Sifting Process Of Empirical Mode Decomposition Research Articles

Eliminating the end effect of empirical mode decomposition using a cubic spline based method

The empirical mode decomposition (EMD) is a method that is commonly applied to extract the intrinsic mode functions (IMFs) of a signal by a sifting process, which requires imposing the extended extrema at both ends of the signal (i.e., the end condition). The imposition of extended extrema can cause an error, which is often presented by the changing shapes of original envelopes and distort extracted IMFs, which is described as the end effect. An important issue during the application of the EMD is restricting the end effect. This paper reveals the decisive factors that can restrict the end effect by determining the uniqueness of the envelope, and provides an interpretation of the end effect in terms of the differences between the original envelope and the extended envelope based on the cubic spline theory. Two principles that are important to the design of an end condition method are provided. The first principle is that the domain of the extended envelope needs to cover the original signal; the second is that the ordinate value of the extended local maxima is greater than or equal to that of the extended local minima. Following these two principles, a new end condition method, the cubic spline based method (CSBM), is proposed in this study. The novelty of the CSBM is that the extended envelope maintains the shape of the original envelope in their intersection domain, and the end effect can be restricted in a limited domain during the sifting process of EMD for each different input signal. Six signals are used to demonstrate the performance of the CSBM by comparing them with two other end condition methods, the extreme method and the improved slope based method (ISBM). The six signals include: a damped sinusoid signal, four monovariate signals with various amplitude modulation-frequency modulation (AM-FM) behaviors, and a one-channel functional near-infrared spectroscopy (fNIRS) signal. Results show that the CSBM in general performs better than the other two methods.

Does mode mixing matter in EMD-based highlight volume methods for hydrocarbon detection? Experimental evidence

Empirical mode decomposition (EMD)-based spectral decomposition methods have been successfully used for hydrocarbon detection. However, mode mixing that occurs during the sifting process of EMD causes the ‘true’ intrinsic mode function (IMF) to be extracted incorrectly and blurs the physical meaning of the IMF. We address the issue of how the mode mixing influences the EMD-based methods for hydrocarbon detection by introducing mode-mixing elimination methods, specifically ensemble EMD (EEMD) and complete ensemble EMD (CEEMD)-based highlight volumes, as feasible tools that can identify the peak amplitude above average volume and the peak frequency volume. Three schemes, that is, using all IMFs, selected IMFs or weighted IMFs, are employed in the EMD-, EEMD- and CEEMD-based highlight volume methods. When these methods were applied to seismic data from a tight sandstone gas field in Central Sichuan, China, the results demonstrated that the amplitude anomaly in the peak amplitude above average volume captured by EMD, EEMD and CEEMD combined with Hilbert transforms, whether using all IMFs, selected IMFs or weighted IMFs, are almost identical to each other. However, clear distinctions can be found in the peak frequency volume when comparing results generated using all IMFs, selected IMFs, or weighted IMFs. If all IMFs are used, the influence of mode mixing on the peak frequency volume is not readily discernable. However, using selected IMFs or a weighted IMFs' scheme affects the peak frequency in relation to the reservoir thickness in the EMD-based method. Significant improvement in the peak frequency volume can be achieved in EEMD-based highlight volumes using selected IMFs. However, if the weighted IMFs' scheme is adopted (i.e., if the undesired IMFs are included with reduced weights rather than excluded from the analysis entirely), the CEEMD-based peak frequency volume provides a more accurate reservoir thickness estimate compared with the other two methods. This study demonstrates that any form of EMD can be beneficial if it is appropriately conditioned. Thus, mode mixing issues will not play an important role in hydrocarbon detection. Because every form of EMD carries strengths and weaknesses in its current implementation, the standardization of such a utility demands further understanding.

Signal analysis via instantaneous frequency estimation of signal components

The empirical mode decomposition (EMD) algorithm, introduced by Huang et al. (Proc Roy Soc Lond Ser A Math Phys Eng Sci 454(1971):903–995, 1998), is arguably the most popular mathematical scheme for non-stationary signal decomposition and analysis. The objective of EMD is to separate a given signal into a number of components, called intrinsic mode functions (IMF’s) after which the instantaneous frequency (IF) and amplitude of each IMF are computed through Hilbert spectral analysis (HSA). On the other hand, the synchrosqueezed wavelet transform (SST), introduced by Daubechies and Maes (Wavelets in Medicine and Biology, pp. 527–546, 1996) and further developed by Daubechies et al. (Appl Comput Harmon Anal 30:243–261, 2011), is applied to estimate the IF’s of all signal components of the given signal, based on one single reference “IF function”, under the assumption that the signal components satisfy certain strict properties of a so-called adaptive harmonic model, before the signal components of the model are recovered. The objective of our paper is to develop a hybrid EMD-SST computational scheme by applying a “modified SST” to each IMF of the EMD, as an alternative approach to the original EMD-HSA method. While our modified SST assures non-negative instantaneous frequencies of the IMF’s, application of the EMD scheme eliminates the dependence on a single reference IF value as well as the guessing work of the number of signal components in the original SST approach. Our modification of the SST consists of applying vanishing moment wavelets (introduced in a recent paper by C.K. Chui, Y.-T. Lin and H.-T. Wu) with stacked knots to process signals on bounded or half-infinite time intervals, and spline curve fitting with optimal smoothing parameter selection through generalized cross-validation. In addition, we formulate a local cubic spline interpolation scheme for real-time realization of the EMD sifting process that improves over the standard global cubic spline interpolation, both in quality and computational cost, particularly when applied to bounded and half-infinite time intervals.

