Finite Number Of Cycles Research Articles

Neural network state observer-based robust adaptive fault-tolerant quantized iterative learning control for the rigid-flexible coupled robotic systems with unknown time delays

In this work, the neural network state observer-based robust adaptive quantized iterative learning output feedback control (RAQILOFC) is investigated for rigid-flexible coupled robotic systems (RFCRSs) with unknown time delays and actuator faults. To deal with hysteresis quantization and actuator defects, a novel fault-tolerant RAQILOFC is designed first, based only on accessible system output data. Then, using the fault-tolerant RAQILOFC laws in combination with the neural network state observer, the two given angular positions are tracked while concurrently suppressing the flexible vibration. Simultaneously, uncertainties associated with system dynamics and unknown time delays are taken into account while designing controllers for RFCRSs. It is demonstrated that the fault-tolerant RAQILOFC technique would converge to and remain inside a predefined small compact set after a finite number of cycles. Additionally, it is shown that the system signal sequences are bounded in presence of unknown time delays and hysteresis quantization. Finally, a numerical example is conducted to illustrate the proposed neural network state observer-based fault-tolerant RAQILOFC strategy’s efficacy.

Non-stationary oscillations of an instantly loaded oscillator under conditions of nonlinear resistance

The motion of an oscillator instantaneously loaded with a constant force under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, are considered. Using the first integral of the equation of motion and the Lambert function, compact formulas for calculating the ranges of oscillations are derived. In order to simplify the search for the values of the Lambert function, asymptotic formulas are given that, with an error of less than one percent, express this special function in terms of elementary functions. It is shown that as a result of the action of the resistance force, including dry friction, the oscillation process has a finite number of cycles and is limited in time, since the oscillator enters the stagnation region, which is located in the vicinity of the static deviation of the oscillator caused by the applied external force. The system dynamic factor is less than two. Examples of calculations that illustrate the possibilities of the stated theory are considered. In addition to analytical research, numerical computer integration of the differential equation of motion was carried out. The complete convergence of the results obtained using the derived formulas and numerical integration is established, which confirms that using analytical solutions it is possible to determine the extreme displacements of the oscillator without numerical integration of the nonlinear differential equation. To simplify the calculations, the literature is also recommended, where tables of the Lambert function are printed, allowing you to find its value for interpolating tabular data. Under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, the process of oscillations of an instantly loaded oscillator has a limited number of cycles. The dependences obtained in this work using the Lambert function make it possible to determine the range of oscillations without numerical integration of the nonlinear differential equation of motion both for an oscillator with quadratic viscous resistance and dry friction, and for an oscillator with quadratic resistance and positional and dry friction.
 Keywords: nonlinear oscillator, instantaneous loading, quadratic viscous resistance, Lambert function, oscillation amplitude.

Exchanging data between computational fluid dynamic and thermodynamic models for improving numerical analysis of Stirling engines

AbstractIn a numerical analysis of a Stirling engine, the thermal and flow fields in the cylinder are three‐dimensional and periodically varying. Therefore, a computational fluid dynamic (CFD) analysis may provide detailed solution but it takes a long computation time to simulate enough number of cycles toward the final stable oscillatory regime. On the contrary, a thermodynamic model is relatively time‐effective; however, it is not sufficiently accurate because it is built under some ideal assumptions. In this study, a method of exchanging data between the two models is proposed to facilitate the simulation of Stirling engines. In this method, the CFD model provides some coefficients required by the thermodynamic model. The simulation is then advanced to the stable oscillatory regime by the thermodynamic model. The information of the stable oscillatory regime predicted by the thermodynamic model is introduced back to the CFD model to renew its initial guesses. Then, the CFD model corrects the required coefficients for the thermodynamic model. The iteration of prediction‐and‐correction continues until the exchanged information converges. Since the predicted initial guesses of the CFD analysis by the thermodynamic model are actually very close to the solutions in the stable oscillatory regime, the CFD model can achieve detailed solutions for the stable oscillatory regime in just a finite number of cycles. In this manner, the overall time consumption can be dramatically reduced and accuracy of the CFD analysis can be improved as well.

