Search results for: linear and non-linear recession

Authors: Sajana Suwal, Ganesh R. Nhemafuki

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Evaluation of ground response under earthquake shaking is crucial in geotechnical earthquake engineering. Damage due to seismic excitation is mainly correlated to local geological and geotechnical conditions. It is evident from the past earthquakes (e.g. 1906 San Francisco, USA, 1923 Kanto, Japan) that the local geology has strong influence on amplitude and duration of ground motions. Since then significant studies has been conducted on ground motion amplification revealing the importance of influence of local geology on ground. Observations from the damaging earthquakes (e.g. Nigata and San Francisco, 1964; Irpinia, 1980; Mexico, 1985; Kobe, 1995; L’Aquila, 2009) divulged that non-uniform damage pattern, particularly in soft fluvio-lacustrine deposit is due to the local amplification of seismic ground motion. Non-uniform damage patterns are also observed in Kathmandu Valley during 1934 Bihar Nepal earthquake and recent 2015 Gorkha earthquake seemingly due to the modification of earthquake ground motion parameters. In this study, site effects resulting from amplification of soft soil in Kathmandu are presented. A large amount of subsoil data was collected and used for defining the appropriate subsoil model for the Kathamandu valley. A comparative study of one-dimensional total-stress equivalent linear and non-linear site response is performed using four strong ground motions for six sites of Kathmandu valley. In general, one-dimensional (1D) site-response analysis involves the excitation of a soil profile using the horizontal component and calculating the response at individual soil layers. In the present study, both equivalent linear and non-linear site response analyses were conducted using the computer program DEEPSOIL. The results show that there is no significant deviation between equivalent linear and non-linear site response models until the maximum strain reaches to 0.06-0.1%. Overall, it is clearly observed from the results that non-linear site response model perform better as compared to equivalent linear model. However, the significant deviation between two models is resulted from other influencing factors such as assumptions made in 1D site response, lack of accurate values of shear wave velocity and nonlinear properties of the soil deposit. The results are also presented in terms of amplification factors which are predicted to be around four times more in case of non-linear analysis as compared to equivalent linear analysis. Hence, the nonlinear behavior of soil prevails the urgent need of study of dynamic characteristics of the soft soil deposit that can specifically represent the site-specific design spectra for the Kathmandu valley for building resilient structures from future damaging earthquakes.

Keywords: deep soil, equivalent linear analysis, non-linear analysis, site response

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

Keywords: Adomian’s decomposition method, magneto-thermoelasticity, finite conductivity, iteration method, thermal load

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Authors: Fang Li, Xie-Yuan Yin, Xie-Zhen Yin

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Instability and breakup of electrified viscoelastic liquid jets are involved in various applications such as inkjet printing, fuel atomization, the pharmaceutical industry, electrospraying, and electrospinning. Studying on the instability of electrified viscoelastic liquid jets is of theoretical and practical significance. We built a one-dimensional electrified viscoelastic model to study the nonlinear instability behavior of a perfecting conducting, slightly viscoelastic liquid jet under a radial electric field. The model is solved numerically by using an implicit finite difference scheme together with a boundary element method. It is found that under a radial electric field a viscoelastic liquid jet still evolves into a beads-on-string structure with a thin filament connecting two adjacent droplets as in the absence of an electric field. A radial electric field exhibits limited influence on the decay of the filament thickness in the nonlinear evolution process of a viscoelastic jet, in contrast to its great enhancing effect on the linear instability of the jet. On the other hand, a radial electric field can induce axial non-uniformity of the first normal stress difference within the filament. Particularly, the magnitude of the first normal stress difference near the midpoint of the filament can be greatly decreased by a radial electric field. Decreasing the extensional stress by a radial electric field may found applications in spraying, spinning, liquid bridges and others. In addition, the effect of a radial electric field on the formation of satellite droplets is investigated on the parametric plane of the dimensionless wave number and the electrical Bond number. It is found that satellite droplets may be formed for a larger axial wave number at a larger radial electric field. The present study helps us gain insight into the nonlinear instability characteristics of electrified viscoelastic liquid jets.

