Power transmission tower line system reliability assessment method, device, equipment and storage medium

Abstract

The invention provides a power transmission tower line system reliability assessment method, device and equipment and a storage medium, and relates to the technical field of power transmission tower line system anti-disaster analysis and evaluation.The power transmission tower line system reliability assessment method comprises the steps that probability space division is conducted on structure parameters and disaster parameters of a power transmission tower line system, and representative point parameter samples are obtained; establishing a first finite element analysis model according to the representative point parameter sample, and performing time domain dynamic analysis on the first finite element analysis model to obtain a dynamic response of the power transmission tower line system; establishing a probability density evolution equation according to the dynamic response; according to the probability density evolution equation, the failure probability of the power transmission tower line system under the disaster effect is calculated, the reliability of the power transmission tower line system is obtained according to the correlation between the failure probability and the reliability, and therefore the reliability of the power transmission tower line system under the multi-disaster effect can be efficiently and accurately evaluated.

Description

Technical Field

[0001] The present invention relates to the technical field of disaster resistance analysis and evaluation of transmission tower line systems, and in particular to a reliability evaluation method, device, equipment and storage medium for a transmission tower line system. Background Art

[0002] The transmission tower line system is an important part of the power transmission and distribution network and an important energy infrastructure related to the national economy and people's livelihood. The transmission tower line system has the characteristics of being tall and long-spanning, with a large structural flexibility. It responds violently to disasters such as wind and earthquakes, and may be damaged or even collapse, causing secondary disasters. Therefore, the reliability assessment of the transmission tower line system under disasters is of great significance.

[0003] The mainstream reliability calculation methods can be divided into two categories: Monte Carlo algorithm and moment method. Among them, the Monte Carlo algorithm requires massive sampling of the statistical characteristics of the random variables of the structure, and then a nonlinear response analysis, and then statistics on the response results, and finally obtains the reliability analysis results. The above process is relatively cumbersome and the amount of calculation is extremely large. It is only applicable to simple structures and cannot be competent for the reliability assessment of transmission tower line systems with a large number of rods. In addition, the moment method is usually used in structural design. Although the calculation efficiency is high, the calculation accuracy is still a certain gap compared with the Monte Carlo algorithm. Summary of the invention

[0004] The purpose of the embodiments of the present invention is to provide a transmission tower line system reliability assessment method, device, equipment and storage medium, which can efficiently and accurately assess the reliability of the transmission tower line system under multiple disasters.

[0005] To achieve the above object, an embodiment of the present invention provides a method for evaluating the reliability of a transmission tower line system, comprising:

[0006] Perform probability space segmentation on the transmission tower line system structure parameters and disaster parameters to obtain representative point parameter samples;

[0007] Establishing a first finite element analysis model according to the representative point parameter sample, performing a time domain dynamic analysis on the first finite element analysis model, and obtaining a dynamic response of a transmission tower line system;

[0008] According to the dynamic response, a probability density evolution equation is established;

[0009] According to the probability density evolution equation, the failure probability of the transmission tower line system under the action of the disaster is calculated, and according to the correlation between the failure probability and the reliability, the reliability of the transmission tower line system is obtained.

[0010] As an improvement of the above solution, the time domain dynamic analysis is performed on the first finite element analysis model to obtain the dynamic response of the transmission tower line system, including performing time domain dynamic analysis on the first finite element analysis model after mass concentration simplification, specifically including:

[0011] Dividing the first finite element analysis model into a plurality of node layers;

[0012] Applying a unit force to the node layer and constructing a flexibility matrix based on the response of the node layer to the unit force;

[0013] Performing an inverse operation on the flexibility matrix to obtain a stiffness matrix;

[0014] According to the stiffness matrix, the concentrated mass of each node layer is calculated, and according to the concentrated mass of each node layer, a mass matrix is ​​constructed;

[0015] Constructing a damping matrix according to the mass matrix and the stiffness matrix;

[0016] The dynamic response of the transmission tower line system is calculated according to the stiffness matrix, the mass matrix and the damping matrix.

[0017] As an improvement of the above scheme, the probability density evolution equation is calculated by the following formula:

[0018]

[0019] Among them, p XΘ (X, θ, t) represents the probability density of the dynamic response of the transmission tower line system when the random variable θ takes the value of θ, and the random variable is a structural parameter or a disaster parameter; It represents the first derivative of the structural response with respect to time when the random variable Θ takes the value of θ; t represents time.

[0020] As an improvement of the above solution, the disaster effect includes at least one disaster effect, and the method for calculating the failure probability specifically includes:

[0021] For each disaster, according to the probability density evolution equation, the probability density function of the dynamic response of the transmission tower line system under different levels of disasters is solved;

[0022] According to the probability density function, the expected response of the transmission tower line system under different levels of disasters is calculated;

[0023] Taking the logarithm of the expected response and disaster level of the transmission tower line system, and performing linear regression to obtain the slope and intercept of the straight line;

[0024] The failure probability of the transmission tower line system under various disasters is calculated based on the slope of the straight line and the intercept.

[0025] As an improvement of the above solution, the failure probability is calculated by the following formula:

[0026]

[0027] Among them, P f (IM) represents the failure probability; IM represents the disaster level; Φ represents the standard normal cumulative distribution function; a2 represents the intercept; a3 represents the slope of the line; X f Indicates the response threshold corresponding to structural damage.

[0028] As an improvement to the above scheme, when there are two or more types of disasters, the failure probability under the action of multiple disasters is calculated by the following formula:

[0029]

[0030] in, represents the failure probability under various disasters; m represents the type of disaster; X represents the dynamic response of the transmission tower line system; P[X>X f |IM] indicates that the structural response under the disaster of level IM exceeds X f The probability of represents the failure probability of the transmission tower line system under the action of the ith disaster; H i (IM) represents the hazard function of the i-th disaster.

