Reduced order modelling of acoustical systems based on measurement data

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A measurement-based modelling approach can be a good alternative in cases where physical models exhibit large deviations from the real-world system. Input-output data in the form of transfer function or, equally, impulse response measurements form the core of such an approach.In practical applications, however, oftentimes high-dimensional measurements for many input-output pairings are needed in order to attain high model fidelity. Hence, established data-driven approaches can quickly lead to computationally demanding models. A solution ispresented in the form of state-space models because they provide access to a plethora of reduced order modelling methods. Recent advances inthe area of numerical linear algebra have brought forth randomized low-rank matrix factorizations that can be used to employ existing data-driven system identification methods on high-dimensional data, thus enabling their practical use in engineering acoustics for the first time. Besides the enhanced computational efficiency, another conceivable advantage of state-space is given by a possible reduction of the measurement effort which can be achieved through parametric state-space models with the spatial location as a parameter. The main goal of this proposal is the establishment of state-of-the-art data-driven system identification methods for the modelling of acoustical transmission systems in the area of engineering acoustics. The proposed actions are designed to increase and create knowledge about the purposeful employment of data-driven modelling and interpolation methods particularly regarding the specific dynamic properties of acoustical systems and to facilitate interdisciplinary scientific exchange with the community of mathematical modelling. Preliminary studies have shown that amodification of the Eigensystem Realization Algorithm (ERA) with a randomized Singular Value Decomposition is well suited for the modelling of an acoustic field in a room. It is intended to validate this method with measurement data from different acoustical systems such as air- and structure-borne transmission systems and the radiation of coupled vibro-acoustical systems. Furthermore, the method is to be augmented in way that the commonly present input-output delays of acoustical systems can be modelled efficiently. Additionally, it is intended to incorporate model parameters into the method such that spatial interpolation and reduced measurement effort can be achieved.