Safety Assessment Method for Steel Arch Bridge Based on Optimal Weights and Fuzzy Theory

doi:10.12068/j.issn.1005-3026.2025.20230234

Abstract

Abstract:

The safety status of in‑service bridges is affected by many factors and there are many evaluation indices. In order to effectively evaluate their safety status， considering the influence of multi‑source factors， a bridge safety assessment method based on the optimal weights and fuzzy theory was proposed. This method obtained the mechanical response of the corresponding monitoring points of the bridge under various preset cases through numerical analysis， and the safety level division standard of the bridge was determined according to the numerical calculation results and the current specifications. The membership function was introduced to establish the fuzzy evaluation vector of each index. Fuzzy analytic hierarchy process and entropy weight method were used to determine the subjective weight and objective weight for each index， and the optimal weight was obtained by combining preference coefficients. The safety level of bridge was determined by fuzzy comprehensive evaluation method according to the principle of maximum membership degree. Taking a steel arch bridge as an example， the safety levels under 24 preset cases were calculated. At the same time， according to the real‑time monitoring data of the bridge in one week， the dynamic safety levels of the bridge in this period were obtained. The results show that the assessment method can fully consider the influences of various subjective and objective factors and dynamically evaluate the safety status of bridge according to real‑time monitoring data.

Key words: bridge engineering, safety assessment, fuzzy comprehensive evaluation, multi?source influence factors, optimal weights

CLC Number:

U 447

Jun-yu YANG, Ming LI, Shuang SUN, Dong-sheng WEI. Safety Assessment Method for Steel Arch Bridge Based on Optimal Weights and Fuzzy Theory[J]. Journal of Northeastern University(Natural Science), 2025, 46(1): 134-144.

Figures/Tables 25

Fig.1 A steel truss arch bridge （unit：mm）

Fig.2 Vehicle load arrangement （unit：m）

Table 1 Combination of case conditions

影响因素	工况
影响因素	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
等效车辆数	2	2	2	2	2	2	4	4	4	4	4	4	8	8	8	8	8	8	48	100	140	1 180	1 415	2 000
风速/（m·s^-1）	0	0	37.6	37.6	0	37.6	0	37.6	0	37.6	0	37.6	0	37.6	0	37.6	0	37.6	37.6	0	0	0	0	0
整体升降温/℃	0	20	0	20	-20	-20	0	0	20	20	-20	-20	0	0	20	20	-20	-20	0	0	0	0	0	0

Fig.3 Implementation framework of assessment method

Fig.4 Classification of bridge safety level

Table 2 Bridge safety level status

安全等级	状态	状况
Ⅰ	完好	功能完好
Ⅱ	良好	轻微损伤，对桥梁运营无影响
Ⅲ	合格	中等损伤，尚能维持正常使用
Ⅳ	不合格	较大缺损，不能保证正常使用
Ⅴ	危险	严重缺损，不能正常使用

Fig.5 Bridge finite element model

Fig.6 Comparison of calculation results

Fig.7 Extraction positions of bridge deflection index

Fig.8 Extraction positions of bridge stress index

Fig.9 Index response curves under multiple loads

Table 3 Classification of safety level

指标	L_Ⅰ	L_Ⅱ	L_Ⅲ	L_Ⅳ	L_Ⅴ
$A 1 ~ A 3$ /mm	52.66	87.05	121.43	155.82	190.20
$A 4 ~ A 9$ /mm	31.52	105.64	179.76	253.88	328.00
$A 10 ~ A 22$ /mm	204.99	371.74	538.49	705.24	872.00
$A 23 ~ A 27$ /mm	29.92	104.44	178.96	253.48	328.00
$A 28 ~ A 30$ /mm	50.52	85.89	121.26	156.63	192.00
$A 31 ~ A 33$ /mm	9.78	36.89	63.99	91.10	118.20
$A 34 ~ A 113$ /MPa	6.10	97.10	188.00	279.00	370.00

Table 3 Classification of safety level

指标	L_Ⅰ	L_Ⅱ	L_Ⅲ	L_Ⅳ	L_Ⅴ
$A 1 ~ A 3$ /mm	52.66	87.05	121.43	155.82	190.20
$A 4 ~ A 9$ /mm	31.52	105.64	179.76	253.88	328.00
$A 10 ~ A 22$ /mm	204.99	371.74	538.49	705.24	872.00
$A 23 ~ A 27$ /mm	29.92	104.44	178.96	253.48	328.00
$A 28 ~ A 30$ /mm	50.52	85.89	121.26	156.63	192.00
$A 31 ~ A 33$ /mm	9.78	36.89	63.99	91.10	118.20
$A 34 ~ A 113$ /MPa	6.10	97.10	188.00	279.00	370.00

Fig.10 Bridge safety level based on Cauchy distribution

Table 4 Values of proportional parameter α

指标	$A 1 ~ A 3$	$A 4 ~ A 9$	$A 10 ~ A 22$	$A 23 ~ A 27$	$A 28 ~ A 30$	$A 31 ~ A 33$	$A 34 ~ A 113$
$α$	3 382.17	728.10	143.86	720.30	3 197.35	5 442.53	4.83e-16

Table 4 Values of proportional parameter α

指标	$A 1 ~ A 3$	$A 4 ~ A 9$	$A 10 ~ A 22$	$A 23 ~ A 27$	$A 28 ~ A 30$	$A 31 ~ A 33$	$A 34 ~ A 113$
$α$	3 382.17	728.10	143.86	720.30	3 197.35	5 442.53	4.83e-16

Table 5 Index evaluation vector

指标	工况1	工况19	工况22
A₁	$0.830 0.170 000$	$0.249 0.751 000$	$000 0.815 0.185$
A₅	$0.813 0.187 000$	$0 0.737 0.263 00$	$00 0.172 0.828 0$
A₁₇	$0.341 0.659 000$	$00 0.439 0.561 0$	$00 0.252 0.748 0$
A₄₃	$0.790 0.210 000$	$0.743 0.257 000$	$00 0.545 0.455 0$
A₆₆	$0 0.741 0.259 00$	$00 0.792 0.208 0$	$0 0.172 0.828 00$
A₁₁₃	$0.772 0.228 000$	$0.405 0.595 000$	$0 0.688 0.312 00$

Table 5 Index evaluation vector

指标	工况1	工况19	工况22
A₁	$0.830 0.170 000$	$0.249 0.751 000$	$000 0.815 0.185$
A₅	$0.813 0.187 000$	$0 0.737 0.263 00$	$00 0.172 0.828 0$
A₁₇	$0.341 0.659 000$	$00 0.439 0.561 0$	$00 0.252 0.748 0$
A₄₃	$0.790 0.210 000$	$0.743 0.257 000$	$00 0.545 0.455 0$
A₆₆	$0 0.741 0.259 00$	$00 0.792 0.208 0$	$0 0.172 0.828 00$
A₁₁₃	$0.772 0.228 000$	$0.405 0.595 000$	$0 0.688 0.312 00$

Fig.11 Distribution of membership degree for each index （case 19）

Fig.12 The membership degree of A1 for each case

Fig.13 Fuzzy complementary judgment matrix

Fig.14 Subjective weights of index

Fig.15 Objective weights of index

Fig.16 Optimal weights

Fig.17 Influence of preference coefficient

Fig.18 Comparison of assessment results

Fig.19 Changes of indicator monitoring data

Fig.20 Monitoring and evaluation results （July 2023）

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