Method and system for evaluating wind resistance reliability of multi-component of long-short leg power transmission tower structure

Abstract

The application discloses a kind of long short leg power transmission tower structure multi-component wind resistance reliability evaluation method and system, belong to the field of power transmission and distribution, including steps: S1, establish long short leg power transmission tower nonlinear finite element analysis model;S2, determine long short leg power transmission tower function function and uncertainty parameter;S3, consider long short leg power transmission tower uncertainty factor, generate random variable sample point;S4, random variable replacement and component function function calculation;S5, the failure probability and reliability index of each component are calculated.The application can greatly reduce the sampling quantity, and obtain the estimated value of certainty, can efficiently and accurately evaluate the long short leg power transmission tower multi-component reliability level, and then targetedly provide maintenance, reinforcement and optimization measures for long short leg power transmission tower structure and component, with important engineering value.

Description

Technical Field

[0001] This invention relates to the field of power transmission and distribution, and more specifically, to a method and system for evaluating the wind resistance reliability of multi-component structures of long and short leg transmission towers. Background Technology

[0002] As a crucial component of power transmission and distribution systems, transmission towers are the carriers of high-load electrical energy and vital lifeline engineering projects. However, due to the uneven distribution of resources in my country, approximately two-thirds of the area covered by the power transmission and distribution system is mountainous. With the needs of power construction, many transmission lines have to traverse steep mountainous areas to connect the entire power grid. Among these, transmission towers with varying leg lengths are widely used in transmission lines in steep mountainous areas because they offer advantages such as protecting the ecological environment of the transmission line corridor, reducing foundation excavation, and adapting well to different terrain conditions.

[0003] However, existing research on transmission towers with varying leg lengths largely focuses on numerical simulations and experimental studies, with little attention paid to their reliability. Furthermore, the structure of a transmission tower with varying leg lengths is a spatial structural system composed of multiple steel components, each with different reliability indicators. Therefore, systematically analyzing the reliability levels of each component of a transmission tower with varying leg lengths (i.e., conducting multi-component reliability analysis) is of great significance for the safety assessment and maintenance reinforcement of the tower structure and its components. Existing multi-component reliability methods include the Monte Carlo method, response surface methodology, and JC method. While the Monte Carlo (MC) method offers high accuracy, its computational cost often reaches millions of dollars. The response surface methodology requires constructing a response surface function for each member; for complex structural systems, the number of finite element calculations required increases exponentially with the number of members, and it also suffers from convergence issues. Similarly, the JC method requires iterative verification at checkpoints for each member, and its computational cost is also affected by the number of members. Furthermore, for transmission tower structures with high nonlinearity, its calculation results may contain significant errors. Therefore, developing efficient reliability analysis methods whose computational cost is unaffected by the number of members for multi-component reliability analysis of transmission towers with varying lengths of legs will have significant theoretical and engineering value. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and system for evaluating the wind resistance reliability of multiple components of long and short leg transmission towers. This method can significantly reduce the number of samples and obtain deterministic estimates. It can efficiently and accurately evaluate the reliability level of multiple components of long and short leg transmission towers, and thus provide targeted maintenance, reinforcement and optimization measures for the structure and components of long and short leg transmission towers, which has important engineering value.

[0005] The objective of this invention is achieved through the following solution:

[0006] A method for evaluating the wind resistance reliability of multi-component transmission tower structures with varying leg lengths in steep mountainous areas includes the following steps:

[0007] S1. Establish a nonlinear finite element analysis model for transmission towers with varying lengths of legs;

[0008] S2, determine the function and uncertainty parameters of the long and short leg transmission towers;

[0009] S3, considering the uncertainties of transmission towers with varying lengths, generate random variable sample points;

[0010] S4, Random variable substitution and component function calculation;

[0011] S5 calculates the failure probability and reliability index of each component.

[0012] Furthermore, in step S1, the establishment of the nonlinear finite element analysis model of the long and short leg transmission tower specifically involves establishing the nonlinear finite element analysis model of the long and short leg transmission tower in conjunction with a specific engineering example.

[0013] Furthermore, in step S2, determining the function and uncertainty parameters of the long and short leg transmission towers specifically involves clarifying the corresponding failure criteria and function based on the stress form of each component of the long and short leg transmission tower; and determining the random variable parameters and distribution type of the long and short leg transmission towers based on the materials, load forms, and environment of the long and short leg transmission towers.

[0014] Further, in step S3, the step of considering the uncertainty factors of transmission towers with varying lengths and generating random variable sample points specifically involves: determining the number of random samples N, combining the selected random variables, using the Sobol sequence sampling method, and combining the specific random vector distribution, and then according to the cumulative distribution function F. X Inverting (θ) yields a random sample, resulting in a sample set x that conforms to the basic random variable.

[0015] Further, in step S4, the random variable replacement and component function calculation specifically involve: developing a program to replace random variables in the finite element calculation file of the long and short leg transmission tower, calling the finite element model of the long and short leg transmission tower to calculate the response set Y of each component at the sample points, and selecting the corresponding function and calculating its function value G according to the stress form of the specific component. mn (x), where m represents the corresponding function, with values ​​of 1, 2, ..., 5; n represents the component number of the long and short leg transmission tower, with values ​​of 1, 2, ..., z, and z is the number of components.

