Periodic Input Research Articles

Utilization of the Resonance Behavior of a Tendon-Driven Continuum Joint for Periodic Natural Motions in Soft Robotics

Continuum joints use structural elastic deformations to enable joint motion, and their intrinsic compliance and inherent mechanical robustness are envisioned for applications in which the robot, the human, and the environment need to be safe during interaction. In particular, the intrinsic compliance makes continuum joints a competitor to soft articulated joints, which require additional integrated spring elements. For soft articulated joints incorporating rigid and soft parts, natural motions have been investigated in robotics research to exploit this energy-efficient motion property for cyclic motions, e.g., locomotion. To the best of the author’s knowledge, there is no robotic system to date that utilizes the natural motion of a continuum joint under periodic excitation. In this paper, the resonant behavior of a tendon-driven continuum joint under periodic excitation of the torsional axis is experimentally investigated in a functional sense. In the experiments, periodic inputs are introduced on the joint side of a tendon driven continuum joint with four tendons. By modulating the pretension of the tendons, both the resonant frequency and the gain can be shifted, from 3 to 4.3 Hz and 2.8 to 1.4, respectively, in the present experimental setup. An application would be the rotation of a humanoid torso, where gait frequencies are synchronized with the resonant frequency of the continuum joint.

On a Class of Periodic Inputs that Passively Quench the Superharmonic Resonance of a Symmetric Duffing Oscillator

Abstract The symmetric mono-stable Duffing oscillator exhibits a superharmonic resonance of order three when excited harmonically at an excitation frequency that is one third its linear natural frequency. In this letter, it is shown that a certain class of periodic excitations can inherently quench the superharmonic resonance of order three. The Fourier series expansion of such excitations yields a harmonic component at the natural frequency whose magnitude can be properly tuned to completely quench the effect of the superharmonic component. Based on this understanding, the parameters of a piecewise periodic function and the modulus of the cosine Jacobi elliptic function are intentionally designed to passively suppress the superharmonic resonance. Such periodic functions can be used to replace single-frequency harmonic excitations whenever the effects of the superharmonic resonance are to be mitigated.

Hybrid Deep-Learning Approach with Geoffrey E. Havers-Based Loss Function and Evaluation Metric for Multilocation Traffic-Flow Forecasting

Traffic forecasting can enhance the efficiency of traffic control strategies such as routing decisions, variable speed limits, and ramp metering, resulting in a decrease in congestion, pollutants, and expenses, and an improvement in journey time predictability. Traffic forecasting, however, remains challenging because of the complex, heterogeneous, and cyclic nature of traffic data. To address this complexity, this research employs a multi-input hybrid deep self-attention network (MIHDSAN) for multilocation forecasting. The model inputs are selected using correlation analysis. New tunable loss and evaluation metrics formulations are proposed based on the traffic-modeling Geoffrey E. Havers (GEH) statistic. The proposed method was validated on two independent real-world traffic datasets from Stockton and Oakland, California. The weekly periodicity was the more relevant periodic input feature compared with daily variations; however, the daily variation was also significant for the Stockton dataset. The inclusion of weekly traffic periodicity (>95% correlated) improved the performance of the model by 3%. Adding daily periodicity was only beneficial for the Stockton dataset (91% correlated). The proposed GEH metric and its standard acceptance criterion offer both quantitative and qualitative means of evaluating the forecasts produced. The GEH loss function was consistent and outperformed current industry-standard methodologies of mean absolute error (MAE) in 80% and mean squared error (MSE) in 94% of cases. Therefore, this research presents evidence to suggest that the proposed GEH loss and evaluation functions validated in this paper become a standard criterion for traffic forecasting.

Ultimate Boundedness of a Stochastic Chemostat Model with Periodic Nutrient Input and Random Disturbance

Ultimate Boundedness of a Stochastic Chemostat Model with Periodic Nutrient Input and Random Disturbance

Diagnosis of Polymer Electrolyte Fuel Cell: Should We Rely Only on Electrical Quantities?

