collapsed at time while in the collapsed state;

[0036] In formula (5), represents the state probability vector of the transmission tower at time ;

[0037] S14. Describe the probability of damage or failure of the transmission tower structure under different load intensities through the vulnerability curve, denoted as the exceedance probability. The exceedance probability of damage or failure of the transmission tower is expressed as follows:

[0038] (6)

[0039] In formula (6), represents the response of the structure under this load intensity; is the limit state index of the structural response, including the limit state index of the damage state and the limit state index of the collapse state ; There is a corresponding relationship between the elements in the transition probability matrix and the exceedance probability of the transmission tower in the previous state under different load intensities as shown in formulas (7)-(11). The transition probability matrix is filled through vulnerability:

[0040] (7)

[0041] (8)

[0042] (9)

[0043] (10)

[0044] (11)

[0045] The influencing factors of different damage states of the transmission tower at least include the change of the wind direction angle. It is assumed that only a certain type of damage occurs under a specific wind direction angle. Use to represent the damage state the set of wind attack angles when occurs, then:

[0046] (12).

[0047] Furthermore, step S2 includes:

[0048] S21. Establish a finite element numerical simulation model of the transmission tower;

[0049] S22. Use a certain threshold of the displacement at the top of the transmission tower as the limit state index to determine the damage state and collapse state of the transmission tower described in step S1;

[0050] S23. Use the linear filtering method to generate random wind speed time history samples of different wind speeds as the input for the dynamic time history analysis of the transmission tower line system, and take the maximum displacement at the top of the transmission tower in the wind-induced response time history as the wind-induced response of the transmission tower;

[0051] S24. Statistically analyze the maximum displacement at the top of the transmission tower under different wind speed time history samples, compare it with the limit state index set in step S22, statistically analyze the damage or collapse probability of the transmission tower under different wind speeds, and use the cumulative distribution function of the lognormal distribution to fit and obtain the vulnerability curve library.

[0052] Further, step S21 specifically includes: establishing a numerical simulation model of a transmission tower and a numerical simulation model of a transmission tower line system in a finite element software respectively.

[0053] Further, step S22 specifically includes:

[0054] (1) For the damage state, define the damage state of the transmission tower as: the critical state where buckling of a member first appears in the transmission tower; the member where buckling first appears is the damaged member of the transmission tower, and different damaged members correspond to different damage states, and use the top displacement of the transmission tower in this state as the limit index of this type of damage state ; judge whether each member of the transmission tower buckles through formula (13):

[0055] (13)

[0056] In formula (13), is the axial compressive force received by the member of the transmission tower; is the cross-sectional area of the member of the transmission tower; is the design value of tensile, compressive and flexural strength; is the stability coefficient of the axially compressed member of the transmission tower;

[0057] During a typhoon, when the wind direction changes, it will cause changes in the magnitude and spatial distribution of the wind load, resulting in different damage paths and affecting the damaged components of the transmission tower. Therefore, combine the Pushover analysis results to check the damage state of the transmission tower, where Pushover analysis represents nonlinear static analysis; at preset angle intervals, there are several types of damage states at wind attack angles from 0° to 360°. Obtain a numerical simulation model of the transmission tower with certain initial damage through the model correction method of reducing the elastic modulus of the damaged member, so as to study the vulnerability of the transmission tower from the damage state to the collapse state;

[0058] (2) For the collapse state, determine the limit state index of the collapse state of the transmission tower according to the Pushover curve The numerical relationship with the tower height is applicable to transmission towers in a sound state and transmission towers in a damaged state.

[0059] Further, step S23 specifically includes:

[0060] First, use the linear filtering method to generate random wind speed time history samples with different wind speeds, and calculate them as the corresponding dynamic wind loads, which are used as the input for the dynamic time history analysis of the transmission tower line system; take the maximum top displacement of the transmission tower in the response time history as the wind-induced response of the transmission tower;

[0061] Then, for each wind speed, a number of wind speed time histories are generated, corresponding to a number of wind-induced response samples, and then the sample size is determined through sensitivity analysis.

[0062] Further, in step S24, when fitting the vulnerability curve of the transmission tower, it is ensured that the vulnerability curve of the damaged state transmission tower is steeper than that of the intact transmission tower, that is, the standard deviation of the vulnerability curve is fitted with the cumulative distribution function of the lognormal distribution is: , where represents the standard deviation of the vulnerability curve , represents the standard deviation of the vulnerability curve . In order to prevent the collapse probability of the intact transmission tower in the probability interval [0, 0.2] from exceeding that of the damaged state transmission tower, formula (14) is used to replace formula (8):

[0063] (14).

[0064] Further, step S3 includes:

[0065] S31. According to the time-varying wind field prediction information, at a certain prediction time step , the wind attack angle and wind speed are substituted into the corresponding vulnerability curve to obtain the value of each element in the transition probability matrix ;

[0066] S32. Repeat step S31 to obtain at each prediction time step;

[0067] S33. Starting from the intact state of the transmission tower with an initial probability of π 0 = [1, 0,0,…,0, 0] T , multiply by , , , to obtain . The updated is used to provide the time-varying collapse probability of the transmission tower considering cumulative damage, and the collapse probability of each transmission tower is used to predict the failure probability of the transmission line in the target area.

