Steady-state Moments Research Articles

The effect of the four-tentacled collaboration on the self-propelled performance of squid robot

This study conducts a numerical investigation of the self-propelled performance of a bio-inspired squid robot equipped with four rigid tentacles, exploring three sets of collaborative modes. Leveraging the open-source platform OpenFOAM, we develop a self-propulsion module incorporating the dynamic overset grid technique to manipulate the complex motion of rigid tentacles. The driving system of a single tentacle is simplified into a two-link mechanism, where the phase difference between the links effectively emulates the oscillatory pattern of fish-like locomotion. The interaction of four tentacles gives rise to three distinct driving modes: reverse, homologous, and interlace modes. The results indicate that the homologous mode follows the hydrodynamic characteristics of fish-like waves, the interlace mode can cause the robot to deviate from the initial path, and the reverse mode outperforms the other two modes, exhibiting a higher ultimate cruising speed. Regardless of the propulsion process, the cruising performance of the robot is significantly influenced by the maximum amplitude angle θmax. An increase in θmax also contributes to an elevation in the instantaneous longitudinal force coefficient CFx, with the most pronounced impact observed in the homologous mode. The disparity among the three modes is also evident in the periodic pressure variation and flow field evolution patterns. The vortex distribution during steady-state moments systematically reveals the collaborative effects among the tentacles in different modes on the self-propulsion performance.

Optimization of DLTS Hinges for the Assembly of the Solar Arrays of a Communication CubeSat

This paper demonstrates the analytical and numerical investigations for the obtainment of the predefined critical parameters of double-layer tape spring (DLTS) hinges. The DLTS hinge is utilized for the coupling between the solar panels to assist the accommodation and formulation of the assumed origami-based pattern of the solar arrays. They are examined for the assurance of safety, durability, non-permanent deformation, and stability from the stowed to the deployment configuration. Von Misses stress (σv) and steady-state moment simulations are investigated by varying the critical hinge design parameters of curvature radius (R), subtended angle (θ) and layer thickness (t). Two optimization models, Taguchi and response surface methodology/RSM, are utilized by employing the computational findings to obtain and validate the modified optimal geometric parameters within this analytical experiment. For the Taguchi method, the optimization of σv and the steady-state moment is accomplished with a t of 1.75–2.25 mm, R of 1.5–2.0 mm, and θ of 1–1.2°. Furthermore, the RSM model shows that the t, R, and θ parameters are determined to be 2.90 mm, 2 mm, and 1.35°, respectively. For optimization of the hinge design, both models should be considered for improved verification and accuracy of the results.

Steady-state moments under resetting to a distribution

Steady-state moments under resetting to a distribution

Analysis of the Mechanical Properties and Study of Influential Factors of Different Materials in Tape Spring

This paper analyzes and calculates the mechanical properties of composite tape spring structures during folding and bending and establishes a non-linear control equation for the folding and bending of composite laminate tape spring structures. Accurate expressions for folding and bending displacements are obtained. The influence of the cross-section’s central angle and the composite tape spring’s ply thickness on their mechanical properties are analyzed. Finite element numerical analysis is performed on [−45 45]s laminated composite tape springs, and the correctness of the theoretical derivation is proved by comparing the curvature radius-bending moment curve. Based on previous research, the mechanical properties of different tape spring materials and structures are compared, further studying the lightweight design of space deployment mechanisms. The results show that the steady-state bending moment performance of composite tape springs is excellent, with a 162.1% improvement in steady-state bending moment performance per unit mass compared to traditional metallic tape springs. Additionally, the critical bending moment performance of negative Poisson ratio honeycomb structure tape springs is also excellent, with a 62.3% improvement in steady-state bending moment performance per unit mass compared to traditional metallic tape springs.

Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise

Because of the increasing demand for electrical energy, vibration energy harvesters (VEHs) that convert vibratory energy into electrical energy are a promising technology. In order to improve the efficiency of harvesting energy from environmental vibration, here we investigate a hybrid VEH. Unlike previous studies, this article analyzes the stochastic responses of the hybrid piezoelectric and electromagnetic energy harvesting system with viscoelastic material under narrow-band (colored) noise. Firstly, a mass-spring-damping system model coupled with piezoelectric and electromagnetic circuits under fundamental acceleration excitation is established, and analytical solutions to the dimensionless equations are derived. Then, the formula of the amplitude-frequency responses in the deterministic case and the first-order and second-order steady-state moments of the amplitude in the stochastic case are obtained by using the multi-scales method. The amplitude-frequency analytical solutions are in good agreement with the numerical solutions obtained by the Monte Carlo method. Furthermore, the stochastic bifurcation diagram is plotted for the first-order steady-state moment of the amplitude with respect to the detuning frequency and viscoelastic parameter. Eventually, the influence of system parameters on mean-square electric voltage, mean-square electric current and mean output power is discussed. Results show that the electromechanical coupling coefficients, random excitation and viscoelastic parameter have a positive effect on the output power of the system.

