In vibration-based condition monitoring, optimal filter design improves fault detection by enhancing weak fault signatures within vibration signals. This process involves optimising a derived objective function from a defined objective. The objectives are often based on proxy health indicators to determine the filter's parameters. However, these indicators can be compromised by irrelevant extraneous signal components and fluctuating operational conditions, affecting the filter's efficacy. Fault detection primarily uses the fault component's prominence in the squared envelope spectrum, quantified by a squared envelope spectrum-based signal-to-noise ratio. New optimal filter objective functions are derived from the proposed generalised envelope spectrum-based signal-to-noise objective for machines operating under variable speed conditions. Instead of optimising proxy health indicators, the optimal filter coefficients of the formulation directly maximise the squared envelope spectrum-based signal-to-noise ratio over targeted frequency bands using standard gradient-based optimisers. Four derived objective functions from the proposed objective effectively outperform five prominent methods in tests on three experimental datasets.

翻译：在基于振动的状态监测中，最优滤波器设计通过增强振动信号中的微弱故障特征来提高故障检测能力。该过程涉及从定义的目标函数中优化导出的目标函数，这些目标函数通常基于代理健康指标来确定滤波器参数。然而，这些指标可能受到无关背景信号分量和波动运行条件的影响，从而降低滤波器的有效性。故障检测主要利用故障分量在平方包络谱中的显著程度，该程度通过基于平方包络谱的信噪比进行量化。针对变速工况下运行的机械，本文从所提出的广义包络谱信噪比目标函数推导出新的最优滤波器目标函数。该公式并非优化代理健康指标，而是直接利用标准梯度优化器，通过最大化目标频带上的平方包络谱信噪比来获取最优滤波器系数。在三个实验数据集上的测试表明，从所提目标函数导出的四个目标函数在性能上显著优于五种主流方法。