Keywords: non linear instability, one-dimensional models, radial electric fields, viscoelastic liquid jets

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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: Ahmed Elsayed Ahmed, Ashraf Hafez, A. N. Ouda, Hossam Eldin Hussein Ahmed, Hala Mohamed ABD-Elkader

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Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized,and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end, the model is checked by matching between the behavior of the states of the non-linear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: UAV, equations of motion, modeling, linearization

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Authors: Skezeer John B. Paz, Ederlina G. Nocon

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Finding an optimal binary linear code is a central problem in coding theory. A binary linear code C = [n, k, d] is called optimal if there is no linear code with higher minimum distance d given the length n and the dimension k. There are bounds giving limits for the minimum distance d of a linear code of fixed length n and dimension k. The lower bound which can be taken by construction process tells that there is a known linear code having this minimum distance. The upper bound is given by theoretic results such as Griesmer bound. One way to find an optimal binary linear code is to make the lower bound of d equal to its higher bound. That is, to construct a binary linear code which achieves the highest possible value of its minimum distance d, given n and k. Some optimal binary linear codes were presented by Andries Brouwer in his published table on bounds of the minimum distance d of binary linear codes for 1 ≤ n ≤ 256 and k ≤ n. This was further improved by Markus Grassl by giving a detailed construction process for each code exhibiting the lower bound. In this paper, we construct new optimal binary linear codes by using some construction processes on existing binary linear codes. Particularly, we developed an algorithm applied to the codes already constructed to extend the list of optimal binary linear codes up to 257 ≤ n ≤ 300 for k ≤ 7.

Keywords: bounds of linear codes, Griesmer bound, construction of linear codes, optimal binary linear codes

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Authors: Yosra Baaziz, Moez Labidi

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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: Heiko Weiß, Andreas Meister, Christoph Ament, Nils Dreifke

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Linear actuators are deployed in a wide range of applications. This paper presents the modeling and system identification of a variable excited linear direct drive (LDD). The LDD is designed based on linear hybrid stepper technology exhibiting the characteristic tooth structure of mover and stator. A three-phase topology provides the thrust force caused by alternating strengthening and weakening of the flux of the legs. To achieve best possible synchronous operation, the phases are commutated sinusoidal. Despite the fact that these LDDs provide high dynamics and drive forces, noise emission limits their operation in calm workspaces. To overcome this drawback an additional excitation of the magnetic circuit is introduced to LDD using additional enabling coils instead of permanent magnets. The new degree of freedom can be used to reduce force variations and related noise by varying the excitation flux that is usually generated by permanent magnets. Hence, an identified simulation model is necessary to analyze the effects of this modification. Especially the force variations must be modeled well in order to reduce them sufficiently. The model can be divided into three parts: the current dynamics, the mechanics and the force functions. These subsystems are described with differential equations or nonlinear analytic functions, respectively. Ordinary nonlinear differential equations are derived and transformed into state space representation. Experiments have been carried out on a test rig to identify the system parameters of the complete model. Static and dynamic simulation based optimizations are utilized for identification. The results are verified in time and frequency domain. Finally, the identified model provides a basis for later design of control strategies to reduce existing force variations.

Keywords: force variations, linear direct drive, modeling and system identification, variable excitation flux

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Authors: Jikhil Joseph, Satish Kumar S R.

