Power transmission tower structure reliability analysis method and device, terminal and medium
By using the adaptive hybrid dimensionality reduction model and iterative maximum entropy method in the reliability analysis of transmission tower structure, the problems of unsatisfactory calculation accuracy and high calculation cost in the prior art are solved, and a high-precision analysis of transmission tower structure reliability is achieved.
Patent Information
- Application Number
- CN202411810673.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-10
- Publication Date
- 2025-03-14
AI Technical Summary
The prior art has problems in the analysis of the reliability of transmission tower structures that are not ideal, have high calculation costs, and rely on a large number of verification points, especially when dealing with functional functions with high nonlinearity or excessive dimensions.
The statistical torch estimation method of the adaptive hybrid dimensionality reduction model is used to automatically determine the appropriate statistical moment order through the iterative maximum entropy method, and high-order statistical moment information is used to analyze the reliability of the transmission tower structure.
The accuracy of the calculation of the reliable index of the transmission tower structure is improved, and the accurate analysis of the reliability of the transmission tower structure is achieved. The method is simple, accurate and easy to implement.
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Figure CN119623101A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of reliability analysis of transmission tower structures, and specifically designs a method, device, terminal and medium for reliability analysis of transmission tower structures. Background Art
[0002] Transmission towers are an important part of transmission lines, and ensuring their safety is of vital importance. Due to the characteristics of high height, high flexibility and relatively low rigidity, the transmission tower structure is sensitive to external loads such as wind load and ice load. Therefore, the structural reliability analysis of transmission towers has become the basis and important guarantee for the design of transmission tower structures.
[0003] At present, the structural reliability analysis methods have formed four types of methods, namely, approximate analytical method (first-order second-moment method), numerical simulation method (Monte Carlo method), surrogate model method (polynomial response surface method) and moment method. Among them, the approximate analytical method will have the problem of multiple verification points when dealing with implicit functional functions or strongly nonlinear functional functions such as transmission towers, resulting in unsatisfactory calculation results. Monte Carlo method (MCS) is often used as a verification method because of its high computational cost and is difficult to use for complex structures and problems with low failure probability. The fitting accuracy of the surrogate model method depends on the selection of functions and the selection of experimental design (DOE), which is subjective. In summary, there are many problems with the above three types of equations, while the moment method does not rely on verification points, does not require complex integral calculations and derivations, and has the advantages of simplicity and efficiency. It has been widely used in the reliability analysis of transmission tower structures. The main idea of the moment method is to first obtain the statistical moment information of the functional function, then obtain the probability density function of the functional function based on the statistical moment information, and finally obtain the reliability index through integration.
[0004] At present, the statistical moment estimation method mainly adopts the dimensionality reduction approximation method, among which the sum dimensionality reduction approximation and the product dimensionality reduction approximation are the most widely used. However, these two methods have poor calculation accuracy when dealing with functional functions with high nonlinearity or too high dimension or both additive and multiplicative properties. For this reason, some scholars have proposed a hybrid dimensionality reduction approximation method to solve the above problems, but this method is currently less studied. In terms of probability density function estimation, in theory, the more statistical moment information is applied, the more accurate the probability density function approximation is, but the current approximation method only applies a small amount of statistical moment information.
[0005] Therefore, it is necessary to study an approximate method that can apply high-order statistical moment information to improve the accuracy of reliability index calculation and realize reliability analysis of transmission tower structures. Summary of the invention
[0006] The present invention provides a transmission tower structure reliability analysis method, device, terminal and medium, which can apply high-order statistical moment information to improve the accuracy of transmission tower structure reliability index calculation and realize accurate analysis of transmission tower structure reliability.
[0007] In a first aspect, the present invention provides a transmission tower structure reliability analysis method, device, terminal and medium, comprising the following steps:
[0008] Determine the functional functions of the transmission tower structure based on relevant specifications and designs;
[0009] Solving the statistical moment information of the functional function by using a statistical torch estimation method of an adaptive hybrid dimensionality reduction model;
[0010] The reliability analysis of the structure based on iterative maximum entropy method is carried out to obtain the reliability analysis results of the transmission tower structure.
[0011] Furthermore, the functional expression of the transmission tower structure is:
[0012] Z = g(X)
[0013] Where Z is the performance function; X is an n-dimensional random vector containing random variables related to the reliability of the transmission tower structure.