[0068] Further, in step S33, the obtained collapse probabilities of each transmission tower are used to predict the failure probability of the transmission line in the target area, which is expressed as:

[0069] (15)

[0070] In formula (15), represents the failure probability of the transmission line at the moment ; represents the number of transmission towers on the transmission line ; represents the collapse probability of the transmission tower on the transmission line at the moment .

[0071] The beneficial effects of the present invention are as follows:

[0072] 1. Traditional risk prediction methods only consider the probability of a transmission tower collapsing from a sound state at each moment, but ignore the intermediate damage state of the transmission tower during a typhoon, resulting in a systematic underestimation of the time-varying collapse risk of the transmission tower; the risk prediction method considering the cumulative damage of the transmission tower proposed by the present invention combines mechanical analysis and considers the possible initial damage of the transmission tower during the prediction process, achieving a more reliable prediction of the collapse risk of the transmission tower.

[0073] 2. Different from a large number of prediction methods that only focus on the collapse of transmission towers, the present invention can also predict the damage risk of transmission towers and determine vulnerable lines, which helps relevant decision-making departments make decisions such as optimizing material allocation and scheduling in response to typhoon disasters, and is of great significance for improving the emergency response ability of the power grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a schematic diagram of the method for predicting the collapse risk of a transmission tower considering cumulative damage during a typhoon according to an embodiment of the present invention.

[0075] Figure 2 is a numerical simulation model of the transmission tower according to an embodiment of the present invention.

[0076] Figure 3 is a numerical simulation model of the transmission tower line system according to an embodiment of the present invention.

[0077] Figure 4 are the front view, side view and sectional view of the damaged transmission tower under a 0° wind attack angle according to an embodiment of the present invention.

[0078] Figure 5 are the front view, side view and sectional view of the damaged transmission tower under 30° and 60° wind attack angles according to an embodiment of the present invention.

[0079] Figure 6 are the front view, side view and sectional view of the damaged transmission tower under a 90° wind attack angle according to an embodiment of the present invention.

[0080] Figure 7 The front view, side view and sectional view of the damaged transmission tower at a wind attack angle of 120° according to the embodiment of the present invention.

[0081] Figure 8 The front view, side view and sectional view of the damaged transmission tower at a wind attack angle of 150° according to the embodiment of the present invention.

[0082] Figure 9 The front view, side view and sectional view of the damaged transmission tower at a wind attack angle of 180° according to the embodiment of the present invention.

[0083] Figure 10 The Pushover curve and the displacement of the top of the collapsed transmission tower at a wind attack angle of 0° - 90° according to the embodiment of the present invention.

[0084] Figure 11 The Pushover curve and the displacement of the top of the collapsed transmission tower at a wind attack angle of 90° - 180° according to the embodiment of the present invention.

[0085] Figure 12 The collapse vulnerability curve of the intact transmission tower at a wind attack angle of 0° with different sample sizes according to the embodiment of the present invention.

[0086] Figure 13 Under the most unfavorable wind attack angle according to the embodiment of the present invention , , , , A total of 5 types of state transition vulnerability curves.

[0087] Figure 14 The wind speed and wind direction forecast information map for the next 12 hours at the location of the exemplary single tower according to the embodiment of the present invention.

[0088] Figure 15 The comparison chart of the prediction results of a single transmission tower by the method considering cumulative damage and not considering cumulative damage according to the embodiment of the present invention.

[0089] Figure 16 The probability map of a single transmission tower in different states at different times according to the embodiment of the present invention. Detailed implementation manners

[0090] To facilitate better understanding of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The following is only exemplary and does not limit the protection scope of the present invention.

[0091] The present invention discloses a method for predicting the collapse risk of a transmission tower considering cumulative damage during a typhoon process, asFigure 1 As shown below, the steps are as follows:

[0092] S1. Establish a risk prediction model based on Markov property: Assume that there are three states of transmission towers during typhoon processes, namely intact state, damaged state, and collapsed state. Model the time-varying risk assessment process of transmission towers as a Markov process, then establish a transmission tower transition probability matrix and determine the corresponding relationship between the vulnerability curve and each element in the transition probability matrix;

[0093] S2. Establish a multi-state transmission tower vulnerability curve library: Based on multi-state vulnerability, according to the risk prediction model based on Markov property established in step S1, use finite element numerical analysis to perform limit state definition, wind-induced response analysis, and statistical analysis fitting to obtain a multi-state transmission tower vulnerability curve library;

[0094] S3. Combine the time-varying wind field prediction information, obtain the transition probabilities between various states of the transmission tower from the multi-state transmission tower vulnerability curve library obtained in step S2, and then fill the transition probabilities between various states of the transmission tower into the transition probability matrix established in step S1, so as to realize the time-varying prediction of the collapse probability of the transmission tower and the failure probability of the transmission line.