[0016] Furthermore, the Sobol sequence sampling method, combined with a specific random vector distribution, and based on the cumulative distribution function F... X(θ) Inverse the random sample to obtain the sample set x that conforms to the basic random variable. This includes the following sub-steps:

[0017] S31, let v i Less than 2 i The expression for a positive odd number is:

[0018]

[0019] In the formula, v i These are called "direct numbers," generated by functional polynomials with coefficients of 0 or 1, as shown in equation (2):

[0020] f(a) = a q +c1a q-1 +…+c q-1 a+c q c i ∈{0,1} (10)

[0021] When i > q, v i There exists a recursive formula:

[0022]

[0023] In the formula, This represents the XOR operation in binary;

[0024] S32, there exists any decimal integer m that uniquely represents an expression with base b = 2:

[0025]

[0026] In the formula, p is the smallest integer greater than or equal to log₂m; a k = 0 or 1; therefore, the z-th element of the Sobol sequence is calculated as follows:

[0027]

[0028] The low-deviation point set θ in the interval [0,1] is generated using equations (1) to (5). ji , i = 1, 2, ..., s; j = 1, 2, ..., N, s is the number of random variables;

[0029] S33, combined with the specific random vector distribution, further based on the cumulative distribution function F X Inverse (θ) yields the random sample x, i.e.:

[0030]

[0031] Furthermore, the programming process includes programming MATLAB programs.

[0032] Furthermore, the response set Y of each component at the sample point of the finite element model of the long and short leg transmission tower specifically includes bending moment and axial force.

[0033] Furthermore, in step S5, the calculation of the failure probability and reliability index of each component is specifically performed using the following formula:

[0034] S51, according to equations (10) and (11),

[0035]

[0036] In the formula, x k The sample points in the k-th simulation, G(x) k Let I be the function value corresponding to the k-th sample point, where I takes values ​​of {0,1}. When G(x(k))≤0, I[G(x)] = 0. k When G(x) = 1, k When )>0, I[G(x) k )] = 0;

[0037] Correspondingly, the reliability index of the structure is expressed as:

[0038] β=-Φ -1 (p f (16)

[0039] In the formula, Ф is the standard normal distribution function;

[0040] S52, using the QMC method, the failure probability p of the nth component of the long and short leg transmission tower is obtained. f,n and reliability index β n .

[0041] A multi-component wind resistance reliability assessment system for long and short leg transmission tower structures in steep mountainous areas includes a computer device, which includes a processor and a memory. The memory stores a computer program, which, when loaded by the processor, executes the method described in any of the preceding descriptions.

[0042] The beneficial effects of this invention include:

[0043] The reliability calculation method for multi-component long and short legs based on low-biased sequences involved in this invention can significantly reduce the number of samples and obtain deterministic estimates. It can efficiently and accurately assess the reliability level of multi-component long and short leg transmission towers, and thus provide targeted maintenance, reinforcement and optimization measures for the structure and components of long and short leg transmission towers, which has important engineering value. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 Examples of applications for transmission towers with varying leg lengths;

[0046] Figure 2 The sampling distribution of Sobol sequences and pseudo-random sequences in two-dimensional space;

[0047] Figure 3 This is a reliability assessment process for long and short leg transmission towers based on the QMC method;

[0048] Figure 4 For plan view and finite element model;

[0049] Figure 5 For stress contour plots and displacement contour plots;

[0050] Figure 6 Frequency graph of component reliability indicators;

[0051] Figure 7 A comparison of long-legged and short-legged main materials;

[0052] Figure 8 For the standard deviation and reliability indicators of short-leg main materials;

[0053] Figure 9 The impact of tower leg level differences on reliability;

[0054] Figure 10 The impact of high fever on reliable indicators;

[0055] Figure 11 The impact of design wind speed on reliability indicators. Detailed Implementation

[0056] All features disclosed in all embodiments of this specification, or steps in all methods or processes implied in the disclosure, may be combined and / or extended or replaced in any way, except for mutually exclusive features and / or steps.

[0057] Low-biased sequences focus on the uniformity of the point set and are an efficient sampling method, typically taking the form of GLP point sets, Halton sequences, Sobol sequences, and HW point sets. Because Sobol sequences have high computational accuracy and good convergence, this invention uses Sobol sequences for reliability analysis of transmission towers with varying leg lengths. The generation method is described below:

[0058] Assume v i Less than 2 i The expression for a positive odd number is:

[0059]

[0060] In the formula, v i It is called a "direct number" and is generated by a functional polynomial with coefficients of 0 or 1, as shown in equation (2).

[0061] f(a) = a q +c1a q-1 +…+c q-1 a+c q c i ∈{0,1} (18)

[0062] When i > q, v i There exists a recursive formula:

[0063]

[0064] In the formula, This represents the XOR operation in binary.

