The dynamic properties of structural and mechanical systems are commonly predicted using frequency response functions (FRFs), which represent the relationship between input forces and the corresponding responses in the frequency domain. Analytically calculated responses seldom coincide with actual responses because of modeling and construction errors, performance deterioration in service, etc. The inconsistency requires the correction of the FRF matrix for subsequent analysis, performance evaluation, etc. Obtaining the complete FRF matrix corresponding to all the degrees of freedom at measurement is not practical. This paper derives the mathematical form to expand the incomplete FRF matrix at measurement using the least-squares approach constrained by measured FRFs and correct the FRF matrix at the intact state. Additionally, this paper provides two analytical methods to predict unknown input dynamic excitations using the expanded FRF matrix and direct approaches. Numerical applications elucidate the validity and drawbacks of the proposed methods.

通常使用频率响应函数（FRF）预测结构和机械系统的动态特性，该函数表示输入力与频域中相应响应之间的关系。由于建模和构造错误，服务性能下降等原因，分析得出的响应很少与实际响应一致。不一致之处要求对FRF矩阵进行校正以用于后续分析，性能评估等。获得与所有度数相对应的完整FRF矩阵测量的自由度是不切实际的。本文推导了一种数学形式，即使用受测FRF约束的最小二乘法来扩展测量中的不完整FRF矩阵，并在完整状态下校正FRF矩阵。另外，本文提供了两种使用扩展的FRF矩阵和直接方法来预测未知输入动态激励的分析方法。数值应用阐明了所提出方法的有效性和缺点。