In this paper two damage sensitive features (DSF), one baseline dependent (DSF₁) and the other one baseline free (DSF₂), are proposed based on the Quaternion analysis of the phase trajectory of a beam vibration due to a moving mass. To that end, new Quaternions are constructed with the displacement, velocity and acceleration of the beam mid-span as the elements of the Quaternion vectors. The new DSFs are obtained based on the concept of the angular velocity of a curve in 3D space characterised by a Quaternion. For the baseline dependent case, the proposed DSF₁ needs to be calculated for both intact and damaged beam subjected to the same experiment, whereas in the baseline free case DSF₂ data from only the damaged beam are sufficient for damage detection. The performance of the proposed DSFs is compared against another technique introduced in the literature through several examples and Monte Carlo simulations. Both road roughness and 10% measurement noise effects are taken into account in performance evaluation of the proposed DSFs. The results show that the proposed DSFs are more successful in locating damage on a simply supported beam.

中文翻译：

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梁多类型振动数据的四元数分析用于损伤检测

在本文中，基于运动质量引起的梁振动相轨迹的四元数分析，提出了两种损伤敏感特征（DSF），一种是依赖于基线（DSF ₁），另一种是无基线（DSF ₂）。为此，以梁中跨的位移、速度和加速度作为四元数向量的元素来构造新的四元数。新的 DSF 是基于以四元数为特征的 3D 空间中曲线的角速度概念获得的。对于依赖基线的情况，需要针对经受相同实验的完整和损坏梁计算建议的 DSF ₁，而在无基线情况下，DSF ₂仅来自损坏光束的数据就足以进行损坏检测。通过几个示例和蒙特卡罗模拟，将所提出的 DSF 的性能与文献中介绍的另一种技术进行了比较。在提议的 DSF 的性能评估中，道路粗糙度和 10% 的测量噪声效应都被考虑在内。结果表明，所提出的 DSF 在定位简支梁上的损伤方面更为成功。