Search results for: Lyapunov theorem

Authors: Gabriela R. Fernandes, Renato F. Denadai, Guido J. Denipotti

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In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoff's hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a slab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. On these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degree s of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.

Keywords: Boundary elements, Building floor structures, Platebending.

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Authors: Mohammad Amin Safi, Mahmud Ashrafizaadeh, Amir Ali Ashrafizaadeh

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A highly optimized implementation of binary mixture diffusion with no initial bulk velocity on graphics processors is presented. The lattice Boltzmann model is employed for simulating the binary diffusion of oxygen and nitrogen into each other with different initial concentration distributions. Simulations have been performed using the latest proposed lattice Boltzmann model that satisfies both the indifferentiability principle and the H-theorem for multi-component gas mixtures. Contemporary numerical optimization techniques such as memory alignment and increasing the multiprocessor occupancy are exploited along with some novel optimization strategies to enhance the computational performance on graphics processors using the C for CUDA programming language. Speedup of more than two orders of magnitude over single-core processors is achieved on a variety of Graphical Processing Unit (GPU) devices ranging from conventional graphics cards to advanced, high-end GPUs, while the numerical results are in excellent agreement with the available analytical and numerical data in the literature.

Keywords: Lattice Boltzmann model, Graphical processing unit, Binary mixture diffusion, 2D flow simulations, Optimized algorithm.

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Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

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In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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Authors: Yu-Lin Liao, Ya-Fu Peng

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An adaptive dynamic cerebellar model articulation controller (DCMAC) neural network used for solving the prediction and identification problem is proposed in this paper. The proposed DCMAC has superior capability to the conventional cerebellar model articulation controller (CMAC) neural network in efficient learning mechanism, guaranteed system stability and dynamic response. The recurrent network is embedded in the DCMAC by adding feedback connections in the association memory space so that the DCMAC captures the dynamic response, where the feedback units act as memory elements. The dynamic gradient descent method is adopted to adjust DCMAC parameters on-line. Moreover, the analytical method based on a Lyapunov function is proposed to determine the learning-rates of DCMAC so that the variable optimal learning-rates are derived to achieve most rapid convergence of identifying error. Finally, the adaptive DCMAC is applied in two computer simulations. Simulation results show that accurate identifying response and superior dynamic performance can be obtained because of the powerful on-line learning capability of the proposed DCMAC.

Keywords: adaptive, cerebellar model articulation controller, CMAC, prediction, identification

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Authors: Omer Cahana, Maya Herman, Ofer Levi

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Magnetic Resonance Imaging (MRI) is a lengthy medical scan that stems from a long acquisition time. Its length is mainly due to the traditional sampling theorem, which defines a lower boundary for sampling. However, it is still possible to accelerate the scan by using a different approach such as Compress Sensing (CS) or Parallel Imaging (PI). These two complementary methods can be combined to achieve a faster scan with high-fidelity imaging. To achieve that, two conditions must be satisfied: i) the signal must be sparse under a known transform domain, and ii) the sampling method must be incoherent. In addition, a nonlinear reconstruction algorithm must be applied to recover the signal. While the rapid advances in Deep Learning (DL) have had tremendous successes in various computer vision tasks, the field of MRI reconstruction is still in its early stages. In this paper, we present an end-to-end method for MRI reconstruction from k-space to image. Our method contains two parts. The first is sensitivity map estimation (SME), which is a small yet effective network that can easily be extended to a variable number of coils. The second is reconstruction, which is a top-down architecture with lateral connections developed for building high-level refinement at all scales. Our method holds the state-of-art fastMRI benchmark, which is the largest, most diverse benchmark for MRI reconstruction.

Keywords: Accelerate MRI scans, image reconstruction, pyramid network, deep learning.

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Authors: H. Loumi-Fergane, A. Belaidi

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The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used.  In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qⁱ, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

Keywords: Field theories, relativistic mechanics, Lagrangian formalism, multisymplectic geometry, symmetries, Noether theorem, conservation laws.

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Authors: Rafic Ayoubi, Jean-Pierre Dubois, Rania Minkara

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In this paper, we study FPGA implementation of a novel supra-optimal receiver diversity combining technique, generalized maximal ratio combining (GMRC), for wireless transmission over fading channels in SIMO systems. Prior published results using ML-detected GMRC diversity signal driven by BPSK showed superior bit error rate performance to the widely used MRC combining scheme in an imperfect channel estimation (ICE) environment. Under perfect channel estimation conditions, the performance of GMRC and MRC were identical. The main drawback of the GMRC study was that it was theoretical, thus successful FPGA implementation of it using pipeline techniques is needed as a wireless communication test-bed for practical real-life situations. Simulation results showed that the hardware implementation was efficient both in terms of speed and area. Since diversity combining is especially effective in small femto- and picocells, internet-associated wireless peripheral systems are to benefit most from GMRC. As a result, many spinoff applications can be made to the hardware of IP-based 4th generation networks.

