Search results for: Jacobi wavelets

Authors: Nidhal Jamia, Sami El-Borgi

Abstract:

In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: functionally graded piezoelectric material (FGPM), mixed-mode crack, non-local theory, Schmidt method

Procedia PDF Downloads 310

Authors: Cheng-yu Hsieh, Bo Zhang, Ahmed Hambaba

Abstract:

Stock market prediction has long been an area of interest for both expert analysts and investors, driven by its complexity and the noisy, volatile conditions it operates under. This research examines the efficacy of combining the Patch Time Series Transformer (PatchTST) with wavelet transforms, specifically focusing on Haar and Daubechies wavelets, in forecasting the adjusted closing price of the S&P 500 index for the following day. By comparing the performance of the augmented PatchTST models with traditional predictive models such as Recurrent Neural Networks (RNNs), Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM) networks, and Transformers, this study highlights significant enhancements in prediction accuracy. The integration of the Daubechies wavelet with PatchTST notably excels, surpassing other configurations and conventional models in terms of Mean Absolute Error (MAE) and Mean Squared Error (MSE). The success of the PatchTST model paired with Daubechies wavelet is attributed to its superior capability in extracting detailed signal information and eliminating irrelevant noise, thus proving to be an effective approach for financial time series forecasting.

Keywords: deep learning, financial forecasting, stock market prediction, patch time series transformer, wavelet transform

Procedia PDF Downloads 55

Authors: Shiji Hu, Lei Li, Wanting Zhou, DaoHong Yang

Abstract:

The data encryption, is the foundation of today’s communication. On this basis, how to improve the speed of data encryption and decryption is always a problem that scholars work for. In this paper, we proposed an elliptic curve crypto processor architecture based on SM2 prime field. In terms of hardware implementation, we optimized the algorithms in different stages of the structure. In finite field modulo operation, we proposed an optimized improvement of Karatsuba-Ofman multiplication algorithm, and shorten the critical path through pipeline structure in the algorithm implementation. Based on SM2 recommended prime field, a fast modular reduction algorithm is used to reduce 512-bit wide data obtained from the multiplication unit. The radix-4 extended Euclidean algorithm was used to realize the conversion between affine coordinate system and Jacobi projective coordinate system. In the parallel scheduling of point operations on elliptic curves, we proposed a three-level parallel structure of point addition and point double based on the Jacobian projective coordinate system. Combined with the scalar multiplication algorithm, we added mutual pre-operation to the point addition and double point operation to improve the efficiency of the scalar point multiplication. The proposed ECC hardware architecture was verified and implemented on Xilinx Virtex-7 and ZYNQ-7 platforms, and each 256-bit scalar multiplication operation took 0.275ms. The performance for handling scalar multiplication is 32 times that of CPU(dual-core ARM Cortex-A9).

Keywords: Elliptic curve cryptosystems, SM2, modular multiplication, point multiplication.

Procedia PDF Downloads 102

Authors: Tanmaya Kumar Dash, Tarun Karamshetty, Soumitra Paul

Abstract:

The Barkhausen Noise Analysis (BNA) technique has been utilized to assess surface integrity of steels. But the BNA technique is not very successful in evaluating surface integrity of ground steels that exhibit poor micro-magnetic response. A new approach has been proposed for the processing of BN signal with Fast Fourier transforms while Wavelet transforms has been used to remove noise from the BN signal, with judicious choice of the ‘threshold’ value, when the micro-magnetic response of the work material is poor. In the present study, the effect of down feed induced upon conventional plunge surface grinding of hardened bearing steel has been investigated along with an ultrasonically cleaned, wet polished and a sample ground with spark out technique for benchmarking. Moreover, the FFT analysis has been established, at different sets of applied voltages and applied frequency and the pattern of the BN signal in the frequency domain is analyzed. The study also depicts the wavelet transforms technique with different levels of decomposition and different mother wavelets, which has been used to reduce the noise value in BN signal of materials with poor micro-magnetic response, in order to standardize the procedure for all BN signals depending on the frequency of the applied voltage.