[0031] As an improvement of the above solution, the dynamic response of the transmission tower line system includes at least one of the following:

[0032] The displacement response at the junction of the main material of the tower body and the cross diaphragm, the displacement response at the cross arm position, the displacement response at the highest point of the tower top, the displacement response at the mid-span of the conductor, the acceleration response at the junction of the main material of the tower body and the cross diaphragm, the acceleration response at the cross arm position, the acceleration response at the highest point of the tower top, the acceleration response at the mid-span of the conductor, the stress of the main material of the tower body, the stress in the mid-span of the conductor and the stress at the mid-span of the ground wire.

[0033] To achieve the above object, an embodiment of the present invention further provides a transmission tower line system reliability assessment device, comprising:

[0034] The probability space segmentation module is used to perform probability space segmentation on the transmission tower line system structure parameters and disaster parameters to obtain representative point parameter samples;

[0035] A dynamic response acquisition module, used to establish a first finite element analysis model according to the representative point parameter sample, perform time domain dynamic analysis on the first finite element analysis model, and obtain the dynamic response of the transmission tower line system;

[0036] A probability density evolution equation establishment module, used to establish a probability density evolution equation according to the dynamic response;

[0037] The reliability calculation module is used to calculate the failure probability of the transmission tower line system under the action of disasters according to the probability density evolution equation, and obtain the reliability of the transmission tower line system according to the correlation between the failure probability and reliability.

[0038] As an improvement of the above solution, the dynamic response acquisition module further includes a mass concentration simplification unit, which is used to perform time domain dynamic analysis after mass concentration simplification on the first finite element analysis model, specifically including:

[0039] Dividing the first finite element analysis model into a plurality of node layers;

[0040] Applying a unit force to the node layer and constructing a flexibility matrix based on the response of the node layer to the unit force;

[0041] Performing an inverse operation on the flexibility matrix to obtain a stiffness matrix;

[0042] According to the stiffness matrix, the concentrated mass of each node layer is calculated, and according to the concentrated mass of each node layer, a mass matrix is ​​constructed;

[0043] Constructing a damping matrix according to the mass matrix and the stiffness matrix;

[0044] The dynamic response of the transmission tower line system is calculated according to the stiffness matrix, the mass matrix and the damping matrix.

[0045] As an improvement of the above solution, the probability density evolution equation establishment module is used to calculate the probability density evolution equation by the following formula:

[0046]

[0047] Among them, p XΘ (X, θ, t) represents the probability density of the dynamic response of the transmission tower line system when the random variable θ takes the value of θ, and the random variable is a structural parameter or a disaster parameter; It represents the first derivative of the structural response with respect to time when the random variable Θ takes the value of θ; t represents time.

[0048] As an improvement of the above solution, the disaster effect includes at least one disaster effect, and the reliability calculation module is used for:

[0049] For each disaster, according to the probability density evolution equation, the probability density function of the dynamic response of the transmission tower line system under different levels of disasters is solved;

[0050] According to the probability density function, the expected response of the transmission tower line system under different levels of disasters is calculated;

[0051] Taking the logarithm of the expected response and disaster level of the transmission tower line system, and performing linear regression to obtain the slope and intercept of the straight line;

[0052] The failure probability of the transmission tower line system under various disasters is calculated based on the slope of the straight line and the intercept.

[0053] As an improvement of the above solution, the reliability calculation module is also used to calculate the failure probability by the following formula:

[0054]

[0055] Among them, P f (IM) represents the failure probability; Φ represents the standard normal cumulative distribution function; a2 represents the intercept; a3 represents the slope of the line; X f It indicates the response threshold corresponding to the structural damage; IM indicates the disaster level.

[0056] As an improvement of the above solution, when there are two or more types of disasters, the reliability calculation module is further used to calculate the failure probability under the action of multiple disasters by the following formula:

[0057]

[0058] in, represents the failure probability under various disasters; m represents the type of disaster; X represents the dynamic response of the transmission tower line system; P[X>X f |IM] indicates that the structural response under the disaster of level IM exceeds X f The probability of represents the failure probability of the transmission tower line system under the action of the ith disaster; H i (IM) represents the hazard function of the i-th disaster.

[0059] As an improvement of the above solution, the dynamic response of the transmission tower line system includes at least one of the following:

[0060] The displacement response at the junction of the main material of the tower body and the cross diaphragm, the displacement response at the cross arm position, the displacement response at the highest point of the tower top, the displacement response at the mid-span of the conductor, the acceleration response at the junction of the main material of the tower body and the cross diaphragm, the acceleration response at the cross arm position, the acceleration response at the highest point of the tower top, the acceleration response at the mid-span of the conductor, the stress of the main material of the tower body, the stress in the mid-span of the conductor and the stress at the mid-span of the ground wire.

[0061] To achieve the above objectives, an embodiment of the present invention further provides a transmission tower line system reliability assessment device, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein when the processor executes the computer program, the transmission tower line system reliability assessment method as described in any of the above embodiments is implemented.

[0062] To achieve the above objectives, an embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium includes a stored computer program, wherein when the computer program is running, the device where the computer-readable storage medium is located is controlled to execute the transmission tower line system reliability assessment method as described in any of the above embodiments.

[0063] Compared with the prior art, the transmission tower line system reliability assessment method, device, equipment and storage medium provided in the embodiments of the present invention perform probability space segmentation on the transmission tower line system structure parameters and disaster parameters to obtain representative point parameter samples; based on the representative point parameter samples, a first finite element analysis model is established, and a time domain dynamic analysis is performed on the first finite element analysis model to obtain the dynamic response of the transmission tower line system; based on the dynamic response, a probability density evolution equation is established; based on the probability density evolution equation, the failure probability of the transmission tower line system under the action of a disaster is calculated, and based on the correlation between the failure probability and reliability, the reliability of the transmission tower line system is obtained, thereby being able to efficiently and accurately assess the reliability of the transmission tower line system under the action of multiple disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a flow chart of a reliability assessment method of a transmission tower line system provided by one embodiment of the present invention;

[0065] Figure 2 is a schematic diagram of a transmission tower provided in Embodiment 1 of the present invention;

[0066] Figure 3 is a schematic diagram of the probability space partition result provided by the first embodiment of the present invention;