Keywords: Femto-internet cells, field-programmable gate array, generalized maximal-ratio combining, Lyapunov fractal dimension, pipelining technique, wireless SIMO channels.

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: Equivalent Martingale Measure, European Put Option, Girsanov Theorem, Martingales, Monte Carlo method, option price valuation, option price valuation formula.

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Authors: Apoorva Vinod, Archana Mathur, Snehanshu Saha

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Though there exists a plethora of Activation Functions (AFs) used in single and multiple hidden layer Neural Networks (NN), their behavior always raised curiosity, whether used in combination or singly. The popular AFs – Sigmoid, ReLU, and Tanh – have performed prominently well for shallow and deep architectures. Most of the time, AFs are used singly in multi-layered NN, and, to the best of our knowledge, their performance is never studied and analyzed deeply when used in combination. In this manuscript, we experiment on multi-layered NN architecture (both on shallow and deep architectures; Convolutional NN and VGG16) and investigate how well the network responds to using two different AFs (Sigmoid-Tanh, Tanh-ReLU, ReLU-Sigmoid) used alternately against a traditional, single (Sigmoid-Sigmoid, Tanh-Tanh, ReLU-ReLU) combination. Our results show that on using two different AFs, the network achieves better accuracy, substantially lower loss, and faster convergence on 4 computer vision (CV) and 15 Non-CV (NCV) datasets. When using different AFs, not only was the accuracy greater by 6-7%, but we also accomplished convergence twice as fast. We present a case study to investigate the probability of networks suffering vanishing and exploding gradients when using two different AFs. Additionally, we theoretically showed that a composition of two or more AFs satisfies Universal Approximation Theorem (UAT).

Keywords: Activation Function, Universal Approximation function, Neural Networks, convergence.

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Authors: Khaldon Lweesy, Luay Fraiwan, Christoph Maier, Hartmut Dickhaus

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This paper describes a new method for extracting the fetal heart rate (fHR) and the fetal heart rate variability (fHRV) signal non-invasively using abdominal maternal electrocardiogram (mECG) recordings. The extraction is based on the fundamental frequency (Fourier-s) theorem. The fundamental frequency of the mother-s electrocardiogram signal (fo-m) is calculated directly from the abdominal signal. The heart rate of the fetus is usually higher than that of the mother; as a result, the fundamental frequency of the fetal-s electrocardiogram signal (fo-f) is higher than that of the mother-s (fo-f > fo-m). Notch filters to suppress mother-s higher harmonics were designed; then a bandpass filter to target fo-f and reject fo-m is implemented. Although the bandpass filter will pass some other frequencies (harmonics), we have shown in this study that those harmonics are actually carried on fo-f, and thus have no impact on the evaluation of the beat-to-beat changes (RR intervals). The oscillations of the time-domain extracted signal represent the RR intervals. We have also shown in this study that zero-to-zero evaluation of the periods is more accurate than the peak-to-peak evaluation. This method is evaluated both on simulated signals and on different abdominal recordings obtained at different gestational ages.

Keywords: Aabdominal ECG, fetal heart rate variability, frequency harmonics, fundamental frequency.

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Authors: Rabha W. Ibrahim

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We study a Dirichlet boundary value problem for Lane-Emden equation involving two fractional orders. Lane-Emden equation has been widely used to describe a variety of phenomena in physics and astrophysics, including aspects of stellar structure, the thermal history of a spherical cloud of gas, isothermal gas spheres,and thermionic currents. However, ordinary Lane-Emden equation does not provide the correct description of the dynamics for systems in complex media. In order to overcome this problem and describe dynamical processes in a fractalmedium, numerous generalizations of Lane-Emden equation have been proposed. One such generalization replaces the ordinary derivative by a fractional derivative in the Lane-Emden equation. This gives rise to the fractional Lane-Emden equation with a single index. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index. The contraction mapping principle and Krasnoselskiis fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space. Ulam-Hyers stability for iterative Cauchy fractional differential equation is defined and studied.

Keywords: Fractional calculus, fractional differential equation, Lane-Emden equation, Riemann-Liouville fractional operators, Volterra integral equation.

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Authors: Alireza Gholami, Amir H. D. Markazi

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In this paper, an observer-based direct adaptive fuzzy sliding mode (OAFSM) algorithm is proposed. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. The input connection matrix is used to combine the sliding surfaces of individual subsystems, and an adaptive fuzzy algorithm is used to estimate an equivalent sliding mode control input directly. The fuzzy membership functions, which were determined by time consuming try and error processes in previous works, are adjusted by adaptive algorithms. The other advantage of the proposed controller is that the input gain matrix is not limited to be diagonal, i.e. the plant could be over/under actuated provided that controllability and observability are preserved. An observer is constructed to directly estimate the state tracking error, and the nonlinear part of the observer is constructed by an adaptive fuzzy algorithm. The main advantage of the proposed observer is that, the measured outputs is not limited to the first entry of a canonical-form state vector. The closed-loop stability of the proposed method is proved using a Lyapunov-based approach. The proposed method is applied numerically on a multi-link robot manipulator, which verifies the performance of the closed-loop control. Moreover, the performance of the proposed algorithm is compared with some conventional control algorithms.