[0065] There exists any decimal integer m that uniquely represents an expression with base b = 2.

[0066]

[0067] In the formula, p is the smallest integer greater than or equal to log₂m; a k = 0 or 1.

[0068] Therefore, the z-th element of the Sobol sequence can be calculated as follows:

[0069]

[0070] Based on the specific random vector distribution, we can further determine the cumulative distribution function F. X Inverse (θ) yields the random sample x, i.e.:

[0071]

[0072] Taking 300 sample points in a two-dimensional distribution space as an example, Figure 2 The sampling distribution diagrams of Sobol sequences and pseudo-random sequences in two-dimensional space are given. Figure 2 (a) shows the distribution of sample points in a pseudo-random sequence. It can be seen that sample points are clustered in some areas and there are also blank areas in some areas, and the sampling results are relatively messy. Figure 2(b) shows the distribution of Sobol sequence sample points. It can be seen that the sample points are evenly distributed in two-dimensional space, with uniform differences, which can avoid generating duplicate or similar sample points and greatly improve the sampling efficiency.

[0073] The QMC method and bias estimation: Traditional MC methods generate pseudo-random sequences that randomly fill the distribution space, failing to guarantee uniform spatial distribution. The basic idea of ​​QMC is to replace the pseudo-random sequences of MC with deterministic, low-biased sequence points. By introducing a low-biased point set, the quality of sampling points can be greatly improved, resulting in faster convergence.

[0074] The integration error of the QMC method is mainly determined by the bias; the smaller the bias, the more uniform the point set distribution, and the higher the computational accuracy. Based on the Kokama-Hlawka theorem, the computational error can be expressed as:

[0075]

[0076] In the formula, d and N represent the dimension and number of elements in M, respectively; V(f) represents the Hardy-Krause bounded total variation; D N * (M) represents star deviation, defined as follows:

[0077]

[0078] In the formula, A N ([0,x),M) represents the number of N samples in sequence M in the interval [0,x), calculated according to equation (18).

[0079]

[0080] In the formula, I is a function taking values ​​of {0,1}, when ξ i When ∈[0,x), I(ξ) i When ) = 1, At that time, I(ξ) i ) = 0.

[0081] After generating random sample points that meet the accuracy requirements using equations (1) to (9), the Monte Carlo method can be further combined to perform N random simulations to obtain the failure probability of the structure, i.e.

[0082]

[0083] In the formula, x k The sample points in the k-th simulation, G(x) k Let I be the function value corresponding to the k-th sample point, where I takes values ​​of {0,1}. When G(x(k))≤0, I[G(x)] = 0. kWhen G(x) = 1, k When )>0, I[G(x) k )]=0.

[0084] Correspondingly, the reliability index of the structure is expressed as:

[0085] β=-Φ -1 (p f (27)

[0086] In the formula, Ф is the standard normal distribution function.

[0087] In summary, the reliability assessment process for multi-component transmission towers with varying leg lengths based on the QMC method is as follows: Figure 3 As shown, the specific steps are as follows:

[0088] Step 1: Based on specific engineering examples, establish a reasonable and accurate nonlinear finite element analysis model for transmission towers with varying lengths of legs;

[0089] Step 2: Determine the function and uncertainty parameters of the long and short leg transmission towers. Based on the stress forms of each component of the long and short leg transmission towers, clarify their corresponding failure criteria and function; based on the materials, load forms, and environment of the long and short leg transmission towers, determine the random variable parameters and distribution types of the long and short leg transmission towers.

[0090] Step 3: Considering the uncertainties of transmission towers with varying lengths, generate random variable sample points. Determine the number of random samples N, and based on the selected random variables, generate a low-deviation point set θ in the interval [0,1] using the Sobol sequence sampling method, i.e., equations (1) to (5). ji (i = 1, 2, ..., s; j = 1, 2, ..., N, s is the number of random variables), and obtain the sample set x that conforms to the basic random variables from equation (6);

[0091] Step 4: Random Variable Replacement and Functional Calculation of Components. A MATLAB program is developed to replace random variables in the finite element analysis file of the transmission tower with varying leg lengths. The program then uses the finite element model of the transmission tower with varying leg lengths to calculate the response set Y (mainly bending moment and axial force) of each component at the sample points. Based on the specific stress form of the component, the corresponding functional function is selected and its value G is calculated. mn (x), where m represents the corresponding function, taking values ​​of 1, 2, ..., 5; n represents the component number of the long and short leg transmission tower, taking values ​​of 1, 2, ..., z, where z is the number of components;

[0092] Step 5: Calculate the failure probability and reliability index of each component. Based on equations (10) and (11), and combined with the QMC method, the failure probability p of the nth component of the long and short leg transmission tower is obtained. f,n and reliability index β n .

[0093] This invention aims to solve the following technical problems:

[0094] (1) Transmission towers with different lengths are widely used in steep mountainous areas, but research on them is mostly focused on numerical simulation and experimental research, while research on the reliability of transmission towers with different lengths is rarely involved.

