基于逐步最小二乘算法的风荷载识别

Wind load identification based on recursive least-squares algorithm

风荷载识别是典型的反问题,其主要思想是通过测量的结构响应来反演作用在其上的风荷载。首先,通过实测响应反演风荷载能为建筑设计及健康监测提供可靠的风荷载数据。基于Davenport风速度谱拟合出风荷载的时程,基于模态叠加法建立动力方程,由精细积分法求解结构动力响应,进行正问题分析,可得到加速度响应与荷载间的线性关系。因常见的荷载反演方法增广卡尔曼滤波方法把荷载也当成一个状态变量,每个时间步的荷载增量是随机的,需要额外给出协方差的信息。而,实际中荷载增量可能并非随机的,且其协方差信息未知,这将导致较大的荷载识别误差。随后,提出了一种逐步最小二乘算法,它以每个时间步的状态方程和观测方程最小二乘为目标函数,逐步识别荷载且不涉及荷载的协方差信息。算例结果表明,在相同的观测数据量下,逐步最小二乘算法的识别结果优于增广卡尔曼滤波的识别结果,并且拥有良好的抗噪性能。

Wind load inversion based on measured response can provide reliable wind load data for building design and health monitoring.In this paper,the time historical of wind load was fitted based on Davenport wind velocity spectrum.The dynamic equation was established based on the modal superposition method.The dynamic response of the structure was solved by the fine integration method,and the positive problem was analyzed to obtain the linear relationship between the acceleration response and the load.Furthermore,wind load inversion is a typical inverse problem,which aims to identify the wind load of a structure by the measured acceleration.Augmented Kalman filter is a common load inversion method which takes the load as a state variable.The load increment at each time step is random,thus requires additional covariance information.In practice,non-random load increment and unknown covariance information can lead to a large load identification error.For this reason,this paper proposes a stepwise least square algorithm,which takes the equation of state and the least square of the observation equation of each time step as the objective function to gradually identify the load.The advantage is that it does not involve covariance information of the load.The result of the example shows that the recognition result of the stepwise least square algorithm is better than that of the augmented Kalman filter with good anti-noise performance.