Research on De-noising of Downhole Engineering Parameters by Wavelet based on Improved Threshold Function

The measurement of downhole engineering parameters is greatly disturbed by the working environment. Effective de-noising methods are required for processing logging-while-drilling (LWD) acquisition signals, in order to obtain downhole engineering parameters accurately and effectively. In this paper, a new de-noising method for measuring downhole engineering parameters was presented, based on a feedback method and a wavelet transform threshold function. Firstly, in view of the mutability and density of downhole engineering data, an improved wavelet threshold function was proposed to de-noise the signal, so as to overcome the shortcomings of data oscillation and deviation caused by the traditional threshold function. Secondly, due to the unknown true value, traditional single denoising effect evaluation cannot meet the requirements of quality evaluation very well. So the root mean square error (RMSE), signal-to-noise ratio (SNR), smoothness (R) and fusion indexs (F) are used as the evaluation parameters of the de-noising effect, which can determine the optimal wavelet decomposition scale and the best wavelet basis. Finally, the proposed method was verified based on the measured downhole data. The experimental results showed that the improved wavelet de-noising method could reduce all kinds of interferences in the LWD signal, providing reliable measurement for analyzing the working status of the drilling bit.

Novel Adaptive Hybrid Discontinuous Galerkin Algorithms for Elliptic Problems

In this work, we develop novel adaptive hybrid discontinuous Galerkin algorithms for second-order elliptic problems. For this, two types of reliable and efficient, modulo a data-oscillation term, and fully computable a posteriori error estimators are developed: the first one is a simple residual type error estimator, and the second is a flux reconstruction based error estimator of a guaranteed type for polynomial approximations of any degree by using a simple postprocessing. These estimators can achieve high-order accuracy for both smooth and nonsmooth problems even with high-order approximations. In order to enhance the performance of adaptive algorithms, we introduce 𝐾-means clustering based marking strategy. The choice of marking parameter is crucial in the performance of the existing strategy such as maximum and bulk criteria; however, the optimal choice is not known. The new strategy has no unknown parameter. Several numerical examples are given to illustrate the performance of the new marking strategy along with our estimators.