natural frequency
Estimation of Minimum Stride Frequency for the Frontal Plane Stability of Bipedal Systems
Karunanayaka, Harsha, Rezazadeh, Siavash
Abstract--Stability of bipedal systems in frontal plane is affected by the hip offset, to the extent that adjusting stride time using feedforward retraction and extension of the legs can lead to stable oscillations without feedback control. This feedforward stabilization can be leveraged to reduce the control effort and energy expenditure and increase the locomotion robustness. However, there is limited understanding of how key parameters, such as mass, stiffness, leg length, and hip width, affect stability and the minimum stride frequency needed to maintain it. This study aims to address these gaps through analyzing how individual model parameters and the system's natural frequency influence the minimum stride frequency required to maintain a stable cycle. We propose a method to predict the minimum stride frequency, and compare the predicted stride frequencies with actual values for randomly generated models. The findings of this work provide a better understanding of the frontal plane stability mechanisms and how feedforward stabilization can be leveraged to reduce the control effort. The stability of bipedal locomotion depends on maintaining balance in both the sagittal and frontal planes. Although most existing research focuses on the sagittal plane, the mechanisms underlying frontal plane stability remain less explored. In human bipedal locomotion, loss of balance in the medial-lateral plane frequently results in falls, and stability in this plane is influenced by body posture and foot placement [1].
Optimal Characteristics of Inspection Vehicle for Drive-by Bridge Inspection
Hurtado, A. Calderon, Atroshchenko, E., Chang, K. C., Kim, C. W., Alamdari, M. Makki
Drive-by inspection for bridge health monitoring has gained increasing attention over the past decade. This method involves analysing the coupled vehicle-bridge response, recorded by an instrumented inspection vehicle, to assess structural integrity and detect damage. However, the vehicles mechanical and dynamic properties significantly influence detection performance, limiting the effectiveness of the approach. This study presents a framework for optimising the inspection vehicle to enhance damage sensitivity. An unsupervised deep learning methodbased on adversarial autoencoders (AAE)is used to reconstruct the frequency-domain representation of acceleration responses. The mass and stiffness of the tyre suspension system of a two-axle vehicle are optimised by minimising the Wasserstein distance between damage index distributions for healthy and damaged bridge states. A Kriging meta-model is employed to approximate this objective function efficiently and identify optimal vehicle configurations in both dimensional and non-dimensional parameter spaces. Results show that vehicles with frequency ratios between 0.3 and 0.7 relative to the bridges' first natural frequency are most effective, while those near resonance perform poorly. Lighter vehicles require lower natural frequencies for optimal detection. This is the first study to rigorously optimise the sensing platform for drive-by sensing and to propose a purpose-built inspection vehicle.
Physics-informed transfer learning for SHM via feature selection
Poole, J., Gardner, P., Hughes, A. J., Dervilis, N., Mills, R. S., Dardeno, T. A., Worden, K.
Data used for training structural health monitoring (SHM) systems are expensive and often impractical to obtain, particularly labelled data. Population-based SHM presents a potential solution to this issue by considering the available data across a population of structures. However, differences between structures will mean the training and testing distributions will differ; thus, conventional machine learning methods cannot be expected to generalise between structures. To address this issue, transfer learning (TL), can be used to leverage information across related domains. An important consideration is that the lack of labels in the target domain limits data-based metrics to quantifying the discrepancy between the marginal distributions. Thus, a prerequisite for the application of typical unsupervised TL methods is to identify suitable source structures (domains), and a set of features, for which the conditional distributions are related to the target structure. Generally, the selection of domains and features is reliant on domain expertise; however, for complex mechanisms, such as the influence of damage on the dynamic response of a structure, this task is not trivial. In this paper, knowledge of physics is leveraged to select more similar features, the modal assurance criterion (MAC) is used to quantify the correspondence between the modes of healthy structures. The MAC is shown to have high correspondence with a supervised metric that measures joint-distribution similarity, which is the primary indicator of whether a classifier will generalise between domains. The MAC is proposed as a measure for selecting a set of features that behave consistently across domains when subjected to damage, i.e. features with invariance in the conditional distributions. This approach is demonstrated on numerical and experimental case studies to verify its effectiveness in various applications.
