Closed-form Formulation Research Articles

Cooperative Transmission Distance in Multi-relay Communication Systems

In this paper, we present the cooperative transmission distance with multiple decode-and-forward relays in a communication system. The investigation of the transmission distance is focused on how to achieve its maximum by minimizing the average symbol-error-ratio (SER) at the receiver. Firstly, we provide a closed-form formulation of the average SER in a multi-relay system, in which a signal is modulated and demodulated with M-quadrature amplitude modulation and is broadcast by the source and relays through narrow-band Rayleigh fading channels. Secondly, taking asymptotically tight approximation, we optimize the power allocation between the source and relays to minimize the SER. Thirdly, we provide a general expression of the transmission distance with the SER. Finally, we discuss the cooperative transmission distance with different parameters.

Micromechanical characterizing elastic, thermoelastic and viscoelastic properties of functionally graded carbon nanotube reinforced polymer nanocomposites

In this work, elastic, thermoelastic and viscoelastic properties of functionally graded carbon nanotube reinforced polymer nanocomposites are investigated using a 3-dimensional micromechanics-based approach. The main advantage of the proposed micromechanical model is its ability to give closed-form formulation for predicting the effective properties of nanocomposites. In the micromechanical modeling, the interphase formed due to non-boned van der Waals interaction between the continuous CNT and polymer matrix is considered through employing an individual representative volume element. The validity of the model is examined by comparing its results with other theoretical approaches and experimental data available in the literature. The effects of various types of CNTs arrangement in the matrix, i.e. uniform distribution and different functionally graded distributions on the elastic, thermoelastic and viscoelastic properties of polymer nanocomposites are investigated in detail. Furthermore, random arrangement of CNTs in the matrix is modelled. The influences of CNT/polymer matrix interphase and CNT volume fraction on the effective properties of nanocomposites are also studied. Finally, the viscoelastic response of nanocomposites under multiaxial loading is extracted and interpreted.

Asymptotic Perturbation Bounds for Probabilistic Model Checking with Empirically Determined Probability Parameters

Probabilistic model checking is a verification technique that has been the focus of intensive research for over a decade. One important issue with probabilistic model checking, which is crucial for its practical significance but is overlooked by the state-of-the-art largely, is the potential discrepancy between a stochastic model and the real-world system it represents when the model is built from statistical data. In the worst case, a tiny but nontrivial change to some model quantities might lead to misleading or even invalid verification results. To address this issue, in this paper, we present a mathematical characterization of the consequences of model perturbations on the verification distance. The formal model that we adopt is a parametric variant of discrete-time Markov chains equipped with a vector norm to measure the perturbation. Our main technical contributions include a closed-form formulation of asymptotic perturbation bounds , and computational methods for two arguably most useful forms of those bounds, namely linear bounds and quadratic bounds . We focus on verification of reachability properties but also address automata-based verification of omega-regular properties. We present the results of a selection of case studies that demonstrate that asymptotic perturbation bounds can accurately estimate maximum variations of verification results induced by model perturbations.

A Closed-Form Dynamics of a Novel Fully Wrist Driven by Revolute Motors

AbstractThis paper proposes a systematic methodology to obtain a closed-form formulation for dynamics analysis of a novel spherical robot that is called a 3(RPSP)-S parallel manipulator. The proposed manipulator provides high rotational displacement of the moving platform for low angular displacement of the motors. The advised robot is suitable for repetitive oscillatory applications (for example, wrist and ankle rehabilitation and table of autopilot and gyroscope life test, etc.). First, we describe the structure of the proposed manipulator and solve the inverse kinematics problem of the manipulator. Next, based on the principle of virtual work, a methodology for deriving the dynamical equations of motion is developed. The elaborated approach shows that the inverse dynamics of the manipulator can be reduced to solving a system of three linear equations in three unknowns. Finally, a computational algorithm to solve the inverse dynamics of the manipulator is advised and several trajectories of the moving platform are simulated and verified by a special dynamics modeling commercial software (MSC ADAMS).

A closed-form formulation of HRBF-based surface reconstruction by approximate solution

The Hermite radial basis functions (HRBFs) implicits have been used to reconstruct surfaces from scattered Hermite data points. In this work, we propose a closed-form formulation to construct HRBF-based implicits by a quasi-solution to approximate the exact one. A scheme is developed to automatically adjust the support sizes of basis functions to hold the error bound of a quasi-solution. Our method can generate an implicit function from positions and normals of scattered points without taking any global operation. Robust and efficient reconstructions are observed in our experimental tests on real data captured from a variety of scenes.

