The Empirical Adaptive Wavelet Decomposition (EAWD): An adaptive decomposition for the variability analysis of observation time series in atmospheric science

Most observational 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 have often characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at different time-scales. The variability analysis of a time series consists in decomposing it into several mode of variability, each mode representing the fluctuations of the original time series at a specific time-scale. Such a decomposition enables to obtain a time-frequency representation of the original time series and turns out to be very useful to estimate the dimensionality of the underlying dynamics. Decomposition techniques very well suited to non-linear and non-stationary time series have recently been developed in the literature. Among the most widely used of these technics are the empirical mode decomposition (EMD) and the empirical wavelet transformation (EWT). The purpose of this paper is to present a new adaptive filtering method that combines the advantages of the EMD and EWT technics, while remaining close to the dynamics of the original signal made of atmospheric observations, which means reconstructing as close as possible to the original time series, while preserving its variability at different time scales.

Connecting the Dots between Geology and Seismic to Mitigate Drilling Risks: Mapping & Characterization of the High Pressure High Temperature Gotnia Formation in Kuwait

As Kuwait focuses on developing the deep Jurassic reservoirs, the Gotnia Formation presents significant drilling challenges. It is the regional seal, consisting of alternating Salt and Anhydrite cycles, with over-pressured carbonate streaks, which are also targets for future exploration. The objective of this study was to unravel the Gotnia architecture, through detailed mapping of the intermediate cycles, mitigating drilling risks and characterizing the carbonate reservoirs. A combination of noise attenuation, bandwidth extension and seismic adaptive wavelet processing (SAWP)) was applied on the seismic data, to improve the signal-to-noise ratio of the seismic data between 50Hz to 70Hz and therefore reveal the Anhydrite cycles, which house the carbonate streaks. The Salt-Anhydrite cycles were correlated, using Triple Combo and Elastic logs, in seventy-six wells, and spatially interpreted on the band-limited P-impedance volume, generated through pre-stack inversion. Pinched out cycles were identified by integrating mud logs with seismic data and depositional trends. Pre-stack stochastic inversion was performed to map the thin carbonate streaks and characterize the carbonate reservoirs. The improved seismic resolution resulted in superior results compared to the legacy cube and aided in enhancing the reflector continuity of Salt-Anhydrite cycles. In corroboration with the well data, three cycles of alternating salt and anhydrite, with varying thickness, were mapped. These cycles showed a distinctive impedance contrast and were noticeably more visible on the P-impedance volume, compared to the seismic amplitude volume. The second Anhydrite cycle was missing in some wells and the lateral extension of the pinch-outs was interpreted and validated based on the P-impedance volume. As the carbonate streaks were beyond the seismic resolution, they were not visible on the Deterministic P-impedance. The amount of thin carbonate streaks within the Anhydrite cycles could be qualitatively assessed based on the impedance values of the entire zone. Areas, within the zone, with a higher number of and more porous carbonate streaks displayed lowering of the overall impedance values in the Anhydrite zones, and could pose drilling risks. This information was used to guide the pre-stack stochastic inversion to populate the thin carbonate streaks and generate a high-resolution facies volume, through Bayesian Classification. Through this study, the expected cycles and over-pressured carbonate layers in the Gotnia formation were predicted, which can be used to plan and manage the drilling risks and reduce operational costs. This study presents an integrated and iterative approach to interpretation, where the well log analysis, seismic inversion and horizon interpretation were done in parallel, to develop a better understanding of the sub-surface. This workflow will be especially useful for interpretation of over-pressured overburden zones or cap rocks, where the available log data can be limited.