[0014] Furthermore, the specific process of solving the statistical moment information of the functional function by the statistical moment estimation method of the adaptive hybrid dimensionality reduction model is as follows:
[0015] Based on the functional function, obtaining an adaptive hybrid dimensionality reduction model;
[0016] Statistical moment estimation is performed based on an adaptive hybrid dimensionality reduction model, and the statistical moment information of the performance function is calculated using a direct numerical integration method.
[0017] Furthermore, the steps for obtaining the adaptive hybrid dimensionality reduction model are as follows:
[0018] A high-dimensional sum model with reserved order s is introduced to approximate the functional function, and the expression is:
[0019]
[0020] Among them, h0 is a constant, h i (U i ) represents the variable U in the function Z i The influence of a single action, h i1i2…is (·) represents the variable U in the functional function Z i1 ,U i2 …U is The impact part of the joint action;
[0021] The exponential function I is introduced to obtain the initial adaptive hybrid dimensionality reduction model, which is expressed as:
[0022]
[0023] in,
[0024] The initial adaptive hybrid dimensionality reduction model is divided into two parts, one part includes component functions with an order of up to l, and the other part includes component functions with orders from l+1 to s, to obtain the adaptive hybrid dimensionality reduction model, which is expressed as:
[0025]
[0026] in, r0 is a constant, r i (U i )express Medium variable U i The influence of a single action, r i1i2…il (·)express Medium variable U i1 ,U i2 …U il The affected part of the joint action.
[0027] Furthermore, the statistical moment information of the functional function includes the mean and the q-order center distance, wherein:
[0028] The calculation formula of the mean value of the functional function is:
[0029]
[0030] The calculation formula of the q-order center distance of the functional function is:
[0031]
[0032] Among them, r is the number of calculation points in each dimension, u i,vi 、w i,vi are the integration nodes and weights of the Gauss-Hermite integral formula with the standard normal density function as the weight function, and n is the number of random variables related to the reliability of the transmission tower structure.
[0033] Furthermore, the specific steps of performing reliability analysis on the structure based on iterative maximum entropy method to obtain the reliability analysis result of the transmission tower structure are as follows:
[0034] Standardizing the functional function to obtain a standardized variable Y;
[0035] The objective function is to take the maximum value of the entropy of the standardized variable Y, and the origin moment information ν of the standardized variable Y Y,q As constraints, establish the objective function;
[0036] Solve the objective function and obtain the probability density calculation model of the standardized variable Y;
[0037] According to the probability density calculation model, the failure probability calculation model and the reliability index calculation model of the transmission tower structure are obtained;
[0038] The convergence mechanism is used to determine the order m of the statistical moment and the threshold ε1 of the relative error;
[0039] The probability density calculation model of the standardized variable Y, the failure probability calculation model of the transmission tower structure and the reliability index calculation model are iteratively solved to obtain the failure probability and reliability index of the transmission tower structure.
[0040] Furthermore, the specific steps of iteratively solving the probability density calculation model of the standardized variable Y, the failure probability calculation model of the transmission tower structure, and the reliability index calculation model are as follows:
[0041] According to the determined statistical moment order m, using the adaptive hybrid dimensionality reduction model to calculate the first m-order statistical moment information of the functional function;
[0042] Using the probability density function calculation model of the standardized variable Y, the failure probability calculation model of the transmission tower structure and the reliability index calculation model, the standardized variable Y, the failure probability and the reliability index of the functional function are estimated;
[0043] The convergence is judged according to the threshold ε1 of the relative error. If converged, the first m-order statistical information, failure probability and reliability index of the functional function are output; otherwise, iterative calculation is performed until convergence.
[0044] In a second aspect, the present invention provides a transmission tower structure reliability analysis device for implementing the method described in the first aspect, the device comprising:
[0045] A functional function determination module, used to determine the functional function of the transmission tower structure according to relevant specifications and designs;
[0046] A first calculation module, used for solving the statistical moment information of the functional function by using a statistical torch estimation method of an adaptive hybrid dimensionality reduction model;
[0047] The second calculation module is used to perform reliability analysis on the structure based on the iterative maximum entropy method to obtain reliability analysis results of the transmission tower structure.
[0048] In a third aspect, the present invention proposes an analysis terminal, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor implements the steps of the transmission tower structure reliability analysis method as described in the first aspect when executing the computer program.
