Search results for: Linear Fredholm integral equations

Authors: Aylin Alin

Abstract:

In this paper, penalized power-divergence test statistics have been defined and their exact size properties to test a nested sequence of log-linear models have been compared with ordinary power-divergence test statistics for various penalization, λ and main effect values. Since the ordinary and penalized power-divergence test statistics have the same asymptotic distribution, comparisons have been only made for small and moderate samples. Three-way contingency tables distributed according to a multinomial distribution have been considered. Simulation results reveal that penalized power-divergence test statistics perform much better than their ordinary counterparts.

Keywords: Contingency table, Log-linear models, Penalization, Power-divergence measure, Penalized power-divergence measure.

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Authors: Anjali Verma, Ram Jiwari, Jitender Kumar

Abstract:

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

Keywords: Shallow water wave equation, Exact solutions, (G'/G) expansion method.

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Authors: Guiding Gu, Guo Liu

Abstract:

We discuss the convergence property of the minimum residual (MINRES) method for the solution of complex shifted Hermitian system (αI + H)x = f. Our convergence analysis shows that the method has a faster convergence than that for real shifted Hermitian system (Re(α)I + H)x = f under the condition Re(α) + λmin(H) > 0, and a larger imaginary part of the shift α has a better convergence property. Numerical experiments show such convergence properties.

Keywords: complex shifted linear system, Hermitian matrix, MINRES method.

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Authors: Biao Qin, Jin Huang, Jiaojiao Ren, Wei Kang

Abstract:

This paper deals with the problem of passivity analysis for stochastic neural networks with leakage, discrete and distributed delays. By using delay partitioning technique, free weighting matrix method and stochastic analysis technique, several sufficient conditions for the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), in which both the time-delay and its time derivative can be fully considered. A numerical example is given to show the usefulness and effectiveness of the obtained results.

Keywords: Passivity, Stochastic neural networks, Multiple time delays, Linear matrix inequalities (LMIs).

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Authors: Wei-hua Ai, Wei Yan, Xiang Li

Abstract:

Data compression is used operationally to reduce bandwidth and storage requirements. An efficient method for achieving lossless weather radar data compression is presented. The characteristics of the data are taken into account and the optical linear prediction is used for the PPI images in the weather radar data in the proposed method. The next PPI image is identical to the current one and a dramatic reduction in source entropy is achieved by using the prediction algorithm. Some lossless compression methods are used to compress the predicted data. Experimental results show that for the weather radar data, the method proposed in this paper outperforms the other methods.

Keywords: Lossless compression, weather radar data, optical linear prediction, PPI image

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Authors: Hamid Maidat, Khedidja Bouhadef, Djamel Eddine Ameziani, Azzedine Abdedou

Abstract:

This work consists of a numerical simulation of convective heat transfer in a vertical plane channel filled with a heat generating porous medium, in the absence of local thermal equilibrium. The walls are maintained to a constant temperature and the inlet velocity is uniform. The dynamic range is described by the Darcy-Brinkman model and the thermal field by two energy equations model. A dimensionless formulation is developed for performing a parametric study based on certain dimensionless groups such as, the Biot interstitial number, the thermal conductivity ratio and the volumetric heat generation, q '''. The governing equations are solved using the finite volume method, gave rise to a multitude of results concerning in particular the thermal field in the porous channel and the existence or not of the local thermal equilibrium.

Keywords: Mixed convection, porous medium, power generation, local thermal non equilibrium model.

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Authors: Yuwaraj M. Ghugal, Ajay G. Dahake

Abstract:

A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick simply supported isotropic beams are considered for the numerical studies to demonstrate the efficiency of the results obtained is discussed critically with those of other theories.

Keywords: Trigonometric shear deformation, thick beam, flexure, principle of virtual work, equilibrium equations, stress.

