Search results for: nonlinear static analysis

Authors: M. H. Korayem, Sh. Ameri, N. Yousefi Lademakhi

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To ensure the stability of closed-loop nonlinear model predictive control (NMPC) within a finite horizon, there is a need for appropriate design terminal ingredients, which can be a time-consuming and challenging effort. Otherwise, in order to ensure the stability of the control system, it is necessary to consider an infinite predictive horizon. Increasing the prediction horizon increases computational demand and slows down the implementation of the method. In this study, a new technique has been proposed to ensure system stability without terminal ingredients. This technique has been employed in the design of the NMPC algorithm, leading to a reduction in the computational complexity of designing terminal ingredients and computational burden. The studied system is a wheeled mobile robot (WMR) subjected to non-holonomic constraints. Simulation has been investigated for two problems: trajectory tracking and adjustment mode.

Keywords: wheeled mobile robot, nonlinear model predictive control, stability, without terminal ingredients

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Authors: Amin Noor, Roslinda Nazar, Norihan Md. Arifin

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In this paper, a numerical and theoretical study has been performed for the stagnation-point boundary layer flow and heat transfer towards a shrinking sheet in a nanofluid. The mathematical nanofluid model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Numerical results are obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction Φ, the shrinking parameter λ and the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It is found that solutions do not exist for larger shrinking rates and dual (upper and lower branch) solutions exist when λ < -1.0. A stability analysis has been performed to show which branch solutions are stable and physically realizable. It is also found that the upper branch solutions are stable while the lower branch solutions are unstable.

Keywords: heat transfer, nanofluid, shrinking sheet, stability analysis, stagnation-point flow

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Authors: Zellagui Redouane, Bellaouar Ahmed, Lachi Mohammed

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The railway axles are the essential parts in the bogie of train, and its failure creates a big problem in the railway transport; during the work of this parts we noticed a premature deterioration. The aim has been presented a predictive model allowing the identification of the probable causes that are the cause of these premature deterioration. The results are employed for predicting fatigue crack growth in the railway axle, Also we want to present the variation value of stress intensity factor in different positions of elliptical crack tip. The modeling of axle in performed by the SOLID WORKS software and imported into ANSYS.

Keywords: crack growth, static load, railway axle, lifetime

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Authors: Dong Wook Lee, Adrian Mistreanu

Abstract:

The authors have studied a method for analyzing containment and penetration using an explicit nonlinear Finite Element Analysis. This method may be used in the stage of concept design for the protection of external configurations or components of aircraft engines and nuclear power plant structures. This paper consists of the modeling method, the results obtained from the method and the comparison of the results with those calculated from simple analytical method. It shows that the containment capability obtained by proposed method matches well with analytically calculated containment capability.

Keywords: computer aided engineering, containment analysis, finite element analysis, impact analysis, penetration analysis

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Authors: D. Venu, N. V. Koteswara Rao

Abstract:

Space – time adaptive processing (STAP) is an effective tool for detecting a moving target in spaceborne or airborne radar systems. Since airborne passive radar systems utilize broadcast, navigation and excellent communication signals to perform various surveillance tasks and also has attracted significant interest from the distinct past, therefore the need of the hour is to have cost effective systems as compared to conventional active radar systems. Moreover, requirements of small number of secondary samples for effective clutter suppression in bi-static passive radar offer abundant illuminator resources for passive surveillance radar systems. This paper presents a framework for incorporating knowledge sources directly in the space-time beam former of airborne adaptive radars. STAP algorithm for clutter mitigation for passive bi-static radar has better quantitation of the reduction in sample size thereby amalgamating the earlier data bank with existing radar data sets. Also, we proposed a novel method to estimate the clutter matrix and perform STAP for efficient clutter suppression based on small sample size. Furthermore, the effectiveness of the proposed algorithm is verified using MATLAB simulations in order to validate STAP algorithm for passive bi-static radar. In conclusion, this study highlights the importance for various applications which augments traditional active radars using cost-effective measures.

