Closed-form Formulation Research Articles

Limit analysis and design-oriented approach for out-of-plane loaded masonry walls strengthened by grouted anchors

Masonry structures without box-like behaviour are often prone to the complete or partial out-of-plane failure of their walls under horizontal actions, i.e. mainly the seismic ones. Steel grouted anchors or tie-rods have been widely used in the past to improve connections between orthogonal walls and avoid out-of-plane mechanisms. However, reliable analytical approaches to design such strengthening systems are lacking, whereas the evaluation of their effectiveness is still a matter of ongoing research. The paper presents a force-based design approach to assess the performance of three-wall masonry systems strengthened by grouted anchors, using a frictional macro-block model and a non-standard limit analysis, previously developed for unreinforced masonry structures. The extension of this model to strengthened masonry systems, with specific reference to the use of grouted anchors, allows assessing their horizontal capacity in terms of minimum load multiplier and expected failure. The novel aspects introduced in the updated model are: (1) a simplified closed-form formulation for the calculation of the stabilising moments provided by the grouted anchors at the onset of the failure mechanism, (2) the possibility of placing the grouted anchors with variable inclinations, which may improve their stabilising contribution and optimise the intervention. The effectiveness of the simplified formulation is firstly proved by the comparison with literature results; then, several parametric analyses are carried out to highlight the influence of some variables on the capacity of both the unreinforced and the strengthened three-wall system. Finally, a literature example related to a traditional intervention with steel tie-rods is used to apply the proposed procedure and investigate the performance of different design solutions with innovative grouted anchors.

Optimized performance analysis of nonrecursive low-density parity-check-coded Gaussian minimum shift keying in 5G-application

We present the low-density parity-check-coded nonrecursive Gaussian minimum shift keying-based hybrid modulation scheme for free-space optical (FSO) communications under optimal signal-to-noise ratio, limited power, and spectrum resources to support 5G and beyond applications with high-throughput efficiency. Our work investigates and approximates the error rate of the proposed scheme across a negative exponential stochastic FSO channel model with misalignment-induced fading. Using the Meijer-G function over the combined channel probability density function, we develop a unique closed-form formulation of outage probability. The potential benefits of utilizing the normalized beamwidth to achieve the desired error rate ( ≈ 10 − 12 ) is discussed. An improvement of 88.64% in the case of narrow beamwidth is perceived which collaborates with the proposed analytical expressions. The precision of our study is supported by numerical data from Monte Carlo simulation.

Coupling model for time-domain analysis of nonparallel overhead wires and buried conductors in the presence of lossy ground

Buried conductors crossing paths with overhead transmission lines is a common occurrence. Interference caused by overhead lines has been found capable of affecting the safe, sustainable operation of the buried conductors. Such occurrences introduce an electromagnetic problem of a nonparallel structure with conductors present in both air and ground half-spaces. Electromagnetic transient (EMT) simulations of such structures are vital in predicting the behaviour of modern power networks. This paper develops a novel EMT compatible time-domain model for nonparallel overhead wires and conductors that are buried in a frequency-dependent lossy (finitely-conducting) ground. Analytical expressions are derived for the per-unit-length (PUL) impedance and admittance matrices based on thin-wire electromagnetic scattering theory. The closed-form formulations derived in this work can be easily incorporated in an EMT simulator to calculate the coupling effect between nonparallel overhead lines and buried conductors. The validity of the proposed approach is examined for various values of the ground conductivity, the radius of the buried conductor, the crossing angle, and burial depth of the conductor by comparing with results with those obtained using a full-wave approach. A case study on the induced voltage in buried conductors due to typical lightning transients in overhead lines has also been performed. • A novel closed-form formulation has been obtained for the mutual coupling of a nonparallel overhead and buried conductors. • Results obtained using the proposed model has been compared with those calculated using a commercial full-wave solver. • Case studies on the induced voltage in buried conductors due to typical lightning and switching transients in overhead lines have also been performed. • Results indicate that hazardous voltages might be induced in buried conductors at such occurrences.