Polymer electrolyte fuel cells (PEMFC) will play a central role in the establishment of a de-carbonized society. They are seen as a key technology to empower electric heavy-duty vehicles. However, the lifespan is still below the fixed standards for their commercialization. A way to increase their durability is to complement them during operation with a mitigation strategy enabling to avoid the arise of faulty states accelerating degradation processes. Nowadays, most of the proposed fault identification and isolation architectures rely on monitoring of the performance through electrochemical impedance spectroscopy (EIS). Nevertheless, the analysis of impedance data is often complicated, since the contribution of many processes in the EIS spectra are coupled with each other and, for this reason, difficult to identify. This constitutes a limiting factor for its employment as diagnostic tool. In the last years, in order to overcome such issues, the use of nonelectrical periodic inputs and/or outputs has been advanced. The idea motivating this research direction is the possibility to detect the contribution of selected processes on the performance of PEMFCs separating them from the others. Novel frequency response techniques involving back pressure, temperature and partial pressure have been developed [1].In this contribution, the so-called concentration frequency response analysis (CFRA) is considered [2, 3]. It consists on perturbing the cathode side of the cell with a feed characterized by a periodic partial pressure of oxygen and water, and the detection of the electric response, voltage or current. A test station has been designed and constructed in order to apply this technique and investigate its capabilities. A model based analysis of the measured CFRA spectra indicates the possibility to decouple the contributions of the water transport into Nafion and oxygen mass transport on the performance of the cell depending on the chosen concentration input and electrical output. In this way, the analysis and identification of the related power losses is simplified with respect to classic EIS.Moreover, the performance of a fault identification and isolation architecture employing CFRA as monitoring technique have been evaluated and compared to EIS. For such purpose, an identifiability analysis of parameters related to faulty states and obtained by model fitting to spectra of each technique has been performed. The results clearly show that the employment of CFRA based on water pressure input offers the most reliable parameter estimation and, consequently, constitutes the most preferable diagnosis method among the others analyzed.

Dynamics of Purcell-type microswimmers with active-elastic joints.

Purcell's planar three-link microswimmer is a classic model of swimming in low-Reynolds-number fluid, inspired by motion of flagellated microorganisms. Many works analyzed this model, assuming that the two joint angles are directly prescribed in phase-shifted periodic inputs. In this work, we study a more realistic scenario by considering an extension of this model which accounts for joints' elasticity and mechanical actuation of periodic torques so that the joint angles are dynamically evolving. Numerical analysis of the swimmer's dynamics reveals multiplicity of periodic solutions, depending on parameters of the inputs-frequency and amplitude of excitation, joints' stiffness ratio, as well as joint's activation. We numerically study swimming direction reversal, as well as bifurcations, stability transitions, and symmetry breaking of the periodic solutions, which represent the effect of buckling instability observed in swimming microorganisms. The results demonstrate that this variant of Purcell's simple model displays rich nonlinear dynamic behavior with actuated-elastic joints. Similar results are also obtained when studying an extended model of a six-link microswimmer.

Optimal control of oscillatory neuronal models with applications to communication through coherence

Macroscopic oscillations in the brain are involved in various cognitive and physiological processes, yet their precise function is not completely understood. Communication through coherence (CTC) theory proposes that these rhythmic electrical patterns might serve to regulate the information flow between neural populations. Thus, to communicate effectively, neural populations must synchronize their oscillatory activity, ensuring that input volleys from the presynaptic population reach the postsynaptic one at its maximum phase of excitability. We consider an Excitatory–Inhibitory (E–I) network whose macroscopic activity is described by an exact mean-field model. The E–I network receives periodic inputs from either one or two external sources, for which effective communication will not be achieved in the absence of control. We explore strategies based on optimal control theory for phase–amplitude dynamics to design a periodic control that sets the target population in the optimal phase to synchronize its activity with a specific presynaptic input signal and establish communication. The control mechanism resembles the role of a higher cortical area in the context of selective attention. To design the control, we use the phase–amplitude reduction of a limit cycle and leverage recent developments in this field in order to find the most effective control strategy regarding a defined cost function. Furthermore, we present results that guarantee the local controllability of the system close to the limit cycle.