Keywords: barkhausen noise analysis, grinding, magnetic properties, signal processing, micro-magnetic response

Procedia PDF Downloads 670

Authors: Seyed Sadegh Naseralavi, Sadegh Balaghi, Ehsan Khojastehfar

Abstract:

Time history dynamic analysis of structures is considered as an exact method while being computationally intensive. Filtration of earthquake strong ground motions applying wavelet transform is an approach towards reduction of computational efforts, particularly in optimization of structures against seismic effects. Wavelet transforms are categorized into continuum and discrete transforms. Since earthquake strong ground motion is a discrete function, the discrete wavelet transform is applied in the present paper. Wavelet transform reduces analysis time by filtration of non-effective frequencies of strong ground motion. Filtration process may be repeated several times while the approximation induces more errors. In this paper, strong ground motion of earthquake has been filtered once applying each wavelet. Strong ground motion of Northridge earthquake is filtered applying various wavelets and dynamic analysis of sampled shear and moment frames is implemented. The error, regarding application of each wavelet, is computed based on comparison of dynamic response of sampled structures with exact responses. Exact responses are computed by dynamic analysis of structures applying non-filtered strong ground motion.

Keywords: wavelet transform, computational error, computational duration, strong ground motion data

Procedia PDF Downloads 380

Authors: Sofia M. Karadimitriou, Kostas Triantafyllopoulos, Timothy Heaton

Abstract:

Reduced dimension Dynamic Spatio-Temporal Models (DSTMs) jointly describe the spatial and temporal evolution of a function observed subject to noise. A basic state space model is adopted for the discrete temporal variation, while a continuous autoregressive structure describes the continuous spatial evolution. Application of such a DSTM relies upon the pre-selection of a suitable reduced set of basic functions and this can present a challenge in practice. In this talk, we propose an online estimation method for high dimensional spatio-temporal data based upon DSTM and we attempt to resolve this issue by allowing the basis to adapt to the observed data. Specifically, we present a wavelet decomposition in order to obtain a parsimonious approximation of the spatial continuous process. This parsimony can be achieved by placing a Laplace prior distribution on the wavelet coefficients. The aim of using the Laplace prior, is to filter wavelet coefficients with low contribution, and thus achieve the dimension reduction with significant computation savings. We then propose a Hierarchical Bayesian State Space model, for the estimation of which we offer an appropriate particle filter algorithm. The proposed methodology is illustrated using real environmental data.

Keywords: multidimensional Laplace prior, particle filtering, spatio-temporal modelling, wavelets

Procedia PDF Downloads 431

Authors: Syed Jawad Hussain Shahzad, Muhammad Zakaria, Mobeen Ur Rehman, Saniya Khaild

Abstract:

This study examines the co-movement between the Pakistan, Indian, S&P 500 and Nikkei 225 stock markets using weekly data from 1998 to 2013. The time-frequency relationship between the selected stock markets is conducted by using measures of continuous wavelet power spectrum, cross-wavelet transform and cross (squared) wavelet coherency. The empirical evidence suggests strong dependence between Pakistan and Indian stock markets. The co-movement of Pakistani index with U.S and Japanese, the developed markets, varies over time and frequency where the long-run relationship is dominant. The results of cross wavelet and wavelet coherence analysis indicate moderate covariance and correlation between stock indexes and the markets are in phase (i.e. cyclical in nature) over varying durations. Pakistan stock market was lagging during the entire period in relation to Indian stock market, corresponding to the 8~32 and then 64~256 weeks scale. Similar findings are evident for S&P 500 and Nikkei 225 indexes, however, the relationship occurs during the later period of study. All three wavelet indicators suggest strong evidence of higher co-movement during 2008-09 global financial crises. The empirical analysis reveals a strong evidence that the portfolio diversification benefits vary across frequencies and time. This analysis is unique and have several practical implications for regional and international investors while assigning the optimal weightage of different assets in portfolio formulation.

