Neural Network Augmented Physics Models for Systems with Partially Unknown Dynamics: Application to Slider-Crank Mechanism

Dynamic models of mechatronic systems are abundantly used in the context of motion control and design of complex servo applications. In practice, these systems are often plagued by unknown interactions, which make the physics-based relations of the system dynamics only partially known. This paper presents a neural network augmented physics (NNAP) model as a combination of physics-inspired and neural layers. The neural layers are inserted in the model to compensate for the unmodeled interactions, without requiring direct measurements of these unknown phenomena. In contrast to traditional approaches, both the neural network and physical parameters are simultaneously optimized, solely by using state and control input measurements. The methodology is applied on experimental data of a slider-crank setup for which the state dependent load interactions are unknown. The NNAP model proves to be a stable and accurate modeling formalism for dynamic systems that ab initio can only be partially described by physical laws. Moreover, the results show that a recurrent implementation of the NNAP model enables improved robustness and accuracy of the system state predictions, compared to its feedforward counterpart. Besides capturing the system dynamics, the NNAP model provides a means to gain new insights by extracting the neural network from the converged NNAP model. In this way, we discovered accurate representations of the unknown spring force interaction and friction phenomena acting on the slider mechanism

The effect of habitual foot strike pattern on the Gastrocnemius medialis muscle-tendon interaction and muscle force production during running

The interaction between Gastrocnemius medialis (GM) muscle and Achilles tendon, i.e. muscle-tendon unit (MTU) interaction, plays an important role in minimizing the metabolic cost of running. Foot strike pattern (FSP) has been suggested to alter MTU interaction and subsequently the metabolic cost of running. However, metabolic data from experimental studies on FSP is inconsistent and a comparison of MTU interaction between FSP is still lacking. We therefore investigated the effect of habitual rearfoot and mid-/forefoot striking on MTU interaction, ankle joint work and plantar flexor muscle force production while running at 10 and 14 km/h. GM muscle fascicles of 9 rearfoot and 10 mid-/forefoot strikers were tracked using dynamic ultrasonography during treadmill running. We collected kinetic and kinematic data, and used musculoskeletal models to determine joint angles and calculate MTU lengths. In addition, we used dynamic optimization to assess plantar flexor muscle forces. During ground contact, GM fascicle shortening (p = 0.02) and average contraction velocity (p = 0.01) were 40 to 45% greater in rearfoot strikers than mid-/forefoot strikers. Differences in contraction velocity were especially prominent during early ground contact. Moreover, GM (p = 0.02) muscle force was greater during early ground contact in mid-/forefoot strikers than rearfoot strikers. Interestingly, we did not find differences in stretch or recoil of the series elastic element between FSP. Our results suggest that, for the GM, the reduced muscle energy cost associated with lower fascicle contraction velocity in mid-/forefoot strikers may be counteracted by greater muscle forces during early ground contact

Prediction of follower jumps in cam-follower mechanisms : the benefit of using physics-inspired features in recurrent neural networks

The high functional performance exhibited by modern applications is very often established by an aggregation of various intricate mechanical mechanisms, providing the required motion dynamics to the overall system. Above all, the mechanism's behavior should be reliable for a wide range of operating conditions to assure at all times appropriate functioning of the entire application. In particular, cam-follower mechanisms, which translate a rotational movement into a linear displacement, are plagued by the high dynamics induced by the reciprocating motions. For specific operating conditions, the follower tends to detach from the cam perimeter, resulting in harmful bouncing behavior. This paper presents the use of recurrent neural networks to estimate the follower jump trajectory, based on cam rotation measurements, for a wide range of operating conditions and system modifications. Although these data-driven models are typically known to learn intricate patterns directly from raw data, enhanced prediction performances are observed when providing physics-inspired features to the model. The effect is especially more pronounced when learning from a small amount of data or from datasets for which the data are not uniformly distributed along the parameter space. In addition, this paper presents the use of an additive feature attribution method to quantify the contribution of features in multivariate timeseries on the prediction output of recurrent neural network models. Hence, we show that, by means of the Shapley additive explanation (SHAP) values, the model prioritizes the incorporation of physics-inspired features, explaining the improved generalization capabilities of the prediction model. In general, these presented results indicate the potential to incorporate physics-inspired expert knowledge into various other prediction models, enabling advanced methodologies to monitor inconvenient phenomena in mechanical systems

Physics-based neural network models for prediction of cam-follower dynamics beyond nominal operations

