Characteristic wavelets construction based on monitoring data and its application

This paper puts forward a new trend extraction method for monitoring data by constructing characteristic wavelet based on monitoring data. Investigating the relation between predictor and updater of second generation wavelet transform and their equivalent filters, predictor and up-dater are designed on the basis of the equivalent filters. In order to get the characteristic wavelet, the information of the monitoring data is taken into account. Then considering vanishing moment number of predictor as constraint condition, and regarding prediction error as an objective function, the characteristic wavelet constructed can represent the localized characteristic of the monitoring data. By using the devised predictor and updater for second generation wavelet transform composition, threshold processing and reconstruction, the data trend can be obtained. The proposed method nicely represents the trend of monitoring data from a machine set in an oil refinery.