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Abstract: Abstract The classical models of risk assessment and the forecasting tools of business revenue typically contain unknown parameters with a range of empirical values that are insufficient for making intuitive predictions. To improve the modeling and simulation approaches, it is necessary to deal with the associated data-sets, subject to several complex constraints, using smart programming tools. These constraints are responsible for the randomness, noise and perturbation, technically termed as the stochastic effects. Such stochastic processes, when incorporated with seasonality lead to the mean reverting L’evy-based Ornstein–Uhlenbeck approach. The Ornstein–Uhlenbeck modeling approach is used here for the assessment of the revenue. Regression learner models of machine learning are developed to explore impact of the change in temperature on pandemic thresholds and with this, the change in revenue. The current research strategy can prove to support the investors in their future investment planning and decisions and to forecast the risks and the fate of small and individual-based businesses. PubDate: 2023-11-29
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Abstract: Abstract Inspired by Ostrich anti-vibration and shock and vibration absorption properties, a novel bio-inspired vibration isolation–absorption (BIVIA) system is presented to design wideband vibration isolation bandwidth, low-frequency/ultra-low-frequency vibration isolation and high stability using toe-leg-spine coupling structure. Considering the kinematic relationship between skeletons and muscle/tendon, the geometrical relationships and dynamical equations of the BIVIA system are deduced for theoretical analysis and model verification. The influences of different parameters on loading capacity, dynamic stability, quasi-zero stiffness (QZS) zone, vibration isolation–absorption performance and vibration transmissibility are discussed. It discovers that high loading capacity and extended QZS zone are achieved by coupled vibration isolation–absorption structures. Moreover, the desirable and adjustable vibration isolation–absorption performance of the BIVIA structure can be obtained by designing key parameters. The BIVIA structure presents a practical method for bio-inspired vibration isolation and could be used in engineering and manufacturing. PubDate: 2023-11-28
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Abstract: Abstract Animals are capable of robust and reliable control in unstructured environments, where they effortlessly overcome the uncertainty of interaction and are capable of exploiting singularities. These conditions are a well-known challenge for robots due to the limitations of projected dynamics, which requires accurate modelling and is susceptible to singularities. This work proposes a compliant passive control method for redundant manipulators based on a superimposition of multiple passive task-space controllers in a hierarchy without requiring any knowledge of the robot dynamics. The proposed control framework of passive controllers is inherently stable, numerically well-conditioned (as no matrix inversions are required), and computationally inexpensive (as no optimisation is used). This method leverages and introduces a novel stiffness profile for a recently proposed passive controller with smooth transitions between the divergence and convergence phases making it particularly suitable when multiple passive controllers are combined through superimposition. The experimental results demonstrate that the proposed method achieves sub-centimetre tracking performance during demanding dynamic tasks with fast-changing references, while remaining safe to interact with and robust to singularities. The data further show that the robot can fully take advantage of the redundancy to maintain the primary task accuracy while compensating for unknown environmental interactions, which is not possible from current frameworks that require accurate contact information. PubDate: 2023-11-27
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Abstract: Abstract This work presents an event-triggered mechanism-based distributed fractional-order fault-tolerant control (FTC) paradigm for multiple unmanned aerial vehicles (multi-UAVs) subject to full-state constraints. Distinct from the existing control solutions for multi-UAVs with constant constraints and symmetric constraints, the time-varying asymmetric constraints considered in this paper are more suitable for practical requirements. Neural networks are exploited to cope with uncertainties arising from unknown nonlinear dynamics. By cleverly combining speed functions with nonlinear state-dependent functions, a novel distributed FTC protocol is established to drive the system states into the boundary functions within a predetermined finite time. Simultaneously, fractional-order calculus is introduced to provide additional adjustment of control parameters, and an event-triggered mechanism is derived to reduce the update frequency of the control signal. It is testified that all signals of each follower UAV are semi-globally uniformly ultimately bounded, and all follower UAVs can follow the attitudes of the leader UAV. In the end, case studies are reported to corroborate the outperformance of the proposed methodology. PubDate: 2023-11-27
