Search results for: nonlinear experimental data

Authors: Ga Ye Kim, Hee Sun Kim, Yeong Soo Shin

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Many studies have been done on the repair and strengthening method of concrete structure, so far. The traditional retrofit method was to attach fiber sheet such as CFRP (Carbon Fiber Reinforced Polymer), GFRP (Glass Fiber Reinforced Polymer) and AFRP (Aramid Fiber Reinforced Polymer) on the concrete structure. However, this method had many downsides in that there are a risk of debonding and an increase in displacement by a shortage of structure section. Therefore, it is effective way to enlarge the structural member with polymer mortar or Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) as a means of strengthening concrete structure. This paper intends to investigate structural performance of reinforced concrete (RC) beams enlarged with polymer mortar and compare the experimental results with analytical results. Nonlinear finite element analyses were conducted to compare the experimental results and predict structural behavior of retrofitted RC beams accurately without cost consuming experimental process. In addition, this study aims at comparing differences of retrofit material between commonly used material (polymer mortar) and recently used material (UHPFRC) by conducting nonlinear finite element analyses. In the first part of this paper, the RC beams having different cover type were fabricated for the experiment and the size of RC beams was 250 millimeters in depth, 150 millimeters in width and 2800 millimeters in length. To verify the experiment, nonlinear finite element models were generated using commercial software ABAQUS 6.10-3. From this study, both experimental and analytical results demonstrated good strengthening effect on RC beam and showed similar tendency. For the future, the proposed analytical method can be used to predict the effect of strengthened RC beam. In the second part of the study, the main parameters were type of retrofit materials. The same nonlinear finite element models were generated to compare the polymer mortar with UHPFRCC. Two types of retrofit material were evaluated and retrofit effect was verified by analytical results.

Keywords: retrofit material, polymer mortar, UHPFRC, nonlinear finite element analysis

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Authors: Ozden Saygili, Eser Cakti

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The masonry building stock in Istanbul and in other cities of Turkey are exposed to significant earthquake hazard. Determination of the safety of masonry structures against earthquakes is a complex challenge. This study deals with experimental tests and non-linear dynamic analysis of masonry structures modeled through discrete element method. The 1:10 scale model of Mustafa Paşa Mosque was constructed and the data were obtained from the sensors on it during its testing on the shake table. The results were used in the calibration/validation of the numerical model created on the basis of the 1:10 scale model built for shake table testing. 3D distinct element model was developed that represents the linear and nonlinear behavior of the shake table model as closely as possible during experimental tests. Results of numerical analyses with those from the experimental program were compared and discussed.

Keywords: dynamic analysis, non-linear modeling, shake table tests, masonry

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Authors: Hua Cao, Laurent Peyrodie, Olivier Agnani, Cecile Donze

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Multiple sclerosis (MS) is a disease, which affects the central nervous system, and causes balance problem. In clinical, this disorder is usually evaluated using static posturography. Some linear or nonlinear measures, extracted from the posturographic data (i.e. center of pressure, COP) recorded during a balance test, has been used to analyze postural control of MS patients. In this study, the trend (TREND) and the sample entropy (SampEn), two nonlinear parameters were chosen to investigate their relationships with the expanded disability status scale (EDSS) score. Forty volunteers with different EDSS scores participated in our experiments with eyes open (EO) and closed (EC). TREND and two types of SampEn (SampEn1 and SampEn2) were calculated for each combined COP’s position signal. The results have shown that TREND had a weak negative correlation to EDSS while SampEn2 had a strong positive correlation to EDSS. Compared to TREND and SampEn1, SampEn2 showed a better significant correlation to EDSS and an ability to discriminate the MS patients in the EC case. In addition, the outcome of the study suggests that the multi-dimensional nonlinear analysis could provide some information about the impact of disability progression in MS on dynamics of the COP data.

Keywords: balance, multiple sclerosis, nonlinear analysis, postural sway

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Authors: B. X. Tchomeni, A. A. Alugongo, L. M. Masu

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An analytical 4-DOF nonlinear model of a de Laval rotor-stator system based on Energy Principles has been used theoretically and experimentally to investigate fault symptoms in a rotating system. The faults, namely rotor-stator-rub, crack and unbalance are modelled as excitations on the rotor shaft. Mayes steering function is used to simulate the breathing behaviour of the crack. The fault analysis technique is based on waveform signal, orbits and Fast Fourier Transform (FFT) derived from simulated and real measured signals. Simulated and experimental results manifest considerable mutual resemblance of elliptic-shaped orbits and FFT for a same range of test data.