Optical Waveguide-based Spider Web Enables Resilient Impact Detection and Localization
Wilson, Dylan, Pontin, Marco, Walters, Peter, Maiolino, Perla
Spiders use their webs as multifunctional tools that enable capturing and localizing prey and more general environmental sensing through vibrations. Inspired by their biological function, we present a spider web-inspired optical waveguide system for resilient impulse detection and localization. The structure consists of six clear thermoplastic polyurethane (TPU) waveguides arranged radially and interconnected by a spiral TPU thread, mimicking orb spider webs. Light transmission losses, induced by vibrations, are measured via coupled LEDs and photo-diodes, allowing real-time detection. We systematically characterize individual waveguides, analyzing key parameters such as tension, impulse position, and break angle to optimize vibrational response. The complete system is validated through controlled experiments, revealing a 5 ms propagation delay in vibration transfer between adjacent radii, enhancing localization capabilities. We demonstrate a robust impulse detection and localization algorithm leveraging time delay analysis, achieving reliable event identification even in cases of sensor failure. This study highlights the potential of bioinspired optical waveguide structures for adaptive sensing, with applications in soft robotics, structural monitoring, and environmental sensing.
Spline Dimensional Decomposition with Interpolation-based Optimal Knot Selection for Stochastic Dynamic Analysis
Kim, Yeonsu, Lee, Junhan, Wang, Bingran, Hwang, John T., Lee, Dongjin
Forward uncertainty quantification in dynamical systems is challenging due to non-smooth or locally oscillating nonlinear behaviors. Spline dimensional decomposition (SDD) addresses such nonlinearity by partitioning input coordinates via knot placement, but its accuracy is highly sensitive to internal knot locations. Optimizing knots using sequential quadratic programming is effective, yet computationally expensive. We propose a computationally efficient, interpolation-based method for optimal knot selection in SDD. The method includes: (1) interpolating input-output profiles, (2) defining subinterval-based reference regions, and (3) selecting knots at maximum gradient points within each region. The resulting knot vector is then applied to SDD for accurate approximation of non-smooth and oscillatory responses. A modal analysis of a lower control arm shows that SDD with the proposed knots yields higher accuracy than SDD with uniformly or randomly spaced knots and a Gaussian process model. In this example, the proposed SDD achieves the lowest relative variance error (2.89%) for the first natural frequency distribution, compared to uniformly spaced knots (12.310%), randomly spaced knots (15.274%), and Gaussian process (5.319%). All surrogates are constructed using the same 401 simulation datasets, and errors are evaluated against a 2000-sample Monte Carlo simulation. Scalability and applicability are demonstrated through stochastic and reliability analyses of one- and three-dimensional benchmark functions, and a ten-dimensional lower control arm model. Results confirm that second-moment statistics and reliability estimates can be accurately obtained with only a few hundred function evaluations or finite element simulations.
Data Driven Approach to Input Shaping for Vibration Suppression in a Flexible Robot Arm
Kotaniemi, Jarkko, Saukkoriipi, Janne, Li, Shuai, Suomalainen, Markku
--This paper presents a simple and effective method for setting parameters for an input shaper to suppress the residual vibrations in flexible robot arms using a data-driven approach. The parameters are adaptively tuned in the workspace of the robot by interpolating previously measured data of the robot's residual vibrations. Input shaping is a simple and robust technique to generate vibration-reduced shaped commands by a convolution of an impulse sequence with the desired input command. The generated impulses create waves in the material countering the natural vibrations of the system. The method is demonstrated with a flexible 3D-printed robot arm with multiple different materials, achieving a significant reduction in the residual vibrations. Undesired residual vibrations occur after performing motions and have multiple negative effects on robots: they decrease accuracy, lower lifespan, and compromise the structural integrity [1].
Improving Swimming Performance in Soft Robotic Fish with Distributed Muscles and Embedded Kinematic Sensing
Soto, Kevin, Hess, Isabel, Schrader, Brandon, He, Shan, Musgrave, Patrick
Bio-inspired underwater vehicles could yield improved efficiency, maneuverability, and environmental compatibility over conventional propeller-driven underwater vehicles. However, to realize the swimming performance of biology, there is a need for soft robotic swimmers with both distributed muscles and kinematic feedback. This study presents the design and swimming performance of a soft robotic fish with independently controllable muscles and embedded kinematic sensing distributed along the body. The soft swimming robot consists of an interior flexible spine, three axially distributed sets of HASEL artificial muscles, embedded strain gauges, a streamlined silicone body, and off-board electronics. In a fixed configuration, the soft robot generates a maximum thrust of 7.9 mN when excited near its first resonant frequency (2 Hz) with synchronized antagonistic actuation of all muscles. When excited near its second resonant frequency (8 Hz), synchronized muscle actuation generates 5.0 mN of thrust. By introducing a sequential phase offset into the muscle actuation, the thrust at the second resonant frequency increases to 7.2 mN, a 44% increase from simple antagonistic activation. The sequential muscle activation improves the thrust by increasing 1) the tail-beat velocity and 2) traveling wave content in the swimming kinematics by four times. Further, the second resonant frequency (8 Hz) generates nearly as much thrust as the first resonance (2 Hz) while requiring only $\approx25$% of the tail displacement, indicating that higher resonant frequencies have benefits for swimming in confined environments where a smaller kinematic envelope is necessary. These results demonstrate the performance benefits of independently controllable muscles and distributed kinematic sensing, and this type of soft robotic swimmer provides a platform to address the open challenge of sensorimotor control.