[0095] (2) For the structure of long and short leg transmission towers, it is a spatial structural system composed of multiple steel components. However, the reliability indicators of each steel component are not the same, and the reliability indicators of each component need to be calculated. However, most existing multi-component reliability analysis methods have problems such as low accuracy and low calculation efficiency. Exploring an accurate and efficient multi-component reliability analysis method for long and short legs will be of great significance for the maintenance and reinforcement of long and short leg transmission tower structures and components.

[0096] In a further inventive concept, this embodiment provides a method for calculating and evaluating the reliability of multiple components of long and short leg transmission towers based on low-deviation sequences. Taking a long and short leg tension tower in a 500kV steep mountain transmission line project as the research object, the reliability of multiple components is evaluated based on the method of this invention. It should be noted that the method of this invention has a certain degree of universality and is not limited to this specific project example. For any other long and short leg transmission tower structure, only corresponding adjustments need to be made within the analytical framework of this invention to conduct a safety evaluation.

[0097] Regarding the function, under external loads, different components of long and short leg transmission towers exhibit different failure modes. For example, tension members typically exhibit strength failure, while compression members can experience both strength failure and stability failure. According to the "Technical Specification for Structural Design of Overhead Transmission Line Towers" (DL / T5486-2020), all components of long and short leg transmission towers are classified according to their stress state into tension members, compression members, tension-bending members, compression-bending members, and bidirectional bending members, with corresponding function functions as follows:

[0098] Axially tensioned members:

[0099]

[0100] In the formula: x is a random variable; N is the axial tension; f u γ is the tensile strength of steel; R η is the resistance partial factor, taken from Table 4.4.1-2 of the standard; η is the component strength reduction factor, taken from Table 6.1.1 of the standard; A n This represents the net cross-sectional area of ​​the component.

[0101] Axially compressed members:

[0102]

[0103] In the formula: fy The yield strength of the steel; The stability coefficient is taken from Appendix B of the standard; A is the gross cross-sectional area of ​​the component; m N The coefficient for reducing the stability strength of the compression member is calculated according to formula (14).

[0104]

[0105] In the formula: w and t represent the free overhang width and flange thickness of the angle steel flange, respectively; η c Indicates the width-to-thickness ratio limit of angle steel members, according to calculate.

[0106] Bending members:

[0107]

[0108] Where: M x M y Wx and Wy represent the bending moments about the x-axis and y-axis, respectively; y These represent the section modulus about the x-axis and y-axis, respectively.

[0109] Compression-bending members:

[0110]

[0111] Where: N EX The axial compression parameter is calculated according to formula (17).

[0112]

[0113] In the formula: λ x Let x be the slenderness ratio of the component about the x-axis.

[0114] Tension-bending components:

[0115]

[0116] Regarding uncertainty parameters, the reliability performance of engineering structures is affected by various uncertain factors, which can be mainly divided into the randomness of the structure itself and the randomness of the load. For transmission tower structures with different leg lengths, the randomness of the structure mainly lies in the material properties, while the randomness of the load is mainly reflected in the randomness of the wind load.

[0117] Regarding the randomness of materials, transmission towers with varying leg lengths are typically composed of angle steel components, whose material properties are usually defined by elastic modulus, Poisson's ratio, and yield strength. According to the "Unified Standard for Reliability Design of Building Structures" (GB50068-2018), the random variables and probability distributions of materials in transmission towers with varying leg lengths are shown in Table 1.

[0118] Table 1. Random variables of materials and their probability distribution parameters

[0119]

[0120] Regarding the randomness of loads, for the randomness of wind loads, existing codes typically use an equivalent static wind load model, which defines the equivalent static wind load as the product of the static wind load and the wind vibration coefficient. Assume the equivalent static wind load W... se Following an extreme value type I distribution, the probability distribution of the equivalent static wind load within the design reference period T is expressed as:

[0121]

[0122] The corresponding mean and standard deviation are as follows:

[0123]

[0124] In the formula: and W respectively se The mean and coefficient of variation.

[0125] In an engineering example, regarding the finite element model of transmission towers with varying leg lengths, a tension tower with varying leg lengths in a 500kV steep mountain transmission line project is used as the research object. This tower is designed according to the "Technical Specification for Structural Design of Overhead Transmission Line Towers" (DL / T5486-2020), and the plan view is shown below. Figure 4 (a) The tower has a height of 48m, a total height of 84.4m, a horizontal span of 450m, a vertical span of 700m, and a length difference of 12m between the long and short legs. The conductor uses JL3 / G1A-630 / 45 type steel-cored aluminum stranded wire with four splits, and the ground wire uses OPGW-17-150-4 type optical cable and JLB35-150 type aluminum-clad steel stranded wire on the left and right sides respectively.

