Wavelet-based Multiresolution Research Articles

A comparison of the finite difference and multiresolution method for the elliptic equations with Dirichlet boundary conditions on irregular domains

We make a comparison of the finite difference and multiresolution method for solving the elliptic equations on irregular domains. The Dirichlet boundary condition is treated by the ghost fluid method (GFM) for the finite difference method and the Lagrange multiplier for the multiresolution method. Numerical results illustrate the improved convergence rate of errors and their gradients with the multiresolution method, up to eighth-order. Moreover, the wavelet-based multiresolution has an advantage of preconditioning of the linear system arising from the discretization of elliptic equation over the finite difference method.

WearAuth: Wristwear-Assisted User Authentication for Smartphones Using Wavelet-Based Multi-Resolution Analysis

WearAuth: Wristwear-Assisted User Authentication for Smartphones Using Wavelet-Based Multi-Resolution Analysis

Characterization of Environmental Drivers Controlling the Baseline of Soil Surface CO2 Flux using Wavelet-based Multiresolution State-Space Model and Wavelet Denoising

Multivariate environmental time series including soil surface CO2 flux (FCO2) have non-stationarity and mutual interdependence, and thus the i.i.d assumption-based conventional regression techniques inevitably lead to spurious regression or lose the dynamic characteristics in the process of variable transformation. In this paper, we adopted a wavelet threshold technique for our newly developed wavelet-based multiresolution state-space model (MRSSM) to overcome such limitations and to quantitatively evaluate the environmental drivers (EDs) controlling the baseline of FCO2. First, the structural characteristics and the potential EDs (PEDs) of FCO2 were explored by wavelet denoised (threshold) SSM for complex environmental observation data. Then, the major EDs (MEDs) were identified using the scale localized correlation and the wavelet coherence analysis between PEDs and observation data. Next, the contribution of MEDs to FCO2 was quantitatively evaluated by calculating the effective dynamic efficiency using the wavelet energy ratio of the maximum-correlation time-frequency bands. Finally, the effectiveness of the wavelet threshold method for MRSSM was discussed. The proposed wavelet denoising method is expected to improve the performance of MRSSM which is effective to identify, evaluate and predict the main environmental factors inherent in the observation data from complex environmental systems where physicochemical and biological processes of various spatio-temporal scales occur simultaneously.

CLSA-MRPID controller for automatic generation control of a three-area hybrid system

In the paper, an optimal controller is proposed for Automatic Generation Control (AGC) of three areas under deregulated power system. In the power system area, each area under the deregulated framework incorporated with the renewable energy sources like Wind Turbine (WT) and Photovoltaic (PV). The proposed optimal controller is the utilization of Combined Lightening Search Algorithm (CLSA) with wavelet based Multi Resolution Proportional-Integral-Derivative (MRPID) controller. The purpose of the proposed controller is to sustain the system frequency close to its nominal value, regulate system output and maintain power balance under load variations. Here, the LSA optimization process is utilized for optimally tuning the parameters of MRPID controller for each area. The attained LSA gain parameters are subject to the minimum Integral Square Error (ISE), which ensures that the system frequency deviation, Area Control Error (ACE) and tie-line power as minimum. The proposed controller is implemented in MATLAB/Simulink platform and analyzed their AGC responses, frequency deviation. Examinations reveal that the LSA enhanced MRPID controller performance is superior to anything others as far as settling time, peak overshoot and magnitude of oscillations in the system for various classes of extensive deregulated cases. Under these circumstances, the simulation results demonstrate that the designed power system model might be a feasible one and the proposed CLSA-MRPID algorithm might be a promising method. In the work, optimization algorithm based control technique is developed for evaluating AGC. Therefore, the convergence graph is analyzed for the proposed and existing methods.

Path-planning with waiting in spatiotemporally-varying threat fields.

