Song Xuegang, Zhang Yuexin, Liang Dakai
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
Key Laboratory of Micro-Inertial Instrument and Advanced Navigation Technology, Ministry of Education, School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China.
Materials (Basel). 2017 Oct 10;10(10):1162. doi: 10.3390/ma10101162.
This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.
这项工作提出了一种新颖的逆算法，用于估计非线性梁系统中随时间变化的输入力。在确定系统参数后，可以根据动态响应实时估计输入力，这可用于结构健康监测。在输入力估计过程中，采用四阶龙格 - 库塔算法离散状态方程；采用平方根容积卡尔曼滤波器（SRCKF）抑制白噪声；利用SRCKF生成的残差创新序列、先验状态估计、增益矩阵和创新协方差，通过非线性估计器估计输入力的大小和位置。该非线性估计器基于最小二乘法。进行了大挠度梁的数值模拟和受非线性弹簧约束的线性梁的实验。结果证明了该非线性算法的准确性。