Frequency-adaptive odd-harmonic repetitive control scheme for three-phase shunt active power filters

Repetitive control (RC), which can track the periodic input or suppress the periodic disturbance with a zero steady-state error, is a promising control strategy for shunt active power filters (SAPF). However, the conventional RC (CRC) scheme will suffer a severe performance degradation caused by the grid frequency variations. In this article, a frequency-adaptive odd-harmonic repetitive control scheme with a single and fixed sampling rate is proposed for SAPF to deal with grid frequency variations and provide fast transient response for RC system. The frequency-adaptability of proposed repetitive control scheme can be implemented by updating the coefficients of the approximate expression for the delay unit in repetitive controller. The FIR filter based on Lagrange linear interpolation is used to transform the multirate repetitive control system into single-rate repetitive control system to address the problems caused by the multirate repetitive control system. Moreover, a fractional-order linear compensator with a simple structure is designed to compensate the magnitude and phase of the system accurately. Compared with other classical repetitive control strategies, the proposed repetitive control scheme can provide a better adaptation to the steady-state deviation and dynamic variation of grid frequency and ensure the control performance of SAPF system. Simulation and experimental results verify the effectiveness of the proposed control scheme.

Modeling the Electrical Activity of the Heart via Transfer Functions and Genetic Algorithms.

Although healthcare and medical technology have advanced significantly over the past few decades, heart disease continues to be a major cause of mortality globally. Electrocardiography (ECG) is one of the most widely used tools for the detection of heart diseases. This study presents a mathematical model based on transfer functions that allows for the exploration and optimization of heart dynamics in Laplace space using a genetic algorithm (GA). The transfer function parameters were fine-tuned using the GA, with clinical ECG records serving as reference signals. The proposed model, which is based on polynomials and delays, approximates a real ECG with a root-mean-square error of 4.7% and an R2 value of 0.72. The model achieves the periodic nature of an ECG signal by using a single periodic impulse input. Its simplicity makes it possible to adjust waveform parameters with a predetermined understanding of their effects, which can be used to generate both arrhythmic patterns and healthy signals. This is a notable advantage over other models that are burdened by a large number of differential equations and many parameters.

Periodic Optimal Control of a Plug Flow Reactor Model with an Isoperimetric Constraint

We study a class of nonlinear hyperbolic partial differential equations with boundary control. This class describes chemical reactions of the type “A→\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A \\rightarrow $$\\end{document} product” carried out in a plug flow reactor (PFR) in the presence of an inert component. An isoperimetric optimal control problem with periodic boundary conditions and input constraints is formulated for the considered mathematical model in order to maximize the mean amount of product over the period. For the single-input system, the optimality of a bang-bang control strategy is proved in the class of bounded measurable inputs. The case of controlled flow rate input is also analyzed by exploiting the method of characteristics. A case study is performed to illustrate the performance of the reaction model under different control strategies.

High Frequency Response of Volatile Memristors

AbstractIn this theoretical study, the high‐frequency response of the electrothermal NbO2‐Mott threshold switch is focused, a real‐world electronic device, which has been proved to be relevant in several applications and is classified as a volatile memristor. Memristors of this kind, have been shown to exhibit distinctive non‐linear behaviors crucial for cutting‐edge neuromorphic circuits. In accordance with well‐established models for these devices, their resistances depend on their body temperatures, which evolve over time following Newton's Law of Cooling. Here, it is demonstrated that HP's NbO2‐Mott memristor can manifest up to three distinct steady‐state oscillatory behaviors under a suitable high‐frequency periodic voltage input, showcasing increased versatility despite its volatile nature. Additionally, when subjected to a high‐frequency periodic voltage signal, the device body temperature oscillates with a negligible peak‐to‐peak amplitude. Since the temperature remains almost constant over an input cycle, the devices under study behave as linear resistors during each input cycle. Based on these insights, this paper presents analytical equations characterizing the response of the NbO2‐Mott memristor to high‐frequency voltage inputs, demarcating regions in the state space where distinct initial conditions lead to various asymptotic oscillatory behaviors. Importantly, the mathematical methods introduced in this manuscript are applicable to any volatile electrothermal resistive switch. Additionally, this work presents analytical equations that accurately reproduce the temperature time‐waveform of the studied device during both its transient and steady‐state phases when subjected to a zero‐mean sinusoidal voltage input oscillating in the high‐frequency limit. This analytical approach not only increases the comprehension of volatile electrothermal memristors but also provides a theoretical framework to harness the enhanced dynamical capabilities of real‐world volatile memristors in practical applications.

