基于样本矩-最大熵法的长短腿输电塔整体可靠度分析

王成; 王涛; 黄兴; 刘翔云; 李正良; 刘畅

doi:10.3969/j.issn.0258-2724.20230105

基于样本矩-最大熵法的长短腿输电塔整体可靠度分析

doi: 10.3969/j.issn.0258-2724.20230105

王成^1,,
王涛^{2, 3, 4, ,},
黄兴¹,
刘翔云¹,
李正良²,
刘畅¹

1.
中国电力工程顾问集团西南电力设计院有限公司，四川成都 610021
2.
重庆大学土木工程学院，重庆 400045
3.
哈尔滨工业大学交通科学与工程学院，黑龙江哈尔滨 150040
4.
哈尔滨工业大学重庆研究院，重庆 401151

基金项目: 国家自然科学基金项目（51611140123）；重庆市博士后研究项目特别资助项目（2022CQBSHBT3009）；国家电网有限公司科技项目（5200-202156071A-0-0-00）

详细信息

作者简介:
王成（1997—），男，助理工程师，硕士，研究方向为输电线路设计理论和工程可靠度，E-mail：1595844211@qq.com

通讯作者:
王涛（1993—），男，讲师，博士（后），研究方向为基础设施不确定性分析、防灾性能设计与韧性评估等，E-mail：taowang@cqu.edu.cn

中图分类号: TU31
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- 文章访问数: 18
- HTML全文浏览量: 17
- PDF下载量: 3
- 被引次数: 0
出版历程
- 收稿日期: 2023-03-09
- 修回日期: 2023-08-28
- 网络出版日期: 2025-02-26

Overall Reliability Analysis of Transmission Towers with Asymmetrical Legs Based on Sample Moment and Maximum Entropy Method

1.
Southwest Electric Power Design Institute Co., Ltd., China Electric Power Engineering Consulting Group, Chengdu 610021, China
2.
School of Civil Engineering, Chongqing University, Chongqing 400045, China
3.
School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150040, China
4.
Chongqing Research Institute of Harbin Institute of Technology, Chongqing 401151, China

摘要

摘要:
为准确评估长短腿输电塔整体安全水平，依托某500 kV输电线路工程，建立长短腿输电塔精细化数值模型，根据《架空输电线路杆塔结构设计技术规程》（DL/T 5486—2020）以及数值分析结果，给出长短腿输电塔不同失效模式下的功能函数，并结合等价极值事件原理加以等价描述；随后，基于低偏差序列方法生成随机样本点，计算样本响应并获得等价功能函数统计矩；最后，通过改进最大熵法计算长短腿输电塔整体可靠指标. 分析结果表明：本文方法所计算的长短腿输电塔整体可靠指标的相对误差和计算成本分别为Monte Carlo法（MCS）的0.46%和0.05%；单一失效模式下得到的长短腿输电塔可靠指标较整体可靠指标偏低，建议采用整体可靠指标衡量长短腿输电塔的安全水平；塔腿级差和长短腿输电塔整体可靠指标成反比，16 m级差工况下的长短腿输电塔整体可靠指标较等长腿降低了15.72%，设计时应避免级差过大的情况.
- 长短腿输电塔 /
- 整体可靠度 /
- 样本矩 /
- 改进最大熵法 /
- 塔腿级差
Abstract:
To accurately assess the overall safety of transmission towers with asymmetrical legs, a refined numerical model for a transmission tower with asymmetrical legs was established based on a 500 kV transmission line project. Based on the Technical Specification for the Design of Steel Supporting Structures of Overhead Transmission Line (DL/T 5486—2020) and numerical results, functional expressions for different failure modes of the transmission tower with asymmetrical legs were derived, and these were equivalently described using the principle of equivalent extreme value events. Subsequently, random sample points were generated based on the low discrepancy sequence method, and the sample responses were calculated to obtain statistical moments of the equivalent functional expressions. Finally, the overall reliability index of the transmission tower with asymmetrical legs was calculated using the improved maximum entropy method. The results show that the relative error and computational cost of the overall reliability index of the transmission tower with asymmetrical legs obtained by this method are 0.46% and 0.05%, respectively, compared with the Monte Carlo simulation (MCS) method. The reliability index derived from a single failure mode is lower than the overall reliability index of the transmission tower with asymmetrical legs, suggesting that the latter is more accurate for the safety assessment of transmission towers with asymmetrical legs. Moreover, there is an inverse relationship between the difference in tower leg lengths and the overall reliability index of the transmission tower with asymmetrical legs. Specifically, the overall reliability index of a transmission tower with a 16-meter leg length difference is 15.72% lower than that of a transmission tower with equal-length legs. Therefore, it is recommended to avoid excessive leg length differences during the design phase.
- transmission tower with asymmetrical leg /
- overall reliability /
- sample moment /
- improved maximum entropy method /
- tower leg length difference

