Advances in Adaptive Data Analysis

This paper presents a new approach of health monitor using the curvature of the influence line. The study included numerical simulation and experimental test of H-beam to demonstrate the effectiveness of the new approach. The specific work includes: loading test method for moving vehicular to measure displacement influence line of beam structure, obtaining Eigen-damage intrinsic mode function (IMF) of displacement influence line with ensemble empirical mode decomposition (EEMD), processing the second-derivative on displacement influence line to obtain curvature influence line of Eigen-damage IMF, fitting against which through polynomial to obtain quasi-undamaged curve, using the product of absolute difference from both curvature influence line and quasi-undamaged curve to identify damage location of beam structures by means of the product of curvature difference map after fitted. Theoretical development and experimental verification are carried out on H-beam in this paper. In the experiment, measures of displacement influence line at middle span (L/2) of the H-beam when moving vehicular pass by. EEMD, curve fitting and calculating curvature of displacement influence line, etc. methods are used to process displacement influence line. The advantages of this experimental method are fast, time-saving, simple equipment set-up, and can avoid the disturbance of surrounding environmental vibration, but also trouble in a shortage of undamaged condition for the structure. ANSYS software in the paper simulates displacement influence line at middle span under loading test for H-beam to understand the change of displacement influence line for damage identification, which is used as a basis of theoretical development. Finally, conduct loading test method for moving vehicular to measure displacement influence line at middle span of H-beam; connecting with EEMD, curve fitting, and calculating the curvature of displacement influence line can effectively and quickly identify damaged location.

In this study, a hybrid decomposition and ensemble framework incorporating Ensemble empirical mode decomposition (EEMD) and selected modeling methodologies are proposed for stock price forecasting. Under the framework, the original stock price series was first decomposed into several subseries including a number of intrinsic mode functions (IMFs) and a residue using EEMD technique. Then, extracted subseries was modeled to generate forecasts respectively. Finally, the forecasts of all extracted subseries were aggregated to produce an ensemble forecasts for the original stock price series. An extensive experiment was conducted to compare the feasibility and validity of the proposed hybrid framework employing different modeling methodologies, such as support vector machines (SVMs) (in the formulation of support vector regression (SVR), feed forward neural networks (FNN), and autoregressive integrated moving average (ARIMA). The real daily closing price series of Thirty Dow Jones industrial stocks from New York Stock Exchange (NYSE) was used for experimental evaluation. The results demonstrate that significant improvement can be achieved with the proposed hybrid decomposition and ensemble framework across all the three modeling methodologies, particularly, hybrid EEMD-based FNN modeling framework achieved the most significant improvement but hybrid EEMD-based SVMs modeling framework performed best in terms of root mean squared error (RMSE), mean absolute percentage error (MAPE), and directional symmetry (DS).

This investigation presents an improved ensemble empirical mode decomposition (EEMD) algorithm that can be applied to discontinuous data. The quality of the algorithm is assessed by creating artificial data gaps in continuous data, then comparing the extracted intrinsic mode functions (IMFs) from both data sets. The results show that errors increase as the gap length increases. In addition, errors in the high-frequency IMFs are less than the low-frequency IMFs. The majority of the errors in the high-frequency IMFs are due to end-effect errors associated with under-defined interpolation functions near the gap endpoints. A method that utilizes a mirroring technique is presented to reduce the errors in the discontinuous decomposition. The improved algorithm provides a more locally accurate decomposition of the data amidst data gaps. Overall, this simple but powerful algorithm expands EEMD's ability to locally extract periodic components from discontinuous data.

The objective of this paper is to apply an assisted noise method for ameliorating the empirical mode decomposition (EMD) error from insufficient sampling rate for a vibration signal. When the intrinsic mode functions (IMFs) are extracted from a signal mixed noise at a certain level on the sifting algorithm, an extraordinary phenomenon, where noise submerges the EMD error, is discovered. Thus, noise-assisted data is proposed to disturb the EMD error in the sifting process. In order to cancel out noise after serving its purpose, the IMFs are processed with an ensemble mean. As a result, the noise-assisted data ameliorates the EMD error from insufficient sampling rate, and the method treats the mean as the final true result. An EMD example of ball bearing vibration is presented to illustrate the validity of the approach. This paper recommends implementing the noise-assisted method in the EMD on vibration and acoustic signals with broad band.

The analysis of nonlinear and nonstationary time series is still a challenge, as most classical time series analysis techniques are restricted to data that is, at least, stationary. Empirical mode decomposition (EMD) in combination with a Hilbert spectral transform, together called Hilbert-Huang transform (HHT), alleviates this problem in a purely data-driven manner. EMD adaptively and locally decomposes such time series into a sum of oscillatory modes, called Intrinsic mode functions (IMF) and a nonstationary component called residuum. In this contribution, we propose an EMD-based method, called Sliding empirical mode decomposition (SEMD), which, with a reasonable computational effort, extends the application area of EMD to a true on-line analysis of time series comprising a huge amount of data if recorded with a high sampling rate. Using nonlinear and nonstationary toy data, we demonstrate the good performance of the proposed algorithm. We also show that the new method extracts component signals that fulfill all criteria of an IMF very well and that it exhibits excellent reconstruction quality. The method itself will be refined further by a weighted version, called weighted sliding empirical mode decomposition (wSEMD), which reduces the computational effort even more while preserving the reconstruction quality.

Empirical mode decomposition (EMD) is a data-driven technique that decomposes a signal into several zero-mean oscillatory waveforms according to the levels of oscillation. Most of the studies on EMD have focused on its use as an empirical tool. Recently, Rilling and Flandrin, [2008] studied theoretical aspects of EMD with extensive simulations, which allow a better understanding of the method. However, their theoretical results have been obtained by considering constraints on the signal such as equally spaced extrema and constant frequency. The present study investigates the theoretical properties of EMD using cubic spline interpolation under more general conditions on the signal. This study also theoretically supports modified EMD procedures in Kopsinis and Mclaughlin, [2008] and developed for improving the conventional EMD. Furthermore, all analyses are preformed in the time domain where EMD actually operates; therefore, the principle of EMD can be visually and directly captured, which is useful in interpreting EMD as a detection procedure of hidden components.