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Authors: Yiqin Lin, Liang Bao

Abstract:

This paper is devoted to the numerical solution of large-scale linear ill-posed systems. A multilevel regularization method is proposed. This method is based on a synthesis of the Arnoldi-Tikhonov regularization technique and the multilevel technique. We show that if the Arnoldi-Tikhonov method is a regularization method, then the multilevel method is also a regularization one. Numerical experiments presented in this paper illustrate the effectiveness of the proposed method.

Keywords: Discrete ill-posed problem, Tikhonov regularization, discrepancy principle, Arnoldi process, multilevel method.

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Authors: G.Y. Zhang , M.L. Xu, R.Q. Zhang, W.H. Tang

Abstract:

MOC (method of cell) is a new method of investigating wave propagating in material with periodic microstructure, and can reflect the effect of microstructure. Wave propagation in periodically laminated medium consisting of linearly elastic layers can be treated as a special application of this method. In this paper, it was used to simulate the dynamic response of carbon-phenolic to impulsive loading under certain boundary conditions. From the comparison between the results obtained from this method and the exact results based on propagator matrix theory, excellent agreement is achieved. Conclusion can be made that the oscillation periodicity is decided by the thickness of sub-cells. In the end, the NHDMOC method, which permits studying stress wave propagation with one dimensional strain, was applied to study the one-dimensional stress wave propagation. In this paper, the ZWT nonlinear visco-elastic constitutive relationship with 7 parameters, NHDMOC, and corresponding equations were deduced. The equations were verified, comparing the elastic stress wave propagation in SHPB with, respectively, the elastic and the visco-elastic bar. Finally the dispersion and attenuation of stress wave in SHPB with visco-elastic bar was studied.

Keywords: MOC, NHDMOC, visco-elastic, wave propagation

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Authors: F. O. Faithpraise, J. Idung, C. R. Chatwin, R. C. D. Young, P. Birch

Abstract:

A continuous time model of the interaction between crop insect pests and naturally beneficial pest enemies is created using a set of simultaneous, non-linear, ordinary differential equations incorporating natural death rates based on the Weibull distribution. The crop pest is present in all its life-cycle stages of: egg, larva, pupa and adult. The beneficial insects, parasitoid wasps, may be present in either or all parasitized: eggs, larva and pupa. Population modelling is used to estimate the quantity of the natural pest enemies that should be introduced into the pest infested environment to suppress the pest population density to an economically acceptable level within a prescribed number of days. The results obtained illustrate the effect of different combinations of parasitoid wasps, using the Pascal distribution to estimate their success in parasitizing different pest developmental stages, to deliver pest control to a sustainable level. Effective control, within a prescribed number of days, is established by the deployment of two or all three species of wasps, which partially destroy pest: egg, larvae and pupae stages. The selected scenarios demonstrate effective sustainable control of the pest in less than thirty days.

Keywords: Biological control, Diamondback moth, Parasitoid wasps, Population modeling.

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Authors: Dimitrios N. Gkritzapis, Elias E. Panagiotopoulos, Dionissios P. Margaris, Dimitrios G. Papanikas

Abstract:

A full six degrees of freedom (6-DOF) flight dynamics model is proposed for the accurate prediction of short and long-range trajectories of high spin and fin-stabilized projectiles via atmospheric flight to final impact point. The projectiles is assumed to be both rigid (non-flexible), and rotationally symmetric about its spin axis launched at low and high pitch angles. The mathematical model is based on the full equations of motion set up in the no-roll body reference frame and is integrated numerically from given initial conditions at the firing site. The projectiles maneuvering motion depends on the most significant force and moment variations, in addition to wind and gravity. The computational flight analysis takes into consideration the Mach number and total angle of attack effects by means of the variable aerodynamic coefficients. For the purposes of the present work, linear interpolation has been applied from the tabulated database of McCoy-s book. The developed computational method gives satisfactory agreement with published data of verified experiments and computational codes on atmospheric projectile trajectory analysis for various initial firing flight conditions.

Keywords: Constant-Variable aerodynamic coefficients, low and high pitch angles, wind.

