共轭斜量法在BP2模式Dirichlet级数参数辨识中应用

研究一种大型结构混凝土徐变函数指数形式表达式参数辨识与拟合方法. 选用混凝土徐变国际标准BP2模式,构建了最普遍的退化核Dirichlet级数形式作为基函数,针对拟合过程中实际变量多于方程未知变量情况,应用最小二乘法原理将矛盾方程转化为相应的法方程,引入共轭斜量法求解法方程,克服了求解过程中的数值不稳定性.在此基础上编制的程序,可将BP2模式的Dirichlet级数形式的所有参数辨识出来.拟合公式和原公式结果吻合良好,验证了该方法的有效性和正确性. 文中给出的BP2模式Dirichlet级数形式的拟合公式,能适应跟踪分析大型结构长期徐变效应,为较为准确和高效地进行服役结构状态评定,提供了必要的准备和依据.

Application of Conjugate Gradient Method in Parameter Identification of Dirichlet Series of BP2 Model

A study of parameter identification and fitting techniques for BP2 model are made to predicte concrete creep of large-scale structures. The Dirichlet series, which is a kind of exponential function and prevalently taken to fitting creep coefficient, is constructed as basis function of BP2 concrete creep model. In view of the fact that the actual parameters are more than unknown variables during using the least square method to transform the inconsistent equation group to its normal equation one, the conjugate gradient method is employed to overcome the problem of numerical instability in the process of parameter identification. Based on the presented techniques, program is performed to determine the parameters of Dirichlet series of BP2 model. The computational results from fitting formula and original formula are in good agreement, which demonstrates the validity and accuracy of the presented method. The paper indicates that the recommended Dirichlet series of BP2 model is useful formula in the analysis of long-term creep behavior of large-scale structures, which provides a solide foundation for performance evaluation of existing concrete structures.