Keywords: bistatic radar, clutter, covariance matrix passive radar, STAP

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Authors: S. N. Derrar, M. Sekkal-Rahal

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The Nonlinear optics (NLO) technique is widely used in the field of biological imaging. In fact, grafting biological entities with a high NLO response on tissues and cells enhances the NLO responses of these latter, and ameliorates, consequently, their biological imaging quality. In this optics, we carried out a theoretical study, in the aim of analyzing the peptide bonds created between alanine amino acid and both unnatural amino acids: L-Dopa and Azatryptophan, respectively. Ramachandran plots have been performed for these systems, and their structural parameters have been analyzed. The NLO responses of these peptides have been reported by calculating the first hyperpolarizability values of all the minima found on the plots. The use of such unnatural amino acids as endogenous probing molecules has been investigated through this study. The Density Functional Theory (DFT) has been used for structural properties, while the Second-order Møller-Plesset Perturbation Theory (MP2) has been employed for the NLO calculations.

Keywords: biological imaging, hyperpolarizability, nonlinear optics, probing molecule

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Authors: A. T. Al-Isawi, P. E. F. Collins

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The behaviour of structures exposed to fire after an earthquake is not a new area of engineering research, but there remain a number of areas where further work is required. Such areas relate to the way in which seismic excitation is applied to a structure, taking into account the effect of soil-structure interaction (SSI) and the method of analysis, in addition to identifying the excitation load properties. The selection of earthquake data input for use in nonlinear analysis and the method of analysis are still challenging issues. Thus, realistic artificial ground motion input data must be developed to certify that site properties parameters adequately describe the effects of the nonlinear inelastic behaviour of the system and that the characteristics of these parameters are coherent with the characteristics of the target parameters. Conversely, ignoring the significance of some attributes, such as frequency content, soil site properties and earthquake parameters may lead to misleading results, due to the misinterpretation of required input data and the incorrect synthesise of analysis hypothesis. This paper presents a study of the post-earthquake fire (PEF) performance of a multi-storey steel-framed building resting on soft clay, taking into account the effects of the nonlinear inelastic behaviour of the structure and soil, and the soil-structure interaction (SSI). Structures subjected to an earthquake may experience various levels of damage; the geometrical damage, which indicates the change in the initial structure’s geometry due to the residual deformation as a result of plastic behaviour, and the mechanical damage which identifies the degradation of the mechanical properties of the structural elements involved in the plastic range of deformation. Consequently, the structure presumably experiences partial structural damage but is then exposed to fire under its new residual material properties, which may result in building failure caused by a decrease in fire resistance. This scenario would be more complicated if SSI was also considered. Indeed, most earthquake design codes ignore the probability of PEF as well as the effect that SSI has on the behaviour of structures, in order to simplify the analysis procedure. Therefore, the design of structures based on existing codes which neglect the importance of PEF and SSI can create a significant risk of structural failure. In order to examine the criteria for the behaviour of a structure under PEF conditions, a two-dimensional nonlinear elasto-plastic model is developed using ABAQUS software; the effects of SSI are included. Both geometrical and mechanical damages have been taken into account after the earthquake analysis step. For comparison, an identical model is also created, which does not include the effects of soil-structure interaction. It is shown that damage to structural elements is underestimated if SSI is not included in the analysis, and the maximum percentage reduction in fire resistance is detected in the case when SSI is included in the scenario. The results are validated using the literature.

Keywords: Abaqus Software, Finite Element Analysis, post-earthquake fire, seismic analysis, soil-structure interaction

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Authors: Michael Gidey Gebru

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Most of Data Envelopment Analysis models operate in a static environment with input and output parameters that are chosen by deterministic data. However, due to ambiguity brought on shifting market conditions, input and output data are not always precisely gathered in real-world scenarios. Fuzzy numbers can be used to address this kind of ambiguity in input and output data. Therefore, this work aims to expand crisp Data Envelopment Analysis into Data Envelopment Analysis with fuzzy environment. In this study, the input and output data are regarded as fuzzy triangular numbers. Then, the Data Envelopment Analysis model with fuzzy environment is solved using a multi-objective method to gauge the Decision Making Units' efficiency. Finally, the developed Data Envelopment Analysis model is illustrated with an application on real data 50 educational institutions.

