摘要： 构造出一类用递推公式进行小波变换的小波基，提出此类小波的优化方法，对其时频特性进行了分析。针对传统ART2网络只利用了模式的相位信息而丢失了幅度信息和网络的性能依赖于样本的学习顺序等不足，提出了改进型ART2网络。对刀具AE信号进行递归小波分解，提取特征并应用于改进的ART2网络识别刀具状态。实验结果表明，递归小波能反映刀具状态信号的特征，且实时性好。改进的ART2网络更具鲁棒性，识别率为100%，训练耗时仅占传统ART2网络的3.79%。

关键词: 优化递归小波, 改进型ART2网络, 刀具状态, 在线监测

Abstract: A general method of recursive mother wavelet is introduced, and an optimal method of wavelet construction is proposed too. Moreover, the time-frequency characteristics of recursive wavelet are analyzed. In view of the fact that traditional ART2 loses the amplitude information of input patterns and is sensitive to pattern sequence, an improved ART2 are presented. The AE signals of tool conditions are decomposed using a recursive wavelet from which the features are extracted and delivered to an improved ART2 network for fault recognition. The results show that recursive wavelet is convenient to analyze tool condition signals with real-time characteristics. The modified ART2 becomes more robust, and its consumed time accounts for only 3.79% that of traditional ART2, and the recognition rate is up to 100%.

Key words: Optimal recursive wavelet, Modified ART2 network, Tool condition, On-line monitor