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Prediction of the Spatiotemporal Dynamics of von Kármán Vortices by ANFIS
Abstract
Wakes and vortices are commonly observed in fluid flows around bluff bodies, a phenomenon which is called vortex shedding. Such vortices are named as von Kármán vortices since their first investigation is performed by the leading fluid dynamicist Theodore von Kármán. Although initially observed in the studies of fluid flows, the same phenomenon can also be observed in different branches of mediums such as condensates. It is possible to model these vortices using numerical techniques that solve the Navier-Stokes equations, however, some dynamic equations such as the complex Ginzburg-Landau (GL) equation is another frequently used model for these purposes. In this paper, we solve the GL equation using a spectral scheme and Runge-Kutta time integrator to simulate the dynamics of von Kármán vortices around a cylinder. The prediction of temporal dynamics is of crucial importance to avoid excessive shedding, resonance, and structural damage of the engineering structures. With this motivation, here we examine the predictability of the von Kármán vortices using the adaptive neuro-fuzzy inference system (ANFIS) which relies on a rule-based relationship between input values and output values that are learned adaptively by being trained with the data set analyzed. We show that the temporal dynamics of the von Kármán vortices can be adequately performed by ANFIS and we report the prediction success of the ANFIS in the solution of this complex prediction problem measured by the coefficient of determination and the root mean square error (RMSE) values. Our results can be used for predicting, interpolating, and extrapolating vortex data to analyze fluid dynamics problems and to develop control strategies for avoiding structural failures.Keywordsvon Kármán vorticesGinzburg-Landau equationANFIS
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Stock market plays a key role in economical and social organization of a country. Stock market forecasting is highly demanding and most challenging task for investors, professional analyst and researchers in the financial market due to highly noisy, nonparametric, volatile, complex, non-linear, dynamic and chaotic nature of stock price time series. Prediction of stock market is a crucial task and prominent research area in financial domain as investing in stock market involves higher risk. However with the development of computational intelligent methods it is possible to reduce most of the risk. In this survey paper, our focus is on application of computational intelligent approaches such as artificial neural network, fuzzy logic, genetic algorithms and other evolutionary techniques for stock market forecasting. This paper presents an up-to-date survey of existing literature on stock market forecasting based on computational intelligent methods. In this article, the selected papers are organized and discussed according to six main point of view: (1) the stock market analyzed and the related dataset, (2) the type of input variables investigated, (3) the pre-processing techniques used, (4) the feature selection techniques to choose effective variables, (5) the forecasting models to deal with the stock price forecasting problem and (6) performance metrics utilized to evaluate the models. The major contribution of this work is to provide the researcher and financial analyst a systematic approach for development of intelligent methodology to forecast stock market. This paper also presents the outlines of proposed work with the aim to enhance the performance of existing techniques.
In this paper we numerically analyze the 1D self-localized solutions of the Kundu-Eckhaus equation (KEE) in nonlinear waveguides using the spectral renormalization method (SRM) and compare our findings with those solutions of the nonlinear Schrödinger equation (NLSE). For cubic-quintic nonlinearity with Raman effect, as a benchmark problem we numerically construct single, dual and N-soliton solutions for the zero optical potential, i.e. V=0, which are analytically derived before. We show that self-localized soliton solutions of the KEE with cubic-quintic nonlinearity and Raman effect do exist, at least for a range of parameters, for the photorefractive lattices with optical potentials in the form of V=Iocos2(x). Additionally, we also show that self-localized soliton solutions of the KEE with saturable cubic-quintic nonlinearity and Raman effect do also exist for some range of parameters. However, for all of the cases considered, these self-localized solitons are found to be unstable. We compare our findings for the KEE with their NLSE analogs and discuss our results. Keywords: Nonlinear optics, Kundu-Eckhaus equation, Spectral renormalization method
Bubble column reactors are ubiquitous in engineering processes. They are used in waste water treatment, as well as in the chemical, pharmaceutical, biological and food industry. Mass transfer and mixing, as well as biochemical or chemical reactions in such reactors are determined by the hydrodynamics of the bubbly flow. The hydrodynamics of bubbly flows is dominated by bubble wake interactions. Despite the fact that bubble wakes have been investigated intensively in the past, there is still a lack of knowledge about how mass transfer from bubbles is influenced by bubble wake interactions in detail. The scientific scope of this work is to answer the question how bubble wakes are influenced by external flow structures like a vortex street behind a cylinder. For this purpose, the flow field in the vicinity of a single bubble is investigated systematically with high spatial and temporal resolution. High-speed Particle Image Velocimetry (PIV) measurements are conducted monitoring the flow structure in the equatorial plane of the single bubble. It is shown that the root mean square (RMS) velocity profiles downstream the bubble are influenced significantly by the interaction of vortices. In the presence of a vortex street, the deceleration of the fluid behind the bubble is compensated earlier than in the absence of a vortex street. This happens due to momentum transfer by cross-mixing. Both effects indicate that the interaction of vortices enhances the cross-mixing close to the bubble. Time series of instantaneous velocity fields show the formation of an inner shear layer and coupled vortices. In conclusion, this study shows in detail how the bubble wake is influenced by a vortex street and gives deep insights into possible effects on mixing and mass transfer in bubbly flows.
