Wavelet Model Research Articles

二阶总广义变分图像放大

To obtain higher resolution images,a new model for image zooming based on total generalized variation is proposed.Original low-resolution image is regarded as sub-space projection of zoomed image to its own space,and the final zoomed image is obtained by application of second order total generalized variation regularization.By analyzing the properties of the new model,an efficient primal-dual algorithm is introduced.Experimental results suggest that the proposed algorithm can remove block effect and keep more details,so the high quality image is reconstructed;the model is better than the total variation mode and the wavelet model in terms of both peak signal to noise ratio and root mean square error.

Suppress the Finger Reflection Error of Littlewood-pelay Wavelet Transformation Device of Surface Acoustic Wave

In this study, a Wavelet Transformation (WT) device of Surface Acoustic Wave (SAW) technology is developed on the basis of acoustics, electronics, wavelet theory, applied mathematics and semiconductor planar technology. The Finger Reflection (FR) error is the primary reason for this kind of device. To solve the problem, a mathematic model of Littlewood-pelay wavelet was established first, which is matched with the model of SAW. Using the methods of split finger and fake finger to design IDT of Littlewood-pelay WT device of SAW with L-edit software, the FR error can be reduced and the equivalent construction of IDT is simulated.

Cardiac mapping of electrical impedance tomography by means of a wavelet model

To improve the identification of cardiac regions in Electrical impedance tomography (EIT) pulmonary perfusion images, a model of wavelet transform was developed. The main goal was to generate maps of the heart using EIT images in a controlled animal experiment using a healthy pig and in two human volunteers. The model was capable of identifying the heart regions, demonstrated robustness and generated satisfactory results. The pig images were compared to perfusion images obtained using injection of a hypertonic solution and achieved an average area of the ROC curve of 0.88. The human images were qualitatively compared with Computerized Tomography scan (CT-scan) images.

The Price and Trading Volume Dynamics Relationship in the EEX Power Market: A Wavelet Modeling

This paper examines the dynamic relationship between power spot prices and related trading volumes in one of the most emergent energy markets. Traditionally, investigating the bivariate stochastic processes has been dominated by linear econometrical methods that proved helpful especially in finance. However, when dealing with intradaily power data, we cannot rely on models developed for financial or other commodity markets. Therefore, wavelet transforms are applied for power markets data to search for and decode nonlinear regularities and hidden patterns existing between the variables. Given its ability to decompose the time series into their time scale components and thus to reveal structure at different time horizons, wavelets are useful in analyzing situations in which the degree of association between processes is likely to change with the time-horizon. Therefore, a wavelet-based cross-analysis is performed between prices and trading volume time series. On the same basis, causality tests and out-of-sample forecasting tasks are carried out to empirically the strong relationship between the two investigated time series.

A wavelet and neural network model for the prediction of dry bulk shipping indices

Shipping markets are typically volatile in nature, as manifest in the dynamics of freight rates. According to shipowners’ risk propensity, volatility-related decisions vary from what kind of contract (time/voyage charter) to engage in to whether to enter/exit the business. After a sharp drop in freight rates at the end of 2008, a discussion about appropriate risk management concepts and statistical tools is needed. Owing to the magnitude of investment required in shipping, any additional information regarding the future direction of market volatility is of the utmost importance. The ambition of this article is exactly the same: to study fluctuations in the freight rates of the Baltic Panamax route 2A and the Baltic Panamax route 3A, using a tool of analysis that is new to shipping economics: a hybrid model of wavelets and neural networks. The wavelet multiscale decomposition of time series reveals volatility dynamics across different time frequencies and will uncover patterns that will be used by neural networks for prediction.

Influence of grain size, shape and compaction on georadar waves: examples of aeolian dunes

Many Ground Penetrating Radar (GPR) profiles acquired in dry aeolian environment have shown good reflectivity inside present-day dunes. We show that the origin of this reflectivity is related to changes in grain size distribution, packing and/or grain shape in a sandy material. We integrate these three parameters into analytical models for bulk permittivity in order to predict the reflections and the velocity of GPR waves. We consider two GPR cross-sections acquired over Aeolian dunes in the Chadian desert. The 2D migration of GPR data suggests that dunes contain different kinds of bounding surfaces. We discuss and model three kinds of reflections using reasonable geological hypothesis about Aeolian sedimentation processes. The propagation and the reflection of radar waves are calculated using the 1D wavelet modelling method in spectral domain. The results of the forward modelling are in good accordance with real observed data.