We address the problem of finding an optimal path for a vehicle in a planar environment where traversal costs are based on a time-varying spatial field defined over the environment. The resulting optimal path may contain instances of waiting, where the vehicle hovers, parks, or loiters. First, we consider path-planning on a uniform grid over the workspace. It is known that the computational complexity of the problem is significantly higher when waiting is allowed. We study the trade-off between the increased computational complexity and potential cost reductions in the resultant path with allowance for waiting. The results of numerical studies in this work identify characteristics of the threat fields in which optimal paths can involve waiting. Furthermore, we provide a local condition on the threat field that precludes waiting from providing any cost reductions in the resultant path. We show that this condition can be used in the path-planning algorithm to prune search trees and provide significant reductions in computation time without significant suboptimality. Next, we consider path-planning on a vehicle-centric multiresolution grid. We use a wavelet-based multiresolution decomposition to evaluate the multiresolution path planner and compare against the uniform resolution grid using the same family of threat fields. We show that with a vehicle-centric multiresolution map and an appropriate path-planning algorithm, the added computational effort of allowance for waiting is negligible.

Wavelet-based On-line Multiscale Subspace Identification of Nuclear Reactor

This paper formulates a methodology of on-line subspace identification in wavelet-based multiresolution framework. The proposed strategy integrates proficiency of wavelets for multiscale data representation with the robust parameter estimation ability of subspace identification. The efficacy of proposed technique is demonstrated on point kinetics nuclear reactor taking the effects of temperature and xenon poisoning into consideration. The nonlinear process is approximated by multiple linear state-space models identified at significant scales. Time variation in the process has been taken into account by updating parameters with the arrival of new dataset. It is validated through simulations that the proposed scheme gives better output prediction as compared to other single-scale and multiscale techniques.

Wavelet-Based Multiresolution Bispectral Analysis for Detection and Classification of Helicopter Drive-Shaft Problems

Condition monitoring and fault diagnostics in rotorcraft have significant effect on improving safety level and reducing operational and maintenance costs. In this paper, a new method is proposed for fault detection and diagnoses of AH-64D (Apache helicopter) tail rotor drive-shaft problems. The proposed method depends on decomposing signal into different frequency ranges using mother wavelet. The most informative part of the vibration signal is then determined by calculating Shannon entropy of each part. Bispectrum is calculated for this part to investigate quadratic nonlinearities in this segment. Then, search algorithm is used to extract minimum number of indicative features from the bispectrum, which are then fed to classification algorithms. In order to quantitatively evaluate the proposed method, six classification algorithms are compared against each other such as fine K-nearest neighbor (KNN), cubic KNN, quadratic discriminant analysis, linear support vector machine (SVM), Gaussian SVM, and neural network. Comparison criteria include accuracy, precision, sensitivity, F score, true alarm, recall, and error classification accuracy (ECA). The proposed method is verified using real-world vibration data collected from a dedicated AH-64D helicopter tail rotor drive train (TRDT) research test bed. The proposed algorithm proves its ability in finding minimum number of indicative features and classifying the shaft faults with superior performance.

Application of wavelet decomposition in time-series forecasting

Observed time series data can exhibit different components, such as trends, seasonality, and jumps, which are characterized by different coefficients in their respective data generating processes. Therefore, fitting a given time series model to aggregated data can be time consuming and may lead to a loss of forecasting accuracy. In this paper, coefficients for variable components in estimations are generated based on wavelet-based multiresolution analyses. Thus, the accuracy of forecasts based on aggregate data should be improved because the constraint of equality among the model coefficients for all data components is relaxed.

Investigation of the scaling characteristics of LANDSAT temperature and vegetation data: a wavelet-based approach.