In this study we discuss the shapes and statistics of the rogue (freak) waves emerging due to wave-current interactions. With this purpose, we use a simple governing equation which is a nonlinear Schrödinger equation (NLSE) extended by R. Smith (1976). This extended NLSE accounts for the effects of current gradient on the nonlinear dynamics of the ocean surface near blocking point. Using a split-step scheme we show that the extended NLSE of Smith is unstable against random chaotic perturbation in the current profile. Therefore the monochromatic wave field with unit amplitude turns into a chaotic sea state with many peaks. By comparing the numerical and analytical results, we show that rogue waves due to perturbations in the current profile are in the form of rational rogue wave solutions of the NLSE. We also discuss the effects of magnitude of the chaotic current profile perturbations on the statistics of the rogue wave generation at the ocean surface. The extension term in Smith's extended NLSE causes phase shifts and it does not change the total energy level of the wave field. Using the methodology adopted in this study, the dynamics of rogue wave occurrence on the ocean surface due to blocking effect of currents can be studied. This enhances the safety of the offshore operations and ocean travel.
In this paper an approach for decreasing the computational effort required
for the split-step Fourier method (SSFM) is introduced. It is shown that using
the sparsity property of the simulated signals, the compressive sampling
algorithm can be used as a very efficient tool for the split-step spectral
simulations of various phenomena which can be modeled by using differential
equations. The proposed method depends on the idea of using a smaller number of
spectral components compared to the classical split-step Fourier method with a
high number of components. After performing the time integration with a smaller
number of spectral components and using the compressive sampling technique with
l1 minimization, it is shown that the sparse signal can be reconstructed with a
significantly better efficiency compared to the classical split-step Fourier
method. Proposed method can be named as compressive split-step Fourier method
(CSSFM). For testing of the proposed method the Nonlinear Schrodinger Equation
and its one-soliton and two-soliton solutions are considered.
A new electromagnetic energy harvester for harnessing energy from vibration induced by Kármán vortex street is proposed. It converts flow energy into electrical energy by fluid flow, vortex shedding from a bluff body and electromagnetic induction. An analytical design method for the energy harvester is developed. A prototype of the energy harvester is fabricated and tested. The prototype has a volume of 37.9 cm3. Experimental results show that an output peak-to-peak voltage of nearly 20 mV in average is generated when the excitation pressure oscillates with an amplitude of 0.3 kPa and a frequency of about 62 Hz. By detecting the voltage drop across a matched load, the instantaneous power is determined as 1.77 μW under a pressure fluctuation frequency of 62 Hz and a pressure amplitude of 0.3 kPa in the Kármán vortex street.
The complex Ginzburg–Landau equation (CGLE), probably the most celebrated nonlinear equation in physics, describes generically the dynamics of oscillating, spatially extended systems close to the onset of oscillations. Using symmetry arguments, this article gives an easy access to this equation and an introduction into the rich spatio-temporal behaviour it describes. Starting out from the familiar linear oscillator, we first show how the generic model for an individual nonlinear oscillator, the so-called Stuart–Landau equation, can be derived from symmetry arguments. Then, we extend our symmetry considerations to spatially extended systems, arriving at the CGLE. A comparison of diffusively coupled linear and nonlinear oscillators makes apparent the source of instability in the latter systems. A concise survey of the most typical patterns in 1D and 2D is given. Finally, more recent extensions of the CGLE are discussed that comprise external, time-periodic forcing as well as nonlocal and global spatial coupling.
