A Deep Learning Approach for Foot Trajectory Estimation in Gait Analysis Using Inertial Sensors

Gait performance is an important marker of motor and cognitive decline in older adults. An instrumented gait analysis resorting to inertial sensors allows the complete evaluation of spatiotemporal gait parameters, offering an alternative to laboratory-based assessments. To estimate gait parameters, foot trajectories are typically obtained by integrating acceleration two times. However, to deal with cumulative integration errors, additional error handling strategies are required. In this study, we propose an alternative approach based on a deep recurrent neural network to estimate heel and toe trajectories. We propose a coordinate frame transformation for stride trajectories that eliminates the dependency from previous strides and external inputs. Predicted trajectories are used to estimate an extensive set of spatiotemporal gait parameters. We evaluate the results in a dataset comprising foot-worn inertial sensor data acquired from a group of young adults, using an optical motion capture system as a reference. Heel and toe trajectories are predicted with low errors, in line with reference trajectories. A good agreement is also achieved between the reference and estimated gait parameters, in particular when turning strides are excluded from the analysis. The performance of the method is shown to be robust to imperfect sensor-foot alignment conditions.

Load Sharing Scheme Incorporating Power Security Margins for Parallel Operation of Voltage Source Inverters

The interconnection of distributed energy resources (DERs) in microgrids (MGs) operating in both islanded and grid-connected modes require coordinated control strategies. DERs are interfaced with voltage source inverters (VSIs) enabling interconnection. This paper proposes a load demand sharing scheme for the parallel operation of VSIs in an islanded voltage source inverter-based microgrid (VSI-MG). The ride-through capability of a heavily loaded VSI-MG, where some of the VSIs are fully loaded due to the occurrence of an event is investigated. In developing analytical equations to model the VSI, the concept of virtual synchronous machines (VSM) is applied to enable the VSI mimic the inertia effect of synchronous machines. A power frame transformation (PFT) that takes the line ratios of the MG network into account is also incorporated to yield satisfactory transient responses of both network frequency and bus voltages in the MG network. A Jacobian-based method is then developed to take into account the operational capacity of each VSI in the VSI-MG. The resulting amendable droop control constrains the VSIs within their power capabilities when an event occurs. Simulation results presented within demonstrate the effectiveness of the proposed procedure which has great potential to facilitate efforts in maintaining system reliability and resiliency.

Cross Sections and Rate Coefficients for Vibrational Excitation of H2O by Electron Impact

Cross-sections and thermally averaged rate coefficients for vibration (de-)excitation of a water molecule by electron impact are computed; one and two quanta excitations are considered for all three normal modes. The calculations use a theoretical approach that combines the normal mode approximation for vibrational states of water, a vibrational frame transformation employed to evaluate the scattering matrix for vibrational transitions and the UK molecular R-matrix code. The interval of applicability of the rate coefficients is from 10 to 10,000 K. A comprehensive set of calculations is performed to assess uncertainty of the obtained data. The results should help in modelling non-LTE spectra of water in various astrophysical environments.

Limitations of Small-Signal Modeling of Grid-Connected VSCs under Phase Jumps and Frequency Deviations

The stability of grid-connected voltage source converters (VSCs) is commonly studied by the small-signal model in the synchronous reference (dq) frame. With phase-locked loop dynamic from VSCs, it is inevitable to convert the small-signal model to a common dq frame. When linearizing the frame transformation, the trigonometric functions of the angle are approximated by first-order terms. In this letter, the limitation of such linearization on the dq-transformation is discussed. The accuracy of the model, in presence of phase jumps and frequency variations, are examined. It is found that even under small phase jumps, mismatches are found between the small-signal model (SSM) and a nonlinear model (NM). It is further revealed that during the dynamics of frequency variation, significant mismatches can occur between the SSM and the NM.

Limitations of Small-Signal Modeling of Grid-Connected VSCs under Phase Jumps and Frequency Deviations

The stability of grid-connected voltage source converters (VSCs) is commonly studied by the small-signal model in the synchronous reference (dq) frame. With phase-locked loop dynamic from VSCs, it is inevitable to convert the small-signal model to a common dq frame. When linearizing the frame transformation, the trigonometric functions of the angle are approximated by first-order terms. In this letter, the limitation of such linearization on the dq-transformation is discussed. The accuracy of the model, in presence of phase jumps and frequency variations, are examined. It is found that even under small phase jumps, mismatches are found between the small-signal model (SSM) and a nonlinear model (NM). It is further revealed that during the dynamics of frequency variation, significant mismatches can occur between the SSM and the NM.