[0095] To better understand the above technical solution, the exemplary embodiments of the present invention will be described in detail below with reference to the accompanying drawings. These are only the exemplary embodiments of the present invention. However, it should be understood that the present invention can be implemented in various forms and is not limited to the embodiments described herein. These embodiments are to make those skilled in the art understand the present invention more clearly and thoroughly.

[0096] A method for predicting the collapse risk of transmission towers considering cumulative damage during typhoon processes, including the following steps:

[0097] S1. Establish a risk prediction model based on Markov property: Assume that there are three states of transmission towers during typhoon processes, namely intact state, damaged state, and collapsed state. Model the time-varying risk assessment process of transmission towers as a Markov process, then establish a transmission tower transition probability matrix and determine the corresponding relationship between the vulnerability curve and each element in the transition probability matrix.

[0098] In this embodiment, step S1 specifically includes the following:

[0099] S11. Assume that there are three states of transmission towers during typhoon processes, namely intact state (Intact), damaged state (Damage), and collapsed state (Collapse), denoted as 、 、 . In the intact state, the members of the transmission tower undergo elastic deformation under the influence of slight wind and self-weight, and the overall tower structure also shows linear deformation. The power supply is normal and no maintenance is required. In the damaged state, some members of the transmission tower undergo inelastic deformation. Although the overall tower structure still shows linear deformation and has little impact on power supply, it reduces the reliability of the tower structure in future events. When the overall tower structure of the transmission tower enters non-linear deformation and a large top displacement occurs, it reaches the collapse state. At this time, the power supply is interrupted and it cannot be used anymore, which is the collapse state.

[0100] S12. Let the probability that the transmission tower is in a certain state at the current moment only depend on the state of the transmission tower at the previous moment , and is independent of the path to reach the current state. Model the time-varying risk assessment process of the transmission tower as a Markov process:

[0101] (1)

[0102] In formula (1), is the probability that the transmission tower is in various states at the moment; is the probability that the transmission tower transfers from the state at the previous moment to the state at the current moment . Among them, , ;

[0103] The probability that the transmission tower is damaged at the moment and collapses at the moment is expressed as: , and this probability is related to the wind load intensity at the moment. The influencing factors of the wind load include wind speed and wind direction. Then let this probability be a function of the wind speed and the wind direction , and is expressed as:

[0104] (2)

[0105] In formula (2), is the predicted wind speed at the moment; is the predicted wind direction at the moment; is abbreviated as , and its subscript indicates that the previous state is the damaged state and the current state is the collapsed state.

[0106] S13. The transmission tower is in a state of being intact, damaged, or collapsed. Among them, the damaged state includes multiple types of damaged states, denoted as , represents the type of damaged state. Let represent the probability of being in state at time , that is, . Among them, , then the state probability vector of the transmission tower at time is:

[0107] (3)

[0108] Among them, for any time, it satisfies , and the initial state probability vector of the transmission tower π 0 = [ π O 0 , π D 1 0 , π D 2 0 ,…, π D n 0 , π C 0 ] T is [1, 0,0,…,0, 0] T , assuming the initial state of the transmission tower is in an intact state;

[0109] According to the total probability formula, establish the transition probability matrix of the transmission tower at any time to realize the multi-state risk prediction of the transmission tower at continuous times. In this embodiment, the transition probability matrix TPM is used to realize the multi-state risk prediction of the transmission tower at continuous times. Since the deformation and buckling of the members of the transmission tower during the typhoon process are usually irreversible, and the transfer between damaged states involves complex mechanical analysis and damage evolution analysis at the member level, which is not within the scope of this embodiment, it is assumed that there is no mutual transfer between various damaged states of the transmission tower. Then there is:

[0110] (4)

[0111] (5)

[0112] In formula (4), represents the probability that the transmission tower remains intact at time when it is in an intact state; represents the probability that the transmission tower suffers the th type of damage at time when it is in an intact state, ; represents the probability that the transmission tower collapses at time when it is in an intact state; represents the transmission tower in the th type of damaged state at time Keep the probability of the type of damage at all times; Denote the probability that the transmission tower collapses at the time under the type of damage state; Denote the probability that the transmission tower returns to the intact state at the time under the type of damage state; Denote the probability that the transmission tower returns to the intact state at the

[0113] In formula (5), Denote the state probability vector of the transmission tower at the

[0114] S14. Describe the probability of damage or failure of the transmission tower structure under different load intensities through the vulnerability curve, denoted as the exceedance probability. The exceedance probability of damage or failure of the transmission tower is expressed as follows:

[0115] (6)

[0116] In formula (6), Denote the response of the structure under this load intensity; is the limit state index of the structural response, including the limit state index of the damage state and the limit state index of the collapse state ; There is a corresponding relationship between the elements in the transition probability matrix and the exceedance probabilities of the transmission tower in the previous state under different load intensities as shown in formulas (7)-(11). Fill the transition probability matrix through vulnerability:

[0117] (7)

[0118] (8)

[0119] (9)

[0120] (10)

[0121] (11)

[0122] The influencing factors of different damage states of the transmission tower at least include the change of the wind direction angle. Assume that only a certain type of damage is generated under a specific wind direction angle. Denote as the damage state The set of wind attack angles when it occurs, then:

[0123] (12).