The Diametrically Loaded Cylinder for the Study of Nanostructured Aluminum–Graphene and Aluminum–Alumina Nanocomposites Using Digital Image Correlation

Non-contact methods for characterization of metal matrix composites have the potential to accelerate the development and study of advanced composite materials. In this study, diametrical compression of small disk specimens was used to understand the mechanical properties of metal matrix micro and nano composites. Analysis was performed using an inverse method that couples digital image correlation and the analytical closed form formulation. This technique was capable of extracting the tension and compression modulus values in the metal matrix nanocomposite disk specimens. Specimens of aluminum and aluminum reinforced with either Al2O3 nanoparticles or graphene nanoplatelets (GNP) were synthesized using a powder metallurgy approach that involved room temperature milling in ethanol, and low temperature drying followed by single action compaction. The elastic and failure properties of MMNC materials prepared using the procedure above are presented.

Energy–Spectral Efficiency Tradeoff in Cognitive Radio Networks

In this paper, we propose a general framework to evaluate the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in cognitive radio networks (CRNs). The proposed framework is discussed in three typical CRN paradigms: underlay CRNs (UCRNs), overlay CRNs (OCRNs), and interweave CRNs (ICRNs). The EE–SE relation for three CRNs is expressed in the closed-form formulation, in which the optimal (suboptimal) EE solution as the function of SE is deduced with the corresponding limits. The theoretical analysis and numerical results indicate that the EE–SE relation in CRNs is not contrary, i.e., an optimal EE–SE tradeoff can be achieved. The proposed framework provides a useful guidance in the design of practical green CRNs.

Full stress and displacement fields for steel-lined deep pressure tunnels in transversely anisotropic rock

An analytical solution is derived that provides closed-form formulations for stresses and displacements for a deep pressure tunnel in a transversely anisotropic rock, with a steel liner, and subjected to a uniform internal pressure. For the derivation, it is assumed that the tunnel support includes a thin steel liner, concrete backfill and that there is an annulus of damaged rock around the concrete. It is also assumed that all materials remain elastic and that the concrete and the damaged rock cannot transmit shear or tangential stresses. The solution is verified by providing comparisons between its results and those from the Finite Element program ABAQUS. For thin steel liners, it can be assumed that the contact pressure between the different materials is uniform, and thus the bending moments in the liner are negligible. This is due to the low bending stiffness of the steel liner. The paper is inspired by and expands the work by Pachoud and Schleiss (2015) who conducted an extensive numerical parametric analysis to obtain correction factors that, when used with an analytical solution for isotropic materials, approximate the maximum principal stress in the liner and intact rock.

Weight function for circumferential semi-elliptical cracks in cylinders due to residual stress fields induced by welding

A method is developed to evaluate the stress intensity factors (SIFs) for semi-elliptical circumferential cracks located at the inner wall of a pipe under arbitrary welding residual stress distribution. To accomplish this, at first, the three-dimensional finite element analysis (FEA) is performed employing singular elements along the crack front. Next, the weight function (WF) is incorporated in conjunction with the finite element results to predict the SIFs of semi-elliptical circumferential cracks in pipes. Then, the presented WF is extended to estimate the SIFs of fully circumferential cracks in pipes. Moreover, a closed-form formulation of SIFs is presented as a function of arbitrary loading condition and crack geometry. Finally, the closed-form relation has been used to predict the stress intensity factors of circumferential cracks under highly nonlinear residual stress fields. Comparison of the results and those in the literature shows an acceptable agreement.

Sensitivity of Pol-InSAR Measurements to Vegetation Parameters

Estimation of forest height from combined polarimetric and interferometric synthetic aperture radar (Pol-InSAR) measurements has been the focus of radar remote sensing studies in the past decade. The simplicity of the random-volume-over-ground (RVoG) model makes it one of the most widely used candidates for estimating canopy height. However, the polarization-independent extinction coefficient assumption in the RVoG model fails in some certain types of the canopies, as suggested by the oriented-volume-over-ground (OVoG) model. The sensitivity of coherence magnitude and phase to different parameters of the canopy is expressed in a closed-form formulation in this paper for the first time. In order to simplify our formulation, the forest is represented by a layer of discrete randomly distributed dielectric scatterers over ground, with azimuthal symmetry. The sensitivity analysis of this work quantifies the contribution of differential extinction due to polarization change in interferometric coherence. Therefore, we can quantitatively evaluate whether the RVoG model is accurate enough to be used for a specific kind of canopy or the OVoG model is needed for better estimation. A simple layer of leaves over ground is used to simulate the sensitivity of Pol-InSAR measurements to different parameters.