[0067] Figure 4 is a schematic diagram of a transmission tower structure model provided in Embodiment 1 of the present invention;

[0068] Figure 5 It is a schematic diagram of the displacement response of the top of the transmission tower under the El-Centro earthquake provided by the first embodiment of the present invention;

[0069] Figure 6 is a comparison diagram of the simplified model provided by the first embodiment of the present invention and the original model;

[0070] Figure 7is a schematic diagram of statistical results of the quality and height of nodes provided in the first embodiment of the present invention;

[0071] Figure 8 is a schematic diagram of the force application position provided in the first embodiment of the present invention;

[0072] Fig. 9 is a schematic diagram of structural response provided by Embodiment 1 of the present invention;

[0073] Fig.10 is a displacement response comparison diagram of the original model and the simplified model provided in the first embodiment of the present invention;

[0074] Fig.11 is a schematic diagram of the process of probability density changing over time provided by the first embodiment of the present invention;

[0075] Fig.12 is another schematic diagram of the process of probability density changing over time provided by the first embodiment of the present invention;

[0076] Fig.13 is a schematic diagram of a structural vulnerability curve under different strength loads provided in Example 1 of the present invention;

[0077] Fig.14 is a schematic diagram of a function of the danger of a transmission tower being subjected to earthquakes of different intensities provided in the first embodiment of the present invention;

[0078] Fig.15 1 is a schematic diagram of a dangerous function of a transmission tower subjected to strong winds of different wind speeds provided by the first embodiment of the present invention;

[0079] Fig.16 It is a structural schematic diagram of a transmission tower line system reliability assessment device provided by one embodiment of the present invention;

[0080] Fig.17 It is a structural schematic diagram of a transmission tower line system reliability assessment device provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0081] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0082] It is worth noting that in recent years, with the continuous improvement of power grid construction, the deterministic dynamic analysis method of the transmission tower line system under the action of a single disaster has become mature, and a series of finite element modeling and simulation calculation methods have been developed, which basically realizes the solution of various nonlinear problems of the structure (material nonlinearity, geometric nonlinearity, boundary condition nonlinearity and special connection unit nonlinearity). However, due to the large number of transmission tower line structure rods, nonlinear random analysis is relatively difficult, and its reliability analysis algorithm is still relatively basic. At present, efficient reliability calculation of the transmission tower line system level under the action of multiple disasters has not been realized. The transmission tower line system reliability assessment method, device, equipment and storage medium provided by the embodiment of the present invention can not only solve the technical problems mentioned in the above background technology, but also can be used to assess the reliability of the transmission tower line system under the action of multiple disasters.

[0083] See also Figure 1 , is a flow chart of a transmission tower line system reliability assessment method provided by an embodiment of the present invention, comprising steps S1 to S4:

[0084] S1. Perform probability space segmentation on the transmission tower line system structure parameters and disaster parameters to obtain representative point parameter samples;

[0085] S2. Establishing a first finite element analysis model according to the representative point parameter sample, and performing time domain dynamic analysis on the first finite element analysis model to obtain a dynamic response of a transmission tower line system;

[0086] S3. Establishing a probability density evolution equation according to the dynamic response;

[0087] S4. According to the probability density evolution equation, the failure probability of the transmission tower line system under the action of the disaster is calculated, and according to the correlation between the failure probability and reliability, the reliability of the transmission tower line system is obtained.

[0088] It is worth noting that when analyzing the reliability of the transmission tower line system under multiple disasters, it is necessary to comprehensively consider the randomness of the structural parameters and the randomness of the disasters. Therefore, in step S1, the probability space is divided according to the statistical results of the structural parameters of the transmission tower line system and the statistical results of the main disaster parameters (such as wind and earthquake). The division results will generate several representative point parameter samples in the probability space, and each representative point parameter sample corresponds to 1 assigned probability.

[0089] For example, let s-dimensional continuous random vector Θ = (Θ1, Θ2, ..., Θ s ) has a value range of set up is the distribution space Ω ΘThe point set consists of n discrete points in the probability space, and the Voronoi set partitioning method is used to partition the probability space into several subsets using the n discrete points. Each discrete point represents a sample in the probability space and corresponds to an assigned probability.

[0090] In step S2, a first finite element analysis model is established based on the representative point parameter samples (structural parameter samples and load parameter samples) obtained by the segmentation in step S1. Exemplarily, the first finite element analysis model is a refined finite element analysis model, which is established by using a parametric modeling method and a commercial finite element software API (Application Programming Interface) to facilitate large-scale calculations.

[0091] Furthermore, the P-delta effect (second-order gravity effect) and geometric nonlinearity of the transmission line are considered to carry out time-domain dynamic analysis to obtain the dynamic response (dynamic response time history result) of the transmission tower line system. Exemplarily, the parametric method is used to extract the dynamic response time history results of the key points of the transmission tower, the conductor, and the ground wire. Exemplarily, the key point dynamic response time history results can be the displacement time history response of the following positions: the junction between the main material of the tower body and the crossbar, the cross arm position, the highest point of the tower top, and the mid-span of the conductor; it can be the acceleration time history response of the following positions: the junction between the main material of the tower body and the crossbar, the cross arm position, the highest point of the tower top, and the mid-span of the conductor; it can be the stress of the following positions: the main material of the tower body, the mid-span of the conductor, and the mid-span of the ground wire. Compared with the linear simplification of the transmission tower line system in the prior art, the embodiment of the present invention retains the nonlinear characteristics of the transmission tower line system, and further uses a nonlinear random response analysis method in step S3 to obtain the probability density of its random response, so that the characteristics of the random response of the transmission tower line system can be more accurately described.

[0092] Exemplarily, in step S3, a probability density evolution equation is established, and the TVD (Total Variation Diminishing) format is used to solve the probability density evolution equation to obtain the time-varying result of the dynamic response of the transmission tower line system corresponding to each assigned probability. Each representative point is looped and superimposed to obtain the time-varying process of the nonlinear random response probability density of the entire transmission tower line system.