On nonlinear forced vibration of micro scaled panels

The main target of this paper is to evaluate the geometrically nonlinear and size-dependent response of shallow sandwich curved micro-panels (SCMPs). In this regard, the governing equations are developed by using modified couple stress theory (MCST) based on the first-order shear deformation theory (FSDT). The proposed sandwich micro panels are assumed to be made of three layers so that the middle layer is a porous core and the other ones are the nanocomposite enriched face-sheets. The extended nonlinear differential equations are analytically solved by using the main concepts of the Galerkin method which results a closed-form formulation for the nonlinear equation of motion of the proposed micro-panels. Then, the obtained equation of motion is solved numerically using the forth-order Runge-Kutta method. Accuracy of the present method is validated by comparing the results of some examples with those are available in the other studies. Using an extensive parametric study, the effects of various mechanical and geometrical properties on the size-dependent forced vibration of proposed micro-panels are evaluated.

Analytical solutions for the dynamic analysis of a modular floating structure for urban expansion

Modular floating structures (MFS) offer a sustainable alternative over traditional land reclamation for the expansion of coastal megalopolises in the context of climate change adaptation. Yet, there are currently no guidelines for structural engineers pertaining to their analysis and design. This work presents analytical solutions readily accessible for the dynamic analysis of MFS utilizing conventional rectangular pontoons subject to regular or irregular waves. Closed-form formulations utilizing linear wave theory proved capable in capturing the response amplitude operators (RAO) for sway, heave, and roll when compared against smoothed particle hydrodynamics (SPH) simulations for a typical MFS to which appropriate damping ratios were obtained. A parametric study was subsequently implemented to examine the contribution of building slenderness and superstructure-to-pontoon mass ratios on critical accelerations induced by different sea states. It was revealed that structural configurations beneficial to static stability may result in larger dynamic effects under wave excitation thus compromising occupant comfort delineated via various international standards. Ultimately, this paper represents a significant step towards the realization of MFS for urban expansion by providing structural engineers with an accessible methodology for the dynamic analysis of floating structures as a precursor to detailed computational modeling.

Closed-form formulation for the response of single floating piles to lateral dynamic loads

This paper presents a mathematical model that provides the response to lateral dynamic loads of single floating piles embedded in a homogeneous viscoelastic soil layer. The formulation results in closed-form expressions of the pile’s swaying, rocking and cross swaying-rocking compliance components, that do not require solving complex integral equations or iterative calculations. The model exploits Tajimi’s elastodynamic theory to compute the dynamic soil resistance to pile movements. One of its main features is allowing for the effect of the thickness of the soil layer on the response of the soil-pile system, by properly accounting for resonance effects associated with the formation of standing waves. The model is validated by comparing its results for the special case of a floating pile embedded in elastic half space against published analytical and numerical results. The paper concludes with a parametric study, focused on exploring under which conditions standing waves may result in “softer” response of the soil-pile system, a phenomenon that may be important for the serviceability analysis of foundation systems sensitive to resonance effects.

Solving Magnetodynamic Problems via Normal Form Method

Closed-form formulations are difficult to find when the material behavior law is nonlinear. A linear approximation, on the other hand, has a very narrow range of validity. In this communication, the normal form (NF) method is used to solve a 1-D nonlinear magnetodynamic problem. The discrete model is formulated in a state-space form suitable for NF applications. The resulting system is then expanded on a linear mode basis to cubic order. Analytical solutions are obtained using the NF technique and compared with traditional solutions. The results show that the cubic polynomial adequately approximates the problem, and the NF solution is valid for some range of magnetic field intensity.

Conditional mixture modeling and model-based clustering

Due to a potentially high number of parameters, finite mixture models are often at the risk of overparameterization even for a moderate number of components. This can lead to overfitting individual components and result in mixture order underestimation. One of the most popular approaches to address this issue is to reduce the number of parameters by considering parsimonious models. The vast majority of techniques in this direction focuses on the reparameterization of covariance matrices associated with mixture components. We propose an alternative approach based on the parsimonious parameterization of location parameters that enjoys remarkable modeling flexibility especially in the presence of non-compact clusters. Due to an attractive closed form formulation, speedy parameter estimation is available by means of the EM algorithm. The utility of the proposed method is illustrated on synthetic and well-known classification data sets.