Wavelet and neuro-fuzzy conjunction model for predicting water table depth fluctuations

The ability of a wavelet and neuro-fuzzy conjunction technique for groundwater depth forecasting was investigated in this study. The wavelet-neuro-fuzzy model was improved by combining two methods, the discrete wavelet transform and the neuro-fuzzy model. The conjunction model was applied to different input combinations of daily groundwater depth data of Bondville and Perry wells. Root mean square error (RMSE) and correlation coefficient (R) statistics were used for evaluating the accuracy of wavelet-neuro-fuzzy models. The accuracy of the conjunction models was compared with those of the single neuro-fuzzy models in one-, two- and three-day-ahead groundwater depth forecasting. Comparison of the results revealed that the wavelet-neuro-fuzzy models perform better than the neuro-fuzzy models especially for the two- and three-day-ahead forecasting cases.

Discrete wavelet neural network approach in significant wave height forecasting for multistep lead time

Recently Artificial Neural network (ANN) was extensively used as non-linear inter-extrapolator for ocean wave forecasting as well as other application in ocean engineering. In this current study, the Wavelet transform was hybridised with ANN naming Wavelet Neural Network (WLNN) for significant wave height forecasting near Mangalore, west coast of India, upto 48h lead time. The main time series of significant wave height data were decomposed to multiresolution time series using discrete wavelet transformations. Then, the multiresolution time series data were used as input of the ANN to forecast the significant wave height at different multistep lead time. It was shown how the proposed model, WLNN, that makes use of multiresolution time series as input, allows for more accurate and consistent predictions with respect to classical ANN models. The proposed wavelet model (WLNN) results revealed that it was better forecasted and consistent than single ANN model because of using multiresolution time series data as inputs.

Long Lead Time Drought Forecasting Using a Wavelet and Fuzzy Logic Combination Model: A Case Study in Texas

Abstract Drought forecasting is important for drought risk management. Considering the El Niño–Southern Oscillation (ENSO) variability and persistence in drought characteristics, this study developed a wavelet and fuzzy logic (WFL) combination model for long lead time drought forecasting. The idea of WFL is to separate each predictor and predictand into their frequency bands and then reconstruct the predictand series by using its predicted bands. The strongest-frequency bands of predictors and predictand were determined from the average wavelet spectra. Applying this combination model to the state of Texas, it was found that WFL had a significant improvement over the fuzzy logic model that did not use wavelet banding. Comparison with an artificial neural network (ANN) model and a coupled wavelet and ANN (WANN) model showed that WFL was more accurate for drought forecasting. Also, it should be noted that the ENSO variability is not a global precursor of drought. For this reason, prior to an application of such a data-driven model in different regions, significant work is required to identify appropriate independent predictors. Drought forecasting with longer lead times and higher accuracy is of significant value in engineering applications.

Multipath Reduction of Shaft Tower Monitoring with GPS in Mine

Safe shaft tower operation is an important guarantee for mine production. It’s necessary for monitoring to develop more effective techniques because the traditional measurements are inadequate for the purpose. For this reason, GPS kinematic positioning (RTK) technique was presented to accomplish the task, meanwhile, the main error sources (multipath error) was systematically analyzed. In addition, the Empirical Mode Decomposition (EMD)-Wavelet model was proposed for extracting multipath model. To eliminate the systematic errors, the EMD decomposes the time series to high-frequency part and low-frequency part with the standards of scale selection, which is given in terms of the mean of the accumulated standardized modes, and the tendency of high-frequency part is extracted by Wavelet. Then low-frequency part and the tendency of high-frequency are reconstructed based on EMD theory and the systematic errors mitigation model is demonstrated as well. The scheme of the multipath error reduction based on the EMD-Wavelet is suggested. The experiment shows that the proposed scheme dramatically improves the precision of dynamic coordinate series about 40-70% after multipath error mitigation.

AUTOMOBILE GEARBOX DIAGNOSTICS ON THE BASIS OF THE REFERENCE MODEL

A method of diagnostics of the automobile gearbox wearing out is presented in this paper. The procedure can be automatically realised during driving. To be able to perform such diagnostics the reference model of the vibration signal on the basis of the synchronously averaged signal was created for a new gearbox (in a good technical con­dition). In order to realize the procedure on-board this model must be easily identifiable. A complicated structural model was given up for the simpler model of the abstract vibrations signal. Three ways of modelling were pre­sented: harmonic series, parametric ARMA (Auto Regressive Moving Average) model, and the wavelet model. The current vibration signal is recorded at the determined moment of driving and then compared with the referen­ce model. After each overhaul or exchange of drive system elements the reference model should be identified again. Diagnostics is being done by comparing measures for the reference model and the currently measured - adequately processed - signal. The method was verified in the active experiment performed on the Fiat Punto automobile with a 5-speed gearbox. The described method can constitute the supplementation of on-board auto­mobile system by the mechanical failures of the drive system. This procedure can be broadened by defects of the main gear, differential gear, articulated joints, bearing, engine exhaust valves, and engine head gasket.

