Multiresolution Wavelet Research Articles

Biophysical metrics for detecting more sustainable urban forms at the global scale

Abstract To test metrics for rapid identification and global evaluation of more sustainable urban forms, we examine the configuration of the Sao Paulo Metropolitan Region (SPMR) in Brazil using satellite remote sensing data and landscape metrics. We adopt principles from landscape ecology and urban planning to evaluate urban heterogeneity and morphology that may constitute more sustainable urban forms, including connectivity, density, geometric complexity (mixed land use), diversity, and greening. Using 2-D wavelet multiresolution analysis and satellite-derived fractional vegetation cover (Fr), the variability of landscape metrics from Landsat (30 m) to MODIS (1 km) scales are investigated. According to our findings, metrics of Patch Density and Landscape Shape Index can be used at the 1-km scale to asses density and geometric complexity of urban form. With the addition of MODIS land surface temperature (LST) data, available at high temporal resolution, a move away from or toward more sustainable urban forms is defined in relation to mitigation of the urban heat island. As the geometric complexity and density of finer-scale urban characteristics are related to climatic impacts at the neighborhood scale, sustainability assessments may be more attainable across urban areas.

Mode shape-based damage identification for a reinforced concrete beam using wavelet coefficient differences and multiresolution analysis

In this paper, the structural mode shapes extracted from the finite element model of a simply supported reinforced concrete beam are employed for damage identification using different types of wavelets. To start with, the parity of signals, wavelets, and their convolution, that is, wavelet transform properties, are verified. In light of the mathematical modeling complexity of modal frequency, which relates to the localization and quantification of damage in the reinforced concrete beam, the maximum curves based on multiresolution wavelet transform coefficient differences and the corresponding theoretical assumptions are described and analyzed. It is concluded that the maximum curve reaches a peak value at a specific scale for a specific case, based upon which, a new mode shape based algorithm and damage index are proposed for damage identification. The accuracy of localization as well as the sensitivity of quantification is further discussed.

Multiresolution wavelet transform based feature extraction and ECG classification to detect cardiac abnormalities

Analysis of electrocardiogram (ECG) signal provides valuable information about the heart conditions of the patient to the clinicians. The wavelet transform is an effective tool for extracting discriminative features in ECG signal classification for automatic diagnosis of cardiac arrhythmia. In this paper we proposed an improved algorithm to detect QRS complex features based on the multiresolution wavelet transform to classify four types of ECG beats. Extracted features are used for classifying cardiac abnormalities: normal (N), left bundle branch block (LBBB), right bundle branch block (RBBB), Paced beats (P) using neural network (NN) and support vector machines (SVM) classifier. The performance of the method is evaluated in terms of sensitivity, specificity, accuracy for 48 recorded ECG signals obtained from the MIT–BIH arrhythmia database. The proposed process achieved high detection performance with less error rate of 0.42% in detecting QRS complex. The classifier confirmed its superiority with an average accuracy of 96.67% and 98.39% in NN and SVM respectively. The classification accuracy of SVM approach proves superior for the proposed method to that of the NN classifier with extracted parameter in detecting ECG arrhythmia beats.

A Novel Technique Using Multiresolution Wavelet Packet Decomposition for Real Time Diagnosis of Hunting in Line Start IPM Motor Drives

A line-start interior permanent magnet (LSIPM) motor operates with inherent hunting phenomena. This paper presents a novel procedure for real-time diagnosis of hunting in LSIPM motors based on stator current signatures. Torsional vibration associated with hunting in a LSIPM motor influences the electrical supply, and introduces variable amplitude lower and upper sidebands in the stator current. In this paper, wavelet packet decomposition is applied to perform multiresolution analysis of the nonstationary current signals for detection and extraction of the sideband frequency components superimposed on the fundamental. Statistical techniques are applied on the extracted data signals and a signature for the diagnosis of hunting phenomenon is established. The proposed technique is validated by performing finite element analysis (FEA) of two three-phase four-pole LSIPM motors of different power ratings for various case scenarios. Experimental investigations have been carried out for a three-phase four-pole 208-V, 1-HP LSIPM motor drive in order to validate the performance of the proposed method under various operating conditions. Based on FEA and experimental results, the proposed technique can successfully diagnose the hunting phenomenon without a vibration sensor.