Distributed Antenna-and-Relay Selection Schemes for MIMO Cooperative Relay Network

Relay selection, antenna selection, and link selection are three potent means to enrich network capacity in MIMO relaying networks. To reduce feedback overhead, in this paper, three distributed antenna-and-relay selection schemes are proposed for AF multiple-relay network, which is equipped with multiple antennas at nodes. Closed-form formulations of system outage probability are derived for these schemes, as well as the lower bounds and upper bounds. Furthermore, the approximate expressions of outage probability at high SNR regime are also derived, showing that the proposed optimal strategy can achieve full diversity order. In addition, link selection scheme can improve spectral efficiency since it saves one time slot when direct link is selected.

A Simplified Approach to Calculate the Earth Fault Current Division Factor Passing Through the Substation Grounding System

The main aim of designing a safe grounding system is to provide a low impedance path to the flow of the earth fault currents without exceeding the operational constraints and equipment limits that will ensure electrical continuity. One of the most significant and well-known parameters to design a safe grounding system in power systems is the exact determination of the maximum earth fault current division factor. This paper presents a simplified and accurate method to calculate the earth fault current division factor in different states of the earth fault occurrence within and the vicinity of the substation under study. In the proposed method, a hybrid overhead-cable line, the impact of the frozen soil, mutual coupling between phase conductors and guard wires, grounding system resistance of adjacent substations, different tower footing resistances, the impact of the phase conductor impedance, and different spans in transmission lines can be considered. In addition, a closed-form formulation is also developed for the occurrence of the earth fault on the transmission line. Finally, details of the analysis results of this study have been compared with other methods in the literature. The validity and accuracy of the proposed approach also have been assayed and confirmed in details.

Hysteresis modeling of timber-based structural systems using a combined data and model-driven approach

This paper presents a novel computational approach to empirical hysteresis modelling applied to timber-based structures based on a combined data model-driven strategy. While the backbone curve is simulated using the experimental cyclic response based on a step-by-step optimization problem (data-driven approach), analytical functions describe the re-loading curves (model-driven approach). Empirical hysteresis models developed so far for timber structures are model-driven. However, the backbone curves can exhibit a highly irregular non-smooth trend, difficult to mirror using analytical formulations. The challenge in mirroring the experimental backbone using closed-form formulations has led to an extended set of parameters to be calibrated in existing literature models This paper presents a novel approach to the empirical hysteresis model, where the experimental data are directly involved, as a whole, in the model formulation. This model aims to be a possible trade-off between model complexity and accuracy. A reduced number of parameters needed to describe the re-loading paths is counterbalanced using an entire subset of the experimental data. The paper delivers the developed Matlab and Python codes for further implementation as a user-defined element within a Finite Element software.

Pin-supported walls as seismic retrofit for existing RC frames: feasibility and preliminary design

The seismic retrofit of the existing building heritage represents an urgent issue to be faced and innovative solutions which allow to overcome renovation barriers are needed. In this scenario, pin-supported (PS) walls represent an eligible solution, enabling linearization of the deformation of the frame along its height and inhibiting soft storey collapse mechanisms. The PS wall can be connected to the existing building from outside, thereby avoiding disruption to occupants or their relocation, which are acknowledged as the main barriers to the renovation nowadays. Suitability of PS wall solutions in the seismic retrofit of the existing building stock has been investigated herein, particularly in the case of existing reinforced concrete (RC) buildings, preliminarily focusing on 2D RC frames. The paper shows the weaknesses and strengths of the PS wall solution in relation to the specific features of the considered buildings. An analytical closed-form formulation is proposed and applied as a preliminary tool to evaluate the load distribution in the existing frame and in the PS wall after the retrofit considering the first mode of vibration of the retrofitted system. The results show that, in some conditions, the application of PS walls may be detrimental to the structural response. Along with the evaluation of the effectiveness of the retrofit solution, the proposed formulation allows a preliminary design of the retrofit system. Finally, a series of finite element model analyses have been carried out for validation purposes showing a good agreement between the proposed analytical formulation and the numerical results.

Vibration attenuation of beam structure with intermediate support under harmonic excitation

The optimal position design of viscoelastic supports is studied for vibration attenuation of a beam under a harmonic excitation. By attaching the supports properly to the structure, the dynamic deflection of the steady-state response can be significantly suppressed. In this work, the derivative analysis of the dynamic deflection is first investigated with respect to the attachment location of a viscoelastic support. A closed-form formulation for the dynamic response sensitivity is gained readily by use of the discrete methodology. Then, a heuristic optimization algorithm is applied on the design sensitivity analysis to achieve the optimal solution of the supporting points to minimize the maximal steady-state displacement vibration of a beam structure. Finally, two typical examples are presented to demonstrate the validity and accuracy of the design sensitivity formulation developed. Numerical results show that the structural vibration deflections can be substantially reduced with optimization of the intermediate support positions.

