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在观测噪声和模型误差等不确定性因素的影响下,结构物理参数识别问题是一个不确定性问题。针对此问题,该文从结构运动微分方程出发,利用小波多分辨率分析原理,建立结构多尺度动力方程,由该方程以结构激励和响应信息在多尺度上的细节信号和最大尺度上的概貌信号为观测量推得物理参数线性回归模型,对该模型应用贝叶斯估计理论得到物理参数后验联合分布,再采用马尔可夫蒙特卡罗方法给出各个物理参数的边缘分布和最优估计值,从而提出了基于结构响应和输入激励的物理参数识别贝叶斯估计方法。通过对四层剪切型结构的数值研究验证了该方法的有效性和正确性,算例还表明该方法在强噪声干扰下仍能获得满足工程要求的识别精度。
Under the influence of uncertainties such as observation noise and model error, the identification of structural physical parameters is an uncertain problem. In order to solve this problem, this paper starts from the structural differential equations of motion, and uses the principle of wavelet multiresolution analysis to establish a multi-scale dynamic equation of structure. From this equation, the detail signal and the profile at the largest scale of structural excitation and response information The signal is a linear regression model of physical parameters. The Bayesian estimation theory is used to obtain the posterior joint distribution of physical parameters. Then the edge distribution and optimal estimation of each physical parameter are given by using Markov-Monte Carlo method Therefore, a Bayesian estimation method based on structural response and input excitation is proposed. The validity and correctness of this method are verified by the numerical study of the four-layer shear structure. The examples also show that the method can still achieve the recognition accuracy that meets the engineering requirements under strong noise.