Vortex shedding from an obstacle potential moving in a Bose-Einstein condensate is investigated. Long-lived alternately aligned vortex pairs are found to form in the wake, which is similar to the Bénard-von Kármán vortex street in classical viscous fluids. Various patterns of vortex shedding are systematically studied and the drag force on the obstacle is calculated. It is shown that the phenomenon can be observed in a trapped system.
The fluid-structure interaction (FSI) in case of fish swimming in the vortex street is investigated by numerical simulations. The vortex street is generated by a D-section cylinder. A 2-D fish model is placed on the downstream centerline of the bluff cylinder at a distance of 4 diameters away from the center of the cylinder. To simulate the fish body undulation and movement, the moving mesh is generated by a coupling approach based on the radial basis function and the overset grid technology. The Navier-Stokes equation in the arbitrary Lagrangian-Eulerian form is solved by coupling with the kinematics equation. Three cases are investigated: in a stationary position without deformation, a passive locomotion without deformation, and an active deformation based on the Kármán gait model. The results indicate that the fish body is acted by an alternating force and moment when it is located in the centerline of the vortex street. Furthermore, the fish could extract sufficient kinetic energy to overcome the drag under suitable conditions even when it keeps rigid and out of the suction zone. When the fish body undulates based on the Kármán gait model, the interaction is evidently shown between the fish body and the vortices. The theoretical analysis demonstrates that the lateral force and the moment acting on the fish body vary in a cosine formula, with the lateral translation and the body rotation as a result. This study focuses on the behavior of the fish body in the bluff cylinder wake and reproduces some phenomena observed in the experiments. Besides, the Kármán gait model is also theoretically analyzed, for the further exploration of the FSI mechanism in case of fish swimming.
In this paper, we discuss the usage and implementation of the compressive sensing (CS) for the efficient measurement and analysis of the von Krmn vortices. We consider two different flow fields, the flow fields around a circle and an ellipse. We solve the governing k−ϵ transport equations numerically in order to model the flow fields around these bodies. Using the time series of the drag, CD, and the lift, CL, coefficients, and their Fourier spectra, we show that compressive sampling can be effectively used to measure and analyze Von Krmn vortices. We discuss the effects of the number of samples on reconstruction and the benefits of using compressive sampling over the classical Shannon sampling in the flow measurement and analysis where Von Krmn vortices are present. We comment on our findings and indicate their possible usage areas and extensions. Our results can find many important applications including but are not limited to measure, control, and analyze vibrations around coastal and offshore structures, bridges, aerodynamics, and Bose-Einstein condensation, just to name a few.
Abstract. Breast cancer is the second leading cause of death for women, so accurate early detection can help decrease breast cancer mortality rates. Computer-aided detection allows radiologists to detect abnormalities efficiently. Medical images are sources of information relevant to the detection and diagnosis of various diseases and abnormalities. Several modalities allow radiologists to study the internal structure, and these modalities have been met with great interest in several types of research. In some medical fields, each of these modalities is of considerable significance. This study aims at presenting a review that shows the new applications of machine learning and deep learning technology for detecting and classifying breast cancer and provides an overview of progress in this area. This review reflects on the classification of breast cancer utilizing multi-modalities medical imaging. Details are also given on techniques developed to facilitate the classification of tumors, non-tumors, and dense masses in various medical imaging modalities. It first provides an overview of the different approaches to machine learning, then an overview of the different deep learning techniques and specific architectures for the detection and classification of breast cancer. We also provide a brief overview of the different image modalities to give a complete overview of the area. In the same context, this review was performed using a broad variety of research databases as a source of information for access to various field publications. Finally, this review summarizes the future trends and challenges in the classification and detection of breast cancer.
This paper aims to reduce the setup cost of water supply systems (SCWSS) by decreasing the peak values at water consumptions Water supply system (WSS) is designed by paying attention to worst scenario. It means that a WSS must supply water demanded to people at each scenario. Therefore, there is waste some part of volume needed for transporting water to certain regions that isn’t utilized all the time. The use of water should be manipulated as desired. If the peak values of water demand occurred at a specific time can be dispersed to whole day, then SCWSS can be reduced due to diminished maximum discharge capacity needed as well. Lately researchers have done so many things on water tank by using fuzzy logic but not considering stabilization of fluctuations at water demands. In this paper, a new intelligent valve (NIV) which aims to reduce the SCWSS is developed for stabilizing the demand of water occurred all day long by using fuzzy logic automation. The NIV can get stabilize water use for a region by optimizing discharge of water to water tank. The paper introduces a new perspective to design phase by focusing water demand change and trend.