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Abstract: Abstract Tire-road friction coefficient is of great significance for vehicle active safety systems, advanced driving assistance systems, and even future autonomous vehicles. Most of the dynamics-based methods for estimating the tire-road friction coefficient neglect the characteristic that the tire stiffness changes with the driving conditions, resulting in a limited number of driving conditions for which the friction coefficient can be effectively estimated. In order to improve the accuracy of the tire-road friction coefficient estimation results, an estimation method is proposed in which the tire stiffness can change adaptively according to the vertical load and the vehicle dynamics response. By analyzing the change in length of the tire-road contact patch, the relationship between vertical load and tire stiffness is established. By adding tire stiffness to the system state, the relationship between tire stiffness and vehicle dynamics response is established. A square-root cubature Kalman filter algorithm with rapid convergence by automatically adjusting the measurement noise covariance matrix is developed to enhance the real-time performance of the estimation method. Finally, the superiority of the method is verified under different test scenarios based on CarSim and MATLAB/Simulink co-simulation platform. The results also show that this method is able to make an accurate identification when tire damage happens. PubDate: 2023-11-27
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Abstract: Abstract We show how the maximum of recurrence-microstates entropy configures a new way to properly compute appropriate recurrence vicinity parameter and time sampling to perform recurrence analysis of continuous data. For experimental data, we show the same procedure may be used to find the optimum sampling or to perform down-sampling of the data, preserving recurrence meaning and adjusting the ideal sampling. The new method retrieves results obtained using traditional methods with the advantage of being independent of any free parameter, since all parameter dependencies are automatically set. Our results are also less sensitive to noise when experimental data are used. Due to the automatized way to capture suitable recurrence parameters, the method is adequate for using in autonomous numerical algorithms, allowing the recovery of relevant recurrence information embedded in time series (including over-sampled data), rationalizing the process of data acquisition and allowing only relevant data to be collected. PubDate: 2023-11-25
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Abstract: Abstract In this paper, we present a delayed half-center oscillator (DHCO) system consisting of two coupling inertial neurons. The multi-coexistence of routes to chaos including periodic-doubling and quasi-periodic bifurcations is analyzed to propose complex dynamical behaviors of the system. The coupling delay is regarded as a bifurcation parameter to produce multiple periodic activities and their dynamical evolution. The whole and unbroken bifurcation diagrams are obtained by employing the continuous extension approach, where the initial conditions of the next numerical integration are chosen as the last data of the previous step. Based on this approach, we illustrate in detail four bifurcation routes to chaos with increasing time delay for the same set of the system’s parameters. Four types of routes to chaos including period-doubling and quasi-periodic bifurcations are obtained for different initial conditions. The DHCO system presents multiple coexistence of bifurcation routes to chaos, which implies extremely complicated coexistence of the dynamical behaviors such as periodic orbits, multi-periodic orbits, quasi-periodic behaviors, and chaotic attractors. PubDate: 2023-11-24
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Abstract: Abstract Chaotic systems have played a vital role within the domain of chaos-based image encryption, owing to its significant advantages including sensitivity to initial values, ergodicity and others. Nonetheless, the current low-dimensional and less-scroll chaotic systems exhibit low complexity and randomness, leading to unsatisfactory security performance of the associated image encryption schemes. To settle the aforementioned issue, this paper introduces a novel hyperchaotic system with five scrolls and explores its application in visually meaningful image encryption (VMIE). Firstly, a new 5-scroll Rossler hyperchaotic system (5-SRHS) is designed building upon the principle of translation transformation (PTT), using the Rossler chaotic system (RCS) as a foundation. The performance of the 5-SRHS is extensively analyzed using various techniques, including but not limited to phase diagrams, Lyapunov exponents, and the NIST test. Subsequently, based on the 5-SRHS, a VMIE method is introduced. Specifically, to improve image reconstruction quality and reasonable allocation of sampling resources, a sub-region adaptive block compressive sensing (SR-ABCS) driven by image texture features is presented and applied to pre-encrypt the plain image, resulting in the generation of the encrypted image. Next, the obtained encrypted image is dynamically embedded into the host image utilizing improved grayscale difference statistics (IGDS) and 2K correction, enhancing imperceptibility of the steganographic image. Moreover, SHA-256 is integrated with the 5-SRHS to generate plaintext-related random sequences, further achieving higher security. Simulation experiments validate that the proposed scheme surpasses existing state-of-the-art (SOTA) schemes regarding steganography and reconstruction quality. Moreover, it is proven not only for secure transmission of natural images but also for medical images. PubDate: 2023-11-24
