Periodic Reporting for period 4 - VirBAcous (Virtual building acoustics: a robust and efficient analysis and optimization framework for noise transmission reduction)
Période du rapport: 2022-02-01 au 2023-01-31
Many people are affected by noise coming from traffic, industrial and construction activities or the neighborhood, resulting in activity disturbance, social tensions and health problems such as sleep deprivation, damage to hearing and cardiovascular diseases. An important way of protecting people from noise is by ensuring a sufficient overall sound insulation of buildings and building units. However, achieving a sufficient sound insulation of buildings is a complex problem since multiple transmission paths are important, uncertainties can have a large effect, and acoustic performance requirements often conflict with structural and thermal requirements. Furthermore, accurate vibro-acoustic modelling across the entire building acoustics frequency range requires a huge computational effort. As a result, the acoustic development of building systems has been typically based on general design rules, insufficiently accurate prediction models and many experimental prototype tests. Such development is costly and time consuming, and leads to suboptimal designs. This project aimed to develop an efficient yet sufficiently accurate prediction framework for the acoustic design of building systems which takes all uncertainties into account and which opens the way for design optimization. Four fundamental breakthroughs have been realized. The first is a new approach to high-frequency subsystem modelling that overcomes the limitations of the statistical energy analysis paradigm and handles a high degree of geometric and material complexity. Second, a modelling framework for built-up systems has been developed that incorporates different component model types and that switches between them as the frequency increases. The third development consists of quantifying the combined effect of all uncertain parameters on the overall sound insulation performance in a logically consistent and computationally efficient way. Finally, a robust optimization approach that spans the entire building acoustics frequency range has been developed. Each development has been complemented by showcase applications in building acoustics, yet the fundamental nature of the developments makes that they can impact all disciplines where the study and/or control of mechanical wave propagation are important.
The aim of the first work package was overcoming crucial limitations in high-frequency analysis by fundamentally changing the way in which vibro-acoustic subsystems are being conceived and modelled. Next to the development of field-based instead of energy-based diffuse subsystem models, a cross-frequency generalization of the diffuse field reciprocity relationship was derived, and the analysis of complex deterministic subsystems was tackled with the aim of striking the right balance between accuracy and computational efficiency. Dedicated methods were developed for analyzing subsystems with complex material behavior but with a layered geometry and for spatially periodic subsystems.
The second work package dealt with the analysis of built-up systems. A general method for hybrid band-averaged (co)variance analysis of vibro-acoustic systems with diffuse subsystems has been developed by making extensive use of cross-frequency diffuse field reciprocity. The method has been used as a basis for quantifying the diffuse field uncertainty in airborne sound insulation and sound absorption. The analysis of built-up vibro-acoustic systems often relies on the assumption that subsystems are weakly coupled. A generally applicable methodology has been developed for assessing the validity of the weak coupling assumption across the entire frequency range.
In the third work package, the many uncertain parameters that affect the acoustic performance of building systems were treated by incorporating the field-based diffuse subsystem models into a Monte Carlo approach that accounts for the additional parametric uncertainty. The method is computationally efficient as the natural frequencies and mode shapes of the diffuse subsystems are directly drawn from conditional universal probability distributions. When subsystems are coupled at an area junction, the diffuse mode shape components are needed at a large number of locations, so a fast analytical decomposition based on prolate spheroidal wave functions has been developed. Virtual round robin testing of airborne sound insulation was developed as a practical showcase.
The fourth work package dealt with design optimization based on the developed prediction models. First, the optimized material distribution of single and double panels for maximized narrowband sound insulation was obtained by topology optimization. Next, the complexity was increased towards the optimization of the airborne sound insulation of complex walls across the entire building acoustics frequency range, with the determination of the optimal cross-sectional shape of metal studs in double-leaf walls under manufacturing and cost constraints as practical showcase. Finally, a further generalization towards distributed systems was achieved. The broadband optimization of locally resonant vibro-acoustic metamaterials with orthotropic host structures has been selected as a target case, leading to new types of rotational and multimodal resonators with realizable designs.
The second work package dealt with the analysis of built-up systems. A general method for hybrid band-averaged (co)variance analysis of vibro-acoustic systems with diffuse subsystems has been developed by making extensive use of cross-frequency diffuse field reciprocity. The method has been used as a basis for quantifying the diffuse field uncertainty in airborne sound insulation and sound absorption. The analysis of built-up vibro-acoustic systems often relies on the assumption that subsystems are weakly coupled. A generally applicable methodology has been developed for assessing the validity of the weak coupling assumption across the entire frequency range.
In the third work package, the many uncertain parameters that affect the acoustic performance of building systems were treated by incorporating the field-based diffuse subsystem models into a Monte Carlo approach that accounts for the additional parametric uncertainty. The method is computationally efficient as the natural frequencies and mode shapes of the diffuse subsystems are directly drawn from conditional universal probability distributions. When subsystems are coupled at an area junction, the diffuse mode shape components are needed at a large number of locations, so a fast analytical decomposition based on prolate spheroidal wave functions has been developed. Virtual round robin testing of airborne sound insulation was developed as a practical showcase.
The fourth work package dealt with design optimization based on the developed prediction models. First, the optimized material distribution of single and double panels for maximized narrowband sound insulation was obtained by topology optimization. Next, the complexity was increased towards the optimization of the airborne sound insulation of complex walls across the entire building acoustics frequency range, with the determination of the optimal cross-sectional shape of metal studs in double-leaf walls under manufacturing and cost constraints as practical showcase. Finally, a further generalization towards distributed systems was achieved. The broadband optimization of locally resonant vibro-acoustic metamaterials with orthotropic host structures has been selected as a target case, leading to new types of rotational and multimodal resonators with realizable designs.
Thanks to the methodological developments summarized above, crucial limitations in the current statistical energy analysis paradigm for the modeling of built-up systems with diffuse wave components were surmounted, such as the assumption that the subsystems should be weakly coupled, the loss of phase information, and the inability to perform a complete probabilistic analysis, especially for frequency-averaged quantities. Subsystems with a high degree of geometrical and material complexity can be modeled. Parametric uncertainty can now be incorporated in a straightforward and natural way, which enables to take all relevant uncertainties into account. Coupling strength between subsystems in an arbitrarily complex built-up system can be rigorously analyzed. Pioneering steps in broadband vibro-acoustic optimization have been taken. The project has therefore realized the breakthroughs necessary for the development of an efficient yet sufficiently accurate prediction and optimization framework for the acoustic design of building systems.