A novel underdetermined multi-source harmonic loads identification approach utilizing sparse signal reconstruction

The identification of multi-source harmonic loads plays an important role in health monitoring of some critical aerospace structures such as aircraft engines and liquid rocket engines. However, the number of available responses is commonly smaller than the number of loads to be identified due to severe restrictions on their operational conditions, which yields an underdetermined multi-source harmonic loads identification problem and thus poses a great challenge for traditional load identification methods. This paper introduces the concept of underdetermined blind source separation into load identification, proposing a novel approach for identifying underdetermined multi-source harmonic loads based on the frequency domain sparsity of the harmonic loads. The approach includes three steps: 1) Determination of the frequencies of all harmonic components of multi-source harmonic loads according to Fourier spectrum of response; 2) A mixing matrix is built based on the frequency response functions and the identified frequencies of harmonic components of multi-source harmonic loads. Then, the source signals are reconstructed according to the measured response signals using the UBSS algorithm. By examining the spectral features of these reconstructed signals, the harmonic component frequency information and acting location of multi-source harmonic loads can be accurately determined; 3) The amplitudes of the multi-source harmonic loads are further identified using a proposed amplitude correction algorithm based on the interior-point method. The simulation studies on the underdetermined multi-source harmonic loads identification approach are conducted for a 4-degree-of-freedom mass-spring-damper system and an elastic beam together with an experimental study for an elastic beam specimen. The results demonstrate that the proposed method can accurately identify the locations and magnitudes of multi-source harmonic loads with different frequencies acting at different locations under the condition of underdetermined response data. The comparative study with the TSVD method and the sparse regularization method demonstrates that the proposed method can effectively identify the harmonic frequency components and amplitudes of harmonic loads under underdetermined conditions. The method also exhibits good robustness against noise contamination and system identification error, provides an effective solution to realize underdetermined multi-source harmonic loads identification.