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To improve noise and vibration quality of mechanical structures, it is important to identify excitation force spectra and the positions at which the force acts. Matrix inversion method is the most frequently used technique for input identification. In this method, excitation force spectra are identified from the inverse problem based on the frequency response function (FRF) and acceleration, which is measured under operational conditions. Although the matrix inversion method is popular because of its simplicity, the identified force can be influenced by measurement error. Therefore, the identification accuracy should be statistically evaluated. To address this issue, in this paper, a variance estimation method of the force spectra identified by the matrix inversion method is proposed. The variance is estimated on the basis of the variance and covariance of FRF, and the proposed method is validated via a numerical model. In addition, the variance estimation method is applied to a vibration test to compare the reliability of the force spectra determined using the estimated variance with the condition number of the FRF matrix, which is also known as an error-propagation indicator of the input identification. Finally, it is proved that the proposed method is suitable for accurately evaluating the identified force.

Variance Estimation for the Identified Force Spectra Based on Matrix Inversion Method