Structural health monitoring of complex structures is often limited by restricted accessibility to locations of interest within the structure and availability of operational loads. In this work, a novel output-only virtual sensing scheme is proposed. This scheme involves the implementation of the modal expansion in an augmented Kalman filter. The performance of the proposed scheme is compared with two existing methods. Method 1 relies on a finite element model updating, batch data processing, and modal expansion (MUME) procedure. Method 2 employs a recursive sequential estimation algorithm, which feeds a substructure model of the instrumented system into an augmented Kalman filter (AKF). The new scheme referred to as Method 3 (ME-AKF), implements strain estimates generated via Modal Expansion into an AKF as virtual measurements. To demonstrate the applicability of the aforementioned methods, a rollercoaster connection was instrumented with accelerometers, strain rosettes, and an optical sensor. A comparison of estimated dynamic strain response at unmeasured locations using three alternative schemes is presented. Although acceleration measurements are used indirectly for model updating, the response-only methods presented in this research use only measurements from strain rosettes for strain history predictions and require no prior knowledge of input forces. Predicted strains using all methods are shown to sufficiently predict the measured strain time histories from a control location and lie within a 95% confidence interval calculated based on modal expansion equations. In addition, the proposed ME-AKF method shows improvement in strain predictions at unmeasured locations without the necessity of batch data processing. The proposed scheme shows high potential for real-time dynamic estimation of the strain and stress state of complex structures at unmeasured locations.

复杂结构的结构健康监测通常受到结构内感兴趣位置的可访问性和操作负载可用性的限制。在这项工作中，提出了一种新颖的仅输出虚拟传感方案。该方案涉及在增强卡尔曼滤波器中实现模态扩展。将所提出方案的性能与两种现有方法进行比较。方法 1 依赖于有限元模型更新、批量数据处理和模态扩展 (MUME) 程序。方法 2 采用递归顺序估计算法，该算法将仪表系统的子结构模型输入到增强卡尔曼滤波器 (AKF) 中。称为方法 3 (ME-AKF) 的新方案将通过模态扩展生成的应变估计作为虚拟测量实施到 AKF 中。为了证明上述方法的适用性，过山车连接配备了加速度计、应变花环和光学传感器。介绍了使用三种替代方案在未测量位置估计动态应变响应的比较。尽管加速度测量被间接用于模型更新，但本研究中提出的仅响应方法仅使用应变花环的测量值进行应变历史预测，并且不需要输入力的先验知识。显示使用所有方法预测的应变可以充分预测来自控制位置的测量应变时间历程，并且位于基于模态扩展方程计算的 95% 置信区间内。此外，提议的 ME-AKF 方法显示了在未测量位置的应变预测的改进，而无需批量数据处理。所提出的方案显示出在未测量位置对复杂结构的应变和应力状态进行实时动态估计的巨大潜力。