[0124] S2. Establish a vulnerability curve library for multi - state transmission towers: Based on multi - state vulnerability, according to the risk prediction model based on Markov property established in step S1, using finite - element numerical analysis, perform limit - state definition, wind - induced response analysis, and statistical - analysis fitting to obtain the vulnerability curve library for multi - state transmission towers.

[0125] Furthermore, step S2 includes:

[0126] S21. Establish a finite - element numerical simulation model: Establish a finite - element numerical simulation model of the transmission tower to provide a basis for subsequent finite - element numerical analysis. Specifically, in the finite - element software, establish a numerical simulation model of the transmission tower and a numerical simulation model of the transmission - tower line system respectively. In this embodiment, taking the 2300ZM1 type cat - head transmission tower as an example, according to relevant materials such as the "Technical Regulations for the Structural Design of Overhead Transmission Line Towers (DL / T5154 - 2012)" (hereinafter referred to as the "Technical Regulations"), establish a numerical model of the transmission tower and a numerical model of the transmission - tower line system in the commercial finite - element software ABAQUS. Among them, in this embodiment, the transmission - tower line system takes the structure of "three towers and two lines" as an example, that is, it includes three transmission towers and the conductors and ground wires connecting two adjacent transmission towers. The three transmission towers are respectively set as Tower A, Tower B, and Tower C. The conductors and ground wires include one middle conductor, two side conductors, and two ground wires. The numerical models of the transmission tower and the transmission - tower line system are respectively as Figure 2 and Figure 3 shown. Among them, since the angle - steel members of the transmission tower are slender members, many studies have shown that beam elements can better simulate the real performance of the angle - steel members of the transmission tower. Therefore, B31 type beam elements are selected for modeling the angle - steel members, and each member is rigidly connected. According to the consistent - mode imperfection method, apply an overall initial geometric imperfection of 0.1% of the tower height according to the lowest - order overall buckling mode. The transmission line can only bear tension and cannot bear bending moment and pressure. Therefore, use multiple three - dimensional truss elements T3D2 that are hinged everywhere and set no - compression characteristics to establish the numerical simulation model of the transmission line, and use the temperature - reduction method to apply prestress to the transmission line.

[0127] S22. Limit - state definition: Use a certain threshold value of the displacement at the top of the transmission tower as the limit - state index to determine the damage state and collapse state of the transmission tower described in step S1.

[0128] Specifically, defining the limit state is a key step in vulnerability analysis. Calculate the static wind load according to the "Technical Regulations" and apply it to the numerical simulation model of a single tower (i.e., the numerical simulation model of a single transmission tower). Conduct nonlinear static analysis (i.e., Pushover analysis) at each wind attack angle in the commercial finite element software ABAQUS. Use a certain threshold value of the displacement at the top of the transmission pole as the limit state index to determine the damage state and collapse state of the transmission tower described in step S1.

[0129] (1) For the damage state, define the damage state of the transmission tower as the critical state where buckling of the members first appears in the transmission tower. Track the axial pressure of each member of the transmission tower during the Pushover process. Refer to the stability calculation formula of the solid-web axially compressed members in the "Steel Structure Design Standard" to determine whether each member buckles (i.e., is damaged). The member where buckling first appears is the damaged member of the transmission tower. Different damaged members correspond to different damage states, and use the displacement at the top of the transmission tower in this state as the limit index for this type of damage state. ; Determine whether each member of the transmission tower buckles through formula (13):

[0130] (13)

[0131] In formula (13), is the axial pressure received by the member of the transmission tower; is the cross-sectional area of the member of the transmission tower; is the design value of the tensile, compressive, and flexural strength; is the stability coefficient of the axially compressed member of the transmission tower, which is obtained according to the slenderness ratio of the member, the steel grade correction coefficient and the cross-section classification according to the "Steel Structure Design Standard". Among them, represents the yield strength of the steel.

[0132] During a typhoon, the wind direction may change significantly. When the wind direction changes, it will cause changes in the magnitude and spatial distribution of the wind load, resulting in different damage paths and affecting the damaged components of the transmission tower. Therefore, check the damage state of the transmission tower in combination with the Pushover results.

[0133] In this embodiment, with an interval of 30°, there are a total of 10 types of damage states at wind attack angles from 0° to 360°. The corresponding wind attack angles are 0°, 30°, or 60° (i.e., the damage states corresponding to wind attack angles 30° and 60° are the same), 90°, 120°, 150°, 180°, 210°, 240°, 270°, 300°, or 330° (i.e., the damage states corresponding to wind attack angles 300° and 330° are the same), as Figures 4 - 9As shown, the damage conditions from 0° to 180° are presented. Since the damage conditions from 210° to 330° are symmetric to those from 30° to 150°, they are omitted. It includes 10 types of states, denoted as . Figures 4 - 9 Each of them includes 3 sub - figures, which are, from left to right, the front view, side view, and sectional view of the damaged transmission tower at different wind attack angles. Figures 4 - 9 In, the parts marked in red represent the damaged members. In damage mechanics, generally, the reduction of the elastic modulus of the members is used to represent damage. By the model correction method of reducing the elastic modulus of the damaged members, a numerical simulation model of the transmission tower with certain initial damage is obtained, which is used to study the vulnerability of the transmission tower from the damaged state to the collapsed state. (2) For the collapsed state, the limit state index of the collapsed state of the transmission tower is determined according to the Pushover curve and the numerical relationship with the tower height. In this embodiment, the Pushover curve is as Figure 10 and Figure 11 shown, where Figure 10 is the Pushover curve and the displacement at the top of the collapsed transmission tower under the wind attack angle of 0° - 90°, Figure 11 is the Pushover curve and the displacement at the top of the collapsed transmission tower under the wind attack angle of 90° - 180°. The limit state index of the collapsed state of the transmission tower is 2.5% of the tower height, which is applicable to the transmission tower in the intact state and the damaged state.