Keywords: co-movement, Pakistan stock exchange, S&P 500, Nikkei 225, wavelet analysis

Procedia PDF Downloads 358

Authors: Mariem Saied, Jens Gustedt, Gilles Muller

Abstract:

We present Dido, a source-to-source auto-generation and optimization framework for multi-dimensional stencil computations. It enables a large programmer community to easily and safely implement stencil codes on distributed-memory parallel architectures with Ordered Read-Write Locks (ORWL) as an execution and communication back-end. ORWL provides inter-task synchronization for data-oriented parallel and distributed computations. It has been proven to guarantee equity, liveness, and efficiency for a wide range of applications, particularly for iterative computations. Dido consists mainly of an implicitly parallel domain-specific language (DSL) implemented as a source-level transformer. It captures domain semantics at a high level of abstraction and generates parallel stencil code that leverages all ORWL features. The generated code is well-structured and lends itself to different possible optimizations. In this paper, we enhance Dido to handle both Jacobi and Gauss-Seidel grid traversals. We integrate temporal blocking to the Dido code generator in order to reduce the communication overhead and minimize data transfers. To increase data locality and improve intra-node data reuse, we coupled the code generation technique with the polyhedral parallelizer Pluto. The accuracy and portability of the generated code are guaranteed thanks to a parametrized solution. The combination of ORWL features, the code generation pattern and the suggested optimizations, make of Dido a powerful code generation framework for stencil computations in general, and for distributed-memory architectures in particular. We present a wide range of experiments over a number of stencil benchmarks.

Keywords: stencil computations, ordered read-write locks, domain-specific language, polyhedral model, experiments

Procedia PDF Downloads 131

Authors: Pranav Gulati, Isha Sharma

Abstract:

Hypertension and hypotension are known to have repercussions on the health of an individual, with hypertension contributing to an increased probability of risk to cardiovascular diseases and hypotension resulting in syncope. This prompts the development of a non-invasive, non-intrusive, continuous and cuff-less blood pressure monitoring system to detect blood pressure variations and to identify individuals with acute and chronic heart ailments, but due to the unavailability of such devices for practical daily use, it becomes difficult to screen and subsequently regulate blood pressure. The complexities which hamper the steady monitoring of blood pressure comprises of the variations in physical characteristics from individual to individual and the postural differences at the site of monitoring. We propose to develop a continuous, comprehensive cardio-analysis tool, based on reflective photoplethysmography (PPG). The proposed device, in the form of an eyewear captures the PPG signal and estimates the systolic and diastolic blood pressure using a sensor positioned near the temporal artery. This system relies on regression models which are based on extraction of key points from a pair of PPG wavelets. The proposed system provides an edge over the existing wearables considering that it allows for uniform contact and pressure with the temporal site, in addition to minimal disturbance by movement. Additionally, the feature extraction algorithms enhance the integrity and quality of the extracted features by reducing unreliable data sets. We tested the system with 12 subjects of which 6 served as the training dataset. For this, we measured the blood pressure using a cuff based BP monitor (Omron HEM-8712) and at the same time recorded the PPG signal from our cardio-analysis tool. The complete test was conducted by using the cuff based blood pressure monitor on the left arm while the PPG signal was acquired from the temporal site on the left side of the head. This acquisition served as the training input for the regression model on the selected features. The other 6 subjects were used to validate the model by conducting the same test on them. Results show that the developed prototype can robustly acquire the PPG signal and can therefore be used to reliably predict blood pressure levels.

Keywords: blood pressure, photoplethysmograph, eyewear, physiological monitoring

Procedia PDF Downloads 282

Authors: S.I.Mukhin, S. Seidov, A. Mukherjee

Abstract:

