参数灵敏度分析的神经网络方法及其工程应用

Neural network method in parameter sensitivity analysis andits application in engineering

在系统分析中,参数灵敏度分析不仅为判断各系统参数的重要性大小提供了依据,量化的灵敏度指标也是后续参数估计的前提。然而,在多数实际系统中,系统参数与系统状态间的显式函数关系不易得到,导致一阶灵敏度指标无法直接求取。简化的单因素分析方法亦存在模型粗糙、精度不高的缺点。本文研究采用人工神经网络的高精度泛化映射,通过少量样本的训练,建立复杂系统中多个系统参数与系统状态间的近似映射关系,继而推导得到统一的灵敏度计算列式。简单结构的神经网络方法和解析方法的对比计算显示了方法的有效性和可靠性。最后,应用该法对某斜拉桥结构的荷载参数和刚度参数进行了考查,得到一般性结论。

In system modelling, the parametric sensitivity analysis is known to be the fundamental work. By applying the sensitivity analysis, the obtained quantitative sensitivity indices (the first|order derivative of system output over system parameter) can then be used for ranking different parameters, as well as identifying the important ones. In most practical systems, however, the explicit functional relationship between system parameters and system output is too complex to be derived and as a result, the first|order derivative sensitivity indices are unable to be computed. The common|used simplified method, single source analysis by use of the finite difference algorithm, has the disadvantage of low accuracy due to the rough model. In this paper, an artificial neural network method is studied to compute the sensitivity indices. Two|layer perceptron is the most widely used type of artificial neural network owing to the simple structure and the ability of high|accuracy simulating of any order nonlinear function. From the mathematical relationships between output variables and input parameters in the trained two|layer perceptron, the first|order derivative sensitivity indices can then be deduced in exact mathematical terms of both normalized and raw input/output data. By this artificial neural network method, the sensitivity indices of multiple parameters are able to be computed at one time through uniform and simple formula, regardless of the system characteristic, i.e. static or dynamic, one stage or multiple stages. Numerical results on one simple structure are presented to show the efficiency and reliability of the proposed method. Finally, the proposed method is employed in the parameter study of cable|stayed bridge construction practice, and valuable information about the influences of stiffness parameter and load parameter on construction control targets is obtained.