A Data-Driven Inverse ARX Framework for Force Reconstruction in Dynamic Systems from Vibration Measurements

A data-driven framework for force reconstruction in dynamic systems based on the Inverse AutoRegressive with eXogenous input (IARX) model is presented. The IARX model is employed with force–acceleration (input–output) signals for the direct identification of the inverse excitation–response cause-and-effect relationship, avoiding the conventional inversion of a forward ARX model and the associated stability issues. A complete model identification procedure is formulated for the IARX model, including systematic model order selection, as well as validation through the introduction of the IARX Frequency Response Function (FRF). The force reconstruction framework consists of two phases: Initially, in the offline (training) phase, an IARX model is identified and validated using exclusively a single excitation–response signal pair with the excitation characterized by a broadband frequency content. Subsequently, in the online phase, the obtained IARX model reconstructs unknown excitation forces from response-only vibration-acceleration measurements, without requiring the online excitation to be of the same type as that in the offline phase. The data-driven framework is systematically assessed through multiple experiments on a metallic cantilever beam for the reconstruction of three different excitation profiles (colored noise, harmonic, and impact), using the response from any of the three installed accelerometer locations. Its performance is compared with a state-of-the-art deep Recurrent Neural Network (RNN)-based method and an established Parametric Transfer Function Inversion (PTFI)-based method. The results indicate that the IARX-based framework achieves higher overall force reconstruction performance than the two benchmark methods in both the time and frequency domains under the considered excitation profiles and accelerometer locations, while avoiding potential stability issues associated with PTFI-based approaches and offering substantially greater transparency and interpretability than the RNN-based method.