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Abstract: Abstract This paper presents a novel resonant parametric feedback controller (RPFC) for suppressing nonlinear resonances and chaos in a cantilever beam using acceleration feedback. The excitation of the system may be due to 1:1 direct excitation, 1:3 subharmonic direct excitation, 3:1 superharmonic direct excitation, 1:2 parametric excitation, 1:4 subharmonic parametric excitation, self excitations, and combinations of two or more of these. The controller is designed in two stages. First, the measured acceleration signal of the beam is fedback to a second-order filter. Subsequently, the states of the second-order filter are used to formulate the nonlinear control function that is applied to the structure as a parametric input such that the controlled parametric variation produces dissipative force at the resonance. The analysis of the system is carried out using the method of multiple time-scales. A number of special cases demonstrating the efficacy of the controller in suppressing various nonlinear resonances and their combinations are studied. Finally, a novel frequency adaptation law is proposed to deal with the uncertainty in the system's natural frequency. The results are verified by numerical simulations and some experiments. Though the analysis is carried out for an SDOF system, the proposed control scheme can easily be extended to any MDOF system, and it can target any mode by tuning the filter frequency. PubDate: 2023-11-24
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Abstract: Abstract The whirl flutter in rotor-driven aircraft is a significant aeroelastic instability resulting from the intricate interplay between structural, gyroscopic, and aerodynamic effects, exacerbated by nonlinearities. This phenomenon manifests as oscillatory behaviors within the aircraft's structure, carrying the risk of severe consequences and potential hazards. In this research endeavor, a nonlinear reduced-order model incorporating quasi-steady aerodynamics is employed to comprehensively analyze the behavior of a nacelle-rotor system and gain valuable insights into the dynamics of whirl flutter and its combined effect with external moments due to base excitations. Specifically, the study investigates the impact of external moment disturbances in conjunction with the aerodynamic excitations on the dynamical responses of a rotor-nacelle system, using parameters of a simplified model from previous studies as a basis for analysis. This investigation utilizes a solution methodology that includes linear and nonlinear approaches in order to explore the influences of rotor angular velocity, blade length, the number of blades, and their interplay with external moments applied to pitch and yaw degrees of freedom. The findings demonstrate the importance of considering these factors concerning the concurrent oscillations due to whirl flutter and other external moments with regard to the potential for resonance, quenching, and nonlinear responses in the system’s dynamics. PubDate: 2023-11-23
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Abstract: Abstract During the early outbreak of the COVID-19 pandemic, the mobility patterns of individuals in many regions in China exhibit notable changes: initially, there was a significant reduction in mobility, followed by a gradual recovery. Based on this observation, here we study epidemic models on a particular type of time-varying network where the links undergo a freeze-recovery process. We first focus on an isolated network and find that the recovery mechanism could lead to the resurgence of an epidemic, while the influence of link freezing on epidemic dynamics is intricate. In particular, we show that the final epidemic size is a non-monotonous function of the freezing rate. This result challenges our conventional idea that stricter prevention measures (corresponding to a larger freezing rate) could always have a better inhibitory effect on epidemic spreading. We further investigate an open system where a fraction of nodes in the network may contract the disease from the “environment” (the outside infected sources). In this case, a second wave can emerge even if the number of infected nodes has declined to zero, which cannot be explained by the isolated network model. PubDate: 2023-11-23