Day-ahead Forecasting of Non-stationary Electric Power Demand in Commercial Buildings: Hybrid Support Vector Regression Based

Abstract Accurate and highly-generalized forecasting models of hourly electric power demand are in urgent need for buildings, as to be the basis of operation management and bottom-up regional energy forecasting. Combined with multi-resolution wavelet decomposition (MWD), a hybrid support vector regression model was applied in a non-stationary operated hotel to predict the hourly electric power. With 15-dimensional parameters of 29 clustered days as the training sample, a nonlinear SVR model was carried out. Relative errors (RE) with and without MWD were compared at different ɛ-non-insensitive values. Results show that the MWD processing can reduce the deviations slightly only when ɛ is higher than 0.1, and the optimal daily mean RE of a typical day is around 5.6%. This paper aims to offer engineers and planners a feasible method for energy prediction based on the historical meter readings.

Adaptive wavelet-enriched hierarchical finite element model for polycrystalline microstructures

This paper proposes an adaptive, wavelet-enriched hierarchical finite element model (FEM) to enhance computational efficiency and solution accuracy for heterogeneous domains of anisotropic elastic materials. It is motivated by the need to overcome shortcomings of conventional methods like the standard FEM or fast Fourier transformation (FFT) based method for analyzing deformation in large polycrystalline microstructures. The multi-resolution wavelet functions are advantageous for selection of an optimal set of functions that can adaptively enrich the solution space with a prescribed level of accuracy. The proposed method introduces a discretization space that conforms to the profile of the solution sought. The method engages a second generation family of wavelets with a lifting scheme to generate hierarchical interpolation functions. An iterative algorithm efficiently calculates estimates of the solution from the previous iterate using a modified Jacobi method. The adaptive FE method performs significantly better than uniformly refined FEM in validation tests with focus on the convergence rate and error mitigation. A polycrystalline microstructure with elastically anisotropic grains is simulated by the adaptive wavelet-enriched hierarchical method, showing high convergence rates.

Short-term prediction of electric demand in building sector via hybrid support vector regression

Reliable and highly-generalized prediction models of short-term electric demand are urgently needed for the building sector, as the crucial basis of sophisticated building energy management. Advances in metering technologies and machine learning methods provide both opportunities and challenges for modified approaches. With multi-resolution wavelet decomposition (MWD) as a preprocessing from the point of view of signal analysis, the hybrid support vector regression (SVR) model was applied in two case study buildings to predict the hourly electric demand intensity. Taking ten-dimensional parameters of 29 workdays as the training sample, this model was carried out in a mall and a hotel, the consumed electric demand sequences of which represented the stationary and non-stationary series respectively.By comparisons between the hybrid SVR and the pure SVR, results indicated that the introduction of MWD can always improve the predicting accuracy for the hotel, while it is not necessary for the mall. Specifically, the similar steady level around 0.65W/m2 of absolute error was obtained for the mall and the hotel buildings, when ε was lower than 0.1. At the same time, the steady quantitative values of relative errors tended to be around 4% and 6% respectively for the hotel and the mall. Based on the limited historical readings, this paper offers an on-line prediction method of short-term electric demand, which is applicable for the further smart energy management.

Does Health Spending Crowd out Defense in the United States? Evidence from Wavelet Multiresolution Analysis

This study investigates the association between defense and health spending using multi-resolution analysis incorporating the structural change model. Our empirical results suggested that a negative correlation between defense and health spending persists over the entire period of 1941–2013 in the very long-run (over 16 years cycle), but there is a change in correlation between defense and health spending in the short-run (2–4 years cycle), medium-run (4–8 years cycle), and long-run (8–16 years cycle) during the same period. In particular, there appears to have been a trade-off relationship between defense and health spending during the ex-Korean War period, but there was a complementary relationship between defense and health spending during the post-Korean War period. The crowding-out effect of health spending on defense spending during the period when the Affordable Care Act was put into effect relies on the strength of the positive correlation in the long-run (8–16 years cycle) and negative correlation in the short-run (2–4 years cycle) and very long-run (over 16 years cycle).

