Due to difficulties in identifying localized and incipient bearing faults, most proposed fault diagnosis methods focus on detecting these faults. However, it is not clear to what extent of fault severity the proposed methods are capable of detecting. In other words, the crucial issue remains in the literature as to what is the criteria for defining an incipient defect for the proposed methods. This study attempts to address this challenge concerning a decomposed-based fault diagnosis method and provide a suitable measure for assessing this method. In this regard, a parameter-optimized VMD approach is used to decompose vibration signals. Proposed optimization algorithm is able to optimize VMD parameters so that the decomposed modes have the minimum bandwidth and noise interference. A new fault-sensitive index called the envelope spectrum weighted kurtosis index (WKI) is then implemented to detect the mode with the most fault information. This index has the highest sensitivity to fault symptoms and detects the most similarity between the original signal and decomposed modes. For introduced index, a related criterion called the sensitivity threshold (Sth) is given. Based on this criterion, the maximum effectiveness of the proposed method or the minimum observable fault severity can be addressed For validation, the proposed parameter-optimized VMD and the established index are challenged by the investigation of simulated vibration signals of a defective bearing at different fault severity and two experimental datasets and comparison with available methods in the literature.

由于难以识别局部和初期的轴承故障，大多数提出的故障诊断方法都集中在检测这些故障上。然而，目前尚不清楚所提出的方法能够检测到何种程度的故障严重性。换句话说，关于定义所提出方法的初期缺陷的标准是什么，关键问题仍然存在于文献中。本研究试图解决有关基于分解的故障诊断方法的这一挑战，并为评估该方法提供合适的措施。在这方面，使用参数优化的 VMD 方法来分解振动信号。提出的优化算法能够优化VMD参数，使分解模式具有最小的带宽和噪声干扰。WKI ) 然后实施以检测具有最多故障信息的模式。该指标对故障征兆的敏感性最高，检测原始信号与分解模式之间的相似度最高。对于引入的指标，给出了一个称为敏感度阈值（Sth）的相关标准。基于这个标准，可以解决所提出的方法的最大有效性或最小可观察到的故障严重程度。为了验证，提出的参数优化的 VMD 和建立的指标受到了不同故障下缺陷轴承模拟振动信号的调查的挑战严重性和两个实验数据集以及与文献中可用方法的比较。