Adaptive Decomposition Scheme Research Articles

An Adaptive Decomposition Scheme for Wideband Signals of Power Systems Based on the Modified Robust Regression Smoothing and Chebyshev-II IIR Filter Bank

Distributed energy resources and new types of electrical loads are morphologically changing the signals of power grids. Grasping the wideband information of field data will play an important role in helping smart grids to operate in a safe manner. A wideband signal model composed of deterministic and stochastic components is proposed to enhance the wideband measurement. Based on the model, an adaptive decomposition scheme is designed for the offline analysis of wideband signals. In the scheme, a modified robust local regression smoothing method is presented to denoise the wideband signal. A totally data-dependent threshold is established to extract adaptively interharmonic components. Further, the Taylor-Fourier transform algorithm is used to estimate the parameters of deterministic components based on the subsignals extracted by the Chebyshev-II infinite impulse response filter bank. Finally, the stochastic components are extracted using the adaptive threshold based on the signal that the deterministic components are removed. The performances of the decomposition scheme under different conditions have been validated. In the end, the proposed decomposition scheme is carried out and verified with the field data of the 24-h current signals at one residence community.

An adaptive dimension decomposition and reselection method for reliability analysis

Recently, the research community in reliability analysis has seen a strong surge of interest in the dimension decomposition approach, which typically decomposes a multi-dimensional system response into a finite set of low-order component functions for more efficient reliability analysis. However, commonly used dimension decomposition methods suffer from two limitations. Firstly, it is often difficult or impractical to predetermine the decomposition level to achieve sufficient accuracy. Secondly, without an adaptive decomposition scheme, these methods may unnecessarily assign sample points to unimportant component functions. This paper presents an adaptive dimension decomposition and reselection (ADDR) method to resolve the difficulties of existing dimension decomposition methods for reliability analysis. The proposed method consists of three major components: (i) an adaptive dimension decomposition and reselection scheme to automatically detect the potentially important component functions and adaptively reselect the truly important ones, (ii) a test error indicator to quantify the importance of potentially important component functions for dimension reselection, and (iii) an integration of the newly developed asymmetric dimension-adaptive tensor-product (ADATP) method into the adaptive scheme to approximate the reselected component functions. The merits of the proposed method for reliability analysis are three-fold: (a) automatically detecting and adaptively representing important component functions, (b) greatly alleviating the curse of dimensionality, and (c) no need of response sensitivities. Several mathematical and engineering high-dimensional problems are used to demonstrate the effectiveness of the ADDR method.

A Nearly Linear-Time Approximation Scheme for the Euclidean k-Median Problem

This paper provides a randomized approximation scheme for the k-median problem when the input points lie in the d-dimensional Euclidean space. The worst-case running time is $O(2^{O((\log(1/\epsilon) / \varepsilon)^{d-1})} n \log^{d+6} n ),$ which is nearly linear for any fixed $\varepsilon$ and d. Moreover, our method provides the first polynomial-time approximation scheme for and uncapacitated facility location instances in d-dimensional Euclidean space for any fixed $d > 2.$ Our work extends techniques introduced originally by Arora for the Euclidean traveling salesman problem (TSP). To obtain the improvement we develop a structure theorem to describe hierarchical decomposition of solutions. The theorem is based on an adaptive decomposition scheme, which guesses at every level of the hierarchy the structure of the optimal solution and accordingly modifies the parameters of the decomposition. We believe that our methodology is of independent interest and may find applications to further geometric problems.

Data‐driven adaptive decomposition of multicomponent seabed recordings

Dual‐sensor (hydrophone and three‐component geophone) data recorded on the sea floor allow the elastic wavefield to be decomposed into its upgoing and downgoing P‐ and S‐wave components. Most decomposition algorithms require accurate knowledge of the elastic properties of the sea floor in the vicinity of the receivers and properly calibrated sensors, in order for the data to be a faithful vector representation of the ground motion. We present a multistep adaptive decomposition scheme that provides the necessary information directly from the data by imposing constraints on intermediate decomposition results. The proposed scheme requires no a priori information and only a minimal amount of user‐defined input, thus allowing multicomponent data to be decomposed in an automated data‐driven fashion. The performance of the technique is illustrated using seabed data acquired in the North Sea with prototype single sensors (multicomponent geophones individually sampled). Realistic sea floor properties and sensor calibration operators are obtained, and elastic decomposition of the calibrated data generally yields good results. Dominant water‐layer reverberations are successfully attenuated and primary reflections are substantially enhanced in the computed upgoing P‐wave potential just below the sea floor. In contrast, the result for the upgoing S‐wave potential is somewhat less convincing; although the energy of water‐layer multiples is substantially reduced, notable amounts of undesired multiple energy remain in this section after decomposition, particularly at high offsets. These imperfections may point to inaccuracies in the parametrization of the sea floor or remaining inaccuracies in the vector fidelity of the horizontal geophone recordings. Nevertheless, the results obtained with the extended data‐driven decomposition scheme are at least comparable to previously published results.

Adaptive decomposition of multicomponent ocean‐bottom seismic data into downgoing and upgoing P‐ and S‐waves

With wavefield decomposition, the recorded wavefield at a certain depth level can be separated into upgoing and downgoing wavefields as well as into P‐ and S‐waves. The medium parameters at the considered depth level (e.g., just below the ocean‐bottom) need to be known in order to be able to do a decomposition. In general, these parameters are unknown and, in addition, measurement‐related issues, such as geophone coupling and crosstalk between the different components, need to be dealt with. In order to apply decomposition to field data, an adaptive five‐stage decomposition scheme was developed in which these issues are addressed. In this study, the adaptive decomposition scheme is tested on a data example with a relatively shallow water depth (∼120 m), consisting recordings from of a full line of ocean‐bottom receivers. Although some of the individual stages in the decomposition scheme are more difficult to apply because of stronger interference between events compared to data acquired over deeper water, the end result is satisfying. Also, a good decomposition result is obtained for the S‐waves. The extension of the decomposition scheme to a complete line of ocean‐bottom cable data consists of a repeated application of the procedure for each receiver. The resulting decomposed upgoing P‐ and S‐wavefields are processed, yielding poststack time migrated images of the subsurface. Comparison with the images obtained from the original (i.e., not decomposed) measurements shows that wavefield decomposition just below the ocean bottom leads to a strong attenuation of multiply reflected events at the sea surface and better event definition in both P‐ and S‐wave sections. Other decomposition effects like improved angle‐dependent amplitudes cannot be evaluated in this way.