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图 1 平面图和有限元模型（单位：m）

Figure 1. Plan view and finite element model (unit: m)

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图 2 轴向应力云图和位移云图

Figure 2. Cloud map of axial stress and displacement

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图 3 样本分布对比

Figure 3. Comparison of sample distribution

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图 4 长短腿输电塔整体可靠度分析流程

Figure 4. Overall reliability analysis process of transmission tower with asymmetrical legs

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图 5 前4阶原点矩-样本数量曲线

Figure 5. Curve of first fourth-order moments about origin versus sample size

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图 6 不同塔腿级差下的CDF曲面

Figure 6. CDF surface for various tower leg length differences

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表 1 输电塔设计参数

Table 1. Design parameters of transmission tower

设计参数	取值/m	设计参数	取值/m
塔高	94.7	呼高	48
对角半根开	12.3	水平档距	450
垂直档距	700	塔腿级差	12

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表 2 材料随机变量及其概率分布参数

Table 2. Random variables of material and their probability distribution parameters

变量	均值	标准差	分布类型
弹性模量/MPa	2.06 × 10⁵	6180	Lognormal
泊松比	0.3	0.009	Lognormal
Q235屈服强度/MPa	263.7	18.46	Lognormal
Q355屈服强度/MPa	387.1	27.10	Lognormal

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表 3 整体可靠度计算结果

Table 3. Calculation results of overall reliability

计算方法	p_f		β		分析次数/次
计算方法	取值	相对误差/%	取值	相对误差/%	分析次数/次
MCS法	9.97 × 10⁻⁵		3.7198		1000000
本文方法	9.32 × 10⁻⁵	6.52	3.7368	0.46	500

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表 4 单失效可靠度计算结果

Table 4. Reliability calculation results under single failure mode

计算方法	应力失效				挠度失效
计算方法	p_f	p_f相对误差/%	β	β相对误差/%	p_f	p_f相对误差/%	β	β相对误差/%
MCS法	8.24 × 10⁻⁵		3.7678		6.28 × 10⁻⁵		3.8349
本文方法	8.94 × 10⁻⁵	8.50	3.7471	0.55	5.80 × 10⁻⁵	7.64	3.8543	0.51

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表 5 不同级差下长短腿输电塔可靠指标

Table 5. Reliability index of transmission tower with asymmetrical legs under different leg length differences

塔腿级差/m	β	p_f	变化率/%
0	4.213	1.26 × 10⁻⁵
1	4.192	1.38 × 10⁻⁵	0.50
2	4.158	1.60 × 10⁻⁵	1.30
3	4.124	1.87 × 10⁻⁵	2.13
4	4.089	2.16 × 10⁻⁵	2.94
5	4.054	2.52 × 10⁻⁵	3.78
6	4.028	2.81 × 10⁻⁵	4.39
7	3.996	3.22 × 10⁻⁵	5.16
8	3.974	3.53 × 10⁻⁵	5.67
9	3.943	4.02 × 10⁻⁵	6.41
10	3.913	4.56 × 10⁻⁵	7.13
11	3.872	5.41 × 10⁻⁵	8.11
12	3.810	6.96 × 10⁻⁵	9.58
13	3.737	9.32 × 10⁻⁵	11.31
14	3.680	1.17 × 10⁻⁴	12.65
15	3.625	1.44 × 10⁻⁴	13.95
16	3.551	1.92 × 10⁻⁴	15.72
注：级差为0表示等长腿.

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