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Authors: Shao-Tzu Huang, Chen-Chien Hsu, Wei-Yen Wang

Abstract:

Matching high dimensional features between images is computationally expensive for exhaustive search approaches in computer vision. Although the dimension of the feature can be degraded by simplifying the prior knowledge of homography, matching accuracy may degrade as a tradeoff. In this paper, we present a feature matching method based on k-means algorithm that reduces the matching cost and matches the features between images instead of using a simplified geometric assumption. Experimental results show that the proposed method outperforms the previous linear exhaustive search approaches in terms of the inlier ratio of matched pairs.

Keywords: Feature matching, k-means clustering, scale invariant feature transform, linear exhaustive search.

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Authors: Yu-Wei Chen, Li-Ren Han

Abstract:

In this paper, we employ the approach of linear programming to propose a new interactive broadcast method. In our method, a film S is divided into n equal parts and broadcast via k channels. The user simultaneously downloads these segments from k channels into the user-s set-top-box (STB) and plays them in order. Our method assumes that the initial p segments will not have fast-forwarding capabilities. Every time the user wants to initiate d times fast-forwarding, according to our broadcasting strategy, the necessary segments already saved in the user-s STB or are just download on time for playing. The proposed broadcasting strategy not only allows the user to pause and rewind, but also to fast-forward.

Keywords: Broadcasting, Near Video-on-Demand (VOD), Linear Programming, Video-Cassette-Recorder (VCR) Functions, Waiting Time.

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Authors: Ana Clara Santos, Maria Manuela Portela, Bettina Schaefli

Abstract:

This work assesses the performance of an analytical model framework to generate daily flow duration curves, FDCs, based on climatic characteristics of the catchments and on their streamflow recession coefficients. According to the analytical model framework, precipitation is considered to be a stochastic process, modeled as a marked Poisson process, and recession is considered to be deterministic, with parameters that can be computed based on different models. The analytical model framework was tested for three case studies with different hydrological regimes located in Switzerland: pluvial, snow-dominated and glacier. For that purpose, five time intervals were analyzed (the four meteorological seasons and the civil year) and two developments of the model were tested: one considering a linear recession model and the other adopting a nonlinear recession model. Those developments were combined with recession coefficients obtained from two different approaches: forward and inverse estimation. The performance of the analytical framework when considering forward parameter estimation is poor in comparison with the inverse estimation for both, linear and nonlinear models. For the pluvial catchment, the inverse estimation shows exceptional good results, especially for the nonlinear model, clearing suggesting that the model has the ability to describe FDCs. For the snow-dominated and glacier catchments the seasonal results are better than the annual ones suggesting that the model can describe streamflows in those conditions and that future efforts should focus on improving and combining seasonal curves instead of considering single annual ones.

Keywords: Analytical streamflow distribution, stochastic process, linear and non-linear recession, hydrological modelling, daily discharges.

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Authors: Hasan.O. Farahneh, Ayman A. Issa

Abstract:

Software development is moving towards agility with use cases and scenarios being used for requirements stories. Estimates of software costs are becoming even more important than before as effects of delays is much larger in successive short releases context of agile development. Thus, this paper reports on the development of new linear use case based software cost estimation model applicable in the very early stages of software development being based on simple metric. Evaluation showed that accuracy of estimates varies between 43% and 55% of actual effort of historical test projects. These results outperformed those of wellknown models when applied in the same context. Further work is being carried out to improve the performance of the proposed model when considering the effect of non-functional requirements.

Keywords: Metrics, Software Cost Estimation, Use Cases

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Authors: Prasannakumar Palaniappan, Dong Ho Shin, Chul Gyu Song

Abstract:

The photoacoustic images are obtained from a custom developed linear array photoacoustic tomography system. The biological specimens are imitated by conducting phantom tests in order to retrieve a fully functional photoacoustic image. The acquired image undergoes the active region based contour filtering to remove the noise and accurately segment the object area for further processing. The universal back projection method is used as the image reconstruction algorithm. The active contour filtering is analyzed by evaluating the signal to noise ratio and comparing it with the other filtering methods.