A New Approach for Classification of Fault in Transmission Line with Combination of Wavelet Multi Resolution Analysis and Neural Networks

An appropriate fault detection and classification of power system transmission line using discrete wavelet transform and artificial neural networks is performed in this paper. The analysis is carried out by applying discrete wavelet transform for obtained fault phase currents. The work represented in this paper are mainly concentrated on classification of fault and this classification is done based on the obtained energy values after applying discrete wavelet transform by taking this values as an input for the neural network. The proposed system and analysis is carried out in Matlab Simulink.

A New Approach for Classification of Fault in Transmission Line with Combination of Wavelet Multi Resolution Analysis and Neural Networks

An appropriate fault detection and classification of power system transmission line using discrete wavelet transform and artificial neural networks is performed in this paper. The analysis is carried out by applying discrete wavelet transform for obtained fault phase currents. The work represented in this paper are mainly concentrated on classification of fault and this classification is done based on the obtained energy values after applying discrete wavelet transform by taking this values as an input for the neural network. The proposed system and analysis is carried out in Matlab Simulink.

Three-Dimensional Segmentation of the Ex-Vivo Anterior Lamina Cribrosa From Second-Harmonic Imaging Microscopy.

The lamina cribrosa (LC) is a connective tissue in the posterior eye with a complex mesh-like trabecular microstructure, through which all the retinal ganglion cell axons and central retinal vessels pass. Recent studies have demonstrated that changes in the structure of the LC correlate with glaucomatous damage. Thus, accurate segmentation and reconstruction of the LC is of utmost importance. This paper presents a new automated method for segmenting the microstructure of the anterior LC in the images obtained via multiphoton microscopy using a combination of ideas. In order to reduce noise, we first smooth the input image using a 4-D collaborative filtering scheme. Next, we enhance the beam-like trabecular microstructure of the LC using wavelet multiresolution analysis. The enhanced LC microstructure is then automatically extracted using a combination of histogram thresholding and graph-cut binarization. Finally, we use morphological area opening as a postprocessing step to remove the small and unconnected 3-D regions in the binarized images. The performance of the proposed method is evaluated using mutual overlap accuracy, Tanimoto index, F-score, and Rand index. Quantitative and qualitative results show that the proposed algorithm provides improved segmentation accuracy and computational efficiency compared to the other recent algorithms.

A dyadic multi-resolution deep convolutional neural wavelet network for image classification

For almost the past four decades, image classification has gained a lot of attention in the field of pattern recognition due to its application in various fields. Given its importance, several approaches have been proposed up to now. In this paper, we will present a dyadic multi-resolution deep convolutional neural wavelets’ network approach for image classification. This approach consists of performing the classification of one class versus all the other classes of the dataset by the reconstruction of a Deep Convolutional Neural Wavelet Network (DCNWN). This network is based on the Neural Network (NN) architecture, the Fast Wavelet Transform (FWT) and the Adaboost algorithm. It consists, first, of extracting features using the FWT based on the Multi-Resolution Analysis (MRA). These features are used to calculate the inputs of the hidden layer. Second, those inputs are filtered by using the Adaboost algorithm to select the best ones corresponding to each image. Third, we create an AutoEncoder (AE) using wavelet networks of all images. Finally, we apply a pooling for each hidden layer of the wavelet network to obtain a DCNWN that permits the classification of one class and rejects all other classes of the dataset. Classification rates given by our approach show a clear improvement compared to those cited in this article.