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Abstract: Abstract In his book Hamel pointed out through an example that the embedding of a nonholonomic constraint directly in the Lagrangian of an unconstrained mechanical system causes one to obtain incorrect equations of motion for the constrained system upon the application of Lagrange’s formalism. Wanichanon and Udwadia provided the reason for this and illustrated their result through a series of examples. They also gave the reason why such an embedding for holonomic constraints in the Lagrangian gives the correct equations of motion, a view conjectured by Rosenberg in his book. A recent paper by Ye-Hwa Chen again raised the issue of Hamel’s Paradox and claimed that embedding holonomic constraints in the Lagrangian of an unconstrained mechanical system can yield, in general, incorrect equations of motion. The purpose of this paper is to provide a resolution to the problem of whether the embedding of holonomic constraints in the Lagrangian yields the correct equations of motion of a constrained mechanical system. It is shown that the complete embedding of honolomic constraints in the Lagrangian when used properly with the Lagrange formalism will yield the correct equations of motion of a mechanical system. PubDate: 2023-11-23
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Abstract: Abstract In this work, the general solutions of the nonlocal long-wave-short-wave resonance interaction (LSRI) equation with nonzero boundary conditions are investigated by using the Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction method. We discussed the cases where N is odd and even, which have a significant impact on the background wave. When N is odd, the solutions are located in the periodic background, while it is on the constant background when N is even. Different forms of solutions are discussed in detail, including the general soliton, line breather and (semi-)rational solutions. For these solutions of the nonlocal LSRI equation, we have obtained a variety of rich and interesting images are obtained through theoretical and graphical analysis, and most of them cannot correspond to the local equation. PubDate: 2023-11-22
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Abstract: Abstract A novel distributed prescribed-time leader–follower tracking consensus control strategy is proposed for high-order nonlinear multi-agent systems with lower triangular time-varying dynamics in directed communication topology. Firstly, a distributed prescribed-time state observer (DPTSO) is presented for each follower to estimate the states of the leader. Based on the DPTSO, the consensus problem is transformed into a tracking control problem; that is, the follower tracks the estimations of the DPTSO. Then, a distributed prescribed-time controller is developed by using the cascade control framework and dynamic control, which avoids the problem of differential explosion in traditional back-stepping control. The convergence time of the DPTSO and distributed prescribed-time controller is not only explicitly pre-specified but also determined regardless of the initial states of the system and control parameters. Finally, it is demonstrated that the closed-loop systems realize prescribed-time full-state leader–follower tracking consensus. Simulation results show that the method is effective and feasible. PubDate: 2023-11-22
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Abstract: Abstract Multiple-direction vibration widely exists in the environment, which is harmful to instruments and people. Hence, the high demand for vibration isolators with exceptional efficiency is thus evident. Although the proposed nonlinear energy sink was proven to be highly utility, most of the developed such devices, even with some inerter enhanced NESs, are limited to one-dimensional vibration suppression. In this paper, we propose a two-dimensional inerter-enhanced NES (2D IE-NES) which is applicable for multiple-directional low-frequency vibration suppression. The Lagrangian method is employed to derive the dynamic equations of the 2D IE-NES. Then these differential equations are solved by means of the Runge–Kutta method. Numerical results show that the novel 2D IE-NES configuration can isolate vibration more efficiently than the traditional NES under instantaneous shock, constant periodic and stochastic excitation. The role of the inerters in the vibration decaying process is highlighted in energy flow. This paper provides a new platform for the low-frequency multiple-direction vibration isolator. PubDate: 2023-11-22
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Abstract: Abstract By imposing a nonlocal reverse-space symmetry constraint on a general coupled nonlinear Schrödinger (NLS) equation, we propose a new general nonlocal reverse-space NLS equation with two free real parameters involving the effects of the self-phase modulation, the cross-phase modulation and the four-wave mixing. The proposed nonlocal equation is physically meaningful in two aspects. One is that, by solving the proposed nonlocal equation, one can obtain corresponding solutions of the general coupled NLS equation with special initial conditions. The other is that the proposed nonlocal equation is an integrable generalization of a physically significant nonlocal reverse-space NLS equation in the literature. For the proposed nonlocal equation, we develop a novel Riemann–Hilbert (RH) method where the spectral analysis is performed from the temporal part of the Lax pair rather than the spatial part as in the traditional RH approach. Firstly, the complicated spectral symmetry structure of the proposed nonlocal equation is explored in detail. Secondly, by solving the RH problem with the complicated spectral symmetry structure, soliton solutions are rigorously obtained for the nonlocal equation. Thirdly, some new soliton dynamical behaviors underlying the soliton solutions are theoretically investigated and graphically simulated. PubDate: 2023-11-22