[0134] S23. Wind - induced response analysis of the multi - state transmission tower: The linear filtering method is used to generate random wind speed time - history samples with different wind speeds as the input for the dynamic time - history analysis of the transmission tower line system. The maximum displacement at the top of the transmission tower in the wind - induced response time - history is taken as the wind - induced response of the transmission tower.

[0135] In order to obtain the wind - induced response of the transmission tower considering the tower - line coupling effect, a non - linear dynamic time - history analysis is required. First, the linear filtering method is used to generate random wind speed time - history samples with different wind speeds, which are converted into dynamic wind loads according to the "Technical Regulations" as the input for the dynamic time - history analysis of the transmission tower line system. The maximum displacement at the top of the transmission tower in the response time - history is taken as the wind - induced response of the transmission tower.

[0136] Then, several wind speed time - histories are generated for each wind speed, corresponding to several wind - induced response samples, and the sample size is determined through sensitivity analysis. The specific determination process is as follows:

[0137] Due to the complexity of the dynamic wind load and the finite element model of the transmission tower-line system, the nonlinear dynamic analysis is very time-consuming. In addition, considering the characteristics of probability analysis, a large number of Monte Carlo simulations need to be carried out under different wind attack angles and transmission tower states, which requires a large amount of computing resources. Therefore, optimizing the calculation efficiency is crucial. Through the results of the sample size sensitivity analysis as Figure 12 and shown in Table 1, Figure 12 Figure Figure 12 shows the collapse vulnerability curves of intact transmission towers fitted under different sample sizes at a wind attack angle of 0°. The cases of 20 samples, 50 samples, 80 samples, and 100 samples are respectively fitted. From Figure 12 it can be observed that although there is an obvious deviation between the results of 20 samples and 100 samples within the low collapse probability range (less than 0.2, that is, less than 20%), this deviation is on the conservative side; within the high collapse probability range (greater than 0.8, that is, greater than 80%), the difference between the results of 20 samples and 100 samples is smaller. Table 1 shows the collapse probabilities of different sample sizes near the median wind speed (collapse probability of 0.5, that is, 50%) (26.3 m / s - 27 m / s). The results with 20 sample sizes have a small error compared with other sample sizes. This difference is mainly due to the change in resolution caused by different sample sizes. For 20 samples, the resolution is 0.05 (that is, 1 / 20 = 0.05), which may lead to a deviation of up to 5% for each wind speed sample. In addition, considering the inherent variability of the results of multiple Monte Carlo simulations, this difference is acceptable in engineering practice. Therefore, this embodiment determines 20 wind speed time history samples to improve the calculation efficiency.

[0138] Table 1 Collapse probabilities of each wind speed under different sample sizes

[0139]

[0140] S24. Fitting the vulnerability curve library: Statistically analyze the maximum top displacement of the transmission tower under different wind speed time history samples, compare it with the limit state index set in step S22, and statistically analyze the damage or collapse probability of the transmission tower at different wind speeds. Use the cumulative distribution function of the lognormal distribution to fit the vulnerability curve library, as Figure 13 shown. When fitting the vulnerability curve of the transmission tower, ensure that the vulnerability curve of the damaged state transmission tower is steeper than that of the intact transmission tower, that is, the standard deviation of the vulnerability curve fitted by the cumulative distribution function of the lognormal distribution is: where, represents the standard deviation of the vulnerability curve and represents the vulnerability curve In order to avoid the collapse probability of the intact transmission tower in the probability interval [0,0.2] exceeding the collapse probability of the damaged transmission tower, formula (14) is used instead of formula (8):

[0141] (14).

[0142] S3. In combination with the time-varying wind field forecast information, the transition probabilities between various states of the transmission tower are obtained from the multi-state transmission tower vulnerability curve library obtained in step S2, and then the transition probabilities between various states of the transmission tower are filled into the transition probability matrix established in step S1, thereby realizing the time-varying prediction of the collapse probability of the transmission tower and the failure probability of the transmission line.

[0143] Specifically, step S3 includes:

[0144] S31. Based on the time-varying wind field forecast information, at a certain prediction time step , substitute the wind angle of attack and wind speed into the corresponding vulnerability curve to obtain the transition probability matrix Each element in The value of .

[0145] S32, repeat step S31 to obtain the .

