Search results for: system of nonlinear equations

Authors: Maor Farid, Oleg Gendelman

Abstract:

The following study deals with fluid vibration of a liquid in a partially filled vessel under periodic ground excitation. This external excitation might lead to hidraulic impact applied on the vessel inner walls. In order to model these sloshing dynamic regimes, several equivalent mechanical models were suggested in the literature, such as series of pendula or mass-spring systems that are able to impact the inner tank walls. In the following study, we use the latter methodology, use parameter values documented in literature corresponding to cylindrical tanks and consider structural elasticity of the tank. The hydraulic impulses are modeled by the high-exponent potential function. Additional system parameters are found with the help of Finite-Element (FE) analysis. Model-driven stress assessment method is developed. Finally, vibration mitigation performances of both tuned mass damper (TMD) and nonlinear energy sink (NES) are examined.

Keywords: nonlinear energy sink (NES), reduced-order modelling, liquid sloshing, vibration mitigation, vibro-impact dynamics

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Authors: Saeid Jalilzadeh

Abstract:

SVC is one of the most significant devices in FACTS technology which is used in parallel compensation, enhancing the transient stability, limiting the low frequency oscillations and etc. designing a proper controller is effective in operation of svc. In this paper the equations that describe the proposed system have been linearized and then the optimum PID controller has been designed for svc which its optimal coefficients have been earned by chaos algorithm. Quick damping of oscillations of generator is the aim of designing of optimum PID controller for svc whether the input power of generator has been changed suddenly. The system with proposed controller has been simulated for a special disturbance and the dynamic responses of generator have been presented. The simulation results showed that a system composed with proposed controller has suitable operation in fast damping of oscillations of generator.

Keywords: chaos, PID controller, SVC, frequency oscillation

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Authors: Yul Y. Nazaruddin, Anas Y. Widiaribowo, Satriyo Nugroho

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Boiler is one of the critical unit in a petrochemical plant. Steam produced by the boiler is used for various processes in the plant such as urea and ammonia plant. An alternative method to optimize the boiler combustion system is presented in this paper. Adaptive Neuro-Fuzzy Inference System (ANFIS) approach is applied to model the boiler using real-time operational data collected from a boiler unit of the petrochemical plant. Nonlinear equation obtained is then used to optimize the air to fuel ratio using Genetic Algorithm, resulting an optimal ratio of 15.85. This optimal ratio is then maintained constant by ratio controller designed using inverse dynamics based on ANFIS. As a result, constant value of oxygen content in the flue gas is obtained which indicates more efficient combustion process.

Keywords: ANFIS, boiler, combustion process, genetic algorithm, optimization.

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Authors: B. X. Tchomeni, A. A. Alugongo, T. B. Tengen

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In this paper, de Laval rotor system has been characterized by a hinge model and its transient response numerically treated for a dynamic solution. The effect of the ensuing non-linear disturbances namely rub and breathing crack is numerically simulated. Subsequently, three analysis methods: Orbit Analysis, Fast Fourier Transform (FFT) and Wavelet Transform (WT) are employed to extract features of the vibration signal of the faulty system. An analysis of the system response orbits clearly indicates the perturbations due to the rotor-to-stator contact. The sensitivities of WT to the variation in system speed have been investigated by Continuous Wavelet Transform (CWT). The analysis reveals that features of crack, rubs and unbalance in vibration response can be useful for condition monitoring. WT reveals its ability to detect non-linear signal, and obtained results provide a useful tool method for detecting machinery faults.

Keywords: Continuous wavelet, crack, discrete wavelet, high acceleration, low acceleration, nonlinear, rotor-stator, rub

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Authors: Hyun-Woo Cho

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Unexpected operational events or abnormalities of industrial processes have a serious impact on the quality of final product of interest. In terms of statistical process control, fault detection and diagnosis of processes is one of the essential tasks needed to run the process safely. In this work, nonlinear representation of process measurement data is presented and evaluated using a simulation process. The effect of using different representation methods on the diagnosis performance is tested in terms of computational efficiency and data handling. The results have shown that the nonlinear representation technique produced more reliable diagnosis results and outperforms linear methods. The use of data filtering step improved computational speed and diagnosis performance for test data sets. The presented scheme is different from existing ones in that it attempts to extract the fault pattern in the reduced space, not in the original process variable space. Thus this scheme helps to reduce the sensitivity of empirical models to noise.