The Dicke model is a key tool for the description of correlated states of quantum atomic systems, excited by resonant photon absorption and subsequently emitting spontaneous coherent radiation in the superradiant state. The Dicke Hamiltonian (DH) is successfully used for the description of the dynamics of the Josephson Junction (JJ) array in a resonant cavity under applied current. In this work, we have investigated a generalized model, which is described by DH with a frustrating interaction term. This frustrating interaction term is explicitly the infinite coordinated interaction between all the spin half in the system. In this work, we consider an array of N superconducting islands, each divided into two sub-islands by a Josephson Junction, taken in a charged qubit / Cooper Pair Box (CPB) condition. The array is placed inside the resonant cavity. One important aspect of the problem lies in the dynamical nature of the physical observables involved in the system, such as condensed electric field and dipole moment. It is important to understand how these quantities behave with time to define the quantum phase of the system. The Dicke model without frustrating term is solved to find the dynamical solutions of the physical observables in analytic form. We have used Heisenberg’s dynamical equations for the operators and on applying newly developed Rotating Holstein Primakoff (HP) transformation and DH we have arrived at the four coupled nonlinear dynamical differential equations for the momentum and spin component operators. It is possible to solve the system analytically using two-time scales. The analytical solutions are expressed in terms of Jacobi's elliptic functions for the metastable ‘bound luminosity’ dynamic state with the periodic coherent beating of the dipoles that connect the two double degenerate dipolar ordered phases discovered previously. In this work, we have proceeded the analysis with the extended DH with a frustrating interaction term. Inclusion of the frustrating term involves complexity in the system of differential equations and it gets difficult to solve analytically. We have solved semi-classical dynamic equations using the perturbation technique for small values of Josephson energy EJ. Because the Hamiltonian contains parity symmetry, thus phase transition can be found if this symmetry is broken. Introducing spontaneous symmetry breaking term in the DH, we have derived the solutions which show the occurrence of finite condensate, showing quantum phase transition. Our obtained result matches with the existing results in this scientific field.

Keywords: Dicke Model, nonlinear dynamics, perturbation theory, superconductivity

Procedia PDF Downloads 135

Authors: Marc Toutain, Pascale Leconte, Antoine Gauthier

Abstract:

Introduction: Eating Disorders (ED), such as anorexia, bulimia, and binge eating, are psychiatric illnesses that mostly affect young people. The main symptoms concern eating (restriction, excessive food intake) and weight control behaviors (laxatives, vomiting). Psychological comorbidities (depression, executive function disorders, etc.) and problematic behaviors toward physical activity (PA) are commonly associated with ED. Acquaintances on ED risk factors are still lacking, and more community sample studies are needed to improve prevention and early detection. To our knowledge, studies are needed to specifically investigate the link between ED risk level, PA, and psychological risk factors in a community sample of adolescents. The aim of this study is to assess the relation between ED risk level, exercise (type, frequency, and motivations for engaging in exercise), and psychological factors based on the Jacobi risk factors model. We suppose that a high risk of ED will be associated with the practice of high caloric cost PA, motivations oriented to weight and shape control, and psychological disturbances. Method: An online survey destined for students has been sent to several middle schools and colleges in northwest France. This survey combined several questionnaires, the Eating Attitude Test-26 assessing ED risk; the Exercise Motivation Inventory–2 assessing motivations toward PA; the Hospital Anxiety and Depression Scale assessing anxiety and depression, the Contour Drawing Rating Scale; and the Body Esteem Scale assessing body dissatisfaction, Rosenberg Self-esteem Scale assessing self-esteem, the Exercise Dependence Scale-Revised assessing PA dependence, the Multidimensional Assessment of Interoceptive Awareness assessing interoceptive awareness and the Frost Multidimensional Perfectionism Scale assessing perfectionism. Machine learning analysis will be performed in order to constitute groups with a tree-based model clustering method, extract risk profile(s) with a bootstrap method comparison, and predict ED risk with a prediction method based on a decision tree-based model. Expected results: 1044 complete records have already been collected, and the survey will be closed at the end of May 2022. Records will be analyzed with a clustering method and a bootstrap method in order to reveal risk profile(s). Furthermore, a predictive tree decision method will be done to extract an accurate predictive model of ED risk. This analysis will confirm typical main risk factors and will give more data on presumed strong risk factors such as exercise motivations and interoceptive deficit. Furthermore, it will enlighten particular risk profiles with a strong level of proof and greatly contribute to improving the early detection of ED and contribute to a better understanding of ED risk factors.