Multipath Reduction of Shaft Tower Monitoring with GPS in Mine

Safe shaft tower operation is an important guarantee for mine production. It’s necessary for monitoring to develop more effective techniques because the traditional measurements are inadequate for the purpose. For this reason, GPS kinematic positioning (RTK) technique was presented to accomplish the task, meanwhile, the main error sources (multipath error) was systematically analyzed. In addition, the Empirical Mode Decomposition (EMD)-Wavelet model was proposed for extracting multipath model. To eliminate the systematic errors, the EMD decomposes the time series to high-frequency part and low-frequency part with the standards of scale selection, which is given in terms of the mean of the accumulated standardized modes, and the tendency of high-frequency part is extracted by Wavelet. Then low-frequency part and the tendency of high-frequency are reconstructed based on EMD theory and the systematic errors mitigation model is demonstrated as well. The scheme of the multipath error reduction based on the EMD-Wavelet is suggested. The experiment shows that the proposed scheme dramatically improves the precision of dynamic coordinate series about 40-70% after multipath error mitigation.

Multilayered Infinite Medium Subject to a Moving Load: Dynamic Response and Optimization Using Coiflet Expansion

A wavelet based approach is proposed in this paper for analysis and optimization of the dynamical response of a multilayered medium subject to a moving load with respect to the material properties and thickness of supporting half-space. The investigated model consists of a load moving along a beam resting on a surface of a multilayered medium with infinite thickness and layers with different physical properties. The theoretical model is described by the Euler-Bernoulli equation for the beam and the Navier's elastodynamic equation of motion for a viscoelastic half-space. The moving load is modelled by a finite series of distributed harmonic loads. A special method based on a wavelet expansion of functions in the transform domain is adopted for calculation of displacements in the physical domain. The interaction between the beam and the multilayered medium is analyzed in order to obtain the vibration response at the surface and the critical velocities associated. The choice of the specific values of the design parameters for each layer, which minimize the vibration response of the multilayered medium, can be seen as a structural optimization problem. A first approach for using optimization techniques to explore the potential of the wavelet model is presented and briefly discussed. Results from the analysis of the vibration response are presented to illustrate the dynamic characterization obtained by using this method. Numerical examples reflecting the results of numerical optimizations with respect to a multilayered medium parameters are also presented.

Multilayered Infinite Medium Subject to a Moving Load: Dynamic Response and Optimization Using Coiflet Expansion

A wavelet based approach is proposed in this paper for analysis and optimization of the dynamical response of a multilayered medium subject to a moving load with respect to the material properties and thickness of supporting half-space. The investigated model consists of a load moving along a beam resting on a surface of a multilayered medium with infinite thickness and layers with different physical properties. The theoretical model is described by the Euler-Bernoulli equation for the beam and the Navier's elastodynamic equation of motion for a viscoelastic half-space. The moving load is modelled by a finite series of distributed harmonic loads. A special method based on a wavelet expansion of functions in the transform domain is adopted for calculation of displacements in the physical domain. The interaction between the beam and the multilayered medium is analyzed in order to obtain the vibration response at the surface and the critical velocities associated. The choice of the specific values of the design parameters for each layer, which minimize the vibration response of the multilayered medium, can be seen as a structural optimization problem. A first approach for using optimization techniques to explore the potential of the wavelet model is presented and briefly discussed. Results from the analysis of the vibration response are presented to illustrate the dynamic characterization obtained by using this method. Numerical examples reflecting the results of numerical optimizations with respect to a multilayered medium parameters are also presented.

Multiscale and multilevel technique for consistent segmentation of nonstationary time series

In this paper, we propose a fast, well-performing, and consistent method for segmenting a piecewise-stationary, linear time series with an unknown number of breakpoints. The time series model we use is the nonparametric Locally Stationary Wavelet model, in which a complete description of the piecewise-stationary second-order structure is provided by wavelet periodograms computed at multiple scales and locations. The initial stage of our method is a new binary segmentation procedure, with a theoretically justified and rapidly computable test criterion that detects breakpoints in wavelet periodograms separately at each scale. This is followed by within-scale and across-scales post-processing steps, leading to consistent estimation of the number and locations of breakpoints in the second-order structure of the original process. An extensive simulation study demonstrates good performance of our method.