Keywords: fault diagnosis, nonlinear technique, process data, reduced spaces

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Authors: Pompa Marcello, Mauro Capocelli, Vincenzo Piemonte

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This work focuses on a mathematical model able to describe the gastro-intestinal physiology and providing a rational tool for the design of an artificial gastro-intestinal system. This latter is mainly devoted to analyse the absorption and bioavailability of drugs and nutrients through in vitro tests in order to overcome (or, at least, to partially replace) in vivo trials. The provided model realizes a conjunction ring (with extended prediction capability) between in vivo tests and mechanical-laboratory models emulating the human body. On this basis, no empirical equations controlling the gastric emptying are implemented in this model as frequent in the cited literature and all the sub-unit and the related system of equations are physiologically based. More in detail, the model structure consists of six compartments (stomach, duodenum, jejunum, ileum, colon and blood) interconnected through pipes and valves. Paracetamol, Ketoprofen, Irbesartan and Ketoconazole are considered and analysed in this work as reference drugs. The mathematical model has been validated against in vivo literature data. Results obtained show a very good model reliability and highlight the possibility to realize tailored simulations for different couples patient-drug, including food adsorption dynamics.

Keywords: gastro-intestinal model, drugs bioavailability, paracetamol, ketoprofen

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Authors: Habib Akbarzadeh Bengar, Mohammad Asadi Kiadehi, Ali Rameeh

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The result of the past earthquakes has shown that insufficient amount of stirrups and brittle behavior of concrete lead to the shear and flexural failure in reinforced concrete (RC) members. In this paper, an analytical model proposed to predict the nonlinear behavior of RC and SFRC elements and frames. In this model, some important parameter such as shear effect, varying axial load, and longitudinal bar buckling are considered. The results of analytical model were verified with experimental tests. The results of verification have shown that the proposed analytical model can predict the nonlinear behavior of RC and SFRC members and also frames accurately. In addition, the results have shown that use of steel fibers increased bearing capacity and ductility of RC frame. Due to this enhancement in shear strength and ductility, insufficient amount of stirrups, which resulted in shear failure, can be offset with usage of the steel fibers. In addition to the steps taken, to analyze the effects of fibers percentages on the bearing capacity and ductility of frames parametric studies have been performed to investigate of these effects.

Keywords: nonlinear analysis, SFRC frame, shear failure, varying an axial load

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is re-examined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness

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Authors: Noureddine Seddari, Mohamed Belaoued, Salah Bougueroua

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The modeling of complex systems is generally based on the decomposition of their components into sub-systems easier to handle. This division has to be made in a methodical way. In this paper, we introduce an industrial control system modeling and simulation based on the Multi-Agent System (MAS) methodology AALAADIN and more particularly the underlying conceptual model Agent/Group/Role (AGR). Indeed, in this division using AGR model, the overall system is decomposed into sub-systems in order to improve the understanding of regulation and control systems, and to simplify the implementation of the obtained agents and their groups, which are implemented using the Multi-Agents Development KIT (MAD-KIT) platform. This approach appears to us to be the most appropriate for modeling of this type of systems because, due to the use of MAS, it is possible to model real systems in which very complex behaviors emerge from relatively simple and local interactions between many different individuals, therefore a MAS is well adapted to describe a system from the standpoint of the activity of its components, that is to say when the behavior of the individuals is complex (difficult to describe with equations). The main aim of this approach is the take advantage of the performance, the scalability and the robustness that are intuitively provided by MAS.

