Input estimation of nonlinear systems using probabilistic neural network

Input estimation is an involved task with wide applications in nonlinear dynamic systems. Model-based input estimation methods are not feasible solutions for problems in which the underlying behavior is not sufficiently known. Data-driven methods have recently shown promise in capturing hidden and subtle nonlinearities in problems from various domains. In this study, we introduce a machine learning approach for input estimation of nonlinear dynamic systems that is applicable for a variety of mechanical properties and system complexities. The proposed neural regression model enables uncertainty quantification in predictions for each time sample which is a novel and helpful tool to analyze the accuracy of the results. For verification, three applications are investigated: (a) a numerical quarter-car model, (b) a real-world building, and (c) a real-world vehicle suspension system. We show that the estimated input signals in a numerically modeled system and real-world dynamic systems closely follow the actual inputs. In particular, the efficacy of input estimations in real-world cases confirms the strength of the proposed approach for similar applications with significant impact. For instance, the findings of this work enables the use of motion sensors mounted inside the vehicles for bridge vibration data collection which is proposed as a scalable and inexpensive paradigm for assessment of transportation infrastructure.