Effects of BEOL on self-heating and thermal coupling in SiGe multi-finger HBTs under real operating condition

Effects of the back-end-of-line layers up to metal-1 on the self-heating and thermal coupling in a multi-finger silicon germanium heterojunction bipolar transistor (SiGe MFT) are investigated. It is observed that the rise in junction temperature is overestimated if the BEOL effects are not considered. A new method for estimating the thermal coupling coefficients is proposed emulating the real operating condition. The proposed methodology demonstrates that the thermal coupling is increased in real operating condition and the estimated coupling coefficients are almost independent of the dissipated power. Further an empirical closed-form formulation is proposed for estimating the coupling coefficients analytically and for subsequently using in compact model simulation. The formulation is found to predict the coefficients quite accurately. Compact model simulations using the analytically obtained coupling coefficients show excellent model agreement with the static and dynamic 3D TCAD simulation data for junction temperature. Finally the model is validated against the measured data corresponding to an SiGe MFT fabricated using B55 technology from ST microelectronics.

Six-Dimensional space expression of workspace of six-DoF parallel manipulators using hyper spherical coordinates (HSC)

A closed-form formulation for the workspace of N-Degrees-of-Freedom (DoF) parallel mechanisms is presented using least-square curve fitting. The concepts of multi-dimensional polynomial (MDP) and in hyper spherical coordinates (HSC) are introduced. The boundary of workspaces of those parallel linkages which are surfaces without voids and concavities can be well approximated by the MDPs in the HSC. First, the boundary points are obtained in HSC considering all physical constrains and probable singularities. Then, an MDP with proper order consisting of sine and cosine functions is fitted to those points. The presented method is general and applicable to all DoF. Three case studies of 2, 3, and 6-DoF mechanisms are investigated to demonstrate the effectiveness of the method.

Analytical Solution of Classic Coupled Thermoelasticity Problem in a Rotating Disk

A fully analytical solution of the classic coupled thermoelasticity problem in a rotating disk subjected to thermal and mechanical shock loads is presented. Axisymmetric thermal and mechanical boundary conditions are considered in general forms of arbitrary heat transfer and traction, respectively, at the inner and outer radii of the disk. To solve the governing system of equations, an analytical procedure based on the Fourier-Bessel transform is employed. Closed form formulations are presented for temperature and displacement fields. The results of the present formulations are in good agreement with the numerical results available in the literature. The radial distribution and time history of temperature, displacement and stresses are shown and discussed. The propagation of elastic waves and their reflection from the boundary of the disk are clearly shown. In addition, effects of coupling parameter and angular velocity on temperature, displacement and stress fields are investigated.

A closed-form formula for the moment arm matrix of a general musculoskeletal model with considering joint constraint and motion rhythm

This paper introduces a new closed-form formulation for the moment arm matrix corresponding to the musculotendon unit in a general computational model of the musculoskeletal system. The novel approach uses matrix calculus to define a “Generalized Musculotendon Line of Action Vector (GMLAV)” in integration with the virtual work principle, hence leveraging both conventional geometry and tendon excursion methods. In contrast to previous methods, the concepts of motion rhythm and joint constraints have been incorporated without restrictions, where each joint variable is defined as an arbitrary smooth function of the generalized coordinate vector. The validity of our formulation was established by performing the simulations on two well-known musculoskeletal models from literature and comparing the outcomes with those obtained using OpenSim. The results presented in this paper show a high degree of fidelity between our novel simulation model and OpenSim (or SIMM).

An efficient method for seismic analysis of structures

Purpose – The purpose of this paper is to present an efficient method for dynamic analysis of structures utilizing a modal analysis with the main purpose of decreasing the computational complexity of the problem. In traditional methods, the solution of initial-value problems (IVPs) using numerical methods like finite difference method leads to step by step and time-consuming recursive solutions. Design/methodology/approach – The present method is based on converting the IVP into boundary-value problems (BVPs) and utilizing the features of the latter problems in efficient solution of the former ones. Finite difference formulation of BVPs leads to matrices with repetitive tri-diagonal and block tri-diagonal patterns wherein the eigensolution and matrix inversion are obtained using graph products rules. To get advantage of these efficient solutions for IVPs like the dynamic analysis of single DOF systems, IVPs are converted to boundary-value ones using mathematical manipulations. The obtained formulation is then generalized to the multi DOF systems by utilizing modal analysis. Findings – Applying the method to the modal analysis leads to a simple and efficient formulation. The laborious matrix inversion and eigensolution operations, of computational complexities of O(n2.373) and O(n3), respectively, are converted to a closed-form formulation with summation operations. Research limitations/implications – No limitation. Practical implications – Swift analysis has become possible. Originality/value – Suitability of solving IVPs and modal analysis using conversion and graph product rules is presented and applied to efficient seismic optimal analysis and preliminary design.

Relations Among Some Low-Rank Subspace Recovery Models.

