Collins, Bradley DeanHeyns, P.S. (Philippus Stephanus)Kok, SchalkWilke, Daniel Nicolas2022-09-212022-09-212021-06-28Collins, B.D.; Heyns, S.; Kok, S.; Wilke, D.N. Application of Anti-Diagonal Averaging in Response Reconstruction. Symmetry 2021, 13, 1165. https://doi.org/10.3390/sym13071165.2073-8994 (online)10.3390/sym13071165https://repository.up.ac.za/handle/2263/87245Response 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 (ADA). Response Reconstruction is cast as an inverse problem whereby an input signal is inferred to generate the desired outputs of a system. By casting the problem as an inverse problem we veer away from the familiarity of symmetry in physical systems since multiple inputs may generate the same output. We differ in our approach from standard force reconstruction problems in that the optimisation goal is the recreated output of the system. This alleviates the need for highly accurate inputs. We focus on offline non-causal linear regression methods to obtain input signals. A new windowing method called AntiDiagonal Averaging (ADA) is proposed to improve the regression techniques’ performance. 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 shown to accurately reproduce the system’s outputs, which outperform related Finite Impulse Response (FIR) methods. In the nonlinear configuration of the numerical quarter car, ADA achieved a recreated output Mean Fit Function Error (MFFE) score of 0.40% compared to the next best performing FIR method, which generated a score of 4.89%. Similar performance was shown for the linear case.en© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution.Linear regressionResponse reconstructionFinite impulse responseSingular spectrum analysisAccelerated destructive testingEngineering, built environment and information technology articles SDG-04SDG-04: Quality educationEngineering, built environment and information technology articles SDG-09SDG-09: Industry, innovation and infrastructureEngineering, built environment and information technology articles SDG-11SDG-11: Sustainable cities and communitiesEngineering, built environment and information technology articles SDG-12SDG-12: Responsible consumption and productionArticle