Keywords: complex systems, modeling and simulation, industrial control system, MAS, AALAADIN, AGR, MAD-KIT

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Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Mokhtar Labiod, Nabil Ikhlef, Keltoum Bouherine, Olivier Leroy

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A numerical model for the radio-frequency (RF) Argon discharge chamber is developed to simulate the low pressure low temperature inductively coupled plasma. This model will be of fundamental importance in the design of the plasma magnetic control system. Electric and magnetic fields inside the discharge chamber are evaluated by solving a magnetic vector potential equation. To start with, the equations of the ideal magnetohydrodynamics theory will be presented describing the basic behaviour of magnetically confined plasma and equations are discretized with finite element method in cylindrical coordinates. The discharge chamber is assumed to be axially symmetric and the plasma is treated as a compressible gas. Plasma generation due to ionization is added to the continuity equation. Magnetic vector potential equation is solved for the electromagnetic fields. A strong dependence of the plasma properties on the discharge conditions and the gas temperature is obtained.

Keywords: direct-coupled model, magnetohydrodynamic, modelling, plasma torch simulation

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Authors: A. Maghari, V. M. Maleki

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In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1 + (2,3)-> 1 + (2,3) as well as recombination 1 + (2,3) -> 2 + (3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the three-dimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.

Keywords: statistical mechanics, nonlocal separable potential, three-body interaction, faddeev equations

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Authors: Biaou Jean-Baptiste Kouchoro, Anissa Meziane, Philippe Micheau, Mathieu Renier, Nicolas Quaegebeur

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Numerous experimental and numerical studies have shown the interest of the local defects resonance (LDR) for the Non-Destructive Testing of metallic and composite plates. Indeed, guided ultrasonic waves such as Lamb waves, which are increasingly used for the inspection of these flat structures, enable the generation of local resonance phenomena by their interaction with a damaged area, allowing the detection of defects. When subjected to a large amplitude motion, a nonlinear behavior can predominate in the damaged area. This work presents a 2D Finite Element Model of the local resonance of a 12 mm long and 5 mm deep Flat Bottom Hole (FBH) in a 6 mm thick aluminum plate under the excitation induced by an incident A0 Lamb mode. The analysis of the transient response of the FBH enables the precise determination of its resonance frequencies and the associate modal deformations. Then, a linear parametric study varying the geometrical properties of the FBH highlights the sensitivity of the resonance frequency with respect to the plate thickness. It is demonstrated that the resonance effect disappears when the ratio of thicknesses between the FBH and the plate is below 0.1. Finally, the nonlinear behavior of the FBH is considered and studied introducing geometrical (taken into account the nonlinear component of the strain tensor) nonlinearities that occur at large vibration amplitudes. Experimental analysis allows observation of the resonance effects and nonlinear response of the FBH. The differences between these experimental results and the numerical results will be commented on. The results of this study are promising and allow to consider more realistic defects such as delamination in composite materials.

Keywords: guided waves, non-destructive testing, dynamic field testing, non-linear ultrasound/vibration

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Authors: M. Meenasaranya, S. Saravanan

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Nonlinear stability analysis is carried out to determine the effect of surface temperature modulation in an infinite horizontal porous layer heated from below. The layer is saturated by an electrically conducting, viscous, incompressible and Newtonian fluid. The Brinkman model is used for momentum equation, and the Boussinesq approximation is invoked. The system is assumed to be bounded by rigid boundaries. The energy theory is implemented to find the global exponential stability region of the considered system. The results are analysed for arbitrary values of modulation frequency and amplitude. The existence of subcritical instability region is confirmed by comparing the obtained result with the known linear result. The vertical magnetic field is found to stabilize the system.

Keywords: Brinkman model, energy method, magnetic field, surface temperature modulation

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Authors: Man Young Kim

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Catalytic combustion is generally accepted as an environmentally preferred alternative for the generation of heat and power from fossil fuels mainly due to its advantages related to the stable combustion under very lean conditions with low emissions of NOx, CO, and UHC at temperatures lower than those occurred in conventional flame combustion. Despite these advantages, the commercial application of catalytic combustion has been delayed because of complicated reaction processes and the difficulty in developing appropriate catalysts with the required stability and durability. To develop the catalytic combustors, detailed studies on the combustion characteristics of catalytic combustion should be conducted. To the end, in current research, quantitative studies on the combustion characteristics of the catalytic combustors, with a Pd-based catalyst for MCFC power generation systems, relying on numerical simulations have been conducted. In addition, data from experimental studies of variations in outlet temperatures and fuel conversion, taken after operating conditions have been used to validate the present numerical approach. After introducing the governing equations for mass, momentum, and energy equations as well as a description of catalytic combustion kinetics, the effects of the excess air ratio, space velocity, and inlet gas temperature on the catalytic combustion characteristics are extensively investigated. Quantitative comparisons are also conducted with previous experimental data. Finally, some concluding remarks are presented.