Cam-follower mechanisms are key in various mechatronic applications to convert rotary to linear reciprocating motions. The dynamic behavior of these systems relies on the design parameters such as the cam shape and follower mass. It appears that for some combinations of system parameters, continuous contact between the cam and follower cannot be assured, leading to harmful periodic impacts. This research presents a data-driven approach to predict the influence of parameter settings on the system dynamics by learning from a limited data set of nominal operating conditions. More specifically, we present a hybrid model architecture encompassing an ordinary differential equation, consisting of a close interconnection of neural and physics-based network layers. Due to an increased generalization established by the physical laws, these physics-based neural network models exhibit enhanced extrapolation capabilities compared to their black-box counterparts. Consequently, the presented models can accurately simulate the system behavior for parameter settings far beyond the nominal values included in the training data. This way, starting from a limited set of nominal time-series data, we could accurately estimate the set of critical system parameters that lead to hazardous jump phenomena in cam-follower systems

Triceps Surae muscle dynamics and energy consumption in forefoot vs rearfoot strikers

status: accepte

Habitual foot strike pattern does not affect simulated Triceps Surae muscle metabolic energy consumption during running

Foot strike pattern affects ankle joint work and Triceps Surae muscle-tendon dynamics during running. Whether these changes in muscle-tendon dynamics also affect Triceps Surae muscle energy consumption is still unknown. In addition, as the Triceps Surae muscle accounts for a substantial amount of the whole body metabolic energy consumption, changes in Triceps Surae energy consumption may affect whole body metabolic energy consumption. However, direct measurements of muscle metabolic energy consumption during dynamic movements is hard. Model-based approaches can be used to estimate individual muscle and whole body metabolic energy consumption based on Hill type muscle models. In this study, we use an integrated experimental and dynamic optimization approach to compute muscle states (muscle forces, lengths, velocities, excitations and activations) of 10 habitual mid-/forefoot striking and 9 habitual rearfoot striking runners while running at 10 and 14 km/h. The Achilles tendon stiffness of the musculoskeletal model was adapted to fit experimental ultrasound data of the Gastrocnemius medialis muscle during ground contact. Next, we calculated Triceps Surae muscle and whole body metabolic energy consumption using four different metabolic energy models provided in literature. Neither Triceps Surae metabolic energy consumption (p>0.35), nor whole body metabolic energy consumption (p>0.14) was different between foot strike patterns, regardless of the energy model used or running speed tested. Our results provide new evidence that mid-/forefoot and rearfoot strike pattern are metabolically equivalent.status: Published onlin

The effect of habitual rearfoot and mid-/forefoot striking on muscle fascicle and tendon behavior during running

status: publishe

Effect of habitual foot-strike pattern on the gastrocnemius medialis muscle-tendon interaction and muscle force production during running

The interaction between gastrocnemius medialis (GM) muscle and Achilles tendon, i.e., muscle-tendon unit (MTU) interaction, plays an important role in minimizing the metabolic cost of running. Foot-strike pattern (FSP) has been suggested to alter MTU interaction and subsequently the metabolic cost of running. However, metabolic data from experimental studies on FSP are inconsistent, and a comparison of MTU interaction between FSP is still lacking. We, therefore, investigated the effect of habitual rearfoot and mid-/forefoot striking on MTU interaction, ankle joint work, and plantar flexor muscle force production while running at 10 and 14 km/h. GM muscle fascicles of 9 rearfoot and 10 mid-/forefoot strikers were tracked using dynamic ultrasonography during treadmill running. We collected kinetic and kinematic data and used musculoskeletal models to determine joint angles and calculate MTU lengths. In addition, we used dynamic optimization to assess plantar flexor muscle forces. During ground contact, GM fascicle shortening ( P = 0.02) and average contraction velocity ( P = 0.01) were 40-45% greater in rearfoot strikers than mid-/forefoot strikers. Differences in contraction velocity were especially prominent during early ground contact. Moreover, GM ( P = 0.02) muscle force was greater during early ground contact in mid-/forefoot strikers than rearfoot strikers. Interestingly, we did not find differences in stretch or recoil of the series elastic element between FSP. Our results suggest that, for the GM, the reduced muscle energy cost associated with lower fascicle contraction velocity in mid-/forefoot strikers may be counteracted by greater muscle forces during early ground contact. NEW & NOTEWORTHY Kinetic and kinematic differences between foot-strike patterns during running imply (not previously reported) altered muscle-tendon interaction. Here, we studied muscle-tendon interaction using ultrasonography. We found greater fascicle contraction velocities and lower muscle forces in rearfoot compared with mid-/forefoot strikers. Our results suggest that the higher metabolic energy demand due to greater fascicle contraction velocities might offset the lower metabolic energy demand due to lower muscle forces in rearfoot compared with mid-/forefoot strikers.status: publishe