[0126] A finite element model of the long and short leg transmission tower was established using the general-purpose finite element software ANSYS / APDL. The main structural members were simulated using BEAM189 elements, and the diagonal members were simulated using LINK8 elements. Fixed constraints were applied to the bottom of the tower legs. The finite element model is shown below. Figure 4(b) The main materials of the tower body, crossarm, and ground wire support are made of Q355 steel, and the diagonal members are made of Q235 steel. The constitutive model adopts the bilinear follower-strengthened model (BKIN). In terms of load application, a quasi-static treatment method is adopted, with three load steps. The first load step applies the self-weight of the tower, the second load step applies the conductor and ground wire tension, and the third load step applies the wind load on the tower body and conductor and ground wire. In terms of wind load calculation, according to the "Load Code for Overhead Transmission Lines" (DL / T5551-2018) 4.2.10, "The most unfavorable wind direction should be calculated for towers. For suspension towers, the basic wind directions at 0°, 45° (60°), and 90° with the line direction should be calculated. For general tension towers, only the wind direction at 90° is required." Since the transmission tower with varying lengths is a double-circuit AC tension tower with a maximum design wind speed of 29 m / s, the wind load calculation for this invention is based on the most unfavorable wind direction, i.e., a design wind speed of 27 m / s and a wind direction of 90°. Finally, the stress and displacement cloud diagrams for the long and short leg transmission towers are as follows: Figure 5 As shown.

[0127] Regarding the reliability analysis of transmission towers with varying lengths, the failure probability and reliability index of multiple components of the tower can be calculated based on the finite element model of the tower and the QMC method using Sobol sequence sampling. First, the random variable distribution parameters are determined according to Table 1 and equations (9) to (10), where the wind load design reference period T is selected based on the voltage level and is chosen as a 50-year return period. Then, the Sobol sequence sampling method (equations (10) to (18)) is used to select 10 5 A random sample point was selected, and a MATLAB program was developed to batch replace the random variables and call the finite element model of the long and short leg transmission tower for mechanical analysis. Then, based on the response information obtained from the finite element analysis, the stress characteristics of the members were divided, and the functional function values ​​of the members were calculated by matching equations (1) to (7). Finally, the failure probability and reliability index of each member of the long and short leg transmission tower were obtained by combining the QMC method (equations (19) to (20)).

[0128] Figure 6 A frequency diagram of component reliability indicators for transmission towers with varying leg lengths, from... Figure 6 It can be seen that the lowest reliability index range for the components of the long and short leg transmission towers is 3.2 to 3.5, while the reliability index of most components is concentrated above 4.2. According to Article 3.0.11 of my country's "Unified Standard for Reliability Design of Building Structures" (GB 50068-2018), "For structural components with safety levels of I, II, and III, the target reliability index β at ductile failure is 3.7, 3.2, and 2.7, respectively." For the long and short leg transmission towers in this project, the safety level is II, and the reliability index of all components is above 3.2, indicating that the tower can meet the requirements of the second-level safety level of the standard and has a certain safety reserve.

[0129] Table 2 Reliability Indicators of Typical Components

[0130]

[0131] Note: lnf in the table represents infinity.

[0132] Table 2 presents the calculated reliability indices for typical components of long-short leg transmission towers. It should be noted that due to space limitations, it is difficult to list the reliability indices for all components. For components in the same location, Table 2 only provides the reliability index for the smallest component in that location. Table 2 shows that the short-leg main member is the weakest component in long-short leg transmission towers, with a reliability index of β = 3.269. This is mainly because the presence of the short leg increases the axial force on the tower leg, causing axial compression failure of the short-leg main member. Compared to the long-short main member reliability index of β = 4.265, the short-leg main member reliability index is reduced by 23.25%. The impact of the short-leg main member should be carefully considered during tower design. Comparing the reliability indices of each component, it is found that the main member at the crossarm of the long-short leg transmission tower bears a larger conductor and ground wire load, resulting in a slightly lower reliability index than the main member of the tower body. Furthermore, regarding the inclined members, the reliability index of the inclined members of transmission towers with both long and short legs is mostly infinite, indicating that the inclined members of the tower are subjected to relatively small forces and have a large safety margin. It is recommended that the inclined members of the tower be reasonably optimized to meet economic requirements.

[0133] The probability density function (PDF) and cumulative distribution function (CDF) of the long-leg and short-leg main materials are as follows: Figure 7 (a) and Figure 7 As shown in (b). Figure 7 (a) and Figure 7 (b) It can be seen that the short leg main material can be approximately regarded as the long leg main material offset along the negative direction of the coordinate axis, which leads to an increase in its failure domain and a decrease in the reliability of the structure. Figure 7 (c) The correspondence between sample points and performance functions of long-leg main materials and short-leg main materials under 1000 sample points is given. The performance function values ​​of long-leg main materials are mainly distributed in 150MPa to 200MPa, while those of short-leg main materials are mainly distributed in 100MPa to 150MPa. The overall performance function values ​​are relatively low, indicating that short-leg main materials are more prone to failure than long-leg main materials and should be given more attention.