Particle Swarm Optimization and Fuzzy C-means for Domain-independent Noisy Image Segmentation

<p>Image segmentation is considered to be one of the foremost image analysis techniques for high-level real-world applications in computer vision. Its task is to change or simplify the representation of an image in order to make it easier to understand or analyze. Although image segmentation has been studied for many years, evolving technology and transformation of demands make image segmentation a continuing challenge. Noise as a side effect of imaging devices is an inevitable part of images in many computer vision applications. Therefore, an important topic in image segmentation is noisy image segmentation which requires extra effort to deal with image segmentation in the presence of noise. Generally, different strategies are needed for different noisy images with different levels/types of noise. Therefore, many approaches in the literature are domain-dependent and applicable only to specific images. A well-recognized approach in noisy image segmentation uses clustering algorithms, among which Fuzzy C-Means (FCM) is one of the most popular. FCM is unsupervised, efficient, and can deal with uncertainty and complexity of information in an image. Dealing with uncertainties is easier with the fuzzy characteristic of FCM, and complexity of information is being taken care of by utilizing different features in FCM, and also combining FCM with other techniques. Many modifications have been introduced to FCM to deal with noisy image segmentation more effectively. Common approaches include, adding spatial information into the FCM process, addressing the FCM initialization problem, and enhancing features used for segmentation. However, existing FCM-based noisy image segmentation approaches in the literature generally suffer from three drawbacks. First, they are applicable to specific domains and images, and impotent in others. Second, they don’t perform well on severely noisy image segmentation. Third, they are effective on specific type and level of noise, and they don’t explore the effect of noise level variation. Recently, evolutionary computation techniques due to their global search abilities have been used in hybridization with FCM, mostly to address FCM stagnation in local optima. Particle Swarm Optimization (PSO) is particularly of interest because of its lower computational costs, easy implementation, and fast convergence, but its potential in this area has not been fully investigated. This thesis develops new domain-independent PSO-based algorithms for an automatic non-supervised FCM-based segmentation of severely noisy images which are capable of extracting the main coherent/homogeneous regions while preserving details and being robust to noise variation. The key approach taken in the thesis is to explore the use of PSO to manipulate and enhance local spatial and spatial-frequency information. This thesis introduces a new PSO feature enhancement approach in wavelet domain for noisy image segmentation. This approach applies adaptive wavelet shrinkage using evaluation based on FCM clustering performance. The results show great accuracy in the case of severe noise because of the enhanced features. Also, due to adaptivity, no parameter-tuning is required according to the type or volume of noise, and the performance is consistent under noise level variation. This thesis presents a scheme under which a fusion of two different denoising algorithms for more effective segmentation is possible. This fusion retains the advantages of each algorithm while leaving out their drawbacks. The fusion scheme uses the noisy image segmentation system introduced above and anisotropic diffusion, the edge-preserving denoising algorithm. Results show greater accuracy and stability in comparison to the individual algorithms on a variety of noisy images. This thesis introduces another PSO-based edge-preserving adaptive wavelet shrinkage system using wavelet packets, bilateral filtering, and a detail-respecting shrinkage scheme. The analysis of the results provide a comparison between the two feature enhancement systems. The first system uses wavelets and the second uses wavelet packets as a domain to enhance features for an FCM-based noisy image segmentation. Also, the highest segmentation accuracy among all the algorithms introduced in this thesis on some benchmarks belong to this system.</p>

Particle Swarm Optimization and Fuzzy C-means for Domain-independent Noisy Image Segmentation