Keywords: Adaptive algorithm, fuzzy systems, membership functions, observer.

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Authors: Vijay R. Khawale, Shashank B. Thakare

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The experiment was carried out to study the performance of solar crop dryer coupled with reversed absorber type solar air heater (SD2). Excel software is used to analyse the raw data obtained from the drying experiment to develop a model. An attempt is made in this paper to correlate the collector efficiency, dryer efficiency and pick-up efficiency. All these efficiencies are dependent on the parameters such as solar flux, ambient temperature, collector outlet temperature and moisture content. The simulation equation was developed to predict the values of collector efficiency. The parameters a, n and drying constant k were determined from a plot of curve using a drying models. Experimental data of drying red chili in conventional solar dryer and solar dryer coupled with reversed absorber solar air heater was compared by fitting with three drying models. The moisture content will be rapidly reduced in solar dryer with reversed absorber due to higher drying temperatures. The best fit model was selected to describe the drying behavior of red chili. For SD2 the values of the coefficient of determination (R²=0.997), mean bias error (MBE=0.00026) and root mean square error (RMSE=0.016) were used to determine the goodness or the quality of the fit. Pages model showed a better fit to drying red chili among Newton model and Henderson & Pabis model.

Keywords: Solar dryer, red chili, reversed absorber, reflector, Buckingham pi theorem, drying model.

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Authors: Meriem Bahij, Ahmed Nafidi, Boujemâa Achchab, Sílvio M. A. Gama, José A. O. Matos

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Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Therefore, the purpose of stochastic modeling is to estimate the probability of outcomes within a forecast, i.e. to be able to predict what conditions or decisions might happen under different situations. In the present study, we present a model of a stochastic diffusion process based on the bi-Weibull distribution function (its trend is proportional to the bi-Weibull probability density function). In general, the Weibull distribution has the ability to assume the characteristics of many different types of distributions. This has made it very popular among engineers and quality practitioners, who have considered it the most commonly used distribution for studying problems such as modeling reliability data, accelerated life testing, and maintainability modeling and analysis. In this work, we start by obtaining the probabilistic characteristics of this model, as the explicit expression of the process, its trends, and its distribution by transforming the diffusion process in a Wiener process as shown in the Ricciaardi theorem. Then, we develop the statistical inference of this model using the maximum likelihood methodology. Finally, we analyse with simulated data the computational problems associated with the parameters, an issue of great importance in its application to real data with the use of the convergence analysis methods. Overall, the use of a stochastic model reflects only a pragmatic decision on the part of the modeler. According to the data that is available and the universe of models known to the modeler, this model represents the best currently available description of the phenomenon under consideration.

Keywords: Diffusion process, discrete sampling, likelihood estimation method, simulation, stochastic diffusion equation, trends functions, bi-parameters Weibull density function.

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Authors: Jihad S. Daba (Jean-Pierre Dubois), Philip Jreije

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Speckled images arise when coherent microwave, optical, and acoustic imaging techniques are used to image an object, surface or scene. Examples of coherent imaging systems include synthetic aperture radar, laser imaging systems, imaging sonar systems, and medical ultrasound systems. Speckle noise is a form of object or target induced noise that results when the surface of the object is Rayleigh rough compared to the wavelength of the illuminating radiation. Detection and estimation in images corrupted by speckle noise is complicated by the nature of the noise and is not as straightforward as detection and estimation in additive noise. In this work, we derive stochastic models for speckle noise, with an emphasis on speckle as it arises in medical ultrasound images. The motivation for this work is the problem of segmentation and tissue classification using ultrasound imaging. Modeling of speckle in this context involves partially developed speckle model where an underlying Poisson point process modulates a Gram-Charlier series of Laguerre weighted exponential functions, resulting in a doubly stochastic filtered Poisson point process. The statistical distribution of partially developed speckle is derived in a closed canonical form. It is observed that as the mean number of scatterers in a resolution cell is increased, the probability density function approaches an exponential distribution. This is consistent with fully developed speckle noise as demonstrated by the Central Limit theorem.