Keywords: a breathing crack, fault, FFT, nonlinear, orbit, rotor-stator rub, vibration analysis

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Authors: Dariush Jafari, Seyed Ali Jafari

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The recommended limit for cadmium concentration in potable water is less than 0.005 mg/L. A continuous biosorption process using indigenous red seaweed, Gracilaria corticata, was performed to remove cadmium from the potable water. The process was conducted under fixed conditions and the breakthrough curves were achieved for three consecutive sorption-desorption cycles. A modeling based on Artificial Neural Network (ANN) was employed to fit the experimental breakthrough data. In addition, a simplified semi empirical model, Thomas, was employed for this purpose. It was found that ANN well described the experimental data (R2>0.99) while the Thomas prediction were a bit less successful with R2>0.97. The adjusted design parameters using the nonlinear form of Thomas model was in a good agreement with the experimentally obtained ones. The results approve the capability of ANN to predict the cadmium concentration in potable water.

Keywords: ANN, biosorption, cadmium, packed-bed, potable water

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Authors: Boo-Sung Koh, Seung-Eock Kim

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In this paper, a direct design using a nonlinear inelastic analysis is suggested. Also, this paper compares the load carrying capacity obtained by a nonlinear inelastic analysis with experiment results to verify the accuracy of the results. The allowable stress design results of a railroad through a plate girder bridge and the safety factor of the nonlinear inelastic analysis were compared to examine the safety performance. As a result, the load safety factor for the nonlinear inelastic analysis was twice as high as the required safety factor under the allowable stress design standard specified in the civil engineering structure design standards for urban magnetic levitation railways, which further verified the advantages of the proposed direct design method.

Keywords: direct design, nonlinear inelastic analysis, residual stress, initial geometric imperfection

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Rakesh Kumar, A. K. Ghosh

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The paper presents the modeling of linear and nonlinear longitudinal aerodynamics using real flight data of Hansa-3 aircraft gathered at low and high angles of attack. The Neural-Gauss-Newton (NGN) method has been applied to model the linear and nonlinear longitudinal dynamics and estimate parameters from flight data. Unsteady aerodynamics due to flow separation at high angles of attack near stall has been included in the aerodynamic model using Kirchhoff’s quasi-steady stall model. NGN method is an algorithm that utilizes Feed Forward Neural Network (FFNN) and Gauss-Newton optimization to estimate the parameters and it does not require any a priori postulation of mathematical model or solving of equations of motion. NGN method was validated on real flight data generated at moderate angles of attack before application to the data at high angles of attack. The estimates obtained from compatible flight data using NGN method were validated by comparing with wind tunnel values and the maximum likelihood estimates. Validation was also carried out by comparing the response of measured motion variables with the response generated by using estimates a different control input. Next, NGN method was applied to real flight data generated by executing a well-designed quasi-steady stall maneuver. The results obtained in terms of stall characteristics and aerodynamic parameters were encouraging and reasonably accurate to establish NGN as a method for modeling nonlinear aerodynamics from real flight data at high angles of attack.

Keywords: parameter estimation, NGN method, linear and nonlinear, aerodynamic modeling

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

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This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: state estimation, control systems, observer systems, nonlinear systems

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Authors: Nicolò Vaiana, Giorgio Serino

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In this paper, a one-dimensional (1d) Parallel Elasto- Plastic Model (PEPM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement, is presented. The parallel modeling concept is applied to discretize the continuously decreasing tangent stiffness function, thus allowing to simulate the dynamic behavior of seismic isolation bearings by putting linear elastic and nonlinear elastic-perfectly plastic elements in parallel. The mathematical model has been validated by comparing the experimental force-displacement hysteresis loops, obtained testing a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted numerically. Good agreement between the simulated and experimental results shows that the proposed model can be an effective numerical tool to predict the forcedisplacement relationship of seismic isolators within relatively large displacements. Compared to the widely used Bouc-Wen model, the proposed one allows to avoid the numerical solution of a first order ordinary nonlinear differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort, and requires the evaluation of only three model parameters from experimental tests, namely the initial tangent stiffness, the asymptotic tangent stiffness, and a parameter defining the transition from the initial to the asymptotic tangent stiffness.

Keywords: base isolation, earthquake engineering, parallel elasto-plastic model, seismic isolators, softening hysteresis loops

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Authors: Hamidullah Binol, Abdullah Bal

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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: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

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In this paper, we considered and applied parametric modeling for some experimental data of dynamical system. In this study, we investigated the different distribution of output measurement from some dynamical systems. Also, with variance processing in experimental data we obtained the region of nonlinearity in experimental data and then identification of output section is applied in different situation and data distribution. Finally, the effect of the spanning the measurement such as variance to identification and limitation of this approach is explained.

