Degree Of Freedom System Research Articles

Adaptive Neuro-Fuzzy Structure Based Control Architecture

The purpose of this paper is to present a practical application of a Sugeno model based adaptive neuro-fuzzy architecture. The main challenge of the project was to realize the real-time control of the system and the real-time parameter adaptation of the controller. The neuro-fuzzy controller module is implemented using High Level Synthesis technique, and it's integrated into a microprocessor based architecture on a System on Chip (SoC) type integrated circuit. The architecture is used to control a two degrees of freedom system, which is composed of two horizontal arms attached to a linear bearing. The bearing is running on a vertical beam so the system can execute a vertical motion and a rotary motion around the vertical axle. The positions according to the two degrees of freedom are determined using an ultrasonic and a magnetic sensor.

履歴型同調質量ダンパーを用いた超高層建物の最適地震応答制御

This paper proposes design method for a hysteric dynamic absorber to reduce seismic response in super high-rise buildings. Friction, rigid-plastic and bi-linear hysteresis type are employed for the absorber. Optimal conditions for the initial stiffness, the post-yielding stiffness and the yielding strength of the damper are estimated by numerous time history analyses using an equivalent two degree of freedom systems. Finally, effectiveness of seismic mitigation for super high-rise buildings having wide variety of natural periods is confirmed through a comparison of a conventional linear viscous absorber.

Deriving the Governing Equations for Shock Damper to Model and Control the Unsteady Flow Caused by Sudden Closer of Valve

This paper focuses on deriving the governing equations for an instrument used in water flow systems known as “shock damper”. Shock damper is a tremulous tool with a single degree of freedom system which includes tank, connecting pipe, mass, spring, and a damper. This tool is then applied as a boundary condition for characteristic lines equations. Additional equations will be included by considering conservation of mass, momentum, and energy. This system of equations is then explicitly solved at each time step. In order to illustrate the performance of the shock damper, a gravity-feed system is considered with and without a damper. The control valve of this system will suddenly be shut to impose a water hammer condition. Then, unsteady flow parameters such as minimum/ maximum of flow velocity and pressure are evaluated along with a sensitivity analysis. Results demonstrate that shock damper despite being simple and economically efficient, is highly capable of moderating unsteady flow characteristics.

Augmented beam elements using unit deflection shapes of the cross section

Wave behavior of line-shaped structures can be analyzed with the help of beam theories if the structures have a simple cross section (beams, rods, etc.), and if the frequency or wavelength is within a range where the theories are still applicable. If the frequencies and wavelengths exceed these limits, the modeling of line- or beam-shaped structures requires volume elements, which results in considerably higher computation time and modeling effort. The goal of this work is to keep the beam-like modeling of structures, but enhance the solution space such that arbitrary deflection shapes of the cross section can be covered. New degrees of freedom are introduced which correspond to the contribution of a unit deflection shape at each node. The unit deflection shapes are defined and computed on the basis of a 2D finite element mesh of the cross section: warp shapes for primary and secondary torsion and shear forces, eigenmodes for the problem of a plate in membrane and a plate in bending action, derived warp shapes for in-plane shapes, shapes which cover the lateral strains and—most importantly—eigenmodes of the infinite waveguide structure. By this transformation of unknowns, the number of system degrees of freedom can be reduced considerably. Different sets of unit deflection shapes are compared according to their efficiency.

Identification of nonlinear vibrating structures by polynomial expansion in the z-domain

A new method in the frequency domain for the identification of nonlinear vibrating structures is described, by adopting the perspective of nonlinearities as internal feedback forces. The technique is based on a polynomial expansion representation of the frequency response function of the underlying linear system, relying on a z-domain formulation. A least squares approach is adopted to take into account the information of all the frequency response functions but, when large data sets are used, the solution of the resulting system of algebraic linear equations can be a difficult task. A procedure to drastically reduce the matrix dimensions and consequently the computational cost – which largely depends on the number of spectral lines – is adopted, leading to a compact and well conditioned problem. The robustness and numerical performances of the method are demonstrated by its implementation on simulated data from single and two degree of freedom systems with typical nonlinear characteristics.