An investigation of the scaling characteristics of vegetation and temperature data derived from LANDSAT data was undertaken for a heterogeneous area in Tamil Nadu, India. A wavelet-based multiresolution technique decomposed the data into large-scale mean vegetation and temperature fields and fluctuations in horizontal, diagonal, and vertical directions at hierarchical spatial resolutions. In this approach, the wavelet coefficients were used to investigate whether the normalized difference vegetation index (NDVI) and land surface temperature (LST) fields exhibited self-similar scaling behaviour. In this study, l-moments were used instead of conventional simple moments to understand scaling behaviour. Using the first six moments of the wavelet coefficients through five levels of dyadic decomposition, the NDVI data were shown to be statistically self-similar, with a slope of approximately -0.45 in each of the horizontal, vertical, and diagonal directions of the image, over scales ranging from 30 to 960m. The temperature data were also shown to exhibit self-similarity with slopes ranging from -0.25 in the diagonal direction to -0.20 in the vertical direction over the same scales. These findings can help develop appropriate up- and down-scaling schemes of remotely sensed NDVI and LST data for various hydrologic and environmental modelling applications. A sensitivity analysis was also undertaken to understand the effect of mother wavelets on the scaling characteristics of LST and NDVI images.

An efficient wavelet-based automated R-peaks detection method using Hilbert transform

Machine-aided detection of R-peaks is becoming a vital task to automate the diagnosis of critical cardiovascular ailments. R-peaks in Electrocardiogram (ECG) is one of the key segments for diagnosis of the cardiac disorder. By recognizing R-peaks, heart rate of the patient can be computed and from that point onwards heart rate variability (HRV), tachycardia, and bradycardia can also be determined. Most of the R-peaks detectors suffer due to non-stationary behaviors of the ECG signal. In this work, a wavelet transform based automated R-peaks detection method has been proposed. A wavelet-based multiresolution approach along with Shannon energy envelope estimator is utilized to eliminate the noises in ECG signal and enhance the QRS complexes. Then a Hilbert transform based peak finding logic is used to detect the R-peaks without employing any amplitude threshold. The efficiency of the proposed work is validated using all the ECG signals of MIT-BIH arrhythmia database, and it attains an average accuracy of 99.83%, sensitivity of 99.93%, positive predictivity of 99.91%, error rate of 0.17% and an average F-score of 0.9992. A close observation of the simulation and validation indicates that the suggested technique achieves superior performance indices compared to the existing methods for real ECG signal.

A new strategy based on power demand forecasting to the management of multi-energy district boilers equipped with hot water tanks

As part of the second phase of the research project “OptiEnR”, aiming to improve the operation of multi-energy district boilers by adding optimally-designed and managed hot water tanks to the plants, a new and generalized predictive strategy is proposed. This phase of the project was first dedicated to developing both a design approach, based on a parametric analysis, and a sequential management strategy. Basically, the excess thermal energy produced by the wood boiler unit(s) during low-demand periods can then be stored and released when demand is high, instead of engaging a gas boiler unit. However, this preliminary study has allowed us to point out possible improvements in the management of a tank. That is why we have decided to develop a flexible and generalized strategy based on anticipating changes in power demand. So, the present paper focuses on the optimal management, using a generalized model-based predictive controller, of an ENGIE Cofely’s multi-energy district boiler equipped with a hot water tank. The plant is located in northeast France, in the Grand Est region (Haut-Rhin). The controller makes use of a generic model of the district boiler and power demand is accurately forecasted over the next 24h thanks to the MRA-ANN approach (i.e. a wavelet-based Multi-Resolution Analysis combined with Artificial Neural Networks). With the predictive strategy, the consumption of gas and carbon dioxide (CO2) emissions are significantly reduced. In the same time, the overall economic gain is increased. Overall performance is the best with a 200m3 hot water tank added to the plant.

Five multiresolution-based calcium volume measurement techniques from coronary IVUS videos: A comparative approach