[0134] Figure 8 The variation of the standard deviation of the short-leg main material response and reliability index is presented under different sample point conditions. Figure 8 (a) shows that when the sample number is in the range of 0–500, the standard deviation of the short-leg main material response fluctuates significantly. When the number of samples exceeds 500, the standard deviation tends to stabilize, indirectly reflecting the high efficiency of Sobol sequence sampling. Figure 8(b) It can be seen that when the number of sample points exceeds 1000, the reliability index appears, and at this time the short leg main material is likely to be damaged. As the number of samples continues to increase, the reliability index increases accordingly, but since the standard deviation tends to be stable at this time, there is no fluctuation. When the number of samples reaches about 3000, the reliability index reaches stability, that is, the true reliability index β of the short leg main material is 3.269.

[0135] Regarding the research on reliability parameters of transmission towers with varying leg lengths, structural parameters and load parameters are crucial factors affecting their reliability indices. In terms of structural parameters, the leg height difference and tower height have a significant impact on reliability. Regarding loads, the main factors are wind load and gravity load. The magnitude of gravity load is related to the number and specifications of the structural members, and has been calculated and considered by changing the tower height and leg height difference. The design parameters for wind load mainly include wind direction angle and design wind speed. The wind direction angle has been considered according to the most unfavorable wind direction according to the specifications; therefore, only the design wind speed's impact on reliability is considered in the wind load analysis. Furthermore, it should be noted that since the reliability indices of various components in transmission towers with varying leg lengths differ, the minimum reliability index of each component is used in the parameter analysis to represent the overall reliability index of the structure. That is, the failure of one component results in the structural failure of the transmission tower.

[0136] Regarding the impact of the tower leg level difference Figure 9 Reliability indicators for transmission towers with varying leg lengths are given under four operating conditions: a tower height of 48m, a design wind speed of 29m / s, and leg height differences of 3m, 6m, 9m, and 12m. Figure 9 (a) shows the curve of the reliability index of the long and short leg transmission tower as a function of the difference in the number of legs. As the difference in the number of legs increases, the reliability index of the long and short leg transmission tower gradually decreases, and the larger the difference in the number of legs, the greater the decrease in the reliability index. Figure 9 (b) shows the CDF curves under different leg differences. The increase in the leg difference leads to an increase in the internal forces of the long and short leg transmission towers, resulting in a larger failure domain and a decrease in reliability index. Table 3 shows the reliability index of long and short leg transmission towers under different leg differences. For every 3m increase in the leg difference, the maximum decrease in the reliability index of the long and short legs can reach 10.48%. The design should avoid excessively large leg differences.

[0137] Table 3 Reliability Indicators under Different Tower Leg Grades

[0138]

[0139] Note: In the formula, Δ=(β) i+1 -β i ) / β i ×100%, i=1,2,3.

[0140] Regarding the impact of raising the height of poles. Figure 10Reliability index results for transmission towers with different leg heights are given under the conditions of a leg height difference of 12m, a design wind speed of 29m / s, and tower heights of 30m, 36m, 42m, and 48m. Figure 10 (a) is the curve of the reliability index of the long and short leg transmission towers as a function of the tower height. It can be seen that the tower height is inversely proportional to the reliability index of the long and short leg transmission towers. The higher the tower height, the greater the self-weight of the tower and the wind load on the tower body, and the lower the reliability index will be. Figure 10 (b) shows the CDF curves for different tower heights. It can be seen that the CDF curves for tower heights are relatively concentrated, compared to the CDF curves for tower leg differences. Figure 9 (b) The effect of tower elevation on reliability indicators is relatively slow.

[0141] Table 4 shows the reliability index for different tower heights. For every 6m increase in tower height, the reliability index of the long and short legs decreases by a maximum of 3.37%. When the tower height is 48m, the reliability index β of the long and short leg transmission tower is 3.269, which is close to the requirement of the standard target reliability of 3.2. For the project in this embodiment, it is recommended that the tower height should not exceed 48m.

[0142] Table 4 Reliability Indicators for Different Exhalation Heights

[0143]

[0144] Regarding the impact of design wind speed Figure 11 Reliability index results for transmission towers with varying leg lengths are presented under the following conditions: tower height of 48m, leg height difference of 12m, and design wind speeds of 27m / s, 28m / s, 29m / s, and 30m / s. Figure 11 It can be seen that increasing the design wind speed will increase the wind load on the tower body and the conductor and ground wire, thus reducing the reliability index of transmission towers with different lengths; CDF curves under different design wind speeds ( Figure 11 (b) Similar to the variation pattern of the tower height, the CDF curve shifts negatively overall as the design wind speed increases, but the change is relatively gradual. Table 5 shows the rate of change of reliability index under different design wind speeds. It can be seen that for every 1 m / s increase in design wind speed, the reliability index of the long and short leg transmission towers can decrease by up to 2.83%.

[0145] Table 5 Reliability Indicators of Transmission Towers with Different Design Wind Speeds (Long and Short Legs)

[0146]

[0147]

[0148] It should be noted that, within the scope of protection defined in the claims of this invention, the following embodiments can be combined and / or extended or replaced in any logical manner from the above specific embodiments, such as the disclosed technical principles, disclosed technical features or implicitly disclosed technical features.

