分形理论在航空液压管路裂纹故障诊断中的应用研究

Application of Fractal Theory in Fault Diagnosis of Aviation Hydraulic Pipeline Cracks

针对航空液压管路振动机制复杂、故障关联性较强、故障表征不明显、早期裂纹故障和扩展状态识别率不高等问题,提出一种基于分形理论的故障诊断方法。利用可以解决复杂分形问题的分形理论,通过仿真正、余弦信号并计算其广义维数,可知广义分形维数可以描述信号特征。利用广义维数对振动信号进行分形分析,由广义维数谱图和广义维数变化规律可看出,广义维数不仅能诊断出航空液压管有无裂纹故障,同时能够识别裂纹早期故障。分析分形广义分形维数表可知:液压管的广义分形维数值随着裂纹长度的增加而增大,其增加值成倍数增长,因此通过广义分形维数的变化可以定量分析液压管裂纹故障的扩展状态。

Aiming at the problems of complicated vibration mechanism,strong fault correlation,insignificant fault characterization,and low identification rate of early crack failure and propagation state of aviation hydraulic pipeline,a fault diagnosis method based on fractal theory was proposed.Firstly,by using the fractal theory that could be used to solve complex fractal problems,the sine-cosine signals were simulated and their generalized dimension were calculated.According to the calculation results,the generalized fractal dimension could be used to describe the signal characteristics.Secondly,fractal analysis was carried out on the vibration signal by using the generalized dimension,according to the spectrum diagram of generalized dimension and the variation rule of generalized dimension,the generalized dimension could not only diagnose whether there was crack fault in the aviation hydraulic pipe,but also identify the early fault and crack propagation state.Finally,the fractal generalized fractal dimension table shows that the value of the fractal dimension increases with the increase of the crack length,and the value of the fractal dimension increases exponentially.Therefore,the crack propagation state of the hydraulic pipe can be quantitatively analyzed by the change of the fractal dimension.