Keywords: Gaussian process, nonlinearity distribution, particle filter, system identification

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Authors: Aleksandr I. Korobov, Natalia V. Shirgina, Aleksey I. Kokshaiskiy, Vyacheslav M. Prokhorov

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The paper presents the results of an experimental study of the effect of reverse mechanical load-unloading on the mechanical, linear, and nonlinear elastic properties of n-AMg6/C60 nanocomposite. Samples for experimental studies of n-AMg6/C60 nanocomposite were obtained by grinding AMg6 polycrystalline alloy in a planetary mill with 0.3 wt % of C60 fullerite in an argon atmosphere. The resulting product consisted of 200-500-micron agglomerates of nanoparticles. X-ray coherent scattering (CSL) method has shown that the average nanoparticle size is 40-60 nm. The resulting preform was extruded at high temperature. Modifications of C60 fullerite interferes the process of recrystallization at grain boundaries. In the samples of n-AMg6/C60 nanocomposite, the load curve is measured: the dependence of the mechanical stress σ on the strain of the sample ε under its multi-cycle load-unloading process till its destruction. The hysteresis dependence σ = σ(ε) was observed, and insignificant residual strain ε < 0.005 were recorded. At σ≈500 MPa and ε≈0.025, the sample was destroyed. The destruction of the sample was fragile. Microhardness was measured before and after destruction of the sample. It was found that the loading-unloading process led to an increase in its microhardness. The effect of the reversible mechanical stress on the linear and nonlinear elastic properties of the n-AMg6/C60 nanocomposite was studied experimentally by ultrasonic method on the automated complex Ritec RAM-5000 SNAP SYSTEM. In the n-AMg6/C60 nanocomposite, the velocities of the longitudinal and shear bulk waves were measured with the pulse method, and all the second-order elasticity coefficients and their dependence on the magnitude of the reversible mechanical stress applied to the sample were calculated. Studies of nonlinear elastic properties of the n-AMg6/C60 nanocomposite at reversible load-unloading of the sample were carried out with the spectral method. At arbitrary values of the strain of the sample (up to its breakage), the dependence of the amplitude of the second longitudinal acoustic harmonic at a frequency of 2f = 10MHz on the amplitude of the first harmonic at a frequency f = 5MHz of the acoustic wave is measured. Based on the results of these measurements, the values of the nonlinear acoustic parameter in the n-AMg6/C60 nanocomposite sample at different mechanical stress were determined. The obtained results can be used in solid-state physics, materials science, for development of new techniques for nondestructive testing of structural materials using methods of nonlinear acoustic diagnostics. This study was supported by the Russian Science Foundation (project №14-22-00042).

Keywords: nanocomposite, generation of acoustic harmonics, nonlinear acoustic parameter, hysteresis

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Authors: A. Keshavarz, Z. Roosta

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In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: paraxial group transformation, nonlocal nonlinear media, cos-Gaussian beam, ABCD law

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Authors: A. Giniatoulline

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A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

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Authors: Mounir Bekaik, Messaoud Ramdani

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We present in this work a new technique of stabilization for fault nonlinear systems. The approach we adopt focus on a fuzzy Luenverger observer. The T-S approximation of the nonlinear observer is based on fuzzy C-Means clustering algorithm to find local linear subsystems. The MOESP identification approach was applied to design an empirical model describing the subsystems state variables. The gain of the observer is given by the minimization of the estimation error through Lyapunov-krasovskii functional and LMI approach. We consider a three tank hydraulic system for an illustrative example.

Keywords: nonlinear system, fuzzy, faults, TS, Lyapunov-Krasovskii, observer

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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: Farhad Asadi, Mohammad Javad Mollakazemi, Aref Ghafouri

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Recent research in neural networks science and neuroscience for modeling complex time series data and statistical learning has focused mostly on learning from high input space and signals. Local linear models are a strong choice for modeling local nonlinearity in data series. Locally weighted projection regression is a flexible and powerful algorithm for nonlinear approximation in high dimensional signal spaces. In this paper, different learning scenario of one and two dimensional data series with different distributions are investigated for simulation and further noise is inputted to data distribution for making different disordered distribution in time series data and for evaluation of algorithm in locality prediction of nonlinearity. Then, the performance of this algorithm is simulated and also when the distribution of data is high or when the number of data is less the sensitivity of this approach to data distribution and influence of important parameter of local validity in this algorithm with different data distribution is explained.