How far to live and with whom? Role of modal accessibility on living arrangement and distance

This study investigates the factors influencing university student’s living arrangement choice, the distance between home and the university, and mode choice. A closed-form probabilistic choice modelling formulation is developed to model three choices jointly: student’s living arrangement choice, the distance between home and the university, and student’s typical commuting mode choice to campus. The proposed joint model harnesses the power of both Random Utility Maximisation (RUM) and Cobb–Douglas direct utility maximisation principle. This study identifies the nature and extent of various systematic and random factors influencing university student’s residence and mode choice behaviour to provide evidence for the planners and policymakers to act upon. Walk and cycling accessibility appear to be the most influential factor in the distance between home and the university. The results suggest that affordable housing choices by university campuses can significantly increase the number of active mode users among the student population in Toronto.

Gradient-based optimization for spectral-based multiple-leak identification

This study tailors an efficient optimization procedure for multiple-leak identification in the frequency domain. Firstly, the maximum likelihood estimation is adopted to build a multi-dimensional optimization problem whose objective function is only in terms of the leak locations. Then, closed-form formulations to compute the gradient of the proposed objective function are presented. Finally, to demonstrate the effectiveness of the developed analytical formulations, the steepest-descent method with multiple initializations is implemented to solve the optimization problem. An initialization algorithm based on a set of points with maximum leak reflections is proposed. The use of the most classical gradient-based technique to find the optimum allowed for a deeper understanding of the multi-dimensional optimization required to pinpoint multiple leaks in transient-based methods in terms of complexity and solvability of the problem. The cases of three leaks and various numbers of resonant frequencies with a clear manifestation of the performance of gradients and their applications in the steepest descent method are investigated and discussed. The procedure is also validated against a laboratory case study having two leaks. The main advantages of the proposed technique, which distinguishes it from previous studies, are (i) the versatility of the process to find leaks with even a single spatial measurement vector and (ii) the efficiency and accuracy of the underlying optimization, as closed-form formulations are employed in the scheme. This work may provide a benchmark for investigating and assessing other methods dealing with multiple leaks due to its comprehensive presentation of the local extrema and the entire identification process.

Characteristic Mode Analysis of Mutual Coupling

Mutual coupling between neighboring antennas is a major concern in the array design. Using the concept of characteristic modes, this work proposes a theoretical framework for the analysis of such electromagnetic interaction and its control mechanism. The root of interelement coupling lies in the mutually induced current in the neighboring elements. Henceforth, the initial part of this work concentrates on computing the coupled current by modeling the interaction of the uncoupled modes. Closed-form formulations have been derived for quantifying the coupling impacts. The proposed formulations have been further verified with numerical examples and method of moment-based commercial solver, such as Antenna Toolbox. Later, the theory of substructure modes has been combined with the theory of coupled characteristic modes to understand the perturbation in coupling behavior in the presence of ground plane or a parasitic element. A design strategy has been suggested to optimize the shape of the intermediate parasitic structure for controlling the coupled current in the neighboring elements. This current-based approach can find applications in different coupled scenarios such as antenna arrays or in printed circuit board components.

Error analysis of L-PPM modulated MIMO based multi-user NOMA-VLC system with perfect and imperfect SIC.

By offering a wide license-free spectrum, visible light communication (VLC) has emerged as a game-changing technology for networks beyond 5G. In this study, the multiple-input multiple-output (MIMO) technology is combined with a non-orthogonal multiple access VLC (NOMA-VLC) system to provide a reliable error-free high data rate network for multi-user scenarios. A generalized L-PPM modulated MIMO based multi-user NOMA-VLC system with M×N line-of-sight connections for each user is presented. Considering a practical scenario of imperfect successive interference cancellation, a novel closed form formulation of error probability for the proposed system is obtained. This study also includes a comprehensive analysis of two-user and three-user L-PPM modulated 2×2 MIMO-NOMA-VLC systems, and exact error probability expressions are derived. With the identical set of parameters, the L-PPM modulated MIMO-NOMA-VLC system totally outperforms the on-off keying modulated MIMO-NOMA-VLC system. As the number of photodetectors per user increases, the error probability of the considered system decreases. An L-PPM modulated 2×2 MIMO based three-user NOMA-VLC system offers the best performance at a power allocation co-efficient of 0.3. The simulation results validate the derived error probability expressions.