[0093] It is worth noting that the dynamic response obtained in step S2 can be understood as a deterministic time-varying function, and step S3 will map the deterministic response obtained in step S2 to the probability space to obtain the probability density function of the response. For example, step S2 can obtain the displacement of the transmission tower line system at any time under the action of a specific earthquake wave; after step S3, the probability of the displacement response of the transmission tower line system at a certain time under a series of earthquakes can be obtained.

[0094] Furthermore, in step S4, the reliability of the transmission tower-line system is calculated based on the probability density information of the nonlinear random response of the transmission tower-line system to guide the optimal design or reinforcement and reconstruction of the transmission tower structure.

[0095] Compared with the prior art, the transmission tower line system reliability evaluation method provided by the embodiment of the present invention calculates reliability based on the probability density evolution theory, which can effectively take into account the high precision and high efficiency of the transmission tower line system reliability evaluation, and can be applied to the efficient reliability calculation of the transmission tower line system level under the influence of multiple disasters.

[0096] As one optional implementation manner, the performing time domain dynamic analysis on the first finite element analysis model to obtain the dynamic response of the transmission tower line system includes performing time domain dynamic analysis on the first finite element analysis model after mass concentration simplification, specifically including:

[0097] Dividing the first finite element analysis model into a plurality of node layers;

[0098] Applying a unit force to the node layer and constructing a flexibility matrix based on the response of the node layer to the unit force;

[0099] Performing an inverse operation on the flexibility matrix to obtain a stiffness matrix;

[0100] According to the stiffness matrix, the concentrated mass of each node layer is calculated, and according to the concentrated mass of each node layer, a mass matrix is ​​constructed;

[0101] Constructing a damping matrix according to the mass matrix and the stiffness matrix;

[0102] The dynamic response of the transmission tower line system is calculated according to the stiffness matrix, the mass matrix and the damping matrix.

[0103] In order to improve the calculation efficiency of the dynamic response, it is necessary to simplify the mass concentration of the first finite element analysis model, that is, to establish a simplified concentrated mass model, and then use the simplified concentrated mass model to perform response analysis. Specifically, the first finite element analysis model is divided into n node layers (also called "nodes") from bottom to top. For example, the positions of the crossarms and the crossbars are usually regarded as a node layer.

[0104] Furthermore, a unit force is applied to the i-th node layer to obtain the response of the structure, which is written in vector form to obtain the flexibility vector:

[0105] δ1={δ 1，1 , δ 2，1 , …, δ n，1} T (1)

[0106] Among them, δi，1 It represents the displacement of the i-th node layer when the unit force acts on the 1-node layer; δ1 represents the flexibility vector when the unit force acts on the 1-node layer; T represents the transpose operation.

[0107] Furthermore, the flexibility vector arrangement is written in matrix form to obtain the flexibility matrix:

[0108] Δ=[δ1,δ2,…,δ n ] (2)

[0109] Where Δ represents the flexibility matrix; δ n Represents the flexibility vector when a unit force acts on the nth node layer.

[0110] Furthermore, the flexibility matrix is ​​inverted to obtain the stiffness matrix [K], that is:

[0111] [K]=[Δ] -1 (3)

[0112] Furthermore, the mass matrix is ​​written as shown in formula (4):

[0113] [M] = diag(m1, m2, ...m n ) (4)

[0114] Where [M] represents the mass matrix; diag() represents the construction of the angle matrix; m i represents the concentrated mass of the i-th node layer, and is solved using formula (5):

[0115]

[0116] Among them, ω i represents the i-th order circular frequency; k i，1 , k i，2 , …, k i，n is the corresponding element in the stiffness matrix; [φ 1，i ,φ 2，i ,…,φ n，i ] T represents the shape of the i-th order vibration mode.

[0117] Furthermore, according to the Rayleigh damping assumption, the damping matrix [C] is obtained:

[0118] [C]=a0[M]+a1[K] (6)

[0119] Among them, a0 and a1 are two proportional coefficients, and:

[0120]

[0121] For the transmission tower structure, the damping ratio ξ is 2%, that is, ξ = 0.02.

[0122] Furthermore, the dynamic response of the transmission tower-line system is calculated based on the stiffness matrix, mass matrix and damping matrix, as shown in formula (8):

[0123]

[0124] in, Represents the acceleration response of the transmission tower-line system; {x} represents the velocity response of the transmission tower-line system; {P} represents the force vector acting on each node.

[0125] As an optional implementation manner, the probability density evolution equation is calculated by the following formula:

[0126]

[0127] Among them, p XΘ (X, θ, t) represents the probability density of the dynamic response of the transmission tower line system when the random variable θ takes the value of θ, and the random variable is a structural parameter or a disaster parameter; represents the first derivative of the structural response with respect to time when the random variable Θ takes the value of θ; t represents time; where the structural response refers to the dynamic response of the transmission tower line system

[0128] For example, the dynamic response of the transmission tower line system (such as the displacement response at the junction of the tower main material and the crossbar, the displacement response of the cross arm position, the displacement response of the highest point of the tower top, the displacement response of the conductor span, the stress of the tower main material, the stress of the conductor span and the stress of the ground wire span, etc.) is recorded as:

[0129] X(t)=(X1,X2,X3,…,X m ) T (10)

[0130] Among them, X1, X2, X3, …, X m They represent the responses of the 1st, 2nd, 3rd...mth points of the structure respectively.

[0131] Then X(t) is a function of the random variable Θ, that is:

[0132] X(t)=H(θ,t)(11)

[0133] Furthermore, the derivative of X(t) with respect to the generalized time parameter t can be expressed as:

[0134]

[0135] The probability density evolution equation of the transmission tower-line system can be expressed as:

[0136]

[0137] Among them, p XΘ (X, θ, t) represents the probability density of the dynamic response of the transmission tower line system when the random variable θ takes the value of θ, which is a function of time t, and the random variable is a structural parameter or a disaster parameter; It represents the first derivative of the structural response with respect to time when the random variable Θ takes the value of θ; t represents time.