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Cold-formed steel frames are preferable for framed constructions due to its low seismic weights and results into low seismic forces, but on the contrary, significant lateral deflections are expected under seismic/wind loading. The various factors affecting the lateral stiffness of steel frames are the stiffness of connections, beams and columns. So, by increasing the stiffness of beam, column and making the connections rigid will enhance the lateral stiffness. The present study focused on Structural elements made of rectangular hollow sections and fastened with screwed in-plane moment connections for the building frames. The self-drilling screws can be easily drilled on either side of the connection area with the help of gusset plates. The strength of screwed connections can be made 1.2 times the connecting elements. However, achieving high stiffness in connections is also a challenging job. Hence in addition to beam and column stiffness’s the connection stiffness are also going to be a governing parameter in the lateral deflections of the frames. SAP 2000 Non-linear static analysis has been planned to study the seismic behavior of steel frames. The SAP model will be consisting of nonlinear spring model for the connection to account the semi-rigid connections and the nonlinear hinges will be assigned for beam and column sections according to FEMA 273 guidelines. The reliable spring and hinge parameters will be assigned based on an experimental and analytical database. The non-linear static analysis is mainly focused on the identification of various hinge formations and the estimation of lateral deflection and these will contribute as an inputs for the direct displacement-based Seismic design. The research output from this study are the modelling techniques and suitable design guidelines for the performance-based seismic design of cold-formed steel frames.

Keywords: buckling, cold formed steel, nonlinear static analysis, screwed connections

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

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In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.

Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle

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Authors: Khaled Sandjak, Boualem Tiliouine

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Structural analysis of flexible pavements has been and still is currently performed using multi-layer elastic theory. However, for thinly surfaced pavements subjected to low to medium volumes of traffics, the importance of non-linear stress-strain behaviour of unbound granular materials (UGM) requires the use of more sophisticated numerical models for structural design and performance of such pavements. In the present work, nonlinear unbound aggregates constitutive model is implemented within an axisymmetric finite element code developed to simulate the nonlinear behaviour of pavement structures including two local aggregates of different mineralogical nature, typically used in Algerian pavements. The performance of the mechanical model is examined about its capability of representing adequately, under various conditions, the granular material non-linearity in pavement analysis. In addition, deflection data collected by falling weight deflectometer (FWD) are incorporated into the analysis in order to assess the sensitivity of critical pavement design criteria and pavement design life to the constitutive model. Finally, conclusions of engineering significance are formulated.

Keywords: FWD backcalculations, finite element simulations, Nonlinear resilient behaviour, pavement response and performance, RLT test results, unbound granular materials

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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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Authors: Maamar Yahiaoui, Abdelrrahmene Kechich, Ismail Elkhallile Bousserhene

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This article presents a study in simulation by means of MATLAB/Simulink software of the nonlinear control in positioning of a linear synchronous machine with the esteemed force of load, to have effective control in the estimator in all tests the wished trajectory follows and the disturbance of load start. The results of simulation prove clearly that the control proposed can detect the reference of positioning the value estimates of load force equal to the actual value.

Keywords: mathematical model, Matlab, PMLSM, control, linearization, estimator, force, load, current

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Authors: Hyun-Woo Cho

Abstract:

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

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

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Authors: 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 Karimi Moridani, Mohammad Abdi Zadeh, Zahra Shahiazar Mazraeh