VIBRATIONS OF AN INSTANTLY LOADED DISSIPATIVE OSCILLATOR

The work investigates non-stationary oscillations of dissipative oscillators. The joint influence of resistance forces of different nature in the composition of the dissipative force on the oscillations of an elastic linear oscillator caused by its instantaneous loading by a constant external force is investigated. The work was limited to the case of small displacements, when the elastic characteristic of the system can be considered linear. The problem is nonlinear due to the account of the action of the dry friction force, but it allows the construction of exact analytical solutions in elementary functions. In this work, by the method of adding solutions, formulas are derived for calculating the amplitude of oscillations and the duration of half cycles. First, a variant is considered when the resistance force consists of linear viscous and dry friction forces. Then a generalization is made to the case of three resistance forces. The third force is the force of positional friction, which arises in elastic elements such as a leaf spring. It is shown that as a result of the action of the total resistance force, the oscillatory process of a loaded oscillator has a finite number of cycles and is limited in time, which is usually observed in practice. The system dynamic factor is less than two. Examples of calculations that illustrate the possibilities of the stated theory are considered. To check the adequacy of the derived calculation formulas, numerical computer integration of the nonlinear differential equations of the oscillator motion was additionally carried out. The full agreement of the numerical results obtained using various methods is shown. In addition to direct problems of dynamics, the inverse problems of determining the characteristics of the load and resistance from the results of measuring the amplitude of oscillations are also considered. The derived calculation formulas are also suitable for identifying the characteristics of the load and resistance based on the results of experimental measurements of the oscillation ranges. Examples of identifying these characteristics are given. The study showed that the nonlinear problem of motion of an instantly loaded oscillator with the total resistance of several forces of different nature has an analytical solution in elementary functions. The presence of such resistance significantly affects the motion of the oscillator after loading. The constructed analytical solutions give results such as the numerical integration of the original nonlinear differential equation on a computer, which confirms the adequacy of the formulas obtained.

Effect of receptors on the resonant and transient harmonic vibrations of Coronavirus

The paper is concerned with the vibration characteristics of the Coronavirus family. There are some 25–100 receptors, commonly called spikes protruding from the envelope shell of the virus. Spikes, resembling the shape of a hot air balloon, may have a total mass similar to the mass of the lipid bi-layer shell. The lipid proteins of the virus are treated as homogeneous elastic material and the problem is formulated as the interaction of thin elastic shell with discrete masses, modeled as short conical cross-sectional beams. The system is subjected to ultrasonic excitation. Using the methods of structural acoustics, it is shown that the scattered pressure is very small and the pressure on the viral shell is simply the incident pressure. The modal analysis is performed for a bare shell, a single spike, and the spike-decorated shell. The predicted vibration frequencies and modes are shown to compare well with the newly derived closed-form solutions for a single spike and existing analytical solutions for thin shells. The fully nonlinear dynamic simulation of the transient response revealed the true character of the complex interaction between local vibration of spikes and global vibration of the multi-degree-of-freedom system. It was shown that harmonic vibration at or below the lowest resonant modes can excite large amplitude vibration of spikes. The associated maximum principal strain in a spike can reach large values in a fraction of a millisecond. Implications for possible tearing off spikes from the shell are discussed. Another important result is that after a finite number of cycles, the shell buckles and collapses, developing internal contacts and folds with large curvatures and strains exceeding 10%. For the geometry and elastic properties of the SARS-CoV-2 virus, these effects are present in the range of frequencies close to the ones used for medical ultrasound diagnostics.

Comparing maximum rate and sustainability of pacing by mechanical vs. electrical stimulation in the Langendorff-perfused rabbit heart.