[0049] In a fourth aspect, the present invention proposes a readable storage medium having a computer program stored thereon; when the computer program is executed by a processor, the steps of the transmission tower structure reliability analysis method as described in the first aspect are implemented.
[0050] Compared with the prior art, the present invention has the following beneficial technical effects:
[0051] The present invention introduces a point estimation method based on an adaptive hybrid dimensionality reduction model to achieve high-order statistical moment estimation of the random response function of the transmission tower system, and then uses the iterative maximum entropy method to automatically determine the appropriate statistical moment order and apply the high-order statistical moment information to solve the reliability index of the transmission tower structure, thereby forming an easy-to-implement high-precision reliability analysis method for the transmission tower structure. At the same time, the present invention also has the advantages of being simple, accurate and easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS
[0052] Figure 1 is a flow chart of the method of the present invention;
[0053] Figure 2 is a specific flow chart of step 3 in the method of the present invention;
[0054] Figure 3 is a flow chart of the maximum entropy method in the method of the present invention;
[0055] Figure 4 is a principle block diagram of the device of the present invention;
[0056] Figure 5 is a principle block diagram of the terminal of the present invention;
[0057] Figure 6 It is a schematic diagram of a single-story single-span perfectly elastic-plastic frame;
[0058] Figure 7 This is a schematic diagram of the location of the main material components of the tower base. DETAILED DESCRIPTION
[0059] The present invention is further described below in conjunction with the embodiments and drawings. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.
[0060] Embodiment 1:
[0061] like Figure 1As shown, this embodiment provides a transmission tower structure reliability analysis method, and the specific steps are as follows:
[0062] Step 1: Determine the functional function of the transmission tower structure based on relevant specifications and designs;
[0063] In the transmission tower system, random responses (such as internal forces, displacements, etc.) can be expressed as functions of load random variables, structural parameter random variables, etc., that is, the function function is:
[0064] Z=g(X) (1)
[0065] Where Z is the performance function; X=(X1,X2,…,X n ) T is an n-dimensional random vector containing random variables such as loads and structural parameters.
[0066] Step 2: Calculate the statistical moment information of the functional function by using the statistical moment estimation method of the adaptive hybrid dimensionality reduction model. The specific correction is as follows:
[0067] Step 2.1, based on the functional function, obtaining an adaptive hybrid dimensionality reduction model;
[0068] A1. Transform random variables with different distribution types into independent standard normal space, and further rewrite the performance function shown in formula (1) through Rosenblatt transformation or Nataf transformation as follows:
[0069]
[0070] Among them, U is an independent standard normal vector, NOR -1 (·) is the inverse transform of Rosenblatt transform or Nataf transform.
[0071] A2. Introducing a high-dimensional sum model (HDMR) with reserved order s, the performance function Z can be expressed as:
[0072]
[0073] Among them, h0 is a constant, h i (U i ) represents the variable U in Z i The influence of a single action, h i1i2…is (·) represents the variable U in Z i1 ,U i2 …U is The affected part of the joint action.
[0074] A3. For equation (3), not all cross terms on the U component have an effect on Z. According to the U proposed in the literature i , Uj The existence criterion of cross terms is introduced into equation (3), and the initial adaptive hybrid dimensionality reduction model can be obtained:
[0075]
[0076] Among them, the exponential function I is expressed as:
[0077]
[0078] A4, equation (4) can be divided into two parts, that is, the initial adaptive hybrid dimensionality reduction model is divided into two parts, one part includes component functions with an order of up to l, and the other part includes component functions with orders from l+1 to s, to obtain the adaptive hybrid dimensionality reduction model, that is:
[0079]
[0080] The present invention adopts a product dimensionality reduction approximation model with an order of l to approximate Right now:
[0081]
[0082] Among them, r0 is a constant, r i (U i )express Medium variable U i The influence of a single action, r i1i2…il (·)express Medium variable U i1 ,U i2 …U il The affected part of the joint action.
[0083] Combining equations (7)-(9) we can get a new adaptive hybrid dimensionality reduction model, namely AH-DRM.
[0084] Step 2.2: Perform statistical moment estimation based on the adaptive hybrid dimensionality reduction model, and use direct numerical integration to calculate the statistical moment information of the functional function:
[0085] The mean value of the performance function Z and the q-order center distance are calculated by direct numerical integration method, that is:
[0086]
[0087] where u i,vi , w i,vi are the integration nodes and weights of the Gaussian integral formula with the standard normal density function as the weight function.