Keywords: efficiency, Data Envelopment Analysis, fuzzy, higher education, input, output

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Authors: Xiang Zhang, Daohong Yang, Ziyuan Wu, Lei Li, Wanting Zhou

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Visual Simultaneous Localization and Mapping (VSLAM) uses cameras to collect information in unknown environments to realize simultaneous localization and environment map construction, which has a wide range of applications in autonomous driving, virtual reality and other related fields. At present, the related research achievements about VSLAM can maintain high accuracy in static environment. But in dynamic environment, due to the presence of moving objects in the scene, the movement of these objects will reduce the stability of VSLAM system, resulting in inaccurate localization and mapping, or even failure. In this paper, a robust VSLAM method was proposed to effectively deal with the problem in dynamic environment. We proposed a dynamic region removal scheme based on semantic segmentation neural networks and geometric constraints. Firstly, semantic extraction neural network is used to extract prior active motion region, prior static region and prior passive motion region in the environment. Then, the light weight frame tracking module initializes the transform pose between the previous frame and the current frame on the prior static region. A motion consistency detection module based on multi-view geometry and scene flow is used to divide the environment into static region and dynamic region. Thus, the dynamic object region was successfully eliminated. Finally, only the static region is used for tracking thread. Our research is based on the ORBSLAM3 system, which is one of the most effective VSLAM systems available. We evaluated our method on the TUM RGB-D benchmark and the results demonstrate that the proposed VSLAM method improves the accuracy of the original ORBSLAM3 by 70%˜98.5% under high dynamic environment.

Keywords: dynamic scene, dynamic visual SLAM, semantic segmentation, scene flow, VSLAM

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Authors: Ezedin Geta Seid

Abstract:

Slope failures are among the common geo-environmental natural hazards in the hilly and mountainous terrain of the world causing damages to human life and destruction of infrastructures. In Ethiopia, the demand for the construction of infrastructures, especially highways and railways, has increased to connect the developmental centers. However, the failure of roadside slopes formed due to the difficulty of geographical locations is the major difficulty for this development. As a result, a comprehensive site-specific investigation of destabilizing agents and a suitable selection of slope profiles are needed during design. Hence, this study emphasized the stability analysis and performance evaluation of slope profiles (single slope, multi-slope, and benched slope). The analysis was conducted for static and dynamic loading conditions using limit equilibrium (slide software) and finite element method (Praxis software). The analysis results in selected critical sections show that the slope is marginally stable, with FS varying from 1.2 to 1.5 in static conditions, and unstable with FS below 1 in dynamic conditions. From the comparison of analysis methods, the finite element method provides more valuable information about the failure surface of a slope than limit equilibrium analysis. Performance evaluation of geometric profiles shows that geometric modification provides better and more economical slope stability. Benching provides significant stability for cut slopes (i.e., the use of 2m and 3m bench improves the factor of safety by 7.5% and 12% from a single slope profile). The method is more effective on steep slopes. Similarly, the use of a multi-slope profile improves the stability of the slope in stratified soil with varied strength. The performance is more significant when it is used in combination with benches. The study also recommends drainage control and slope reinforcement as a remedial measure for cut slopes.

Keywords: slope failure, slope profile, bench slope, multi slope

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Authors: Shangerganesh Lingeshwaran

Abstract:

In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: Siddhartha Bhattacharya

Abstract:

Steam Turbine-Generators (STG) and Combustion Turbine-Generator (CTG) are used in almost all modern petrochemical, LNG plants and power plant facilities. The reinforced concrete table top foundations are required to support these high speed rotating heavy machineries and is one of the most critical and challenging structures on any industrial project. The paper illustrates through a practical example, the step by step procedure adopted in designing a table top foundation supported on piles for a steam turbine generator with operating speed of 60 Hz. Finite element model of a table top foundation is generated in ANSYS. Piles are modeled as springs-damper elements (COMBIN14). Basic loads are adopted in analysis and design of the foundation based on the vendor requirements, industry standards, and relevant ASCE & ACI codal provisions. Static serviceability checks are performed with the help of Misalignment Tolerance Matrix (MTM) method in which the percentage of misalignment at a given bearing due to displacement at another bearing is calculated and kept within the stipulated criteria by the vendor so that the machine rotor can sustain the stresses developed due to this misalignment. Dynamic serviceability checks are performed through modal and forced vibration analysis where the foundation is checked for resonance and allowable amplitudes, as stipulated by the machine manufacturer. Reinforced concrete design of the foundation is performed by calculating the axial force, bending moment and shear at each of the critical sections. These values are calculated through area integral of the element stresses at these critical locations. Design is done as per ACI 318-05.