Keywords: catalytic combustion, methane, BOP, MCFC power generation system, inlet temperature, excess air ratio, space velocity

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Authors: J. P. Chollom, G. M. Kumleng, S. Longwap

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The search for higher order A-stable linear multi-step methods has been the interest of many numerical analysts and has been realized through either higher derivatives of the solution or by inserting additional off step points, supper future points and the likes. These methods are suitable for the solution of stiff differential equations which exhibit characteristics that place a severe restriction on the choice of step size. It becomes necessary that only methods with large regions of absolute stability remain suitable for such equations. In this paper, high order block implicit multi-step methods of the hybrid form up to order twelve have been constructed using the multi-step collocation approach by inserting one or more off step points in the multi-step method. The accuracy and stability properties of the new methods are investigated and are shown to yield A-stable methods, a property desirable of methods suitable for the solution of stiff ODE’s. The new High Order Block Implicit Multistep methods used as block integrators are tested on stiff differential systems and the results reveal that the new methods are efficient and compete favourably with the state of the art Matlab ode23 code.

Keywords: block linear multistep methods, high order, implicit, stiff differential equations

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Authors: Mary Chriselda A

Abstract:

This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Nicolò Vaiana, Giorgio Serino

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In this paper, an advanced Nonlinear Exponential Model (NEM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement in the relatively large displacements range and a hardening or softening behavior at large displacements, is presented. The mathematical model is validated by comparing the experimental force-displacement hysteresis loops obtained during cyclic tests, conducted on a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted analytically. Good agreement between the experimental and simulated results shows that the proposed model can be an effective numerical tool to predict the force-displacement relationship of seismic isolation devices within the large displacements range. Compared to the widely used Bouc-Wen model, unable to simulate the response of seismic isolators at large displacements, the proposed one allows to avoid the numerical solution of a first order nonlinear ordinary differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort. Furthermore, the proposed model can simulate the smooth transition of the hysteresis loops from small to large displacements by adopting only one set of five parameters determined from the experimental hysteresis loops having the largest amplitude.

Keywords: base isolation, hardening behavior, nonlinear exponential model, seismic isolators, softening behavior

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Authors: Jun-Ho Chung, Sung-Hyun Yoo, In-Hwan Choi, Hyun-Kook Lee, Moon-Kyu Song, Choon-Ki Ahn

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The extended finite impulse response (EFIR) filter is addressed to optimize membership functions (MFs) of the fuzzy model that has strong nonlinearity. MFs are important parts of the fuzzy logic system (FLS) and, thus optimizing MFs of FLS is one of approaches to improve the performance of output. We employ the EFIR as an alternative optimization option to nonlinear fuzzy model. The performance of EFIR is demonstrated on a fuzzy cruise control via a numerical example.

Keywords: fuzzy logic system, optimization, membership function, extended FIR filter

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Authors: Ramzi B. Albadarneh

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In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: Ch. Surawut, D. Sukawat

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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: dynamic equation, downscaling, inverse distance, weight interpolation

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Authors: S. A. Al-Qallaf, S. A. Al-Mawsawi, A. Haider

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In order to evaluate the performance of a unified power flow controller (UPFC), mathematical models for steady state and dynamic analysis are to be developed. The steady state model is mainly concerned with the incorporation of the UPFC in load flow studies. Several load flow models for UPFC have been introduced in literature, and one of the most reliable models is the decoupled UPFC model. In spite of UPFC decoupled load flow model simplicity, it is more robust compared to other UPFC load flow models and it contains unique capabilities. Some shortcoming such as additional set of nonlinear equations are to be solved separately after the load flow solution is obtained. The aim of this study is to investigate the different control strategies that can be realized in the decoupled load flow model (individual control and combined control), and the impact of the location of the UPFC in the network on its control parameters.