[0138] When X(t) has a definite initial value x0 independent of the random vector Θ, the initial condition of the probability density evolution equation can be expressed as:

[0139] p XΘ (X, θ, t)| t＝0 =δ(x-x0)P Θ (θ) (13)

[0140] Where, δ() represents the Dirac function; P Θ (θ) denotes the joint probability density function of Θ.

[0141] Furthermore, by solving the above probability density evolution equation, we can obtain the probability density function of X(t):

[0142]

[0143] For example, the probability density evolution equation is solved using the TVD format. First, the xt solution is discretized in the plane, and j is set to 0, ±1, ±2, ..., and k is set to 0, 1, 2, .... At this time, It means that p(x, t) is at the point (x j , t k ) is p(x j , t k ), where x j =j·Δx,t k =k·Δt, Δx represents the discrete step length of space, and Δt represents the discrete step length of time.

[0144] According to the TVD difference format, we can get:

[0145]

[0146] Wherein, λ = Δt / Δx represents the grid ratio; a represents the derivative of the desired physical quantity; represents the flux limiter. To ensure the stability and convergence of the TVD format, the CFL condition (Courant-Friedrichs-Lewy condition) must be satisfied, that is, |λa|≤1.

[0147] As an optional implementation manner, the disaster effect includes at least one disaster effect, and the method for calculating the failure probability specifically includes:

[0148] For each disaster, according to the probability density evolution equation, the probability density function of the dynamic response of the transmission tower line system under different levels of disasters is solved;

[0149] According to the probability density function, the expected response of the transmission tower line system under different levels of disasters is calculated;

[0150] Taking the logarithm of the expected response and the disaster level of the transmission tower line system, and performing linear regression to obtain the slope and intercept of the straight line;

[0151] The failure probability of the transmission tower line system under various disasters is calculated based on the slope of the straight line and the intercept.

[0152] For example, first, the disaster can be divided into several levels, and IM is used to represent the disaster level. For example, for earthquake action, it can be divided into IM = 0.05g (gravitational acceleration), 0.1g to 0.8g and other levels; for wind load, it can be divided into IM = 10m / s, 15m / s to 40m / s and other levels. For the i-th level disaster, the probability density function p of the dynamic response of the transmission tower line system is solved according to formula (9) and formula (14): X |IM, further, the expected response E(X)|IM of the transmission tower line system under the disaster of level IM is:

[0153] E(X)|IM=∫X·p x |IMdx (16)

[0154] Furthermore, let IM take n groups of different values. According to formula (16), the expected response of the transmission tower line system under different levels of disasters can be obtained: E(X)|IM1, E(X)|IM2, …, E(X)|IM n . For E(X)|IM i and disaster level IM i Take the logarithm respectively and get ln(E(X)|IM i ) and ln(IM i ). Further, for ln(E(X)|IM i ) and ln(IM i ) to perform linear regression and obtain the linear slope a3 and intercept a2. Define the response threshold corresponding to structural damage as X f , then the failure probability of the transmission tower line system under this type of disaster is expressed as:

[0155]

[0156] Among them, P f (IM) represents the failure probability; Φ represents the standard normal cumulative distribution function; a2 represents the intercept; a3 represents the slope of the line; X f It indicates the response threshold corresponding to the structural damage; IM indicates the disaster level.

[0157] Repeat the above process for z different disasters, and the failure probability under z disasters can be obtained:

[0158] Let H i (IM) represents the hazard function of the i-th disaster, and the failure probability of the transmission tower line system under various types of disasters is:

[0159]

[0160] in, represents the failure probability under various disasters; m represents the type of disaster; X represents the dynamic response of the transmission tower line system; P[X>X f |IM] indicates that the structural response under the disaster of level IM exceeds X f The probability of represents the failure probability of the transmission tower line system under the action of the ith disaster; H i (IM) represents the hazard function of the i-th disaster.

[0161] Furthermore, considering the correlation between failure probability and reliability, the reliability index can be obtained:

[0162]

[0163] Among them, β(t) represents the reliability index; Φ represents the standard normal cumulative distribution function, Φ -1 represents the corresponding inverse function.

[0164] As an optional implementation manner, the dynamic response of the transmission tower line system includes at least one of the following:

[0165] The displacement response at the junction of the main material of the tower body and the cross diaphragm, the displacement response at the cross arm position, the displacement response at the highest point of the tower top, the displacement response at the mid-span of the conductor, the acceleration response at the junction of the main material of the tower body and the cross diaphragm, the acceleration response at the cross arm position, the acceleration response at the highest point of the tower top, the acceleration response at the mid-span of the conductor, the stress of the main material of the tower body, the stress in the mid-span of the conductor and the stress at the mid-span of the ground wire.

[0166] In order to have a clearer understanding of the reliability assessment method of the transmission tower line system, the reliability calculation of a transmission tower line system under earthquake and wind action will be used as an example to illustrate.

[0167] Assume that the design service life of a transmission tower is 50 years, and its three-dimensional shape is shown in the figure.

[0168] The first step is to perform probability space segmentation. The transmission tower line system contains many types of random variables, such as material resistance, cross-sectional dimensions, external loads, etc. In order to simplify the calculation, only permanent loads, rod resistance, seismic action and wind loads are selected as random variables. Referring to the "Code for Design of Steel Structures" (GB50017-2020) and the "Technical Regulations for the Structural Design of Overhead Transmission Line Towers" (DL / T 5154-2012), it is assumed that the permanent load obeys a normal distribution with a coefficient of variation of 0.07, and the rod resistance is calculated as an axial force component, obeying a logarithmic normal distribution with a coefficient of variation of 0.07. According to the "Code for Seismic Design of Power Facilities" (GB 50260-2013), the transmission tower line system is set to a fortification intensity of 7 degrees, corresponding to the recurrence periods of frequent earthquakes, occasional earthquakes, and rare earthquakes of 50 years, 475 years, and 2475 years, respectively. Wind vibration defines the wind load level with the average wind speed at a height of 10 meters as an indicator. The Voronoi set partitioning method is used to select points and partition the probability space. The results are as follows: Figure 3 shown.