Keywords: eating disorders, risk factors, physical activity, machine learning

Procedia PDF Downloads 84

Authors: Olivier Delage, Thierry Portafaix, Hassan Bencherif, Guillaume Guimbretiere

Abstract:

Most observation data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several time and space scales. As a consequence, measurements time series in geophysics have often characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at all time-scales and require a time-frequency representation to analyze their variability. Empirical Mode Decomposition (EMD) is a relatively new technic as part of a more general signal processing method called the Hilbert-Huang transform. This analysis method turns out to be particularly suitable for non-linear and non-stationary signals and consists in decomposing a signal in an auto adaptive way into a sum of oscillating components named IMFs (Intrinsic Mode Functions), and thereby acts as a bank of bandpass filters. The advantages of the EMD technic are to be entirely data driven and to provide the principal variability modes of the dynamics represented by the original time series. However, the main limiting factor is the frequency resolution that may give rise to the mode mixing phenomenon where the spectral contents of some IMFs overlap each other. To overcome this problem, J. Gilles proposed an alternative entitled “Empirical Wavelet Transform” (EWT) which consists in building from the segmentation of the original signal Fourier spectrum, a bank of filters. The method used is based on the idea utilized in the construction of both Littlewood-Paley and Meyer’s wavelets. The heart of the method lies in the segmentation of the Fourier spectrum based on the local maxima detection in order to obtain a set of non-overlapping segments. Because linked to the Fourier spectrum, the frequency resolution provided by EWT is higher than that provided by EMD and therefore allows to overcome the mode-mixing problem. On the other hand, if the EWT technique is able to detect the frequencies involved in the original time series fluctuations, EWT does not allow to associate the detected frequencies to a specific mode of variability as in the EMD technic. Because EMD is closer to the observation of physical phenomena than EWT, we propose here a new technic called EAWD (Empirical Adaptive Wavelet Decomposition) based on the coupling of the EMD and EWT technics by using the IMFs density spectral content to optimize the segmentation of the Fourier spectrum required by EWT. In this study, EMD and EWT technics are described, then EAWD technic is presented. Comparison of results obtained respectively by EMD, EWT and EAWD technics on time series of ozone total columns recorded at Reunion island over [1978-2019] period is discussed. This study was carried out as part of the SOLSTYCE project dedicated to the characterization and modeling of the underlying dynamics of time series issued from complex systems in atmospheric sciences

Keywords: adaptive filtering, empirical mode decomposition, empirical wavelet transform, filter banks, mode-mixing, non-linear and non-stationary time series, wavelet

Procedia PDF Downloads 140

Authors: I. Hosni, L. Bennaceur Farah, N. Saber, R Bennaceur

Abstract:

Soil moisture content is a key variable in many environmental sciences. Even though it represents a small proportion of the liquid freshwater on Earth, it modulates interactions between the land surface and the atmosphere, thereby influencing climate and weather. Accurate modeling of the above processes depends on the ability to provide a proper spatial characterization of soil moisture. The measurement of soil moisture content allows assessment of soil water resources in the field of hydrology and agronomy. The second parameter in interaction with the radar signal is the geometric structure of the soil. Most traditional electromagnetic models consider natural surfaces as single scale zero mean stationary Gaussian random processes. Roughness behavior is characterized by statistical parameters like the Root Mean Square (RMS) height and the correlation length. Then, the main problem is that the agreement between experimental measurements and theoretical values is usually poor due to the large variability of the correlation function, and as a consequence, backscattering models have often failed to predict correctly backscattering. In this study, surfaces are considered as band-limited fractal random processes corresponding to a superposition of a finite number of one-dimensional Gaussian process each one having a spatial scale. Multiscale roughness is characterized by two parameters, the first one is proportional to the RMS height, and the other one is related to the fractal dimension. Soil moisture is related to the complex dielectric constant. This multiscale description has been adapted to two-dimensional profiles using the bi-dimensional wavelet transform and the Mallat algorithm to describe more correctly natural surfaces. We characterize the soil surfaces and sub-surfaces by a three layers geo-electrical model. The upper layer is described by its dielectric constant, thickness, a multiscale bi-dimensional surface roughness model by using the wavelet transform and the Mallat algorithm, and volume scattering parameters. The lower layer is divided into three fictive layers separated by an assumed plane interface. These three layers were modeled by an effective medium characterized by an apparent effective dielectric constant taking into account the presence of air pockets in the soil. We have adopted the 2D multiscale three layers small perturbations model including, firstly air pockets in the soil sub-structure, and then a vegetable canopy in the soil surface structure, that is to simulate the radar backscattering. A sensitivity analysis of backscattering coefficient dependence on multiscale roughness and new soil moisture has been performed. Later, we proposed to change the dielectric constant of the multilayer medium because it takes into account the different moisture values of each layer in the soil. A sensitivity analysis of the backscattering coefficient, including the air pockets in the volume structure with respect to the multiscale roughness parameters and the apparent dielectric constant, was carried out. Finally, we proposed to study the behavior of the backscattering coefficient of the radar on a soil having a vegetable layer in its surface structure.