Keywords: UPFC, decoupled model, load flow, control parameters

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Authors: Souici Abdelaziz, Tehami Mohamed, Rahal Nacer, Said Mohamed Bekkouche, Berthet Jean-Fabien

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In this paper, the influence of the concrete slab creep on the initial deformability of a bent composite beam is modelled. This deformability depends on the rate of creep. This means the rise in value of the longitudinal strain ε c(x,t), the displacement D eflec(x,t) and the strain energy E(t). The variation of these three parameters can easily affect negatively the good appearance and the serviceability of the structure. Therefore, an analytical approach is designed to control the status of the deformability of the beam at the instant t. This approach is based on the Boltzmann’s superposition principle and very particularly on the irreversible law of deformation. For this, two conditions of compatibility and two other static equilibrium equations are adopted. The two first conditions are set according to the rheological equation of Dischinger. After having done a mathematical arrangement, we have reached a system of two differential equations whose integration allows to find the mathematical expression of each generalized internal force in terms of the ability of the concrete slab to creep.

Keywords: composite section, concrete, creep, deformation, differential equation, time

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Authors: Jiashu Shen

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Objectives: Spirometry is a basic reference for health evaluation which is widely used in clinical. Previous reference of spirometry is not applicable because of drastic changes of social and natural circumstance in China. A new reference values for the spirometry of the Chinese population is extremely needed. Method: Spirometric reference value was established using the statistical modeling method Generalized Additive Models for Location, Scale and Shape for forced expiratory volume in 1 s (FEV1), forced vital capacity (FVC), FEV1/FVC, and maximal mid-expiratory flow (MMEF). Results: Data from 236,606 healthy non-smokers aged 4–90 years was collected from the MJ Health Check database. Spirometry equations for FEV1, FVC, MMEF, and FEV1/FVC were established, including the predicted values and lower limits of normal (LLNs) by sex. The predictive equations that were developed for the spirometric results elaborated the relationship between spirometry and age, and they eliminated the effects of height as a variable. Most previous predictive equations for Chinese spirometry were significantly overestimated (to be exact, with mean differences of 22.21% in FEV1 and 31.39% in FVC for males, along with differences of 26.93% in FEV1 and 35.76% in FVC for females) or underestimated (with mean differences of -5.81% in MMEF and -14.56% in FEV1/FVC for males, along with a difference of -14.54% in FEV1/FVC for females) the results of lung function measurements as found in this study. Through cross-validation, our equations were established as having good fit, and the means of the measured value and the estimated value were compared, with good results. Conclusions: Our study updates the spirometric reference equations for Chinese people of all ages and provides comprehensive values for both physical examination and clinical diagnosis.

Keywords: Chinese, GAMLSS model, reference values, spirometry

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Authors: Vishwesh Kulkarni, Nikhil Bellarykar

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Cellular complexity stems from the interactions among thousands of different molecular species. Thanks to the emerging fields of systems and synthetic biology, scientists are beginning to unravel these regulatory, signaling, and metabolic interactions and to understand their coordinated action. Reverse engineering of biological networks has has several benefits but a poor quality of data combined with the difficulty in reproducing it limits the applicability of these methods. A few years back, many of the commonly used predictive algorithms were tested on a network constructed in the yeast Saccharomyces cerevisiae (S. cerevisiae) to resolve this issue. The network was a synthetic network of five genes regulating each other for the so-called in vivo reverse-engineering and modeling assessment (IRMA). The network was constructed in S. cereviase since it is a simple and well characterized organism. The synthetic network included a variety of regulatory interactions, thus capturing the behaviour of larger eukaryotic gene networks on a smaller scale. We derive a new set of algorithms by solving a nonlinear optimization problem and show how these algorithms outperform other algorithms on these datasets.