An Empirical Mode Decomposition Approach to Peak Load Demand Forecasting

An accurate and reliable electric load forecasting model is very essential for efficient and effective operation of the Electricity Supply Industry (ESI). Several single models have been developed for electric load forecast for ESI but it is becoming increasingly difficult to obtain accurate forecast by these models because of the volatility coupled with the nonlinear and non- stationary nature of electric load series. In this paper, we propose a novel Electric Peak load forecasting model that combines empirical mode decomposition (EMD) and artificial neural network (ANN). The propose model involves three stages of development. In the first stage, the historical load data obtained from Power holding company of Nigeria (PHCN), Bida is decomposed into several intrinsic mode functions and a residue component using the EMD sifting process. The second stage involves building separate neural network models for each of these IMFS and residue component and the last stage involves combining the predictions from these models and making forecast. When the forecast from this model is compared with that obtained from a conventional neural network model, it was observed that the proposed model outperforms the conventional neural network model, by 2.3% for the whole year model and by 1.8% for the weekday model, judging by the forecast accuracy of both models.

Does restraining end effect matter in EMD-based modeling framework for time series prediction? Some experimental evidences

Following the “decomposition-and-ensemble” principle, the empirical mode decomposition (EMD)-based modeling framework has been widely used as a promising alternative for nonlinear and nonstationary time series modeling and prediction. The end effect, which occurs during the sifting process of EMD and is apt to distort the decomposed sub-series and hurt the modeling process followed, however, has been ignored in previous studies. Addressing the end effect issue, this study proposes to incorporate end condition methods into EMD-based decomposition and ensemble modeling framework for one- and multi-step ahead time series prediction. Four well-established end condition methods, Mirror method, Coughlin′s method, Slope-based method, and Rato′s method, are selected, and support vector regression (SVR) is employed as the modeling technique. For the purpose of justification and comparison, well-known NN3 competition data sets are used and four well-established prediction models are selected as benchmarks. The experimental results demonstrated that significant improvement can be achieved by the proposed EMD-based SVR models with end condition methods. The EMD–SBM–SVR model and EMD–Rato–SVR model, in particular, achieved the best prediction performances in terms of goodness of forecast measures and equality of accuracy of competing forecasts test.

Adaptive Boundary Effect Processing For Empirical Mode Decomposition Using Template Matching

This paper is contributed to the boundary effect problem of the empirical mode decomposition algorithm, which results in a serious distortion in the EMD sifting process. An adaptive method for processing boundary effect in the empirical mode decomposition sifting process is presented, which has exploited the local time- or spatial- scales and the waveform or texture characteristics near boundary of the signal or image to extend the signal or image so that additional subsignal or subimage are obtained. The extended section is taken as the most suited subsignal or subimage to the inner signal or image by template matching operation. The multiple components of the original signal or image are available by applying EMD algorithm to the extended signal or image and then leaving out the extended parts of the decomposed components. Simulation results have proved that the proposed template matching based decomposition method outperforms the neural network extending method, the mirror extrema extending method and the AR model extending method for 1D signals, and perform texture extraction effectively for 2D natural images such as defect-free and defect fabrics.

Underdetermined Blind Identification of Structures by Using the Modified Cross-Correlation Method

The modified cross-correlation (MCC) blind identification method is extended to handle the underdetermined case of structural system identification. The underdetermined case is one in which the number of sensors is less than the number of identifiable modes. The basic framework of the modified cross-correlation method is retained in cases in which multiple covariance matrices constructed from the correlation of the responses are diagonalized. The solution to the underdetermined blind identification consists of two stages: the generation of intrinsic mode functions (IMFs) from the measurements by using empirical mode decomposition (EMD) and the application of the modified cross-correlation method to the decomposed signals. The available measurements are first decomposed into IMFs by using the sifting process of EMD. Subsequently, the IMFs are used as initial estimates for the sources, and the MCC method is implemented in an iterative framework. Initial estimates for the mixing matrix necessary to start the iterative process are selected using assumed shape functions that satisfy the essential boundary conditions. The need for sensor measurements at all the relevant degrees of freedom (DOF) to identify the mode shapes is alleviated in this approach. This is the main advantage of the proposed method. Vibration responses collected from the apron control tower located at the Toronto Pearson International Airport are used for demonstration.

End Effect Processing for Empirical Mode Decomposition Using Fuzzy Inductive Reasoning

This paper focuses on the end effect problem of the empirical mode decomposition (EMD) algorithm, which results in a serious distortion in the EMD sifting process. A new method based on fuzzy inductive reasoning (FIR) is proposed to overcome the end effect. Fuzzy inductive reasoning method has simple inferring rules and strong predictive capability. The fuzzy inductive reasoning based method uses the sequence near the end as the input signal of fuzzy inductive reasoning model. This predictive value can be obtained after fuzzification, qualitative modeling ,qualitative simulation and debluring. The simulation results have shown that the fuzzy inductive reasoning based method has equivalent performance to the neural network based method.