退化RC桥梁检测-维护规划的贝叶斯决策方法

王晓明; 汪帆; 翟岸; 赵建领

doi:10.19818/j.cnki.1671-1637.2025.03.008

退化RC桥梁检测-维护规划的贝叶斯决策方法

doi: 10.19818/j.cnki.1671-1637.2025.03.008

王晓明^1, ,,
汪帆²,
翟岸¹,
赵建领³

1.
长安大学公路学院, 陕西西安 710064
2.
宁波市北仑区(开发区)房屋征收管理服务中心, 浙江宁波 315899
3.
中国铁路设计集团有限公司, 天津 300308

基金项目:

国家自然科学基金项目 52178104

中央高校基本科研业务费专项资金项目 300102214901

详细信息

作者简介:
王晓明(1983-)，男，山西朔州人，长安大学教授，工学博士，从事长寿命桥梁建养即时决策研究

通讯作者:
WANG Xiao-ming (1983-), male, professor, PhD, wxm512061228@ gmail.com

中图分类号: U445.7
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- 文章访问数: 294
- HTML全文浏览量: 70
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- 被引次数: 0
出版历程
- 收稿日期: 2024-03-01
- 录用日期: 2024-12-12
- 修回日期: 2024-10-29
- 刊出日期: 2025-06-28

Bayesian decision method of inspection and maintenance planning for deteriorating RC bridges

1.
School of Highway, Chang'an University, Xi'an 710064, Shaanxi, China
2.
Housing Acquisition Management Service Center of Beilun, Ningbo, Ningbo 315899, Zhejiang, China
3.
China Railway Design Corporation, Tianjin 300308, China

Funds:

National Natural Science Foundation of China 52178104

Fundamental Research Funds for the Central Universities 300102214901

Article Text (Baidu Translation)

摘要

摘要: 为了确定退化钢筋混凝土(RC)桥梁的最优检测和维护方案，进而实现结构可靠性水平与全寿命周期成本的最佳平衡，提出了一种基于风险检验(RBI)的贝叶斯决策方法；在氯离子侵蚀环境下的RC桥梁理论劣化模型基础上，发展了锈蚀损伤评估的量化指标体系，建立起基于动态贝叶斯网络的随机劣化过程模型与可靠度更新方法；综合考虑环境参数、损伤检测、维护决策等多源不确定性，引入描述检测行为的决策节点及量化预期损益的效用节点，对贝叶斯网络进行拓展，形成了基于有限记忆影响图(LIMID)的检测-维护决策体系；将上述方法应用于某在役组合梁桥的RC桥面板检测-维护规划问题。分析结果表明：该桥面板的理论锈蚀失效概率随使用年限增加而大幅上升，在服役的第40和60年将达到19.4%与45.5%，亟需采取必要的维护措施；采用本文方法对其进行检测-维护规划，获得的最优检测时间为第18、33、48及61年，其期望相对总成本为260.3，其中，检测成本为0.769，维护成本为187.8，失效成本为71.7，相较于该桥的实际维修方案，成本降幅高达36.3%；定期检查(PI)方法的相对成本为271.1，可靠度阈值(RT)方法则为270.4，证明所提方法可以提供更优的求解结果。
- 桥梁工程 /
- 检测与维护规划 /
- 贝叶斯决策方法 /
- 钢筋混凝土桥梁 /
- 锈蚀退化 /
- 动态贝叶斯网络 /
- 有限记忆影响图
Abstract: In order to determine the optimal inspection and maintenance plan for deteriorating reinforced concrete (RC) bridges and achieve the best balance between structural reliability level and life cycle cost, a Bayesian decision method based on risk-based inspection (RBI) was proposed. Based on the theoretical deterioration model of RC bridges in a chloride-ion erosion environment, a quantitative index system for corrosion damage assessment was developed. A stochastic deterioration process model and a reliability updating method based on a dynamic Bayesian network were established. By comprehensively considering the uncertainties of environmental parameters, damage detection, and maintenance decisions, the Bayesian network was expanded by introducing decision nodes describing inspection actions and utility nodes quantifying expected costs and benefits. A inspection and maintenance decision system based on a limited memory influence diagram (LIMID) was formed. The proposed method was applied to the inspection and maintenance planning of the RC bridge deck of an in-service composite girder bridge. Analysis results show that the theoretical corrosion failure probability of the bridge deck increases significantly with the extension of service life, reaching 19.4% and 45.5% in the 40th and 60th years, respectively. Necessary maintenance measures are urgently needed. By using the method in this article for inspection and maintenance planning, the optimal inspection times are obtained as the 18th, 33rd, 48th, and 61st years. The expected relative total cost is 260.3, including an inspection cost of 0.769, a maintenance cost of 187.8, and a failure cost of 71.7. Compared with the actual maintenance plan of the bridge, the cost is reduced by 36.3%. The relative total cost under the periodic inspection (PI) method is 271.1, and that under the reliability threshold (RT) method is 270.4. The proposed method provides an optimal solution.
- bridge engineering /
- inspection and maintenance planning /
- Bayesian decision method /
- reinforced concrete bridge /
- corrosion degradation /
- dynamic Bayesian network /
- limited memory influence diagram