Goal-Directed CPG-Based Control for Tensegrity Spines with Many Degrees of Freedom Traversing Irregular Terrain

Abstract To further the ability of robots to achieve goals in environments with irregular terrain, we have developed a series of tensegrity spines as an abstraction of the many degrees of freedom (DOF) compliant spines seen in nature, with full six DOF between vertebrae (constrained by a tensile network). This work provides insight into control strategies for such many DOF and compliant systems, which lack the rigidly connected segments needed by traditional control. Our Central Pattern Generator (CPG)-based controller receives both proprioceptive feedback and goal-directed input. We utilize artificial neural networks to process both the feedback and the input, and only use feedback available to our analogous robotic hardware. This approach seeks to maximize the low-level competence of the control system, by combining local reflexes with structural compliance. This is, to our knowledge, the first example of a robot controlled by CPGs that is simultaneously capable of goal-directed behavior and locomotion ...

Computing Transition Rates for the 1-D Stochastic Ginzburg–Landau–Allen–Cahn Equation for Finite-Amplitude Noise with a Rare Event Algorithm

In this paper we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude white noise, as well as for small and large domain. We demonstrate that extremely rare reactive trajectories corresponding to direct transitions between two metastable states are efficiently computed using an algorithm called adaptive multilevel splitting. This algorithm is dedicated to the computation of rare events and is able to provide ensembles of reactive trajectories in a very efficient way. In the small noise limit, our numerical results are in agreement with large-deviation predictions such as instanton-like solutions, mean first passages and escape probabilities. We show that the duration of reactive trajectories follows a Gumbel distribution like for one degree of freedom systems. Moreover, the mean duration growths logarithmically with the inverse temperature. The prefactor given by the potential curvature grows exponentially with size. The main novelty of our work is that we also perform an analysis of reactive trajectories for large noises and large domains. In this case, we show that the position of the reactive front is essentially a random walk. This time, the mean duration grows linearly with the inverse temperature and quadratically with the size. Using a phenomenological description of the system, we are able to calculate the transition rate, although the dynamics is described by neither Freidlin--Wentzell or Eyring--Kramers type of results. Numerical results confirm our analysis.

3-dimensional flutter kinematic structural stability

Having recalled the kinematic structural stability (ki.s.s) issue and its solution for divergence-type instability, we address the same problem for flutter-type instability for the minimal required configuration of dimensions—meaning 3 degree of freedom systems. We first get a sufficient non optimal condition. In a second time, the complete issue is tackled by two different ways leading to same results. A first way using calculations on Grassmann and Stiefel manifolds that may be generalized for any dimensional configuration. A second way using the specific dimensional configuration is brought back to calculations on the sphere. Differences with divergence ki.s.s are highlighted and examples illustrate the results.

Response analysis of a nonlinear magnetoelectric energy harvester under harmonic excitation

Magnetostrictive (MS) piezoelectric composites provide interesting possibilities to harvest energy from low amplitude and low frequency vibrations with a relative high energy outcome. In this paper a magnetoelectric (ME) vibration energy harvester has been designed, which consists of two ME transducers a magnetic circuit and a magnetic spring. The ME transducers consist of three layered Terfenol-D and Lead Zirconate Titanate (PZT) laminated composites. The outcoming energy is collected directly from the piezo layer to avoid electrical losses. In the system under consideration, the magnetic forces between the ME transducers and the magnetic circuit introduce additional stiffness on the magnetic spring. The one degree of freedom system is analysed analytically and the corresponding governing equation is solved with the Lindstedt-Poincare method. The effects of the structure parameters, such as the nonlinear magnetic forces and the magnetic field distribution, are analysed based on finite element analysis for optimization of electric output performances. Investigations demonstrate that 1.56 mW output power across 8 MΩ load resistance can be harvested for an excitation amplitude of 1 mm at 21.84 Hz.

