Inverse methods and their application in vibro-acoustic measurements

Many measurement approaches in acoustics and vibration rely on inverse methods to obtain unknown inputs or system properties from measured outputs. For example, methods like inverse force synthesis are able to probe inside structures to obtain forces which could never be measured directly. Inverse methods are not without their problems however, and considerable care is required to obtain reliable results from practical measurements. The most common problems encountered are described with reference to the classical frequency domain formulation and approaches to treatment by regularisation are discussed. Potential advantages of a time domain approach are considered and an example of a working approach is presented. Some special techniques that have been developed for extracting useful information from vibro-acoustic systems are then described. First, the in situ blocked force method enables us to extract information about vibration sources from measurements made in situ on a working installation. The method is illustrated using measurements from real installations including a building-mounted wind turbine and it is shown how the blocked forces extracted are an intrinsic property of the machine and independent of the specific installation. A method for extracting the dynamic stiffness of isolators and other intermediate structures from in situ measurements using an inverse approach is then described. Measurement examples with real isolators are provided. Finally, the 'round trip identity' is described, which enables frequency response functions to be obtained at 'passive locations', i.e. at locations where excitation cannot be applied for example due to lack of access. The approach is illustrated with example measurements from practical structures and the application of previously described regularisation techniques is discussed.