AimsMechanical stimulation (MS) represents a readily available, non-invasive means of pacing the asystolic or bradycardic heart in patients, but benefits of MS at higher heart rates are unclear. Our aim was to assess the maximum rate and sustainability of excitation by MS vs. electrical stimulation (ES) in the isolated heart under normal physiological conditions.Methods and resultsTrains of local MS or ES at rates exceeding intrinsic sinus rhythm (overdrive pacing; lowest pacing rates 2.5±0.5 Hz) were applied to the same mid-left ventricular free-wall site on the epicardium of Langendorff-perfused rabbit hearts. Stimulation rates were progressively increased, with a recovery period of normal sinus rhythm between each stimulation period. Trains of MS caused repeated focal ventricular excitation from the site of stimulation. The maximum rate at which MS achieved 1:1 capture was lower than during ES (4.2±0.2 vs. 5.9±0.2 Hz, respectively). At all overdrive pacing rates for which repetitive MS was possible, 1:1 capture was reversibly lost after a finite number of cycles, even though same-site capture by ES remained possible. The number of MS cycles until loss of capture decreased with rising stimulation rate. If interspersed with ES, the number of MS to failure of capture was lower than for MS only.ConclusionIn this study, we demonstrate that the maximum pacing rate at which MS can be sustained is lower than that for same-site ES in isolated heart, and that, in contrast to ES, the sustainability of successful 1:1 capture by MS is limited. The mechanism(s) of differences in MS vs. ES pacing ability, potentially important for emergency heart rhythm management, are currently unknown, thus warranting further investigation.

Durability enhancement of polymer gear using compressed air cooling

Polymer gears can replace metallic gears in many engineering applications; however, thermal sensitive mechanical properties of the polymers limit its wide application. Gear tooth surface interaction as well as material hysteresis generates heat in the gear operation. There have been many attempts to improve the gear performance by design modifications as well as with new materials to withstand against thermal damages. In this work, compressed air cooling method is adopted to improve the wear resistance of injection molded polypropylene spur gears. For the chosen gear and test conditions, continuous measurement of gear surface temperature confirmed that compressed air cooling lowers the temperature up to 15 ℃. Periodical measurement of gear tooth thickness confirms that wear resistance increases up to 100%. Continuous measurements of torque available in driver and driven end confirmed that a 2% increase in transmission efficiency of the gear pair. Test gear tooth surface after a finite number of cycles also confirms the effect of compressed air cooling on wear resistance. Mao model is used to predict the gear surface temperature and found to be in close agreement with experimental results.

Stress-strain Diagrams of Concrete Under Repeated Loads with Compressive Stresses

The article discusses the general characteristics of the deformation of concrete under repeated cyclic loads of compressive stresses observed in the experiments executed by the authors, as well as domestic and foreign researchers. Based on experimental data of fixed and variable levels of stress, limits have been defined for reference points of stabilization of strains and stresses. The plotted stabilization diagram outlines the accumulated deformation with the increase of the number of cycles and shows the stress level above which the concrete fails after a finite number of cycles. The total deformation of concrete in the initial system of coordinates is determined by summing up the incremental strain of each cycle calculated in the new system of coordinates. This technique is used to determine the number of cycles until the stabilization of the deformation at low stress levels and the number of cycles until the failure of concrete at high levels of stress.

Existence and uniqueness of attractors in frictional systems with uncoupled tangential displacements and normal tractions

We consider the class of two or three-dimensional discrete contact problems in which a set of contact nodes can make frictional contact with a corresponding set of rigid obstacles. Such a system might result from a finite element discretization of an elastic contact problem after the application of standard static reduction operations. The Coulomb friction law requires that the tractions at any point on the contact boundary must lie within or on the surface of a ‘friction cone’, but the exact position of any ‘stuck’ node (i.e., a node where the tractions are strictly within the cone) depends on the initial conditions and/or the previous history of loading. If the long-term loading is periodic in time, we anticipate that the system will eventually approach a steady periodic cycle.Here we prove that if the elastic system is ‘uncoupled’, meaning that changes in slip displacements alone have no effect on the instantaneous normal contact reactions, the time-varying terms in this steady cycle are independent of initial conditions. In particular, we establish the existence of a unique ‘permanent stick zone’ T comprising the set of all nodes that do not slip after some finite number of cycles. We also prove that the tractions and slip velocities at all nodes not contained in T approach unique periodic functions of time, whereas the (time-invariant) slip displacements in T may depend on initial conditions.Typical examples of uncoupled systems include those where the contact surface is a plane of symmetry, or where the contacting bodies can be approximated locally as half spaces and Dundurs’ mismatch parameter β=0. An important consequence of these results is that systems of this kind will exhibit damping characteristics that are independent of initial conditions. Also, the energy dissipated at each slipping node in the steady state is independent of initial conditions, so wear patterns and the incidence of fretting fatigue failure should also be so independent.

