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The calculation of the probability distribution of performance functions is a core issue in uncertainty quantification and reliability design, and the recently proposed equivalent expectation method (EEM) is an effective way to solve this problem. This paper proposes an improved EEM. Putting forward an empirical calculation formula for the standard deviation coefficient of auxiliary random variablesand obtaining a more accurate probability distribution of the auxiliary function. Meanwhile, aiming at the accuracy issue in calculating the probability distribution of theperformance function is proposed, the calculation formula for the PDF of the performance function is derived using only one auxiliary function. In the process of calculating the PDF, proposing an exact theoretical transformation of probability distribution from auxiliary functions to performance functions is proposed, resulting in a more accurate PDF of the performance function. Finally, the effectiveness and accuracy of the method are verified through three numerical examples. The results indicate that this method is suitable for computing the probability distribution of high-dimensional nonlinear or implicit performance functions.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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