Entropic stochastic resonance of finite-size particles in confined Brownian transport.

We demonstrate the existence of entropic stochastic resonance (ESR) of passive Brownian particles with finite size in a double- or triple-circular confined cavity, and compare the similarities and differences of ESR in the double-circular cavity and triple-circular cavity. When the diffusion of Brownian particles is constrained to the double- or triple-circular cavity, the presence of irregular boundaries leads to entropic barriers. The interplay between the entropic barriers, a periodic input signal, the gravity of particles, and intrinsic thermal noise may give rise to a peak in the spectral amplification factor and therefore to the appearance of the ESR phenomenon. It is shown that ESR can occur in both a double-circular cavity and a triple-circular cavity, and by adjusting some parameters of the system, the response of the system can be optimized. The differences are that the spectral amplification factor in a triple-circular cavity is significantly larger than that in a double-circular cavity, and compared with the ESR in a double-circular cavity, the ESR effect in a triple-circular cavity occurs within a wider range of external force parameters. In addition, the strength of ESR also depends on the particle radius, and smaller particles can induce more obvious ESR, indicating that the size effect cannot be safely neglected. The ESR phenomenon usually occurs in small-scale systems where confinement and noise play an important role. Therefore, the mechanism that is found could be used to manipulate and control nanodevices and biomolecules.

Synchronization in a Three Level Network of All-to-All Periodically Forced Hodgkin–Huxley Reaction–Diffusion Equations

This article focuses on the analysis of dynamics emerging in a network of Hodgkin–Huxley reaction–diffusion equations. The network has three levels. The three neurons in level 1 receive a periodic input but do not receive inputs from other neurons. The three neurons in level 2 receive inputs from one specific neuron in level 1 and all neurons in level 3. The neurons in level 3 (all other neurons) receive inputs from all other neurons in levels 2 and 3. Furthermore, the right-hand side of pre-synaptic neurons is connected to the left-hand side of the post-synaptic neurons. The synchronization phenomenon is observed for neurons in level 3, even though the system is initiated with different functions. As far as we know, it is the first time that evidence of the synchronization phenomenon is provided for spatially extended Hodgkin–Huxley equations, which are periodically forced at three different sites and embedded in such a hierarchical network with space-dependent coupling interactions.

Ionospheric behaviors and characteristics in Asian sector during the April 2023 geomagnetic storm with multi-instruments observations

Geomagnetic storms frequently affect satellite navigation, communication and satellite orbits. Monitoring and understanding the ionospheric disturbances and responses to geomagnetic storms are crucial. The detailed ionospheric responses and physical mechanisms to various geomagnetic storms, however, have not yet been extensively studied. In this paper, the ionospheric variation behaviors and features following the April 2023 magnetic storm along the Asian sector are thoroughly studied using multi-instrument observation data, including the Global Navigation Satellite System (GNSS), ionosonde, and other satellites. Large-scale Traveling Ionospheric disturbances (LSTIDs) are observed from BeiDou Geostationary Earth Orbit (GEO) satellites, GPS and GLONASS. LSTIDs traveled with a speed of 760–1300 m/s from high latitude region to low latitude region with a period of about 40 min. The equatorial propagating LSTIDs were generated by coronal mass ejections (CMEs), which occurred in April 2023 with periodic energy input from the auroral area. The poleward LSTIDs are also observed with a velocity of approximately 600–750 m/s and the period is similar. Neutral wind also influenced the characteristics of the ionospheric response. The [O]/[N2] ratio declined during the storm, which led to the formation of the negative storm phases. The largest vertical total electron content (VTEC) is found, and the strengthened region of TEC is mainly centered between ± 20° within geographical latitude. Equatorial Ionospheric Anomaly (EIA) is also observed, which is probably influenced by the electric field. As the time goes on, the peak on the south side of the EIA is disappearing. Meanwhile, the height of the ionospheric maximum electron density rises, and the electron density falls.