[0146] S33, from the initial probability π 0 = [1, 0,0,…,0, 0] T The transmission tower is intact and rolling Multiply , , , ,get , updated It is used to provide the time-varying collapse probability of transmission towers considering cumulative damage. The collapse probability of each transmission tower is used to predict the failure probability of the transmission line in the target area, which is expressed as:

[0147] (15)

[0148] In formula (15), Indicated in Transmission lines at all times The failure probability; Indicates transmission line The number of upper transmission towers; Indicated in Transmission lines at all times Transmission tower Collapse probability

[0149] In this embodiment, combined with meteorological forecast information, the time-varying collapse risk of transmission towers under the scenario of Typhoon F that occurred in a coastal province (designated as Province Z) in XXXX was predicted. Typhoon F made landfall in the coastal area of Province Z at 1:45 on August 10, XXXX (17:45 on August 9, UTC time). Here, UTC (Coordinated Universal Time) refers to Coordinated Universal Time. To illustrate the effectiveness of considering cumulative damage in the present invention, in the case, the 2300ZM1 cathead straight transmission tower was taken as an example to predict the failure probability (regional scale) of the transmission network in Province Z and the collapse probability of a single example tower (i.e., at the scale of a single transmission tower), and a comparison was made with the traditional model that does not consider cumulative damage.

[0150] In this embodiment, Province Z is a coastal area, and the total length of the transmission system used exceeds 9000 kilometers, including more than 700 transmission lines and more than 30,000 transmission towers. The time range considered is from 12:00 on August 9, XXXX UTC time to 24:00 on August 9, XXXX (including the forecast landfall time of Typhoon F). The numerical meteorological forecast model of the example single tower was forecasted once per hour within this range. The wind speed and wind direction information map of the location where the example single tower is located in the next 12 hours is as Figure 14 shown.

[0151] The results under Typhoon F are analyzed as follows.

[0152] (1) Comparison at the scale of a single transmission tower

[0153] The prediction results of the method considering cumulative damage and the traditional method not considering cumulative damage for a single transmission tower in this embodiment are as Figure 15 shown. Both the method considering cumulative damage and the traditional method not considering cumulative damage described in this embodiment show that the collapse risk of the transmission tower increased significantly at 16:00 on August 9, UTC time. Table 2 counts the number of transmission towers (unit: "pcs") in different collapse probability intervals obtained by the method considering cumulative damage and the traditional method not considering cumulative damage described in this embodiment since 15:00 on August 9, UTC time. The results in Table 2 show that when cumulative damage is not considered, the number of transmission towers at high risk (collapse probability greater than 0.9) is significantly underestimated. At the level of a single transmission tower, ignoring cumulative damage leads to an underestimation of the collapse risk by about 25%. Figure 16Further shows the probabilities of a single transmission tower being in different states at different times, indicating that the underestimation of the traditional method without considering cumulative damage mainly stems from the failure to consider the cumulative damage during the typhoon process, which significantly increases the risk of collapse in subsequent time steps. For example, at 15:00, although the probability of the transmission tower collapsing is relatively low and similar to the prediction result of the traditional method without considering cumulative damage, the probability of being in a damaged state is high. A transmission tower in a damaged state is more likely to collapse. Therefore, the risk of collapse significantly increases at 16:00, thus affecting the risk assessment of the regional power grid. Therefore, transmission towers with a high probability of damage should be monitored and maintained in a timely manner, otherwise the wind resistance performance of the transmission tower under future strong wind events may be reduced. This result also demonstrates the potential of applying the risk prediction results of multiple states to links such as collapse trend warning and maintenance resource deployment.

[0154] Table 2 Number of transmission towers with collapse probabilities in different intervals

[0155]

[0156] (2) Regional scale comparison

[0157] The regional time-varying risk forecasts for all transmission towers within the scope of Province Z were respectively carried out using the method considering cumulative damage in this embodiment and the traditional method without considering cumulative damage. Table 3 statistics the number of transmission lines (unit: "pieces") within the region in different failure probability intervals obtained by the method considering cumulative damage and the traditional method without considering cumulative damage described in this embodiment since 15:00 UTC on August 9. It can be seen from Table 3 that compared with the traditional method without considering cumulative damage, the number of transmission lines predicted by the method considering cumulative damage described in this embodiment in the high-risk interval (failure probability greater than 0.8) is more than that of the traditional method without considering cumulative damage. Although the increase is small, the influence range of a single transmission line is usually large. Therefore, the method considering cumulative damage described in this embodiment is of great significance for actual power grid risk management. At the regional level, at the moment of typhoon landing, the failure probability of the transmission lines near the typhoon landing point is relatively high, and ignoring cumulative damage leads to an underestimation of the transmission line failure risk by about 15%, which is lower than the error observed at the single-tower level. The reason for this difference is that under typhoon conditions, most transmission towers are located in low-wind-speed areas, and the probability of their collapse is almost zero; while the transmission towers exposed to extremely high wind speeds tend to collapse earlier, making the impact of cumulative damage during the typhoon smaller. The prediction differences are small in both low-wind-speed (≤22 m / s) and extremely high-wind-speed (≥28 m / s) cases. Therefore, at the regional level, the prediction gap is smaller than that at the single-tower level. This actual typhoon case fully shows that for the risk forecast of transmission towers during typhoon processes, cumulative damage cannot be ignored, which is of great significance for disaster loss assessment, emergency response and recovery strategies, and enhancing the resilience of the power grid.

