Time-domain approach for multi-exciter random environment test

This paper presents a time-domain method for multi-exciter random environment tests. Traditional random environment test theory has been formulated in the frequency domain, where an important step is taking the inverse of the frequency response function matrices (FRFMs). The accuracy of this inversion tends to be poor, particularly at frequencies near lightly damped resonances. The currently used control algorithms face difficulties in suppressing abnormal spectral lines caused by this inverse problem. In this paper, traditional formulations of the environment test are reformed, and the time-domain method is adopted; this results in a more precise inverse operation in environment tests. To achieve this, reference spectra are converted into time-domain response signals. The finite long driving signals are derived by the state-space method with estimated state vectors. During the process, the inverse of rank-deficient Toeplitz matrices are stabilized with truncated singular value decomposition (TSVD) to suppress all abnormally high-level components in the driving forces; thus, overall, the spectra lines produced by noise within the frequency band are filtered out. A numerical simulation of a single-axis random vibration test of a cantilever beam is conducted using the traditional frequency-domain procedure (FDP) and the proposed time-domain procedure (TDP). The response spectra generated by both procedures are tested by control algorithms, and the result shows that responses generated by the proposed TDP are more easily controlled. The conditions of stability for both the FDP and the TDP are also determined and introduced in the simulation. Moreover, a multi-axis vibration experiment further validates the effectiveness of the TDP.