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In recent years, the use of intelligent systems in biomedical engineering has increased dramatically, especially in the diagnosis of various diseases. Also, due to the relatively simple recording of the electrocardiogram signal (ECG), this signal is a good tool to show the function of the heart and diseases associated with it. The aim of this paper is to design an intelligent system for automatically detecting a normal electrocardiogram signal from abnormal one. Using this diagnostic system, it is possible to identify a person's heart condition in a very short time and with high accuracy. The data used in this article are from the Physionet database, available in 2016 for use by researchers to provide the best method for detecting normal signals from abnormalities. Data is of both genders and the data recording time varies between several seconds to several minutes. All data is also labeled normal or abnormal. Due to the low positional accuracy and ECG signal time limit and the similarity of the signal in some diseases with the normal signal, the heart rate variability (HRV) signal was used. Measuring and analyzing the heart rate variability with time to evaluate the activity of the heart and differentiating different types of heart failure from one another is of interest to the experts. In the preprocessing stage, after noise cancelation by the adaptive Kalman filter and extracting the R wave by the Pan and Tampkinz algorithm, R-R intervals were extracted and the HRV signal was generated. In the process of processing this paper, a new idea was presented that, in addition to using the statistical characteristics of the signal to create a return map and extraction of nonlinear characteristics of the HRV signal due to the nonlinear nature of the signal. Finally, the artificial neural networks widely used in the field of ECG signal processing as well as distinctive features were used to classify the normal signals from abnormal ones. To evaluate the efficiency of proposed classifiers in this paper, the area under curve ROC was used. The results of the simulation in the MATLAB environment showed that the AUC of the MLP and SVM neural network was 0.893 and 0.947, respectively. As well as, the results of the proposed algorithm in this paper indicated that the more use of nonlinear characteristics in normal signal classification of the patient showed better performance. Today, research is aimed at quantitatively analyzing the linear and non-linear or descriptive and random nature of the heart rate variability signal, because it has been shown that the amount of these properties can be used to indicate the health status of the individual's heart. The study of nonlinear behavior and dynamics of the heart's neural control system in the short and long-term provides new information on how the cardiovascular system functions, and has led to the development of research in this field. Given that the ECG signal contains important information and is one of the common tools used by physicians to diagnose heart disease, but due to the limited accuracy of time and the fact that some information about this signal is hidden from the viewpoint of physicians, the design of the intelligent system proposed in this paper can help physicians with greater speed and accuracy in the diagnosis of normal and patient individuals and can be used as a complementary system in the treatment centers.

Keywords: neart rate variability, signal processing, linear and non-linear features, classification methods, ROC Curve

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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: Aristeidis Samitas, Evangelos Vasileiou

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The aim of this study is to examine the month and the trading month effect under changing financial trends. We choose the Greek stock market to implement our assumption because there are clear and long term periods of financial growth and recession. Daily financial data from Athens Exchange General Index for the period 2002-2012 are considered. The paper employs several linear and non-linear models, although the TGARCH asymmetry model best fits in this sample and for this reason we mainly present the TGARCH results. Empirical results show that changing economic and financial conditions influences the calendar effects. Especially, the trading month effect totally changes in each fortnight according to the financial trend. On the other hand, in Greece the January effect exists during the growth periods, although it does not exist when the financial trend changes. The findings are helpful to anybody who invest and deals with the Greek stock market. Moreover, they may pave the way for an alternative calendar anomalies research approach, so it may be useful to investors who take into account these anomalies when they draw their investment strategy.

Keywords: month effect, trading month effect, economic cycles, crisis

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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: Brouri Adil, Giri Fouad

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The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent.

Keywords: Wiener-Hammerstein systems, Fourier series expansions, frequency identification, automation science

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Authors: Wesam Jasim, Dongbing Gu

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This paper presents an iterative linear quadratic regulator optimal control technique to solve the problem of quadrotors path tracking. The dynamic motion equations are represented based on unit quaternion representation and include some modelled aerodynamical effects as a nonlinear part. Simulation results prove the ability and effectiveness of iLQR to stabilize the quadrotor and successfully track different paths. It also shows that iLQR controller outperforms LQR controller in terms of fast convergence and tracking errors.

Keywords: iLQR controller, optimal control, path tracking, quadrotor UAVs

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Authors: Mohamed Khiatine, Ramdane Bahar

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The research performed during the last years has revealed that the seismic response of the soilis significantly non linear and hysteresis to the deformationsitundergoes during earthquakes and notably during violent shaking. This nonlinear behavior of soils can be characterized by curves showing the evolution of shearmodulus and damping versus distortion. Also, in this context, geotechnical seismic engineering problems often require the characterization of dynamic soil properties over a wide range of deformation. This determination of dynamic soil properties is key to predict the seismic response of soils for important civil engineering structures. This communication discusses a numerical analysis method for evaluating the nonlinear dynamic properties of soils in Algeriausing the FLAC2D software and the database resulting from geophysical and geotechnical studies when laboratory dynamic tests are not available. The nonlinear model proposed by Ramberg-Osgood and limited by the Mohr-coulomb criterion is used.