[0088] The present invention introduces the AH-DRM dimensionality reduction model with l=1 and s=3 to reduce the n-dimensional function h(u 1,v1 ,u 2,v2 ,…,u n,vn ) is simplified to a low-dimensional function, namely:
[0089]
[0090] in:
[0091]
[0092] Combining equations (10) to (14), the present invention adopts a method based on AH-DRM and direct numerical integration for statistical moment estimation, namely:
[0093]
[0094] Where r is the number of calculation points in each dimension, and in this embodiment, r=7. i,vi , w i,vi The abscissa χ of the Gauss-Hermite quadrature formula GH,vi and weight w GH,vi Determine, that is:
[0095]
[0096] Step 3: Perform reliability analysis based on the structure of the iterative maximum entropy method to obtain the reliability analysis results of the transmission tower structure. The specific steps are as follows: Figure 2 As shown:
[0097] Step 3.1: After obtaining the statistical moment information, the maximum entropy method is used to fit the probability density function f of the functional function Z of the transmission tower structure. Z (z), and thus calculate the failure probability of the structure. In actual calculation engineering, the transmission tower structure function Z is usually standardized to obtain the standardized variable Y:
[0098]
[0099] Step 3.2: Take the maximum entropy of the standardized variable Y as the objective function, and the origin moment information ν of the standardized variable Y Y,q As constraints, establish the objective function;
[0100] Since the center distances of each order of the functional function Z and the standardized variable Y have the following relationship:
[0101]
[0102] Among them, ν Y,q is the q-order origin moment of Y.
[0103] Therefore, the maximum entropy of Y can be used as the objective function, and the origin moment information ν of Y Y,q As constraints, an optimization model, namely the objective function, is established:
[0104]
[0105] Step 3.3, solve the objective function and obtain the probability density calculation model of the standardized variable Y:
[0106] The embodiment of the present invention introduces the Lagrange multiplier to solve the optimization problem of formula (20) and constructs the Lagrange function, namely:
[0107]
[0108] The Lagrange coefficient λ can be obtained by solving the nonlinear equation q (q=0,1,…,m), thus obtaining the probability density function f of Y Y (y), that is:
[0109]
[0110] Step 3.4: Obtain the failure probability calculation model and reliability index calculation model of the transmission tower structure according to the probability density calculation model, namely:
[0111]
[0112] Among them, P f,m , β m They are respectively the failure probability and reliability index calculated using the first m-order statistical moment information.
[0113] Step 3.5. Generally, as the order m of the statistical moment increases, the failure probability and reliability index tend to a stable value. Based on this, a convergence mechanism is used to reasonably determine the order m of the moment; at the same time, the threshold ε1 of the relative error is set to obtain the convergence judgment equation:
[0114] ||β m+1 -β m || / ||β m ||≤ε1 (24)
[0115] Here, ε1 is a relative error threshold, and in the embodiment of the present invention, 1e-2 is used.
[0116] Step 3.6, iteratively solve the probability density calculation model of the standardized variable Y, the failure probability calculation model of the transmission tower structure, and the reliability index calculation model to obtain the failure probability and reliability index of the transmission tower structure.
[0117] In this embodiment, the specific steps of iteratively solving the probability density calculation model of the standardized variable Y, the failure probability calculation model of the transmission tower structure, and the reliability index calculation model in step 3.6 are as follows: Figure 3 As shown:
[0118] B1. Obtain the order of the determined statistical moment m=4;
[0119] B2. Calculate the first m-order statistical moment information μ of the transmission tower structure function function Z using equations (15)-(17) Z 、M Z,q (q=0,1,…,m);
[0120] B3. Estimate the probability density function f of the standardized variable Y of the transmission tower structure function function Z using equations (18)-(23) Y (y) and the failure probability P f,m , reliability index β m ;
[0121] B4, using the relative error threshold ε1 to judge the convergence, specifically using equation (24) to judge the convergence, if convergence, that is, equation (24) is satisfied, then go to step B5; otherwise, let m = m + 1, and repeat steps B2-B4;
[0122] B5. Output the first m-order statistical moment information μ of the transmission tower structure function function Z Z 、M Z,q (q=0,1,…,m) and failure probability P f,m , reliability index β m .
