Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability ...Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.展开更多
The ubiquitous occurrence of branched glycerol dialkyl glycerol tetraethers(br GDGTs) in soils has allowed development of new proxies for reconstruction of past climate and environment. The methylation and cyclization...The ubiquitous occurrence of branched glycerol dialkyl glycerol tetraethers(br GDGTs) in soils has allowed development of new proxies for reconstruction of past climate and environment. The methylation and cyclization degrees of br GDGTs, expressed as MBT and CBT, respectively, are reported to be mainly controlled by mean annual air temperature(MAAT) and soil p H. However, the br GDGT-derived temperatures and soil p H scatter widely when data from different environmental conditions are considered. In this study, we collected over 300 soil samples from China, which are representative of humid(Xishuangbanna, Guangzhou, and Shanghai), semi-arid(Dongying) and semi-arid/arid(Lanzhou, Tibetan Plateau) regions. Collectively we have the most extensive dataset that broadly characterizes the distribution of br GDGTs according to climate zones in China. The overall data demonstrate that the MBT/CBT derived temperatures better match the measured MAATs in humid and non-alkaline regions than those from regions of low MAP(<400 mm/yr) and above neutral soil p H(>7.0–7.5). Similarly, CBT describes soil p H much better in humid and non-alkaline soils than in semi-arid/arid and alkaline soils; the semi-arid/arid and alkaline soils tend to show a positive correlation between soil p H and CBT, which contradicts that in the humid and non-alkaline soils. While soil p H, MAAT and mean annual precipitation(MAP) are dominating factors controlling the br GDGT distribution across all climate zones, conductivity, total organic carbon and total nitrogen, as well as soil water content can also play an important role locally. Removing br GDGT-II resulted in a revised CBT index that provides more accurate estimation of p H, especially in semi-arid/arid and alkaline soils. The overall Chinese dataset demonstrates that continental air temperature derived from br GDGT-proxies can vastly deviate from real measurements and should be used with extreme caution in paleo-climate or-environment studies.展开更多
基金Project(50978112) supported by the National Natural Science Foundation of China
文摘Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.
基金supported by the National Natural Science Foundation of China(Grant Nos.41373072 and 40873011)Shanghai Bureau of Science and Technology(Grant No.13JC1405200)the National Thousand Talents Program through the State Key Laboratory of Marine Geology at Tongji University
文摘The ubiquitous occurrence of branched glycerol dialkyl glycerol tetraethers(br GDGTs) in soils has allowed development of new proxies for reconstruction of past climate and environment. The methylation and cyclization degrees of br GDGTs, expressed as MBT and CBT, respectively, are reported to be mainly controlled by mean annual air temperature(MAAT) and soil p H. However, the br GDGT-derived temperatures and soil p H scatter widely when data from different environmental conditions are considered. In this study, we collected over 300 soil samples from China, which are representative of humid(Xishuangbanna, Guangzhou, and Shanghai), semi-arid(Dongying) and semi-arid/arid(Lanzhou, Tibetan Plateau) regions. Collectively we have the most extensive dataset that broadly characterizes the distribution of br GDGTs according to climate zones in China. The overall data demonstrate that the MBT/CBT derived temperatures better match the measured MAATs in humid and non-alkaline regions than those from regions of low MAP(<400 mm/yr) and above neutral soil p H(>7.0–7.5). Similarly, CBT describes soil p H much better in humid and non-alkaline soils than in semi-arid/arid and alkaline soils; the semi-arid/arid and alkaline soils tend to show a positive correlation between soil p H and CBT, which contradicts that in the humid and non-alkaline soils. While soil p H, MAAT and mean annual precipitation(MAP) are dominating factors controlling the br GDGT distribution across all climate zones, conductivity, total organic carbon and total nitrogen, as well as soil water content can also play an important role locally. Removing br GDGT-II resulted in a revised CBT index that provides more accurate estimation of p H, especially in semi-arid/arid and alkaline soils. The overall Chinese dataset demonstrates that continental air temperature derived from br GDGT-proxies can vastly deviate from real measurements and should be used with extreme caution in paleo-climate or-environment studies.