Keywords: steam turbine generator foundation, finite element, static analysis, dynamic analysis

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Authors: Yangsu Kwon, Hyo-Gyoung Kwak

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Nonlinear tendon constitutive model for nonlinear analysis of pre-stressed concrete structures are presented. Since the post-cracking behavior of concrete structures, in which bonded reinforcements such as tendons and/or reinforcing steels are embedded, depends on many influencing factors(the tensile strength of concrete, anchorage length of reinforcements, concrete cover, and steel spacing) that are deeply related to the bond characteristics between concrete and reinforcements, consideration of the tension stiffening effect on the basis of the bond-slip mechanism is necessary to evaluate ultimate resisting capacity of structures. In this paper, an improved tendon model, which considering the slip effect between concrete and tendon, and effect of tension stiffening, is suggested. The validity of the proposed models is established by comparing between the analytical results and experimental results in pre-stressed concrete beams.

Keywords: bond-slip, prestressed concrete, tendon, ultimate strength

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Authors: David C. Ni

Abstract:

In the previous efforts, we constructed N-Body Systems by an extended Blaschke product (EBP), which represents a non-temporal and nonlinear extension of Lorentz transformation. In this construction, we rely only on two parameters, nonlinear degree, and relative momentum to characterize the systems. We further explored root computation via iteration with an algorithm extended from Jenkins-Traub method. The solution sets demonstrate a form of σ+ i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various canonical distributions. In this paper, we correlate the convergent sets in the original domain with solution sets, which demonstrating large-deviation distributions in the codomain. We proceed to compare our approach with the formula or principles, such as Donsker-Varadhan and Wentzell-Freidlin theories. The deterministic model based on this construction allows us to explore applications in the areas of finance and statistical mechanics.

Keywords: nonlinear Lorentz transformation, Blaschke equation, iteration solutions, root computation, large deviation distribution, deterministic model

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Authors: S. H. Kazmi, T. Ahmed, K. Javed, A. Ghani

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In this paper static scheme of under-frequency based load shedding is considered for chemical and petrochemical industries with islanded distribution networks relying heavily on the primary commodity to ensure minimum production loss, plant downtime or critical equipment shutdown. A simplistic methodology is proposed for in-house implementation of this scheme using underfrequency relays and a step by step guide is provided including the techniques to calculate maximum percentage overloads, frequency decay rates, time based frequency response and frequency based time response of the system. Case study of FFL electrical system is utilized, presenting the actual system parameters and employed load shedding settings following the similar series of steps. The arbitrary settings are then verified for worst overload conditions (loss of a generation source in this case) and comprehensive system response is then investigated.

Keywords: islanding, under-frequency load shedding, frequency rate of change, static UFLS

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Authors: Ayad Salih Sabbar, Amin Chegenizadeh, Hamid Nikraz

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Investigation of liquefaction susceptibility of materials that have been used in embankments, slopes, dams, and foundations is very essential. Many catastrophic geo-hazards such as flow slides, declination of foundations, and damage to earth structure are associated with static liquefaction that may occur during abrupt shearing of these materials. Many artificial backfill materials are mixtures of sand with fines and other composition. In order to provide some clarifications and evaluations on the role of fines in static liquefaction behaviour of sand sandy soils, the effect of fines on the liquefaction susceptibility of sand was experimentally examined in the present work over a range of fines content, relative density, and initial confining pressure. The results of an experimental study on various sand-fines mixtures are presented. Undrained static triaxial compression tests were conducted on saturated Perth sand containing 5% bentonite at three different relative densities (10, 50, and 90%), and saturated Perth sand containing both 5% bentonite and slag (2%, 4%, and 6%) at single relative density 10%. Undrained static triaxial tests were performed at three different initial confining pressures (100, 150, and 200 kPa). The brittleness index was used to quantify the liquefaction potential of sand-bentonite-slag mixtures. The results demonstrated that the liquefaction susceptibility of sand-5% bentonite mixture was more than liquefaction susceptibility of clean sandy soil. However, liquefaction potential decreased when both of two fines (bentonite and slag) were used. Liquefaction susceptibility of all mixtures decreased with increasing relative density and initial confining pressure.  

