大坝变形监控指标的小波变换与特征根分析研究

A study on dam deformation monitoring index based on wavelet transformation and characteristic polynomial root of an auto-regression model

为解决大坝变形监控指标难以确定的问题,以某拱坝为例,根据该坝的运行状况,将变形数据分为5个不同时段,对各时段分别进行小波分解,提取趋势项,对趋势项建立自回归模型(AR(p)模型),求出各时段AR(p)模型特征多项式B(z)的根,再根据各时段AR(p)模型特征根距离单位圆的远近来判断大坝结构性态的变化情况。当特征多项式B(z)的根逐渐靠近单位圆,趋势项逐渐失去平稳性,大坝结构性态将趋于安全;反之,特征多项式B(z)的根逐渐远离单位圆,趋势项保持平稳性,大坝结构性态趋于不安全。应用示例计算结果表明,上述方法计算出各时段特征根距离单位圆远近的变化趋势与该拱坝实际运行变化情况基本一致,表明该方法是合理的、可行的。

A method was proposed to analyze the observed concrete dam deformation. The trend component was extracted by using the wavelet decomposition method for the observed deformation, and the dam operation process was separated into five stages according to abnormal phenomena. The trend component at each stage was modeled by using the auto-regression method. The characteristic roots were obtained by using the characteristic polynomials of the auto-regression models. The trend of the minimum moduli of the characteristic roots was employed to determine whether the dam was safe or not. When the roots of B （z） are all out of the unit circle and the minimum moduli of the characteristic polynomial roots increase at each stage, the dam deformation increases. Otherwise, the deformation is decreasing or stabilizing. Results of the application demonstrated that the method was consistent with the actual situation.