Built-up vibro-acoustic systems may contain components whose vibration field is sensitive to uncertainty from small spatial variations in geometry, material properties, or boundary conditions, which have a wave scattering effect. Such components can be modeled as diffuse. Statistical energy analysis (SEA) and related approaches are frequently employed for analyzing built-up systems with diffuse components, but their scope is limited because subsystems must be weakly coupled, the displacement fields are not modeled but only the total energies, the joint response probability density function is not available, and the computational efficiency decreases when there is additional parametric uncertainty. Recently, a method of analysis was presented that overcomes those limitations. It is a computationally efficient Monte Carlo method in which the subsystem displacement fields rather than the total energies are modeled. The method relies on the fact that the undamped eigenvalues of a diffuse wave field conform to those of a Gaussian Orthogonal Ensemble (GOE) matrix, while the mode shapes are Gaussian random fields. In this paper, the method is generalized such that diffuse components that are not homogeneous and isotropic, and that have a non-constant modal density, can be analyzed. This is achieved by transforming the GOE eigenvalue spacings to conform to the modal density of a diffuse component, and by relating its mode shape correlation function to the Green’s function of the corresponding unbouded subsystem. Parametric uncertainty is included in a straightforward way. The accuracy and computational efficiency of this field-based method is investigated by comparison with the energy-based (hybrid deterministic-)SEA method and with a detailed Monte Carlo method, where the diffuse field assumption is not made and local random wave scatterers are explicitly modeled. It is found that the new approach is more accuracte than SEA and also more computationally efficient when there are several or many uncertain parameters.

组合式振动声系统可能包含其振动场对几何形状，材料特性或边界条件的微小空间变化（具有波散射效应）的不确定性敏感的组件。可以将此类组件建模为扩散。统计能量分析（SEA）和相关方法经常用于分析具有扩散成分的组合系统，但是由于子系统必须是弱耦合的，位移模型不是建模而是仅对总能量，联合响应概率进行建模，因此其范围受到限制。密度函数不可用，并且当存在其他参数不确定性时，计算效率会降低。最近，提出了一种克服这些限制的分析方法。这是一种计算有效的蒙特卡洛方法，其中对子系统位移场而不是总能量进行了建模。该方法依赖于以下事实：扩散波场的无阻尼特征值与高斯正交集合（GOE）矩阵的特征值一致，而振型为高斯随机场。在本文中，对方法进行了概括，可以分析不均匀且各向同性且具有非恒定模态密度的扩散分量。这可以通过将GOE特征值间距转换为与散射分量的模态密度相符，并将其模态形状相关函数与相应的未绑定子系统的格林函数相关联来实现。参数不确定性以直接方式包括在内。通过与基于能量的（混合确定性）SEA方法和详细的蒙特卡洛方法进行比较，研究了这种基于场的方法的准确性和计算效率，在该方法中，没有进行弥散场假设，而明确地使用了局部随机波散射体模仿。发现新方法比SEA更加精确，并且在存在多个不确定参数的情况下也具有更高的计算效率。