Abstract Degradation trend estimation (DTE) of rotating machinery plays a vital role in prognostics and health management (PHM). It enables us to foresee future conditions and avoid unexpected risks. Recently, considerable accomplishments in the field of rotating machinery PHM has achieved through regression analysis based data-driven prognostics, which assist in directly analyzing and exploring the relationships between degradation trend and characterization indicators. Internal static structures still widely exist in most of them, inevitably restricting the natural extrapolation or generalization to future moments. Thus, the autoregression theories with complete mathematical foundations are first introduced and extended the methodologies for rotating machinery DTE. Meanwhile, the characterization ability of degradation or damage information from a single indicator rather than multi-endogenous indicators considering their causality and interactions may significantly reduce in the existing regression analysis based prognostics, and it further influences the final prognostics. Therefore, the idea of exploring internal dynamic structural regression based prognostics containing establishing multi-endogenous degradation indicators with weak-stationary traits and an interpretable and lightweight vector autoregression based DTE modeling method is motivated. The above dilemmas are well addressed through the in-depth study of autoregression based prognostics, namely stationary subspaces-vector autoregressive with exogenous terms (SSVARX). To be specific, multi-channel vibration signals are first picked up, and non-stationary signals are converted into time and frequency domain based weak-stationary degradation indicators via double stationary subspace decomposition and differential operation. Then the above two domain endogenous variables are feed into our proposed DTE models after stationarity test, order determination, and impulse response analysis. Finally, promising results from two run-to-failed life tests of rolling and slewing bearings are obtained via our multi-endogenous variables based extrapolation model. Compared with existing prediction methodologies, SSVARX of this study achieves not only high-accurate prediction results but also fast-computing speed and reasonable mathematical supports.

中文翻译：

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滚动和回转支承退化趋势估计的带外生项的平稳子空间矢量自回归方法

摘要 旋转机械的退化趋势估计（DTE）在预测和健康管理（PHM）中起着至关重要的作用。它使我们能够预见未来情况并避免意外风险。近年来，旋转机械PHM领域通过基于回归分析的数据驱动预测取得了相当大的成就，有助于直接分析和探索退化趋势与表征指标之间的关系。其中大部分仍然广泛存在内部静态结构，不可避免地限制了对未来时刻的自然外推或概括。因此，首先引入并扩展了具有完整数学基础的自回归理论，扩展了旋转机械 DTE 的方法论。同时，在现有的基于回归分析的预测中，从单一指标而不是多内生指标考虑它们的因果关系和相互作用来表征退化或损坏信息的能力可能会显着降低，并进一步影响最终的预测。因此，激发了探索基于内部动态结构回归的预测的想法，其中包括建立具有弱平稳特征的多内源退化指标和基于 DTE 建模方法的可解释和轻量级向量自回归。通过深入研究基于自回归的预测，即固定子空间-向量自回归与外生项 (SSVARX)，可以很好地解决上述难题。具体来说，首先拾取多通道振动信号，非平稳信号通过双平稳子空间分解和微分运算转化为基于时域和频域的弱平稳退化指标。然后，经过平稳性检验、阶次确定和脉冲响应分析后，将上述两个域内生变量输入到我们提出的 DTE 模型中。最后，通过我们基于多内生变量的外推模型，从滚动轴承和回转轴承的两次运行到失败寿命测试中获得了有希望的结果。与现有的预测方法相比，本研究的SSVARX不仅预测结果准确，而且计算速度快，数学支持合理。