Response reconstruction is used to obtain accurate replication of vehicle structural responses of field recorded measurements in a laboratory environment, a crucial step in the process of Accelerated Destructive Testing (ADT). Response Reconstruction is cast as an inverse problem whereby the desired input is inferred using the measured outputs of a system. ADT typically involves large shock loadings resulting in a nonlinear response of the structure. A promising linear regression technique known as Spanning Basis Transformation Regression (SBTR) in con- junction with non-overlapping windows casts the low dimensional nonlinear problem as a high dimensional linear problem. However, it is determined that the original implementation of SBTR struggles to invert a broader class of sensor configurations. A new windowing method called AntiDiagonal Averaging (ADA) is developed to overcome the shortcomings of the SBTR im- plementation. ADA introduces overlaps within the predicted time signal windows and averages them. The newly proposed method is tested on a numerical quarter car model and is shown to successfully invert a broader range of sensor configurations as well as being capable of describing nonlinearities in the system. / Dissertation (MEng)--University of Pretoria, 2021. / Mechanical and Aeronautical Engineering / MEng / Unrestricted