Keywords: local nonlinear estimation, LWPR algorithm, online training method, locally weighted projection regression method

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Authors: Hyun-Woo Cho

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Automatic process monitoring schemes are designed to give early warnings for unusual process events or abnormalities as soon as possible. For this end, various techniques have been developed and utilized in various industrial processes. It includes multivariate statistical methods, representation skills in reduced spaces, kernel-based nonlinear techniques, etc. This work presents a nonlinear empirical monitoring scheme for batch type production processes with incomplete process measurement data. While normal operation data are easy to get, unusual fault data occurs infrequently and thus are difficult to collect. In this work, noise filtering steps are added in order to enhance monitoring performance by eliminating irrelevant information of the data. The performance of the monitoring scheme was demonstrated using batch process data. The results showed that the monitoring performance was improved significantly in terms of detection success rate of process fault.

Keywords: batch process, monitoring, measurement, kernel method

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation.

Keywords: new method AGM, sets of coupled nonlinear equations at engineering field, waves equations, integro-differential, fluid and thermal

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Authors: Karima Kimouche

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In this paper, we consider the asymptotic problems in spectral analysis of stationary causal random fields. We impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear random fields. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given.

Keywords: spatial nonlinear processes, spectral estimators, GMC condition, bootstrap method

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Authors: Mohamed A. Shanan, Ashraf H. El-Zanaty, Kamal G. Metwally

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This paper presents the effect of concrete compressive strength and rectangularity ratio on strength and ductility of normal and high strength reinforced concrete columns confined with transverse steel under axial compressive loading. Nineteen normal strength concrete rectangular columns with different variables tested in this research were used to study the effect of concrete compressive strength and rectangularity ratio on strength and ductility of columns. The paper also presents a nonlinear finite element analysis for these specimens and another twenty high strength concrete square columns tested by other researchers using ANSYS 15 finite element software. The results indicate that the axial force – axial strain relationship obtained from the analytical model using ANSYS are in good agreement with the experimental data. The comparison shows that the ANSYS is capable of modeling and predicting the actual nonlinear behavior of confined normal and high-strength concrete columns under concentric loading. The maximum applied load and the maximum strain have also been confirmed to be satisfactory. Depending on this agreement between the experimental and analytical results, a parametric numerical study was conducted by ANSYS 15 to clarify and evaluate the effect of each variable on strength and ductility of the columns.

Keywords: ANSYS, concrete compressive strength effect, ductility, rectangularity ratio, strength

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Authors: Hyun-Woo Cho

Abstract:

The detection and identification of multivariate manufacturing processes are quite important in order to maintain good product quality. Unusual behaviors or events encountered during its operation can have a serious impact on the process and product quality. Thus they should be detected and identified as soon as possible. This paper focused on the efficient representation of process measurement data in detecting and identifying abnormalities. This qualitative method is effective in representing fault patterns of process data. In addition, it is quite sensitive to measurement noise so that reliable outcomes can be obtained. To evaluate its performance a simulation process was utilized, and the effect of adopting linear and nonlinear methods in the detection and identification was tested with different simulation data. It has shown that the use of a nonlinear technique produced more satisfactory and more robust results for the simulation data sets. This monitoring framework can help operating personnel to detect the occurrence of process abnormalities and identify their assignable causes in an on-line or real-time basis.

Keywords: detection, monitoring, identification, measurement data, multivariate techniques

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Authors: Ahmed M. Ashteyat

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Artificial Neural Network (ANN) models have been widely used in material modeling, inter-correlations, as well as behavior and trend predictions when the nonlinear relationship between system parameters cannot be quantified explicitly and mathematically. In this paper, ANN was used to predict the residual modulus of elasticity (RME) of self compacted concrete (SCC) damaged by heat. The ANN model was built, trained, tested and validated using a total of 112 experimental data sets, gathered from available literature. The data used in model development included temperature, relative humidity conditions, mix proportions, filler types, and fiber type. The result of ANN training, testing, and validation indicated that the RME of SCC, exposed to different temperature and relative humidity levels, could be predicted accurately with ANN techniques. The reliability between the predicated outputs and the actual experimental data was 99%. This show that ANN has strong potential as a feasible tool for predicting residual elastic modulus of SCC damaged by heat within the range of input parameter. The ANN model could be used to estimate the RME of SCC, as a rapid inexpensive substitute for the much more complicated and time consuming direct measurement of the RME of SCC.

