乔列斯基分解应用于偏相干问题的可行性研究

摘要

在应用传统的偏相干方法进行噪声源识别时,计算条件输入和耦合较为繁琐、复杂.文章首先通过对偏相干和乔列斯基分解的分析,得到两者之间的关系;进一步运用数学归纳法,从理论上证明了乔列斯基分解应用于偏相干问题的可行性;然后指出对归一化互谱矩阵进行乔列斯基分解,可直接得到各源的贡献比大小;最后给出了应用乔列斯基分解解决偏相干问题的一般步骤.舱段试验验证了该方法的可行性和实时性.%The computation of conditional inputs and couplings is complicated when using traditional partial coherence methods to identify noise sources. In this paper, a simpler calculating method for engineering practice is presented. Firstly, the relationship between Cholesky decomposition and partial coherence was derived. Secondly, the feasibility of applying Cholesky decomposition to partial coherence calculation problems was validated by mathematical induction method. Then the percentage of each source's contribution was determined after Cholesky decomposition of the normalized cross-spectral matrix. The process of applying Cholesky decomposition to partial coherence problems was proposed lastly. The feasibility and real time capability of this method was validated by cabin test.