Embedding measured data within a computational framework for vibro-acoustic design

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The design of products to achieve acceptable levels of noise and vibration is a major concern across a range of industries. In many cases there is a large trade off between cost and performance, and this means that achieving an efficient design is crucial to commercial success. In principle design optimisation can be achieved through testing and improving physical prototypes, but the production of a prototype is time consuming and costly. For this reason there is a pressing need for virtual design methodologies, in which computational models are used to produce a near-final design before a physical prototype is built. Computational models used for noise and vibration analysis must be able to predict the performance of the system over a wide frequency range, potentially ranging from low frequency vibration problems at several hertz to high frequency noise problems at several kilohertz, and this presents severe difficulties. High frequency motions require a very detailed computer model, and this leads to long run times that are not ideal for iterative design. Furthermore, the high frequency performance of a system can be very sensitive to small manufacturing imperfections, and hence the predicted performance may not match the performance of the actual system. These difficulties can be largely overcome by employing recent advances in noise and vibration modelling in which a technique known as Statistical Energy Analysis (SEA) is combined with more conventional analysis methods such as the finite element method (FEM) or the boundary element method (BEM); this approach is known as the Hybrid Method. The Hybrid Method leads to a very large reduction in the run time of the model, while also providing an estimate of the variance in the performance caused by manufacturing imperfections. However, this approach does not fully solve the prediction problem, as a further major difficulty remains: some components in a system can be so complex that it is not possible to produce a detailed computational model of the component, and hence some degree of physical testing is unavoidable. Frequently experimental measurements are used to validate a computational model, or to update the parameters in a computational model, but the requirement here is quite different: the measured data must be used to complete the computational model by coupling a representation of the missing complex component to the other parts of the model. This issue forms the core of the current research proposal. The aim of the present work is to add "experimental" components to the Hybrid Method, and one way to do this is to model a component as a grey or black box: a grey box model consists of mathematical equations with experimentally determined parameters, while a black box model is based purely on measured input-output properties. These models must be capable of being coupled to either FEM, BEM, or SEA component models, and the project will address this issue. A major challenge is to determine the appropriate experimental tests and machine learning algorithms that are required to produce such models in the context of complex vibro-acoustic components. A second major challenge is to quantify the uncertainty in such models, and to include this uncertainty in the combined system model. The model must predict outputs that are useful to the designer, and such outputs include noise and vibration levels, together with uncertainty bounds on the predictions. In some cases "sound quality" rather than the overall noise level is of concern, and the project will develop techniques for the "auralisation" of the output of the combined model. A number of case studies will be developed with industrial partners to explore the application of the proposed approach.The present research programme will produce an efficient and reliable vibro-acoustic "design by science" prediction tool that meets the needs of a wide range of industrial sectors.