A wavelet analysis of mean and volatility spillovers between oil and BRICS stock markets

This paper investigates the spillover effects of volatility and shocks between oil prices and the BRICS stock markets using multivariate approach and wavelet analysis at different time horizons. Hence, we combine a multivariate ARMA-GARCH model and wavelet multiresolution analysis to study this phenomenon. A bivariate ARMA(1,1)-GARCH(1,1)-cDCC-Student-t model was joined with MODWT filter to capture a broad range of possible spillover effects in mean and variances of level prices at various time horizons. Generally, empirical results provide strong evidence of time-varying volatility in all markets under study. However, our proposed approach shows that oil price and stock market prices are directly affected by their own news and volatilities and indirectly affected by the volatilities of other prices and wavelet scale. The results show also, that mean and volatility spillover effects was decomposed into many sub-spillovers on different time scales according to heterogeneous investors and market participants. The practical implications of this study are critical, innovative and useful for the local and international investors and also for the portfolio managers. They can utilize this study to formulate the optimal oil-BRICKS stock portfolios as well as lead to more accurate predictions of volatility spillovers patterns also in developing their hedging strategies.

Hybrid Time-Variant Frequency Response Function Estimates Using Multiple Sets of Basis Functions

A new method for estimating the nonparametric time-variant frequency response function (TV-FRF) and its variance of a hybrid time-varying system is proposed. By parameterizing the hybrid time variation using Legendre polynomials and Haar multiresolution wavelets, the TV-FRF identification problem is reduced to a time-invariant FRF estimation problem. The stepwise regression method and Akaike information criterion are applied to select the significant basis functions without manual intervention. This method can achieve high estimation accuracy and small uncertainty without requiring prior knowledge of the time variation of system dynamics. Simulations and an experiment are included to illustrate the method.

Multi-time-scale hydroclimate dynamics of a regional watershed and links to large-scale atmospheric circulation: Application to the Seine river catchment, France

In the present context of global changes, considerable efforts have been deployed by the hydrological scientific community to improve our understanding of the impacts of climate fluctuations on water resources. Both observational and modeling studies have been extensively employed to characterize hydrological changes and trends, assess the impact of climate variability or provide future scenarios of water resources. In the aim of a better understanding of hydrological changes, it is of crucial importance to determine how and to what extent trends and long-term oscillations detectable in hydrological variables are linked to global climate oscillations.In this work, we develop an approach associating correlation between large and local scales, empirical statistical downscaling and wavelet multiresolution decomposition of monthly precipitation and streamflow over the Seine river watershed, and the North Atlantic sea level pressure (SLP) in order to gain additional insights on the atmospheric patterns associated with the regional hydrology. We hypothesized that: (i) atmospheric patterns may change according to the different temporal wavelengths defining the variability of the signals; and (ii) definition of those hydrological/circulation relationships for each temporal wavelength may improve the determination of large-scale predictors of local variations.The results showed that the links between large and local scales were not necessarily constant according to time-scale (i.e. for the different frequencies characterizing the signals), resulting in changing spatial patterns across scales. This was then taken into account by developing an empirical statistical downscaling (ESD) modeling approach, which integrated discrete wavelet multiresolution analysis for reconstructing monthly regional hydrometeorological processes (predictand: precipitation and streamflow on the Seine river catchment) based on a large-scale predictor (SLP over the Euro-Atlantic sector). This approach basically consisted in three steps: 1 – decomposing large-scale climate and hydrological signals (SLP field, precipitation or streamflow) using discrete wavelet multiresolution analysis, 2 – generating a statistical downscaling model per time-scale, 3 – summing up all scale-dependent models in order to obtain a final reconstruction of the predictand. The results obtained revealed a significant improvement of the reconstructions for both precipitation and streamflow when using the multiresolution ESD model instead of basic ESD. In particular, the multiresolution ESD model handled very well the significant changes in variance through time observed in either precipitation or streamflow. For instance, the post-1980 period, which had been characterized by particularly high amplitudes in interannual-to-interdecadal variability associated with alternating flood and extremely low-flow/drought periods (e.g., winter/spring 2001, summer 2003), could not be reconstructed without integrating wavelet multiresolution analysis into the model. In accordance with previous studies, the wavelet components detected in SLP, precipitation and streamflow on interannual to interdecadal time-scales could be interpreted in terms of influence of the Gulf-Stream oceanic front on atmospheric circulation.

A Hybrid Wavelet-Based Method for the Peak Detection of Photoplethysmography Signals.