Memory feedback signals in nonlinear coupled pitch-roll ship motions under narrow-band stochastic excitations

Initiating from the complexity of ship sailing environment and the nonlinear coupling hysteresis effect of its motion, we focus on the memory feedback shake-reducing strategy turning from the delay generally considered to exhibit undesired effects, and introduce it into the nonlinear coupled pitch-roll ship motions under loads incorporating stochastic disturbances to control the ship shaking and optimize the frequency band distribution of the stable navigation associated with the saturation. This paper then reports the deterministic equilibrium solutions of the roll and pitch response via the perturbation analysis of the third-order scale and successively explains the stability closely related to the saturation and bifurcations. Instead of just formula deduction, visually depict the distinction of equilibrium points and the determination conditions, and the effective shake-reducing frequency band coupled with the drift modulated by the memory feedback signals, and then integrate the moment method and stochastic Itô law to compute the steady-state moment and the mean square scale checked by numerical simulations. Set basic samples of the equation parameters for dual scenarios, and then track time histories of ship rolling and pitching as well as the marginal and joint probability evolutions to illustrate the resonance behavior and modes transition with the energy penetration in complementary ways. The results of our investigation present a new insight into the stability schemes of ship sailing issues.

Matrix calculations for moments of Markov processes

AbstractMatryoshka dolls, the traditional Russian nesting figurines, are known worldwide for each doll’s encapsulation of a sequence of smaller dolls. In this paper, we exploit the structure of a new sequence of nested matrices we callmatryoshkan matricesin order to compute the moments of the one-dimensional polynomial processes, a large class of Markov processes. We characterize the salient properties of matryoshkan matrices that allow us to compute these moments in closed form at a specific time without computing the entire path of the process. This simplifies the computation of the polynomial process moments significantly. Through our method, we derive explicit expressions for both transient and steady-state moments of this class of Markov processes. We demonstrate the applicability of this method through explicit examples such as shot noise processes, growth–collapse processes, ephemerally self-exciting processes, and affine stochastic differential equations from the finance literature. We also show that we can derive explicit expressions for the self-exciting Hawkes process, for which finding closed-form moment expressions has been an open problem since their introduction in 1971. In general, our techniques can be used for any Markov process for which the infinitesimal generator of an arbitrary polynomial is itself a polynomial of equal or lower order.

Frequency response in splicing regulation under mRNA auto-depletion control.

Nowadays, there exists a huge literature about stochastic model of transcriptional and translational control in gene networks. However, results related to post-transcriptional regulation via splicing and its connection with transcriptional and translational regulation are almost missing in the current literature and only related to the steady state moments investigation. Nowadays, it is becoming of paramount importance the need for modeling post-transcriptional regulation via splicing especially for DNA viruses or retroviruses. However, there exists only few studies in the literature about splicing regulation and none of them investigate its behavior in the frequency domain that can unveil important features of dynamical stochastic systems that cannot be revealed by the sole steady state moment investigation. The aim of this work is to theoretically investigate a simple gene network subject to splicing regulation with negative feedback control, implemented through mRNA auto-depletion under a frequency domain perspective. This study showed the pivotal role of the burst size, enhancing the noise power spectrum, as well as the splicing conversion rates capable to increase and decrease the noise power spectrum in the pre-mRNA and mRNA, respectively, for high values of conversion rates. Importantly, it shows the capability of the mRNA autodepletion control to modulate the noise as a frequency-dependent amplifying control as a function of the negative feedback strengths.

The Unsteady-State Response of Tires to Slip Angle and Vertical Load Variations

The tire is the only part that connects the vehicle and the road surface. Many important properties of vehicles are related to the mechanical properties of tires, such as handling stability, braking safety, vertical vibration characteristics, and so on. Although a great deal of research on tire dynamics has been completed, mainly focusing on steady-state tire force and moment characteristics, as well as linear unsteady force characteristics, less research has been conducted on nonlinear unsteady characteristics, especially when the vertical load changes dynamically. Therefore, the main purpose of this paper is to improve the tire unsteady-state model and verify it by experiment. To achieve this goal, we first study the nonlinear unsteady tire cornering theoretical model and obtain clear force and torque frequency response functions. Then, based on the results of the theoretical model, a high-precision and high-efficiency semi-physical model is developed. Finally, model identification and accuracy verification are carried out based on the bench test data. The model developed in this paper has high accuracy, and it significantly improves the expression of the aligning torque, which helps to improve the virtual simulation of transient conditions, such as vehicle handling and dynamic load conditions.