Sequential Equivalence Checking for Clock-Gated Circuits

Sequential logic synthesis often leads to substantially easier equivalence checking problems, compared to general-case sequential equivalence checking (SEC). This paper theoretically investigates when SEC can be reduced to a combinational equivalence checking (CEC) problem. It shows how the theory can be applied when sequential transforms are used, such as sequential clock gating, retiming, and redundancy removal. The legitimacy of such transforms is typically justified intuitively, by the designer or software developer believing that the two circuits reach the same state after a finite number of cycles, and no difference is observed at the outputs due to fanin non-controllability and fanout non-observability effects.

Cycle structure of random permutations with cycle weights

We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the parameters, while the distributions of finite cycles are usually independent Poisson random variables.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 109-133, 2014

Theory and simulation of the folded waveguide traveling-wave tube working in low voltage with changed period and big size

The folded waveguide traveling-wave tube which works at 3 mm band and above the band is limited to machining accuracy and power capacity. So a slow-wave folded waveguide structure which has a finite number of cycles and whose period can be changed nonasymptotically is proposed. Firstly, the theory for effectively increasing the high-order space harmonic coupling impedance of the structure is given. And the expressions for dispersion and coupling impedance are derived. Then through the simulation, a set of optimized design parameters is achieved. Thus the operating point of the traveling-wave tube is determined. Finally, it is simulated by MAFIA. And an effective gain is obtained. The traveling-wave tube which works at low voltage, relatively large size and relatively large period, is designed.

Iterative Learning Control With Unknown Control Direction: A Novel Data-Based Approach

Iterative learning control (ILC) is considered for both deterministic and stochastic systems with unknown control direction. To deal with the unknown control direction, a novel switching mechanism, based only on available system tracking error data, is first proposed. Then two ILC algorithms combined with the novel switching mechanism are designed for both deterministic and stochastic systems. It is proved that the ILC algorithms would switch to the right control direction and stick to it after a finite number of cycles. Moreover, the input sequence converges to the desired one under the deterministic case. The input sequence converges to the optimal one with probability 1 under stochastic case and the resulting tracking error tends to its minimal value.

Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology

We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. The dust and radiation dominated closed Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find a mechanism where quantum oscillations of the Dirac wave functions can prevent the formation of the big bang or big crunch singularity. Thus before the big crunch, the collapse of the universe is stopped by quantum effects and reversed to an expansion, so that the universe opens up entering a new era of classical behavior. Numerical examples of such space-times are given, and the dependence on various parameters is discussed. Generically, one has a collapse after a finite number of cycles. By fine-tuning the parameters we construct an example of a space-time which is time-periodic, thus running through an infinite number of contraction and expansion cycles.

Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems

A residual‐type a posteriori error estimator is introduced and analyzed for a discontinuous Galerkin formulation of a model second‐order elliptic problem with Dirichlet–Neumann‐type boundary conditions. An adaptive algorithm using this estimator together with specific marking and refinement strategies is constructed and shown to achieve any specified error level in the energy norm in a finite number of cycles. The convergence rate is in effect linear with a guaranteed error reduction at every cycle. Results of numerical experiments are presented.

