Identification of modal parameters of non-stationary systems with the use of wavelet based adaptive filtering Andrzej Klepka n , Tadeusz Uhl AGH University of Science and Technology, Department of Mechatronics and Robotics, Al. Mickiewicza 30, 30-059 Krakow, Poland article info Article history: Received 27 February 2012 Received in revised form 5 August 2013 Accepted 11 September 2013 Available online 31 October 2013 Keywords: Identification of non-stationary systems Wavelet transform Time–frequency analysis Wavelet filtering Recursive identification abstract 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 signifi- cantly 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. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction The operational modal analysis is based only on response measurements of the structure in order to identify the modal characteristics. It is widely used in civil, mechanical and aerospace engineering communities and applied to identify the modal parameters of such structures as buildings, towers, bridges, offshore platforms, airplanes, etc. [1]. However, the OMA has some limitations. Among them, the following are the most important [2]: the structure is assumed to be linear, the structure is time invariant, the structure is observable and in the system of interest damping is small or proportional. Due to these assumptions, results which can be achieved with modal technique are an approximation of the real structure behavior, but still, they are good enough to be applied in diagnostics, monitoring, control, etc. In practice, many engineering structures like traffic-excited bridges, rotating machinery working with varying speed, aircrafts, robots, cranes and many others should be treated as non-stationary systems. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ymssp Mechanical Systems and Signal Processing 0888-3270/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ymssp.2013.09.001 n Corresponding author. Tel.: þ48 6173128; fax: þ48 126343505. E-mail address: klepka@agh.edu.pl (A. Klepka). Mechanical Systems and Signal Processing 47 (2014) 21–34