Zooplankton Bio-indicators Against Changing Hydrological Parameters at Bidyadhari River of Indian Sundarbans

Sundarban Estuarine System is influenced by periodic tidal input and fresh water inflow. It is surrounded by world’s largest mangrove ecosystem and harbour naturally grown fishery. The total system is intersected by a network of many rivers and creeks. Bidyadhari is one of the major rivers of Sundarbans that is surrounded by human habitation on both banks. The dynamic condition of the river due to tidal inflow and fresh water input which is further increased many folds due to human interventions. In the present study, 26 zooplankton taxa have been recorded where 16 taxa were found perennial in all three seasons. 19 species showed its highest density in the monsoon season, 4 in post-monsoon and 3 in pre-monsoon season. Considering all seasons, Pseudodiaptomus serricaudatus was found to be the most abundant species in monsoon when there was a marked increase in temperature, nitrate, phosphate, silicate and a decrease in salinity, DO, TDS, EC and chlorophyll-a concentration. On the other hand, Acrocalanus longicornis was most abundant during the post-monsoon season when pH, EC, DO, chlorophyll-a were found to be highest and temperature was lowest of all seasons. Only 3 of the 26 taxa were found in highest concentration during pre-monsoon season when salinity was found in highest concentration. The Shannon-Weiner Diversity Index, Simpson 1_D Index and Margalef Richness Index of zooplankton diversity were found highest in station 3 (nearest to the sea) during all the three seasons. Pearson Correlation Analysis showed some significant correlation between different hydrological parameters and zooplankton diversity indices. The result of the study indicates the presence of organic pollutants and eutrophication in Bidyadhari river that demands regular monitoring of water quality for maintenance of long-term sustainability of one the largest naturally grown fisheries in the world.

Proper generalized decomposition-based iterative enrichment process combined with shooting method for steady-state forced response analysis of nonlinear dynamical systems

This paper presents a novel framework combining proper generalized decomposition (PGD) with the shooting method to determine the steady-state response of nonlinear dynamical systems upon a general periodic input. The proposed PGD approximates the response as a low-rank separated representation of the spatial and temporal dimensions. The Galerkin projection is employed to formulate the subproblem for each dimension, then the fixed-point iteration is applied. The subproblem for the spatial vector can be regarded as computing a set of reduced-order basis vectors, and the shooting problem projected onto the subspace spanned by these basis vectors is defined to obtain the temporal coefficients. From this procedure, the proposed framework replaces the complex nonlinear time integration of the full-order model with the series of solving simple iterative subproblems. The proposed framework is validated through two descriptive numerical examples considering the conventional linear normal mode method for comparison. The results show that the proposed shooting method based on PGD can accurately capture nonlinear characteristics within 10 modes, whereas linear modes cannot easily approximate these behaviors. In terms of computational efficiency, the proposed method enables CPU time savings of about one order of magnitude compared with the conventional shooting methods.

Modeling and Analysis of a Radiative Thermal Memristor

This study presents a theoretical framework for a radiative thermal memristor (RTM), utilizing Tungsten-doped vanadium dioxide (WVO) as the phase-change material (PCM) and silicon carbide (SiC) in the far-field regime. The behavior of the RTM is depicted through a Lissajous curve, illustrating the relationship between net flux (Q) and a periodically modulated temperature difference ΔT(t). It is established that temperature variations in the memristance (M) of the RTM form a closed loop, governed by PCM hysteresis. The analysis explores the impact of thermal conductivity contrast (r) and periodic thermal input amplitude (θ) on the Q–ΔT curve and the M–ΔT curve and negative differential thermal resistance (NDTR), revealing notable effects on the curve shapes and the emergence of NDTR. An increasing r leads to changes in the Lissajous curve’s shape and enhances the NDTR influence, while variations in both r and (θ) significantly affect the Q values and Lissajous curve amplitudes. In the M–ΔT curve, the height is linked to thermal conductivity contrast (r), with increasing r resulting in higher curve heights.