[0169] The second step is to calculate the dynamic response of the transmission tower line system based on the refined finite element model. Multiple finite element modeling and calculations are performed based on the representative point parameter samples extracted in the first step, see Figure 4 , is a transmission tower structure model calculated and established by the embodiment of the present invention using the Python language and the API interface program provided by SAP2000. Figure 5 , is the time history function of the displacement response of the top of the transmission tower under the El-Centro earthquake. The dynamic response calculation process of other key points of the transmission tower line system is similar to this and will not be repeated here.

[0170] The third step is to calculate the dynamic response of the transmission tower line system based on the simplified model. The refined finite element model of the second step is simplified by the method described in the above embodiment, and the nodes are divided according to the positions of the crossarms and the crossbars, and the transmission tower structure model is divided into 21 nodes from bottom to top, see Figure 6 , is a comparison diagram of the simplified model and the original model. Apply unit force to the node layer in turn to obtain the response of the simplified model, and then obtain the flexibility matrix of the structure. Further, the mass matrix is ​​obtained by formula (4) and formula (5), see Figure 7 , is the statistical result of the mass and height of each node in the embodiment of the present invention. In order to make the displacement response of the structure more obvious, the unit force is magnified by a certain multiple and then applied. The force application position is shown in the following example. Figure 8 As shown, the response of the structure is Fig. 9Furthermore, in order to verify the accuracy of the results calculated based on the simplified model, the displacement responses of the original model and the simplified model were compared after applying the same earthquake force. The comparison results are shown in Fig.10 As shown by Fig.10 It can be seen that the displacement responses output by the two models are basically the same, which means that the calculation results of the simplified model still have a high accuracy.

[0171] Step 4: Establish and solve the probability density evolution equation. Based on the dynamic response calculation of the transmission tower line system calculated in the second and / or third steps, the probability density evolution equation is established according to formula (9), and the probability density change over time is calculated according to formula (15), as follows: Fig.11 and Fig.12 shown.

[0172] Step 5: Reliability assessment. The structural fragility curve under different load intensity can be obtained from the probability density evolution results. Fig.13 As shown. Referring to the structural seismic and wind resistance specifications, the hazard functions of transmission towers subjected to earthquakes of different intensities or gales of different wind speeds during their service life are as follows: Fig.14 and Fig.15 According to formula (18), the failure probability of the transmission tower line system within the 50-year service life is 1.999×10 -4 According to formula (19), the reliability of the structure subjected to earthquake and wind load disasters during its entire life cycle is 3.54.

[0173] Compared with the prior art, the transmission tower line system reliability assessment method provided by the embodiment of the present invention performs probability space segmentation on the transmission tower line system structure parameters and disaster parameters to obtain representative point parameter samples; a first finite element analysis model is established based on the representative point parameter samples, and a time domain dynamic analysis is performed on the first finite element analysis model to obtain the dynamic response of the transmission tower line system; a probability density evolution equation is established based on the dynamic response; based on the probability density evolution equation, the failure probability of the transmission tower line system under the action of a disaster is calculated, and based on the correlation between the failure probability and reliability, the reliability of the transmission tower line system is obtained, thereby being able to efficiently and accurately assess the reliability of the transmission tower line system under the action of multiple disasters.

[0174] See also Fig.16 The embodiment of the present invention further provides a transmission tower line system reliability assessment device 10, comprising:

[0175] The probability space segmentation module 11 is used to perform probability space segmentation on the transmission tower line system structure parameters and disaster parameters to obtain representative point parameter samples;

[0176] A dynamic response acquisition module 12 is used to establish a first finite element analysis model according to the representative point parameter sample, perform time domain dynamic analysis on the first finite element analysis model, and obtain the dynamic response of the transmission tower line system;

[0177] A probability density evolution equation establishing module 13, used to establish a probability density evolution equation according to the dynamic response;

[0178] The reliability calculation module 14 is used to calculate the failure probability of the transmission tower line system under the action of disasters according to the probability density evolution equation, and obtain the reliability of the transmission tower line system according to the correlation between the failure probability and reliability.

[0179] As an optional implementation, the dynamic response acquisition module 12 further includes a mass concentration simplification unit, which is used to perform time domain dynamic analysis after mass concentration simplification on the first finite element analysis model, specifically including:

[0180] Dividing the first finite element analysis model into a plurality of node layers;

[0181] Applying a unit force to the node layer and constructing a flexibility matrix based on the response of the node layer to the unit force;

[0182] Performing an inverse operation on the flexibility matrix to obtain a stiffness matrix;

[0183] According to the stiffness matrix, the concentrated mass of each node layer is calculated, and according to the concentrated mass of each node layer, a mass matrix is ​​constructed;

[0184] Constructing a damping matrix according to the mass matrix and the stiffness matrix;

[0185] The dynamic response of the transmission tower line system is calculated according to the stiffness matrix, the mass matrix and the damping matrix.

[0186] As an optional implementation, the probability density evolution equation establishment module 13 is used to calculate the probability density evolution equation by the following formula:

[0187]

[0188] Among them, p XΘ (X, θ, t) represents the probability density of the dynamic response of the transmission tower line system when the random variable θ takes the value of θ, and the random variable is a structural parameter or a disaster parameter; It represents the first derivative of the structural response with respect to time when the random variable Θ takes the value of θ; t represents time.

[0189] As an optional implementation manner, the disaster effect includes at least one disaster effect, and the reliability calculation module 14 is used for:

[0190] For each disaster, according to the probability density evolution equation, the probability density function of the dynamic response of the transmission tower line system under different levels of disasters is solved;

[0191] According to the probability density function, the expected response of the transmission tower line system under different levels of disasters is calculated;

[0192] Taking the logarithm of the expected response and disaster level of the transmission tower line system, and performing linear regression to obtain the slope and intercept of the straight line;

[0193] The failure probability of the transmission tower line system under various disasters is calculated based on the slope of the straight line and the intercept.

