基于小波包的数值积分误差分析及消除方法

在结构损伤识别的时域法研究中，数值积分的误差将直接影响反演参数结果的精度。积分初值的未知、消除数值积分引入的误差是结构损伤反演计算中信号处理的难题。针对积分初值、数值积分积累误差和数值积分引入的偏移误差进行了理论分析，得出此类误差均具有低频特性的性质，可作为信号低频噪声进行处理。根据数值计算误差的特点分析及小波包多尺度、高分辨的特性，设计了一种基于小波包的滤波器，较好地解决了消除数值积分计算引入误差的问题。通过四层剪切结构模型算例验证，结构刚度反演误差由73％-32．2％降低到0．6％-0．24％，获得了较理想的效果。该方法同样可以用于其它领域的数值处理。

The Design and Application of Filter Based on Wavelet Packet Analysis

In study on structure damage identification in time domain,error of numerical integral will affect directly accuracy of parameters resulted from reversion.It is problems that the integral initial values are unknown and how to eliminate the error with the numerical integral in reversion for detecting structure damage.The thecretical analysis is done for the problems of the integral initial values,the accumulated error and the excursive error induced by numerical integrals.It is found that these errors possess characteristics of lower frequencies and they can be treated as the low frequency noise.A filter is designed based on wavelet packet according to the features of numerical integral errors and those of multiple scales and high resolving power of wavelet packet.The example of a fowr-story shear structure model shows that the reversion error of the structural stiffness decreases from 73~32.2% to 0.6~0.24% after using the filter.The proposed method may be used for numerical treatments in other fields.