Background and objectiveFast intravascular ultrasound (IVUS) video processing is required for calcium volume computation during the planning phase of percutaneous coronary interventional (PCI) procedures. Nonlinear multiresolution techniques are generally applied to improve the processing time by down-sampling the video frames. MethodsThis paper presents four different segmentation methods for calcium volume measurement, namely Threshold-based, Fuzzy c-Means (FCM), K-means, and Hidden Markov Random Field (HMRF) embedded with five different kinds of multiresolution techniques (bilinear, bicubic, wavelet, Lanczos, and Gaussian pyramid). This leads to 20 different kinds of combinations. IVUS image data sets consisting of 38,760 IVUS frames taken from 19 patients were collected using 40 MHz IVUS catheter (Atlantis® SR Pro, Boston Scientific®, pullback speed of 0.5 mm/sec.). The performance of these 20 systems is compared with and without multiresolution using the following metrics: (a) computational time; (b) calcium volume; (c) image quality degradation ratio; and (d) quality assessment ratio. ResultsAmong the four segmentation methods embedded with five kinds of multiresolution techniques, FCM segmentation combined with wavelet-based multiresolution gave the best performance. FCM and wavelet experienced the highest percentage mean improvement in computational time of 77.15% and 74.07%, respectively. Wavelet interpolation experiences the highest mean precision-of-merit (PoM) of 94.06 ± 3.64% and 81.34 ± 16.29% as compared to other multiresolution techniques for volume level and frame level respectively. Wavelet multiresolution technique also experiences the highest Jaccard Index and Dice Similarity of 0.7 and 0.8, respectively. Multiresolution is a nonlinear operation which introduces bias and thus degrades the image. The proposed system also provides a bias correction approach to enrich the system, giving a better mean calcium volume similarity for all the multiresolution-based segmentation methods. After including the bias correction, bicubic interpolation gives the largest increase in mean calcium volume similarity of 4.13% compared to the rest of the multiresolution techniques. The system is automated and can be adapted in clinical settings. ConclusionsWe demonstrated the time improvement in calcium volume computation without compromising the quality of IVUS image. Among the 20 different combinations of multiresolution with calcium volume segmentation methods, the FCM embedded with wavelet-based multiresolution gave the best performance.

Performance of Wavelet-based Multiresolution Motion Estimation for Inbetweening in Old Animated Films

This paper investigates the performance of wavelet-based multiresolution motion estimation (MRME) for inbetweening in old animated films using three different MRME schemes. The three schemes are: coarse-to fine with a wavelet-based MRME, one of Zhang’s MRMEs, and an MRME in the spatial domain. In order to make a performance comparison of these MRME schemes, two video sequences were used for a simulation. The experimental results show that the coarse-to-fine method performed better than Zhang’s MRME and the MRME in the spatial domain. The evaluation results on block size 9x9 indicate that the coarse-to-fine method had an average peak signal-to-noise ratio (PSNR) of 23.48 dB for the first sequence and 29.84 for the second sequence.

A Novel Approach of Multiscale Feature Extraction for Gearbox Condition Monitoring

This paper proposes a novel multiscale slope feature extraction method using wavelet-based multiresolution anlaysis for gearboxes fault identification. The new method mainly includes the discrete wavelet transform (DWT), the variances calculation of multiscale detailed signals, and the wavelet-based multiscale slope features estimation. Experimental results show that the wavelet-based multiscale slope features show excellent clustering for different work conditions and have the merits of high accuracy and stability in classifying different conditions of gearbox.

Implementation of Wavelet-Based Controller for Battery Storage System of Hybrid Electric Vehicles

This paper presents a wavelet-based multiresolution proportional integral derivative (MRPID) controller for temperature control of the ambient air of battery storage system of the hybrid electric vehicles. In the proposed wavelet MRPID controller, the discrete wavelet transform (DWT) is used to decompose temperature error into frequency components at various resolution of the error signal. The wavelet transformed coefficients are scaled by suitable gains and then added together to generate the control signal of thermal system. The proposed wavelet controller is implemented for battery storage system in both simulation and experiments. The digital signal processor board is used for real-time implementation of the proposed controller. The performance of the proposed wavelet-based MRPID controller is compared with conventional proportional-integral-derivative (PID) and adaptive neural network controllers. The proposed wavelet controller for battery storage system is found more robust and quicker than the conventional and adaptive controllers.

Wavelet-Based Multiresolution NURBS Curve Fairing

A multiresolution approach is presented for NURBS curve fairing based on nonuniform semiorthogonal B-spline wavelets built. This method provides greater flexibility and applicability than uniform B-spline wavelets for multiresolution curve fairing. An example is presented to validate effectiveness of this multiresolution fairing method. Furthermore, the algorithm can be easily applied to NURBS curves in three dimensions as well as in two.