Do Chains-of-Thoughts of Large Language Models Suffer from Hallucinations, Cognitive Biases, or Phobias in Bayesian Reasoning?
Learning to reason and carefully explain arguments is central to students' cognitive, mathematical, and computational thinking development. This is particularly challenging in problems under uncertainty and in Bayesian reasoning. With the new generation of large language models (LLMs) capable of reasoning using Chain-of-Thought (CoT), there is an excellent opportunity to learn with them as they explain their reasoning through a dialogue with their artificial internal voice. It is an engaging and excellent opportunity to learn Bayesian reasoning. Furthermore, given that different LLMs sometimes arrive at opposite solutions, CoT generates opportunities for deep learning by detailed comparisons of reasonings. However, unlike humans, we found that they do not autonomously explain using ecologically valid strategies like natural frequencies, whole objects, and embodied heuristics. This is unfortunate, as these strategies help humans avoid critical mistakes and have proven pedagogical value in Bayesian reasoning. In order to overcome these biases and aid understanding and learning, we included prompts that induce LLMs to use these strategies. We found that LLMs with CoT incorporate them but not consistently. They show persistent biases towards symbolic reasoning and avoidance or phobia of ecologically valid strategies.
MC-GRU:a Multi-Channel GRU network for generalized nonlinear structural response prediction across structures
Accurate prediction of seismic responses and quantification of structural damage are critical in civil engineering. Traditional approaches such as finite element analysis could lack computational efficiency, especially for complex structural systems under extreme hazards. Recently, artificial intelligence has provided an alternative to efficiently model highly nonlinear behaviors. However, existing models face challenges in generalizing across diverse structural systems. This paper proposes a novel multi-channel gated recurrent unit (MC-GRU) network aimed at achieving generalized nonlinear structural response prediction for varying structures. The key concept lies in the integration of a multi-channel input mechanism to GRU with an extra input of structural information to the candidate hidden state, which enables the network to learn the dynamic characteristics of diverse structures and thus empower the generalizability and adaptiveness to unseen structures. The performance of the proposed MC-GRU is validated through a series of case studies, including a single-degree-of-freedom linear system, a hysteretic Bouc-Wen system, and a nonlinear reinforced concrete column from experimental testing. Results indicate that the proposed MC-GRU overcomes the major generalizability issues of existing methods, with capability of accurately inferring seismic responses of varying structures. Additionally, it demonstrates enhanced capabilities in representing nonlinear structural dynamics compared to traditional models such as GRU and LSTM.
Harnessing the Power of Vibration Motors to Develop Miniature Untethered Robotic Fishes
Jiang, Chongjie, Dai, Yingying, Le, Jinyang, Chen, Xiaomeng, Xie, Yu, Zhou, Wei, Niu, Fuzhou, Li, Ying, Luo, Tao
Miniature underwater robots play a crucial role in the exploration and development of marine resources, particularly in confined spaces and high-pressure deep-sea environments. This study presents the design, optimization, and performance of a miniature robotic fish, powered by the oscillation of bio-inspired fins. These fins feature a rigid-flexible hybrid structure and use an eccentric rotating mass (ERM) vibration motor as the excitation source to generate high-frequency unidirectional oscillations that induce acoustic streaming for propulsion. The drive mechanism, powered by miniature ERM vibration motors, eliminates the need for complex mechanical drive systems, enabling complete isolation of the entire drive system from the external environment and facilitating the miniaturization of the robotic fish. A compact, untethered robotic fish, measuring 85*60*45 mm^3, is equipped with three bio-inspired fins located at the pectoral and caudal positions. Experimental results demonstrate that the robotic fish achieves a maximum forward swimming speed of 1.36 body lengths (BL) per second powered by all fins and minimum turning radius of 0.6 BL when powered by a single fin. These results underscore the significance of employing the ERM vibration motor in advancing the development of highly maneuverable, miniature untethered underwater robots for various marine exploration tasks.