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Abstract: Abstract A passive dynamic walker is a mechanical system that walks down a slope without any control, and gives useful insights into the dynamic mechanism of stable walking. This system shows specific attractor characteristics depending on the slope angle due to nonlinear dynamics, such as period-doubling to chaos and its disappearance by a boundary crisis. However, it remains unclear what happens to the basin of attraction. In our previous studies, we showed that a fractal basin of attraction is generated using a simple model over a critical slope angle by iteratively applying the inverse image of the Poincaré map, which has stretching and bending effects. In the present study, we show that the size and fractality of the basin of attraction sharply change many times by changing the slope angle. Furthermore, we improved our previous analysis to clarify the mechanisms for these changes and the disappearance of the basin of attraction based on the stretching and bending deformation in the basin formation process. These findings will improve our understanding of the governing dynamics to generate the basin of attraction in walking. PubDate: 2023-11-22
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Abstract: Abstract This paper proposes a decentralized dynamic event-triggered control method of aero-engine T-S fuzzy system, aiming to achieve both exponential stabilization of aero-engine networked control systems (NCSs) and reduction in network communication loads. Firstly, a novel decentralized dynamic event-triggered mechanism (DETM) is developed to regulate data transmissions in each communication channel independently. The closed-loop model is then established, by considering network-induced delays, dynamic quantization effects, external disturbance, and parameter perturbation. Stability criteria are derived using the Lyapunov–Krasovskii method, and a collaborative design method based on linear matrix inequalities (LMIs) is proposed for controller, quantizers, and DETM. Lastly, a parameter tuning method based on the iL-SHADE algorithm is proposed for better feasibility of the obtained LMIs. Simulation results show that the proposed method has good robustness to multi-uncertainty conditions and can effectively reduce communication resource wastage while ensuring well control performance across a wide range of flight envelopes. PubDate: 2023-11-21
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Abstract: Abstract We study the vibration characteristics of an ideal string in the presence of a curved boundary obstacle which is a common constructional feature of sitar, veena and tanpura. It has been well-established that these plucked string instruments have attractive tonal qualities like better harmonicity, presence of amplitude as well as frequency modulations, and appearance of a large number of overtones. The smooth wrapping and unwrapping of the string over the curved obstacle introduces quadratic nonlinearities whose effect on the vibration characteristics is elucidated through a perturbative analysis using the method of multiple scales. Modal interactions facilitated by the obstacle results in neutrally stable mode-locked periodic solutions in our model thereby accounting for the complex frequency and amplitude modulations. In particular, we find a mode-locked state which tends to an equipartition of energy with an increase in the number of modes. Our numerical simulations suggest that a plucked disturbance favors this state and hence, several overtones can be clearly identified in the sound of these plucked instruments. A good qualitative agreement between the results from our idealized model and the sound of these instruments highlights the role of the finite curved bridge in deciding the tonal quality of sitar, veena and tanpura. PubDate: 2023-11-21
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Abstract: Abstract In this paper, we propose a convergence analysis of evolutionary dynamics with limited learning ability within a double-layer network, exceeding the constraints of current approaches. To model the diversity in the agents’ ability to perceive their surroundings, we first design the dynamics model for continuous action iterated dilemma with limited learning ability. The agents are initialized with a fixed parameter that represents their maximum probability of strategy switching during the evolution process. Secondly, we extend the dynamics model to double-layer networks, in which the agents interact exclusively with neighbors in the same layer and update their strategies based on a weighted sum of their payoff in the two layers. Then, we evaluate the environmental influences on learning capacity using a dynamics formula and adapt to the unknown environment dynamics with radial basis function neural network (RBF-NN). Lastly, we conduct a convergence analysis of the dynamics models and confirm their effectiveness with experiments. This method may be utilized to analyze evolutionary processes in hierarchically structured networks. PubDate: 2023-11-21
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