| 线性常微分方程灵敏度分析的精细积分法 |
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| 引用本文： | 刘诗源,陈飙松,丁海宽. 线性常微分方程灵敏度分析的精细积分法[J]. 计算力学学报, 2009, 26(4): 453-459 |
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| 作者姓名： | 刘诗源 陈飙松 丁海宽 |
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| 作者单位： | 大连理工大学运载工程与力学学部工业装备结构分析国家重点实验室,大连,116024;中国石油吉林石化分公司乙二醇厂,吉林,132022 |
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| 基金项目： | 国家自然科学基金(10721062,90715037);;国家基础性发展规划(2005CB321704)资助项目 |
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| 摘 要： | 利用指数矩阵的导数计算来求解一类一阶线性常系数微分方程组对某一设计变量的灵敏度计算问题。对于初值问题,利用指数矩阵的导数,递推得到状态向量的灵敏度;对于线性两点边值问题,通过两点之间的状态向量的导数关系,得到全部初始条件,进而转化为初值问题计算。指数矩阵及其导数阵的高精度计算基于2N类算法,在此基础上可实施灵敏度分析的计算。本文给出了初值和两点边值常微分方程的高精度灵敏度计算方法,计算结果可认为是计算机上的精确解,算例验证了算法的有效性。
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| 关 键 词： | 精细积分 指教矩阵 指教矩阵导数 灵敏度分析 |
| 收稿时间： | 2007-07-16 |
Precise integration method for sensitivity analysis of linear ODEs |
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| LIU Shi-yuan,CHEN Biao-song and DING Hai-kuan. Precise integration method for sensitivity analysis of linear ODEs[J]. Chinese Journal of Computational Mechanics, 2009, 26(4): 453-459 |
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| Authors: | LIU Shi-yuan CHEN Biao-song DING Hai-kuan |
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| Affiliation: | 1.State Key Laboratory of Structural Analysis for Industrial Equipment;Faculty of Vehicle Engineering and Mechanics;Dalian University of Technology;Dalian 116024;China;2.Glycol Factory of Jilin Petrochemical Company;Petro China;Jilin 132022;China |
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| Abstract: | In this paper,the derivatives of matrix exponential is employed to solve the sensitivity analysis of linear ordinary differential equations(ODEs) with respect to a given design variable.For the initial value problems,the derivatives of state vector with respect to design variables can be obtained by using the derivatives of matrix exponential.For the two-point boundary value problem,the matrix exponential and its derivatives are employed to link the boundary derivative conditions between the two points.With... |
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| Keywords: | Precise time integration matrix exponential derivatives of matrix exponential sensitivity analysis |
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