Keywords: degradation, shear modulus, damping, ramberg-osgood, numerical analysis.

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

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This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: Lukas Reznak, Maria Reznakova

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Recession of an economy has a profound negative effect on all involved stakeholders. It follows that timely prediction of recessions has been of utmost interest both in the theoretical research and in practical macroeconomic modelling. Current mainstream of recession prediction is based on standard OLS models of continuous GDP using macroeconomic data. This approach is not suitable for two reasons: the standard continuous models are proving to be obsolete and the macroeconomic data are unreliable, often revised many years retroactively. The aim of the paper is to explore a different branch of recession forecasting research theory and verify the findings on real data of the Czech Republic and Germany. In the paper, the authors present a family of discrete choice probit models with parameters estimated by the method of maximum likelihood. In the basic form, the probits model a univariate series of recessions and expansions in the economic cycle for a given country. The majority of the paper deals with more complex model structures, namely dynamic and bivariate extensions. The dynamic structure models the autoregressive nature of recessions, taking into consideration previous economic activity to predict the development in subsequent periods. Bivariate extensions utilize information from a foreign economy by incorporating correlation of error terms and thus modelling the dependencies of the two countries. Bivariate models predict a bivariate time series of economic states in both economies and thus enhance the predictive performance. A vital enabler of timely and successful recession forecasting are reliable and readily available data. Leading indicators, namely the yield curve and the stock market indices, represent an ideal data base, as the pieces of information is available in advance and do not undergo any retroactive revisions. As importantly, the combination of yield curve and stock market indices reflect a range of macroeconomic and financial market investors’ trends which influence the economic cycle. These theoretical approaches are applied on real data of Czech Republic and Germany. Two models for each country were identified – each for in-sample and out-of-sample predictive purposes. All four followed a bivariate structure, while three contained a dynamic component.

Keywords: bivariate probit, leading indicators, recession forecasting, Czech Republic, Germany

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Authors: Haowen Xi

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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: 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: 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: Kedar Hardikar, Joe Varghese

Abstract:

Conductive adhesives have found wide-ranging applications in electronics industry ranging from fixing a defective conductor on printed circuit board (PCB) attaching an electronic component in an assembly to protecting electronics components by the formation of “Faraday Cage.” The reliability requirements for the conductive adhesive vary widely depending on the application and expected product lifetime. While the conductive adhesive is required to maintain the structural integrity, the electrical performance of the associated sub-assembly can be affected by the degradation of conductive adhesive. The degradation of the adhesive is dependent upon the highly varied use case. The conventional approach to assess the reliability of the sub-assembly involves subjecting it to the standard environmental test conditions such as high-temperature high humidity, thermal cycling, high-temperature exposure to name a few. In order to enable projection of test data and observed failures to predict field performance, systematic development of an acceleration factor between the test conditions and field conditions is crucial. Common acceleration factor models such as Arrhenius model are based on rate kinetics and typically rely on an assumption of linear degradation in time for a given condition and test duration. The application of interest in this work involves conductive adhesive used in an electronic circuit of a capacitive sensor. The degradation of conductive adhesive in high temperature and humidity environment is quantified by the capacitance values. Under such conditions, the use of established models such as Hallberg-Peck model or Eyring Model to predict time to failure in the field typically relies on linear degradation rate. In this particular case, it is seen that the degradation is nonlinear in time and exhibits a square root t dependence. It is also shown that for the mechanism of interest, the presence of moisture is essential, and the dominant mechanism driving the degradation is the diffusion of moisture. In this work, a framework is developed to incorporate nonlinear degradation of the conductive adhesive for the development of an acceleration factor. This method can be extended to applications where nonlinearity in degradation rate can be adequately characterized in tests. It is shown that depending on the expected product lifetime, the use of conventional linear degradation approach can overestimate or underestimate the field performance. This work provides guidelines for suitability of linear degradation approximation for such varied applications

Keywords: conductive adhesives, nonlinear degradation, physics of failure, acceleration factor model.

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