基于DKF和稀疏约束的激励和响应估计

Excitation and response estimation based on DKF and sparse constraint

针对使用加速度测量响应进行激励和响应估计时发生低频漂移的问题,提出基于DKF(dual Kalman filter)和稀疏约束的激励和响应估计的方法.首先根据状态空间模型建立DKF算法,将激励和状态估计分开进行;然后考虑到激励的稀疏性和测量噪声的不确定性,根据压缩感知CS(compressive sensing)理论建立激励估计的不等式约束优化模型,利用伪测量PM(pseudo measurement)技术求解该优化问题,得到更新后的激励,进而利用模态叠加法重构各类型响应;最后通过数值仿真和简支梁试验验证本文方法的可行性.结果表明,当加速度传感器并置时,本文方法能够得到激励的稀疏解,通过对比激励、位移的时程曲线和频谱图发现,激励和位移的低频分量受到有效抑制,且对噪声具有较好的鲁棒性,在两个激励作用下依然能够保持激励的稀疏性.当加速度传感器非并置时,无法估计完整的空间稀疏激励,但是依然可以估计未知的响应.

To solve the problem of low frequency drift in excitation and response estimation by acceleration measurements,a method of excitation and response estimation based on DKF and sparse constraint is proposed. Firstly,the DKF algorithm is established based on a state-space model to separate the estimation of excitation and state.Secondly,considering the sparsity of excitation and the uncertainty of measurement noise,an inequality-constrained optimization model for excitation estimation is established based on CS.PM technique is used to solve the optimization problem so that the updated excitation is obtained.Finally,the modal superposition method is used to reconstruct various responses.The proposed method is verified by numerical simulation and test of a simply supported beam.The results show that,when acceleration sensors are collocated,the sparse solution of excitation can be obtained by the proposed method.By comparing the time history curve and the spectral diagrams of excitation and displacement,it is found that the low frequency components of the excitation and displacement are effectively suppressed with good robustness to noise,the method can still maintain the sparsity when two excitations are applied.When the acceleration sensors are non-collocated,the complete spatial sparse excitation cannot be estimated,but the unknown responses can still be estimated.