ABSTRACT

This paper presents a numerical study of an augmented Kalman filter extended with a fixed-lag smoother. The smoother solves the joint input and state estimation problem based on sparse vibration measurements. Two numerical examples are examined in order to study the influence of model errors and measurement noise on the estimate quality. From simulations of a simply supported beam, it is shown that estimates from the smoother are superior to those of a conventional Kalman filter, both when the level of model error and measurement noise are increased. By studying simulations of a truck component, the improvement due to smoothing over a conventional Kalman filter is shown to be even greater when the model error is present in both the eigenfrequencies and the mode shapes. In addition, a sensitivity analysis of a tuning methodology with the assumption of constant noise covariance matrices is performed. The result indicates that the proposed tuning methodology results in stable estimates with a good trade-off between estimator adaptability and noise sensitivity. The presented approach of tuning and evaluating the estimates is therefore suggested as a guideline for using the fixed-lag smoother when solving input and state estimation problems in vibrating structures.

摘要

本文介绍了一个用固定滞后平滑器扩展的增强卡尔曼滤波器的数值研究。平滑器解决了基于稀疏振动测量的联合输入和状态估计问题。为了研究模型误差和测量噪声对估计质量的影响，我们检查了两个数值例子。从简支梁的模拟中可以看出，当模型误差和测量噪声水平增加时，平滑器的估计优于传统卡尔曼滤波器的估计。通过研究卡车部件的模拟，当特征频率和模式形状中都存在模型误差时，由于对传统卡尔曼滤波器进行平滑而产生的改进甚至更大。此外，执行调谐方法的灵敏度分析，假设为恒定噪声协方差矩阵。结果表明，所提出的调整方法产生了稳定的估计，并在估计器适应性和噪声敏感性之间取得了良好的平衡。因此，建议将所提出的调整和评估估计方法作为在解决振动结构中的输入和状态估计问题时使用固定滞后平滑器的指南。