Keywords: residual modulus of elasticity, artificial neural networks, self compacted-concrete, material modeling

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Authors: Hung-Sheng Lin, Cheng-Hsuan Li

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Over the past few years, kernel-based algorithms have been widely used to extend some linear feature extraction methods such as principal component analysis (PCA), linear discriminate analysis (LDA), and nonparametric weighted feature extraction (NWFE) to their nonlinear versions, kernel principal component analysis (KPCA), generalized discriminate analysis (GDA), and kernel nonparametric weighted feature extraction (KNWFE), respectively. These nonlinear feature extraction methods can detect nonlinear directions with the largest nonlinear variance or the largest class separability based on the given kernel function. Moreover, they have been applied to improve the target detection or the image classification of hyperspectral images. The double nearest proportion feature extraction (DNP) can effectively reduce the overlap effect and have good performance in hyperspectral image classification. The DNP structure is an extension of the k-nearest neighbor technique. For each sample, there are two corresponding nearest proportions of samples, the self-class nearest proportion and the other-class nearest proportion. The term “nearest proportion” used here consider both the local information and other more global information. With these settings, the effect of the overlap between the sample distributions can be reduced. Usually, the maximum likelihood estimator and the related unbiased estimator are not ideal estimators in high dimensional inference problems, particularly in small data-size situation. Hence, an improved estimator by shrinkage estimation (regularization) is proposed. Based on the DNP structure, LDA is included as a special case. In this paper, the kernel method is applied to extend DNP to kernel-based DNP (KDNP). In addition to the advantages of DNP, KDNP surpasses DNP in the experimental results. According to the experiments on the real hyperspectral image data sets, the classification performance of KDNP is better than that of PCA, LDA, NWFE, and their kernel versions, KPCA, GDA, and KNWFE.

Keywords: feature extraction, kernel method, double nearest proportion feature extraction, kernel double nearest feature extraction

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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Authors: Rajkumar N. Ingle

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In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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Authors: Yasser Rammah, Wolf-Christian Mueller

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Nonlinear triad interactions in incompressible three-dimensional magnetohydrodynamic (3D-MHD) turbulence are studied by analyzing data from high-resolution direct numerical simulations of decaying isotropic (5123 grid points) and forced anisotropic (10242 x256 grid points) turbulence. An accurate numerical approach toward analyzing nonlinear turbulent energy transfer function and triad interactions is presented. It involves the direct numerical examination of every wavenumber triad that is associated with the nonlinear terms in the differential equations of MHD in the inertial range of turbulence. The technique allows us to compute the spectral energy transfer and energy fluxes, as well as the spectral locality property of energy transfer function. To this end, the geometrical shape of each underlying wavenumber triad that contributes to the statistical transfer density function is examined to infer the locality of the energy transfer. Results show that the total energy transfer is local via nonlocal triad interactions in decaying macroscopically isotropic MHD turbulence. In anisotropic MHD, turbulence subject to a strong mean magnetic field the nonlinear transfer is generally weaker and exhibits a moderate increase of nonlocality in both perpendicular and parallel directions compared to the isotropic case. These results support the recent mathematical findings, which also claim the locality of nonlinear energy transfer in MHD turbulence.

Keywords: magnetohydrodynamic (MHD) turbulence, transfer density function, locality function, direct numerical simulation (DNS)

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Authors: Anton S. Perin, Vladimir M. Shandarov

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Compensation for the nonlinear diffraction of narrow laser beams with wavelength of 532 and the formation of photonic waveguides and waveguide circuits due to the contribution of pyroelectric effect to the nonlinear response of lithium niobate crystal have been experimentally demonstrated. Complete compensation for the linear and nonlinear diffraction broadening of light beams is obtained upon uniform heating of an undoped sample from room temperature to 55 degrees Celsius. An analysis of the light-field distribution patterns and the corresponding intensity distribution profiles allowed us to estimate the spacing for the channel waveguides. The observed behavior of bright soliton beams may be caused by their coherent interaction, which manifests itself in repulsion for anti-phase light fields and in attraction for in-phase light fields. The experimental results of this study showed a fundamental possibility of forming optically complex waveguide structures in lithium niobate crystals with pyroelectric mechanism of nonlinear response. The topology of these structures is determined by the light field distribution on the input face of crystalline sample. The optical induction of channel waveguide elements by interacting spatial solitons makes it possible to design optical systems with a more complex topology and a possibility of their dynamic reconfiguration.

Keywords: self-action, soliton, lithium niobate, piroliton, photorefractive effect, pyroelectric effect

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