[0123] Embodiment 2:
[0124] like Figure 4 As shown, this embodiment provides a transmission tower structure reliability analysis device for implementing the method described in Example 1, and the device includes:
[0125] A functional function determination module, used to determine the functional function of the transmission tower structure according to relevant specifications and designs;
[0126] A first calculation module, used for solving the statistical moment information of the functional function by using a statistical torch estimation method of an adaptive hybrid dimensionality reduction model;
[0127] The second calculation module is used to perform reliability analysis on the structure based on the iterative maximum entropy method to obtain reliability analysis results of the transmission tower structure.
[0128] Embodiment 3:
[0129] like Figure 5As shown, this embodiment provides an analysis terminal, including a processor, a memory and a network interface connected by a system bus. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to manage relevant data of the system, such as basic information of convalescents, nutritional assessment results, recipes, nutritional reports, etc. When the computer program is executed by the processor, the processor executes the steps of the transmission tower structure reliability analysis method described in Example 1.
[0130] Those skilled in the art will understand that Figure 5 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.
[0131] Embodiment 4:
[0132] This embodiment provides a readable storage medium, on which a computer program is stored; when the computer program is executed by a processor, the steps of the transmission tower structure reliability analysis method as described in Example 1 are implemented.
[0133] In order to prove the accuracy and efficiency of the invented method in statistical moment estimation and structural reliability assessment, three examples are used, including one numerical example and two engineering examples, to compare the invented method with the method proposed by Zhang Xufang, Song Xiaohui, etc. in terms of statistical moment estimation and structural reliability index calculation. At the same time, the result of the Monte Carlo simulation method (denoted as MCS) with a sampling number of N is taken as the standard solution.
[0134] In these examples, the relative error ε is defined as
[0135]
[0136] Among them, Value is the result of other methods, and MCS represents the result of Monte Carlo simulation method.
[0137] Numerical example:
[0138] In this example, it is assumed that the expression of the response function Z is:
[0139]
[0140] In this case, all random variables X i(i=1,2,3,4) all obey lognormal distribution, and their means are 10, 100, 17, 2.5×10 5 , and the standard deviations are 1, 30, 0.1, and 0.312×10 5 Table 1 gives the central moment results calculated by different methods, where the standard solution is N = 1 × 10 6 The results of the Monte Carlo simulation method for sample points.
[0141] Table 1 Comparison of the first four central moments of Example 1
[0142]
[0143] From Table 1, we can see that all three methods can improve the mean value to a fairly accurate level, but the results of the higher-order central moments vary greatly. Among them, the higher-order central moments estimated by Zhang and Song have poor accuracy, while M 3,z The relative error is as high as 17.64%. The method provided by the present invention can provide more accurate results with higher efficiency. Compared with the Zhang and Song methods, M z,3 and M z,4 The relative error is further reduced, and the maximum relative error is only 4.28%.
[0144] Table 2 Comparison of reliability indices obtained by different methods in Example 1
[0145]
[0146] It can be seen from Table 2 that the relative error of the reliability index estimated by Zhang's method reaches 11.69%, which is the lowest precision. In comparison, the method of the present invention can obtain the most accurate reliability index result with higher efficiency, and the relative error is only 1.88%.
[0147] Engineering example 1:
[0148] Example 1 of this project is a single-story single-span ideal elastic-plastic frame structure subjected to lateral load S. Figure 6 The cross-sectional area of all components is 0.09m 2 , the elastic modulus of the material is E = 2.06 × 10 5 Mpa, each random variable is independent of each other, and the statistical information of the random variables is shown in Table 3.
[0149] Table 3 Random variable distribution parameters of engineering example 1
[0150]
[0151] According to the complete system destruction process, the failure probability of the framework can be equivalently expressed as:
[0152] P f =Pr{Pmax (M1,M2,M3)-S<0} (27)
[0153] Where P max (·) is the ultimate bearing capacity corresponding to the load parameter S.
[0154] Table 4 Comparison of the first four central moments of engineering example 1
[0155]
[0156] Table 4 shows the results of the first four central moments estimated by different methods, including the relative error and the number of times the function is called. It can be seen that the calculation results of the high-order central moments by the method proposed by Zhang and Song are not ideal. 2,Z , M 3,Z The relative errors are 7.13% and 17.37% respectively. The inventive method can obtain relatively accurate first four-order center distances, with a maximum relative error of 11.12%, but requires additional calculation of cross terms.
