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IntroductionBiomechanical changes due to aging increase the oxygen consumption of walking by over 30%. When this is coupled with reduced oxygen uptake capacity, the ability to sustain walking becomes compromised. This reduced physical activity and mobility can lead to further physical degeneration and mortality. Unfortunately, the underlying reasons for the increased metabolic cost are still inadequately understood. While motion capture systems can measure signals with high temporal resolution, it is impossible to directly characterize the fluctuation of metabolic cost throughout the gait cycle. MethodsTo address this issue, this research focuses on computing the metabolic cost time series from the mean value using two neural-network-based approaches: autoencoders (AEs) and expanders. For the AEs, the encoders are designed to compress the input time series down to their mean value, and the decoder expands those values into the time series. After training, the decoder is extracted and applied to mean metabolic cost values to compute the time series. A second approach leverages an expander to map the mean values to the time series without an encoder. The networks are trained using ten different metabolic cost models generated by a computational walking model that simulates the gait cycle subjected to 35 different robotic perturbations without using experimental input data. The networks are validated using the estimated metabolic costs for the unperturbed gait cycle. ResultsThe investigation found that AEs without tied weights and the expanders performed best using nonlinear activation functions, while the AEs with tied weights performed best with linear activation functions. Unexpectedly, the results show that the expanders outperform the AEs. DiscussionA limitation of this research is the reliance on time series for the initial training. Future efforts will focus on developing methods that overcome this issue. Improved methods for estimating within-stride fluctuations in metabolic cost have the potential of improving rehabilitation and assistive devices by targeting the gait phases with increased metabolic cost. This research could also be applied to expand sparse measurements to locations or times that were not measured explicitly. This application would reduce the number of measurement points required to capture the response of a system. 

Purpose This research introduces an innovative solution that revolutionizes the study of linear and nonlinear dynamical systems—a smart automatic modal hammer. With its affordability and intelligent capabilities, this automatic modal hammer becomes an invaluable tool for research and industry, enabling repeatable strikes with precise force control. This system's significance becomes particularly evident when studying nonlinear systems, which heavily rely on the excitation level for their dynamics. By offering a cost-effective design this proposed system proves to be robust in accelerating research on nonlinear dynamics, providing researchers with an efficient and accessible means to delve deeper into these complex systems. Methods The proposed design integrates a commercial modal hammer, commonly used in modal testing, and a stepper motor. This stepper motor is enhanced with an encoder and servo driver, all expertly controlled by a Raspberry Pi. Results What sets this system apart is its clever utilization of regression models to acquire knowledge of the intrinsic relationship between the applied force and hammer velocity precisely during the impact. This acquired knowledge is the foundation for controlling the motor's behavior, ensuring consistent and accurate excitation of the structure with the desired force. Conclusion The capabilities of the proposed automatic modal hammer are demonstrated using a linear two-story tower and a model airplane wing with a nonlinear vibration absorber.