[0194] As an optional implementation manner, the reliability calculation module 14 is further used to calculate the failure probability by the following formula:

[0195]

[0196] Among them, P f (IM) represents the failure probability; Φ represents the standard normal cumulative distribution function; a2 represents the intercept; a3 represents the slope of the line; X f It indicates the response threshold corresponding to the structural damage; IM indicates the disaster level.

[0197] As an optional implementation, when there are two or more types of disasters, the reliability calculation module 14 is further used to calculate the failure probability under the action of multiple disasters by the following formula:

[0198]

[0199] in, represents the failure probability under various disasters; m represents the type of disaster; X represents the dynamic response of the transmission tower line system; P[X>X f |IM] indicates that the structural response under the disaster of level IM exceeds X f The probability of represents the failure probability of the transmission tower line system under the action of the ith disaster; H i (IM) represents the hazard function of the i-th disaster.

[0200] As an optional implementation manner, the dynamic response of the transmission tower line system includes at least one of the following:

[0201] The displacement response at the junction of the main material of the tower body and the cross diaphragm, the displacement response at the cross arm position, the displacement response at the highest point of the tower top, the displacement response at the mid-span of the conductor, the acceleration response at the junction of the main material of the tower body and the cross diaphragm, the acceleration response at the cross arm position, the acceleration response at the highest point of the tower top, the acceleration response at the mid-span of the conductor, the stress of the main material of the tower body, the stress in the mid-span of the conductor and the stress at the mid-span of the ground wire.

[0202] The transmission tower line system reliability assessment device provided in the embodiment of the present invention can implement all the process steps of the transmission tower line system reliability assessment method described in the above embodiment. The functions of each module and unit in the device and the technical effects achieved are respectively the same as the functions and technical effects achieved by the transmission tower line system reliability assessment method described in the above embodiment, and the specific implementation method is not repeated here.

[0203] See also Fig.17 The embodiment of the present invention further provides a transmission tower line system reliability assessment device 20, comprising a processor 21, a memory 22, and a computer program stored in the memory 22 and configured to be executed by the processor 21. When the processor 21 executes the computer program, the steps in the above-mentioned transmission tower line system reliability assessment method embodiment are implemented, for example Figure 1 or, the processor 21 implements the functions of each module in the above-mentioned device embodiments when executing the computer program.

[0204] The transmission tower line system reliability assessment device 20 may be a computing device such as a desktop computer, a notebook, a PDA, and a cloud server. The transmission tower line system reliability assessment device 20 may include, but is not limited to, a processor 21 and a memory 22. Those skilled in the art may understand that the schematic diagram is only an example of the transmission tower line system reliability assessment device 20 and does not constitute a limitation on the transmission tower line system reliability assessment device 20. It may include more or less components than shown in the figure, or combine certain components, or different components. For example, the transmission tower line system reliability assessment device 20 may also include input and output devices, network access devices, buses, etc.

[0205] The processor 21 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or the processor 21 may also be any conventional processor, etc. The processor 21 is the control center of the transmission tower line system reliability assessment device 20, and uses various interfaces and lines to connect various parts of the entire transmission tower line system reliability assessment device 20.

[0206] The memory 22 can be used to store the computer program and / or module. The processor 21 realizes various functions of the transmission tower line system reliability assessment device 20 by running or executing the computer program and / or module stored in the memory 22 and calling the data stored in the memory 22. The memory 22 can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system, an application required for at least one function, etc.; the data storage area can store data created according to the use of the controller, etc. In addition, the memory 22 can include a high-speed random access memory, and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (SmartMedia Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0207] Wherein, if the module integrated in the transmission tower line system reliability assessment device 20 is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-mentioned various method embodiments can be implemented. Wherein, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electric carrier signal, telecommunication signal and software distribution medium.

[0208] The above is a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A reliability assessment method for a transmission tower line system, characterized in that: include: Perform probability space segmentation on the transmission tower line system structure parameters and disaster parameters to obtain representative point parameter samples; Establishing a first finite element analysis model according to the representative point parameter sample, performing a time domain dynamic analysis on the first finite element analysis model, and obtaining a dynamic response of a transmission tower line system; According to the dynamic response, a probability density evolution equation is established; According to the probability density evolution equation, the failure probability of the transmission tower line system under the action of the disaster is calculated, and according to the correlation between the failure probability and the reliability, the reliability of the transmission tower line system is obtained.

2. The reliability assessment method of a transmission tower line system according to claim 1, characterized in that: The performing time domain dynamic analysis on the first finite element analysis model to obtain the dynamic response of the transmission tower line system includes performing time domain dynamic analysis on the first finite element analysis model after mass concentration simplification, specifically including: Dividing the first finite element analysis model into a plurality of node layers; Applying a unit force to the node layer and constructing a flexibility matrix based on the response of the node layer to the unit force; Performing an inverse operation on the flexibility matrix to obtain a stiffness matrix; According to the stiffness matrix, the concentrated mass of each node layer is calculated, and according to the concentrated mass of each node layer, a mass matrix is ​​constructed; Constructing a damping matrix according to the mass matrix and the stiffness matrix; The dynamic response of the transmission tower line system is calculated according to the stiffness matrix, the mass matrix and the damping matrix.

3. The reliability assessment method of a transmission tower line system according to claim 1, characterized in that: The probability density evolution equation is calculated by the following formula: Among them, p XΘ (X,θ,t) represents the probability density of the dynamic response of the transmission tower-line system when the random variable θ takes the value of θ, and the random variable is the structural parameter or disaster parameter; It represents the first derivative of the structural response with respect to time when the random variable Θ takes the value of θ; t represents time.

4. The reliability assessment method of a transmission tower line system according to claim 1, characterized in that: The disaster effect includes at least one disaster effect, and the method for calculating the failure probability specifically includes: For each disaster, according to the probability density evolution equation, the probability density function of the dynamic response of the transmission tower line system under different levels of disasters is solved; According to the probability density function, the expected response of the transmission tower line system under different levels of disasters is calculated; Taking the logarithm of the expected response and disaster level of the transmission tower line system, and performing linear regression to obtain the slope and intercept of the straight line; The failure probability of the transmission tower line system under various disasters is calculated based on the slope of the straight line and the intercept.

