Identification of modal parameters of non-stationary systems with the use of wavelet based adaptive filtering

• We introduce an adaptive formula of wavelet filtering.
• The adaptive formula of wavelet filter simplified identification process.
• The algorithm allows estimate modal parameters of structures in real-time.
• The method enables tracking modal parameters even if their changes are significant.

The Operational Modal Analysis (OMA) is a common tool for identification of parameters of mechanical structures during operation. Modal analysis can be applied for linear, stationary and undamped systems or systems with small and proportional damping. To apply this technique to other systems, mainly to non-stationary systems, new procedures are required.The paper focuses on the application of time–frequency signal filtration to the recursive method of the modal parameters' identification based on operational measurements, dedicated for non-stationary systems. The presented technique uses an adaptive wavelet signal filtering method to separate signal components and reduce the model order. This approach considerably facilitates selection of the wavelet function parameters and significantly improves the quality of the separated modal components. Thanks to the reduction of model order, estimation of modal parameters can be performed using a relatively simple mathematical formula. This approach significantly reduces the demand for computing power which has a direct impact on system's costs and modal parameter's estimation time. This is particularly an important problem when the system parameters are changing rapidly and the information about this changes is required in real-time. The algorithm allows assessing the quality of the estimated parameters by simultaneous estimation of confidence bounds. The method has been tested on numerical models, experimental laboratory test rig and applied to real data.