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图 1 劣化RC结构的I&M规划问题

Figure 1. I&M planning problem of deteriorating RC structures

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图 2 I&M规划的贝叶斯决策框架

Figure 2. Bayesian decision framework for I&M planning

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图 3 氯离子侵蚀引起的钢筋点蚀

Figure 3. Chloride-induced pitting corrosion of steel bars

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图 4 劣化RC结构DBN的拓扑结构

Figure 4. Topology of DBN for deteriorating RC structures

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图 5 劣化RC结构的LIMID拓扑

Figure 5. Topology of LIMID for deteriorating RC structures

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图 6 威斯康星河大桥的位置与实景

Figure 6. Location and image of Wisconsin River Bridge

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图 7 桥梁构造

Figure 7. Structure of bridge

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图 8 锈蚀起始时间的PDF

Figure 8. PDF of corrosion initiation time

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图 9 锈蚀深度的时变情况

Figure 9. Time-varying state of corrosion depth

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图 10 基于LIMID的决策网络预测误差

Figure 10. Prediction error of LIMID-based decision network

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图 11 最优策略的时变可靠度

Figure 11. Time-varying reliability of optimal strategy

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图 12 PI方法的最优解

Figure 12. Optimal solution of PI method

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图 13 RT方法的最优解

Figure 13. Optimal solution of RT method

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图 14 威斯康星河大桥的维修历史

Figure 14. Maintenance history of Wisconsin River Bridge

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表 1 随机变量的概率分布特性

Table 1. Probability distribution of random variables

变量	分布类型	均值	标准差
c_cr/[g·(mm³)^-1]	对数正态	0.035	0.003 5
c₀/[g·(mm³)^-1]	对数正态	0.15	0.015
D_c/(mm²·a^-1)	对数正态	110.0	11.0
D/mm	对数正态	50.8	5.08
d₀/mm	对数正态	19.05	0.381
f_c/MPa	对数正态	28.0	5.04
α_p/m	正态	0.04	0.06

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表 2 检测-维护规划的参数取值

Table 2. Parameter values for I&M planning

参数	δ_0.5	δ_m	α_i	r_i	C_r	C_f	γ
取值	0.01	0.001	0.5	20	100	1 000	0.98

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表 3 节点离散区间及条件概率表

Table 3. Discrete interval and CPT of different nodes

变量	节点状态数	离散区间边界	离散区间长度	CPT
t_p,t	80	[-10, 70]	1	P(t_p,t∈a_j),a_j为t_p,t的第j个离散区间
δ_t	200	[0, 1]	0.005	P(δ_t∈u_j),u_j为δ_t的第j个离散区间
δ′_t	200	[0, 1]	0.005	P(δ′_t∈v_j),v_j为δ′_t的第j个离散区间
E_t	2	E_t = 0为失效; E_t = 1为可靠		$P\left(E_t\right)= \begin{cases}P\left(d_{\mathrm{p}} \geqslant 4.43 \mathrm{~mm}\right)=P_{\mathrm{f}}(t) & E_t=0 \\ P\left(d_{\mathrm{p}}＜4.43 \mathrm{~mm}\right)=1-P_{\mathrm{f}}(t) & E_t=1\end{cases}$
I_t	2	I_t = 0为不检测I_t = 1为检测
O_t	3	O_t = 0为不检测; O_t = 1为检测但未发现损伤; O_t = 2为检测且发现损伤		$P\left(O_t \mid I_t, \delta_t\right)= \begin{cases}1 & I_t=0, O_t=0 \\ 1-P_{\mathrm{D}}\left(\delta_t\right) & I_t=1, O_t=1 \\ P_{\mathrm{D}}\left(\delta_t\right) & I_t=1, O_t=2 \\ 0 & \text { 其他 }\end{cases}$
C_Ⅰ,t	1			$ C_{\mathrm{I}}= \begin{cases}0 & I_t=0 \\ -C_{\mathrm{i}} & I_t=1\end{cases}$
C_R,t	1			$ C_{\mathrm{R}}= \begin{cases}0 & O_t=1,2 \\ -C_{\mathrm{r}} & O_t=1,2\end{cases}$
C_F,t	1			$ C_{\mathrm{F}}= \begin{cases}0 & E_t=1 \\ -C_{\mathrm{f}} & E_t=0\end{cases}$

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表 4 劣化RC桥面板的检测-维护方法最优解

Table 4. Optimal solution of I&M method for deteriorating RC deck

t_I /年	18	33	48	61
P_f	0.017 0	0.008 1	0.007 1	0.005 7
P_R	0.999 3	0.999 1	0.999 9	0.999 9
C_I	0.284 3	0.210 0	0.155 1	0.119 3
C_R	69.46	51.29	37.91	29.16
C_F	11.82	4.16	2.69	1.66

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表 5 四类检测-维护方法的结果对比

Table 5. Result comparison of four I&M methods

方法	相对成本	成本降幅/ %	检修间隔/ 年	寻优耗时/ s
本文LIMID方法	260.3	38.7	18, 33, 48, 61	19.4
PI方法	271.1	36.2	16, 32, 48, 64	2.3
RT方法	270.4	36.3	15, 29, 44, 59	8.9
实际维护行动	424.7		23, 32, 51

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