Keywords: Contour filtering, linear array, photoacoustic tomography, universal back projection.

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Authors: Aneta Oblouková, Eva Vítková

Abstract:

The article deals with the issue of water and sewerage charge rate prices in the Czech Republic. The research is specifically focused on the analysis of the development of the average prices of water and sewerage charge rate in the Czech Republic in 1994-2021 and on the validation of the chosen methodology relevant for the prediction of the development of the average prices of water and sewerage charge rate in the Czech Republic. The research is based on data collection. The data for this research were obtained from the Czech Statistical Office. The aim of the paper is to validate the relevance of the mathematical linear trend estimate technique for the calculation of the predicted average prices of water and sewerage charge rates. The real values of the average prices of water and sewerage charge rates in the Czech Republic in 1994-2018 were obtained from the Czech Statistical Office and were converted into a mathematical equation. The same type of real data was obtained from the Czech Statistical Office for 2019-2021. Prediction of the average prices of water and sewerage charge rates in the Czech Republic in 2019-2021 was also calculated using a chosen method – a linear trend estimation technique. The values obtained from the Czech Statistical Office and the values calculated using the chosen methodology were subsequently compared. The research result is a validation of the chosen mathematical technique to be a suitable technique for this research.

Keywords: Czech Republic, linear trend estimation, price prediction, water and sewerage charge rate.

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Authors: Md. Alal Hosen

Abstract:

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x^1/3. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this article, different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. We find a modified harmonic balance method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the x^1/3 force nonlinear oscillator but it is also useful for many other nonlinear problems.

Keywords: Approximate solutions, Harmonic balance method, Nonlinear oscillator, Perturbation.

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Authors: P.-W. Tsai, W.-L. Hong, C.-W. Chen, C.-Y. Chen

Abstract:

In this paper, we present a neural-network (NN) based approach to represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov Stability, Parallel Particle Swarm Optimization, Linear Differential Inclusion, Artificial Intelligence.

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Authors: Ramesh K. Sunkaria

Abstract:

The linear methods of heart rate variability analysis such as non-parametric (e.g. fast Fourier transform analysis) and parametric methods (e.g. autoregressive modeling) has become an established non-invasive tool for marking the cardiac health, but their sensitivity and specificity were found to be lower than expected with positive predictive value <30%. This may be due to considering the RR-interval series as stationary and re-sampling them prior to their use for analysis, whereas actually it is not. This paper reviews the non-linear methods of HRV analysis such as correlation dimension, largest Lyupnov exponent, power law slope, fractal analysis, detrended fluctuation analysis, complexity measure etc. which are currently becoming popular as these uses the actual RR-interval series. These methods are expected to highly accurate cardiac health prognosis.

Keywords: chaos, nonlinear dynamics, sample entropy, approximate entropy, detrended fluctuation analysis.

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Authors: Moghiman Mohammad, Amiri Maryam, Amiri Amirhosein

Abstract:

The present paper develops and validates a numerical procedure for the calculation of turbulent combustive flow in converging and diverging ducts and throuh simulation of the heat transfer processes, the amount of production and spread of Nox pollutant has been measured. A marching integration solution procedure employing the TDMA is used to solve the discretized equations. The turbulence model is the Prandtl Mixing Length method. Modeling the combustion process is done by the use of Arrhenius and Eddy Dissipation method. Thermal mechanism has been utilized for modeling the process of forming the nitrogen oxides. Finite difference method and Genmix numerical code are used for numerical solution of equations. Our results indicate the important influence of the limiting diverging angle of diffuser on the coefficient of recovering of pressure. Moreover, due to the intense dependence of Nox pollutant to the maximum temperature in the domain with this feature, the Nox pollutant amount is also in maximum level.