A physics-based digital twin for model predictive control of autonomous unmanned aerial vehicle landing

This paper proposes a two-level, data-driven, digital twin concept for the autonomous landing of aircraft, under some assumptions. It features a digital twin instance (DTI) for model predictive control (MPC); and an innovative, real-time, digital twin prototype for fluid-structure interaction and flight dynamics to inform it. The latter digital twin is based on the linearization about a pre-designed glideslope trajectory of a high-fidelity, viscous, nonlinear computational model for flight dynamics; and its projection onto a low-dimensional approximation subspace to achieve real-time performance, while maintaining accuracy. Its main purpose is to predict in realtime, during flight, the state of an aircraft and the aerodynamic forces and moments acting on it. Unlike static lookup tables or regression-based surrogate models based on steady-state wind tunnel data, the aforementioned real-time digital twin prototype allows the DTI for MPC to be informed by a truly dynamic flight model, rather than a less accurate set of steady-state aerodynamic force and moment data points. The paper describes in detail the construction of the proposed two-level digital twin concept and its verification by numerical simulation. It also reports on its preliminary flight validation in autonomous mode for an off-the-shelf unmanned aerial vehicle instrumented at Stanford University. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

Torque vectoring control system for distributed drive electric bus under complicated driving conditions

PurposeThe purpose of this study is to propose a torque vectoring control system for improving the handling stability of distributed drive electric buses under complicated driving conditions. Energy crisis and environment pollution are two key pressing issues faced by mankind. Pure electric buses are recognized as the effective method to solve the problems. Distributed drive electric buses (DDEBs) as an emerging mode of pure electric buses are attracting intense research interests around the world. Compared with the central driven electric buses, DDEB is able to control the driving and braking torque of each wheel individually and accurately to significantly enhance the handling stability. Therefore, the torque vectoring control (TVC) system is proposed to allocate the driving torque among four wheels reasonably to improve the handling stability of DDEBs.Design/methodology/approachThe proposed TVC system is designed based on hierarchical control. The upper layer is direct yaw moment controller based on feedforward and feedback control. The feedforward control algorithm is designed to calculate the desired steady-state yaw moment based on the steering wheel angle and the longitudinal velocity. The feedback control is anti-windup sliding mode control algorithm, which takes the errors between actual and reference yaw rate as the control variables. The lower layer is torque allocation controller, including economical torque allocation control algorithm and optimal torque allocation control algorithm.FindingsThe steady static circular test has been carried out to demonstrate the effectiveness and control effort of the proposed TVC system. Compared with the field experiment results of tested bus with TVC system and without TVC system, the slip angle of tested bus with TVC system is much less than without TVC. And the actual yaw rate of tested bus with TVC system is able to track the reference yaw rate completely. The experiment results demonstrate that the TVC system has a remarkable performance in the real practice and improve the handling stability effectively.Originality/valueIn view of the large load transfer, the strong coupling characteristics of tire , the suspension and the steering system during coach corning, the vehicle reference steering characteristics is defined considering vehicle nonlinear characteristics and the feedforward term of torque vectoring control at different steering angles and speeds is designed. Meanwhile, in order to improve the robustness of controller, an anti-integral saturation sliding mode variable structure control algorithm is proposed as the feedback term of torque vectoring control.

On the analysis of the tristable vibration isolation system with delayed feedback control under parametric excitation

In this paper, the delayed feedback control of a tristable vibration isolation system (TVIS) under the stochastic parametric excitation is investigated. Firstly, theoretical solutions of the frequency response equation that governs the dynamical performance of the TVIS are derived. Meanwhile, the stability conditions are obtained. The controlled performance and response properties induced by the time delay, the feedback gains and the excitation amplitude are discussed. The existence of the time delay can considerably suppress the vibration amplitude. Particular phenomena induced by the time delay are observed. In addition, the first-order and second-order steady-state moments of the TVIS are obtained based on the Itô stochastic differential equations under the stochastic parametric excitation. The phenomenon of the time delay island about steady-state moments is found. The stationary probability density is discussed for the parametric resonance by means of the finite difference method. The variation of the noise bandwidth and the time delay can induce the transition of the stationary probability density between trivial solutions and non-trivial solutions. Overall, the response mechanism of the TVIS under the stochastic parametric excitation is revealed.