Energy Spectra of Constant Ductility Factors for Orthogonal Bidirectional Earthquake Excitations

Current research findings about energy spectra are almost entirely based on the single-degree of freedom system that is only fit for two dimensional analyses. Therefore, it is necessary to establish energy spectra of multidimensional systems subjected to multidirectional earthquake excitations. The bidirectional energy balance equation is established based on the single-mass bi-degrees of freedom system. The equation of normalized energy spectra is presented with earthquake motions, periods, and strength reduction factors as variables. The approximate relation of strength reduction factors between the x and y directions are derived from the seismic influence coefficient spectra. The 89 pairs of bidirectional earthquake motion records are selected as earthquake excitations to establish mean normalized input energy spectra and hysteretic energy spectra. The spectral values of normalized energy are compared between the single-mass bi-degrees of freedom system and single degree of freedom system, which shows that in some cases traditional energy spectra may underestimate the energy responses. The influence factors of mean spectra such as period, ductility factor, period ratio, and soil site are analyzed. Analytic results show that the coupling influences of nonlinear responses of structural two lateral components are considered in normalized energy spectra and are theoretically more rational than traditional spectra. In addition, two kinds of energy spectra have the typical spectral pattern features of the soil site, while the pattern and values of the two kinds of spectra are affected by the ductility factor, period ratio and the soil site.

Full distribution of work done on a quantum system for arbitrary initial states

We propose an approach to define and measure the statistics of work, internal energy and dissipated heat in a driven quantum system. In our framework the presence of a physical detector arises naturally and work and its statistics can be investigated in the most general case. In particular, we show that the quantum coherence of the initial state can lead to measurable effects on the moments of the work done on the system. At the same time, we recover the known results if the initial state is a statistical mixture of energy eigenstates. Our method can also be applied to measure the dissipated heat in an open quantum system. By sequentially coupling the system to a detector, we can track the energy dissipated in the environment while accessing only the system degrees of freedom.

Characterization of Phase Space Topology Using Density: Application to Fault Diagnostics

Almost all engineered systems are nonlinear and show nonlinear phenomena that can only be predicted by nonlinear models. However, the application of model-based approaches for diagnostics has been constrained mostly to linearized or simplified models. This paper introduces a fundamental approach for characterization of nonlinear response of systems based on the topology of the phase space trajectory. The method uses the density distribution of the system states to quantify this topology and extracts features that can be used for system diagnostics. The proposed method has been employed to diagnose a multi degree of freedom system with various simultaneous defects.

Enabling 5G mobile wireless technologies

Research on 5G mobile wireless technologies has been very active in both academia and industry in the past few years. While there has been certain consensus on the overall requirements of 5G wireless systems (e.g., in data rate, network capacity, delay), various enabling wireless technologies have been considered and studied to achieve these performance targets. It has been quite clear, however, that there would be no single enabling technology that can achieve all diverse and even conflicting 5G requirements. In general, many fundamental changes and innovations to re-engineer the overall network architecture and algorithms in different layers and to exploit new system degrees of freedom would be needed for the future 5G wireless system. In particular, we may need to consider other potential waveform candidates that can overcome limitations of the orthogonal frequency multiple access (OFDM) waveform employed in the current 4G system, develop disruptive technologies to fulfill 5G rate and capacity requirements including network densification, employment of large-scale (massive) multiple input multiple output (MIMO), and exploitation of the millimeter wave (mmWave) spectrum to attain Gigabit communications. In addition, design tools from the computer networking domain including software defined networking, virtualization, and cloud computing are expected to play important roles in defining the more flexible, intelligent, and efficient 5G network architecture. This paper aims at describing key 5G enabling wireless mobile technologies and discussing their potentials and open research challenges. We also present how papers published in our special issue contribute to the developments of these disruptive 5G technologies.