Linear time periodic system approximation based on Floquet and Fourier transformations for operational modal analysis and damage detection of wind turbine

Operational Modal Analysis (OMA) identifies modal properties of mechanical structures from vibration data collected from a few sensors under operation conditions. These methods are widely used to monitor civil engineering structures that are modeled as time-invariant systems. However, when dealing with wind turbines and rotating machines, many dedicated OMA techniques were developed to deal with the time-periodic behavior. Existing methods pre-process the data to adapt them to classical identification techniques. Yet, these methods present limitations as either requiring a high number of measured rotation periods, assuming the assumption of an isotropic rotor (i.e. undamaged), or the knowledge of the rotational speed. This work proposes to lift these difficulties by proving that the application of the classical system identification methods can produce meaningful estimates for anisotropy monitoring. This observation is based on directly approximating the time-periodic dynamic behavior of the wind turbine as a properly defined time-invariant system under periodic inputs. It results in the possibility of using classical identification methods without modification to retrieve the system matrices of the approximated time-invariant system. This approach does not require knowing the rotor speed, requiring relatively fewer measurements and it is not restricted to isotropic rotors. The identified modes can be used reliably for the monitoring of operating wind turbines and more especially for fault detection, at the expense of losing a part of the complete description of the periodic system. The resulting anisotropy monitoring approach and its capacities are illustrated in two cases. Firstly, on an academic model of a wind turbine and then on an aero-servo-elastic numerical model of a rotating 10 MW wind turbine to demonstrate the ability of the method to deal with realistic and representative data. It is shown for the latest case, from sensors located on the blades of the wind turbine, the approach is able to identify correctly the system properties (frequencies and mode shapes) and is also able to detect efficiently a fault on a blade.

Dynamics of a delayed discrete size-structured chemostat with periodic nutrient supply

In this work, we introduce and start the analysis of a periodic and nonlinear system of delay difference equations describing a chemostat with periodic inputs of limiting nutrient and size-structured biomass. The main novelties of this article are the following: (i) this is the first study of a discrete, structured, and periodic chemostat model taking into account the existence of a time delay between the absorption of nutrient by the biomass cells and its corresponding effects on the cell growth, (ii) we obtain a set of sufficient conditions ensuring the existence of periodic solutions, and (iii) we emphasize that the inclusion of a delay prevents us to follow the standard dimensional reduction and motivated us to carry out an original way to proof the existence of periodic solutions, which is based in a truncation method combined with the use of a theorem by F. Browder on the continuation of fixed points.

Iterative Learning for Laboratory Electro-Hydraulic Fully Flexible Valve Actuation System Transient Control

<div>Fully flexible valve actuation (FFVA) is a key enabling technology of internal engine combustion research and development. Two laboratory electro-hydraulic FFVA systems have been developed and implemented in R&D test cells. These FFVA systems were designed using repetitive control (RC), which is based on internal model principle (IMP), for constant engine speed operation. With the engine operating in a steady-state condition, the valve profile input is periodic. This can be accommodated by a repetitive controller, which provides the function of flexible control to step changes in valve lift, valve opening duration, and cam phase angle position.</div> <div>During engine speed transients, as the valve reference trajectory becomes aperiodic in the time domain, the controllers based on the linear time invariant (LTI) IMP, such as RC, are no longer applicable. Engine speed transient control is a desired function to engine research and other similar applications, such as motor control. Several investigations are reported with limited results because of the assumption of IMP and periodic input.</div> <div>This article presents the control design and verification of the iterative learning control (ILC) algorithm for the laboratory electro-hydraulic FFVA system. This algorithm tracks valve lift profiles under steady-state and transient operation. A dynamic model of the plant was obtained from experimental data to design and verify the effectiveness and robustness of this approach. The simple structure of the ILC in implementation and low cost in computation are crucial benefits to recommend the ILC. It is not an IMP-based approach, and its structure does not depend on the system input. Therefore, it has higher robustness to perturbation and modeling errors than other control methods for repetitive valve lift profile tracking tasks.</div>