Multi-layer controller with state-constraint: Vehicle lateral stability control based on fuzzy logic

This paper deals with a new state-constrained control (SCC) system of vehicle, which includes a multi-layer controller, in order to ensure the vehicle’s lateral stability and steering performance under complex environment. In this system, a new constraint control strategy with input and state constraints is applied to calculate the steady-state yaw moment. It ensures the vehicle lateral stability by tracking the desired yaw rate value and limiting the allowable range of the side slip. Through the linkage of the three-layer controller, the tire load is optimized and achieve minimal vehicle velocity reduction. The seven-degree-of-freedom (7-DOF) simulation model was established and simulated in MATLAB to evaluate the effect of the proposed controller. Through the analysis of the simulation results, compared with the traditional ESC and integrated control, it not only solves the problem of obvious velocity reduction, but also solves the problem of high cost and high hardware requirements in integrated control. The simulation results show that designed control system has better performance of path tracking and driving state, which is closer to the desired value. Through hardware-in-the-loop (HIL) practical experiments in two typical driving conditions, the effectiveness of the above proposed control system is further verified, which can improve the lateral stability and maneuverability of the vehicle.

Stability and moment bounds under utility-maximising service allocations: Finite and infinite networks

AbstractWe study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For finite networks we establish stability and some steady-state moment bounds under natural conditions and rather weak assumptions on utility functions. These results are obtained using direct applications of Lyapunov–Foster-type criteria, and apply to a wide class of systems, including those for which fluid-limit-based approaches are not applicable. We then establish stability and some steady-state moment bounds for two classes of infinite networks, with single-hop and multi-hop message routes. These results are proved by considering the infinite systems as limits of their truncated finite versions. The uniform moment bounds for the finite networks play a key role in these limit transitions.

Maximal Lyapunov Exponents and Steady-State Moments of a VI System based Upon TDFC and VED

This paper focuses on the investigation of a vibro-impact (VI) system based upon time-delayed feedback control (TDFC) and visco-elastic damping (VED) under bounded random excitations. A pretreatment for the TDFC and VED is necessary. A further simplification for the system is achieved by introducing the mirror image transformation. The averaging approach is adopted to analyze the above system relying on a parametric principal resonance consideration. By means of the first kind of a modified Bessel function, explicit asymptotic formulas for the maximal Lyapunov exponent (MLE) are given to examine the almost sure stability or instability of the trivial steady-state amplitude solution. Besides, the steady-state moments (SSM) of the nontrivial solutions of the system’s amplitude are derived by the application of the moment method and Itô’s calculus. Finally, the stability and its critical situations of the trivial solution are explored in detail through the important system parameters, i.e. embodying the TDFC parameters, the VED parameters, the restitution coefficient, the excitation amplitude and the random noise intensity. They are tested by numerical simulations. Additionally, the exploration of the steady-state moments involves the emergence of the general frequency response curve and the frequency island, discussions of conditions satisfied by the unstable boundary, and variations of the time-delayed island. Stochastic jumps and bifurcations are observed for the stationary joint transition probability density of the system’s trivial and nontrivial solutions based on parameter schemes of VED and TDFC.

Parameters optimization design of tape spring considering fatigue performance

As a crucial part of micro-satellite, the spatial deployable mechanism has the direct effects on satellite performance and success or failure of flight mission. With requirements of lightless and low cost for satellite, the tape spring hinges are widely used for their simple structural form, high reliability of deployment, high-driving performance and accurate positioning in deployable mechanism. Strain energy stored in the folding process of tape spring hinge is transformed into kinetic energy to achieve the deployment of solar panels. When in full deployment, the tape spring hinge can realize self-locking based on its critical moment. Tape spring is the crucial component of a novel space deployable structure that applied to solar panels. Its full deployment determines the normal function of satellite in space. Mechanical properties, steady-state moment and fatigue life, are observed in folding and deploying processes, which are affected by geometric parameters. Influences of thickness, subtended angle, radius and length on the fatigue life of tape spring are carried out to through numerical simulations so as to ensure a multi folding and deploying cycles for tape spring hinge. Results show that thickness has the greatest influence on the fatigue life, subtended angle and radius are second, and the influence of length on fatigue life is relatively small. On the basis, the optimal model is established based on response surface methodology with the thickness and radius as design variables, steady moment as constraint, and fatigue life as optimization objective. By using genetic algorithm to solve the model, optimal design is obtained within the constraint, and then the optimal design is remodeled and simulated, and the obtained results indicate the accuracy of the optimal design. This research could be a reference for the stability design of space deployable structures.