We investigate the Zeno dynamics of the optical rogue waves. Considering their usage in modeling rogue wave dynamics, we analyze the Zeno dynamics of the Akhmediev breathers, Peregrine and Akhmediev–Peregrine soliton solutions of the nonlinear Schrödinger equation. We show that frequent measurements of the wave inhibits its movement in the observation domain for each of these solutions. We analyze the spectra of the rogue waves under Zeno dynamics. We also analyze the effect of observation frequency on the rogue wave profile and on the probability of lingering of the wave in the observation domain. Our results can find potential applications in optics including nonlinear phenomena.
We report on the experimental observation of vortex cluster shedding from a moving obstacle in an oblate atomic Bose-Einstein condensate. At low obstacle velocities v above a critical value, vortex clusters consisting of two like-sign vortices are generated to form a regular configuration like a von Kármán street, and as v is increased, the shedding pattern becomes irregular with many different kinds of vortex clusters. In particular, we observe that the Stouhal number associated with the shedding frequency exhibits saturation behavior with increasing v. The regular-to-turbulent transition of the vortex cluster shedding reveals remarkable similarities between a superfluid and a classical viscous fluid. Our work opens a new direction for experimental investigations of the superfluid Reynolds number characterizing universal superfluid hydrodynamics.
A method of quantitative flow visualization of the Karman street is presented. Image processing creates the ability for quantitative evaluation of the phenomena and enables the determination of geometric parameters of the vortex street. The methodology and appropriate software for image processing are described, and the analysis of both individual pictures and a series of images was feasible. The distances between the adjoining vortices and the hydrodynamic wavelength have been calculated. The most fundamental conclusion is the experimental confirmation that in the close neighborhood of the bluff body, the vortices move slower than at a greater distance from their origin. A 7% decrease of the convection velocity was found in the closest neighborhood of the bluff body. The calculated ratios of wavelength to bluff body diameter, equal to 4.09 and 3.65 for the 10mm and 12mm bluff body diameter, respectively, are close to the theoretical values based on mathematical modeling.
A method is described for the solution of time-dependent problems concerning the flow of viscous incompressible fluids in several space dimensions. The method is numerical, using a high-speed computer for the solution of a finite-difference approximation to the partial differential equations of motion. The application described here is to a study of the development of a vortex street behind a plate which has impulsively accelerated to constant speed in a channel of finite width; the Reynolds-number range investigated was 15 ≤ R ≤ 6000. Particular attention was given to those features for which comparison could be made with experiments, namely, critical Reynolds number for vortex shedding, drag coefficient, Strouhal number, vortex configuration, and channel-wall effects. The nature of the early stages of flow-pattern development was also investigated.
This paper proposes an adaptive neuro-fuzzy system, HyFIS (Hybrid neural Fuzzy Inference System), for building and optimising fuzzy models. The proposed model introduces the learning power of neural networks to fuzzy logic systems and provides linguistic meaning to the connectionist architectures. Heuristic fuzzy logic rules and input–output fuzzy membership functions can be optimally tuned from training examples by a hybrid learning scheme comprised of two phases: rule generation phase from data; and rule tuning phase using error backpropagation learning scheme for a neural fuzzy system. To illustrate the performance and applicability of the proposed neuro-fuzzy hybrid model, extensive simulation studies of nonlinear complex dynamic systems are carried out. The proposed method can be applied to an on-line incremental adaptive learning for the prediction and control of nonlinear dynamical systems. Two benchmark case studies are used to demonstrate that the proposed HyFIS system is a superior neuro-fuzzy modelling technique.
The author presents a condensed exposition of some basic ideas underlying fuzzy logic and describes some representative applications. He covers basic principles; meaning representation and inference; basic rules of inference; and the linguistic variable and its application to fuzzy control.< >
Introduction to artificial neural network (ANN) methods
- A D Dongare
- R R Kharde
- A D Kachare