Keywords: Converging and Diverging Duct, Combustion, Diffuser, Diverging Angle, Nox

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Authors: Igor Astrov, Mikhail Pikkov, Rein Paluoja

Abstract:

This paper focuses on a critical component of the situational awareness (SA), the control of autonomous vertical flight for vectored thrust aerial vehicle (VTAV). With the SA strategy, we proposed a linear-quadratic-Gaussian (LQG) flight control procedure for an unmanned helicopter model with vectored thrust configuration. This LQG control for chosen model of VTAV has been verified by simulation of take-off and landing maneuvers using software package Simulink and demonstrated good performance for fast flight stabilization of model, consequently, fast SA with economy in energy can be asserted during search-and-rescue operations.

Keywords: Linear-Quadratic-Gaussian (LQG) controller, situational awareness, vectored thrust aerial vehicle.

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Authors: András Király, Tamás Varga, János Abonyi

Abstract:

Since supply chains highly impact the financial performance of companies, it is important to optimize and analyze their Key Performance Indicators (KPI). The synergistic combination of Particle Swarm Optimization (PSO) and Monte Carlo simulation is applied to determine the optimal reorder point of warehouses in supply chains. The goal of the optimization is the minimization of the objective function calculated as the linear combination of holding and order costs. The required values of service levels of the warehouses represent non-linear constraints in the PSO. The results illustrate that the developed stochastic simulator and optimization tool is flexible enough to handle complex situations.

Keywords: stochastic processes, empirical distributions, Monte Carlo simulation, PSO, supply chain management

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Authors: S. Bhattacharyya, Partha P. Gopmandal

Abstract:

A numerical study on the influence of electroosmotic flow on analyte preconcentration by isotachophoresis ( ITP) is made. We consider that the double layer induced electroosmotic flow ( EOF) counterbalance the electrophoretic velocity and a stationary ITP stacked zones results. We solve the Navier-Stokes equations coupled with the Nernst-Planck equations to determine the local convective velocity and the preconcentration dynamics of ions. Our numerical algorithm is based on a finite volume method along with a secondorder upwind scheme. The present numerical algorithm can capture the the sharp boundaries of step-changes ( plateau mode) or zones of steep gradients ( peak mode) accurately. The convection of ions due to EOF reduces the resolution of the ITP transition zones and produces a dispersion in analyte zones. The role of the electrokinetic parameters which induces dispersion is analyzed. A one-dimensional model for the area-averaged concentrations based on the Taylor-Aristype effective diffusivity is found to be in good agreement with the computed solutions.

Keywords: Interfaces, Electroosmotic flow, QUICK Scheme, Dispersion, Effective Diffusivity.

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Authors: H. Nasiraghdam, A. Jalilian

Abstract:

DSTATCOM is one of the equipments for voltage sag mitigation in power systems. In this paper a new control method for balanced and unbalanced voltage sag mitigation using DSTATCOM is proposed. The control system has two loops in order to regulate compensator current and load voltage. Delayed signal cancellation has been used for sequence separation. The compensator should protect sensitive loads against different types of voltage sag. Performance of the proposed method is investigated under different types of voltage sags for linear and nonlinear loads. Simulation results show appropriate operation of the proposed control system.

Keywords: Custom power, power quality, voltage sagmitigation, current vector control.

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Authors: P. C. Tewari, Rajiv Kumar, Dinesh Khanduja

Abstract:

This paper discusses the performance modeling and availability analysis of Yarn Dyeing System of a Textile Industry. The Textile Industry is a complex and repairable engineering system. Yarn Dyeing System of Textile Industry consists of five subsystems arranged in series configuration. For performance modeling and analysis of availability, a performance evaluating model has been developed with the help of mathematical formulation based on Markov-Birth-Death Process. The differential equations have been developed on the basis of Probabilistic Approach using a Transition Diagram. These equations have further been solved using normalizing condition in order to develop the steady state availability, a performance measure of the system concerned. The system performance has been further analyzed with the help of decision matrices. These matrices provide various availability levels for different combinations of failure and repair rates for various subsystems. The findings of this paper are therefore, considered to be useful for the analysis of availability and determination of the best possible maintenance strategies which can be implemented in future to enhance the system performance.

