D-S理论和Markov链组合的桥梁性能退化预测研究

杨国俊; 田里; 唐光武; 毛建博; 杜永峰

doi:10.21656/1000-0887.440343

D-S理论和Markov链组合的桥梁性能退化预测研究

doi: 10.21656/1000-0887.440343

杨国俊^{1, 2, ,},
田里¹,
唐光武²,
毛建博¹,
杜永峰¹

1.
兰州理工大学土木工程学院，兰州 730050
2.
招商局重庆交通科研设计院有限公司桥梁工程结构动力学国家重点实验室，重庆 400067

(我刊编委唐光武来稿)

基金项目:

国家自然科学基金 52168042

甘肃省科技计划 22JR5RA250

甘肃省优秀研究生“创新之星”项目 2023CXZX-460

详细信息

通讯作者:
杨国俊(1988—)，男，副教授，博士(通讯作者. E-mail: yanggj403@163.com)

中图分类号: U448.33;O29
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- 文章访问数: 230
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- PDF下载量: 35
- 被引次数: 0
出版历程
- 收稿日期: 2023-12-02
- 修回日期: 2024-01-10
- 刊出日期: 2024-04-01

Research on Bridge Performance Degradation Prediction Based on Combination of the D-S Theory and the Markov Chain

1.
School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, P.R.China
2.
State Key Laboratory of Bridge Engineering Structural Dynamics, China Merchants Chongqing Communications Technology Research & Design Institute Co., Ltd., Chongqing 400067, P.R.China

(Contributed by TANG Guangwu, M. AMM Editorial Board)

摘要

摘要: 为准确预测桥梁性能退化，考虑到数据随机性和微小扰动发生状态跳跃，提出了一种D-S(Dempster-Shafer)证据理论和Markov链组合的桥梁性能退化组合预测模型和性能退化率的概念.该模型基于指数平滑(exponential smoothing, ES)方法获得新的预测数据序列，并利用Markov链和D-S理论不断进行优化，从而实现桥梁性能退化的组合预测.实际工程的应用结果表明：性能退化率可以直观地表征在梁性能退化的速度.其次，该模型的平均相对误差为1.54%，较于回归、灰色和模糊加权Markov链模型，精度分别提高了1.11%，0.88%和2.8%，而后验差比值为0.242，小于0.35；模型的标准差为9.021，相比其他模型分别减小了3.978，3.405和7.500，而变异系数为0.109，均小于其他模型，验证了组合预测模型在精度和稳定性方面的优越性，可为在役桥梁结构性能退化预测与维护提供理论基础.
- 桥梁工程 /
- 性能退化预测 /
- D-S证据理论 /
- Markov链 /
- 组合预测模型 /
- 桥梁性能退化率
Abstract: To accurately predict bridge performance degradation, the inherent data randomness and the subtle perturbations leading to state transitions were considered. A combined prediction method for the bridge performance degradation based on the D-S theory and the Markov chain, and the performance degradation rate concept, were proposed. In this model, the exponential smoothing (ES) methodology was employed as the basis for generating new sequences of predictive data. It was continuously optimized through the utilization of the Markov chains and the Dempster-Shafer (D-S) evidence theory. The combined prediction of bridge performance degradation was achieved. The application results from practical engineering show that, the performance degradation rate serves as an intuitive indicator of the speed at which the bridge performance degrades. Subsequently, the combined model demonstrates an average relative error of 1.54%, improves by 1.11%, 0.88%, and 2.8% in accuracy, respectively in comparison with other models of the regression, the grey system, and the fuzzy weighted Markov chain. Additionally, the calculated posterior difference ratio is 0.242, well below the established threshold of 0.35. In terms of stability, the standard deviation of the model is 9.021, reduces by 3.978, 3.405 and 7.500, respectively compared with those of the other 3 models. The coefficient of variation is 0.109, indicating a significant reduction in comparison to those of the other models. The combined prediction model, with verified accuracy and stability, establishes a theoretical foundation for prediction and maintenance of in-service bridges' structural performance degradation.
- bridge engineering /
- performance degradation prediction /
- D-S evidence theory /
- Markov chain /
- combination prediction model /
- bridge performance degradation rate
edited-by

edited-by
注释:

1) (我刊编委唐光武来稿)

HTML全文

图 1 D-S理论和Markov链组合的桥梁性能退化预测流程

Figure 1. The combination prediction process of bridge performance degradation based on the D-S theory and the Markov chain

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图 2 不同平滑系数下绝对误差平方和对比

Figure 2. The absolute error square sum comparison under different smoothing coefficients

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图 3 损失函数值曲线

Figure 3. The loss function value curve

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图 4 状态集合

Figure 4. The state collection

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图 5 桥梁服役16~20年不同模型的相对误差

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 5. Relative errors of different models for bridges in service for 16~20 years