New perspectives on the Erlang-A queue

AbstractThe nonstationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large-scale multiserver service systems that may experience customer abandonments, such as call centers, hospitals, and urban mobility systems. In this paper we develop novel approximations to all of its transient and steady state moments, the moment generating function, and the cumulant generating function. We also provide precise bounds for the difference of our approximations and the true model. More importantly, we show that our approximations have explicit stochastic representations as shifted Poisson random variables. Moreover, we are also able to show that our approximations and bounds also hold for nonstationary Erlang-B and Erlang-C queueing models under certain stability conditions.

Open-Circuit Ultrafast Generation of Nanoscopic Toroidal Moments: The Swift Phase Generator

Efficient and flexible schemes for a swift, field-free control of the phase in quantum devices have far-reaching impact on energy-saving operation of quantum computing, data storage, and sensoring nanodevices. We report a novel approach for an ultrafast generation of a field-free vector potential that is tunable in duration, sign, and magnitude, allowing to impart non-invasive, spatio-temporally controlled changes to the quantum nature of nanosystems. The method relies on triggering a steady-state toroidal moment in a donut-shaped nanostructure that serves as a vector-potential generator and quantum phase modulator. Irradiated by moderately intense, few cycle THz pulses with appropriately shaped polarization states, the nano donut is brought to a steady-state where a nearby object does not experience electric nor magnetic fields but feels the photo-generated vector potential. Designing the time structure of the driving THz pulses allows for launching picosecond trains of vector potentials which is the key for a contact-free optimal control of quantum coherent states. During the toroidal moment rise up time radiation is emitted which can be tuned in a very broad frequency band. We carry out full-fledged quantum dynamic simulations, and theoretical analysis to illuminate the underlying principles and to endorse the feasibility, robustness, and versatility of the scheme. This research could trigger a new class of ultrafast quantum devices operated and switched in an energy-efficient, contact and field-free manner, enabling new techniques for use in quantum information, magnetic nanostructures and superconducting tunnel junctions as well as in toroidally ordered systems and multiferroics.

Resonance responses in a two-degree-of-freedom viscoelastic oscillator under randomly disordered periodic excitations

An investigation is presented for primary resonance and internal resonance of two-degree-of-freedom (TDOF) viscoelastic system with some complex nonlinear coupled terms under randomly disordered periodic excitations. The assumed viscoelastic damping depending on the past history of motion is chosen as the form of convolution integrals over an exponentially decaying kernel function. Then, the steady-state responses of the TDOF system are discussed in detail through the method of multiple scales (MMS), which is employed to derive the determined and stochastic differential equations of amplitude and phase modulation for the internal and external resonance modes. Further, the numerical simulation method is absorbed to test the effectiveness and accuracy of the theoretical analysis solutions for steady-state moments with the changing excitation amplitude. The appearance of (random) jump, (random) saturation, and double-jumping can be explored by the development of steady-state moments with different excitation amplitudes and frequency, which also show the resonance bandwidth increases with the excitation amplitude. Besides, viscoelastic damping parameters have great influence on the steady-state responses under the different detuning conditions, which accelerate or delay the appearance of the above mentioned phenomena. Numerical simulation results of phase portraits tell that the increase of the intensity of the random excitation leads to the steady-state solutions changing from a limit cycle to a diffused limit cycle, thus, such multi-valued steady-state responses produce jump from one stable branch to another also response to the previous analysis conclusion.

Stochastic coagulation-fragmentation processes with a finite number of particles and applications

Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention especially in stochastic analysis and statistical physics of cellular biology, as novel experimental data are now available, but their interpretation remains challenging. We derive here probability distribution functions for clusters that can either aggregate upon binding to form clusters of arbitrary sizes or a single cluster can dissociate into two sub-clusters. Using combinatorics properties and Markov chain representation, we compute steady-state distributions and moments for the number of particles per cluster in the case where the coagulation and fragmentation rates follow a detailed balance condition. We obtain explicit and asymptotic formulas for the cluster size and the number of clusters in terms of hypergeometric functions. To further characterize clustering, we introduce and discuss two mean times: one is the mean time two particles spend together before they separate and the other is the mean time they spend separated before they meet again for the first time. Finally, we discuss applications of the present stochastic coagulation-fragmentation framework in cell biology.