[0149] Example 1

[0150] A method for evaluating the wind resistance reliability of multi-component transmission tower structures with varying leg lengths in steep mountainous areas includes the following steps:

[0151] S1. Establish a nonlinear finite element analysis model for transmission towers with varying lengths of legs;

[0152] S2, determine the function and uncertainty parameters of the long and short leg transmission towers;

[0153] S3, considering the uncertainties of transmission towers with varying lengths, generate random variable sample points;

[0154] S4, Random variable substitution and component function calculation;

[0155] S5 calculates the failure probability and reliability index of each component.

[0156] Example 2

[0157] Based on Example 1, in step S1, the establishment of a nonlinear finite element analysis model for a transmission tower with varying lengths of legs specifically involves establishing such a model in conjunction with a specific engineering example.

[0158] Example 3

[0159] Based on Example 1, in step S2, determining the function and uncertainty parameters of the long and short leg transmission towers specifically involves clarifying the corresponding failure criteria and function based on the stress form of each component of the long and short leg transmission tower; and determining the random variable parameters and distribution type of the long and short leg transmission towers based on the materials, load forms, and environment of the long and short leg transmission towers.

[0160] Example 4

[0161] Based on Example 1, in step S3, considering the uncertainty factors of transmission towers with varying lengths, generating random variable sample points specifically involves: determining the number of random samples N, combining the selected random variables, using the Sobol sequence sampling method, and combining the specific random vector distribution, and then according to the cumulative distribution function F. X Inverting (θ) yields a random sample, resulting in a sample set x that conforms to the basic random variable.

[0162] Example 5

[0163] Based on Example 1, in step S4, the random variable replacement and component function calculation specifically involve: developing a program to replace random variables in the finite element calculation file of the long and short leg transmission tower, calling the finite element model of the long and short leg transmission tower to calculate the response set Y of each component at the sample point, and selecting the corresponding function and calculating its function value G according to the stress form of the specific component. mn (x), where m represents the corresponding function, with values ​​of 1, 2, ..., 5; n represents the component number of the long and short leg transmission tower, with values ​​of 1, 2, ..., z, and z is the number of components.

[0164] Example 6

[0165] Based on Example 4, the Sobol sequence sampling method, combined with a specific random vector distribution, and then according to the cumulative distribution function F... X (θ) Inverse the random sample to obtain the sample set x that conforms to the basic random variable. This includes the following sub-steps:

[0166] S31, let v i Less than 2 i The expression for a positive odd number is:

[0167]

[0168] In the formula, v i These are called "direct numbers," generated by functional polynomials with coefficients of 0 or 1, as shown in equation (2):

[0169] f(a) = a q +c1a q-1 +…+c q-1 a+c q c i ∈{0,1} (38)

[0170] When i > q, v i There exists a recursive formula:

[0171]

[0172] In the formula, This represents the XOR operation in binary;

[0173] S32, there exists any decimal integer m that uniquely represents an expression with base b = 2:

[0174]

[0175] In the formula, p is the smallest integer greater than or equal to log₂m; a k = 0 or 1; therefore, the z-th element of the Sobol sequence is calculated as follows:

[0176]

[0177] The low-deviation point set θ in the interval [0,1] is generated using equations (1) to (5). ji , i = 1, 2, ..., s; j = 1, 2, ..., N, s is the number of random variables;

[0178] S33, combined with the specific random vector distribution, further based on the cumulative distribution function F X Inverse (θ) yields the random sample x, i.e.:

[0179]

[0180] Example 7

[0181] Based on Example 5, the programming process includes developing a MATLAB program.

[0182] Example 8

[0183] Based on Example 5, the response set Y of each component at the sample point of the finite element model of the long and short leg transmission tower specifically includes bending moment and axial force.

[0184] Example 9

[0185] Based on Example 5, in step S5, the failure probability and reliability index of each component are calculated using the following formula:

[0186] S51, according to equations (10) and (11),

[0187]

[0188] In the formula, x k The sample points in the k-th simulation, G(x) k Let I be the function value corresponding to the k-th sample point, where I takes values ​​of {0,1}. When G(x(k))≤0, I[G(x)] = 0. k When G(x) = 1, k When )>0, I[G(x) k )] = 0;

[0189] Correspondingly, the reliability index of the structure is expressed as:

[0190] β=-Φ -1 (p f (44)

[0191] In the formula, Ф is the standard normal distribution function;

[0192] S52, using the QMC method, the failure probability p of the nth component of the long and short leg transmission tower is obtained.f,n and reliability index β n .

[0193] Example 10

[0194] A multi-component wind resistance reliability assessment system for long and short leg transmission tower structures in steep mountainous areas includes a computer device, which includes a processor and a memory. The memory stores a computer program, and when the computer program is loaded by the processor, it executes the method described in any one of Examples 1 to 9.

[0195] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0196] According to one aspect of the present invention, a computer program product or computer program is provided, the computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and executes the computer instructions, causing the computer device to perform the methods provided in the various optional implementations described above.

[0197] In another aspect, embodiments of the present invention also provide a computer-readable medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The computer-readable medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to perform the methods described in the above embodiments.