[0157] Table 5 Comparison of reliability indices obtained by different methods in Engineering Example 1
[0158]
[0159] Table 5 shows the reliability index results calculated by different algorithms, among which the result calculated by the invented method is the most accurate, with a relative error of only 0.76%, and the calculation efficiency is comparable to that of Zhang and Song. Zhang's method has the worst accuracy, with a relative error of 13.6%.
[0160] Engineering example 2:
[0161] This example selects a 220kV double-circuit self-supporting transmission tower to verify the performance of the invented method. Among them, the tower shape is 2C2C-Z1-42 / 30. The main material of the tower leg, the web and the cross partition use equilateral angle steel as the material. The design conditions of the line are: the conductor is a double-split JL / G1A-400 / 35 steel-core aluminum stranded wire with a unit mass of 2.375kg / m; the ground wire is a LBGJ-150-40AC aluminum-clad steel stranded wire with a unit mass of 1.22kg / m. The horizontal span is 350m and the vertical span is 550m. The basic wind pressure is 0.951kN / m 2 , load condition 90° high wind condition; the design basic period T of the component is 50 years. The finite element model of the transmission tower is modeled using Beam188 beam elements, with a tower height of 60.4m. The main material of the tower body is Q345 cold-rolled equilateral angle steel. The main rods are connected to each other through flanges, and the diagonal braces are connected to the main rods through bolts. Some positions are intersected and reinforced.
[0162] In this example, the load on the transmission tower structure only considers horizontal wind load and self-weight load. To simplify the model, the loads of the ground wire and metal insulator are directly applied to the suspension point, that is, the node between the cross arm and the horn. The main material of the transmission tower is the main force-bearing part, and the force near the bottom of the tower is relatively large. Therefore, this example Figure 7 The main material component of a tower foot is studied, and the function of the transmission tower component is as follows:
[0163] Z=g(W,G,R,E,ν) (28)
[0164] The limit state of the functional function Z is when the stress of the component reaches the yield strength. In formula (28), W is the wind load, R is the yield strength of the material, G is the gravity load, E is the elastic modulus of the material, and ν is the Poisson's ratio. Table 6 gives the random variables and their probability distribution parameters.
[0165] Table 6 Random variables and their probability distribution parameters
[0166]
[0167]
[0168] Table 7 Comparison of the first four central moments of engineering example 2
[0169]
[0170] Table 8 Comparison of reliability indices obtained by different methods in Engineering Example 2
[0171]
[0172] Table 8 shows the reliability index results calculated by the three methods, among which Song's method has the worst accuracy, with a relative error of 3.44%. In comparison, the method of the present invention can obtain the most accurate reliability index with higher calculation efficiency.
[0173] In summary, the present invention realizes the estimation of high-order statistical moments of the random response function of the transmission tower system by introducing a point estimation method based on an adaptive hybrid dimensionality reduction model, and then uses the iterative maximum entropy method to automatically determine the appropriate statistical moment order and apply the high-order statistical moment information to solve the reliability index of the transmission tower structure, thereby forming an easy-to-implement high-precision reliability analysis method for the transmission tower structure, which can improve the accuracy of the calculation of the reliability index of the transmission tower structure and realize accurate analysis of the reliability of the transmission tower structure.
[0174] Finally, it should be noted that the above description is only a preferred embodiment of the present invention. Under the guidance of the present invention, ordinary technicians in this field can make various similar expressions without violating the purpose and claims of the present invention, and such changes all fall within the scope of protection of the present invention.
Claims
1. A transmission tower structure reliability analysis method, characterized in that: The steps include: Determine the functional functions of the transmission tower structure based on relevant specifications and designs; Solving the statistical moment information of the functional function by using a statistical torch estimation method of an adaptive hybrid dimensionality reduction model; The reliability analysis of the structure based on iterative maximum entropy method is carried out to obtain the reliability analysis results of the transmission tower structure.
2. The transmission tower structure reliability analysis method according to claim 1, characterized in that: The expression of the functional function of the transmission tower structure is: Z = g(X) Where Z is the performance function; X is an n-dimensional random vector containing random variables related to the reliability of the transmission tower structure.
