Integrating Model-Based and Data-Driven Approaches for Input/State Estimation of Mechanical Systems

Virtual sensing refers to a concept in which measurements or data that are not directly acquired through physical sensors are estimated or ``virtually'' generated using mathematical models, algorithms, or data fusion techniques. Virtual sensing allows the prediction or estimation of certain variables or parameters of interest based on available measurements and the understanding of the underlying system behavior. Current virtual sensing strategies for indirect estimation of inputs and states of mechatronic systems are flexible and cost-effective, but they are often limited by the accuracy of the underlying models used in their development. This can be especially challenging for reconstructing broadband input forces, as consistent and precise modeling across large frequency bands is rarely achieved. Therefore, there is a need to develop frameworks that rely solely on observations for input identification, while still taking advantage of any available approximated models for state estimation. This work proposes a combined approach for estimating forces and states based on a sequential implementation of an impulse response matrix deconvolution and a Kalman filter. The split implementation allows for improved input estimates, which current joint estimation techniques struggle to determine when model mismatches are introduced. The enhanced forces are then incorporated into the Kalman filter to generate estimates of the states at any particular location in the geometric domain, covering the deficiency of the impulse response filter to estimate unmeasured states. To further improve the accuracy of the estimates, a sensor fusion technique based on weighted least squares was introduced to balance the contributions of each sensor based on an a priori target impact force estimation. The examination of the estimate outcomes yielded results that prevented estimate deterioration due to noise amplification in the process of inversion of noisy sensor data, as well as overall improvement in conditioning of the system and quality of the force estimates.

The developed tools were found to be robust for structures with complex boundary conditions, large frequency bands, and high modal density, resulting in a significant reduction in the error between observed and estimated broadband forces. The framework was validated on two complex commercial mechanical systems: a hammer driller and a vehicle drive-train. To establish the proposed methodology and provide insight into the behavior of current model-based estimators, we conducted a thorough review of previous experimental and numerical findings. The results demonstrate the efficacy of our approach, even in challenging real-world scenarios.