Multiscale mapping of aggregated signal features to embedded time-frequency localized operations using wavelets

Aggregated signals are referred to as the measurements of system-level responses generated by the multiple operations embedded in a system. While an extensive literature exists on the analysis of general signal profiles, limited research has been performed on the topic of how to map features of the aggregated signals to the responses of individual operations, which is important for individual operation performance monitoring and assessment. In this paper, a two-step mapping algorithm is developed to obtain those mapping features using a mutiscale wavelet analysis integrated with statistical hypothesis testing and engineering knowledge. It is shown that multiscale wavelet analysis is effective for mapping aggregated signals to the embedded individual operations that generate localized time-frequency responses. This algorithm is further demonstrated in a stamping process, in which the extracted wavelet coefficients of aggregated press tonnage signals are explicitly mapped to individual or a few contributing embedded operations. The mapping allows for efficient monitoring and quality assessment of the embedded operations based on the aggregated signals, thereby avoiding installing additional in-die sensors in all operations.