基于频域分解法正交模态分离的阻尼比识别研究

Damping Ratio Identification Through Orthogonal Separation Frequency Domain Decomposition Method

频域分解法是一种频域模态参数识别方法,因其操作简单、抗噪声能力强而被广泛使用。虽然频域分解法对于振型和固有频率有着较高的识别精度,但是对于阻尼比的识别精度不够高,其原因是在多自由度结构下,求解阻尼比需要将固有频率窄带范围内的最大奇异值数据傅里叶逆变换到时域,并通过对数衰减法求解阻尼比,而窄带范围的数据很可能会受到其他阶模态的干扰,进而影响阻尼比的识别。因此提出了正交模态分离频域分解法识别结构的阻尼比。首先,通过结构响应计算出结构的输出功率谱矩阵,并使用频域分解法识别结构各阶固有频率和振型;然后,将识别出的固有频率和振型代入计算公式,使用振型正交等方法将各阶模态分离,并计算出各阶模态的增强输出功率谱函数,通过增强功率谱在频域计算出结构各阶的阻尼比;最后,在数值算例中对比了频域分解法以及正交模态分离频域分解法的阻尼比识别结果,并将理论应用于实桥的测试中,计算出该桥梁的前4阶阻尼比。结果表明:该方法可以将多阶输出功率谱矩阵分离成多个单阶的增强输出功率谱函数,并且通过分析增强输出功率谱函数的曲线直接在频域计算出结构的阻尼比,避免了在阻尼比识别中不同模态的相互干扰以及频时域转化带来的影响,提高了阻尼比的识别精度。

A frequency domain decomposition method is a widely used frequency domain modal parameter identification method owing to its simple operation and strong anti-noise ability.Although the frequency domain decomposition method has high accuracy in identifying natural frequencies and mode shapes,the damping ratios cannot be accurately identified.This is because,under the structure of multiple degrees of freedom,the maximum singular value data in the narrow band of the natural frequency must be transformed into the time domain.In addition,the damping ratio generally must be solved using the logarithmic attenuation method.However,the narrow-band data may be interfered with by other modes,affecting the identification of the damping ratio.This paper presents an orthogonal separation frequency domain decomposition method for identifying the damping ratios of structures.First,the output power spectrum matrix of the structure was calculated using the response of the structure.The natural frequencies and modes of the structure were identified by the frequency domain decomposition method.Then,the identified natural frequencies and modes were input into equations to separate the modes using the mode orthogonal method and other methods.An enhanced output power spectrum function was calculated for each mode.The damping ratio of each order was calculated through the enhanced power spectrum in the frequency domain.Finally,the damping ratio identification results from the frequency domain decomposition method and orthogonal separation frequency domain decomposition method were compared using a numerical example.The theory was also applied in a test of a real bridge,where the 1-4th order damping ratios of the bridge were calculated.The results show that the multi-order output power spectrum matrix can be separated into multiple single-order enhanced output power spectrum functions using this method.Moreover,the damping ratios of the structure can be calculated directly in the frequency domain by analyzing the curve(s)of the enhanced output power spectrum functions.The interference from different modes and the influence of the frequency time domain conversion can be avoided.In addition,the accuracy of the damping ratio identification is improved.