3. The transmission tower structure reliability analysis method according to claim 1, characterized in that: The specific process of solving the statistical moment information of the functional function by the statistical moment estimation method of the adaptive hybrid dimensionality reduction model is as follows: Based on the functional function, obtaining an adaptive hybrid dimensionality reduction model; Statistical moment estimation is performed based on an adaptive hybrid dimensionality reduction model, and the statistical moment information of the performance function is calculated using a direct numerical integration method.
4. The transmission tower structure reliability analysis method according to claim 3, characterized in that: The steps for obtaining the adaptive hybrid dimensionality reduction model are as follows: A high-dimensional sum model with reserved order s is introduced to approximate the functional function, and the expression is: Among them, h0 is a constant, h i (U i ) represents the variable U in the function Z i The influence of a single action, h i1i2…is (·) represents the variable U in the functional function Z i1 ,U i2 …U is The impact part of the joint action; The exponential function I is introduced to obtain the initial adaptive hybrid dimensionality reduction model, which is expressed as: in, The initial adaptive hybrid dimensionality reduction model is divided into two parts, one part includes component functions with an order of up to l, and the other part includes component functions with orders from l+1 to s, to obtain the adaptive hybrid dimensionality reduction model, which is expressed as: in, r0 is a constant, r i (U i )express Medium variable U i The influence of a single action, r i1i2…il (·)express Medium variable U i1 ,U i2 …U il The affected part of the joint action.
5. The transmission tower structure reliability analysis method according to claim 4, characterized in that: The statistical moment information of the functional function includes the mean and the q-order center distance, where: The calculation formula of the mean value of the functional function is: The calculation formula of the q-order center distance of the functional function is: Among them, r is the number of calculation points in each dimension, u i,vi 、w i,vi are the integration nodes and weights of the Gauss-Hermite integral formula with the standard normal density function as the weight function, and n is the number of random variables related to the reliability of the transmission tower structure.
6. The transmission tower structure reliability analysis method according to claim 1, characterized in that: The specific steps of performing reliability analysis on the structure based on iterative maximum entropy method to obtain the reliability analysis result of the transmission tower structure are as follows: Standardizing the functional function to obtain a standardized variable Y; The objective function is to take the maximum value of the entropy of the standardized variable Y, and the origin moment information ν of the standardized variable Y Y,q As constraints, establish the objective function; Solve the objective function and obtain the probability density calculation model of the standardized variable Y; According to the probability density calculation model, the failure probability calculation model and the reliability index calculation model of the transmission tower structure are obtained; The convergence mechanism is used to determine the order m of the statistical moment and the threshold ε1 of the relative error; The probability density calculation model of the standardized variable Y, the failure probability calculation model of the transmission tower structure and the reliability index calculation model are iteratively solved to obtain the failure probability and reliability index of the transmission tower structure.
7. The transmission tower structure reliability analysis method according to claim 6, characterized in that: The specific steps of iteratively solving the probability density calculation model of the standardized variable Y, the failure probability calculation model of the transmission tower structure and the reliability index calculation model are as follows: According to the determined statistical moment order m, using the adaptive hybrid dimensionality reduction model to calculate the first m-order statistical moment information of the functional function; Using the probability density function calculation model of the standardized variable Y, the failure probability calculation model of the transmission tower structure and the reliability index calculation model, the standardized variable Y, the failure probability and the reliability index of the functional function are estimated; The convergence is judged according to the threshold ε1 of the relative error. If converged, the first m-order statistical information, failure probability and reliability index of the functional function are output; otherwise, iterative calculation is performed until convergence.
8. A transmission tower structure reliability analysis device, characterized in that: Used to implement the transmission tower structure reliability analysis method according to any one of claims 1 to 7, the device comprises: A functional function determination module, used to determine the functional function of the transmission tower structure according to relevant specifications and designs; A first calculation module, used for solving the statistical moment information of the functional function by using a statistical torch estimation method of an adaptive hybrid dimensionality reduction model; The second calculation module is used to perform reliability analysis on the structure based on the iterative maximum entropy method to obtain reliability analysis results of the transmission tower structure.
9. An analysis terminal, characterized in that: The invention comprises a processor, a memory and a computer program stored in the memory and configured to be executed by the processor, wherein the processor implements the steps of the transmission tower structure reliability analysis method according to any one of claims 1 to 7 when executing the computer program.
10. A readable storage medium, characterized in that: The readable storage medium stores a computer program; when the computer program is executed by a processor, the steps of the transmission tower structure reliability analysis method according to any one of claims 1 to 7 are implemented.