[0198] All parts not covered in this invention are the same as or can be implemented using existing technologies.

[0199] The above technical solution is only one embodiment of the present invention. For those skilled in the art, based on the application methods and principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the methods described in the above specific embodiments of the present invention. Therefore, the methods described above are only preferred and are not restrictive.

[0200] In addition to the examples above, other embodiments may be obtained by those skilled in the art based on the above disclosure or by making modifications using knowledge or technology in related fields. The features of each embodiment may be interchanged or replaced. Modifications and changes made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for evaluating the wind resistance reliability of multi-component structures of transmission towers with varying leg lengths, characterized in that... Includes the following steps: S1. Establish a nonlinear finite element analysis model for transmission towers with varying lengths of legs; S2, determine the function and uncertainty parameters of the long and short leg transmission towers; S3, considering the uncertainties of transmission towers with varying lengths, generate random variable sample points; S4, Random variable substitution and component function calculation; S5, calculate the failure probability and reliability index of each component; In step S2, determining the function and uncertainty parameters of the long and short leg transmission tower specifically involves clarifying the corresponding failure criteria and function based on the stress form of each component of the long and short leg transmission tower; and determining the random variable parameters and distribution type of the long and short leg transmission tower based on its material, load form, and environment. In step S3, considering the uncertainties of transmission towers with varying lengths, generating random variable sample points specifically involves: determining the number of random samples. N Combining the selected random variables, based on the Sobol sequence sampling method, and in conjunction with the specific random vector distribution, and then according to the cumulative distribution function... F X ( θ Taking the inverse yields a random sample, resulting in a sample set that conforms to the basic random variable. x ; In step S4, the random variable replacement and component function calculation specifically involve: developing a program to perform random variable replacement on the finite element calculation file of the long and short leg transmission tower, and calling the finite element model of the long and short leg transmission tower to calculate the response set of each component at the sample points. Y Based on the specific stress form of the component, select the appropriate function and calculate its function value. G mn ( x ),in m This represents the corresponding function, with values ​​1, 2, ..., 5; n This indicates the component number of the transmission tower with different leg lengths, with values ​​ranging from 1, 2, ... z , z The number of components; In step S5, the failure probability and reliability index of each component are calculated using the following formula: S51, the failure probability of a component is expressed as: （10） In the formula, x k For the first k Sample points from the second simulation. G ( x k ) is the first k The function value corresponding to each sample point I A function taking values ​​of {0, 1}, when G ( x ( k When ))≤0, I [ G ( x k When )]=1, G ( x k When )>0, I [ G ( x k )]=0; Correspondingly, the reliability index of the component is expressed as: （11） In the formula, Ф is the standard normal distribution function; S52, combined with the QMC method, to obtain the first leg of the long and short leg transmission tower. n Failure probability of individual components p f,n and reliability indicators β n .

2. The method for evaluating the wind resistance reliability of multi-component structures of long and short leg transmission towers according to claim 1, characterized in that, In step S1, the establishment of a nonlinear finite element analysis model for transmission towers with varying lengths of legs specifically involves establishing such a model in conjunction with a specific engineering example.

3. The method for evaluating the wind resistance reliability of multi-component transmission tower structures with varying leg lengths as described in claim 1, characterized in that... The Sobol sequence sampling method, combined with a specific random vector distribution, and then based on the cumulative distribution function... F X ( θ Taking the inverse yields a random sample, resulting in a sample set that conforms to the basic random variable. x Specifically, it includes the following sub-steps: S31, let... v i Less than 2 i The expression for a positive odd number is: （1） In the formula, v i These are called "direct numbers," generated by functional polynomials with coefficients of 0 or 1, as shown in equation (2) below: （2） when i > q hour, v i There exists a recursive formula: （3） In the formula, This represents the XOR operation in binary; S32, there exists any decimal integer. M Unique representation of number base b The expression with =2: （4） p greater than or equal to log2 M The smallest integer; a k =0 or 1; therefore, the Sobol sequence is... z The calculations for each element are as follows: （5） The set of low-deviation points in the interval [0,1] is generated using equations (1) to (5). θ ji , i =1,2,…, s ; j =1,2,…, N , s Where is the number of random variables, and N is the number of random samples; S33, combined with the specific random vector distribution, further based on the cumulative distribution function F X ( θ Inverse the random sample x ,Right now: （6）。 4. The method for evaluating the wind resistance reliability of multi-component structures of long and short leg transmission towers according to claim 1, characterized in that, The programming process includes programming MATLAB programs.

5. The method for evaluating the wind resistance reliability of multi-component structures of long and short leg transmission towers according to claim 1, characterized in that, The finite element model of the long and short leg transmission tower calculates the response set of each component at the sample points. Y Specifically, this includes bending moment and axial force.

6. A multi-component wind resistance reliability assessment system for transmission tower structures with varying leg lengths, characterized in that... The device includes a computer device comprising a processor and a memory, the memory storing a computer program that, when loaded by the processor, executes the method as described in any one of claims 1 to 5.

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