Keywords: liquefaction, bentonite, slag, brittleness index

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Authors: R. Periyasamy, Deepak Joshi, Sneh Anand

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Foot posture assessment is important to evaluate foot type, causing gait and postural defects in all age groups. Although different methods are used for classification of foot arch type in clinical/research examination, there is no clear approach for selecting the most appropriate measurement system. Therefore, the aim of this study was to develop a system for evaluation of foot type as clinical decision-making aids for diagnosis of flat and normal arch based on the Arch Index (AI) and foot pressure distribution parameter - Power Ratio (PR) data. The accuracy of the system was evaluated for 27 subjects with age ranging from 24 to 65 years. Foot area measurements (hind foot, mid foot, and forefoot) were acquired simultaneously from foot pressure intensity image using portable PedoPowerGraph system and analysis of the image in frequency domain to obtain foot pressure distribution parameter - PR data. From our results, we obtain 100% classification accuracy of normal and flat foot by using the linear discriminant analysis method. We observe there is no misclassification of foot types because of incorporating foot pressure distribution data instead of only arch index (AI). We found that the mid-foot pressure distribution ratio data and arch index (AI) value are well correlated to foot arch type based on visual analysis. Therefore, this paper suggests that the proposed system is accurate and easy to determine foot arch type from arch index (AI), as well as incorporating mid-foot pressure distribution ratio data instead of physical area of contact. Hence, such computational tool based system can help the clinicians for assessment of foot structure and cross-check their diagnosis of flat foot from mid-foot pressure distribution.

Keywords: arch index, computational tool, static foot pressure intensity image, foot pressure distribution, linear discriminant analysis

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Authors: Abderraouf Gaaloul, Faouzi Msahli

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The use of standard sliding mode controller, usually, leads to the appearing of an undesirable chattering phenomenon affecting the control signal. Such problem can be overcome using a higher-order sliding mode controller (HOSMC) which preserves the main properties of the standard sliding mode and deliberately increases the control smoothness. In this paper, we propose a new HOSMC for a class of uncertain multi-input multi-output nonlinear systems. Based on high gain and integral sliding mode paradigms, the established control scheme removes theoretically the chattering phenomenon and provides the stability of the control system. Numerical simulations are developed to show the effectiveness of the proposed controller when applied to solve a control problem of two water levels into a quadruple-tank process.

Keywords: nonlinear systems, sliding mode control, high gain, higher order

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Authors: Dong Sang Yoo

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We consider nonlinear uncertain systems such that a priori information of the uncertainties is not available. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound and design a continuous robust control which renders nonlinear uncertain systems ultimately bounded.

Keywords: adaptive control, estimation, Fredholm integral, uncertain system

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Authors: Saeed Rahjoo, Babak H. Mamaqani

Abstract:

Concentric bracing systems have been in practice for many years because of their effectiveness in reducing seismic response. Depending on concept, seismic design codes provide various response modification factors (R), which itself consists of different terms, for different types of lateral load bearing systems but configuration of these systems are often ignored in the proposed values. This study aims at considering the effect of different x-bracing diagonal configuration on values of ductility dependent term in R computation. 51 models were created and nonlinear push over analysis has been performed. The main variables of this study were the suitable location of X–bracing diagonal configurations, which establishes better nonlinear behavior in concentric braced steel frames. Results show that some x-bracing diagonal configurations improve the seismic performance of CBF significantly and explicit consideration of lateral load bearing systems seems necessary.

Keywords: bracing configuration, concentrically braced frame (CBF), push over analyses, response reduction factor

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Authors: Michael Ayomoh, Adriaan Roux, Oyindamola Omotuyi

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This paper presents an efficient robot navigation model in a multi-target domain amidst static and dynamic workspace obstacles. The problem is that of developing an optimal algorithm to minimize the total travel time of a robot as it visits all target points within its task domain amidst unknown workspace obstacles and finally return to its initial position. In solving this problem, a classical algorithm was first developed to compute the optimal number of paths to be travelled by the robot amidst the network of paths. The principle of shortest distance between robot and targets was used to compute the target point visitation order amidst workspace obstacles. Algorithm premised on the standard polar coordinate system was developed to determine the length of obstacles encountered by the robot hence giving room for a geometrical estimation of the total surface area occupied by the obstacle especially when classified as a relevant obstacle i.e. obstacle that lies in between a robot and its potential visitation point. A stochastic model was developed and used to estimate the likelihood of a dynamic obstacle bumping into the robot’s navigation path and finally, the navigation/obstacle avoidance algorithm was hinged on the hybrid virtual force field (HVFF) method. Significant modelling constraints herein include the choice of navigation path to selected target points, the possible presence of static obstacles along a desired navigation path and the likelihood of encountering a dynamic obstacle along the robot’s path and the chances of it remaining at this position as a static obstacle hence resulting in a case of re-routing after routing. The proposed algorithm demonstrated a high potential for optimal solution in terms of efficiency and effectiveness.