Optimal power allocation in nonlinear MDM‐WDM systems using Gaussian noise model

Mode-division multiplexing (MDM) using few-mode fibre (FMF) has received increasing attention to address the exponential growth of data traffic in long-haul optical communication systems. Also, combining the MDM with wavelength-division multiplexing (WDM) is a promising approach for dramatically growing the transmission capacity in such systems. However, a major barrier in this regard is the FMF nonlinear effects, which can significantly reduce the link performance. In this paper, in order to alleviate the FMF nonlinear effects, we focus on power allocation in FMF links by optimizing the input power of each optical WDM channel of each spatial mode, which leads to maximizing the total capacity transmission and also the minimum signal to noise ratio (SNR) margin. The FMF nonlinearity has been already modelled as the Gaussian noise (GN) for which no closed-form formulation has been developed so far. Here, we derive a closed-form GN model for this problem and verify it by comparing with the integral-form GN model and split-step Fourier method. In this approach, an optimal power is independently determined for each channel of each mode by optimizing a capacity maximization and a minimum SNR margin maximization problem in convex forms. The performance of different links including the single mode fibre-WDM, MDM-single channel, and MDM-WDM are compared using computer simulations. These systems are comprehensively investigated in equal/non-equal required SNR as well as flat/non-flat amplifier gain scenarios. It is shown that optimized power allocation to each channel of each mode has a significant enhancement in the minimum SNR margin maximization scheme compared to the best equal power allocation. Furthermore, this improvement is much more in non-equal required SNR and the non-flat amplifier gain scenarios, showing the efficiency of the established approach in practical communication links.

Closed-Form Formulation of the Thermodynamically Consistent Electrochemical Model Considering Electrochemical Co-Oxidation of CO and H2 for Simulating Solid Oxide Fuel Cells

Achieving efficient solid oxide fuel cell operation and simultaneous prevention of degradation effects calls for the development of precise on-line monitoring and control tools based on predictive, computationally fast models. The originality of the proposed modelling approach originates from the hypothesis that the innovative derivation procedure enables the development of a thermodynamically consistent multi-species electrochemical model that considers the electrochemical co-oxidation of carbon monoxide and hydrogen in a closed-form. The latter is achieved by coupling the equations for anodic reaction rates with the equation for anodic potential. Furthermore, the newly derived model is capable of accommodating the diffusive transport of gaseous species through the gas diffusion layer, yielding a computationally efficient quasi-one-dimensional model. This resolves a persistent knowledge gap, as the proposed modelling approach enables the modelling of multi-species fuels in a closed form, resulting in very high computational efficiency, and thus enable the model’s real-time capability. Multiple validation steps against polarisation curves with different fuel mixtures confirm the capability of the newly developed model to replicate experimental data. Furthermore, the presented results confirm the capability of the model to accurately simulate outside the calibrated variation space under different operating conditions and reformate mixtures. These functionalities position the proposed model as a beyond state-of-the-art tool for model supported development and control applications.

Novel Formulations of Multireflections and Their Applications to High-Speed Channel Design

Reflection theory has been long established for over decades targeted at microwave and radio frequency (RF) applications. With ultra-high-bandwidth applications emerging, such as 112 Gb/s and higher speed Ethernet protocols, discontinuities in high-speed channels negatively impact signal quality, where reflections become one of the most critical concerns in high-speed designs. In this article, for the first time, we analyzed the traditional reflection theory and proposed and verified a new formulation, which exhibits the reflection-related parameters explicitly, indicating where design optimization can be made for high-bandwidth applications using the backtracked propagation method. Our closed-form formulation is applied to high-speed channel examples, where effective mitigation of negative impact from reflections on signal integrity can be identified to be used as a prelayout channel design guide. Our proposed formulation of the reflection theory provides more accurate prediction of high-speed channel behavior to minimize the negative signal integrity impact from reflections.