5. The reliability assessment method of a transmission tower line system according to claim 4, characterized in that: The failure probability is calculated by the following formula: Among them, P f (IM) represents the failure probability; Φ represents the standard normal cumulative distribution function; a2 represents the intercept; a3 represents the slope of the line; X f It indicates the response threshold corresponding to the structural damage; IM indicates the disaster level.

6. The reliability assessment method of a transmission tower line system according to claim 4, characterized in that: When there are two or more types of disasters, the failure probability under the action of multiple disasters is calculated by the following formula: in, represents the failure probability under various disasters; m represents the type of disaster; X represents the dynamic response of the transmission tower line system; P[X>X f |IM] indicates that the structural response under the disaster of level IM exceeds X f probability; represents the failure probability of the transmission tower line system under the action of the ith disaster; H i (IM) represents the hazard function of the i-th disaster.

7. The reliability assessment method of a transmission tower line system according to claim 1, characterized in that: The dynamic response of the transmission tower line system includes at least one of the following: The displacement response at the junction of the main material of the tower body and the cross diaphragm, the displacement response at the cross arm position, the displacement response at the highest point of the tower top, the displacement response at the mid-span of the conductor, the acceleration response at the junction of the main material of the tower body and the cross diaphragm, the acceleration response at the cross arm position, the acceleration response at the highest point of the tower top, the acceleration response at the mid-span of the conductor, the stress of the main material of the tower body, the stress in the mid-span of the conductor and the stress at the mid-span of the ground wire.

8. A transmission tower line system reliability assessment device, characterized in that: include: The probability space segmentation module is used to perform probability space segmentation on the transmission tower line system structure parameters and disaster parameters to obtain representative point parameter samples; A dynamic response acquisition module, used to establish a first finite element analysis model according to the representative point parameter sample, perform time domain dynamic analysis on the first finite element analysis model, and obtain the dynamic response of the transmission tower line system; A probability density evolution equation establishment module, used to establish a probability density evolution equation according to the dynamic response; The reliability calculation module is used to calculate the failure probability of the transmission tower line system under the action of disasters according to the probability density evolution equation, and obtain the reliability of the transmission tower line system according to the correlation between the failure probability and reliability.

9. The transmission tower line system reliability assessment device according to claim 8, characterized in that: The dynamic response acquisition module further includes a mass concentration simplification unit, which is used to perform time domain dynamic analysis after mass concentration simplification on the first finite element analysis model, specifically including: Dividing the first finite element analysis model into a plurality of node layers; Applying a unit force to the node layer and constructing a flexibility matrix based on the response of the node layer to the unit force; Performing an inverse operation on the flexibility matrix to obtain a stiffness matrix; According to the stiffness matrix, the concentrated mass of each node layer is calculated, and according to the concentrated mass of each node layer, a mass matrix is ​​constructed; Constructing a damping matrix according to the mass matrix and the stiffness matrix; The dynamic response of the transmission tower line system is calculated according to the stiffness matrix, the mass matrix and the damping matrix.

10. The transmission tower line system reliability assessment device according to claim 8, characterized in that: The probability density evolution equation establishment module is used to calculate the probability density evolution equation by the following formula: Among them, p XΘ (X,θ,t) represents the probability density of the dynamic response of the transmission tower-line system when the random variable θ takes the value of θ, and the random variable is the structural parameter or disaster parameter; It represents the first derivative of the structural response with respect to time when the random variable Θ takes the value of θ; t represents time.

11. The transmission tower line system reliability assessment device according to claim 8, characterized in that: The disaster effect includes at least one disaster effect, and the reliability calculation module is used for: For each disaster, according to the probability density evolution equation, the probability density function of the dynamic response of the transmission tower line system under different levels of disasters is solved; According to the probability density function, the expected response of the transmission tower line system under different levels of disasters is calculated; Taking the logarithm of the expected response and disaster level of the transmission tower line system, and performing linear regression to obtain the slope and intercept of the straight line; The failure probability of the transmission tower line system under various disasters is calculated based on the slope of the straight line and the intercept.

12. The transmission tower line system reliability assessment device according to claim 11, characterized in that: The reliability calculation module is also used to calculate the failure probability by the following formula: Among them, P f (IM) represents the failure probability; Φ represents the standard normal cumulative distribution function; a2 represents the intercept; a3 represents the slope of the line; X f It indicates the response threshold corresponding to the structural damage; IM indicates the disaster level.

13. The transmission tower line system reliability assessment device according to claim 11, characterized in that: When there are two or more types of disasters, the reliability calculation module is further used to calculate the failure probability under the action of multiple disasters by the following formula: in, represents the failure probability under various disasters; m represents the type of disaster; X represents the dynamic response of the transmission tower line system; P[X>X f |IM] indicates that the structural response under the disaster of level IM exceeds X f probability; represents the failure probability of the transmission tower line system under the action of the ith disaster; H i (IM) represents the hazard function of the i-th disaster.

14. The transmission tower line system reliability assessment device according to claim 8, characterized in that: The dynamic response of the transmission tower line system includes at least one of the following: The displacement response at the junction of the main material of the tower body and the cross diaphragm, the displacement response at the cross arm position, the displacement response at the highest point of the tower top, the displacement response at the mid-span of the conductor, the acceleration response at the junction of the main material of the tower body and the cross diaphragm, the acceleration response at the cross arm position, the acceleration response at the highest point of the tower top, the acceleration response at the mid-span of the conductor, the stress of the main material of the tower body, the stress in the mid-span of the conductor and the stress at the mid-span of the ground wire.

15. A transmission tower line system reliability assessment device, characterized in that: The method comprises a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein when the processor executes the computer program, the method for evaluating the reliability of a transmission tower line system according to any one of claims 1 to 7 is implemented.

16. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored computer program, wherein when the computer program is executed, the device where the computer-readable storage medium is located is controlled to execute the transmission tower line system reliability assessment method according to any one of claims 1 to 7.

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