<p>Image segmentation is considered to be one of the foremost image analysis techniques for high-level real-world applications in computer vision. Its task is to change or simplify the representation of an image in order to make it easier to understand or analyze. Although image segmentation has been studied for many years, evolving technology and transformation of demands make image segmentation a continuing challenge. Noise as a side effect of imaging devices is an inevitable part of images in many computer vision applications. Therefore, an important topic in image segmentation is noisy image segmentation which requires extra effort to deal with image segmentation in the presence of noise. Generally, different strategies are needed for different noisy images with different levels/types of noise. Therefore, many approaches in the literature are domain-dependent and applicable only to specific images. A well-recognized approach in noisy image segmentation uses clustering algorithms, among which Fuzzy C-Means (FCM) is one of the most popular. FCM is unsupervised, efficient, and can deal with uncertainty and complexity of information in an image. Dealing with uncertainties is easier with the fuzzy characteristic of FCM, and complexity of information is being taken care of by utilizing different features in FCM, and also combining FCM with other techniques. Many modifications have been introduced to FCM to deal with noisy image segmentation more effectively. Common approaches include, adding spatial information into the FCM process, addressing the FCM initialization problem, and enhancing features used for segmentation. However, existing FCM-based noisy image segmentation approaches in the literature generally suffer from three drawbacks. First, they are applicable to specific domains and images, and impotent in others. Second, they don’t perform well on severely noisy image segmentation. Third, they are effective on specific type and level of noise, and they don’t explore the effect of noise level variation. Recently, evolutionary computation techniques due to their global search abilities have been used in hybridization with FCM, mostly to address FCM stagnation in local optima. Particle Swarm Optimization (PSO) is particularly of interest because of its lower computational costs, easy implementation, and fast convergence, but its potential in this area has not been fully investigated. This thesis develops new domain-independent PSO-based algorithms for an automatic non-supervised FCM-based segmentation of severely noisy images which are capable of extracting the main coherent/homogeneous regions while preserving details and being robust to noise variation. The key approach taken in the thesis is to explore the use of PSO to manipulate and enhance local spatial and spatial-frequency information. This thesis introduces a new PSO feature enhancement approach in wavelet domain for noisy image segmentation. This approach applies adaptive wavelet shrinkage using evaluation based on FCM clustering performance. The results show great accuracy in the case of severe noise because of the enhanced features. Also, due to adaptivity, no parameter-tuning is required according to the type or volume of noise, and the performance is consistent under noise level variation. This thesis presents a scheme under which a fusion of two different denoising algorithms for more effective segmentation is possible. This fusion retains the advantages of each algorithm while leaving out their drawbacks. The fusion scheme uses the noisy image segmentation system introduced above and anisotropic diffusion, the edge-preserving denoising algorithm. Results show greater accuracy and stability in comparison to the individual algorithms on a variety of noisy images. This thesis introduces another PSO-based edge-preserving adaptive wavelet shrinkage system using wavelet packets, bilateral filtering, and a detail-respecting shrinkage scheme. The analysis of the results provide a comparison between the two feature enhancement systems. The first system uses wavelets and the second uses wavelet packets as a domain to enhance features for an FCM-based noisy image segmentation. Also, the highest segmentation accuracy among all the algorithms introduced in this thesis on some benchmarks belong to this system.</p>

An adaptive wavelet collocation method for the optimal heat source problem

Purpose This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP). Design/methodology/approach The main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction. Findings This paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution. Originality/value The proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.

Adaptive Multiple Second-order Synchrosqueezing Wavelet Transform and Its Application in Wind Turbine Gearbox Fault Diagnosis

Wind turbines usually operate in harsh environments and in working conditions of variable speed, which easily causes their key components such as gearboxes to fail. The gearbox vibration signal of a wind turbine has nonstationary characteristics, and the existing Time-Frequency (TF) Analysis (TFA) methods have some problems such as insufficient concentration of TF energy. In order to obtain a more apparent and more congregated Time-Frequency Representation (TFR), this paper proposes a new TFA method, namely Adaptive Multiple Second-order Synchrosqueezing Wavelet Transform (AMWSST2). Firstly, a short-time window is innovatively introduced on the foundation of classical Continuous Wavelet Transform (CWT), and the window width is adaptively optimized by using the center frequency and scale factor. After that, a smoothing process is carried out between different segments to eliminate the discontinuity and thus Adaptive Wavelet Transform (AWT) is generated. Then, on the basis of the theoretical framework of Synchrosqueezing Transform (SST) and accurate Instantaneous Frequency (IF) estimation by the utilization of second-order local demodulation operator, Adaptive Second-order Synchrosqueezing Wavelet Transform (AWSST2) is formed. Considering that the quality of actual time-frequency analysis is greatly disturbed by noise components, through performing multiple Synchrosqueezing operations, the congregation of TFR energy is further improved, and finally, the AMWSST2 algorithm studied in this paper is proposed. Since Synchrosqueezing operations are performed only in the frequency direction, this method AMWSST2 allows the signal to be perfectly reconstructed. For the verification of its effectiveness, this paper applies it to the processing of the vibration signal of the gearbox of a 750 kW wind turbine.