Estimating Applied Loads and Response Accelerations on a Dynamic System Using Vibration Data
Measured infield accelerometer data is very useful when evaluating the structural dynamics of any mechanical system. Researchers have great difficulty to make measurements from all particular regions where they are interested in due to shortage of measure
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Estimating Applied Loads and Response Accelerations on a Dynamic System Using Vibration Data Eren Koçak, Caner Genço˘glu, Bülent Acar, and Kenan Gürses
Abstract Measured infield accelerometer data is very useful when evaluating the structural dynamics of any mechanical system. Researchers have great difficulty to make measurements from all particular regions where they are interested in due to shortage of measurement channels and difficulty of instrumentation. Thus the vibrations on the rest of the structure should be estimated with limited measured data. In this study a response acceleration estimation method based on input force estimation is employed. For estimation of applied forces and acceleration data form unmeasured locations of the structure, an accurate model of the system is required. Thus at first stages of the study, FE model is established and updated using experimental modal analysis results. Having the accurate dynamic model, vibration measurements of the structure are done under unknown forces to simulate operational conditions. To estimate applied load location, a state space model (SMM) of the structure is established using updated FE model. By employing augmented Kalman filter (AKF) approach, the location of the applied force is estimated from candidate force input locations, and the force signal is reconstructed. Knowing the force input location and the transfer function (TF) matrix of the structure, response acceleration power spectral density (PSD) data of the unmeasured locations can be estimated from measured locations. Employing Frequency Response Functions (FRFs) between excitation and measured location, PSD of the input force is obtained. Using input force PSD and FRF between excitation and unmeasured location, the unmeasured PSD data can be predicted. The methodology presented in this study is applied to the GARTEUR structure which is an internationally accepted de facto model. The FE model of the GARTEUR structure is set up first and subsequently the FE model is verified by modal tests. In the laboratory tests, GARTEUR structure is excited by impact hammer from an arbitrary location. Using the SMM of the GARTEUR and AKF approach, the location of the excitation force is estimated from candidate locations. After this step, PSD for the unmeasured locations are estimated from TF matrix of the structure and measured vibration data. Finally, both estimated and measured acceleration and force data are compared and satisfactory results are obtained. Keywords Force data estimation · GARTEUR structure · Augmented Kalman filter · Frequency response function
20.1 Introduction For engineering structures such as bridges, aeroplanes, missiles, satellite launch vehicles, etc., knowing vibration levels on many locations on the structure during operational conditions is not an easy task and even impossible. Due to shortage of measurement channels, difficulties on instrumentation and cost effects drive engineer to find an alternative solution. Thus, operational vibrations of the whole structure should
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