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  • 1.
    Josefsson, Andreas
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Ahlin, Kjell
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Broman, Göran
    Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering.
    Bias errors due to leakage effects when estimating frequency response functions2012In: Shock and Vibration, ISSN 1070-9622, E-ISSN 1875-9203, Vol. 19, no 6, p. 1257-1266Article in journal (Refereed)
    Abstract [en]

    Frequency response functions are often utilized to characterize a system's dynamic response. For a wide range of engineering applications, it is desirable to determine frequency response functions for a system under stochastic excitation. In practice, the measurement data is contaminated by noise and some form of averaging is needed in order to obtain a consistent estimator. With Welch's method, the discrete Fourier transform is used and the data is segmented into smaller blocks so that averaging can be performed when estimating the spectrum. However, this segmentation introduces leakage effects. As a result, the estimated frequency response function suffers from both systematic (bias) and random errors due to leakage. In this paper the bias error in the H_1 and H_2-estimate is studied and a new method is proposed to derive an approximate expression for the relative bias error at the resonance frequency with different window functions. The method is based on using a sum of real exponentials to describe the window's deterministic autocorrelation function. Simple expressions are derived for a rectangular window and a Hanning window. The theoretical expressions are verified with numerical simulations and a very good agreement is found between the results from the proposed bias expressions and the empirical results.

  • 2.
    Xu, Fei
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Li, Chuanri
    Beihang Univ, Sch Reliabil & Syst Engn, 37 Xueyuan Rd, Beijing 100191, Peoples R China..
    Jiang, Tongmin
    Beihang Univ, Sch Reliabil & Syst Engn, 37 Xueyuan Rd, Beijing 100191, Peoples R China..
    On the Shaker Simulation of Wind-Induced Non-Gaussian Random Vibration2016In: Shock and Vibration, ISSN 1070-9622, E-ISSN 1875-9203, article id 5450865Article in journal (Refereed)
    Abstract [en]

    Gaussian signal is produced by ordinary random vibration controllers to test the products in the laboratory, while the field data is usually non-Gaussian. Two methodologies are presented in this paper for shaker simulation of wind-induced non-Gaussian vibration. The first methodology synthesizes the non-Gaussian signal offline and replicates it on the shaker in the Time Waveform Replication (TWR) mode. A new synthesis method is used to model the non-Gaussian signal as a Gaussian signal multiplied by an amplitude modulation function (AMF). A case study is presented to show that the synthesized non-Gaussian signal has the same power spectral density (PSD), probability density function (PDF), and loading cycle distribution (LCD) as the field data. The second methodology derives a damage equivalent Gaussian signal from the non-Gaussian signal based on the fatigue damage spectrum (FDS) and the extreme response spectrum (ERS) and reproduces it on the shaker in the closed-loop frequency domain control mode. The PSD level and the duration time of the derived Gaussian signal can be manipulated for accelerated testing purpose. A case study is presented to show that the derived PSD matches the damage potential of the non-Gaussian environment for both fatigue and peak response.

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