B-Spline Wavelet-Based Multiresolution Analysis of Surface Texture in End-Milling of Aluminum

Modern manufacturing requires close monitoring by correlating finer frequency regimes of the surface texture to process parameters. This paper presents a study of B-spline wavelet-based multiresolution analysis (MRA) for surface texture characterization and process parameter correlation in end-milling. Motivated by multiresolution curves in computer graphics, an initial B-spline surface is first interpolated to the measured points of the surface texture. With a B-spline wavelet transform, the initial surface is decomposed into higher-frequency details and lower-frequency approximations. By taking the reconstructed surface roughness, waviness, and form based on different frequency regimes as the responses, regression models are created by considering the feed rate, spindle speed, axial depth of cut, and tool wear as controllable variables. The case studies and comparisons with an International Organization for Standardization (ISO) Gaussian filter have demonstrated the effectiveness of the proposed B-spline wavelet-based MRA algorithm for a surface texture analysis and manufacturing process diagnostics.

Extraction of Line Features from Multifidus Muscle of CT Scanned Images with Morphologic Filter Together with Wavelet Multi Resolution Analysis

A method for line feature extraction from multifidus muscle of Computer Tomography (CT) scanned image with morphologic filter together with wavelet based Multi Resolution Analysis (MRA) is proposed. The contour of the multifidus muscle can be extracted from hip CT image. The area of multifidus muscle is then estimated and is used for an index of belly fat because there is a high correlation between belly fat and multifidus muscle. When the area of the multifidus muscle was calculated from the CT image, the MRA with Daubechies base functions and with the parameter of MRA of level is three would appropriate. After the wavelet transformation is applied to the original hip CT image three times and LLL (3D low frequency components) is filled “0” then inverse wavelet transformation is applied for reconstruction. The proposed method is validated with four patients.

A wavelet-based multiresolution approach to large-eddy simulation of turbulence

The wavelet-based multiresolution analysis (MRA) technique is used to develop a modelling approach to large-eddy simulation (LES) and its associated subgrid closure problem. The LES equations are derived by projecting the Navier–Stokes (N–S) equations onto a hierarchy of wavelet spaces. A numerical framework is then developed for the solution of the large and the small-scale equations. This is done in one dimension, for the Burgers equation, and in three dimensions, for the N–S problem. The proposed methodology is assessed in a priori tests on an atmospheric turbulent time series and on data from direct numerical simulation. A posteriori (dynamic) tests are also carried out for decaying and force-driven Burgers turbulence.

Single-resolution and multiresolution extended-Kalman-filter-based reconstruction approaches to optical refraction tomography

The problem of reconstruction of a refractive-index distribution (RID) in optical refraction tomography (ORT) with optical path-length difference (OPD) data is solved using two adaptive-estimation-based extended-Kalman-filter (EKF) approaches. First, a basic single-resolution EKF (SR-EKF) is applied to a state variable model describing the tomographic process, to estimate the RID of an optically transparent refracting object from noisy OPD data. The initialization of the biases and covariances corresponding to the state and measurement noise is discussed. The state and measurement noise biases and covariances are adaptively estimated. An EKF is then applied to the wavelet-transformed state variable model to yield a wavelet-based multiresolution EKF (MR-EKF) solution approach. To numerically validate the adaptive EKF approaches, we evaluate them with benchmark studies of standard stationary cases, where comparative results with commonly used efficient deterministic approaches can be obtained. Detailed reconstruction studies for the SR-EKF and two versions of the MR-EKF (with Haar and Daubechies-4 wavelets) compare well with those obtained from a typically used variant of the (deterministic) algebraic reconstruction technique, the average correction per projection method, thus establishing the capability of the EKF for ORT. To the best of our knowledge, the present work contains unique reconstruction studies encompassing the use of EKF for ORT in single-resolution and multiresolution formulations, and also in the use of adaptive estimation of the EKF's noise covariances.