Keywords: multi-target, mobile robot, optimal path, static obstacles, dynamic obstacles

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Authors: A. Oukaci, R. Toufouti, D. Dib, l. Atarsia

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This article presents a multitude of alternative techniques to control the vector control, namely the nonlinear control and sliding mode control. Moreover, the implementation of their control law applied to the high-performance to the induction motor with the objective to improve the tracking control, ensure stability robustness to parameter variations and disturbance rejection. Tests are performed numerical simulations in the Matlab/Simulink interface, the results demonstrate the efficiency and dynamic performance of the proposed strategy.

Keywords: Induction Motor (IM), Non-linear Control (NLC), Sliding Mode Control (SMC), nonlinear sliding surface

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Authors: Hamidullah Binol, Abdullah Bal

Abstract:

Nowadays, food safety is a great public concern; therefore, robust and effective techniques are required for detecting the safety situation of goods. Hyperspectral Imaging (HSI) is an attractive material for researchers to inspect food quality and safety estimation such as meat quality assessment, automated poultry carcass inspection, quality evaluation of fish, bruise detection of apples, quality analysis and grading of citrus fruits, bruise detection of strawberry, visualization of sugar distribution of melons, measuring ripening of tomatoes, defect detection of pickling cucumber, and classification of wheat kernels. HSI can be used to concurrently collect large amounts of spatial and spectral data on the objects being observed. This technique yields with exceptional detection skills, which otherwise cannot be achieved with either imaging or spectroscopy alone. This paper presents a nonlinear technique based on kernel Fukunaga-Koontz transform (KFKT) for detection of fat content in ground meat using HSI. The KFKT which is the nonlinear version of FKT is one of the most effective techniques for solving problems involving two-pattern nature. The conventional FKT method has been improved with kernel machines for increasing the nonlinear discrimination ability and capturing higher order of statistics of data. The proposed approach in this paper aims to segment the fat content of the ground meat by regarding the fat as target class which is tried to be separated from the remaining classes (as clutter). We have applied the KFKT on visible and nearinfrared (VNIR) hyperspectral images of ground meat to determine fat percentage. The experimental studies indicate that the proposed technique produces high detection performance for fat ratio in ground meat.

Keywords: food (ground meat) inspection, Fukunaga-Koontz transform, hyperspectral imaging, kernel methods

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Authors: Tran Gia Khanh, Dao Phuong Nam, Do Trong Tan, Nguyen Van Huong, Mai Xuan Sinh

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This work presents the problem of tube-based robust model predictive controller for a class of continuous-time systems in the presence of input disturbances. The main objective is to point out the state trajectory of closed system being maintained inside a sequence of tubes. An estimation of attraction region of the closed system is pointed out based on input state stability (ISS) theory and linearized model in each time interval. The theoretical analysis and simulation results demonstrate the performance of the proposed algorithm for a wheeled inverted pendulum system.

Keywords: input state stability (ISS), tube-based robust MPC, continuous-time nonlinear systems, wheeled inverted pendulum

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Authors: Yosra Baaziz, Moez Labidi

Abstract:

Given limited research on monetary policy rules in revolutionary countries, this paper challenges the suitability of the Taylor rule in characterizing the monetary policy behavior of the Tunisian Central Bank (BCT), especially in turbulent times. More specifically, we investigate the possibility that the Taylor rule should be formulated as a threshold process and examine the validity of such nonlinear Taylor rule as a robust rule for conducting monetary policy in Tunisia. Using quarterly data from 1998:Q4 to 2013:Q4 to analyze the movement of nominal short-term interest rate of the BCT, we find that the nonlinear Taylor rule improves its performance with the advent of special events providing thus a better description of the Tunisian interest rate setting. In particular, our results show that the adoption of an appropriate nonlinear approach leads to a reduction in the errors of 150 basis points in 1999 and 2009, and 60 basis points in 2011, relative to the linear approach.

Keywords: policy rule, central bank, exchange rate, taylor rule, nonlinearity

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Authors: V. D. Thi, M. Li, M. Khelifa, M. El Ganaoui, Y. Rogaume

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This paper presents a two-dimensional model to study the heat and moisture transfer through porous building materials. Dynamic and static coupled models of heat and moisture transfer in porous material under low temperature are presented and the coupled models together with variable initial and boundary conditions have been considered in an analytical way and using the finite element method. The resulting coupled model is converted to two nonlinear partial differential equations, which is then numerically solved by an implicit iterative scheme. The numerical results of temperature and moisture potential changes are compared with the experimental measurements available in the literature. Predicted results demonstrate validation of the theoretical model and effectiveness of the developed numerical algorithms. It is expected to provide useful information for the porous building material design based on heat and moisture transfer model.