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图 6 桥梁服役16~20年不同模型的桥梁技术状况

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 6. Bridge technical conditions from different models in service for 16~20 years

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图 7 不同模型的平均相对误差比较

Figure 7. The average relative error comparison between different models

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图 8 不同模型的后验差比值C对比

Figure 8. Comparison of posterior error ratio C values of different models

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图 9 桥梁服役35年预测曲线平滑比较

Figure 9. The smooth comparison of prediction curves of bridges in service for 35 years

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图 10 不同模型稳定性对比

Figure 10. The comparison of stability of different models

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图 11 桥梁性能退化预测及退化率

Figure 11. The bridge performance degradation prediction and degradation rates

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图 12 桥梁性能退化预测曲线

Figure 12. The bridge performance degradation prediction curve

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图 13 使用年限内性能退化及维护

Figure 13. Performance degradation and maintenance of bridges during service lives

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表 1 预测模型精度等级

Table 1. Prediction model accuracy levels

accuracy class	average relative error Δ	posterior difference ratio C
class 1	0.01	C≤0.35
class 2	0.05	0.35 < C≤0.50
class 3	0.10	0.50 < C≤0.60
class 4	0.20	C＞0.65

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表 2 基于ES法预测桥梁技术状况

Table 2. Prediction of bridge technical conditions based on the ES method

age m/a	scores	S_m⁽¹⁾	S_m⁽²⁾	S_m⁽³⁾	a_m	b_m	c_m	prediction	relative error R/%
1	100	100	100	100	100	0	0	100	0
2	98.1	99.088 0	99.562 2	99.789 9	98.367 2	-0.998 1	-0.105 1	100.00	1.94
3	96.5	97.845 8	98.738 3	99.285 1	96.607 4	-1.609 6	-0.147 3	97.264	0.79
4	95.8	96.863 8	97.838 6	98.590 8	95.666 5	-1.405 4	-0.094 8	94.851	-0.99
5	95.2	96.065 2	96.987 3	97.821 1	95.054 6	-1.052 0	-0.037 6	94.166	-1.09
6	94.3	95.217 9	96.138 0	97.013 2	94.252 9	-0.951 3	-0.019 1	93.965	-0.36
7	93.4	94.345 3	95.277 5	96.180 1	93.383 5	-0.927 8	-0.012 6	93.282	-0.13
8	92.1	93.267 6	94.312 7	95.283 8	92.148 2	-1.133 3	-0.031 6	92.443	0.37
9	90.4	91.891 1	93.150 4	94.259 7	90.482 0	-1.502 9	-0.063 8	90.983	0.65
10	89.3	90.647 4	91.948 9	93.150 5	89.245 9	-1.428 5	-0.042 6	88.915	-0.43
11	88.1	89.424 6	90.737 3	91.992 2	88.054 3	-2.013 7	-0.024 6	87.775	-0.37
12	87.8	88.644 8	89.732 9	90.907 7	87.643 5	-0.807 3	0.037 0	86.016	-2.03
13	86.6	87.663 3	88.739 5	89.867 0	86.638 4	-0.876 9	0.021 9	86.873	0.32
14	85.4	86.576 9	87.701 5	88.827 5	85.453 9	-1.034 6	0.000 7	85.783	0.45
15	84.6	85.628 0	86.706 2	87.809 3	84.574 7	-0.938 7	0.010 6	84.420	-0.21
16	82.8	-	-	-	-	-	-	83.647	1.02
17	81.1	-	-	-	-	-	-	82.740	2.02
18	80.2	-	-	-	-	-	-	81.854	2.06
19	79.1	-	-	-	-	-	-	80.990	2.39
20	78.0	-	-	-	-	-	-	80.146	2.75

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表 3 基本概率数

Table 3. Basic probabilities

serial number	1	2	3	4	5	6	7	8
relative error R/%	0	1.94	0.79	-0.99	-1.09	-0.36	-0.13	0.37
f(a)	0	0	0	0	0	0	0	0
f(ab)	0	0	0	0	0.18	0	0	0
f(b)	1	0	0	1	0.82	1	1	0.26
f(bc)	0	0	0.42	0	0	0	0	0.74
f(c)	0	1	0.58	0	0	0	0	0

serial number	9	10	11	12	13	14	15
relative error R/%	0.65	-0.43	-0.37	-2.03	0.32	0.45	-0.21
f(a)	0	0	0	1	0	0	0
f(ab)	0	0	0	0	0	0	0
f(b)	0	1	1	0	0.36	0.1	1
f(bc)	0.7	0	0	0	0.64	0.9	0
f(c)	0.3	0	0	0	0	0	0

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