基于变分模态分解和奇异值分解的结构模态参数识别方法

为了准确获得结构的固有频率、阻尼比与振型, 将变分模态分解与奇异值分解相结合, 提出一种新的结构模态参数识别方法; 基于已有时频参数识别方法, 根据测量的脉冲激励与加速度响应估计系统的频响函数, 对系统的频响函数进行反傅里叶变换得到脉冲响应函数; 对各测点的脉冲响应函数进行变分模态分解, 得到与结构固有频率对应的本征模态分量; 提取本征模态分量的固有频率, 利用与固有频率相近的本征模态分量作为行向量构造奇异值分解矩阵, 对所构矩阵做奇异值分解, 利用最大奇异值重构左、右奇异值向量, 识别结构的振型、固有频率和阻尼比; 通过四自由度质量-弹簧-阻尼模态仿真试验和车体横梁锤击模态试验, 验证了所提出的模态参数识别方法的有效性。研究结果表明: 在四自由度理论模型参数识别中, 系统固有频率和阻尼比的识别结果与理论计算结果的最大相对误差分别不超过0.025%和1.490%, 理论计算与识别的1~4阶振型的模态置信度分别为0.999、1.000、0.999和0.999;在车体横梁锤击模态试验中, 提出方法识别的固有频率和阻尼比与理论计算结果的最大相对误差分别不超过1.57%和1.47%, 且车体横梁的理论振型与识别振型趋势相同。可见, 提出的方法能有效识别结构的模态参数。 

Structural modal parameter identification method based on variational mode decomposition and singular value decomposition

To obtain the structural natural frequency, damping ratio and vibration mode, a new modal parameter identification method was proposed by combining the variational mode decomposition with the singular value decomposition. Based on the existing time-frequency parameter identification method, the system frequency response function was estimated according to the measured impulse excitations and accelerations. The inverse Fourier transform was applied to the system frequency response function to obtain the impulse response function. The intrinsic mode components corresponding to the structural natural frequencies were obtained by executing the variational mode decomposition on the impulse response function for each measuring point. The natural frequencies of intrinsic mode components were extracted, and the intrinsic mode components close to the natural frequency were used as the row vectors to construct the singular value decomposition matrix, and the singular value decomposition was performed on the constructed matrix. The left and right singular value vectors reconstructed by the maximum singular values were used to identify the vibration mode, natural frequency and damping ratio of the structure. The effectiveness of the proposed modal parameter identification method was verified through a four-degree-of-freedom mass-spring-damping theoretical model and a hammering modal test on the vehicle body crossbeam. Research result indicates that in the parameter identification of four-degree-of-freedom theoretical model, the maximum relative errors of system natural frequencies and damping ratios between the identified and theoretical values are no more than 0.025% and 1.490%, respectively. The modal assurance criterions of 1 to 4-order vibration modes between the theoretical and identified values are 0.999, 1.000, 0.999 and 0.999, respectively. In the hammering modal test on the vehicle body crossbeam, the maximum relative errors of natural frequency and damping ratio between the results identified by the proposed method and the theoretical results are not more than 1.57% and 1.47%, respectively, and the theoretical and identified vibration modes have the same trend. Therefore, the proposed method can effectively identify the structural modal parameters.