Keywords: synthetic gene network, network identification, optimization, nonlinear modeling

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Authors: Hongshan Guo

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Ground-source heat pumps provide stable and reliable heating and cooling when designed properly. The confounding effect of the borehole depth for a GSHP system, however, is rarely taken into account for any optimization: the determination of the borehole depth usually comes prior to the selection of corresponding system components and thereafter any optimization of the GSHP system. The depth of the borehole is important to any GSHP system because the shallower the borehole, the larger the fluctuation of temperature of the near-borehole soil temperature. This could lead to fluctuations of the coefficient of performance (COP) for the GSHP system in the long term when the heating/cooling demand is large. Yet the deeper the boreholes are drilled, the more the drilling cost and the operational expenses for the circulation. A controller that reads different building load profiles, optimizing for the smallest costs and temperature fluctuation at the borehole wall, eventually providing borehole depth as the output is developed. Due to the nature of the nonlinear dynamic nature of the GSHP system, it was found that between conventional optimal controller problem and model predictive control problem, the latter was found to be more feasible due to a possible history of both the trajectory during the iteration as well as the final output could be computed and compared against. Aside from a few scenarios of different weighting factors, the resulting system costs were verified with literature and reports and were found to be relatively accurate, while the temperature fluctuation at the borehole wall was also found to be within acceptable range. It was therefore determined that the MPC is adequate to optimize for the investment as well as the system performance for various outputs.

Keywords: geothermal borehole, MPC, dynamic modeling, simulation

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Authors: Martin Goubej, Tomas Popule, Alois Krejci

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This paper deals with experimental identification of mechanical systems with nonlinear friction characteristics. Dynamic LuGre friction model is adopted and a systematic approach to parameter identification of both linear and nonlinear subsystems is given. The identification procedure consists of three subsequent experiments which deal with the individual parts of plant dynamics. The proposed method is experimentally verified on an industrial-grade robotic manipulator. Model fidelity is compared with the results achieved with a static friction model.

Keywords: mechanical friction, LuGre model, friction identification, motion control

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Authors: Viet-Hung Truong, Seung-Eock Kim

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This paper presents a robust software package for practical advanced analysis of space steel framed structures. The pre- and post-processors of the presented software package are coded in the C++ programming language while the solver is written by using the FORTRAN programming language. A user-friendly graphical interface of the presented software is developed to facilitate the modeling process and result interpretation of the problem. The solver employs the stability functions for capturing the second-order effects to minimize modeling and computational time. Both the plastic-hinge and fiber-hinge beam-column elements are available in the presented software. The generalized displacement control method is adopted to solve the nonlinear equilibrium equations.

Keywords: advanced analysis, beam-column, fiber-hinge, plastic hinge, steel frame

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Authors: Harendra Singh, Rajesh Pandey

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The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.

Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis

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Authors: Merouane Salhi, Mohamed Roudane, Abdelkader Kirad

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In this work, we present a new form of characteristics method, which is a technique for solving partial differential equations. Typically, it applies to first-order equations; the aim of this method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data. This latter developed under the real gas theory, because when the thermal and the caloric imperfections of a gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with the gas parameters. The gas doesn’t stay perfect. Its state equation change and it becomes for a real gas. The presented equations of the characteristics remain valid whatever area or field of study. Here we need have inserted the developed Prandtl Meyer function in the mathematical system to find a new model when the effect of stagnation pressure is taken into account. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation, the thermodynamic parameters and the value of Prandtl Meyer function. However, with the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analyzing the supersonic flow for thermally and calorically imperfect gas. The supersonic parameters depend directly on the stagnation parameters of the combustion chamber. The resolution has been made by the finite differences method using the corrector predictor algorithm. As results, the developed mathematical model used to design 2D minimum length nozzles under effect of the stagnation parameters of fluid flow. A comparison for air with the perfect gas PG and high temperature models on the one hand and our results by the real gas theory on the other of nozzles shapes and characteristics are made.

Keywords: numerical methods, nozzles design, real gas, stagnation parameters, supersonic expansion, the characteristics method

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