[0158] Table 3 Number of Transmission Lines with Failure Probabilities in Different Intervals

[0159]

[0160] Only the basic principles and preferred embodiments of the present invention are described above. Those skilled in the art can make many changes and improvements based on the above description, and these changes and improvements should fall within the protection scope of the present invention.

Claims

1. A method for predicting the risk of transmission tower collapse considering the cumulative damage during a typhoon, characterized in that: The steps include: S1. Establish a risk prediction model based on Markov property: Assume that there are three states of transmission towers during a typhoon, namely intact state, damaged state, and collapsed state. Model the time-varying risk assessment process of transmission towers as a Markov process, then establish the transmission tower transfer probability matrix and determine the corresponding relationship between the vulnerability curve and each element in the transfer probability matrix; S2. Establishing a multi-state transmission tower vulnerability curve library: Based on multi-state vulnerability, according to the Markov-based risk prediction model established in step S1, using finite element numerical analysis, limit state definition, wind-induced response analysis and statistical analysis fitting are performed to obtain a multi-state transmission tower vulnerability curve library; S3, combining the time-varying wind field forecast information, obtaining the transition probability between various states of the transmission tower from the multi-state transmission tower vulnerability curve library obtained in step S2, and then filling the transition probability between various states of the transmission tower into the transition probability matrix established in step S1, thereby realizing the time-varying prediction of the collapse probability of the transmission tower and the failure probability of the transmission line; Step S3 includes: S31. Based on the time-varying wind field forecast information, at a certain prediction time step , substituting the wind angle of attack and wind speed into the corresponding vulnerability curve to obtain the transition probability matrix Each element in The value of S32, repeat step S31 to obtain the ; S33, from the initial probability The transmission tower is intact and rolling Multiply , , , ,get , updated It is used to provide the time-varying collapse probability of transmission towers considering cumulative damage. The collapse probability of each transmission tower is used to predict the failure probability of the transmission line in the target area. The obtained collapse probability of each transmission tower is used to predict the failure probability of the transmission line in the target area, which is expressed as: （15） In formula (15), Indicated in Transmission lines at all times The failure probability of Indicates transmission line The number of upper transmission towers; Indicated in Transmission lines at all times Transmission tower probability of collapse.

2. The method for predicting the risk of transmission tower collapse considering the cumulative damage during a typhoon according to claim 1 is characterized in that: Step S1 includes: S11. Assume that during a typhoon, there are three states of transmission towers, namely intact state, damaged state, and collapsed state; S12. Assume that the probability that the transmission tower is in a certain state at the current moment depends only on the state of the transmission tower at the previous moment, and model the time-varying risk assessment process of the transmission tower as a Markov process; S13. According to the total probability formula, a transfer probability matrix of the transmission tower at any time is established; S14. Determine the corresponding relationship between the vulnerability curve and each element in the transfer probability matrix.