Keywords: multiscale, bidimensional, wavelets, backscattering, multilayer, SPM, air pockets

Procedia PDF Downloads 126

Authors: Rosimeire Araújo Silva, Philip Martin Fearnside

Abstract:

Extreme droughts and floods in the Amazon have serious consequences for natural ecosystems and the human population in the region. The frequency of these events has increased in recent years, and projections of climate change predict greater frequency and intensity of these events. Understanding the links between these extreme events and different patterns of sea surface temperature in the Atlantic and Pacific Oceans is essential, both to improve the modeling of climate change and its consequences and to support efforts of adaptation in the region. The relationship between sea temperatures and events in the Amazon is much more complex than is usually assumed in climatic models. Warming and cooling of different parts of the oceans, as well as the interaction between simultaneous temperature changes in different parts of each ocean and between the two oceans, have specific consequences for the Amazon, with effects on precipitation that vary in different parts of the region. Simplistic generalities, such as the association between El Niño events and droughts in the Amazon, do not capture this complexity. We investigated the variability of Sea Surface Temperature (SST) in the Tropical Pacific Ocean during the period 1950-2022, using Empirical Orthogonal Functions (FOE), spectral analysis coherence and wavelet phase. The two were identified as the main modes of variability, which explain about 53,9% and 13,3%, respectively, of the total variance of the data. The spectral and coherence analysis and wavelets phase showed that the first selected mode represents the warming in the central part of the Pacific Ocean (the “Central El Niño”), while the second mode represents warming in the eastern part of the Pacific (the “Eastern El Niño The effects of the 1982-1983 and 1976-1977 El Niño events in the Amazon, although both events were characterized by an increase in sea surface temperatures in the Equatorial Pacific, the impact on rainfall in the Amazon was distinct. In the rainy season, from December to March, the sub-basins of the Japurá, Jutaí, Jatapu, Tapajós, Trombetas and Xingu rivers were the regions that showed the greatest reductions in rainfall associated with El Niño Central (1982-1983), while the sub-basins of the Javari, Purus, Negro and Madeira rivers had the most pronounced reductions in the year of Eastern El Niño (1976-1977). In the transition to the dry season, in April, the greatest reductions were associated with the Eastern El Niño year for the majority of the study region, with the exception only of the sub-basins of the Madeira, Trombetas and Xingu rivers, which had their associated reductions to Central El Niño. In the dry season from July to September, the sub-basins of the Japurá Jutaí Jatapu Javari Trombetas and Madeira rivers were the rivers that showed the greatest reductions in rainfall associated with El Niño Central, while the sub-basins of the Tapajós Purus Negro and Xingu rivers had the most pronounced reductions. In the Eastern El Niño year this season. In this way, it is possible to conclude that the Central (Eastern) El Niño controlled the reductions in soil moisture in the dry (rainy) season for all sub-basins shown in this study. Extreme drought events associated with these meteorological phenomena can lead to a significant increase in the occurrence of forest fires. These fires have a devastating impact on Amazonian vegetation, resulting in the irreparable loss of biodiversity and the release of large amounts of carbon stored in the forest, contributing to the increase in the greenhouse effect and global climate change.

Keywords: sea surface temperature, variability, climate, Amazon

Procedia PDF Downloads 67