Tacho-less rotational speed estimation is critical for vibration-based prognostics and health management (PHM) of rotating machinery, yet traditional methods--such as time-domain periodicity, cepstrum, and harmonic comb matching--struggle under noise, non-stationarity, and inharmonic interference. Probabilistic tracking offers a principled way to fuse multiple estimators, but a major challenge is that heterogeneous estimators produce evidence on incompatible axes and scales. We address this with ARC (Alignment-based RPM Estimation with Curvature-adaptive Tracking) by unifying the observation representation. Each estimator outputs a one-dimensional evidence curve on its native axis, which is mapped onto a shared RPM grid and converted into a comparable grid-based log-likelihood via robust standardization and a Gibbs-form energy shaping. Standard recursive filtering with fixed-variance motion priors can fail under multi-modal or ambiguous evidence. To overcome this, ARC introduces a curvature-informed, state-dependent motion prior, where the transition variance is derived from the local discrete Hessian of the previous log-posterior. This design enforces smooth tracking around confident modes while preserving competing hypotheses, such as octave alternatives. Experiments on synthetic stress tests and real vibration-table data demonstrate stable, physically plausible trajectories with interpretable uncertainty, and ablations confirm that these gains arise from uncertainty-aware temporal propagation rather than per-frame peak selection or ad hoc rules.

翻译：摘要：无转速计旋转速度估计对于基于振动的旋转机械预测与健康管理至关重要，但传统方法（如时域周期性分析、倒频谱和谐波梳匹配）在噪声、非平稳性和非谐波干扰下效果有限。概率跟踪为融合多个估计器提供了系统性框架，但主要挑战在于异质估计器在不兼容的坐标轴和尺度上生成证据。我们提出的ARC方法（基于对齐与曲率自适应跟踪的转速估计）通过统一观测表示解决了该问题：每个估计器在其原始坐标轴上输出一维证据曲线，经映射至共享RPM网格后，通过鲁棒标准化和吉布斯形式能量整形转换为可比较的网格对数似然。固定方差的运动先验标准递归滤波在多模态或模糊证据场景下可能失效，为此ARC引入基于曲率的状态相关运动先验，其转移方差由上一时刻对数后验的局部离散海森矩阵推导得出。该设计在置信模式周围实施平滑跟踪，同时保留竞争假设（如倍频方案）。在合成应力测试和真实振动台数据上的实验表明，该方法能生成稳定、物理合理的轨迹并附带可解释的不确定性，消融实验证实这些优势源于不确定性感知的时间传播机制，而非逐帧峰值选取或经验规则。