Input estimation of nonlinear systems using probabilistic neural network

• Published in: Mechanical systems and signal processing 2022-03, Vol.166, p.108368, Article 108368
• Main Authors: Sadeghi Eshkevari, Soheil, Cronin, Liam, Sadeghi Eshkevari, Soheila, Pakzad, Shamim N.
• Format: Article
• Language: English
• Subjects: Data collection; Deconvolution; Deep learning; Dynamical systems; Inverse problem; Machine learning; Mechanical properties; Motion sensors; Neural networks; Nonlinear dynamics; Nonlinear systems; Nonlinearity; Regression models; Statistical analysis; Suspension systems
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2021.108368

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. •Probabilistic neural network is proposed for input estimation of nonlinear systems.•The model requires no prior system information and is fully data-driven.•The model recurrently estimates the input by processing a short slice of the output.•For each estimated input, the model automatically quantifies the uncertainty.•Model is verified in three case studies: one numerical and two experimental.•Model performs well in estimating inputs with varying number of channels, DOFs, and SNR.•The model provides estimation confidence which is useful for uncertainty quantification.•Testing sensors are built for synchronized data collection at multiple points in vehicles.•The sensor bundle has applications in other domains of experimental mechanics.