3. The method for predicting the risk of transmission tower collapse considering the cumulative damage during a typhoon according to claim 2 is characterized in that: Step S1 specifically includes the following: S11. Assume that there are three states of transmission towers during a typhoon: intact state, damaged state, and collapsed state, denoted by , , ; S12, set the transmission tower current The probability of being in a certain state at any time Depends only on the last moment Transmission tower status , the time-varying risk assessment process of transmission towers is modeled as a Markov process: （1） In formula (1), For transmission towers The probability of being in various states at all times; The transmission tower from the previous moment Status Transfer to current Status of the moment The probability of , ; Transmission towers Damage occurs at any time, The probability of collapse at a certain moment is expressed as: , the probability is The wind load intensity at the moment is related to the wind load intensity. The factors affecting the wind load include wind speed and wind direction. Let the probability be the wind speed and wind direction The function is expressed as: （2） In formula (2), for The forecast wind speed at the time; for The forecast wind direction at the moment; Abbreviated as , its corner mark Indicates that the state at the previous moment is a damaged state, and the state at the current moment is a collapsed state; S13. The transmission tower is in an intact state, a damaged state, or a collapsed state. The damage state includes multiple types of damage states, which are expressed as , Indicates the type of damage state, Indicated in Always in state The probability of ,in, , then the transmission tower is The state probability vector at the moment is: （3） Among them, for any Moment, satisfaction , and the initial state probability vector of the transmission tower for , assuming that the initial state of the transmission tower is intact; According to the total probability formula, the transfer probability matrix of the transmission tower at any time is established to realize the multi-state risk prediction of the transmission tower at continuous time. Assuming that the various damage states of the transmission tower will not transfer to each other, then: （4） （5） In formula (4), It means that the transmission tower is in good condition. The probability of remaining intact at all times; It means that the transmission tower is in good condition. The moment occurs The probability of class damage, ; It means that the transmission tower is in good condition. The probability of collapse occurring at any moment; Indicates that the transmission tower is In the case of damage Always keep the Probability of class damage; Indicates that the transmission tower is In the case of damage The probability of collapse occurring at any moment; Indicates that the transmission tower is In the case of damage The probability of returning to an intact state at any time; Indicates that the transmission tower is in a collapsed state. The probability of returning to an intact state at any moment; Indicates that the transmission tower is in a collapsed state. Always keep the probability of collapse in mind; In formula (5), Indicates that the transmission tower is The state probability vector at the moment; S14. The probability of damage or failure of the transmission tower structure under different load intensities is described by the fragility curve, which is recorded as the exceedance probability. The exceedance probability of damage or failure of the transmission tower is expressed as follows: （6） In formula (6), represents the response of the structure under this load intensity; is the limit state index of the structural response, including the limit state index of the damage state and collapse state limit state indicators ; The elements in the transfer probability matrix and the exceedance probability of the transmission tower at the previous moment under different load intensities have a corresponding relationship as shown in formula (7)-formula (11). The transfer probability matrix is ​​filled by vulnerability: （7） （8） （9） （10） （11） The factors affecting the different damage states of transmission towers include at least the change of wind direction angle. Assuming that only a certain type of damage occurs under a specific wind direction angle, Indicates damage status The wind attack angle set when it occurs is: （12）。 4. The method for predicting the risk of transmission tower collapse considering the cumulative damage during a typhoon according to claim 3 is characterized in that: Step S2 includes: S21. Establish a finite element numerical simulation model of the transmission tower; S22, using a certain threshold of the top displacement of the transmission tower as a limit state indicator to determine the damage state and collapse state of the transmission tower described in step S1; S23, using a linear filtering method to generate random wind speed time history samples of different wind speeds as input for the dynamic time history analysis of the transmission tower line system, and taking the maximum top displacement of the transmission tower in the wind-induced response time history as the wind-induced response of the transmission tower; S24, the maximum top displacement of the transmission tower under different wind speed time series samples is counted, and compared with the limit state index set in step S22, the probability of damage or collapse of the transmission tower under different wind speeds is counted, and the cumulative distribution function of the log-normal distribution is used to fit to obtain a vulnerability curve library.

5. The method for predicting the risk of transmission tower collapse considering the cumulative damage during a typhoon according to claim 4 is characterized in that: Step S21 specifically includes: establishing a numerical simulation model of a transmission tower and a numerical simulation model of a transmission tower line system in finite element software respectively.

6. The method for predicting the risk of transmission tower collapse considering the cumulative damage during a typhoon according to claim 4 is characterized in that: Step S22 specifically includes: (1) For the damage state, the damage state of the transmission tower is defined as: the critical state where the pole buckling first occurs in the transmission tower; the pole that buckles for the first time is the damaged pole of the transmission tower. Different damaged poles correspond to different damage states, and the top displacement of the transmission tower in this state is taken as the limit indicator of this type of damage state. ; Use formula (13) to determine whether each member of the transmission tower is buckled: （13） In formula (13), is the axial pressure on the poles of the transmission tower; is the cross-sectional area of ​​the pole of the transmission tower; It is the design value of tensile, compressive and flexural strength; is the stability factor of the axially compressed members of the transmission tower; During a typhoon, changes in wind direction will cause changes in the size and spatial distribution of wind loads, resulting in different damage paths and affecting the damaged components of the transmission tower. Therefore, the damage state of the transmission tower is checked in combination with the Pushover analysis results, where Pushover analysis represents nonlinear static analysis. With preset angles as intervals, there are several types of damage states under wind attack angles from 0° to 360°. The numerical simulation model of the transmission tower with a certain initial damage is obtained by the model correction method of reducing the elastic modulus of the damaged rod, which is used to study the vulnerability of the transmission tower from the damaged state to the collapsed state. (2) For the collapse state, determine the limit state index of the transmission tower collapse state based on the Pushover curve The numerical relationship with tower height is applicable to transmission towers in intact state and transmission towers in damaged state.

7. The method for predicting the risk of transmission tower collapse considering the cumulative damage during a typhoon according to claim 4 is characterized in that: Step S23 specifically includes: Firstly, the linear filtering method is used to generate random wind speed time history samples of different wind speeds, and the corresponding dynamic wind loads are calculated as the input of the dynamic time history analysis of the transmission tower line system; the maximum top displacement of the transmission tower in the response time history is taken as the wind-induced response of the transmission tower; Then, several wind speed time histories are generated for each wind speed, corresponding to several wind-induced response samples, and the sample size is determined through sensitivity analysis.

8. The method for predicting the risk of transmission tower collapse considering the cumulative damage during a typhoon according to claim 4 is characterized in that: In step S24, when fitting the fragility curve of the transmission tower, it is ensured that the fragility curve of the damaged transmission tower is steeper than the fragility curve of the intact transmission tower, that is, the standard deviation of the fragility curve is fitted by the cumulative distribution function of the lognormal distribution for: ,in, Vulnerability curve The standard deviation of Vulnerability curve In order to avoid the collapse probability of the intact transmission tower in the probability interval [0,0.2] exceeding the collapse probability of the damaged transmission tower, formula (14) is used instead of formula (8): （14）。

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