Self-Tuneable Velocity Feedback for Active Isolation of Random Vibrations in Subcritical Two Degree Of Freedom Systems

It has been previously shown that skyhook damping can be used to actively reduce vibration transmission between masses in supercritical 2 degree of freedom (dof) systems. The method is based on measuring the absolute velocity of the clean body, multiplying it by a negative gain, and feeding the result back to a force actuator reacting between the clean and the dirty body. This approach results in a broadband vibration isolation. For subcritical 2 dof systems this is normally not possible due to control stability problems. These stability problems can be mitigated by including an appropriate amount of relative damping between the clean and the dirty body in addition to the absolute damping. This approach has been referred to as blended velocity feedback. In this paper the application of the blended velocity feedback on subcritical 2 dof systems is investigated using an auto-tuning controller. An algorithm to gradually change the relative and absolute feedback gains until the active isolation performance reaches its best by applying an optimal combination of the two gains is applied. There is only one such optimal combination which minimises the kinetic energy of the clean body, and consequently the performance surface has a global minimum. Furthermore there are no local minima so a trial and error algorithm could be applied. Although in the frequency domain finding the minimum of the performance surface is straightforward, in the time domain the determining the clean body mean squared velocity can take a considerable time per step of the algorithm, such that the convergence of the trial and error algorithm can be relatively slow. It is hypothesized that more sophisticated algorithms may speed-up the convergence but this would be at cost of using a model-based approach.

On the use of positive feedback for improved torque control

This paper considers the torque control problem for robots with flexible joints driven by electrical actuators. It is shown that the achievable closed-loop tracking bandwidth using PI torque controllers may be limited due to transmission zeros introduced by the load dynamics. This limitation is overcome by using positive feedback from the load motion in unison with PI torque controllers. The positive feedback is given in terms of load velocity, acceleration and jerk. Stability conditions for designing decentralized PI torque controllers are derived in terms of Routh-Hurwitz criteria. Disturbance rejection properties of the closed system are characterized and an analysis is carried out investigating the use of approximate positive feedback by omitting acceleration and/or jerk signals. The results of this paper are illustrated for a two DoF (degrees of freedom) system. Experimental results for a one DoF system are also included.

Reliability and fragility curve assessment of steel concentrically braced frames

This article presents the results of a study in which a newly developed performance-based plastic design (PBPD) methodology was applied to steel special concentric braced frames (SCBF). In PBPD method, pre-selected target drifts and yield mechanisms are used as performance limit states. The design base shear for selected hazard level(s) is calculated by equating the work needed to take the structure monotonically up to the target drift to that required by an equivalent elastic-plastic single degree of freedom system to achieve the same state. In addition, a new lateral force distribution has been developed based on the relative distribution of maximum story shears obtained from inelastic dynamic analysis. Plastic design method is performed to detail the frame members and connections to achieve the intended yield mechanism and behaviour. Results of inelastic dynamic analyses carried out on example frames designed by PBPD method showed that the frames met all the intended performance objectives in terms of yield mechanisms and target drift levels. On the other hand, when designed by current seismic design code as SCBF, they showed very poor response due to premature brace fractures leading to unacceptably large drifts and instability. Reliability-based assessment based on FEMA 351 indicated that PBPD frames have much higher confidence levels against global collapse than those of corresponding SCBFs designed by current seismic codes. Finally, the results are proved by determining the seismic fragility curves of model frames.

Order and chaos in a three dimensional galaxy model

We explore the orbital dynamics of a realistic three dimensional model describing the properties of a disk galaxy with a spherically symmetric central dense nucleus and a triaxial dark matter halo component. Regions of phase space with regular and chaotic motion are identified depending on the parameter values for triaxiality of the dark matter halo and for breaking the rotational symmetry. The four dimensional Poincaré map of the three degrees of freedom system is analyzed by a study of its restriction to various two dimensional invariant subsets of its domain.