The construction of a nose shape of minimum drag for specified external dimensions and volume using Euler equations

The problem of constructing the axisymmetric nose shape which gives minimum wave drag for a specified volume and external dimensions is solved by a direct method using Euler equations. As in the Newton's formula approximation, the optimum contours together with the front faces – a segment of the boundary extremum along the longitudinal coordinate and the gently sloping segment of the bilateral extremum – may contain a cylindrical end part with a horizontal segment of the boundary extremum with respect to the maximum admissible radial coordinate. In the direct method, the required parameters (“controls”), which define the shape of the optimum contour, are the radii corresponding to the points of the segment of a bilateral extremum, including the radius of the face for fixed abscissas. For each aspect ratio (the ratio of the length to the radius of the base), when a certain value of the volume coefficient (the ratio of the volume to the volume of a cylinder of maximum external dimensions) is exceeded, the optimum nose shape is completed by a rear cylindrical part. The optimum nose shape, which begins from a certain initial contour, that satisfies the limitations of the problem, is constructed after a finite number of cycles. In each cycle, all the controls are corrected, and together with the directions of the change, their increments are found, while the information necessary for this for any number of controls is obtained after three direct calculations. One other advantage of the method is the rapid, close to quadratic, convergence. The nose shapes constructed are compared with the nose shapes that are optimum in the Newton's formula approximation.

In Vitro Fertilization with Immune Patients

Two problems need to be solved before being able to give proper advice to couples undergoing in vitro fertilization therapy. Firstly, does the long-run success rate really converge to 100%? Secondly, what the success rate can be expected within a reasonable finite number of cycles? We propose a model based on a Weibull distribution. Data on 23,520 couples were used to calculate the cumulative pregnancy rate.

Experimental Analysis of the Wear, Life and Behavior of PTFE Coated Thrust Washer Bearings Under Non-Axisymmetric Loading

In this work the behavior and life of a PTFE coating on a flat thrust washer bearing is investigated. The thrust washer bearing is located between a helical gear and its carrier, and is subjected to non-axisymmetric loading and wear. The volume of worn material is approximated by measuring the difference in height between the worn and unworn surfaces. It was also found that the surface roughness of tested washers increases with the severity of wear, in most cases. After a finite number of cycles the effective coefficient of friction between the surfaces increases, suggesting that the coating is wearing off and losing effectiveness. The rate at which the coating wears off also varies with load and speed, hence, there is a region of operation that minimizes the wear and friction. Presented at the 58th Annual Meeting in New York City April 28–May 1, 2003

A NOTE ON MULTILOOP CALCULUS IN P-ADIC STRING THEORY

The technique for finding correlation functions on homogeneous spaces of PGL(ℚp) groups (factorized Bruhat-Tits trees Tp/ΓN with finite number of cycles) is presented. It was shown in Refs. 5 and 6 that the homogeneous spaces Tp/ΓN are in fact the multiloop world sheets in p-adic string theory.

Effect of Cyclic Formation-Pressure Changes on Permeability

Summary Unconsolidated sandpacks of various mesh sizes and consolidated Berea sandstone cores were subjected to repeated pressurization/depressurization cycles under constant confining pressure, after which their absolute and relative permeabilities were measured during the relaxation periods. The permeabilities of the sandpacks decreased as a result of the pressurization, and the reduction in permeability increased as the magnitude and duration of the applied net core pressure increased. The permeabilities continued to decrease with successive pressurization/depressurization cycles, albeit at a decreasing rate. After a finite number of cycles, no further reduction was observed. The number of cycles needed for stabilization was inversely proportional to the duration of the pressurization cycles and was found to be lower for fine sand than for coarser sand. Some recovery in permeability was achieved after the cores were allowed to relax; however, the cores were permanently damaged. Berea sandstone cores also exhibited reductions in permeability as a result of pressurization/depressurization cycling. The reduction increased in direct proportion to the magnitude and duration of net core pressure. However, no reduction in permeability was observed below peak net core pressure levels of <3,500 psi [<24.1 MPa]. It was found that no significant recovery of permeability had taken place after the cores were allowed to relax at low pressure, indicating that the cores were permanently damaged. Two models are proposed for explaining the mechanisms of permeability reduction under the present test conditions for both unconsolidated sand and consolidated cores.