Wavelet and neuro-fuzzy conjunction model for streamflow forecasting

In this study the wavelet-neuro-fuzzy model, which combines the wavelet transform and the neuro-fuzzy technique, has been employed to forecast monthly streamflows. The observed monthly streamflow data are decomposed into some sub-series (components) by discrete wavelet transform and then appropriate sub-series are used as inputs to the neuro-fuzzy models for forecasting monthly streamflows. The data from two stations, Durucasu and Tanir, in Turkey are used as case studies. The wavelet-neuro-fuzzy forecasts are compared with those of the single neuro-fuzzy models. Comparison results indicate that the wavelet-neuro-fuzzy model is superior to the classical neuro-fuzzy method especially for the peak values. For the Durucasu and Tanir stations, it was found that the wavelet-neuro-fuzzy models are superior in forecasting monthly streamflows than the optimal neuro-fuzzy models.

Lack-of-fit tests in linear mixed models with application to wavelet tests

We obtain the asymptotic distribution of score and restricted likelihood ratio statistics for testing whether variance components are equal to zero in linear mixed models with a fixed and finite number of random effects. The main new innovation of this paper is in deriving the components of the distribution, which are not chi-squared. The proposed test statistics are used for lack-of-fit testing using wavelets, where the finest scale wavelet coefficients are allowed to have a different variance than the other wavelet coefficients in the mixed effect wavelet model. We study the power of a wavelet-based test for a hypothesised parametric model within a mixed model framework in a simulation study.

Hierarchical wavelet modelling of environmental sensor data

Motivated by the need to smooth and to summarize multiple simultaneous time series arising from networks of environmental monitors, we propose a hierarchical wavelet model for which estimation of hyperparameters can be performed by marginal maximum likelihood. The result is an empirical Bayes thresholding procedure whose results improve on those of wavethresh in terms of mean square error. We apply the approach to data from the SensorScope environmental modelling system, and briefly discuss issues that arise concerning variance estimation in this context.

A combined generalized regression neural network wavelet model for monthly streamflow prediction

The ability of a combined model, Wavelet-Generalized Regression Neural Network (WGRNN), is investigated in the current study for the prediction of monthly streamflows. The WGRNN model is obtained by combining two methods, Discrete Wavelet Transform (DWT) and Generalized Regression Neural Network (GRNN), for one-month-ahead streamflow forecasting. The monthly flow data of two stations, the Gerdelli Station on the Canakdere River and the Isakoy Station on the Goksudere River, in the Eastern Black Sea region of Turkey are used in the study. The forecasts of the WGRNN model are tested using the Root Mean Square Error (RMSE), Variance Account For (VAF) and correlation coefficient (R) statistics and the results are compared with those of the single GRNN and Feed Forward Neural Network (FFNN). The comparison results revealed that the WGRNN performs better than the GRNN and FFNN models in monthly streamflow prediction. For the Gerdelli and Isakoy stations, it is found that the WGRNN models with RMSE = 5.31 m3/s, VAF = 52.3%, R = 0.728 and RMSE = 3.36 m3/s, VAF = 55.1%, R = 0.742 in the test period are superior in forecasting monthly streamflows than the best accurate GRNN models with RMSE = 6.39 m3/s, VAF = 30.1%, R = 0.553 and RMSE = 4.19 m3/s, VAF = 30.1%, R = 0.549, respectively.

Wavelet Modeling Using Finite Mixtures of Generalized Gaussian Distributions: Application to Texture Discrimination and Retrieval

This paper addresses statistical-based texture modeling using wavelets. We propose a new approach to represent the marginal distribution of the wavelet coefficients using finite mixtures of generalized Gaussian (MoGG) distributions. The MoGG captures a wide range of histogram shapes, which provides better description and discrimination of texture than using single probability density functions (pdf's), as proposed by recent state-of-the-art approaches. Moreover, we propose a model similarity measure based on Kullback-Leibler divergence (KLD) approximation using Monte Carlo sampling methods. Through experiments on two popular texture data sets, we show that our approach yields significant performance improvements for texture discrimination and retrieval, as compared with recent methods of statistical-based wavelet modeling.