Reduced Operator Approximation for Modelling Open Quantum Systems

We present the reduced operator approximation: a simple, physically transparent and computationally efficient method of modelling open quantum systems. It employs the Heisenberg picture of the quantum dynamics, which allows us to focus on the system degrees of freedom in a natural and easy way. We describe different variants of the method, low- and high-order in the system–bath interaction operators, defining them for either general quantum harmonic oscillator baths or specialising them for independent baths with Lorentzian spectral densities. Its wide applicability is demonstrated on the examples of systems coupled to different baths (with varying system–bath interaction strength and bath memory length), and compared with the exact pseudomode and the popular quantum state diffusion approach. The method captures the decoherence of the system interacting with the bath, while conserving the total energy. Our results suggest that quantum coherence effects persist in open quantum systems for much longer times than previously thought.

Force limited vibration testing: an evaluation of the computation of C<sup>2</sup> for real load and probabilistic source

To prevent over-testing of the test-item during random vibration testing Scharton proposed and discussed the force limited random vibration testing (FLVT) in a number of publications. Besides the random vibration specification, the total mass and the turn-over frequency of the load (test item), <TEX>$C^2$</TEX> is a very important parameter for FLVT. A number of computational methods to estimate <TEX>$C^2$</TEX> are described in the literature, i.e., the simple and the complex two degrees of freedom system, STDFS and CTDFS, respectively. The motivation of this work is to evaluate the method for the computation of a realistic value of <TEX>$C^2$</TEX> to perform a representative random vibration test based on force limitation, when the adjacent structure (source) description is more or less unknown. Marchand discussed the formal description of getting <TEX>$C^2$</TEX>, using the maximum PSD of the acceleration and maximum PSD of the force, both at the interface between load and source. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and source are connected, consisting of modal effective masses and the spring stiffness's associated with the natural frequencies. When the random acceleration vibration specification is given the CSMA method is suitable to compute the value of the parameter <TEX>$C^2$</TEX>. When no mathematical model of the source can be made available, estimations of the value <TEX>$C^2$</TEX> can be find in literature. In this paper a probabilistic mathematical representation of the unknown source is proposed, such that the asparagus patch model of the source can be approximated. The chosen probabilistic design parameters have a uniform distribution. The computation of the value <TEX>$C^2$</TEX> can be done in conjunction with the CSMA method, knowing the apparent mass of the load and the random acceleration specification at the interface between load and source, respectively. Data of two cases available from literature have been analyzed and discussed to get more knowledge about the applicability of the probabilistic method.

Force limited random vibration testing: the computation of the semi-empirical constant $$C^2$$ C 2 for a real test article and unknown supporting structure

To prevent over-testing of the test-item during random vibration testing Scharton proposed and discussed the force limited random vibration testing (FLVT) in a number of publications. Besides the random vibration specification, the total mass and the turn-over frequency of the test article (load), \(C^2\) is a very important parameter for FLVT. A number of computational methods to estimate \(C^2\) are described in the literature, i.e. the simple and the complex two degree of freedom system, STDFS and CTDFS, respectively. The motivation of this work is to evaluate the method for the computation of a realistic value of \(C^2\) to perform a representative random vibration test based on force limitation, when the description of the supporting structure (source) is more or less unknown. Marchand discussed the formal description of obtaining \(C^2\), using the maximum PSD of the acceleration and maximum PSD of the force, both at the interface between test article and supporting structure. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and source are connected. The asparagus patch model consists of modal effective masses and spring stiffnesses associated with the natural frequencies. When the random acceleration vibration specification is given the CSMA method is suitable to compute the value of the parameter \(C^2\). When no mathematical model of the source can be made available, estimations of the value \(C^2\) can be find in literature. In this paper a probabilistic mathematical representation of the unknown source is proposed, such that the asparagus patch model of the source can be approximated. The chosen probabilistic design parameters have a uniform distribution. The computation of the value \(C^2\) can be done in conjunction with the CSMA method, knowing the apparent mass of the load and the random acceleration specification at the interface between load and source, respectively. Data of two cases available from literature has been analyzed and discussed to get more knowledge about the applicability of the probabilistic method.