Recovering intrinsic low-dimensional subspaces from data distributed on them is a key preprocessing step to many applications. In recent years, a lot of work has modeled subspace recovery as low-rank minimization problems. We find that some representative models, such as robust principal component analysis (R-PCA), robust low-rank representation (R-LRR), and robust latent low-rank representation (R-LatLRR), are actually deeply connected. More specifically, we discover that once a solution to one of the models is obtained, we can obtain the solutions to other models in closed-form formulations. Since R-PCA is the simplest, our discovery makes it the center of low-rank subspace recovery models. Our work has two important implications. First, R-PCA has a solid theoretical foundation. Under certain conditions, we could find globally optimal solutions to these low-rank models at an overwhelming probability, although these models are nonconvex. Second, we can obtain significantly faster algorithms for these models by solving R-PCA first. The computation cost can be further cut by applying low-complexity randomized algorithms, for example, our novel l2,1 filtering algorithm, to R-PCA. Although for the moment the formal proof of our l2,1 filtering algorithm is not yet available, experiments verify the advantages of our algorithm over other state-of-the-art methods based on the alternating direction method.

Moment-Based Translation Model for Hardening Non-Gaussian Response Processes

AbstractThe translation process theory has widely been used in assessing extreme and fatigue damage of stochastic non-Gaussian response processes. It relates a non-Gaussian process to an underlying Gaussian process through a monotonic translation function. For softening non-Gaussian processes with kurtosis larger than three, the Hermite polynomials model has been used in those situations in which the model coefficients are determined from the skewness and kurtosis of the process with closed-form formulations. This study presents a moment-based translation model for hardening non-Gaussian processes with kurtosis less than three. Closed-form formulations for determining the model coefficients in terms of skewness and kurtosis are presented. The accuracy and limitations of moment-based translation model in representing non-Gaussian processes are also discussed. The proposed moment-based translation model facilitates the analysis of extreme and fatigue of hardening non-Gaussian processes.

Improving the Sustainability of Transportation: Environmental and Functional Benefits of Right Turn By-Pass Lanes at Roundabouts

The functional performances of conventional roundabouts (single-lane and multi-lane) and innovative roundabouts (spiral, flower, C and turbo) can be improved through right-turn bypass lanes controlled by stop, yield or free-flow signs. The article presents evaluations of the emissions of air pollutants (carbon dioxide, nitrogen oxides, particle pollution (PM10 and PM2.5)), fuel consumption and construction, management, energetic and environmental costs in roundabouts without or with bypass lanes (controlled by stop, yield or free-flow). The suggested methodology has a general character and can be applied as a multi-parametric criterion for choosing road intersections, although, in the present paper, it has been employed only for a case study. For the aims of this research, we employed recent closed-form formulations to determine roundabout performances; moreover, we used the COPERT IV® software to estimate air emissions in nine different types of vehicles. Numerous traffic simulations were carried out. The variation in the maximum hourly traffic Qmax and annual traffic QTOT provided the appropriate domains of the examined geometric layouts, both in functional and environmental terms and with regard to generalized costs, estimated for a 10-year period. It resulted that the introduction of right-turn bypasses in all arms of conventional roundabouts with a one ring lane and one lane at the entries (single-lane roundabouts) is the most cost-effective when the flows entering the roundabout are higher than Qmax = 2000 veh/h. Moreover, free-flow bypass lanes always provide greater capacity and lower delays than stop- or yield-signaled bypasses. However, with extremely high Qmax values, stop-controlled bypasses guarantee lower fuel consumption, while those with a yield sign lower total costs.

Control performance assessment for a class of nonlinear systems using second-order Volterra series models based on nonlinear generalised minimum variance control

In this paper, control performance assessment for a class of nonlinear systems modelled by autoregressive second-order Volterra series with a general linear additive disturbance is presented. The proposed approach employs the nonlinear generalised minimum variance (NGMV) controller concept. The Volterra series models provide a natural extension of a linear convolution model with the nonlinearity considered in an additive term. The polynomial operator form is used throughout this paper for the description of the system input–output model. The closed form formulation of NGMV controller for autoregressive second-order Volterra series is presented in a polynomial form then a control assessment criterion based on the NGMV control is given. Simulation results and comparison studies are used to show the effectiveness of the proposed approach for a class of nonlinear systems.

Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation

This paper investigates static and dynamic behavior of carbon nanotube-reinforced composite plates resting on the Pasternak elastic foundation including shear layer and Winkler springs. The plates are reinforced by single-walled carbon nanotubes with four types of distributions of uni-axially aligned reinforcement material. Exact solutions obtained from closed-form formulation based on generalized shear deformation plat theory which can be adapted to various plate theories for bending, buckling and vibration analyses of such plates are presented. An accuracy of the present solutions is validated numerically by comparisons with some available results in the literature. Various significant parameters of carbon nanotube volume fraction, spring constant factors, plate thickness and aspect ratios, etc. are taken into investigation. According to the numerical results, it is revealed that the deflection of the plates is found to decrease as the increase of spring constant factors; while, the buckling load and natural frequency increase as the increment of the factors for every type of plate.