Keywords: Availability Analysis, Markov Process, Performance Modeling, Steady State Availability.

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Authors: Naresh Yadav, I.A. Khan, Sandeep Grover

Abstract:

This paper presents a unified approach based graph theory and system theory postulates for the modeling and analysis of Simple open cycle Gas turbine system. In the present paper, the simple open cycle gas turbine system has been modeled up to its subsystem level and system variables have been identified to develop the process subgraphs. The theorems and algorithms of the graph theory have been used to represent behavioural properties of the system like rate of heat and work transfers rates, pressure drops and temperature drops in the involved processes of the system. The processes have been represented as edges of the process subgraphs and their limits as the vertices of the process subgraphs. The system across variables and through variables has been used to develop terminal equations of the process subgraphs of the system. The set of equations developed for vertices and edges of network graph are used to solve the system for its process variables.

Keywords: Simple open cycle gas turbine, Graph theoretic approach, process subgraphs, gas turbines system modeling, systemtheory

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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Authors: Alok Madan, Ashok Gupta, Arshad K. Hashmi

Abstract:

Non-linear dynamic time history analysis is considered as the most advanced and comprehensive analytical method for evaluating the seismic response and performance of multi-degree-of-freedom building structures under the influence of earthquake ground motions. However, effective and accurate application of the method requires the implementation of advanced hysteretic constitutive models of the various structural components including masonry infill panels. Sophisticated computational research tools that incorporate realistic hysteresis models for non-linear dynamic time-history analysis are not popular among the professional engineers as they are not only difficult to access but also complex and time-consuming to use. In addition, commercial computer programs for structural analysis and design that are acceptable to practicing engineers do not generally integrate advanced hysteretic models which can accurately simulate the hysteresis behavior of structural elements with a realistic representation of strength degradation, stiffness deterioration, energy dissipation and ‘pinching’ under cyclic load reversals in the inelastic range of behavior. In this scenario, push-over or non-linear static analysis methods have gained significant popularity, as they can be employed to assess the seismic performance of building structures while avoiding the complexities and difficulties associated with non-linear dynamic time-history analysis. “Push-over” or non-linear static analysis offers a practical and efficient alternative to non-linear dynamic time-history analysis for rationally evaluating the seismic demands. The present paper is based on the analytical investigation of the effect of distribution of masonry infill panels over the elevation of planar masonry infilled reinforced concrete [R/C] frames on the seismic demands using the capacity spectrum procedures implementing nonlinear static analysis [pushover analysis] in conjunction with the response spectrum concept. An important objective of the present study is to numerically evaluate the adequacy of the capacity spectrum method using pushover analysis for performance based design of masonry infilled R/C frames for near-field earthquake ground motions.

Keywords: Nonlinear analysis, capacity spectrum method, response spectrum, seismic demand, near-field earthquakes.

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Authors: A. Shafaghat, H. Khabbaz, S. Moravej, Ah. Shafaghat

Abstract:

The bearing capacity of closely spaced shallow footings alters with their spacing and the shape of footing. In this study, the bearing capacity and settlement of two adjacent footings constructed on a sand layer are investigated. The effect of different footing shapes including square, circular, ring and strip on sandy soil is captured in the calculations. The investigations are carried out numerically using PLAXIS-3D software and analytically employing conventional settlement equations. For this purpose, foundations are modelled in the program with practical dimensions and various spacing ratios ranging from 1 to 5. The spacing ratio is defined as the centre-to-centre distance to the width of foundations (S/B). Overall, 24 models are analyzed; and the results are compared and discussed in detail. It can be concluded that the presence of adjacent foundation leads to the reduction in bearing capacity for round shape footings while it can increase the bearing capacity of rectangular footings in some specific distances.

Keywords: Bearing capacity, finite element analysis, loose sand, settlement equations, shallow foundation.

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