基金项目:国家自然科学基金项目?1870536(/div>
详细信息
孙荧。主要研究方向:古建木构残损 Email9a href="//www.inggristalk.com/j/article/doi/10.12171/mailto:Sunying11@bjfu.edu.cn">Sunying11@bjfu.edu.cn 地址?00083 北京市海淀区清华东 35 叶/p>
戴璐,博士,副教授。主要研究方向:古建木构监测、木结构基本力学性能、结构振动评估 Email9a href="//www.inggristalk.com/j/article/doi/10.12171/mailto:dailu@bjfu.edu.cn">dailu@bjfu.edu.cn 地址:同三/span>
漆楚生,博士,副教授。主要研究方向:木质复合材料、木结构建筑 Email9a href="//www.inggristalk.com/j/article/doi/10.12171/mailto:qichusheng@bjfu.edu.cn">qichusheng@bjfu.edu.cn 地址:同三/span>
中图分类叶TU366.2;K928.71;S781.2
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出版历程
- 收稿日期:2022-11-17
- 修回日期:2023-01-09
- 录用日期:2023-02-06
- 网络出版日期:2023-02-07
- 刊出日期:2023-02-25
Reliability study of damaged wood components of ancient buildings based on probability density evolution method
Key Laboratory of Wood Material Science and Application of Ministry of Education, Beijing Forestry University, Beijing 100083, China
摘要:
目的建立随时间变化的古建筑残损木构件多因子强度退化模型,验证基于概率密度演化方法对残损木构件进行可靠度分析的适用性,提高古建筑残损木构件可靠度分析的计算精度和效率,为古建筑保护中构件力学性能的量化和评估提供科学依据、/sec>
方法综合考虑长期荷载、腐朽、虫蛀和干缩开裂对木材损伤的影响,借助已有模型和理论,建立木构件多因子损伤时变模型并推导出强度退化模型。以某古建筑木结构的典型柱为例,根据强度退化模型确定影响参数,对残损影响参数进行灵敏度计算及排序,通过设定阈值确定影响构件残损的关键参数,将非关键参数常数化以实现参数的初步降维。通过拉丁超立方法在关键参数的参数域内选点得到1 000组代表点,基于强度退化模型计算残余强度变化率,根据概率密度守恒构建概率密度演化方程,利用差分法求解得到残余强度比与随机参数的联合概率密度函数,在随机参数域内积分求得残余强度比随时间变化的概率密度函数,最后将概率密度函数在安全域内积分得到构件可靠度;同时基于蒙特卡罗法随机抽样产生10 000组参数数据对残损木柱进行可靠度分析,对比分析两种方法计算出木柱服役时间为1 ~ 1 000 a时的失效概率、/sec>
结果随服役时间增加,木柱损伤变量逐渐增大,服役时间为1 000 a? 000组不同参数值的构件几乎都达到失效界限;概率密度演化曲面中概率最高的残余强度比逐渐减小;构件失效概率随时间增大,即可靠度降低;服役时间?00?00?00?00?00 a?个节点,蒙特卡罗法和概率密度演化方法计算所得的木柱失效概率差值分别为9.48%?.92%?.10%?.40%?.40%,在蒙特卡罗法参数取样量更多、计算用时更长的前提下,两者计算所得失效概率差值不超过10%、/sec>
结论建立的多因子强度退化模型可用于木柱残余强度的评估和预测,但仍需要进一步的修正。基于概率密度演化方法对残损木构件进行可靠度分析是可行的,与蒙特卡罗法相比具有更高的效率、/sec>
Abstract:
ObjectiveThis paper establishes a multi-factor strength degradation model of damaged wood members of ancient buildings that changes with time, verifies the applicability of reliability analysis of damaged wood members based on probability density evolution method, so as to improve the calculation accuracy and efficiency of reliability analysis of damaged wood members of ancient buildings, and provide scientific basis for the quantification and evaluation of mechanical properties of members in the protection of ancient buildings.
MethodConsidering the effects of long-term loading, decay, insect and shrinkage cracking on wood damage, a multi-factor damage time-varying model of wood components was constructed and a strength degradation model was derived with the help of existing models and theories. Typical columns of an ancient timber structure building were used as an example, the influence parameters were determined according to the strength degradation model, the sensitivity of the influence parameters of the damage was calculated and ranked, the key parameters affecting the wood damage were determined by setting the threshold, and the non-key parameters were stabilized to achieve the preliminary dimension reduction of the parameters. 1000 groups of representative points were selected in the parameter domain of key parameters by Latin overshot method. The changing rate of residual strength was calculated based on the intensity degradation model. The probability density evolution equation was constructed according to the probability density conservation, and the joint probability density function of residual strength ratio and random parameters was obtained by the difference method. The probability density function of the residual strength ratio over time was obtained by integrating in the random parameter domain. Finally, the reliability of the component was obtained by integrating the probability density function in the safety domain. At the same time, 10 000 sets of parameter data were randomly sampled by Monte Carlo method to analyze the reliability of the damaged wooden pillar, and the failure probability of the wooden pillar with service time of 1?000 years was calculated by comparing the two methods
ResultWith the increase of service time, the damage variable of wooden pillar gradually increased, and the 1 000 groups of members with different parameter values whose service time was 1 000 years almost reached the failure limit. On the probability density evolution surface, the residual intensity ratio with the highest probability decreased gradually. Component failure probability increased with time, which means the reliability decreased. For nodes with service time of 100, 300, 500, 700 and 900 years, the difference of failure probability calculated by Monte Carlo method and probability density evolution method was 9.48%, 3.92%, 6.10%, 8.40% and 4.40%, respectively. Under the premise of more parameter sampling and longer calculation time of Monte Carlo method, the difference of failure probability calculated by the two methods was less than 10%.
ConclusionThe multi-factor strength degradation model can be used to evaluate and predict the residual strength of wooden columns, but it still needs further modification. It is feasible to analyze the reliability of damaged wood structures based on probability density evolution method, and compared with Monte Carlo method, probability density evolution method has higher computational efficiency.
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