基于随机分布特性的退化结构可靠度评估方法

doi:10.12068/j.issn.1005-3026.2024.10.007

摘要/Abstract

摘要：

为了解决在基于随机载荷及强度退化的结构可靠度评估中采用近似算法而存在结果不准确、对模型参数敏感等问题，提出了基于随机分布特性的建模方法.该方法考虑随机载荷出现的分布特性，应用载荷-强度模型和随机过程理论以提高可靠度计算的准确性.以随机载荷计数模型是泊松过程为例，分析证明了随机载荷到达时间的分布特性，基于此推导了第1次载荷作用的可靠度公式，并根据全概率公式对结构可靠度的计算公式进行了理论推导.算例分析表明，该方法与Monte Carlo仿真结果一致，验证了方法的正确性，与其他方法对比提高了可靠度计算的准确性.

关键词: 结构可靠度, 随机分布, 退化结构, 载荷-强度模型, Monte Carlo

Abstract:

To solve such problems as inaccurate results and sensitivity to model parameters in structural reliability evaluation based on random load and strength degradation， a modeling method based on random distribution characteristics was proposed. The distribution characteristics of random load were considered， and the load-strength model and stochastic process theory were used to improve the accuracy of reliability calculation. Taking the counting model of random load as the Poisson process for example， the distribution characteristics of random load arrival time were analyzed and proved. Based on this， the reliability formula of the first load was derived， and the calculation formula of structural reliability was derived theoretically according to the total probability formula. An example analysis showed that the proposed method is consistent with Monte Carlo simulation results， which verifies the correctness of the proposed method and improves the accuracy of reliability calculation compared with the other methods.

Key words: structural reliability, random distribution, degraded structure, load-strength model, Monte Carlo

中图分类号:

TH 122

杨再有, 吕昊, 赵亚平. 基于随机分布特性的退化结构可靠度评估方法[J]. 东北大学学报（自然科学版）, 2024, 45(10): 1417-1424.

Zai-you YANG, Hao LYU, Ya-ping ZHAO. Reliability Evaluation Method of Degraded Structures Based on Random Distribution Characteristics[J]. Journal of Northeastern University(Natural Science), 2024, 45(10): 1417-1424.

图/表 12

参考文献 16

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转数×10^-4	MC仿真可靠度	文献[12]		本文方法		文献[13]
转数×10^-4	MC仿真可靠度	可靠度	RE/%	可靠度	RE/%	可靠度	RE/%
2	0.974 559	0.974 022	0.06	0.974 558	0	0.616 038	36.79
5	0.971 183	0.966 536	0.48	0.971 192	0	0.891 471	8.21
8	0.968 472	0.950 476	1.86	0.968 547	-0.01	0.950 808	1.82

转数×10^-4	MC仿真可靠度	文献[12]		本文方法		文献[13]
转数×10^-4	MC仿真可靠度	可靠度	RE/%	可靠度	RE/%	可靠度	RE/%
2	0.974 559	0.974 022	0.06	0.974 558	0	0.616 038	36.79
5	0.971 183	0.966 536	0.48	0.971 192	0	0.891 471	8.21
8	0.968 472	0.950 476	1.86	0.968 547	-0.01	0.950 808	1.82

参数	数值	来源
D₀/ GPa	1.5	文献[14]
β_d1/（GPa·r^-1）	5×10^-6	近似假设
β_d2/（GPa·r^-1）	1×10^-5	对比假设
μ/ GPa	1.2	文献[13]
σ/ GPa	0.2	文献[13]
λ₁/ r	6×10^-5	对比假设
λ₂/ r	5×10^-5	文献[14]

参数	数值	来源
D₀/ GPa	1.5	文献[14]
β_d1/（GPa·r^-1）	5×10^-6	近似假设
β_d2/（GPa·r^-1）	1×10^-5	对比假设
μ/ GPa	1.2	文献[13]
σ/ GPa	0.2	文献[13]
λ₁/ r	6×10^-5	对比假设
λ₂/ r	5×10^-5	文献[14]

转数×10^-4	MC仿真可靠度	文献[12]		本文方法		文献[13]
转数×10^-4	MC仿真可靠度	可靠度	RE/%	可靠度	RE/%	可靠度	RE/%
3	0.262 698	0.257 366	2.03	0.262 732	0.01	0.204 109	22.30
6	0.083 124	0.074 339	10.57	0.083 143	0.02	0.079 004	4.94
9	0.020 184	0.015 242	24.48	0.020 181	0.01	0.019 957	1.12