Substructuring methods are a very common and efficient way to solve complex vibroacoustic problems. The Condensed Transfer Function (CTF) approach is a substructuring method based on the concept of subsystem condensed transfer functions (corresponding to admittances or impedances) that allows assembling acoustical or mechanical subsystems coupled along lines or surfaces. For certain practical applications, it may be more efficient to subtract or to decouple a subsystem to a global system rather than assembling different subsystems. In this paper, a reverse formulation of the CTF method is proposed. This formulation allows us to predict the behavior of a subsystem that is part of a larger system, from the knowledge of the condensed transfer functions (CTFs) of the global system and of the residual subsystem that must be removed. For purposes of validation, the scattering problem of a rigid sphere in an infinite water domain impacted by an acoustic plane wave is considered. Comparisons with theoretical calculations are used to validate the formulation proposed and permit studying its accuracy for two types of condensation functions defining the CTFs.

子结构化方法是解决复杂的振动声学问题的一种非常常见且有效的方法。压缩传递函数（CTF）方法是一种基于子系统压缩传递函数（对应于导纳或阻抗）概念的子结构方法，该方法允许组装沿线或面耦合的声学或机械子系统。对于某些实际应用，将子系统减去或解耦到全局系统可能比组装不同的子系统更有效。在本文中，提出了CTF方法的反向公式。这种表述使我们能够根据全局系统的浓缩传递函数（CTF）以及必须除去的残留子系统的知识来预测属于较大系统的子系统的行为。为了验证的目的，考虑了在声平面波影响下的无限水域中刚性球体的散射问题。与理论计算的比较用于验证所提出的公式，并允许研究定义CTF的两种缩合函数的准确性。