Keywords: finite element method, heat transfer, moisture transfer, porous materials, wood

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Authors: K. Karuppasamy

Abstract:

In this paper analysis of an infinite beam resting on multilayer tensionless extensible geosynthetic reinforced granular fill - poor soil system overlying soft soil strata under moving the load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear Winkler springs representing the underlying the very poor soil. The multilayer tensionless extensible geosynthetic layer has been assumed to deform such that at the interface the geosynthetic and the soil have some deformation. Nonlinear behavior of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Governing differential equations of the soil foundation system have been obtained and solved with the help of appropriate boundary conditions. The solution has been obtained by employing finite difference method by means of Gauss-Siedel iterative scheme. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil – foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. These parameters include the magnitude of applied load, the velocity of the load, damping, the ultimate resistance of the poor soil and granular fill layer. The range of values of parameters has been considered as per Indian Railways conditions. This study clearly observed that the comparisons of multilayer tensionless extensible geosynthetic reinforcement with poor foundation soil and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil – foundation system. However, for the considered range of velocity, the response has been found to be insensitive towards velocity. The ultimate resistance of granular fill layer has also been found to have no significant influence on the response of the system.

Keywords: infinite beams, multilayer tensionless extensible geosynthetic, granular layer, moving load and nonlinear behavior of poor soil

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Authors: Haowen Xi

Abstract:

We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Priyanka Kumari Gupta, Punya Prasanna Paltani, Shrivishal Tripathi

Abstract:

This paper proposes a nonlinear photonic crystal ring resonator-based all-optical 2 × 2 switch. The nonlinear Kerr effect is used to evaluate the essential 2 x 2 components of the photonic crystal-based optical switch, including the bar and cross states. The photonic crystal comprises a two-dimensional square lattice of dielectric rods in an air background. In the background air, two different dielectric materials are used for this comparison study separately. Initially with chalcogenide glass rods, then with GaAs rods. For both materials, the operating wavelength, bandgap diagram, operating power intensities, and performance parameters, such as the extinction ratio, insertion loss, and cross-talk of an optical switch, have also been estimated using the plane wave expansion and the finite-difference time-domain method. The chalcogenide glass material (Ag20As32Se48) has a high refractive index of 3.1 which is highly suitable for switching operations. This dielectric material is immersed in an air background with a nonlinear Kerr coefficient of 9.1 x 10-17 m2/W. The resonance wavelength is at 1552 nm, with the operating power intensities at the cross-state and bar state around 60 W/μm2 and 690 W/μm2. The extinction ratio, insertion loss, and cross-talk value for the chalcogenide glass at the cross-state are 17.19 dB, 0.051 dB, and -17.14 dB, and the bar state, the values are 11.32 dB, 0.025 dB, and -11.35 dB respectively. The gallium arsenide (GaAs) dielectric material has a high refractive index of 3.4, a direct bandgap semiconductor material highly preferred nowadays for switching operations. This dielectric material is immersed in an air background with a nonlinear Kerr coefficient of 3.1 x 10-16 m2/W. The resonance wavelength is at 1558 nm, with the operating power intensities at the cross-state and bar state around 110 W/μm2 and 200 W/μm2. The extinction ratio, insertion loss, and cross-talk value for the chalcogenide glass at the cross-state are found to be 3.36.19 dB, 2.436 dB, and -5.8 dB, and for the bar state, the values are 15.60 dB, 0.985 dB, and -16.59 dB respectively. This paper proposes an all-optical 2 × 2 switch based on a nonlinear photonic crystal using a ring resonator. The two-dimensional photonic crystal comprises a square lattice of dielectric rods in an air background. The resonance wavelength is in the range of photonic bandgap. Later, another widely used material, GaAs, is also considered, and its performance is compared with the chalcogenide glass. Our presented structure can be potentially applicable in optical integration circuits and information processing.

Keywords: photonic crystal, FDTD, ring resonator, optical switch

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Authors: L. A. Ostrovsky, Yu. A. Stepanyants

Abstract:

Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described.

Keywords: Earth rotation, internal waves, nonlinear waves, solitons

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