The noninvasive peripheral oxygen saturation (SpO2) and the pulse rate can be extracted from photoplethysmography (PPG) signals. However, the accuracy of the extraction is directly affected by the quality of the signal obtained and the peak of the signal identified; therefore, a hybrid wavelet-based method is proposed in this study. Firstly, we suppressed the partial motion artifacts and corrected the baseline drift by using a wavelet method based on the principle of wavelet multiresolution. And then, we designed a quadratic spline wavelet modulus maximum algorithm to identify the PPG peaks automatically. To evaluate this hybrid method, a reflective pulse oximeter was used to acquire ten subjects' PPG signals under sitting, raising hand, and gently walking postures, and the peak recognition results on the raw signal and on the corrected signal were compared, respectively. The results showed that the hybrid method not only corrected the morphologies of the signal well but also optimized the peaks identification quality, subsequently elevating the measurement accuracy of SpO2 and the pulse rate. As a result, our hybrid wavelet-based method profoundly optimized the evaluation of respiratory function and heart rate variability analysis.

Wavelet Decomposition of the Financial Cycle: An Early Warning System for Financial Tsunamis

We propose a wavelet-based approach for construction of a financial cycle proxy. Specifically, we decompose three key macro-financial variables – private credit, house prices, and stock prices – on a frequency-scale basis using wavelet multiresolution analysis. The resulting “wavelet-based” sub-series are aggregated into a composite index representing our cycle proxy. Selection of the sub-series deemed most relevant is done by emphasizing early warning properties. The wavelet-based financial cycle proxy is shown to perform well in detecting banking crises in out-of-sample exercises, outperforming the credit-to-GDP gap and a financial cycle proxy derived using the approach of Schuler et al. (2015).

An Adaptive and Time-Efficient ECG R-Peak Detection Algorithm.

R-peak detection is crucial in electrocardiogram (ECG) signal analysis. This study proposed an adaptive and time-efficient R-peak detection algorithm for ECG processing. First, wavelet multiresolution analysis was applied to enhance the ECG signal representation. Then, ECG was mirrored to convert large negative R-peaks to positive ones. After that, local maximums were calculated by the first-order forward differential approach and were truncated by the amplitude and time interval thresholds to locate the R-peaks. The algorithm performances, including detection accuracy and time consumption, were tested on the MIT-BIH arrhythmia database and the QT database. Experimental results showed that the proposed algorithm achieved mean sensitivity of 99.39%, positive predictivity of 99.49%, and accuracy of 98.89% on the MIT-BIH arrhythmia database and 99.83%, 99.90%, and 99.73%, respectively, on the QT database. By processing one ECG record, the mean time consumptions were 0.872 s and 0.763 s for the MIT-BIH arrhythmia database and QT database, respectively, yielding 30.6% and 32.9% of time reduction compared to the traditional Pan-Tompkins method.

SOLUTION OF 1D AND 2D POISSON'S EQUATION BY USING WAVELET SCALING FUNCTIONS

The use of multiresolution techniques and wavelets has become increasingly popular in the development of numerical schemes for the solution of partial differential equations (PDEs). Therefore, the use of wavelet scaling functions as a basis in computational analysis holds some promise due to their compact support, orthogonality and localization properties. Daubechies and Deslauriers-Dubuc functions have been successfully used as basis functions in several schemes like the Wavelet- Galerkin Method (WGM) and the Wavelet Finite Element Method (WFEM). Another possible advantage of their use is the fact that the calculation of integrals of inner products of wavelet scaling functions and their derivatives can be made by solving a linear system of equations, thus avoiding the problem of using approximations by some numerical method. These inner products were defined as connection coefficients and they are employed in the calculation of stiffness matrices and load vectors. In this work, some mathematical foundations regarding wavelet scaling functions, their derivatives and connection coefficients are reviewed. A scheme based on the Galerkin Method is proposed for the direct solution of Poisson's equation (potential problems) in a meshless formulation using interpolating wavelet scaling functions (Interpolets). The applicability of the proposed method and some convergence issues are illustrated by means of a few examples.

Analysis of Stock Index Futures Market Fluctuation Based on Wavelet Multi Resolution

Analysis of Stock Index Futures Market Fluctuation Based on Wavelet Multi Resolution