The primary aim of the presented research is to introduce a new approach based on the probabilistic analysis, which provides an accurate prediction for the improvement of the impact sound pressure level of a floating floor considering the uncertainty of material parameters. The theoretical background of the novel method was provided. It embraces two theorems describing the propagation of uncertainty of a random variables function. The introduced technique leads to the determination of the probability density function of a considered output parameter based on the joint distribution of an input random vector. Secondly, the algorithm was applied to investigate the insulation improvement of an exemplary floating floor. The considered construction was composed of extruded polystyrene as a resilient material and cement screed as a floating slab. The dynamic stiffness and the loss factor of the resilient layer and the density of cement screed served as input variable parameters with Gaussian distributions. The probabilistic analysis was based on two models providing the insulation improvement of a floating floor, e.g., Cremer-Vér formula and the recently proposed transmissibility model. Finally, the accuracy of the described methodology was verified by comparing it to the results obtained by Monte Carlo, performing 10⁶ simulations. Additionally, we introduced a simplified model using the linearization of the Cremer-Vér relation, which can be applied to determine the probability density of sound insulation improvement for floating floor composed of XPS and cement screed in a simple and efficient way.

所提出研究的主要目的是引入一种基于概率分析的新方法，该方法考虑到材料参数的不确定性，为改善浮动地板的冲击声压级提供了准确的预测。提供了新方法的理论背景。它包含两个描述随机变量函数不确定性传播的定理。引入的技术导致基于输入随机向量的联合分布确定所考虑的输出参数的概率密度函数。其次，应用该算法来研究示例性浮动地板的绝缘改进。所考虑的结构由作为弹性材料的挤塑聚苯乙烯和作为浮板的水泥砂浆组成。弹性层的动态刚度和损耗因子以及水泥砂浆层的密度作为具有高斯分布的输入变量参数。概率分析基于提供浮动地板绝缘改进的两个模型，例如 Cremer-Vér 公式和最近提出的传输率模型。最后，通过将其与 Monte Carlo 获得的结果进行比较来验证所描述方法的准确性，执行 10^{6 次}模拟。此外，我们还引入了使用 Cremer-Vér 关系线性化的简化模型，该模型可用于以简单有效的方式确定由 XPS 和水泥砂浆组成的浮动地板隔音改进的概率密度。