Sparse optimization for nonlinear group delay mode estimation

Nonlinear group delay signals with frequency-varying characteristics are common in a wide variety of fields, for instance, structural health monitoring and fault diagnosis. For such applications, the signal is composed of multiple modes, where each mode may overlap in the frequency-domain. The resulting decomposition and forming of time-frequency representations of the nonlinear group delay modes is a challenging task. In this study, the nonlinear group delay signal is modelled in the frequency-domain. Exploiting the sparsity of the signal, we present the nonlinear group delay mode estimation technique, which forms the demodulation dictionary from the group delay. This method can deal with crossed modes and transient impulse signals. Furthermore, an augmented alternating direction multiplier method is introduced to form an efficient implementation. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. In addition, the included analysis of Lamb waves as well as of a bearing signal show the method's potential for structural health monitoring and fault diagnosis.