Superconducting radio-frequency (SRF) cavities are preferred in many modern accelerator facilities to reduce the operation cost of the RF power systems. SC cavities are usually sensitive to small mechanical perturbations because of their narrow bandwidth. These perturbations such as microphonics and Lorentz force detuning (LFD) can significantly detune the SRF cavity and therefore not only deteriorate the cavity field stabilities but also increase the RF power requirements. Piezo-electric actuators are widely adopted to suppress the cavity detuning caused by LFD and microphonics. Many advanced detuning compensation strategies were proposed to suppress the microphonics and LFD in recent years. The dynamic models of the LFD and piezo actuator are essential in these activities. Generally, the models of LFD can be identified by modulating the cavity field with sinusoidal signals and then measuring the corresponding steady-state amplitude and phase response of the cavity. However, for some SRF cavities, the cavity field may becomes unstable because of the presence of the ponderomotive effects, leading to a unacceptable measurement result. We present a new approach to identify the dominant modes of the LFD model based on a grey-box models estimation method. The validity of the approach was demonstrated by comparing the model output and measurement results on SRF cavities of real accelerator facilities.

超导射频 (SRF) 腔是许多现代加速器设施的首选，以降低射频功率系统的运行成本。SC 腔通常对小的机械扰动敏感，因为它们的带宽很窄。这些扰动，如麦克风和洛伦兹力失谐 (LFD) 可以显着地使 SRF 腔失谐，因此不仅会降低腔场稳定性，还会增加 RF 功率要求。压电致动器被广泛用于抑制由 LFD 和麦克风引起的腔失谐。近年来提出了许多先进的失谐补偿策略来抑制麦克风和 LFD。LFD 和压电执行器的动态模型在这些活动中是必不可少的。通常，可以通过用正弦信号调制腔场，然后测量腔相应的稳态幅度和相位响应来识别 LFD 模型。然而，对于一些SRF腔，由于质动力效应的存在，腔场可能变得不稳定，导致不可接受的测量结果。我们提出了一种基于灰盒模型估计方法来识别 LFD 模型主要模式的新方法。通过比较模型输出和实际加速器设施的 SRF 腔的测量结果，证明了该方法的有效性。