Keywords: Doubly stochastic filtered process, Poisson point process, segmentation, speckle, ultrasound

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Authors: Luiz G. Véras, Felipe L. Medeiros, Lamartine F. Guimarães

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This work approaches the automatic planning of paths for Unmanned Aerial Vehicles (UAVs) through the application of the Rapidly Exploring Random Tree Star-Smart (RRT*-Smart) algorithm. RRT*-Smart is a sampling process of positions of a navigation environment through a tree-type graph. The algorithm consists of randomly expanding a tree from an initial position (root node) until one of its branches reaches the final position of the path to be planned. The algorithm ensures the planning of the shortest path, considering the number of iterations tending to infinity. When a new node is inserted into the tree, each neighbor node of the new node is connected to it, if and only if the extension of the path between the root node and that neighbor node, with this new connection, is less than the current extension of the path between those two nodes. RRT*-smart uses an intelligent sampling strategy to plan less extensive routes by spending a smaller number of iterations. This strategy is based on the creation of samples/nodes near to the convex vertices of the navigation environment obstacles. The planned paths are smoothed through the application of the method called quintic pythagorean hodograph curves. The smoothing process converts a route into a dynamically-viable one based on the kinematic constraints of the vehicle. This smoothing method models the hodograph components of a curve with polynomials that obey the Pythagorean Theorem. Its advantage is that the obtained structure allows computation of the curve length in an exact way, without the need for quadratural techniques for the resolution of integrals.

Keywords: Path planning, path smoothing, Pythagorean hodograph curve, RRT*-Smart.

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Authors: Mohsen Nikaein

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Because of importance of energy, optimization of power generation systems is necessary. Gas turbine cycles are suitable manner for fast power generation, but their efficiency is partly low. In order to achieving higher efficiencies, some propositions are preferred such as recovery of heat from exhaust gases in a regenerator, utilization of intercooler in a multistage compressor, steam injection to combustion chamber and etc. However thermodynamic optimization of gas turbine cycle, even with above components, is necessary. In this article multi-objective genetic algorithms are employed for Pareto approach optimization of Regenerative-Intercooling-Gas Turbine (RIGT) cycle. In the multiobjective optimization a number of conflicting objective functions are to be optimized simultaneously. The important objective functions that have been considered for optimization are entropy generation of RIGT cycle (Ns) derives using Exergy Analysis and Gouy-Stodola theorem, thermal efficiency and the net output power of RIGT Cycle. These objectives are usually conflicting with each other. The design variables consist of thermodynamic parameters such as compressor pressure ratio (Rp), excess air in combustion (EA), turbine inlet temperature (TIT) and inlet air temperature (T0). At the first stage single objective optimization has been investigated and the method of Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used for multi-objective optimization. Optimization procedures are performed for two and three objective functions and the results are compared for RIGT Cycle. In order to investigate the optimal thermodynamic behavior of two objectives, different set, each including two objectives of output parameters, are considered individually. For each set Pareto front are depicted. The sets of selected decision variables based on this Pareto front, will cause the best possible combination of corresponding objective functions. There is no superiority for the points on the Pareto front figure, but they are superior to any other point. In the case of three objective optimization the results are given in tables.

Keywords: Exergy, Entropy Generation, Brayton Cycle, DesignParameters, Optimization, Genetic Algorithm, Multi-Objective.

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Authors: Rawaa H. El-Bidweihy, Hisham M. Abdelsalam, Ihab A. El-Khodary

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Bayesian networks are now considered to be a promising tool in the field of energy with different applications. In this study, the aim was to indicate the states of a previous constructed Bayesian network related to the solar energy in Egypt and the factors affecting its market share, depending on the followed data distribution type for each factor, and using either the Z-distribution approach or the Chebyshev’s inequality theorem. Later on, the separate and the conditional probabilities of the states of each factor in the Bayesian network were derived, either from the collected and scrapped historical data or from estimations and past studies. Results showed that we could use the constructed model for scenario and decision analysis concerning forecasting the total percentage of the market share of the solar energy in Egypt by 2035 and using it as a stable renewable source for generating any type of energy needed. Also, it proved that whenever the use of the solar energy increases, the total costs decreases. Furthermore, we have identified different scenarios, such as the best, worst, 50/50, and most likely one, in terms of the expected changes in the percentage of the solar energy market share. The best scenario showed an 85% probability that the market share of the solar energy in Egypt will exceed 10% of the total energy market, while the worst scenario showed only a 24% probability that the market share of the solar energy in Egypt will exceed 10% of the total energy market. Furthermore, we applied policy analysis to check the effect of changing the controllable (decision) variable’s states acting as different scenarios, to show how it would affect the target nodes in the model. Additionally, the best environmental and economical scenarios were developed to show how other factors are expected to be, in order to affect the model positively. Additional evidence and derived probabilities were added for the weather dynamic nodes whose states depend on time, during the process of converting the Bayesian network into a dynamic Bayesian network.

Keywords: Bayesian network, Chebyshev, decision variable, dynamic Bayesian network, Z-distribution

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