形态学广义分形维数在发动机故障诊断中的应用

发动机故障信号是一种典型的非线性信号，分形几何理论为描述非线性故障信号的特性提供了一个有力的分析工具。广义分形维数能够很好的描述信号的几何特征和局部尺度行为，所蕴含的信息比单一的分形维数要深刻而全面。针对传统的广义分形维数计算方法的缺陷，本文提出基于数学形态学操作的广义分形维数计算方法，并对发动机正常、失火和气门间隙过大故障信号进行了分析，结果表明，与传统的盒计数法计算的广义分形维数相比，形态学广义分形维数能够更加有效地区分发动机在不同状态下的信号，并且数学形态学只涉及简单的加减和取大、取小运算，因此计算简单快速，为准确判断发动机故障状态提供了一种快速有效的新方法。

Application of mathematical morphology based generalized fractal dimensions for engine fault diagnosis

The vibration signals generated by engine can be regarded as a typical nonlinear signal. The fractal geometrical theory has provided an efficient tool to characterize the nonlinearity of such a signal. Multifractal contains more information compared to the single fractal dimension and can characterize the geometrical feature and local scale feature more appropriately. In order to overcome the deficiency of the traditional calculation method of the generalized fractal dimensions, a mathematical morphology based generalized fractal estimation technique is proposed in this study. Signals acquired from different types of engine condition, i.e. normal condition, misfire fault and intake valve clearance fault were employed to evaluate this new method. Results have revealed that the generalized fractal dimensions calculated by mathematical morphology were very stable and have a superior capacity to distinguish the different engine operating states. Otherwise, mathematical morphology operation contains only the simple addition，subtraction, maximum and minimum operations which can dramatically reduce the computational complexity compared to other techniques. Thus the proposed method has demonstrated a more fast and effective technique for accurate fault diagnosis of engine.