小波包变换频率混淆的消除及其在桥梁健康监测中的应用

Frequency Aliasing Improvement of Wavelet Packet Transform and Its Application in Bridge Health Monitoring

在分析离散小波包Mallat算法引起频率混淆的原因基础上,提出消除频率混淆的改进算法。运用改进算法对斜拉桥的加速度信号进行分析,结果表明:小波包能量分布同结构的固有频率一样能够表征结构的固有特征,而且还能够反映结构的局部特性。利用损伤前后结构信号的小波能量互熵,并引入相应的权重,在一定的置信水平下能够准确识别损伤的位置。损伤识别结果表明:对于单一损伤状态,小波能量互熵能够较好地定性和定量描述损伤程度;对于复杂的多处损伤状态,小波能量互熵只能识别出损伤的位置,难以定量描述各处的损伤程度。该方法具有较强的抗噪能力。

Based on the analysis of the reasons for frequency aliasing in discrete wavelet packet Mallat algorithm, this paper presents an improved algorithm for eliminating frequency aliasing. The improved algorithm is applied to analyze the acceleration signals of the cable-stayed bridge. Results show that the distribution of wavelet packet energy, like the structural natural frequency, can reflect the structural inherent characteristics and local characteristics as well. By using the wavelet energy cross entropy of the structural signal before and after damage, and by introducing the corresponding weight, to a certain level of confidence, the location of damage can be accurately identified. Results of damage identification indicate that for single damage state, wavelet energy cross entropy can better qualitatively and quantitatively describe damage degree. However, for complicated multiple damage state, it can only identify the location of damage, it is difficult to describe damage degree for every location. The method has relatively strong anti-noise ability.