3 ALGORITHMS FOR INTERPRETING MODELS CONSISTING OF ORDINARY DIFFERENTIAL-EQUATIONS - SENSITIVITY COEFFICIENTS, SENSITIVITY FUNCTIONS, GLOBAL OPTIMIZATION
3 ALGORITHMS FOR INTERPRETING MODELS CONSISTING OF ORDINARY DIFFERENTIAL-EQUATIONS - SENSITIVITY COEFFICIENTS, SENSITIVITY FUNCTIONS, GLOBAL OPTIMIZATION
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DOI：
10.1016/0025-5564(82)90064-5
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发表时间：
1982-01-01
影响因子：
4.3
通讯作者：
STARK, LW
中科院分区：
文献类型：
--
作者：
LEHMAN, SL;STARK, LW
本文报道了用于分析和模拟由常微分方程组组成的数学模型的三种强大算法的发展和应用。描述了一种扩展的参数灵敏度分析，并测量了模型的许多动态行为对每个参数摄动的相对灵敏度。在小范围和大范围内检查了对参数变化的敏感性。这两个常见技术的扩展在参数估计和实验设计中都有应用。然后计算灵敏度函数，使用一种只需要一个模型模拟的有效算法来获得状态变量对所有参数作为时间函数的所有灵敏度。分析被扩展到不是状态变量的行为。以一种新的方式应用无约束全局优化算法来确定模型的输入，给出了最优性准则和典型输出。该算法本身对于高阶问题是一种有效的算法，不会陷入局部极值。将灵敏度分析、灵敏度函数和优化算法应用于人眼运动的六阶非线性常微分方程组模型。应用表明，该算法不仅适用于高阶模型，而且可作为概念性工具使用。
This paper reports the development and application of 3 powerful algorithms for the analysis and simulation of mathematical models consisting of ordinary differential equations. An extended parameter sensitivity analysis was described and the relative sensitivities of many dynamic behaviors of the model to perturbations of each parameter were measured. Sensitivities to parameter variation were checked over both small and large ranges. These 2 extensions of a common technique have applications in parameter estimation and in experimental design. Sensitivity functions were then computed, using an efficient algorithm requiring just 1 model simulation to obtain all sensitivities of state variables to all parameters as functions of time. The analysis was extended to a behavior which is not a state variable. An unconstrained global optimization algorithm was applied in a novel way to determine the input to the model, given an optimality criterion and typical outputs. The algorithm itself is an efficient one for high-order problems, and does not get stuck at local extrema. The sensitivity analysis, sensitivity functions and optimization algorithm were applied to a 6th-order nonlinear ordinary differential equation model for human eye movements. This application shows that the algorithms are not only practicable for high-order models, but also useful as conceptual tools.